Data of Geochemistry

Chapter L. Phase-Equilibrium Relations of 

the Common Rock-Forming Oxides Except 

Water

GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-L
Data of Geochemistry

MICHAEL FLEISCHER, Technical Editor

Chapter L. Phase-Equilibrium Relations of 

the Common Rock-Forming Oxides Except 

Water

By GEORGE W. MOREY

GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-L

A discussion of the melting relations of the common 

rock-forming oxides and the binary, ternary, quaternary, and quinary systems formed by them.

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402
DATA OF GEOCHEMISTRY, SIXTH EDITION

Michael Fleischer, Technical Editor

The first edition of the Data of Geochemistry, by F. W. Clarke, was published in 1908 as U.S. Geological 

Survey Bulletin 330. Later editions, also by Clarke, were published in 1911, 1916, 1920, and 1924 as Bulletins 

491, 616, 695 and 770. This, the sixth edition, has been written by several scientists in the Geological Survey 

and in other institutions in the United States and abroad, each preparing a chapter on his special field. The 

current edition is being published in individual chapters, titles of which are listed below. Chapters already 

published are indicated by boldface.

Chapter A. The chemical elements

B. Cosmochemistry

C. Internal structure and composition of the earth

D. Composition of the earth's crust

E. Chemistry of the atmosphere

F. Chemical composition of subsurface waters, by Donald E. White, John D. Hem, and G. A. 

Waring

G. Chemical composition of rivers and lakes, by Daniel A. Livingstone

H. Chemistry of the oceans 

I. Geochemistry of the biosphere

J. Chemistry of rock-forming minerals

K. Volcanic emanations, by Donald E. White and G. A. Waring

L. Phase-equilibrium relations of the common rock-forming oxides except water, by George W. 

Morey

M. Phase-equilibrium relations of the common rock-forming oxides with water and (or) carbon 

dioxide

N. Chemistry of igneous rocks

O. Chemistry of rock weathering and soils

P. Chemistry of bauxites and laterites

Q. Chemistry of nickel silicate deposits

R. Chemistry of manganese oxides

S. Chemical composition of sandstones excluding carbonate and volcanic sands, by F. J. Pettijohn

T. Nondetrital siliceous sediments, by Earle R. Cressman

U. Chemical composition of shales and related rocks

V. Chemistry of carbonate rocks

W. Chemistry of iron-rich rocks

X. Chemistry of phosphorites

Y. Marine evaporites, by Frederick H. Stewart

Z. Continental evaporites 

AA. Chemistry of coal

BB. Chemistry of petroleum, natural gas, and miscellaneous carbonaceous substances 

CC. Chemistry of metamorphic rocks

DD. Abundance and distribution of the chemical elements and their isotopes 

EE. Geochemistry of ore deposits 

FF. Physical chemistry of sulfide systems 

GG. The natural radioactive elements 

HH. Geochronology

II. Temperatures of geologic processes

JJ. Composition of fluid inclusions

HI

CONTENTS

Abstract..-- _____..--

Introduction- ____..__

The component oxides . 

Silica _ _________

Aluminum oxide_. 

Titanium oxide. _. 

Binary systems. _ _ 

Na20-Al203 .___._ 

Na2 0-Si02 .-_ 

Na20-Ti02 --._ 

K20-Al203 --___- 

K2 0-Si03 ---_-_ 

MgO-CaO--.-... 

MgO-FeO--_-__ 

MgO-Al203 --__- 

MgO-Fe203 -_-_- 

MgO-Si02-_-_- 

MgO-TiO» 

CaO-Al208 - 

CaO-Fe203 --__ __

CaO-Si03 ___- 

CaO-Ti02 -__ 

FeO-Al203 __- _ - 

FeO-Fe203 - 

FeO-Si02 -----_-

FeO-Ti02 -__ 

Al,0r-Si0i __ 

Al2 08-Ti02 _-- 

Fe203-Al203 -_-- 

Fe203-Si02 _-- 

Fe2 03-Ti02 _ ___ 

Si02-Ti02 __._- 

Ternary systems _ _._ 

Na2 0-K20-Si02 _ _ 

Na2 0-MgO-Si02 _. 

Na2 0-CaO-Al203 _ 

Na2 0-CaO-Si02 _ _ 

Na2 0-FeO-Si02 -- 

Na2 0-Al203-Si02 _ 

Na2 0-Fe203-Si02 - 

K2 0-MgO-Si02 _.. 

K2 0-CaO-Al203 - - 

K2 0-CaO-Si02 ___ 

K20-FeO-Si02 _ - -

K2 0-Fe203-Si02_

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Ternary systems Continued

MgO-CaO-Al203 ------------------------------- L52

MgO-CaO-Fe203 __----------------------------- 52

MgO-CaO-Si02 _------------------------------- 52

MgO-CaO-Ti02 ---_------_-------------- 55

MgO-FeO-Si02 _ --___......______._ __ 55

MgO-Al203-Si02 -__-__- -_..-_----- .- 55

MgO-FeO-Fe203 ------ - 57

CaO-FeO-Fe203 -------------------~-------- 57

CaO-FeO-Si02 ------------------------------- 57

CaO-Al2Os-Fe203 __._.__.._ .. - 69

CaO-Al203-Si02 __----------------------------- 70

CaO-Fe203-Si02 ---_---- ---- .... 71

CaO-SiOj-TiOi--- --- 73

FeO-Fe203-Al203 __ _- -_ __ _ 74

FeO-Al2 03-Si02 _ ---------------------------- 75

FeO-Fe203-Si02 __------------------------------ 75

AUOs-SiO^TiO-i------------------------ ----- 77

Quaternary systems. - -_ -- ---- - 78

Na,<>-K,0-Al,0«-SiOi_~ ------------------------ 79

Na2 0-MgO-CaO-SiO2 _-_-_---.-.------------ 79

NaaO-MgO-AljOr-SiOi 81

Na2 0-CaO-Al2 03-Fe203 ------------------------ 85

Na2 0-CaO-Al203-Si02 -.------------------------ 86

Na2 0-CaO-Fe203-Si02 -------------------------- 97

Na2 0-FeO-Al203-Si02 ------------------------ 97

K3 0-MgO-Al203-Si02 ------------------ 98

K^-CaO-AUOs-SiO-i- ----------------------- 107 K2 0-FeO-Al2 03-Si02 ------------------------ 108

MgO-CaO-FeO-Si02 ------------------------- 109

MgO-CaO-A^Os-Fe-iOs ---------------------- 110

MgO-CaO-Al203-Si02 ------------------- HO

MgO-FeO-Fe,Or-SiO,_- 126

CaO-FeO-Al203-Si02 ----------------------- 126

CaO-Al303-Fe203-Si02 _------------------------- 135

CaO-Al.Os-SiOz-TiO^-------------------------- 137

FeO-Al2 03-Fe2 03-Si02 ------------------------ 137

Quinary systems...--------------------------------- 139

Na2 0-K2 0-CaO-Al203-Si02 --------------------- 139

Na2 0-MgO-CaO-Al208-Si02 - _._._..___ 140

K2 0-MgO-CaO-Al208-Si02 - ..__..___ __. 146

MgO-CaO-Al203-Fe2 03-Si02 -_------------------ 147

Na2 0-CaO-Al2 03-Si02-Ti02 - ----------------- 147

Petrogeny's residua system___ _ __- _ - - - 147

References. __ ___- -_ _ -- - 152

Index.-. __-__---_-- --------------- 159
VI CONTENTS

ILLUSTRATIONS

Page

FIGURE 1. Graphic representation of the relations among the forms of silica ________________________________________ L3

2. Pressure-temperature curves for several inversions between forms of silica_______________________________ 6

3. The binary system Na2O-SiO2 --_____-_________________-_____-_-_-_---_----_------__-_----__--_---_- 8

4. The binary system K2O-SiO2 ____________________________________________________________________ 10

5. The binary system MgO-SiO2 ___________________________________________________________________ 12

6. The binary system CaO-Al_O3 ________________________________________________________ 13

7. The system CaO-Fe2O3 in air_________________________________________________________________ 15

8. The binary system CaO-SiO2 _____________________________________-___-_-_-_-_______________ 17

9. The binary system CaO-TiO2 ________________-__-_________________________________ 19

10. The system il-on-oxygen____________________________________________________________________________ 20

11. The stability fields of iron and its oxides__________-__-_-_-_-___-_____-_______-_________--__-___-_-_- 22

12. The system FeO-SiO2 ______________________________________________________ 23

13. The system Al2O3-SiO2 _____________________________________________________________________________ 24

14. Tentative phase diagram of the composition Al2O3 -SiO2 _______________________________________________ 25

15. Phase equilibria in the system iron oxide-A!2O3 in air_________________________________________________ 26

16. Phase relations in the system iron oxide-TiO2 in air______-___--_-_-_-_____-_-_-_-_---_-_-_----__-_-_-_- 27

17. The ternary system K2O-SiO2-Na2O-SiO2-SiO2 ________________-________________________ 28

18. The ternary system Na2O-MgO-SiO2 _____________________________________________ 30

19. The ternary system Na2O-CaO-Al2O3 ________________________________________________ 31

20. The ternary system Na2O-CaO-SiO2 ______________________-___-._______________________________ 32

21. The binary system Na2O.SiO2-CaO.SiO2 --______-_-_--_-----_-----_-----_-_ .____. .._ .__-_ _ 34

22. The ternary system Na2O-FeO-SiO2 ______-_______________-__--_--__-_________________________ 37

23. The ternary system Na2O-Al2O3-SiO2 ____________________--___-_____-_____---__________________ 38

24. The binary system Na2O-SiO2 (sodium metasilicate)-Na2O-Al2O3 -2SiO2 (carnegieite, nepheline)._____________ 40

25. The binary system Na2O-2SiO2 (sodium disilicate)-Na2O-A!2O3 -2SiO2 (carnegieite, nepheline)______________ 41

26. The binary system Na2O-Al2O3.2SiO2 (carnegieite, nepheline)-Na2O-Al2O3 -6SiO2 (albite)_______________ 42

27. The ternary system Na2O-SiO2-Fe2O3-SiO2 --_-__-_--------__--------________________-_-______--_- 44

28. The system K2O-MgO-SiO2 ____________________________________________________________.___-____.___ 45

29. The system K2O-CaO-Al2O3 ___________________________________.__________________________________ 47

30. The system K2O-CaO-SiO2 ____________________________________________________ 48

31. The system K2O-FeO-SiO2_ _ _ _ _______ _ _______ _ _________________________________ 50

32. The system K2O-Al2Or-SiO2 __ _______________________________________________ 51

33. The system MgO-CaO-SiO2 _______________________________________________________ 53

34. The binary system CaO-SiO2 (wollastonite)-CaO-MgO-2SiO2 (diopside)_________________________ 54

35. The system MgO-FeO-SiO2 ____________________________________________________ 56

36. The system MgO-Al2O3-SiO2 __________________________________________________ 58

37. The stability field of 3MgO-Al2Os-3SiO2 (pyrope)______-__________________________________ 59

38. The system CaO-FeO-SiO2 _________________________________________________ 60

39. The system 2CaO-SiO2-2FeO-SiO2 ______________ __________________________________ 61

40. Phase-equilibrium diagram for mixtures of CaO-SiO2 and FeO-SiO2 _____________________________________ 63

41. Isothermal planes showing phase-equilibrium relations in the system CaO-FeO-SiO2 ________-_____-_-__---- 66

42. The system CaO-Al2O3-Fe2O3 __ _____________________________________________________________________ 69

43. The system CaO-Al2O3-SiO2 _-_____________________________________________-__________._________---- 70

44. Phase relations in the system CaO-Fe2Or-SiO2 in air___________________________________________________ 72

45. The system CaO-SiO_-TiO2 ________________________________________________________________________- 74

46. The effect of temperature on solid solutions in the spinel series-_________________________________________ 75

47. Subsolidus relations in the system FeO-Fe2O3-Al2O$__________________________________________________ 75

48. The system FeO-Al2O3-SiO2_______________________________________________________________________ 76

49. The system FeC-Fe^s-SiCV....................................................................... 77

50. The system Al2Or-SiO2-TiO2 ___________________________________________________ 78

51. Projection of the tetrahedron Na2O-K2O-Al2O3-SiO2 on the base Na2O-K2O-SiO2 ________________________ 80

52. The system Na2O-Al2O3 .2SiO2 (carnegieite, nepheline)-K2O-A!2O3 .2SiO2 (kaliophilite)-SiO2 ____._____.__-_-- 81

53. The system Na2O-Al2O3-6SiO2 (albite)-2MgO-2A!2O3 -5SiO2 (cordierite)-SiO2 ._________________________ 82

54. The system Na2O-Al2O3 -6SiO2 (albite)-2MgO-SiO2 (forsterite)-2MgO-2Al2O3 -5SiO2 (cordierite) _____________ 83

55. The system Na2O-Al2O3 -6SiO2 (albite)-MgO-SiO2 (enstatite)-2MgO-2Al,O3-5SiO2 (cordierite)__________-___ 84

56. The system Na2O-Al2O3-2SiO2 (carnegieite, nepheline)-MgO-Al2O3 (spinel)-SiO2 _____________--_-_____-_---_ 85

57. Preliminary diagram of the system Na-AAl2O3-6SiOj (albite)-2MgO-SiO2 (forsterite)-SiO2 __________________ 86

58. The system Na2O-CaO-Al2Or-Fe2O3, showing the position of planes which have been studied______________ 87

59. The pseudoternary system CaO-the composition Na*O,3Al2Os-the compound 4CaO-Al2O3-Fe.O3_________ _ 88

60. The system Na2O.Al2O3.6SiO2 (albite)-CaO.Al2O3 -2SiO2 (anorthite)__________________________________---_- 89
CONTENTS VII

Page 

FIGURE 61. The tetrahedron representing the system Na2O- CaO-Al2O3-SiO2 , showing the numerous planes which have been

studied. _________________________________________________________________ L90

62. The plane Na2O-Al2O3 -2SiO2 (carnegieite, nepheline)-CaO-SiO2 (wollastonite)-Na2O-Al2O3-6SiO2 (albite) through

the tetrahedron Na2O-CaO-Al2 03-SiO2 _________________________________.________________ 91

63. The plane Na2O-Al2O3-2SiO2 (carnegieite, nepheline)-CaO-SiO2 (wollastonite)-CaO-Al2O3 -2SiO2 (anorthite)

through the tetrahedron Na2O-CaO-Al2O-SiO2 ____-______-_-_____-_--__---------_------__-_----___ 92

64. The plane Na2 0-SiO2-CaO-SiO2 (wollastonite)-Na2O-Al2O3-2SiO2 (carnegieite, nepheline) through the tetra- 

% hedron Na^O-CaO-AUOs-SiOz____________________________________________ _ 93

65. The plane obtained by adding 10 percent CaO-Al2O3 -2SiO2 to the plane Na2O-Al2O3-2SiO2-CaO-SiOi-2CaO-Al2O3-

SiO2 through the tetrahedron Na2O-CaO-Al2Os-SiO2 _________________________________________ 94

66. The plane CaO-Al2O3-2SiO2 (anorthite)-2CaO-A!2O3 -SiO2 (gehlenite)-Na2O-A!2O3-2SiO2 (carnegieite, nepheline)

through the tetrahedron Na2O-CaO-Al2O3-SiO2 _____-__._________----__-____--._______ 95

67. The plane Na2O-Al2O3-2SiO2 (carnegieite, nepheline)-CaO-Al2O3 -2SiO2 (anorthite)-SiO2 through the tetrahedron

Na2O-CaO-Al2O3-SiO2 _____________________________________________________________________ 96

68. The plane Na2O-Al2O3-2SiO2 (carnegieite, nepheline)-FeO-SiO2 through the tetrahedron Na2O-FeO-Al2O3-SiO2 - 97

69. Diagrammatic representation of the tetrahedron K2O-MgO-Al2O3-SiO2, showing planes through it which have

been studied-_________________________________________________________________________________ . 98

70. The plane K2O-Al2O3 -4SiO2 (leucite)-2MgO-SiO2 (forsterite)-SiO2 through the tetrahedron K2O-MgO-Al2O3-

SiO._-__----_.__________________________________________________________________________ 99

71. The system K2O-MgO-Al2O3-SiO_________________________________________________ 100

72. The plane K2O-Al2O3-4SiO2 (leucite)-2MgO-SiO2 (forsterite)-2MgO-2Al2O3 -5SiO2 (cordierite) through the tetrahedron K2O-MgO-Al2O3-SiO2 _ ____________________________________________ 102

73. The plane K2O-Al2O3 .4SiO2 (leucite)-2MgO-2Al2O3 -5SiO2 (cordierite)-SiO2 through the tetrahedron K2O-MgOAl2O3-SiO2 _____________________________________________________ 103

74. The plane K2O-Al2O3 -4SiO2 (leucite)-MgO-SiO2 (enstatite)-2MgO-2A!2O3 -5SiO2 (cordierite) through the tetrahedron K2O-MgO-Al2O3-SiO2 ______________________________________________ 105

75. The plane 2MgO-2Al2O3-5SiO2 (cordierite)-3Al2O3.2SiO2 (mullite)-K2O-Al2O3 -6SiO2 (potassium feldspar) through

the tetrahedron KiO-MgO-Al2O3-SiO2 ____________________________________________________ 106

76. The plane K2O-Al2O3 -4SiO2 (leucite)-MgO-A!2O3 (spinel)-A12O3 (corundum) through the tetrahedron K2O-MgOAl2O3-SiO2 _______________.____________________________________________________________________ 107

77. The plane K2O-Al2O3 -4Si02 (leucite)-2MgO-SiO2 (forsterite) (-MgO-Al2O3 (spinel) through the tetrahedron

K2O-MgO-Al2O3-SiO2 _____________________ _____________________________________________________ 108

78. The system K2O-Al2O3 -4SiO2 (leucite)-CaO-A!2O3 -2SiO2 (anorthite)-SiO2, a part of a plane through the tetrahedron K2O-CaO-Al2O3-SiO2 _.-_-_____________ _____________________________________________.-.___ 109

79. A preliminary study of the section K2O-Al2O3 -4SiO2 (leucite)-2FeO-SiO2 (fayalite)-SiO2, which is part of the

plane K2O-Al2O3-2FeO-SiO2-SiO2 through the tetrahedron K2O-FeO-Al2O3-SiO2 __ ______________ 110

80. Phase equilibrium diagram of the area CaO-SiO2 (wollastonite)-CaO-MgO-SiO2 (monticellite)-FeO, a part of the

plane CaO-SiO2-MgO-FeO, through the tetrahedron MgO-CaO-FeO-SiO2 ____________________ 111

81. The tetrahedron MgO-CaO-Al2O3-SiO2 _______--_____-________________-______________________ 112

82. The plane MgO-Al2Os-2CaO-SiO2 through the tetrahedron MgO-CaO-Al-ArSiO...-___ _____________ 113

83. The plane MgO (periclase)-Al_O3 (corundum)-CaO-A!2O3 -2SiO2 (anorthite) through the tetrahedron MgOCaO-Al2O3-SiO2 -__--________-_______________________________________________________________ 114

84. The plane MgO (periclase)-2MgO-SiO2 (forsterite)-CaO-Al2O3 -2SiO2 (anorthite) through the tetrahedron

MgO-CaO-Al2O3-SiO2 __________________________________________________________________ 115

85. Phase-equilibrium diagram for the plane MgO-SiO2 (enstatite)-CaO-Al2O3 -2SiO2 (anorthite)-CaO-MgO-2SiO2

(diopside)__________ ? ________________________________________________________________________ 116

86. The plane MgO-Al2O3 (spinel)-2MgO-SiO2 (forsterite)-CaO-A!2O3 .2SiO2 (anorthite) through the tetrahedron

MgO-CaO-Al2O3 -SiO2 __________________________________________________________________________ 117

87. The plane 2CaO-Al2O3 -SiO2 (gehlenite)-A!2O3 (corundum)-MgO-A!2O3 (spinel), through the tetrahedron MgOCaO-Al2O3-SiO2 _ ______________________________________________________ 118

88. The plane 2CaO.Al2O3-SiO2 (gehlenite)-CaO-A!2O3-2SiO2 (anorthite)-MgO-A1203 (spinel) through the tetrahedron

MgO-CaO-A] 2O3-SiO2 ____-_.______________________________________________ 119

89. The plane 2MgO-SiO2 (forsterite)-CaO-MgO-2SiO2 (diopside)-CaO-A!2O3-2SiO2 (anorthite) through the tetrahedron MgO-CaO-Al2O3-SiO2 __ _________________________________________________ 120

90. The plane 2MgO-SiO2 (forsterite)-CaO-Al2O3 -2SiO2 (anorthite)-SiO2 through the tetrahedron MgO-CaOAl2O3-SiO2 _.__________________________________________________________________________________ 121

91. The plane MgO-SiO2 (enstatite)-CaO-SiO2 (wollastonite)-Al2O3 through the tetrahedron MgO-CaO-Al2O3-Si02 - 122

92. The section CaO-SiO2 (wollastonite)-CaO-MgO-2SiO2 (diopside)-CaO-A!2O3-2SiO2 (anorthite), part of a plane

through the tetrahedron MgO-CaO-Al2O3-SiO2 _.______________________________________________ 123

93. The section CaO-SiO2 (wollastonite)-2CaO-A!2O3 -SiO2 (gehlenite)-2CaO-MgO-2SiO2 (akermanite) of the plane

MgO-CaO-Al2O3-CaO-SiO2 through the tetrahedron MgO-CaO-Al2O3-SiO2 ___ ----- _ ____ - ___ - _ _ 124

94. The plane through the tetrahedron MgO-CaO-Al2O3-SiO2 parallel to the side CaO-AlaOs-S^ and containing

10 percent MgO.__--___-_--______-__---____--_________-____-______-____--.-____-___----------- 125
VIII CONTENTS

Page 

FIGDRE 95. The join 3CAO-Al2O3 -3SiO2 (grossularite)-3MgO-Al2O3 -3SiO2 (pyrope)_____.._______________________ L126

96. Phase-equilibrium relations in air of the system MgO-FeO-Fe2O3-SiO2 represented as projected on the plane

MgO-SiO2-FeO-Fe2O3 ________________________________________________ 127

97. Diagrams to show changes in phase-equilibrium relations in the system MgO-FeO-Fe2O3-SiO2 with change in

oxygen pressure.______________________________________________________________________________ 128

98. The tetrahedron CaO-FeO-Al2O3-SiO2, showing the position of the several planes on which phase-equilibrium

studies have been made_________________________________-______________________________________ 129

99. The plane SiO-j-CaO-AlzOs^SiO-j (anorthite)-FeO through the tetrahedron CaO-FeO-Al2O3-SiO2_____^_ 130

100. Diagram showing relations between univariant lines, ternary invariant points in the limiting systems, and quaternary invariant points-______________________________________________________________________ 131

101. The plane CaO-SiO2 (woliastonite)-CaO-Al2O3 -2SiO2 (anorthite)-FeO through the tetrahedron CaO-FeOAl2O3-SiO2 ___________________________________________________________ 132

102. The plane 2CaO-Al2O3 -SiO2 (gehlenite)-CaO-Al2O3 -2SiO2 (anorthite)-FeO through the tetrahedron CaO-FeOAi2O8-SiO2 __________________________________________________________ 133

103. The plane CaO-SiO2 (wollastonite)-2CaO.Ai2O3 -SiO2 (gehlenite)-FeO through the tetrahedron CaO-FeOAUOs-SKV--._______________________________________________________________________ 134

104. The plane 2CaO-SiO2-2CaO-Al2O3 -SiO2 (gehlenite)-FeO through the tetrahedron CaO-FeO-Al2O3-SiO2 ____ 135

105. Diagrammatic representation of part of the tetrahedron CaO-Al2O3-Fe2O3-SiO2 __________________________ 136

106. The system iron oxide-A!2O8-SiO2 in air____________________________________________________________ 137

107. The system iron oxide-A!2O3-SiO2 at 1 atm oxygen pressure..___________________________________________ 138

108. Crystallization of mixtures of three feldspars._________________________________________________________ 139

109. Crystallization of mixtures of Na2O-Al2O3-6SiO2 (albite)-CaO-MgO-2SiO2 (diopside)-CaO-Al2O3 -2SiO2 (anorthite)________________________________________________________________ 140

110. Phase relations at 1230° and 1250° C in the system Na_O-Al2O3 -6SiO2 (albite)-CaO-MgO-2SiO2 (diopside)-

CaO-Al2O3 -2SiO2 (anorthite)___________.___________________________________ 141

111. Crystallization paths of mixtures in the diopside field in the system Na2O-Al2O3 -6SiO2 (albite)- CaO-MgO-2SiO2

(diopside)-CaO-A!2O3 .2SiO2 (anorthite),____-____________________________________ 143

112. Crystallization paths of mixtures in the plagioclase field in the system Na2O-Al.O3 -6SiO2 (albite)-CaO-MgO-2SiO^

(diopside)-CaO-Ai2O3 -2SiO2 (anorthite)__________________________________________ 144

113. The quaternary system Na2O-Al2O3 -2SiO2 (nepheline)-2MgO-SiO2 (forsterite)-CaO-MgO-2SiO2 (diopside)-SiO2,

showing the ternary sections which have been studied________________________________i_____________ 145

114. The ternary system Na2O-Al2O3 -2SiO2 (nepheline)-CaO-MgO-2SiO2 (diopside)-SiO2 -_______-_______ 146

115. The ternary system Na2O-Al2O3 -6SiO2 (albite)-2MgO-SiO2 (forsterite)-CaO-MgO-2SiO2 (diopside)___________ 147

116. The system MgOSiO2 (protoenstatite)-Na2O-Al2O3 .6SiO2 (albite)-CaO-MgO-2SiO2 (diopside)__________ 148

117. The system 2MgO-SiO2 (forsterite)-Na.O-Al2O3-2SiO2 (nepheline)-CaO-MgO-2SiO2 (diopside)____________ 149

118. The ternary system K2O-Al2O3 -4SiO2 (ieucite)-CaO-MgO-2SiO2 (diopside)-SiO2 _______________________ 150

119. The triangular section Na2O Al2O3 -6SiO2 (albite)-CaO-A!2O3 -2SiO2 (anorthite)-CaO-SiO2 -TiO2 (sphene) showing

isotherms _____________________________________________________________________________________ 151

120. Petrogeny's residua system_____________________________________ ____________________________________ 152

TABLES

Page 

TABLE 1. Phase transformations of oxides.____________________________________________________________________ 2

2. Modes of silica.___________________________________________________________________________________ 2

3-9. Invariant points in binary systems.

3. Na2O-SiO2________________________________________________________________________________ 9

4. K2O-SiO2 _________________________________________________________________________________ 9

5. MgO-SiO2 ____--_-________________________________----_-_____-._-__-_____-____----____ 11

6. CaO-Al2O3 ___--___._________________________________________________ 14

7. CaO-Fe2O3 ________________________________________________________________________________ 14

8. CaO-SiO2 _______________________________________________________________________________ 16

9. CaO-TiO2 _______________________________________________________________________________ 18

10. Significant points of the system iron-oxygen__ ________________________________________________________ 21
CONTENTS IX

TABLE 11-28. Invariant points in ternary systems. Page

11. K2O-SiO2-Na2O-SiO2-SiO2 _--._--_--______--__-_-.______--_.---_-__--.--------_.-_--__---.. L29

12. Na2O-CaO-Al2O3 _-------_-_----------___-_-----_----_------_------_-----_____-__-__-_-_- 30

13. Na2O-CaO-SiO2 _______________________________________________________________________ 33

14. Na2O-FeO-SiO2 ________________________________________________________________________ 37

15. Na2O~Al2O3-SiO2_______________________________________________________________________ 39

16. Na2O-Fe2O3-SiO2 ____.__._.__.___________________________________________________________ 44

17. K2O-MgO-SiO2_____-____-_______________________________________________________________ 46

18. K2O-CaO-Al2O3 ________________________________________________________ 46

19. K2CM3aO-SiO2 __________________________________________________________________________ 49

20. K2O-Al2O3-SiO2 ________--________-____________-___________________-_________-____________ 52

21. MgO-CaO-Al2O3__-----_--_---------------__--------_---_-----_-------------_---_----__- 52

22. MgO-CaO-SiO2 ___-_-_________-__--______________________________--___--____-___-________ 54

23. MgO-FeO-SiO2 __-___-____-___-__-_________________-___________________-___-___._________ 56

24. MgO-Al2O3-SiO2 ____-___-_-___-____-_______________-___-_______.____--__-________-_______ 58

25. CaO-FeO-SiO2 _____________________________________________________.__ 61

26. CaO-Al2O3-SiO2__________________________________________________________________________ 71

27. CaO-Fe2Os-SiO2 -_-_-------_-_--__--____-_______-___-_---___--_-__--__-__--_---_-____--__ 73

28. CaO-SiO2-TiO2 ---_----_-_--___--_-_-_-___-_---_--___-_-----__---_-_-_--_--_--_.»-_--_-_- 73

29. FeO-Al_O3-SiO2 ______-____--__-_______-_____-_____-_-___-___--__--__--______-___-________ 76

30. Significant points in the system K2O-MgO-Al2O3-SiO2-----_-------_-------_---------_--------------- 101

31. Temperatures and compositions of piercing points in the 10 percent MgO plane-_-__-_-_-__-____-__----_ 125

32. The system CaO-FeO-Al.O_-SiO2 ____________________________________________________ 131

DATA OF GEOCHEMISTRY

PHASE-EQUILIBRIUM RELATIONS OF THE COMMON ROCK-FORMING OXIDES EXCEPT WATER

By GEORGE W. MOREY

ABSTRACT

A major concern of geology is to explain the characteristic 

association of certain minerals in well-known rock types and 

the relation of these minerals to each other. In considering 

the genesis of the minerals it is necessary to know the melting 

and crystallization relations of the various oxides which make 

up the greater proportion of the earth's crust. The available 

information about the melting points and phase-equilibrium 

relations of these nine oxides (NajO, K2O, MgO, CaO, FeO, 

AlaOs, FejOs, SiO2, and TiCM are summarized in this chapter, 

and a discussion is given of various types of phase-equilibrium 

diagrams, which are illustrated by examples.

INTRODUCTION

A major concern of geology is to explain the characteristic association of certain minerals in well-known 

rock types and the relation of these rocks to each other. 

Some rocks are of sedimentary origin, formed by the 

weathering of more primitive rocks and the subsequent 

consolidation of the sediments. Other rocks, the metamorphic rocks, are formed by the alteration by heat or 

pressure either of such sediments or of the primary igneous rocks, which are formed by the cooling and crystallization of a rock magma. In considering the genesis 

of the minerals of which the many igneous rock types 

are composed, it is necessary to know the melting and 

crystallization relations of the various oxides which 

make up the greater proportion of the earth's crust. It 

was shown by Clarke and Washington (1922) that 10 

oxides make up 99 percent of the earth's crust. One of 

these is water, which is excluded from consideration in 

this chapter. The other nine oxides and their percentages are: Na2O 3.84, K2O 3.13, MgO 3.49, CaO 5.08, 

FeO 3.80, A12O3 15.34, Fe2O3 3.08, SiO2 59.12, TiO2 1.05. 

The available information about the melting points and 

phase-equilibrium relations of these nine oxides is summarized in this chapter. The oxides are considered in 

the order of the periodic system, except that FeO is 

placed after MgO and CaO, and Fe2O3 after A12O3 .

The consideration of the melting phenomena in mixtures involves a discussion of the often complex phaseequilibrium relations, and the further consideration of 

the changes in these relations at temperatures below that 

at which a liquid can be formed is often pertinent to 

geologic phenomena. One hundred and forty phaseequilibrium diagrams, which represent the relation between composition and temperature, with reference to 

the melting and crystallizing process, and subsequent 

changes in the nature of the solid phases, have been assembled. They offer a means of expressing in graphic 

and compact form a large amount of information which 

is vital to our understanding of the processes of magmatic differentiation. To those conversant with such 

diagrams the information thus available is apparent at 

a glance, but much thought and study and actual use of 

these diagrams is necessary to attain such a degree of 

competence. Much of the discussion is based on purely 

geometrical relations, which arise in part from the 

methods used in expressing composition by means of geometrical figures ; but in larger part from the thermodynamic relations underlying the study of heterogeneous 

equilibrium. 

The usual expression of the phase rule,

in which P is the number of phases, F the number of 

degrees of freedom, and C the number of components, is 

an incidental qualitative consequence of the equations 

(Gibbs, 1906) between those quantities which connect 

the thermodynamic stability of the different phases with 

their composition. These equations may be applied 

analytically, or, as is commonly done, graphically. It 

is from a consideration of the fundamental equations, or 

of the surface of thermodynamic stability derived from 

them, that the various theorems are derived that govern 

the application of geometric laws to the chemical relationships expressed in phase-equilibrium diagrams. In 

the following pages many examples illustrating special 

points in phase-equilibrium theory are considered in 

detail.

Ll
L2 DATA OF GEOCHEMISTRY

The derivation of these theorems is out of place here. 

They are covered in some detail in well-known textbooks. One elementary text is Findlay (1951); more 

advanced ones are Ricci (1951); Darken and Gurry 

(1953), and Zernicke (1955). The several volumes of 

Bakhuis Roqzeboom (1901-13) remain unsurpassed. 

The treatise by Korzhinskii (1959) specially pertains to 

the physiocochemical basis of paragenesis. The volume 

"Phase Diagrams for Ceramists," by Levin and others 

(1956) contains an excellent discussion of elementary 

principles as well as an extensive collection of phaseequilibrium diagrams. The review papers by Schairer 

(195Ya), Roedder (1959), and Stewart (1960) give excellent surveys of phase-equilibrium relations in silicate 

systems. The classic book by Bowen (1956) on the 

"Evolution of the Igneous Rocks" is a necessity for 

the comprehension of the process of magmatic differentiation.

The phase-equilibrium diagrams are arranged in the 

following sections: The component oxides, binary 

systems, ternary systems, quaternary systems, quinary 

systems, and petrogeny's residua system. In the introduction to each section is a short discussion of pertinent 

phase-equilibrium theory, with references to systems 

which illustrate the points in question. These systems 

are discussed in considerable detail. As far as possible 

the references include all work up to January 1, 1961. 

Compositions are in weight percent unless otherwise 

specified.

THE COMPONENT OXIDES

In the introduction are listed the nine oxides which 

form the components of the systems discussed below. 

K2O is not known in pure form, and little is known 

about Na2O except that its melting point is 917° C 

(Brewer and Margrave, 1955) ; neither of these oxides 

is known in nature. A12O3 , SiO2, FeO, FesOg, and TiO2 

require individual discussion. FeO and Fe2O3 are discussed in the section on the binary system FeO-FesOa. 

Pertinent information about melting points and inversion of oxides is assembled in table 1.

TABLE 1. Phase transformations of oxides

Oxide

MgO. ...

CaO. .......

CaO . ....

AljOj... ... .

TiO» .....

Transformation

Melting. _ . .....

Melting ...........

Melting...........

Temperature (°C)

2800

2572

420

2040

1825

Reference

SILICA

Silica (silicon dioxide, SiO2 ), is noteworthy for the 

number of its polymorphous crystalline forms, and for 

the sluggishness with which many of the forms, when

unstable, change over into the form stable under the 

conditions of the experiment. The interrelations of 

these various forms were but vaguely understood until 

the work of Fenner (1913), which is a classic of the 

literature of silica. It forms the basis of the exhaustive 

discussion by Sosman (192Y). The best known crystalline modifications of silica are listed in table 2, and 

shown graphically in figure 1.

TABLE 2. Modes of silica 

[From R. B. Sosman, unpublished data, 1957]

Crystalline:

Tridymite 8-1................

Tridymite 8-IV.. __

Tridymite S-V.... ..... ...

Tridymite S-VI... .... .

Tridymite M-I-. ___

Tridymite M-II . ...... ....

Tridymite M-IIL... .........

Cristobalite, high ... .......

Keatite . __ .... _ ........

Silica W... ...... ..... .....

Amorphous:

Silica M....... ....... .... _ .

Temperature 

range (°C)

-273-573

573-867 -273-64

64-117

117-163

163-210

210-475

/ 745-867

I 867-1470 -273-117

117-163

>163 -273-267

f 267-1470

X 1470-1713 

ca. 200-1700

Monotropic?

>1723

-273-1723

Stability

Stable......

.....do... 

.....do.......

.....do.......

.....do. ...

.....do ....

.....do.......

Stable 

Metastable 

.....do. ...

.....do ....

.....do.......

.....do ...

Stable... _ . 

.....do ...

Stable. 

Metastable..

.....do ...

.....do ..

«

Pressure 

(atmospheres)

1

1

1

1

1

1

1

} 1

1

1

1

1

1

ca. 21-40

1

1

1

1

ca. 35 up

ca. 100 up

i Produced from all other phases by high-speed neutrons.

The stable form at ordinary temperature is low 

quartz,1 the commonest of minerals. When low quartz 

is heated to 573C C it changes into high quartz. This 

inversion is an example of a kind of inversion called 

by Sosman the "high-low" type, which is characterized 

by proceeding promptly and rapidly throughout the 

crystal, whether from higher or lower temperature. 

The principal features of the high-low quartz inversion 

are (1) a gradual increase in the rate of change of all 

properties with increasing temperature, beginning 

50°C or more before the inversion is reached; Day, 

Sosman, and Hostetter (1914) found that the volume 

increased more and more rapidly as the temperature approached the inversion temperature; (2) an absence of 

a similar preliminary effect on the high-temperature 

side of the inversion point, and a small rate of change 

in properties above the inversion point; and (3) a 

change in symmetry, and an abrupt change in nearly 

all the physical properties at the inversion point.

The speed of the inversion is great, and there is little 

superheating or undercooling. Several observers have 

found the inversion to take place at a higher tempera1 This is often called 0-quartz, sometimes o-quartz. To avoid this confusion, 

Sosman (1927) introduced the terms "high quartz" and "low quartz" to designate 

the high- and low-temperature forms. He also extended this system, which is 

generally adopted, to the other crystalline forms of silica.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L3

Silica W

Vitreous Silica

--O

o I o 1

C\J I

Low-Cristobalite VDc\j

-0-0- -0-7 Liquid

High-Cristobalite ~k> 

i

ro

Tridymite S

 Q

Low -Quartz

co HighIn Quartz

= J>'

^

\tj

»_______________i

i i i i i i i i i i i i i ill

-273 0 1000

TEMPERATURE, IN DEGREES CENTIGRADE

FIGURE 1. Graphic representation of the relations among the forms of silica, as revised by R. B. Sosman (unpublished data, 1957).

2000

ture on heating, a lower temperature on cooling. Bates 

and Phelps (1927), who worked with blocks of quartz, 

found that at the beginning of the inversion reached 

with increasing temperature there was a slight drop in 

temperature. They give 573.3°C for the low-high inversion, 572.4° C for the high-low inversion. Gibson 

(1928b) found that the inversion was accompanied by 

a little superheating or undercooling, and that the true 

temperature of equilibrium between the high and low 

forms of quartz is at 572.3° ±0.2°C. Before a block 

of low-quartz changes to the high variety, it superheats 

so much that its temperature never falls to the equilibrium value. If the inversion is considered to take place 

adiabatically, the apparent heat capacity of low quartz, 

about 573°C was calculated to be 4±1 cal per gram per 

degree, a value more than 10 times that of low quartz 

at 550°C, or of high quartz at 600°C.

Keith and Tuttle (1952), using a highly sensitive differential thermal method, found that quartz, instead of 

being invariably pure SiO2 as previously believed, often 

contains material in solid solution which affects the 

high-low inversion. Synthetic quartz grown in the 

presence of germanium was found to have an inversion 

break 40°C above the normal range, and quartz grown 

in the presence of lithium and aluminum had the inversion temperature lowered as much as 120° C. Schreyer 

and Schairer (1960) found that when glasses in the system MgO-Al2O3-SiO2 of composition between SiO2 

and MgOAl2O3 were crystallized, solid solutions were 

obtained which were isostructural with high quartz. 

Members of the series having SiO2 content less than 73 

percent could be quenched to»room temperature as high

quartz, but an inversion takes place on cooling more 

siliceous mixtures. These solid solutions are similar to 

the phases called "silica O" by Koy (1959).

Gibson (1928a) studied the increase in the inversion 

temperature of quartz resulting from hydrostatic pressures up to 2,640 bars, and Yoder (1950) extended the 

study to 10,000 bars. The quartz used by Yoder had 

an inversion temperature at atmospheric pressure of 

572.3°±0.2°C, which was raised to 815°C by 10,000 

bars pressure. The experimental results are represented by the equation

Ar= -1.6+2.871 X 10-2p -4.284 X 10'7p2

in which AT1 represents the increase in inversion temperature produced by a pressure of p bars, and the P-T 

curve is shown in figure 2.

High quartz is the stable form of silica from 573° to 

867°C, at which temperature high tridymite becomes 

stable (Kracek, 1939). The transition is sluggish, and 

quartz can be overheated for long periods without 

change. When a transition takes place in the absence 

of fluxes, cristobalite is almost invariably formed, and 

Sosman (1927) states that the direct transformation of 

quartz to tridymite by heat alone has not been definitely 

proved. Fenner (1913) accelerated the transitions by 

fluxes, of which sodium tungstate was most frequently 

used, and obtained some conversion to tridymite at 

875°C in 24 hours; at 1000°C the conversion was complete within 118 hours, and at 1300°C in 3 hours.

Mosesman and Pitzer (1941) calculated from the 

thermodynamic properties of high quartz and tridy-
L4 DATA OF GEOCHEMISTRY

mite that the transition temperature of quartz to tridymite would be raised by pressure. Tuttle and Bowen 

(1958) determined the transition curve up to 1,000 

atm and Kennedy and others (1962) determined it up 

to the quadruple point gas + liquid + quartz + tridymite 

in the binary system H2O-SiO2 , at 1160°C, 1,500 atm. 

Their results are represented by a straight-line equation,

in which t= temperature in degrees centigrade and p 

is the pressure in atmospheres.

The change of high quartz to cristobalite is the usual 

one when quartz is heated without a flux, but the amount 

of inversion becomes appreciable only above 1000 °C. 

Day and Shepherd (1906) found the transformation to 

be largely complete after 6 days at 1160°C; Fenner 

found only a small percentage transformed at 1250 °C 

after 108 hours, two-thirds transformed after 90 hours 

at 1300°C, 85 percent after 4 hours at 1500°C, and the 

transformation was practically complete after one hour 

at 1570 °C. The metastable inversion temperature at 

which quartz and cristobalite would be in equilibrium 

(the metastable invariant point quartz + cristobalite + 

vapor) is difficult to determine directly; Sosman (1927) 

estimates it to be below 1250 °C.

The metastable melting of quartz has been observed. 

The metastable melting point is probably below 1470 °C, 

according to Sosman (1927). The rate of melting is 

slow and in this temperature range may be equalled or 

exceeded by the rate of crystallization of the liquid into 

cristobalite; above 1500 °C melting is more rapid than 

crystallization, and glass is obtained on cooling. Various samples of quartz differ greatly in their readiness 

to melt or to invert to cristobalite.

The formation of quartz directly from other forms 

of silica without the aid of flux is practically unknown. 

Below 867° C quartz is the stable crystalline form, but 

there is no record of either cristobalite or tridymite 

changing over into the stable quartz without the aid of 

a flux, and the transformation with such aid requires 

special treatment. The occurrence of tridymite and 

cristobalite as low-temperature minerals is pertinent. 

The forms of tridymite and their relationship were an 

outstanding puzzle which has been solved by the work 

of Hill and Eoy (1958 a, b) ; indeed, Florke (1955) 

questioned the existence of tridymite as a phase. Hill 

and Eoy found that there is one form of tridymite, 

which they designated by tridymite S (for stable) 

which is stable in the range they studied, 870° to 

1300 °C. This presumably is the form found by Kracek 

(1939) at the transition point of high quartz and remains the stable form up to 1470 °C, when it inverts to 

cristobalite. Tridymite S probably is characterized by

a 20-H stacking. Tridymite M (for metastable) resembles tridymite S, but is metastable at all temperatures. Most laboratory samples of tridymite contain S 

mixed with M. Tridymite M can be prepared from 

any form of silica in a few days in the range of 870° 

to 1200 °C either hydrothermally or by fusion with 

sodium tungstate, and with increasing length of run 

S always grows at the expense of M. The distinction 

between these phases is made by means of the X-ray 

powder diffraction patterns. A third powder pattern, 

which cannot be wholly ascribed to poor crystallinity 

of phase M, is obtained in the earliest stages of the 

conversion of some materials to tridymite. It has been 

termed tridymite IT, for unstable.

These forms of tridymite show a series of displacive 

transitions, easily detected by differential thermal analysis. These are summarized in the following scheme:

113°C 152°C 

Trid-M-I <=± Trid-M-II <=± Trid-M-III

64°C 113°C 138°C 

Trid-S-I <=± Trid-S-II *± Trid-S-III *± Trid-S-IV

and correspond to heat effects previously ascribed as 

caused by inversions of tridymite II to III to IV to V.

The inversion temperature of quartz to tridymite is 

raised by pressure. Mosesman and Pitzer (1941) predicted that such would be the case from thermodynamic 

considerations and that the quartz-tridymite curve 

would terminate at a triple point quartz + tridymite 

+cristobalite. Tuttle and Bowen (1958) found the inversion temperature to be raised to 1040 °C by 103 bars, 

and Kennedy and others (1962) realized the triple 

point quartz+tridymite+cristobalite at 1470 °C, 400 

bars.

Above 1470 °C, tridymite becomes unstable with respect to cristobalite, but the transition takes place so 

slowly that it is possible to heat tridymite to its metastable melting point, which Ferguson and Merwin 

(1918) found to be 1670°±10°C. The rate of melting 

is small as compared with the melting of metals and 

ordinary salts. Cristobalite is a primary phase in many 

of the silicate systems which have been studied in the 

Geophysical Laboratory of the Carnegie Institution of 

Washington, and in these systems its appearance is 

sometimes erratic. Not infrequently cristobalite will 

appear within the field of tridymite, and sometimes 

long heating is necessary to transform it into stable 

tridymite.

Cristobalite is the stable form of silica from 1470 °C 

to the melting point, 1713 °C.2 It has a high-low in2 Most of the temperatures in this section are given in the Qeophysical Laboratory 

Scale of 1912. This is essentially the same as the International Celsius scale of 1948 

up to 1550°C, slightly lower above 1660°C. The melting point of pure silica as cristobalite is 1713°C on the Geophysical Laboratory Scale of 1912, 1723°C on the International Scale of 1948. This subject is thoroughly discussed by Sosman (1952).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L5

version which differs from others of high-low type in 

that its temperature appears to be greatly affected by 

the previous thermal history, and even by the source of 

the cristobalite. Fenner (1913) found cristobalite made 

from amorphous silica to have a higher inversion temperature than cristobalite made from quartz, even 

though both samples were made at the same temperature. Hill and Roy (1958b) found that the temperature of the a-/3 inversion depends on the structure of the 

starting material and on the temperature and length of 

the heat treatment. There is no specific order characteristic of a particular temperature. The completely 

ordered 3-C stacking is the most stable cristobalite 

throughout the temperature range, and in it the a-/3 

inversion is at 267°±2°C. All disordered cristobalites 

will tend toward the 3-C cristobalite with time.

Ordinarily the high form of cristobalite cannot be 

cooled to room temperatures without inverting, but 

when small cristobalite crystals are embedded in glass 

they may remain isotropic, presumably because of 

failure to invert. This was mentioned by Andersen 

(1919) and later discussed by Greig (1932), who offered 

additional evidence that the inversion from the high 

to the low form had failed to take place. The reason 

probably is that the matrix of adhering glass imposes 

a mechanical restraint which prevents the change. 

Levine and Ott (1932) showed that some opals contain 

high cristobalite, an observation confirmed by E. Posnjak (cited by Greig, 1932) and here again the failure 

to convert is probably caused by the mechanical restraint of the matrix in which the crystals are embedded.

The stable melting point of crystalline silica is the 

melting point of high cristobalite, since any of the other 

forms should invert to high cristobalite before melting, 

if equilibrium were reached, and will so invert if not 

too rapidly heated. Finely powdered cristobalite may 

be expected to melt completely to a liquid if held at 

1715° to 1720°C for about 10 to 15 minutes. The value 

of the present melting temperature of cristobalite rests 

on two sets of experiments. The first was by Ferguson 

and Merwin (1918), who found 1710°±10°C. Later 

Greig (1927a) redetermined this as 1713°±5°C. He 

found that his purest cristobalite melted practically 

completely in 30 minutes at 1713 °C and that it was 

largely crystalline, but contained some glass, after 30 

minutes at 1710 °C. He also cited evidence to show that 

the small amount of glass appearing at lower temperatures is accounted for by the impurities invariably present in quartz.

Natural silica glass, called lechatelierite, is never 

pure SiO2 . It is sometimes formed by lightning striking sand, when it is known as a fulgurite, and it is 

sometimes found as inclusions in volcanic rock. The

silica glass found in Meteor Crater, in Arizona, and in 

the Libyan desert (Cohen, 1959) probably was formed 

by the impact of a meteor on sandstone.

Crystallization of dry silica glass below 870°C has 

never been observed; crystallization with the aid of 

"mineralizers" usually results first in the formation of 

tridymite, which is later transformed into quartz. 

Fenner's (1913) experiments showed this sequence, and 

other examples are cited by Sosman (1927). Quartz, 

however, can be crystallized directly from alkali silicate melts in which it is the primary phase, a crystallization first effected by Morey and Bowen (1924). It 

is easily formed by hydrothermal crystallization, and 

quartz is noteworthy for the ease with which it can be 

obtained in excellent crystals by heating appropriate 

mixtures with water under pressure. Morey and 

Ingerson (1937) gave a critical bibliography of hydrothermal reactions, including the formation of quartz 

and other forms of silica, and this subject is discussed 

in Chapter M of this publication series.

Quartz, tridymite, and cristobalite may be termed 

the classical forms of silica, in contrast to three new 

forms recently prepared. One of these is coesite, first 

prepared by Goes (1953) and named by Sosman (1954). 

Coesite is a high-pressure phase with a density of 2.93, 

and the change in the inversion temperature of quartz 

to coesite with pressure has been studied by MacDonald 

(1956) and by Boyd and England (1959), whose curve 

is reproduced as figure 2. Coesite has recently been 

found in nature. Chao, Shoemaker, and Madsen 

(1960) found it with the glass formed by impact in 

Coconino Sandstone (Permian) in Meteor Crater, in 

Arizona. Pecora (1960) discussed this occurrence, and 

also mentioned the finding of coesite by Chao in a 

specimen of "suevite" (pumiceous tufflike material) 

collected by Shoemaker near the rim of the Rieskessel 

in Bavaria, Germany. A third natural occurrence of 

coesite was discovered from Waber, near Al Hadida in 

Arabia (Chao, Fahey, and Littler, 1961). Coesite also 

has been found in the Teapot Ess Crater at the Nevada 

test site, formed by the explosion of a 1.2 kiloton atomic 

device (Chao, Fahey, and Littler, oral communications, 

1961).

An even denser modification of SiO2 was synthesized 

by Stishov and Popova (1961) at a reported pressure 

in excess of 160 kilobars, at temperatures of 1200° to 

1400 °C. This occurs in coesite-bearing sandstone at 

Meteor Crater, in Arizona, and has been named 

stishovite (Chao and others, 1962). Stishovite is tetragonal with an X-ray powder pattern very similar to 

that of rutile, suggesting that it is isostructural with 

rutile, with silicon in sixfold coordination. The unitcell dimensions (natural material) are a=4.179 A,
L6 DATA OF GEOCHEMISTRY

LJ 

QL 

LJ 

X 

Q_ 

(/)

o

^

O

I

O

1C

cr

C/5 

C/) 

LJ

cr 

a.

50

40

30

20

10

0

I ' 1 I ' I ' I

Coesite

I ' I I ' I

/ High Quartz

Low Quartz

I . 1 i I . I i I .

Tridymite Cristobalite

Liquid /

V H

VrrTi ,! I i I , I i. I

100 500 1000 1500

TEMPERATURE, IN DEGREES CENTIGRADE

FIGURE 2. Pressure-temperature curves for several inversions between forms of silica. Modified from Boyd and England (1959).

1800

c 2.665 A, the calculated specific gravity is 4.28, and 

measured specific gravity (synthetic material) 4.35. 

The higher index of refraction is 1.826, the lower is 

1.799, both ±0.002 (synthetic material). The synthetic material consisted of fibrous aggregates and 

acicular and rarely elongate tabular crystals of maximum size 0.5 mm. The natural crystals are of submicron size. Stishovite is less readily attacked by hydrofluoric acid than coesite, but is readily dissolved by 

alkaline solutions and by melts.

Another newly discovered form of silica is keatite, 

produced hydrothermally by Keat (1954) from amorphous precipitated silica in the presence of a small 

amount of alkali at temperatures from 380° to 585 °C, 

and water pressures of 500 to 18,000 psi. This form has 

also been called silica K. Shropshire, Keat, and 

Vaughan (1959) found it to be tetragonal and determined its structure. A third new form, silica W, was 

discovered by Weiss and Weiss (1954) on cooling gaseous SiO. Silica W is formed as microcrystalline fibers 

composed of chains of SiO4 tetrahedra joined at edges 

instead of at corners as in the usual silica structure. It 

has a density of 1.98, the lightest known phase of silica.

There also appear to be different forms of vitreous 

silica. Bridgman (1939) showed that at 31 to 33 kilobars the compressibility of vitreous silica shows a sharp 

reversible change. When it is subjected to pressures 

of above 100 kilobars, there is a permanent change in 

density of about 18 percent, up to 2.61, which is almost 

the density of quartz (2.651 at 0°C and atmospheric 

pressure).

ALUMINUM OXIDE

Aluminum oxide, A12O3 , occurs as the mineral corundum, or a-alumina. Corundum appears to be the 

stable form at all temperatures. Kanolt (1914) found 

a melting point of 2050°C; Geller and Yavorsky (1945) 

found 2015°±15°C and state that a more accurate determination necessitates the prevention of contamination of the alumina by vapors of other elements in the 

furnace atmosphere. The boiling point is 2250°C (Kuff 

and Schmidt, 1921). A second form, metastable yalumina, discovered by Hansen and Brownmiller 

(1928), is formed when a hydrated aluminum oxide is 

heated at 550°-950°C. Heating a hydrated alumina at 

a lower temperature apparently gives amorphous
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L7

alumina (Edwards and Tosterud, 1933) and heating 

to a higher temperature gives corundum.

Several other forms of aluminum oxide have been 

described but their existence has not been fully established. Beta-alumina, described by Rankin and Merwin (1916) apparently is an aluminate, the sodium form 

of which has the formula Na2O'llAl2O3 (Ridgeway, 

Klein, and O'Leary, 1936; Bragg, Gottfried, and West, 

1931; Beevers and Ross, 1937). The literature of this 

subject has been critically discussed by Schairer and 

Bowen (1955), who found ^-alumina to be unstable 

with respect to corundum in their silicate melts.

The decomposition of A12O3 -3H2O (gibbsite) or 

A12O3 -H2O (boehmite), leads to metastable aluminas, 

three of which have been described; namely, y-alumina, 

8-alumina, and 0-alumina: of these, y-alumina has an 

undersaturated cubic spinel structure, 8-alumina a tetragonal structure, and 0-alumina is isomorphous with 

£-Ga2O3 (Ervin, 1952; Saalfeld, 1958; Rooksby and 

Rooymans, 1961).

TITANIUM OXIDE

Titanium oxide, TiO2, is found in nature as the minerals rutile, anatase, and brookite, of which rutile appears 

to be the stable form, the other two, monotropic. Bunting (1933) found the melting point to be 1825° ±20°C. 

Several observers have studied the conversion of anatase 

and brookite to rutile. Schroder (1928) found that the 

expansion curve of anatase has a sharp break at 

642° ±3°C, resulting from an inversion from the holohedral low-temperature form to a probably tetragonal 

high-temperature form. He found the monotropic inversion of anatase to rutile to take place readily at 

915°C; that of brookite to rutile to be detectable at 

650°C. Bunting (1933) found that anatase and brookite 

change to rutile in the presence of a flux at much lower 

temperatures than found by Schroder, and concluded 

that if there is a temperature at which rutile is at equilibrium with either anatase or brookite it must be below 

400°C.

BINARY SYSTEMS

In this section are given the binary systems formed 

by the nine oxides listed in the Introduction, with the 

combinations arranged in the order of that listing, which 

is essentially the order of the periodic table. The simplest type of system is that in which no compounds 

are formed, there is no solid solution, and a simple 

binary eutectic is formed. Nine of the following systems 

meet these requirements, but examples illustrating many 

of the possible complications in phase-equilibrium relations are explained in detail. The system CaO-SiO2 

shows the following: simple eutectics; compounds like

6&5-3S2 O 64 2

CaOSiO2 with congruent melting points; a compound, 3CaO2SiO2 , that has an incongruent melting 

point; a compound, 2CaO SiO2 , that shows reactions in 

the solid state; and reactions in which two liquid layers 

are formed. The system NaaO-CaO-SiO2 has examples 

of both congruently and incongruently melting compounds. Several simple binary systems are discussed in 

connection with the ternary system Na2O-Al2O3-Si02. 

The binary system Na2O-Al2O3 -6SiO2 (albite)- 

CaOAl2O3 -2SiO2 (anorthite) is an example of a system 

showing complete solid solution with the melting point 

rising from one component to another. The system 

2CaOSiO2 (calcium orthosilicate)-2FeOSiO2 (fayalite) is a more complicated solid-solution system and 

CaO-SiO2-FeO'SiO2 is an illustration of a binary join 

which is only in part binary.

Na2O-Al2O3

No reliable phase-equilibrium data exist for the 

system Na2O-Al2O3 , chiefly because of the high temperature and the change in composition of mixtures resulting from volatilization of sodium oxide. Schairer 

and Bowen (1956) estimated the melting point of 

Na2O-Al2O3 to be 1850°±30°C. Matignon (1923) 

estimated its melting point as 1650°C but Brownmiller 

and Bogue (1932) and Kammermeyer and Peck (1933), 

who determined optical properties and X-ray pattern, 

found the melting point to be above 1700°C. The substance known as "^-alumina" is an alkali or alkaline 

earth aluminate.

Na2O-SiO2

The binary system Na2O-SiO2 is basic to the study of 

the sodium feldspars and feldspathoids and also of glass 

and other ceramic products. The original phase equilibrium was by Morey and Bowen (1924) who worked on 

that part of the system between Na2O SiO2 and SiO2 . 

Kracek (1930) extended the study to the sodium orthosilicate composition, 2Na2O Si02 . Bowen and Schairer 

(1929b) and Bowen, Schairer, and Willems (1930) in 

studies on the system Na2SiO3-Fe2O3-SiO2 , obtained 

additional data. Two crystalline compounds: sodium 

metasilicate, Na2OSiO2 , first described by Niggli 

(1913), and sodium disilicate (Morey, 1914), each melts 

congruently, but sodium orthosilicate, 2Na2O-SiO2 , 

melts incongruently with formation of crystalline Na2O 

and liquid. Sodium disilicate has several polymorphic 

forms described by Morey, Kracek, and England (1953). 

There are rapid reversible transformations at 707° and 

678° C.

The phase-equilibrium diagram is figure 3, and the invariant points are given in table 3. With the exception 

of compositions near the disilicate-quartz eutectic, there
TEMPERATURE, IN DEGREES CENTIGRADE

m 

o

T)

m

o 

m

o

ro
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L9

TABLE 3. Invariant points in the system Na20-Si02

Phase reaction

2Na20.Si02 ^±Na20+ L ________

2Na_0-Si02 +Na_0-Si02 ^iL____ 

Na_O.Si02^L___ __ _____ _ _

Na_O.SiO2 + Na20.2SiO2^L _ _ _ _ 

Na20-2Si02 ?±L________ _______

Na20-2Si02 +Si02 (quartz)^±L_

Temperature (°C)

1120 

1022 

1089 

837 

874 

789

Composition of liquid 

(percent by weight)

NajO

59.3 

56.9 

50. 79 

37.9 

34.04 

25.8

Si02

40.7 

43. 1 

49.21 

62. 1 

65.96 

74.2

is little difficulty in reaching equilibrium in this system. 

Sodium metasilicate can be studied either by the quenching method or by the heating-curve method (Morey, 

1923). It crystallizes so readily that melts of 25 g. or 

more cannot be cooled as glass, but always crystallize. 

On the other hand, it undercools to such an extent that 

the cooling curve method is not reliable. The 

Na2O'2SiO2-quartz eutectic shows the remarkable melting point lowering of 924° C from the melting point of 

SiO2 , resulting from the addition of 25.8 percent of 

NasO. The forms 3Na2O-2SiO2, described by D'Ans 

and Loeffler (1930), and Na2O3SiO2 , described by Budnikov and Mateev (1956), do not exist.

NasO-TiO2

Washburn and Bunting (1934) found the congruent 

melting point of Na2OTiO2 to be 1030°C, of 

Na2O2TiO2 985° C, and of Na2O3TiO2 ,1128°C.

K2O-A12O3

Brownmiller (1935) found that the compound 

K2OA12O3 melts above 1650° C and that "/8-alumina," 

an alkali aluminate, is formed from mixtures richer in 

alumina.

K20-Si02

The phase-equilibrium relations in the system 

K2O-SiO2 were first inferred from the study of the 

ternary system H2O-K2SiO3-SiO2 by Morey and Fenner (1917), who found the hydrate, K2O-4SiO2 -H2O, 

but did not prepare the anhydrous tetrasilicate itself. 

The compound K2O 2SiO2 was first prepared by Morey 

(1914). The results of the study of the the system 

K2O-SiO2-SiO2 by Kracek, Bowen, and Morey (1929, 

1939) are shown in figure 4 and the invariant points are 

given in table 4. Evidence that no orthosilicate exists 

was given by Morey and Fenner, but it was not conclusive and more study is needed. Potassium metasilicate, K2OSiO2, melts at 976 °C and crystallizes 

readily. The melt retains CO2 tenaciously and is hygroscopic. When melted in an atmosphere of steam,

water is taken up, the melting point is lowered, and 

on cooling, the melt crystallizes with evolution of steam, 

giving an excellent second boiling point. Potassium 

disilicate, K2O2SiO2 , melts at 1045°C, crystallizes 

readily, and has an enantiotropic inversion at 594°C. 

Potassium tetrasilicate, K2O4SiO2 , melts at 770° C, has 

a reversible inversion at 594°C, and is very difficult to 

crystallize. Potassium silicate glasses richer in SiO2 

than the disilicate are more difficult to crystallize than 

the corresponding sodium silicate glasses, and both glass 

and crystals are very hygroscopic.

TABLE 4, Invariant points in the system K2O-Si02

Phase reaction

K2O.SiO_-*L__________-______

K2O-Si02+ K20-2Si02^L_ _____

K20.2Si02 -*L__________-_____

K20-2Si02+ K20-4SiO2 ^L__ _ _ _

K20.4Si02 -*L_____ ___________

K20-4Si02 +Si02 (quartz) ;^-L__

Temperature (°C)

976 

780 

1045 

742 

770 

769

Composition of liquid 

(percent by weight)

K20

61.07 

54.5 

43.95 

32.4 

28. 17 

27.5

Si02

38.93 

45. 5 

56.05 

67.6 

71.83 

72.5

MgO-CaO

Rankin and Merwin (1916) from extrapolation of 

the MgO-CaO boundary in the ternary system MgOCaO-Al2O3 estimated that the binary eutectic between 

these two oxides is at 67 percent CaO and 2300° ±50°C. 

There is no compound formation.

MgO-FeO

FeO is metastable in air at ordinary temperatures 

and the invariant point Fe+FeaO^FeO at Fo^O.21 

atm is at 570°C (Ralston, 1929, p. 96). FeO melts incongruently with separation of metallic iron and a 

liquid containing oxygen in excess of the ferrous ratio 

(Bowen and Schairer, 1932), and forms with MgO a 

complete series of solid solutions, the magnesiowustistes 

(Bowen and Schairer, 1935) which have not been 

studied beyond ascertaining that the melting temperature rises rapidly as MgO is added to FeO, soon reaching a value above the melting point of iron.

MgO-Al2O3

Rankin and Merwin (1916) concluded that spinel, 

MgO-Al2O3 , which melts congruently at 2135°±20°C 

forms with o-A!2O3 a nearly complete series of solid 

solutions. Satisfactory melting temperatures could not 

be obtained except for spinel; its eutectic with MgO, 

2030° ± 20°C and 55 percent A12O3 ; and its eutectic 

with A12O3, 1925°±40°C, and 98 percent A12O3 .
TEMPERATURE, IN DEGREES CENTIGRADE

m 

cr>

13

m

33

o

m

2 

H

CO

O 

ro
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER Lll

MgQ-FejOs

Roberts and Merwin (1931) found that the compound 

MgO-Fe2O3 takes limited quantities of either MgO or 

Fe2O3 into solid solution. On heating in air it loses 

some oxygen, and the resulting solid solution in the system MgO-FeO-Fe2O3 begins to melt at about 1725° ± 

25°C.

MgO-SiO2

The system MgO-SiO2 shows the relations between 

the pyroxenes and the olivines, in that the pyroxene 

enstatite, MgO-SiO2 , melts incongruently with formation of the olivine, forsterite, 2MgO-SiO2 , and more 

silicious liquid. The phase-equilibrium diagram is 

figure 5, and the invariant points are given in table 5. 

The basic study was by Bowen and Andersen (1914), 

and the region of liquid immiscibility was discovered by 

Greig (1927a). MgO melts at 2800°C and forms a 

eutectic with magnesium orthosilicate (forsterite). 

The chemistry of the magnesium metasilicates is complex and was not clearly understood until Schairer 

(1954) summarized the older work and clarified the 

relations among the various forms. MgO-SiO2 melts 

incongruently at 1557°C to forsterite and a more silicious liquid, and becomes completely liquid on the forsterite liquidus curve. The form found in nature, 

orthorhombic enstatite, inverts at atmospheric pressure 

on heating to 1125°±25°C to a form now known as 

protoenstatite, which is the stable form at the incongruent melting point. Atlas (1952) placed this inversion at 985°C in the presence of alkali fluoride and 

carbonate fluxes. Foster (1951) concluded that while 

protoenstatite (sometimes called mesoenstatite) is the 

stable form at elevated temperatures, it inverts at a 

reasonably rapid rate during cooling to clinoenstatite, 

which bears a relation to protoenstatite similar to that 

which low cristobalite bears to high cristobalite. 

Schairer (1954) found that a sample of protoenstatite 

was completely changed in two years at room temperature to clinoenstatite.

TABLE 5. Invariant points in the system MgO-SiO2

Phase reaction

MgO +2MgO-SiO2-^L__ ________

2MgO-SiO2^±L_________________

MgO-SiO2 ^2MgO.SiO2 + L _____

MgO-SiO2 +SiO2 (cristobalite) ^±L. 

SiO2 (cristobalite) + L2~^Li.. __

Temperature (°C)

1850 

1890 

1557 

1543 

fL, 1695 

\L2 1695

Composition of 

liquid (percent 

by weight)

MgO

62.0 

57.3 

39. 2 

35.2 

30. 5 

.8

SiO2

38.0 

42. 7 

60. 8 

64. 8 

69. 5 

99.2

Boyd and England (1960, 1961a) studied the effects 

of pressure up to 30,000 atm on the melting of enstatite, 

and found that the incongruent melting of enstatite is 

eliminated by application of pressure at least as low as 

15,000 atm and probably as low as 6,000 atm. Also, 

protoenstatite, is replaced at high pressure by orthoenstatite. At pressures present in the upper mantle, and 

probably in the lower parts of the continental crust, 

orthoenstatite is stable up to the liquidus and melts 

congruently.

There is a eutectic between protoenstatite and cristobalite at 1543°C, after which the liquidus curve of 

cristobalite rises to the invariant point, at which a second 

liquid layer, rich in silica, is formed. Greig (1927a) 

also found that the addition of 3 percent of Na2O or 5 

percent of A12O3 was sufficient to cause the two layers to 

become miscible, and showed that the immiscibility 

could not be significant in petrology.

MgO-TiO2

The system MgO-TiO2 was studied by von Wartenberg and Prophet (1932) and by Coughanour and 

DeProsse (1953). Coughanour and DeProsse report 

that three compounds are formed, each of which melts 

congruently: 2MgOTiO2 at 1732°C, MgOTiO2 at 

1630°C, and MgO2TiO2 at 1652°C. The MgO2MgO-TiO2 eutectic is at 1707°C and 35.9 percent 

TiO2 ; the 2MgO-TiO2-MgO-TiO2 eutectic at 1583°C 

and 60.9 percent TiO2 ; the MgO-2TiO2 at 1592°C and 

70.8 percent TiO2 ; and the MgO2TiO2-2TiO2 eutectic 

at 1606°C and 91.2 percent TiO2. No evidence of solid 

solution was obtained.

CaO-Al2O3

The original study of the system CaO-Al2O3 was by 

Rankin and Wright (1915) and it has been further 

studied by several authors. The phase-equilibrium diagram is figure 6, and the invariant points are given in 

table 6. Several compounds are formed in this system. 

3CaO-Al2O3 melts incongruently at 1535°C with formation of CaO and a liquid richer in A12O3. Rankin 

and Wright found a eutectic between 3CaO-Al2O3 and 

12CaO-7Al2O at 1395°C and 50 percent by weight of 

A12O3 .

Rankin and Wright reported a stable and an unstable form of 5CaO-3Al2Oa which contain 52.17 percent A12O3 . Biissem and Eitel (1936) determined the 

structure of the stable form, and on the basis of density 

measurements gave the compound the revised formula 

12CaO-7Al2O3 , which contains 51.46 percent A12O8 .
TEMPERATURE, IN DEGREES CENTIGRADE

m 

o

H 

CO
TEMPERATURE, IN DECREES CENTIGRADE

ro

> O 

> O 

) O

r

ro

> £
L14 DATA OF GEOCHEMISTRY

The melting point of this compound is uncertain. It 

has been given as 1455°C, but Nurse (1962) states that

the melting point of the latter can be as low as 1391°C; the higher value which have been obtained by the quenching method are 

explained by the amazingly rapid growth of this compound during quenching and by the effect of furnace atmosphere. Unless 

special precautions are taken the normal furnace atmosphere 

contains enough water to influence the melting curve. In drier 

atmospheres the field of stability of 12CaO-7Al_Oa narrows and 

although it has not been observed to disappear it seems probable that it may do so in the complete absence of water. At 

1000 degrees centigrade 12CaO7AlsOa can take up just over one 

percent of water.

The temperature 1391 °C is lower than the eutectic 

given by Kankin and Wright between 3CaOAl2O3 and 

5CaO-Al2O3 and also than that between 5CaO'3Al203 

and CaO A1203 (1400°C). In figure 6, the original diagram of Kankin and Wright is reproduced, but a question mark has been superimposed to indicate the uncertainty in this region. 12CaO7Al2O3 is one of the few 

compounds in which the index of refraction of the 

crystalline compound is lower than that of the glass of 

the same composition. The existence of the unstable 

form of 5CaO-3Al2O3 has been confirmed and its structure established (Aruja, 1959). CaOAl2O3, one of the 

main constitutents of high-alumina cement, melts congruently at 1600 °C. It forms a eutectic with 

CaO2Al2O3 at 1590°C, 66.5 percent A12O3. The 

compound identified by Kankin and Wright as 

3CaO 5A12O3 has been shown by Goldsmith (1948) to be 

CaO2Al2O3 , which Filonenko and Lavrov (1953) 

found to melt congruently at 1750°C. They also found 

a compound CaO6Al2O3, which melts incongruently at 

1850°C with formation of corundum and a liquid containing 89 percent A12O3 , and which forms a eutectic 

with CaO2Al2O3 at 1730°C and 80.5 percent A12O3 .

TABLE 6. Invariant points in the system CaO-AljOs

Phase reaction

3CaO-Al203^CaO+L_ ________

3CaO-Al2 03+ 12CaO.7Al2O3^L_ 

12CaO.7Al203^L. ----------

12Ca0.7Al203+ CaO-Al2 03^LCaO.Al2O3^L _____________

CaO.Al2O3 +CaO-2Al2O3^L. ... 

CaO-2 A12O3^L__ ......_ ._..-

CaO-2Al2O3+ CaO-6Al2O3^L___ 

CaO- 6A1_03^ A12 03 + L _ _______

Temperature (°C)

1535 

1395 

1458 

1400 

1600 

1590 

1750 

1730 

1850

Composition of liquid 

(percent by weight)

CaO

59 

50 

48. 54 

47 

35. 49 

33.5 

21.54 

19. 5 

11

A1203

41 

50 

51.46 

53 

64. 51 

66.5 

78.46 

80. 5 

89

CaO-Fe2O3

A preliminary report on the system CaO-Fe_O3 

was published by Sosman and Merwin (1916), and further work was done by Swayze (1946). Phillips and 

Muan (1958) studied the system by the quenching 

method in air (Po 2=0.21 atm) and in oxygen at 1 atm 

pressure. The system is actually ternary, with components Ca, Fe, and O, but in the upper part of figure 7 

it is shown projected on the join CaO-Fe2O3 . 

Projections are made by straight lines pointing to the 

O-corner of the composition triangle, called reaction 

lines. By reaction with the atmosphere during equilibration, 02 is added or subtracted from the condensed 

phases with a proportional change in the ratio of Fe2O3 

to FeO in the mixture. The compositions of all crystalline phases except magnetite are represented by points 

close to the join CaO-Fe2O3 , and the compositions of 

the magnetites are represented by points close to the 

join FeO-Fe2O3 and slightly on the Fe2O3 side of the 

FeOFe203 composition. The lower part of figure 7 

shows these relations, and also the compositions of liquids at the liquidus temperature in air. In oxygen at 

1 atm pressure the ratios of Fe203 to FeO are slightly 

different, and the amount of change from Po^O.21 atin 

to Po = 1 atm for some invariant points is given in 

table 7. A noticeable feature of the system in the subsojidus relations is the decomposition of CaO-2Fe_O8 

to CaO-Fe2O3 and F^O3 below 1155°C in air, 1172°C 

hi oxygen at 1 atm pressure.

TABLE 7. Invariant points in the system CaO-FetOt 

[a, solid solution]

Phase reaction

CaO+2CaO-FejOi^L. _________

2CaO-Fe_O3:p±L ________________

CaO-Fe_03^2CaO-Fe_03+ L_ _ _ _ _

CaO-Fe2O3+Ca2O-2Fe_03 ^L_ . __ 

CaO-Fe_03+ Ca_0-2Fe_O3 ;riL_ . . _ 

CaO-Fe203 +Fe2O3^CaO.2Fe2O3 _ 

Do--.. --.. --------------

CaO-2Fe203^L+Fe_O3ss -----

CaO.2Fe_O3 ;?±L+Fe2O3ss. ____

Fe3O4ss "L + FejOsss-. .___-_---

Fe304ss^I + Fe_O3ss _______

Temperature (°C)

1438 

1449 

1216 

i 1206 

1205 

1155 

' 1172 

i 1228 

1226 

i 1430 

1358

Composition of liquid 

(percent by weight)

CaO

42.0 

41.5 

29. 0 

21. 5 

20.0

20.0 

19. 0 

10. 5 

13. 0

FeO

1.0 

1.5 

2.0

2.0 

2.5 

8.0 

7.0

Fe,O,

58.0 

58.5 

75.0 

77.0 

78.0

78.0 

78.5 

81.5 

80.0

> Po2 =1 atm. At all other temperatures listed, Po,=0.21 atm.

The compound 2CaO-Fe2O3 melts congruently at 

1449°C in air and forms a eutectic with CaO at 1438°C 

and 58 percent Fe2O3 . The compound CaO-Fe2O3 

melts incongruently at 1216 °C with formation of 

2CaO Fe203 and a liquid containing excess Fe2O3 and 

some FeO. There is a eutectic between CaO-Fe2O3 and 

CaO-2Fe2O3 at 1206°C at 1 atm oxygen pressure, at 

1205°C in air (Po2 =0.21 atm). CaO-2Fe2 03 melts incongruently with formation of a hematite solid solu-
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L15

1700

1600 -

1500 -

1400 -

1300 -

1700

1200 -

1000-

WEIGHT PERCENT Fe2 03

To CoO

30 

FeO-Fe203

100

Fe203

FIGUBE 7. The system CaO-FezOs in air. The system is actually ternary, since the ratio of Fe20s to FeO in the liquid changes, 

as is shown by the line A'A in the lower part of the figure, which is a portion of the system CaO-FeO-Fe203. The uppei part of 

the system is a projection onto the side CaO-FejOs. ss, solid solution. Based on Phillips and Muan (1958).
L16 DATA OF GEOCHEMISTRY

tion at 1228 °C at 1 atm oxygen pressure, 1226° C in air. 

The hematite solid solution decomposes to a magnetite 

solid solution at 1430°C in 1 atm oxygen pressure, 

1358°C in air.

CaO-SiOj

The system CaO-SiO2 is of fundamental importance 

both to geology and to the portland cement industry. 

The basic work, which was by Day and Shepherd 

(1906) and Day, Shepherd, and Wright (1906), was 

the first binary oxide system to be worked out in the 

Geophysical Laboratory of the Carnegie Institution of 

Washington. Kankin and Wright (1915), in their 

study of the ternary system CaO-Al2O3-SiO2, added 

further details, and Greig (1927a) discovered the region of immiscibility in mixtures high in silica. Much 

additional work bearing on this system has been summarized by Bogue (1955), by Lea and Desch (1956), 

and by Welch and Gutt (1959). The phase-equilibrium 

diagram is figure 8, and the invariant points are given 

in table 8.

The compound a-CaOSiO2 (pseudowollastonite) 

melts congruently that is, to a liquid of its own composition at 1544°C. On cooling to 1125°C (Osborn 

and Schairer, 1941), a-CaO-SiO2 inverts to 

£-CaO*SiO2, wollastonite, which becomes the stable 

phase at lower temperatures. The inversion does not 

take place readily and usually is over-stepped in either 

direction. Bowen, Schairer, and Posnjak (1933b) 

showed that there is no solid solution near the composition CaO-SiOa.

TABLE 8. Invariant points in the system CaO-SiO2

Phase reaction

3 CaO. Si O, ;=i C&O+L..... ___ -

3CaO-SiOj ;=i CaO+o-2CaO.SiO,- 

3CaO-SiO,+o-2CaO.SiO2^L.....

a-2CaO- SiO,^iL.. _________ .

a-2CaO SiO2;=±j8-2CaO SiO,. .._...

0-2CaO- Si02^>-2CaO. SiO* .. . .

3CaO 2SiOs^a-2CaO Si02 + L. . _ . 

3CaO- 2SiO2 +a-CaO- SiOj^L. _ .

CaO-SiO^L. ___________ .

a-CaO- SiOs^/S-CaO. SiO2 _ . . .

a-CaO . SiO2 + SiOs (tridymite) ^L . . 

SiO2 (cristobalite) + L^L3 . .. ... ..

Temperature (°C)

2070 

1250 

2050 

2130 

1420 

675 

1464 

1455 

1544 

1125 

1436 

fL, 1698 

\L2 1698

Composition of 

liquid 

(percent by 

weight)

CaO

71.5 

76. 75 

69.5 

65. 11 

Noli 

Noli 

55. 5 

54. 5 

48.27 

Nol 

36. 1 

27.5 

. 6

SiO2

28.5 

32.25 

30. 5 

34.89 

quid] 

quid 

44. 5 

45. 5 

51. 73 

quid 

63.9 

72.5 

99.4

If a mixture containing 55 percent SiO2 is cooled 

from the completely molten condition, it will not begin 

to crystallize until the liquidus curve of a-CaO SiO2 is 

reached at 1522°C. Wlien the mety has cooled to

1500°C the liquid will contain 60 percent SiO2 . Since 

CaO SiO2 contains 51.73 percent SiO2 , the mixture at 

this point will contain crystalline a-CaO-SiO2 and 

liquid in the proportions to give a total SiO2 content 

of 55 percent or in the proportions to give the center 

of mass at 55 percent SiO2 . These proportions will be 

(55-51.73) -J- (60-51.73) or 40 percent CaO-SiO2 and 

(60-55) * (60-51.73) or 60 percent liquid. This same 

center-of-mass principle holds true in all problems of 

the relative proportions of phases in systems of any 

number of components. When the temperature has 

fallen to 1470°C, the liquid contains 62 percent of SiO2 , 

and the mixture consists of 68 percent of CaO-SiO2 

and 32 percent of liquid. The eutectic temperatures is 

1436°C and the liquid contains 63.9 percent SiO2., Just 

before tridymite begins to crystallize at the eutectic, 

the mixture contains 73.1 percent CaO-SiO2, 26.9 percent of a liquid containing 36.1 percent CaO, 63.9 percent SiO2 . When crystallization is complete at the 

eutectic, the mixture contains 93 percent of o-CaO SiO2 

(pseudowollastonite) and 7 percent of SiO2 (tridymite) . The eutectic point is an invariant point, since 

there are three phases, liquid, o-CaO-SiO2, and tridymite, coexisting at a constant pressure and temperature. 

This eutectic with SiO2 is the lowest temperature invariant point in this system, as in most silicate systems. 

If the original mixture contains more CaO than corresponds to CaO-SiO2, the liquidus curve falls to the 

eutectic at 1455°C and 45.5 percent SiO2, where it solidifies to a mixture of 3CaO-2SiO2 (rankinite) and 

o-CaO-SiO2 . When pure 3CaO-2SiO2 is heated, it 

remains unchanged until 1464°C (Osborn, 1943) is 

reached, when it begins to melt. The system remains at 

1464°C until the reaction 3CaO -2SiO2 =L+2CaO -SiO2 

is complete, and the liquid contains 44.5 percent SiO2 . 

This is an example of what is called incongruent melting in which one of the solids melts to form a liquid 

and another solid, and the composition of the melting 

solid is between the liquid and the new solid formed by 

the phase reactions. The invariant point at which reaction takes place is called an incongruent melting 

point, a reaction point (Powen, 1922), or sometimes 

a peritectic point. When a melt of composition 

3CaO-2SiO2 is cooled from the liquid condition, 

2CaO-SiO2 begins to crystallize at about 1700°C. As 

cooling continues the liquid becomes enriched in SiO2 , 

until at 1464°C the reverse reactions take place and 

crystalline 3CaO-2SiO2 is formed until all the 

2CaO-SiO2 and liquid are used.

The compounds 2CaO-SiO2 melts at 2130°C. It is 

known in several forms (Bredig, 1950). The hightemperature form, o-2CaO-SiO2, inverts to an orfhorhombic form (Bredig, 1945) at 1438°C, which Tilley
TEMPERATURE, IN DEGREES CENTIGRADE

o

8

(7)

8

->l 

o 

o

a> 

o 

o

O

0

ro 

o 

o 

o

o

o

ro 

8

O

OJ

o 

a

O Q O

 3 Q 

co a. o

,$>

and 

3CaO-Si02

- 2CaO-Si02 and 3CaO-Si02

/Q-2CaO-Si(>2

and 

3CaO- 2Si02

*c-2CaO-Si02 and LIQUID _ _ 

"~~~'

3CaO- 2Si02

and 

<<-CaO-Si02

o

9

CO

i.

CO

o

o

c
L18 DATA OF GEOCHEMISTRY

and Vincent (1948) found as a mineral and named 

bredigite. The inversion temperature is greatly lowered in complex systems. The orthorhombic form inverts at 650 °C to the y-form with an increase in volume 

of about 10 percent and a resulting "dusting" to a fine 

powder. When the a-form is undercooled to 675 °C, it 

changes to a monotropic form which corresponds to the 

mineral larnite. It was called the /?-form by Rankin 

andWright (1915).

Tricalcium silicate, 3CaO SiO2 , is the most CaO-rich 

compound in the binary system, CaO-SiO2 . It is of 

great industrial importance as a constituent of portland cement, called "alite" by Tornebohm (1897). It 

was formerly considered to decompose at 1900 °C, but 

Welch and Gutt (1959) found that it melts incongruently at 2070°C, with formation of liquid and CaO. 

Hence, it has a short composition range of stability in 

contact with melt, as shown in figure 8. A mixture of 

the composition 3CaOSiO2 on cooling first separates 

CaO at about 2110°C, and on cooling to the reaction 

point CaO+Z=3CaO-SiO2 at 2070° C, the CaO reacts 

with liquid to form 3CaO SiO2. There are metastable 

inversions at 923° and 980°C (Nurse, 1960). Finally, 

if the compound is cooled to 1250°C it decomposes into 

CaO and 2CaO SiO2. This also is an invariant point 

in a condensed system, at which the phase reaction is 

3CaO SiO2 =CaO+2CaO SiO2.

An important phenomenon is shown in mixtures rich 

in silica, namely, the formation of two immiscible 

liquid phases (Greig, 1927a). The stable phases immediately below the eutectic temperature, 1436°C, in any 

mixture containing more SiO2 than CaO SiO2 is a mixture of CaO SiO2 and SiO2, as tridymite. If the mixture contains more than the eutectic composition, 63.9 

percent SiO2 , at the eutectic temperature all the 

CaO SiO2 melts, leaving tridymite. On further heating the tridymite inverts to cristobalite at 1470°C. If 

the mixture contains between 72.5 and 99.4 percent of 

SiO2 , at 1698°C the liquid separates into two immiscible liquids. This is an invariant point, since there 

are two liquid phases and a solid phase, cristobalite, 

coexisting at a constant pressure greater than the 

vapor pressure of any of the melts.

It is evident from the phase-equilibrium diagram 

that CaO SiO2 is the only solid phase which can exist 

in equilibrium with SiO2 . 3CaO 2SiO2 or 2CaO SiO2 

are incompatible with SiO2 , and their fields are not adjacent to the field of silica.

CaO-TiO2

The system CaO-TiO2 has been studied by von 

Wartenburg, Reusch and Saran (1937), Coughanour,

Phase reaction

CaO+3CaO-2Ti02 ^L__ __-_--

3CaO.2Ti02^4CaO-3Ti02+L~ 

4CaO-3TiO2^CaO.Ti02+ L .... 

CaO-Ti02 ^L- ---------------

CaO-Ti02+Ti02^L_ .__... _

Temperature (°C)

1725 

1740 

1755 

1915 

1475

Composition of liquid 

(percent by weight)

CaO

61 

54 

53 

41.24 

17

TiOj

39 

46 

47 

58.56 

83

Roth, and DeProsse (1954), and DeViries, Roy, and 

Osborn (1954b). The latest revision is by Roth (1958), 

whose phase-equilibrium diagram is shown in figure 9. 

Data on the invariant points in the system are given 

in table 9. The compound CaO-TiO2 which corresponds to the mineral perovskite, melts congruently at 

1915°C, and has a eutectic with TiO2 at 1475°C. The 

compound 4CaO'3TiO2 melts incongruently at 

1755°C with formation of a CaO-richer liquid and 

3CaO-TiO2 which melts incongruently at 1740°C. The 

eutectic CaO-3CaO'2TiO2 is at 1725°C.

TABLE 9. Invariant points of the system CaO-TiOz

FeO-Al2O3

The system FeO-Al2O3 was studied by M'lntosh, 

Rait, and Hay (1937) , who found compounds provisionally identified as 3FeO-Al2O3 and FeO-Al2O3 . However, Schairer and Yagi (1952) point out that these 

investigations took no cognizance of the equilibrium 

between ferrous oxide melts and metallic iron, and conclude that no reliable data in this system are available.

FeO-F2O3 is part of the system iron-oxygen, and the 

relation between the compositions of the iron oxide 

phases and the pressure of oxygen must be considered 

at every temperature. This is true in all systems in 

which an oxide of iron is a component. The work by 

Darken and Gurry (1945, 1945) presents a study of 

these relationships at temperatures both below and 

above those at which liquid oxide is formed, and include 

the results of Greig, Posnjak, Merwin, and Sosman 

(1935 ) . Figure 10 gives their temperature-composition 

phase-equilibrium diagram at a total pressure of 1 atm ; 

significant data for the lettered points are given in 

table 10. Low oxygen pressures are given in this table 

by the ratio Pco2/Pco, from which may be calculated 3 

the partial pressure of oxygen. Addition of oxygen to

s The free energy of the reaction CO+^ 62^002 calculated from the free 

energy changes for the reaction C (graphite)+Oj (j)^COj (g) and C (graphite)+ 

J.SO2(0)^CO (ff) is given by Coughlin (19S4) as AF°=- 67600+20.71 T from 

which the pressure of oxygen at any temperature can be calculated.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L19

1900 -

CaO 20 40 y" 50

3CaO-2Ti02

90 Ti02

CaOTiOg

4CaO-3Ti02 

WEIGHT PERCENT Ti02

FIGTTBE 9. The binary system CaO-TiOi. Modified from Roth (1958).

iron lowers its melting point from 1535°C to B at 

1524°C, when a second liquid layer of composition O 

appears. With increase in temperature the two layers 

probably approach each other in composition as indicated. On further increase in oxygen content, the melting point curve is lowered from C to N, at which invariant point wiistite of composition near FeO appears. 

At invariant point / magnetite becomes the solid phase, 

and melts congruently at point V, after which the melting curve falls to a eutectic at which the solid phases 

are a magnetite solid solution of composition T and a 

hematite solid solution of composition Z. Where the

line of A>2= 1 atm, a magnetite of composition R is in 

equilibrium with iron-oxide liquid of composition R1 . 

Below the temperature of Q (560°C), FeO (wiistite) 

is not a stable phase, and at oxygen pressures less than 

about 10~24 atm metallic iron and Fe3O4 are the stable 

phases; at slightly greater oxygen pressures the stable 

phase pair is Fe3O4 and Fe2O3 ; and at higher pressures 

only Fe2O3 . Above 560°C a field of wiistite solid solutions separates the fields of iron+ wiistite and wiistite+ 

magnetite. Most of the diagram of figure 10 corresponds to a partial pressure of oxygen less than that in 

air that is, 0.21 atm.
TEMPERATURE, IN DEGREES CENTIGRADE 

«t 5.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L21

TABLE 10. Significant points of the system iron-oxygen 

[Reprinted from Darken and Gurry, 1946,1946]

Invariant 

point on fig. 10

A.... .......

B. ..........

C. ..........

G. ..........

H...........

I............

J. ..........

L. ..........

N... ........

Q. ..........

R.. .........

Rf . .........

s

V... ........

Y. ..........

Z. ..........

Temperature (°C)

1535

1524

1524

1400

1424

1424

1371

911

1371

560

1583

1583

1424

1597

1457

1457

0 

(percent)

0

0. 16

22. 60

22. 84

25.60

25.31

23. 16

23. 10

22. 91

23.26

28.30

28. 07

27.64

27. 64

28.36

30.04

Pco2/Pco

0.209

.209

.263

16.2

16.2

.282

.447

. 282

1. 05

16.2

Po2 (atm)

1

1

.0575

1

1

Figure 11 shows the fields of iron and its oxides in a 

P-T diagram in which the pressure of oxygen is represented by Po2=PH2o/Pn2 * At temperatures below 

1070°C, Fe-jOs is the stable phase in the equilibrium 

with water vapor. Bozorth (1927) found that the protective layer formed on iron by steam at 713° C was built 

up of layers of FeO, Fe3O4, and FeaOa, of thickness 

ID"2, 2X10-4, and 2XICT5 cm, respectively.

FeO-SiO2

The system FeO-SiO2 cannot be studied accurately as 

a binary system because the liquids are never purely 

ferrous, but Bowen and Schairer (1932) made a close 

approximation by working in iron crucibles in an atmosphere of oxygen-free nitrogen, obtained by passing 

the nitrogen through ammoniacal copper solution and 

then over hot copper gauze. They analyzed the resulting mixtures for the Fe2O3 content, with results shown 

in the upper curve of figure 12. The approach to a binary system is very close except at the iron-rich end, and 

the melts in their actual behavior are sensibly binary. 

Bowen and Schairer "without serious misrepresentation 

and with enormous gain in the utility of the diagram" 

drew the binary diagram of figure 12 by calculating all 

iron in each mixture to FeO and plotting the results 

accordingly. The point given as the melting point of 

FeO, 1380°C, is the invariant point Fe + liquid=FeO

« The free energy of the reaction H2+}4 Oj=H2O(<7) is given by Coughlin (1954) as

AF° =-58,850+13.12 T

from which the pressure of oxygen at any temperatuie can be calculated. (See also 

Eugster, 1959.)

in the binary system, Fe-O, and the liquid contains 11.56 

percent Fe2O3 . From this point the liquidus falls, with 

FeO (wiistite) as solid phase, to the eutectic with 

2FeO-SiO2 (fayalite), at 1177°C. Pure fayalite melts 

congruently with separation of about 0.75 percent of 

metallic iron, but a mixture having nearly the composition of theoretical fayalite melts at 1205°C about as 

sharply as the purest silicate compounds in spite of its 

containing 2.25 percent Fe2O3 .

From the melting point of fayalite, the melting-point 

curve falls with increasing FeO to a eutectic with FeO 

(wiistite) at 1177°C, and with increasing SiO2 content 

to a eutectic with tridymite at 1176°C. From this point 

the liquids curve rises until a region of liquid immiseibility is reached. Greig (1927b) found that at 

1689°±10°C the FeO-rich layer in equilibrium with 

cristobalite contains 42 percent FeO, the SiO2-rich 

layer, 3 percent FeO.

Bernal (1936) suggested that common olivine might 

invert to a spinel-type structure at high pressure, and 

Blngwood (1958) prepared a spinel form of 2FeO SiO2 

at 35 to 40 kilobars pressure and 600°C. Boyd and 

England (1960) confirmed Ringwood's result and obtained a point on the P-T curve at 60 kilobars and 

1500°C.

FeO-TlO2

Grieve and White (1939) found that each of the two 

ferrous titanates, 2FeO'TiO2 (ulvospinel), and 

FeO-TiO2 (ilmenite), melted congruently at about 

1470°C. 2FeO TiO2 has a eutectic with FeO at 1380°C, 

5 percent TiO2 , and with FeO-TiO2 at 1320°C and 42 

percent TiO2 . The FeO TiO2-TiOa eutectic is at 

1330°C, 68 percent TiO2 .

Al2O3-SiO2

The binary system Al2O3-SiO2 is fundamental to the 

most widely used refractories and to the clay-working 

industries in general. The original study of this system 

was by Shepherd, Rankin, and Wright (1909), but they 

did not recognize the existence of 3A12O3 2SiO2 (mullite), which was discovered by Bowen and Greig (1924). 

The present Al2O3-SiO2 diagram (figure 13) is by 

Aramaki and Roy (1959), who found that mullite melts 

congruently at 1850°C, and has a eutectic with A12O3 at 

1840°C and 78 percent by weight A12O3 . Toropov and 

Galakhov (1951) and Budnikov, Tresvyatskii, and 

Kushnakovskii (1953) had previously found that mullite melts congruently, as indicated in the diagram. 

There is an area of solid solution of A12O3 in mullite.
L22 DATA OF GEOCHEMISTRY

1800

1600

} 1400

Q 

< 

DC.

p 1200

UJ

O

o

UJ 

Q

1000

- 800

UJ

cr

£ 600

UJI400

200

0

i r 

\

 i r 

\ x V, \ \ \ \

\ LIQUID IRON \ | L \U|D OX;DE \ \ 

1_\ __________\v__j\ \ \ ^-Vr- \

\ \ 

\ \

\

\

/ \ \ \

\/ \ \\

kr°

\

\

-3 -2 0

f IGTJEE 11. The stability fields of iron and its oxides in which the pressure of oxygen is given by PO^P^O/PH^. Heavy solid lines are boundary curves between phase areas. 

Light dot-dash lines are oxygen isobars which may be correlated with the isobars of figure 10. The heavy long-short dash line equilibrium ratios PHJO/.PHJ of pure water 

vapor as a function of temperature at a total pressure of 1 atm. Modified from Muan (1958a).

The relations among the three minerals sillimanite, 

kyanite, and andalusite, each of which has the composition A12O3 SiO2 , are not clear. Greig (1926) found 

that each of them decomposes on heating into mullite 

and silica, probably in the form of cristobalite, or into 

mullite and a siliceous liquid. For none of them was 

the decomposition reversible, nor was there a definite 

temperature of decomposition but rather a rate of decomposition increasing with the temperature. Kyanite 

apparently began to change at the lowest temperature, 

sillimanite at the highest. Kyanite appeared unaltered 

except for loss of color on heating 48 hours at 1000°C, 

but some decomposition had taken place. Morey and

Ingerson (1941) obtained sillimanite in experiments 

with superheated steam at high pressure, and Hoy 

(1954) and Koy and Koy (1955) synthesized andalusite. 

They found no definite stability range, but andalusite 

formed in the temperature range 450° to 700° C with 

H2O pressures of 10,000 to 30,000 psi. Kobertson, 

Birch, and MacDonald (1955) mention in an abstract 

that they have found a tentative boundary between the 

sillimanite and. kyanite fields, but give no details. 

Griggs and Kennedy (1956) give a P-T curve for the 

change of sillimanite to kyanite, which goes to higher 

temperatures and pressures from about 700 °C and 

15,000 psi., where it intersects the dissociation curve of
PHASE-EQUILIBRTlTM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L23

pyrophyllite, (Al2O3 -4SiO2 -H2O). At a quintuple 

point are pyrophyllite, quartz, H2O, sillimanite, and 

kyanite. Clark, Robertson, and Birch (1957) found 

points on the curve of equilibrium between sillimanite 

and kyanite at 18,200 bars at 1000°C and 21,000 bars at 

1300°C, with kyanite being the high-pressure phase. In 

their report they give a tentative phase diagram showing the relationship among the phases kyanite, sillimanite, andalusite, and (mullite+quartz), which is 

reproduced as figure 14. Clark (1960) determined the 

kyanite-sillimanite curve more precisely. The agreement was within 1 kilobar in the range from 1000° to 

1300°C. The slope of the P-T curve between 1000° and

1500°C is 13.1 bars per degree. The minerals in this 

system are among the best refractories known. They 

are extraordinarily reluctant to take part in chemical 

reaction, and forms persist for long periods outside of 

their regions of stability.

The system Al2O3-TiO2 has been studied by von 

Wartenberg and Reusch (1932) and by Bunting 

( 1933) ; A12O3 TiO2 melts congruently at about 1860°C ; 

the eutectic with A12O3 is at 1850°C and 38 percent 

TiO2 ; that with TiO2 at 1715°C and 85 percent TiO2.

10

5

0

1800

1700

£ 1600 

O

c/)

UJ 

UJ 

C£

UJ

Q 1500

z

1400

1300

1200

CRISTOBALITE and LIQUID

LIQUID

I380±5 l

FeO 

W'USTITE

and 

LIQUID

2FeO- Si02

FAYALITE

and 

LIQUID

1177 + 5'

I I

TWO LIQUIDS 

I689±IO°-

1470 ±10

TRIDYMITE and LIQUID

II78±5°

WUSTITE and FAYALITE FAYALITE and TRIDYMITE

FeO 10 20 /30 

2FeO -Si02

50 60 70 80 90 Si02

WEIGHT PERCENT Si02

FIGUEE 12. The system FeO-SiO2. Modified from Bowen and Schaker (1932).

695-382 O - 64 - 3
L24

Q 

<

oc

05

LJ

o

C/) 

LJ 

LJ 

CC 

O 

LJ 

Q

2100

2000

1900

1800

10 20 30

DATA OF GEOCHEMISTRY

WEIGHT PERCENT AI2 03 

40 50 60 70 80 90

- 1700

LJ 

CC

cc

LJ 

CL

LJ

1600

1500

1400

LIQUID

3 AI 2 03 - 2Si02 (MULLITE)-t- LIQUID

I850%X

_ Si02 +LIQUID

Si02

AI 203 +3A!203-2Si02 ss

3AI203 -2Si02 ss

SiOc 10 20 30 40 50 60 70

MOLE PERCENT AI203

FIGURE 13. The system AljOs-SiOj. ss, Solid solution. Modified from Aramakl and Boy (1959).

80 90 AI 203

Muan and Gee (1956) and Muan (1958b) studied the 

system Fe2O3-Al2O3 by the quenching method in air 

(Po2 = 0.21 atm) and in oxygen at 1 atm. The system 

Fe-jGs-ALOs can be considered as binary until FeaOs 

starts to dissociate to oxygen and FeO, when a spinel 

phase is formed. The results are shown in figure 15; 

the diagram at 1 atm oxygen pressure is a little different. The phase Fe2O3 -Al2O3 (hercynite) is unstable relative to hematite solid solution plus corundum 

solid solution below 1318°C (Muan, 1958b). The system becomes ternary, neglecting the possible appearance 

of a metallic iron. As in all systems containing iron 

oxide, the partial pressure of oxygen must be considered.

Fe2O3-SiO2

Bowen, Schairer, and Willems (1930) inferred from 

the curve of the tridymite-hematite boundary in the 

system Na^O-Fe-jOg-SiOo that no compound exists in

this binary system, and that there is almost complete 

immiscibility between Fe2O3 and SiO2 in the liquid 

state.

The system Fe2O3-TiO2 was studied by MacChesney 

and Muan (1959a) in air by the quenching method. 

The results are shown in figure 16. There is 

extensive solid solution, and the crystalline phases have 

compositions approximately represented by parts of the 

joins FeOFe2O3-2FeOTiO2 , Fe2O3-FeOTiO2 , and 

Fe2O3 TiO2 (pseudobrookite) -Fe2O3 2TiO2 . The most 

notable feature of the subsolidus relations is the marked 

influence of TiO2 on the equilibrium decomposition 

temperature of the sesquioxide (a-Fe2O3 ) structure of 

hematite to the spinel structure of magnetite. This decomposition temperature in air rises from 1390° C for 

the pure iron oxide end member to a maximum of 

1524°C as TiO2 is added.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L25

SiCv-TiO,

The system SiO2-TiO2 was studied by DeVries, Roy, 

and Osborn (1954a) who critically reviewed the results 

of earlier observers. The melting point curve falls 

from the melting point of SiO2 , 1713°C, to a eutectic 

with rutile, TiO2 , and cristobalite at 1556° ±4°C, 10.5 

percent TiO2. The curve then rises rapidly until at 

1780°'±10°C, two liquid layers of composition 19 percent TiO2 and 93 percent TiO2 are formed in equilibrium 

with rutile. On further increase in temperature, the 

TiO2 -rich liquid rises to the melting point of TiO2 at 

1830°C.

TERNARY SYSTEMS

The ternary systems formed by the nines oxides under 

consideration are given in this section. The combinations of the oxides are arranged in the order of their 

enumeration in the Introduction. At an invariant point 

in a ternary condensed system four phases coexist, and 

at most of the invariant points considered three solids 

coexist with a liquid. When the composition of the 

liquid lies within the triangle formed by the compositions of the three solid phases the liquid is a eutectic, 

and the phase reaction is of the type Si+S2 +S3 =Z, 

When the composition of the liquid is outside of the

UJ

cc

UJ

S 20 

O

^ 

<

u_ 

O

Q

KYANITE

o

I

UJ ct:

UJ ct:

0

ANDALUSITE

0

MULLITE + QUARTZ

0 500 1000

TEMPERATURE, IN DEGREES CENTIGRADE

FIOUEE 14. Tentative phase diagram of the composition AUOs-SlO2. Phase boundaries indicated by short dashes are not experimentally determined and no quantitative 

significance should be attached to them: longer dasbes are an extrapolation of the kyanite-sillimanite equilibrium curve. Modified from Clark, Robertson, and Birch 

(1957).
L26 DATA OF GEOCHEMISTRY

2100 -

2000

1800

5 1700

LU 1600

1500

a

z 

! 

HEMATITE ss 

+ SPINEL ss

1300

1200

1100

LIQUID

SPINEL ss 

SPINEL ss / + CORUNDUM ss

ss + e23 23

Fe203 -AI 203 ss 

 * CORUNDUM ss

- 2100

2000

T

1800

1700

1600

1500

I4OO

1300

1200

1100

T

Fe2 03 10 

Fe203

20 30 y"40 50 6 

Fe203 -AI203

WEIGHT PERCEIS 

Fe2 03 -AI203

0 70 80 90 AI 203

T

AI 203

FeO-Fe 20 3,

FeO-AI203

FeO

FIQTTBE 15. Phase equilibria in the system iron oxide-alumina in air (Poj=0.21 atm). The upper half of the figure has the appearance of a binary system and is obtained 

by projecting all compositions onto the join FesOa-A^Os along the oxygen reaction line originating in the oxygen comer of the triangle representing the system Fe-Al-O. 

The phase boundaries are solid lines where the system is binary, dashed lines where the solid phase, spinel, has a composition not on the join FezOs-AlsOj. ss, solid 

solution. Modified from Muan and Gee (1956).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L27

uj 1800

Q

1700

CC 

uT O

Q_ LL) 

K O

LU

Q

- 1600

MAGNETITE SS ^--^

1500

MAGNETITE SS 

HEMATITE SS 

1400

LIQUID

1594 PSEUDOBROOKITE SS

PSEUDOBROOKITE SS 

RUTILE SS

PSEUDOBROOKITE (SS) N 

_J____________|___________|___________|____________|___________|___________|___________1

10 20 30 40 50 60 70 80 90 Ti02

WEIGHT PERCENT 

Fe203-Ti02 (PSEUDOBROOKITE) TiO;

FeO-Fe203 FeO-2TI02

FeO-Ti02

2FeO-Ti02

FeO

FIGURE 16. Phase relations in the system iron oxide-TiOz in air. The upper half of the figure has the appearance of a binary system and is obtained by projecting all compositions along oxygen reaction lines originating in the oxygen corner of the triangle representing the system Fe-Ti-O. The cuive abcde represents the composition 

of liquids along the liquidus surface in air; line/s gives the composition of the solid solution at 1524° C. f«», solid solution.) Modified from MacChesney and Muan (1959).
L28 DATA OF GEOCHEMISTRY

triangle formed by the solid phases, the phase reaction is of the type Si + S2 = S3 +Z, and the invariant point is called a reaction point. At temperatures 

below the invariant point, the univarlant assemblies 

may be Si + S2 + S3 or Si+S2 +Z; above the invariant 

point, Si+Ss + Z or S2 + S3 +Z. When the composition of one of the solids, say S3 , is within the composition triangle Si S2 Z, below the invariant point the 

univariant assemblies may be Si+S2 + S3 , Si + S3 +Z, 

or S2 + S3 + Z, but above the invariant point the only 

stable assembly of phases is Si + S2 +Z. In this case 

the invariant point is a maximum temperature for 

phase S3 . When the composition of two reacting solids 

and the coexisting liquid lie on a straight line, that line 

is one of maximum temperature in the ternary system, 

and the phase reactions are those of a binary system, 

with either congruent or incongruent melting. When a 

solid melts to a liquid of its own composition, that congruent melting point is a maximum on the surface of

equilibrium between that solid and liquids in the ternary system.

Some examples of phase relations in ternary systems 

are discussed in detail. The system Na2O-K2O-SiO2 

contains an example of a eutectie and of a reaction 

point. The phase relations in the ternary system 

Na2O-Al2O3-SiO2 are discussed in terms of binary systems within the ternary system and of the boundaries 

of the several fields. The crystallization paths in the 

system Na2O-CaO-SiO2 are considered. The determination of three-phase boundaries is discussed in connection with the system Na2O A12O3 6SiO2 (albite)- 

CaO-MgO-2SiO2 (diopside)-CaO-Al2O3 -2SiO2 (anorthite) . There is an extended discussion of subliquidus 

relations in the system CaO-FeO-SiO2 .

The part of the system Na2O-K2O-SiO2 within the 

limits Na2OSiO2 (sodium metasilicate)-K2OSiO2 

(potassium metasilicate)-SiO2 (fig. 17 and table 11)

Nd20-Si02 

50

40 

K2 0-Si02

70 

K20 4Si02

WEIGHT PERCENT Si02 

FIGURE 17. The ternary system KjO-SiOj-NajO-SiOj-SiOj. Modified from Kracek (1932).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 11. Invariant points in the system K2O-SiO2-Na2O-SiO.-SiO2

L29

Invariant 

point on 

fig. 17

A.......... .

B.... ........

a _______ __

C____________

b. ___________

£____________

e______ _ ___

Phase reaction

K2O-4SiO2 -"K2O.2SiO2 + SiO2 (quartz) + L.... ..... ......... .

Na2O-2SiO2 +K2O-2SiO2 -|-SiO2 (quartz) -"L____ ___ _ __ _

NazO^SiC^+KaO^SiO.-^------ ___ _ _________ _ _

Na2O.2SiO2 +K2O-2SiO2 +Na2 O-Si02 ^L---_- _ _...._._______

Na2O-SiO2 +K2O-2SiO2 ^L____ _____________ _ ______________

Na2O-SiO2 +K2O-SiO2 + K2 0.2Si02 -"L___.____________________

Na2O-SiO2 +K2O-SiO2^Z/ _ __ _______ _ _ __ ______

Temperature (°C)

640 

540 

705 

655 

680 

645 

745

Composition of liquid (percent 

by weight)

Na2O

4.5 

8 

15.0 

17. 2 

17.6 

11.7 

15

K2 0

25. 7 

23 

24.5 

25.4 

28. 7 

40. 1 

43

SiO2

69.8 

69 

60.5 

57.4 

53.7 

48.2 

42

was studied by Kracek (1932) . No ternary compounds 

are formed, and simple binary systems are formed by 

Na2O SiO2-K2O SiO2 , by Na2O SiO2-K2O 2SiO2 , 

and by Na2O-2SiO2-K2O-2SiO2 . Both Na2O-2SiO2 

and K2O -2SiO2 take into solid solution limited amounts 

of Na2O, K2O, or SiO2 , depending on the composition 

of the liquid from which they crystallize. The field of 

K2O4SiO2 occupies but a small portion of the ternary 

diagram, and is terminated at the reaction point A, 

where the phase reaction

K2O-4SiO2 =£ + K2O-2SiO 

takes place. The phase assemblages

(quartz)

2O-2SiO2 +K2O-4SiO2 ) and (Z + K2O4SiO2 + 

SiO2 ) go to higher temperatures at the side K2O'SiO2- 

SiO2 ; the assemblage

(£ + K2O-2SiO2

goes to the lower temperature and ends at the ternary 

eutectic B, where the phase reaction is

and the liquid is inside the triangle formed by three 

solid phases. A second eutectic is at D where the phase 

reaction is Na2O-SiO2 + K2O-SiO2 +K2O-2SiO2 =Z. 

K2O-4SiO2 also exists in two polymorphic modifications with an inversion at 592°C at a pressure of 1 atm 

(Goranson and Kracek, 1932), which is below the lowest liquidus temperature; hence the low temperature 

modification K2O4SiO2 II does not reach the liquidus. 

Mixtures containing less SiO2 than the disilicate join 

are not hard to crystallize, but those near the ternary 

eutectic and reaction points cannot be crystallized dry 

and hydrothermal crystallization must be resorted to. 

At the eutectic with Na2 2SiO2 , K2O -2SiO2 , and quartz,

10 days heating was not sufficient to ensure equilibrium. 

Many of the mixtures are extremely hygroscopic.

Na2O-MgO-SiO2

Preliminary studies of the system Na2O-MgO-SiO2 

were published by Schairer, Yoder, and Keene (1953, 

1954) who found the phase diagrams published by Botvinkin and Popova (1937), and Manuilova (1937) to be 

seriously in error. The preliminary phase-equilibrium 

diagram by Schairer, Yoder, and Keene is figure 18, 

and on it are given the temperature of the invariant 

points. The compositions have not been published.

A part of the system Na2O-CaO-Al2O3 low in Na2O 

was studied by Brownmiller and Bogue (1932) (figure 

19 and table 12) . Two ternary compounds are formed : 

Na2O 8CaO 3A12O3 , which melts incongruently at 

1508° C with separation of crystalline CaO, and 

2Na2O 3CaO 5A12O3 , which does not dissociate or melt 

up to 1630° C. No melting was observed on the join 

2Na2O-3CaO-5Al2O3-Na2O-Al2O3 up to 1630°C, but 

from the correlation of all the data obtained a complete series of solid solutions was inferred. There is 

no solid solution with the ternary compound and 

CaO 2A12O3 , CaO A12O3 , or 5CaO 3A12O3 , but a series 

of binary eutectics, at points «, d, and h, and the ternary 

eutectics B and F. The point q is the eutectic between 

CaO and Na2O-Al2O3 . Point / is a reaction point at 

which liquid is formed. Point r is the binary eutectic 

between Na2O 8CaO 3 A12O3 and 2Na2O 3CaO 5 A12O3 , 

and in the region above the line r-2Na2O 3CaO 5A12O3 

the solid phase is one of the solid solution series 

2Na2O-3CaO-5Al2O3-Na2O-Al2O3 . The area IJMP 

is the field in which Na2O 8CaO 3A12O3 is the primary 

phase. Compositions richer in CaO than the line qPM 

have CaO as primary phase. At P the phases are CaO,
L30 DATA OF GEOCHEMISTRY 

To MgO

TEMPERATURE, IN 

DEGREES CENTIGRADE

A 12501 5 

B 1190+ 5 

C 1040 ± 5 

D 9I5± 5 

E 868 ± 5 

F 865+10 

G 798 ± 5 

H 825 + 

/ 735 + 

J 7I3± 

K 7I3± 

L 733 ± 

4/ 725±IO 

/V 785 ± 5 

0 773+ 5 

/> 780 ± 5 

<? 775± 5 

/P 867 ± 3 

S 1018 ± 5 

r 1470+10 

U 763 ± 5 

^ 716+ 5 

W743 + 5 

81 8 ± 5

I045± 5

NcuO 30 40/50 

Na20 ; Si02 Na2 0-2Si02

WEIGHT PERCENT Si02 

FIGURE 18. The ternary system NajO-MgO-SiOj. Modified from Schairer, Yoder, Mid Keene (1954).

TABLE 12. Invariant points in the system Na20-CaO-Al2O3

CRISTOBALITE

Invariant 

point on 

fig. 19

a

B

d

F... .........

h--.-_ ... ....

/__..________

/__.__-___._.

q...... ._.

r.... ___ _ _

P.. ... . .

M. ..........

Phase reactions

CaO.2Al2O3 +2Na2O-3CaO.5Al2O3 -"L__.__... ___ ________ _ _

CaO.Al2O3 +2Na2O.3CaO.5Al2O3 +CaO.2Al2O3 ^L_. __________ _

CaO.Al2O3 +2Na2O.3CaO.5Al2O3 ^L. ________________________

5CaO-3Al2O3 +2Na2O-3CaO.5Al2O3 +CaO-Al2O3 -"L.___- _______

5CaO.3Al2O3 +2Na2O-3CaO.5Al2O3 L____ . _ __ __________

5CaO.3Al2O3 +Na2O.8CaO.3Al2O3 +2Na2 0-3CaO.5Al2O3-"L.____

5CaO.3Al2O3 + Na2O.8CaO.3Al2O3 ^3CaO- A12O3 + L ............

CaO+Na2O-Al2O3 L ___ ._ _ _______ ___ _ _ ____

Na2O-8CaO.3Al2O3 + 2Na2O.3CaO.5Al2O3 -"L_ __.___._._.._____

Na2O.8CaO.3Al2O3^±(Na2O.Al2O3-2Na20-3CaO.5Al2O3)ss+L. . _ _ 

3CaO.Al2O3 +Na2O.8CaO.3Al2O3 -"CaO+L__ __________________

Temperature 1°C)

1550 

1465 

1515 

1430 

1450 

1420 

1423 

1565 

1462 

1475 

1490

Composition of liquid (percent 

by weight)

Na20

8.6 

6 

5.4 

4.0 

4.3 

5.0 

4. 5 

30 

10.2 

13. 0 

6.0

CaO

21.3 

27.5 

30.2 

38.0 

40.4 

46.0 

46. 5 

20 

43. 7 

42. 5 

50.0

A12O3

70. 1 

66. 5 

64.3 

58.0 

55.3 

49.0 

49. 0 

50 

46. 1 

44. 5 

44.0
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L31

To 

Na2 0

50

To 

CaO

Na 20-8CaO-3AI203 

ToCaQ

30 ] 40 

3CaO AI203

50 \ 60 \ 70 

5CaO-3AI203 CaO-AI 203

80 

CaO- 2AI203

AI203

WEIGHT PERCENT AI203 

FIGTIEE 19. The ternary system NajO-CaO-AljOa. Modified from Brownmiller and Bogue (1932).

Na2O8CaO3Al2O3 , a solid solution of the 

Na2OAl2O3-2Na2O3CaO5Al2O3 series, and liquid, 

but since the solid solution is on the straight line 

Na2O8CaO3Al2O3-P the CaO does not enter into the 

reaction.

Na2O-CaO-SiO2

Morey and Bowen (1925) and Morey (1930a) made 

the first studies of the system Na2O-CaO-SiO2 which

included only that portion of the system richer in SiO2 

than the join Na2O-SiO2-CaO-SiO2 . Segnit (1953) 

extended the study to higher Na2O contents, where the 

difficulties caused by the volatilization of Na2O became 

serious. Both sets of results are included in figure 20, 

and the data of the invariant points are in table 13.

The region around the field of the compound 

Na2O-3CaO-6SiO2 (devitrite) (Morey and Bowen, 

1931) is of special interest in glass technology, because
L32 DATA OF GEOCHEMISTRY

CaO

80

 SiO,

NaoO

TRIDYMITE \CRISTOBALITE

TWO 

LIQUIDS

Na20-Si02

\ 70 F 

Na20-2Si02

90 SiO;,

WEIGHT PERCENT 

FIGURE 20. The ternary system NajO-CaO-SiOj. Based on Morey and Bowen (1925) and Segnit (1953).

the primary crystalline phase formed upon devitrification in most commercial glassware is this compound. 

The region of two liquid layers was discovered by 

Greig (1927a), and it is noteworthy that addition of 

less than 2 percent of Na2O suffices to cause the two 

immiscible liquids in the binary system CaO-SiO2 to 

become completely miscible. The compound devitrite 

is an extreme example of incongruent melting and a 

mixture of its composition has a liquidus of 1325°C in 

the field of CaO-SiO2 . The pure compound when

heated decomposes at 1060°C into CaO-SiO2 and a 

liquid containing 15 percent CaO, and its field of primary stability is NRQPO in figure 20. It extends 

down to the ternary eutectic at point 0, where the 

liquidus temperature is 725°C. Liquids of this composition, and in the field of devitrite and the immediately 

adjacent fields of quartz and tridymite, are so viscous 

at their liquidus temperature that it is difficult to crystallize them. This is the region of most commercial 

glassware.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 13. Invariant points in the system Na_O-CaO-SiO2

L33

Invariant 

point on 

fig. 20

P._ _______

Q _________

0..-. ........

N. ..........

h. ...........

R- --------

m_ _______

L _________

#___________

c_ _____

&_--_._______

a..-. _______

C.__. ________

B___-________

A -------

H... ________

£>___-________

(?_____.______

F_____. ______

/--______-___

#____________

Phase reaction

SiO2 (quartz) ^SiO2 (tridymite) ___ _ _____ __________ _

Na2O-3CaO-6SiO2 +SiO2 ^CaO-SiO2 +L __ __ _ ___ _ ____

Na2O.2SiO2 +Na2O.3CaO.6SiO2 +SiO2 ^L___ __________________

Na_0. 2SiO2 + Na2O-3CaO-6SiO2^Na2O.2CaO.3SiO2 + L_ ________

Na2O.3CaO.6SiO2^CaO-SiO2 -|-L- __-_---_---_______-----_-__

Na2O.2CaO.3SiO2 +Na2O.3CaO-6SiO2 ^CaO.SiO2 + L____.___.__

Na2O.2SiO2 + Na2O-2CaO-3SiO2 ^L_ _________________________

Na2O-2SiO2 +2Na2O-CaO-3SiO2 ^Na2O.2CaO-3SiO2 +L_ __ _ ___

Na_O-SiO2 +2Na2O.CaO.3SiO2 +Na2O.2SiO2 ^L________________

Na2O.2CaO-3SiO2 +CaO.SiO2 ^L_ ___________________________

Na2O-2CaO.3SiO2 ^L_ _____________________________________

2Na2O.CaO.3SiO2 ^Na2O-2CaO-3SiO2 +L_____________________

Na_O-SiO2 +2Na2O-CaO-3SiO2 ^L____- ______________________

Na2O.2CaO.3SiO2 +CaO.SiO2 +Na2O.2CaO.2SiO2 ^L.__ ________

3CaO.2SiO2 +CaO.SiO2 +Na2O.2CaO.2SiO2 ^L____ ____________

2CaO-SiO2 +3CaO.2SiO2 +Na2O-2CaO.2SiO2 ^L_ ______________

Na2O-SiO2 +4Na2O.3CaO.5SiO2^2Na2O.CaO.3SiO2 +L__________

NazO^CaO-SSiOz+NasO-CaO-SiOz+NazO^CaO^SiOa^L- _.__

4Na2O.3CaO.5SiO2+ 2Na2O.CaO-3SiO2 ^Na2 0.2CaO-3SiO2 -|- L ___ 

4Na2O-3CaO-5SiO2 ^Na2O.2CaO.3SiO2 +Na2O.CaO.SiO2 +L_____

Na2O.SiO2 +Na2O.CaO.SiO2 ^4Na2O.3CaO.5SiO2 +L------__-_-

Na2O-2CaO-2SiO2 ^L_ _____________________________________

2CaO-SiO2 +Na2O-CaO.SiO2 +Na2O.2CaO.2SiO2 ^L__-_._______

Temperature (°C)

867 

1030 

725 

760 

1060 

1060 

862 

827 

821 

1282 

1284 

1141 

1060 

1255 

1270 

1280 

990 

1260 

1120 

1130 

950 

1450 

1440

Composition of liquid 

(percent by weight)

NazO

18.8 

13.6 

21.9 

25.0 

17.6 

18.8 

32.5 

36.6 

37.5 

16. 1 

17.49 

38.7 

47.6 

12.5 

8.2 

8.8 

45.0 

24.0 

40. 0 

39.8 

48.0 

21.06 

23.0

CaO

7 

12.7 

5.0 

5.0 

15.0 

15. 1 

3.0 

2.0 

1.8 

33.0 

31.65 

11.5 

3 

39.5 

44.5 

44.5 

10.5 

32.0 

16.0 

16.7 

10.5 

39. 11 

37.6

Si02

74.2 

73.7 

73.1 

70.0 

67.4 

66.1 

64.5 

61.4 

60.7 

50.9 

60.86 

50.2 

49.4 

48.0 

47.3 

46.7 

44.5 

44.0 

440 

43.5 

41.5 

40.83 

39.4

The join Na2O SiO2-CaO SiO2 is a binary system 

(fig. 21) in the ternary system in which there are two 

metasilicate compounds. 2Na2O CaO 3SiO2 melts incongruently at 1141°C with formation of

Na2O-2CaO-3SiO2

which melts congruently at 1284r°C. The eutectic 

Na2O SiO2 +2Na2O CaO 3SiO2 =L

is at 1060°C, 3. percent CaO, and the eutectic 

Na2O 2CaO 3SiO2 + CaO SiO2 =L

is at 1282°C, 33 percent CaO.

Na2O-2CaO-3SiO2 has a large field of stability, 

LGFDCRN (fig. 20). It forms a binary system with 

Na2O-2SiO2 , with a eutectic at m, and also with 

Na2O-2CaO-2SiO2 , with a eutectic at d. This compound crystallizes readily throughout its field, but 

when melted it can be quenched to glass.

The course of crystallization of any mixture in the 

ternary diagram can be deduced from figure 20, in 

which the boundary curves are drawn, as well as the 

lines joining the compositions of the various solid 

phases. Consider first a mixture in the area 

Na2O-SiO2-&ZZT. Any composition within this area 

deposits Na2O SiO2 as primary phase, and the residual 

liquid follows a crystallization path lying on the 

straight line joining the liquid composition with

that of Na2O-SiO2 until either the boundary ~bL or 

KL is reached. Here either 2Na2O CaO 3SiO2 or 

Na2O-2SiO2 , respectively, appear, and the liquid follows the boundary curve down to the ternary eutectic, 

where it solidifies completely to a mixture of 

Na2O-SiO2 , 2Na2O-CaO-3SiO2 , and Na2O-2SiO2 , in 

proportions such that the original composition corresponds to the center of gravity of the masses of the 

three solids.

A composition within the area dbLK follows an 

equally simple course, depositing first

2Na2O-CaO-3SiO2 ;

then the liquid composition follows the straight line 

through the point 2Na2O-CaO-3SiO2 and the original 

composition, until it meets a boundary curve. This is 

of Na2O SiO2 , except for mixtures lying in the triangle 

1)LK, where Na 2O-2SiO2 is the second phase to separate. For all these compositions, the mixture solidifies 

completely at the ternary eutectic K.

Crystallization of mixtures lying within the region 

where Na2O-2CaO-3SiO2 is the primary phase is usually a less simple matter. Consider first a composition 

within the triangle

Na^O SiO2-Na2O -2SiO2-2Na2O -CaO -3SiO2

bounded by the curve bL and the straight line joining 

L with Na2O-2CaO-3SiO2 . The primary phase is 

Na2O -2CaO -3SiO2 ; the liquid follows a crystallization
TEMPERATURE, IN DEGREES CENTIGRADE

a 

roO

o 

o o

o

Ul o

o o

8

ro 

o o

ro8

Ol

o o

01 

Ul o

o o
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L35

path passing through the composition of the primary 

phase and of the original mixture, until this path 

cuts the boundary curve bL. At this intersection 

2Na2OCaO3SiO2 crystallizes; the liquid then follows 

the boundary curve, the reaction

Na2O -2CaO -3SiO2 + liquid =2Na2O -CaO -3SiO2

takes place, and the proportion of the former compound 

decreases, while that of the latter increases, until at Z, 

where Na2O2SiO2 appears, the compound

Na2O-2CaO-3SiO2

has been decomposed entirely. The liquid then follows 

the boundary curve, LK, finally solidifying completely 

at the ternary eutectic, A", to a mixture of 

Na2O-SiO2 -Na2O2SiO2 and 2Na2O CaO 3SiO2 . If 

the composition lies within the same triangle, but to the 

right of the join Z-Na2O2CaO3SiO2 , the end 

products will be the same, but the secondary phase 

will be Na2O-2SiO2, on the boundary mZ; at Z, 

reaction takes place resulting in the formation of 

2Na20-CaO-3SiO2 and the disappearance of

Na2O-2CaO3SiO2.

Any mixture in the triangle Na2O-2CaO-3SiO2- 

2Na20-CaO-3SiO2-Na2O-2SiO2 will solidify completely to a mixture of the above phases and 

Na2O-2SiO2 , but the crystallization path will differ 

according to the side of the line Z-Na2O-2CaO-3SiO2 

on which the original composition lies. If the point 

representing the composition of the glass is to the left 

of the above line, the secondary phase is

2Na2O-CaO3SiO2

and the liquid follows the boundary, &Z, until the point 

Z, is reached. Here the reaction

Z+Na2O-2CaO-3SiO2 =

2Na2O CaO 3SiO 2SiO2

takes place until the mixture has solidified completely. 

If the original mixture lies to the right of the line 

Z-Na2O-2CaO-3SiO2 , the same three phases separate, 

and at Z the liquid of composition Z reacts with the 

primary phase to form

Na2O 2SiO2 and 2Na20 GaO 3SiO2 .

Mixtures whose compositions lie within the field of 

Na2O-2CaO3SiO2, also in the triangle Na2O-2SiO2- 

Na2O-2CaO-3SiO2-Na2O-3CaO-6SiO2 have a simple 

crystallization sequence, namely, initial separation of 

Na2O-2CaO-3SiO2 , crystallization of Na2O-2SiO2 on

the boundary mN, and final solidification at N as the 

result of a reaction

Na2O2CaOSiO2 +liquid N=

Na2O 2SiO2 +Na2O 3CaO 6SiO2.

This invariant point is thus a minimum temperature 

for Na2O2CaO-3SiO2 and both boundary curves Nm 

and NR go to higher temperatures. At m there is a 

maximum temperature on the curve, NmL, and 'any 

mixture exactly on the join

Na2O 2SiO2-Na2O 2CaO 3SiO2

will crystallize completely at m to a mixture of these 

two phases; m is the eutectic in the binary system 

Na2O 2SiO2-Na2O 2CaO 3SiO2 .

Mixtures in the above field, but lying between the 

boundaries mN and NRS, and the tie line Na2O -2SiO2- 

Na2O-3CaO-6SiO2 run a less simple course. If the 

composition is to the left of the tie line

#-Na2O2CaO3SiO2 ,

the second phase to separate is again Na2O-2SiO2 ; 

if to the right of this line, Na2O3CaO-6SiO2 ; 

but on either side the primary phase,

Na2O-2CaO3SiO2,

must disappear at the reaction point N, as it is not possible for a mixture having the composition under discussion to solidify completely to a mixture of three phases 

whose composition triangle does not include the original 

mixture. All these mixtures must solidify as conglomerates of quartz, Na2O-2SiO2, and Na2O 3CaO 6SiO2 

and at the reaction point, N, all the Na-sO -2CaO -3Si02 

will be consumed. The liquid will then follow the 

boundary curve NO, until at O quartz appears, and the 

mixture will solidify completely. This is, of course, 

the sequence when equilibrium is attained, in the mixtures under discussion and in all mixtures whose crystallization gives rise to a liquid near the ternary eutectic, O, in composition, the attainment of equilibrium 

is an extremely slow process; one which cannot be carried out satisfactorily under the most favorable conditions except in experiments extending over weeks of 

time.

Glasses in which pseudowollastonite is the primary 

phase may follow several different crystallization paths 

depending on the composition, but all the reactions are 

complicated. Mixtures within the triangle

Na2O 2CaO 3SiO2-Na2 0 3CaO 6SiO2-CaO SiO2

will solidify ultimately as a conglomerate of these three 

phases, but the path followed is not a simple one.
L36 DATA OF GEOCHEMISTRY

Initial crystallization of pseudowollastonite is followed 

by a secondary appearance of Na2O -2CaO -3SiO2 , along 

the boundary curve, CSR, entirely outside of the triangle under consideration. The liquid follows this 

curve until the invariant point, $, is reached, at which 

temperature the pseudowollastonite is inverted to wollastonite. At the still lower temperature invariant 

point R, the reaction CaO SiO2 +liquid R=

Na2O 2CaO 3SiO2 +Na2O 3CaO 6SiO2

takes place, going on until the liquid is entirely consumed. If the initial composition of the mixture is 

within the triangle CaO SiO2-SiO2-Na2O 3CaO 6SiO2 

but in the pseudowollastonite field, the result will be 

similar, except that the second phase to separate is 

tridymite, on the boundary UTQP, and reaction takes 

place at point Q, CaO SiO2 +liquid Q =

Na2O-3CaO-6SiO2,

the same type of reaction as that taking place at 

the invariant point, N, but with the compound 

Na2O 2CaO 3SiO2 replaced by SiO2 . 

All mixtures lying within the triangle

Na2O 2SiO2-Na2O 3CaO 6SiO2-SiO2

will solidify completely as these crystalline compounds 

at the ternary eutectic point, (9, if equilibrium is 

attained. The only effect of change in composition is 

to change the crystallization path by which these phases 

are formed. If the mixture lies within the area to the 

left of the CaO-SiO2-Na2O-3CaO-6SiO2 join, but 

within the wollastonite or pseudowollastonite fields, 

crystallization will result either in intersection of the 

boundary curve NRSC, with consequent separation of 

Na2O-2CaO-3SiO2 , which must later disappear at the 

reaction point N; or the boundary curve, RQ, is intersected by the crystallization path; Na2O 3CaO 6SiO2 

is formed directly, followed by the crystallization of 

Na2O -2SiO2 along the boundary NO, followed by complete solidification at O. If the mixture lies to the right 

of the CaO-SiO2-Na2O-3CaO-6SiO2 join, the initial 

separation of wollastonite will in all cases be followed 

by reaction at the line RQ, with formation of

Na2O-3CaO-6SiO2

and disappearance of CaO-SiO2 . Depending on the 

composition, the next phase to separate will be

Na2O-2SiO2

or tridymite, or quartz ; in all separations the liquid runs 

down to the ternary eutectic at (9, where crystallization 

becomes complete.

Crystallization paths in the various silica fields all 

run down from SiO2 to the boundary between the fields 

of CaO-SiO2 or Na2O-3CaO-SiO2 (UTQPO) or 

Na2O-2SiO2 (FO).

In the former case pseudowollastonite, wollastonite, or 

Na2O-3CaO-6SiO2 is the second phase to separate, the 

liquid traces the path UTQP, solidifying at O to a mixture of Na2O-3CaO-6SiO2, quartz, and Na2O-2SiO2. 

The same final mixture of crystalline phases will result 

if the crystallization paths cuts the boundary FO ; in 

this case Na2O-2SiO2 is the second phase to crystallize, 

and Na2O-3CaO-6SiO2 first appears at the ternary 

eutectic.

In the region richer in Na2O, Segnit (1953) found 

two new compounds. Na2O-2CaO-2SiO2 melts congruently, at about 1450° C, and its field is bounded by 

those of Na2O-CaO-SiO2, 2CaO-SiO2, 3CaO-2SiO2, 

CaO-SiO2, and Na2O-2CaO-3SiO2. The compound

4Na2O-3CaO-5SiO2

melts incongruently and has a small field, IFGH. The 

compound Na2O CaO SiO2 , found by Morey and 

Bowen (1925), occurs in the region studied by Segnit. 

The structure of this compound was worked out by 

Wyckoff and Morey (1926). The compounds 

2Na2O-8CaO-5SiO2 and 2Na2O-4CaO-3SiO2 mentioned by ToropOv and Arakelyan (1950) probably do 

not exist.

Carter and Ibrahim (1952) studied the system 

Na2O-FeO-SiO2 , in part by the use of a "high-temperature microscope" and in part by the quenching 

method. The only ternary compound, Na2O FeO SiO2, 

melts incongruently at 976°C, to FeO (wiistite) and 

liquid, and becomes completely liquid at 985°C. The 

phase-equilibrium diagram is figure 22 and the data 

for the invariant points are given in table 14. Schairer, 

Yoder, and Kean (1954) made a reconnaissance of this 

system and indicated that several compounds might be 

formed. Ostrovskii ( 1956 ) , in addition to

Na-iO-FeO-SiO.,,

found the compound 4Na2O-6FeO-15SiO2 (?) with a 

congruent melting point at 750° to 800° C.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER

FeO

L37

-2FeO-Si00

SiO,

WEIGHT PERCENT Si02

FIGURE 22. The ternary system NaiO-FeO-SiOj. Modified from Carter and Ibrahim (1952). 

Table 14. Invariant points in the system Na_O-FeO-SiO2

Invariant 

point on 

fig. 22

A... .........

B. ...... ... .

C... .........

D-.__ ... ...

E..... .......

F._ ..........

G-. ........

H. ..........

Phase reaction

2FeO-SiO2+Na20- 2SiO2 +SiO2^L______ ______ . ......____

FeO+Na_O.2SiO_+2FeO.Si02^L_. ________ __ ________ .....

FeO+Na2O.FeO.SiO2+Na2O.SiO2 ^L_ _______________________

Na.O-FeO.SiO2 + Na.O.2SiO2^Na2O-SiO.+ L__ _ __ _ _ . _ ._.__..

2FeO.SiO_+Na20.2SiOrt________ _________________________

FeO+Na20.2SiO2^L_ _____________________________________

Na_O.FeO.Si02 +Na_O.SiO2^L______ ________________________

FeO+NajO-FeO-SiO. L______________ _____________________

Temperature (°C)

<500 

667 

703 

724 

675 

±720 

934 

976

Composition of liquid (percent 

by weight)

Na2O

(') 

18.5 

23 

!26. 5 

18 

22 

40. 5 

32

FeO

(')

33.5 

35.5 

1 29.5 

33.5 

36 

19.5 

36.5

Si02

C1) 

46 

41.5 ) 44

48.5 

42 

40 

31.5

1 Only approximately determined.
L38 DATA OF GEOCHEMISTRY

Na2O-Al2O3-SiO2

Portions of the system Na2O-Al2O3-SiO2 were studied by Bowen and Greig (1925), Tilley (1933), Greig 

and Earth (1938), and Spivak (1944). The complete 

diagram was published by Schairer and Bowen (in 

preliminary form, in 1947; in complete form, in 1956). 

The revision of the side Al2O3-SiO2 is by Aramaki and 

Koy (1959). The final diagram is figure 23 and the 

invariant points are given in table 15. In general, the 

quenching method was used in the study of this system. 

The compositions on and near the line albite-silica and

compositions in the fields of mullite or of corundum 

with liquidus temperatures below about 1400° C were 

very viscous and required periods of weeks or months at 

temperatures about 75 C C below the liquidus to grow 

enough tiny crystals for the quenching studies. The 

crystallization of pure albite, Na2O A12O3 6SiO2 , which 

melts congruently at 1118°C, is possible at atmospheric 

pressure only by following in detail the procedure described by Schairer and Bowen (1956), but Boyd and 

England (1961b) found that it crystallizes readily at 

high pressures. Albite glass can be crystallized comAI2 03

-3AI203-2SJ02

NcuO

80

90

10 20

v a 

30 f

2Na20'Si02

40 /50 

Nd20-Si02

v \ jK v A/ v

60 7 70 \ 80

Na 20-2Si02 QUARTZ

90 \ Si02 

CRISTOBALITE

WEIGHT PERCENT

FIGUBE 23. The ternary system NaaO-AhOs-SiOj. Based on Schairer and Bowen (1956) and Aramaki and Koy (1959).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L39

pletely at 1100°C in 8 hr at 25,000 atm; a year would be 

insufficient to crystallize it completely at this temperature at atmospheric pressure. X-ray studies of synthetic 

albites (MacKenzie, 1957) revealed a wide variation in 

lattice parameters of the crystals, depending on the 

conditions of crystallization. The results suggest that 

for each temperature there is a stable crystalline form 

of Na2O-Al2O3 -6SiO2 , which is intermediate between 

high-temperature albite, which is stable only above 

1000°C, and low-temperature albite, which is stable only 

below about 450°C. McConnell and McKie (1960) discussed the kinetics of the ordering process in MacKenzie's experiments and concluded that there is a 

"smeared" polymorphic transformation that is, a 

transformation in which continuity can be associated 

with the stable coexistence of two or more structural 

modifications, in this case high- and low-temperature 

albite over a range of temperatures.

The compound Na2O-Al2O3 -2SiO2 exists in four 

polymorphic forms discussed in detail by Smith and 

Tuttle (1957). The form stable at the melting point, 

high-carnegieite (cubic), is stable down to 1250°C 

where it transforms into a high-nepheline (orthorhombic) form. At a temperature near 900 °C, high-nepheline inverts to low-nepheline (hexagonal) which is 

stable down to room temperatures. The transformation of high-carnegieite into high-nepheline is sluggish 

and high-carnegieite may be obtained by quenching in 

the stability field of nepheline, but at 690°C it undergoes a displacive inversion into low-carnegieite, of lo~w 

symmetry.

The phase equilibrium relations in the ternary system Na2O-Al2O3-SiO2 may be made clearer by discussing some binary systems in the ternary system. 

One of these is the binary system Na2O-SiO2 (sodium 

metasilicate) Na2O-Al2O3 -2SiO2 (nepheline, carnegieite) studied by Tilley (1933) (fig. 24). There is a 

binary eutectic at 902°C (Spivak, 1944) and 46.75 percent Na2O-Al2O3 -2SiO2, at which the solid phases are 

Na2O SiO2 and nepheline, neither of which shows solid 

solution. The inversion temperature of pure

Na2O-Al2 (V2SiO2

from nepheline to carnegieite is at 1248°C (Bowen, 

1912) but carnegieite takes Na2O-SiO2 into solid solution, thus lowering the inversion temperature from 

1248° to 1163°C (curve CE). This is in accordance 

with the general rule (Morey, 1936) that when the 

high-temperature form takes more of the other material into solid solution the inversion temperature is 

lowered. When a mixture of crystalline sodium metasilicate and 85 percent nepheline is heated, at 902 °C 

liquid begins to form and the temperature remains constant until all the Na2O-SiO2 is melted. On further 

heating, the liquid of the mixture of liquid and nepheline increases in content of Na2O A12O3 2SiO2 until at 

1163 °C the liquid has the composition of point B of

TABLE 15. Invariant points in the system Na2O-Al2O3-SiO2

Invariant 

point on 

fig. 23

a

A

B

5

£»

£__________

E

d

c

F

Q

e

H. ..........

j

a

£_-._______

L

Phase reaction

SiO2 (tridymite) ^SiO2 (cristobalite) ______ _______ _____

SiO2 (tridymite) iSiO2 (cristobalite) _________________ ____

SiOo+Na?O-Al O -6SiO _ 1L

SiO2 (quartz) "SiO2 (tridymite) _ _ ___ _ _ _ _________

Na2O-2SiO2 +SiO2 + Na2O.Al2O3 -6SiO2 ^L__.__ _________________

Na2O-Al2O3 .6SiO2 + 3Al2O3 -2SiO2 ^Al2 O3 + L___ _________________

Na2O.Al2O3 -6SiO2 ^L_________________ _____________ _ _____

Na2O-2SiO2 + Na2O- Al2O3 -6SiO2 ^L (Di 62, Ab 38) ._-_____--___

Na2O-Al2O3 -2SiO2 +Na2O-Al2O3 -6SiO2 +Al2O3 ^L_ __ ____ _____

Na2O-2SiO2 + Na2O- Al2O3 -2SiO2 + Na2O-Al2O3 .6SiO3 ^L__ _ _______

Na2O-2SiO2 +Na2O-Al2O3 -2SiO2 "L (Di 71, Ne 29) __

Na2O-Al2O3 -2SiO2 (nepheline) ^Na2O-Al2O3 -2SiO2 (carnegieite) 

+ 3 Al2O3 -2SiO2 _ _______ __ _____________________ ________

Na2O-Al2O3 -2SiO2 (nepheline) ^ Na2O-Al2O3 -2SiO2 (carnegieite) 

+ 3 Al2O3 -2SiO2 _ ______ _ ____ __ ____ __________

Na2O-Al2O3 .2SiO2 (nepheline) ^Na2O-Al2O3 .2SiO2 (carnegieite) ___ 

Na2O-SiO2 +Na2O.Al2O3 .2SiO2 ^L (Na2SiO3 53, Ne 47) _ ______

Na2O-Al2O3 -2SiO2 (nepheline) ^Na2O-Al2O3 -2SiO2 (carnegieite) ___ 

Na2O-Al2O3 -2SiO2 (nepheline) ^±Na2O-Al5,O3 -2Si02 (carnegieite) ___ 

Na2O-Al2O3 -2SiO2 (carnegieite) ^L_ __ _ ______

2Na2O-SiO2ss(?) + Na2O-Al2O3 -2SiO2ss-^Na2O-SiO2 + L __ _

Temperature

1470 

1470 

1050 

1062 

867 

740 

1104 

1118 

767 

1068 

1063 

732 

768 

760

1280

1270 

1248 

900 

1163 

915 

1526 

955

Composition of liquid (percent by 

weight)

Na2O

3.7 

2 

7.8 

8. 1 

15 

21. 5 

11. 2 

11.82 

25.6 

14. 2 

13.8 

26. 0 

30. 5 

32.0

17.5

17.0 

25. 3 

37. 2 

30.8 

37.4 

21.82 

44.0

A12O3

6. 1 

9 

13.5 

13.3 

9 

4. 7 

20. 0 

19.44 

7.4 

23.4 

23.8 

12.5 

10.4 

10. 1

28.8

29. 5 

25.6 

16.9 

24. 8 

18.7 

35.89 

16. 5

SiO2

90. 2 

89 

77.7 

78. 6 

76 

73.8 

68. 8 

68. 73 

67 

62.4 

62.4 

61. 5 

59. 1 

57. 9

53.7

53. 5 

49. 1 

45.9 

44.4 

43.9 

42.29 

39.5

695-382 O - 64 - 4
L40 DATA OF GEOCHEMISTRY

1500

1400

1300

1200

K 1100 

< 1089°

1000

900

800

1526°

LIQUID + / 

CARNEGIEITE /

CARNEGIEITE + 

NEPHELINE

LIQUID + NEPHELINE

LIQUID + No2 0 Si02

No2 0-Si02 + NEPHELINE

1248°

1163°

10 20 30

No20-SiO

40 50 60 70 

WEIGHT PERCENT NdgO AI2 03 '2Si02

FIGURE 24. The binary system NajO-SiO* (sodium metasilicate) Na>O-Al>O3-2SiOj (carnegieite, nepheline). Modified from Tilley (1933).

80 90 

No20-> 

CARNEGIEITE NEPHELINE

figure 24. On further heating, the liquid disappears 

and the composition passes into a region of nepheline 

plus carnegieite containing Na2OSiO2 in solid solution. On crossing the curve CE, all the nepheline disappears, and the mixture passes into a divariant region 

in which carnegieite solid solution is the only phase 

present, and liquid is not formed until the broken curve 

CA is reached. If the original mixture of Na2O-SiO2 

and nepheline had had a gross composition between B 

and <7, at 1163°C all the nepheline would have disappeared, and the phases present would have been a liquid 

of composition on the line BA and a carnegieite solid 

solution on the line CA.

Another binary system is NaaO -AlsArGSiOjj (albite)-silica. This has a eutectic at 1062°C and 31.5 percent SiO2 , and shows the tridymite-cristobalite inversion at 1470°C. All glasses (liquids) in the system 

albite-silica are extremely viscous, and periods of many 

months to a year at temperatures about 75° below

liquidus temperatures melts were required to obtain 

any crystallization in these. The system Na2O-2SiO2 

(sodium disilicate)-Na2O-Al2O3 -6SiO2 (albite) also is 

of the simple eutectic type, with a eutectic at 767°C and 

38 percent albite. The system

Na2O SiO2-Na2O A12O3 6SiO2

is not a binary system because the tie line crosses the 

fields of Na2O-2SiO2 and Na2O-Al2O8 -6SiO2. These 

are incompatible phases.

NasO A12O3 6SiO2 (albite) AljOa (corundum) also 

is a simple system with the binary eutectic at 1108 °C, 

1.5 percent corundum. Preparations in this system 

required many months for equilibrium to be reached. 

Na2O-Al2O3 -2SiO2 (carnegieite) A12O3 also is a 

binary system with a eutectic at 1475 °C, 7 percent 

A12O3 . Owing to the presence of £-Al2O3 in all 

the crystallized glasses of these compositions, it was
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L41

difficult to locate the eutectic temperature precisely. 

The binary system Naj.0 -AljjOs'BSiOjj (camegieite)- 

Na2O-Al2O3 probably shows a complete series of solid 

solutions, but the study was difficult because of loss of 

Na2O by volatilization.

Tilley (1933) also studied the binary system 

Na2O 2SiO2 (sodium disilicate) -Na2O A12O3 2SiO2 

(nepheline, camegieite) (fig. 25). In this case there is 

no solid solution and the nepheline-carnegieite inversion 

is at 1248°C.

The binary system Na2O-Al2O3 -2SiO2 (nepheline, 

camegieite)-Na2OAl2O3 -6SiO2 (albite) was studied 

by Greig and Earth (1938) (fig. 26). Both nepheline 

and camegieite take some albite into solid solution.

The inversion temperature of nepheline is raised to 

1280°C, and there is a narrow strip of coexistence of 

nepheline and camegieite solid solutions. A mixture 

containing about 5 percent albite on heating passes from 

a field of nepheline solid solution to a camegieite solid 

solution, then into a field of camegieite plus liquid; 

a mixture containing 40 percent albite at low temperatures is in the field of nepheline solid solution plus 

albite; at 1068°C the albite melts and the field of nepheline solid solution plus albite is entered, and at 1080 °C 

the nepheline changes to camegieite. The binary eutectic is at 1068 °C and 76 percent albite. Experimentally, however, it was not possible to crystallize tridymite in any of the preparations, and cristobalite crystals 

persisted in the tridymite field.

1500-

1400-

1300-

70

Na20 2Si02 

SODIUM DISILICATE

80 90

CARNEGIEITE NEPHELINE

WEIGHT PERCENT Na 2 0-AI 203-2Si02 

FIGURE 25.-The binary system NajO-2SiOs (sodium disilicate)-Na»O-AljO3-2SiO» (camegieite, nepheline). Modified from Tilley (1933).
L42 DATA OF GEOCHEMISTRY

1524

1500

1400

UJ

o 

if)

UJ 

UJ

CC 

C3

UJ

Q

1300

1254

1200

MOO

LIQUID

CARNEGIEITE + 

NEPHELINE

\

\

LIQUID + 

NEPHELINE

NEPHELINE

\

\

\

NEPHELINE + ALBITE 

j_______I_______u

ALBITE7

1118°

10

Na20'AI203 -2Si02 

CARNEGIEITE, NEPHELINE

20 30 40 50 60

WEIGHT PERCENT ALBITE

70 80 90

Na2 0-AI203 -6SI02 

ALBITE

FIGURE 26. The binary system NazO-AhOs-aSiOa (carnegieite, nepheline)-NajO-Al2O3-6SiO2 (albite). Modified from Qreig and Earth (1938).

The boundaries of the several fields of figures 24 to 26 

need some discussion. The boundary between the fields 

of cristobalite and tridymite is one of constant temperature, 1470°C, because there is no solid solution in either 

silica phase, and the same is true of the boundary between quartz and tridymite. The field of albite is 

bounded by the field of tridymite (BbC], with a maximum at &/ quartz, (CD) ; Na2O-2SiO2 (DdG), with a 

maximum at d, the eutectic in the binary system 

Na2O 2SiO2-Na2O A12O3 6SiO2 ; £-Na2O A12O3 2SiO2 

(GcF), with a maximum at c; A12O3 (FE)\ and 

3Al2O3 -2SiO2 (EB). The field of 3Al2O3 -2SiO2 , mullite, is bounded by the side Al2O3-SiO2 , the fields of 

cristobalite,tridymite (^S),Na2OAl2O3 -6SiO2 (BE], 

and A12O3 . Temperature falls from the A12O3-

3Al2O3 -2SiO2 eutectic (1840°C) to E, where the phase 

reaction is

Na2O A12O3 6SiO2 + 3 A12O3 2SiO2 =L + A12O3 , 

then to B, the eutectic

Na2O A12O3 6SiO2 + 3 A12O3 2SiO2 + SiO2 =Z,

at 1050°C. The field of £-Na2O-Al2O3 -2SiO2 is 

bound by the field of albite (FcG), with a maximum 

at c; Na2O'SiO2 (GeH), with a maximum at ej 

Na 2O-SiO2 (HhK] with a maximum at h; and 

2Na2O-Al,O3 -2SiO2 (Kkgfl), with maxima at k in the 

binary system Xa 2O-SiOL.-Na2O-ALO3 -2SiO2 , at g in 

the binary system Na2O -2SiO2-Na2O A12O3 -2SiO2 , and 

at /, 1280°C. The point /, 1270°C, is the ternary eutectic
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L43

liquid+carnegieite+nepheline+corundum. The fields 

of Na2O-2SiO2 and Na2O-SiO2 have already been 

bounded except for the boundary between Na2O 2SiO2 

and quartz, from the eutectic D to the side Na^O SiO2 ; 

the boundary between the fields of Na2O-SiO2 and 

Na2O 2SiO2 , from the eutectic H to the side; and the 

boundary between the fields of Na2O'SiO2 and 

2Na2O-SiO2 , from L to the side. The field of 

2Na2O-SiO2 has not been outlined, nor that of Na^O, 

because of extreme experimental difficulties. At the 

invariant point Z, the solid phases are Na2O-SiO2 , 

probably free from solid solution, a carnegieite solid 

solution of unknown composition, and a third phase, 

which may be a sodium orthosilicate solid solution of 

unknown composition, but the composition of the two 

solid solutions must be such as to make point L be a reaction point, not a eutectic. Compositions in this highsodium region were extremely hygroscopic; they attacked the platinum crucibles to give deep-orange 

colored melts, and "smoked" at their melting temperatures owing to the volatilization of Na2O.

Pablo-Galan and Foster (1959) studied mixtures 

low in silica, in which the so-called /?-alumina, 

Na2O-llAl2O3 , is the primary phase. They consider 

^-alumina to be a stable compound, with a field of 

stability extending well into the phase-equilibrium 

diagram, at least down to the 1600°C isotherm.

Work at high pressures has extended our knowledge 

of compounds in this system. Boyd and England 

(1956) found that nepheline in the range from 10,000 

to 35,000 atm decomposed into two new and unknown 

phases, one of which had optical properties close to those 

of jadeite and was evidently a pyroxene. Birch and 

LeComte (1960) found that the melting point of albite 

is raised by pressure. Measurements were made up to 

22,000 atm, and the results are represented by the relation, £=1115+0.011 P, in which t is °C and P is the 

pressure in bars. At higher pressures albite is decomposed with formation of jadeite and quartz. This reaction is represented by the relation

P=6000 (±500)+20 (±2) t.

The stability of jadeite had previously been discussed 

by Yoder (1950), Yoder and Weir (1951), Kracek, 

Neuvonen, and Burley (1951), and Adams (1953).

Na2O-Fe2O3-SiO2

Study of the system Na2O-Fe2O3-SiO2 by Bowen and 

Schairer (1929b) and by Bowen, Schairer, and Willems 

(1930) was restricted to the region

Na2O SiO2-Fe2O3-SiO2.

The results are summarized in figure 27 and table 16. 

The iron content of the liquids is given in terms of 

Fe2O3 , but they always contained a small amount of ferrous iron, ranging up to 1.09 percent FeO for a liquid 

in the acmite field containing 16.64 percent Na2 0,48.36 

percent SiO2 . The course of the tridymite-hematite 

boundary makes it improbable that any binary compound exists between Fe2O3 and SiO2 and makes it 

probable that there is almost complete immiscibility between Fe2O3 and SiO2 in the liquid state. The ternary 

compound Na2O Fe2O3 4SiO2 (acmite) melts incongruently at 990°C, with separation of hematite, and the 

liquidus for this composition is at 1275 °C. A second 

compound, 5Na2O-Fe2O3 -8SiO2 , melts congruently at 

838°C. A third compound, 6Na2O -4Fe2O3 5SiO2 , with 

a composition outside of the restricted composition triangle Na2SiO3-SiO2-Fe2O3 melts congruently at 

1091 °C. Indications were obtained of a compound 

2Na2O Fe2O3 SiO2 , but this was not followed further. 

Because of the incongruent melting of acmite, and the 

large area in the composition triangle occupied by the 

hematite field, some unusual courses of crystallization 

were found in mixtures rich in acmite. In some mixtures hematite crystallizes out at an early stage, is completely resorbed by reaction with liquid at intermediate 

stages, and again crystallizes out at a late stage.

K2O-MgO-SiO2

The system K2O-MgO-SiO2 was studied by Koedder 

(195la) with results shown in figure 28 and table 17. 

Four ternary compounds are formed. K2O'MgO-SiO2 

melts congruently at 1650°C to a thin liquid, has a 

large field of stability in the ternary diagram and 

forms binary eutectics with MgO, K2O MgO 3SiO2 , 

K2O-2SiO2 , and K2O-SiO2 . K2O-MgO3SiO2 melts 

congruently at 1134°C, and forms binary eutectics with 

K2O-MgO-SiO2 , K2O-MgO-5SiO2 , K2O-2SiO2 , and 

2MgOSiO2 . K2O-MgO-5SiO2 melts congruently 

at 1089°C but to a viscous liquid. It forms binary 

eutectics with K2O MgO 3SiO2 , 2MgO-SiO2 , SiO2 

and K2O-4SiO2 . The compound K2O-5MgO-12SiO2 

melts incongruently and has a small field of 

stability on the liquidus surfaces. The pure crystals 

begin to melt at 1174°C to form MgO-SiO2 and 

liquid of composition T. Above 1174°C, MgO-SiO2 

goes into solution, but at 1398°C the line

MgO SiO2-K2O 5MgO 12SiO2-r

crosses the boundary between the fields of MgO-SiO2 

and 2MgO SiO2 , and MgO SiO2 decomposes with formation of 2MgO-SiO2 and a liquid on the boundary 

curve. At 1453 °C this reaction is complete, the liquid
L44 DATA OF GEOCHEMISTRY

Fe203

Na2 OSi02

10

WEIGHT PERCENT Si02 

FIGURE 27. The ternaiy system NajO-SiOz-FeaOs-SiOz. Modified from Bowen, Schairer, and Willems (1930).

TABLE 16. Invariant points in the system Na2O-Fe2Oa-SiO2

Invariant 

point on 

fig. 27

A.........

B-. ______

C._.______

a. ... ___

F... ......

b. ........

c ... .

G.. .......

d. ........

H.........

I.. .......

K.........

Phase reaction

SiO2 (quartz) + Na2O-2SiO2 +Na2O.Fe2O3 -4SiO2 ^L_ -__--_-_-___

SiO2 (quartz) ^SiO2 (tridvmite)___ . ___

Na2O.Fe_O3 .4SiO2 + SiO2 (tridymite) -^Fe,O3 + L... ............

Na2O.2SiO2 + Na2O.Fe2O3 -4SiO2^L_._ ._ _ ______ _.

Na2O-2SiO2 + Na2O-Fe2O3 .4SiO2 + 5Na2O-Fe2O3 -8SiO2 ^L ________

Na2O.2SiO2 + 5Na2O-Fe2O3 .8SiO2 ^L__._ ___________________

5Na2O-Fe2Or8SiO2 ^L_ ____________ ___________________

Na2O-SiO2 + 5Na2O.Fe2O3 -8SiO2 -^L _________________

5Na2O.Fe2O3 .8SiO2 +Na2O.Fe2O3 .4SiO2 +Fe2O3 ^L_ ____________

5Na2O-Fe2O3 .8SiO2 + Fe2 O3 -^L___ _

Na.O.SiO2 + Fe2O3 + 5Na2O-Fe2O3 .8SiO2 ^L

Na2O.SiO2 + Fe2O3 ^6Na2O.4Fe2 03 .5SiO2 +L.._ __-.___-__..__..

Na2O-SiO2 + Na2O-2SiO2 + 5Na2O.Fe2O3 .8SiO2 ^L_._ _ ______._._.

Temperature (° C)

760 

867 

955 

810 

800 

818 

838 

837 

809 

816 

815 

845 

816

Composition of liquid 

(percent by weight)

Na2O-SiO2

46. 6 

31. 0 

20. 5 

54.0 

59.8 

65.5 

64.2 

65.3 

50.7 

55. 0 

59.2 

58.6 

70. 1

SiO2

49. 2 

54. 2 

57.8 

35.0 

31. 2 

25.6 

19. 0 

18.4 

20.5 

16. 2 

11.9 

4.4 

23.9

Fe203

4. 2 

14.8 

21.7 

10. 2 

11. 0 

8.9 

16.8 

16.3 

28. 8 

28.8 

28.9 

37.0 

6.0

NaaO

23. 7 

15.7 

10. 4 

27.8 

29.4 

33.3 

32.6 

33. 2 

25.8 

27.9 

30. 1 

29.8 

35.6

SiO2

72. 1 

69. 5 

67.9 

62 

59.6 

57.8 

50. 6 

50.5 

45.4 

43.3 

41. 1 

33. 2 

58.4
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER

MgO

10

L45

2MgO-Si02

2MgO-Si02 

' FORSTERITE

60 MgO-Si02

10 20 30

(T»V «* X g « T^ 1C 

|40/' 50 ^ 60 70 

K20-4Si02

80 90 SiO,

WEIGHT PERCENT 

FIGURE 28. The system K2O-MgO-SiOs. Modified from Roedder (1951a).

composition leaves the boundary curve, and melting is 

complete at 146T°C. A large part of the phase-equilibrium diagram is taken up by the fields of MgO, 

2MgO-SiO2 , and MgO-SiO2 . Mixtures high in K2O,

including K2OSiO2 , K2O MgO SiO2 , and more K20- 

rich mixtures, are practically impossible to work with 

because of hygroscopicity, the difficulty of expelling 

CO2 , and the volatility of K2O.
L46 DATA OF GEOCHEMISTRY 

TABLE 17. Invariant points in the system K2O-MgO-SiO2

Invariant 

point on 

fig. 28

N.-. --------

0. -------

P _________

a

b. ___________

R- ------

U. ..........

X... ........

c... .........

g .......

Z ----. ... .

B --------

T__ ______

h.- ------

i... . --------

F-. --------

k_. ----------

G ---------

I...... ---_.

M.- ......

K.. .........

n---------.-.

p .-------.-..

Phase reaction

SiO2 (tridymite) -^SiO2 (cristobalite) _____________ _ _____ _ _

K2O-5MgO-12SiO2 +SiO2 ^MgO-SiO2 +L_ ________ ___ _ _ ___

K2O-MgO-5SiO2 +K2O.5MgO-12SiO2 +SiO2 ^L_ ______________

K2O-MgO-5SiO2 +SiO2 (tridymite) -"L ... . ________________ ___

K2O.5MgO-12SiO2 ^MgO-SiO2 +L___-__-___-_______-__-

K2O-4SiO2 +K2O.MgO-5SiO2 +SiO2 (tridymite) 1 -kL ___ _____

K2O.5MgO-12SiO2 +2MgO.SiO2 -^MgO-SiO2 +L--___ _ -___ _

K2O-4SiO2 + K2O.MgO-5SiO2^L___ ______ ____________ ______

K2O.MgO-5SiO2^L__- __ __ _ ____________ _ ____ __ __ _

K2O-MgO.5SiO2 +K2O.5MgO-12SiO2 +2MgO-SiO2 ^L_ _________

2MgO.SiO2 +K2O-MgO-5SiO2 ^L_ ____________________ _ ____

K2O.4SiO2 +K2O.2SiO2 +K2O.MgO.5SiO2^L__-_-____-______

K2O.MgO.3SiO2 +K2O-MgO.5SiO2^L___-_--_-___--__-__

2MgO.SiO2 +K2O.MgO.5SiO2 +K2O.MgO.3SiO2 ^L__ __ ___ _

K2O.2SiO2 +K2O.MgO.5SiO2 ^K2O.MgO-3SiO2 +L_-__-___-_

K2O.MgO.3SiO2 ^L_____--____-_-____-- _---_-____

K2O-5MgO-12SiO2 ^MgO-SiO2 +L_ _ ____________________ _

2MgO-SiO2 +K2O-MgO.3SiO2 ^L_ ________________________ ___

K2O.2SiO2 +K2O.MgO-3SiO2^L________--___-----____

K2O.2SiO2 +K2O.MgO.SiO2 +K2O-MgO.3SiO2 ^L______________

K2O-MgO-SiO2 +K2O-MgO.3SiO2 -^L__ ______________ _ ______

K2O.MgO-SiO2 +2MgO.SiO2 +K2O-MgO.3SiO2^L_ ____________

K2O.2SiO2 +K2O.MgO-SiO2 ^L___--_-____--___-_______

K2O.SiO2 +K2O.MgO-SiO2 +K2O.2SiO2^L______-___-___--

2MgO.SiO2+K2O-MgO.SiO2^MgO+L________-____-_____-

K2O-MgO.SiO2 ^L_-_-____-____-_________-_-_--_-_

K2O-SiO2 +K2O-MgO-SiO2-"L_ _____ _ ___t __ _ _____

K20-MgO.Si02 +MgO^L__ ________________________________

Temperature

?C)

1470 

1165 

963 

987 

1174 

715 

1155 

730 

1089 

1042 

1053 

685 

1030 

1013 

795 

1134 

1174 

1131 

933 

905 

1110 

1105 

910 

720 

1350 

1650 

±950 

>1650

Composition of liquid 

(percent by weight)

K20

11.6 

15.1 

15. 5 

13.5 

245 

16.4 

" 26.5 

21.7 

20.2 

20.5 

30.0 

248 

23.9 

31.6 

29.9 

13. 5 

29.5 

38.3 

40. 5 

33.0 

33.0 

448 

542 

36 

18.4 

60. 1

MgO

8.8 

7.2 

6.7 

10.5 

2.0 

11. 5 

2. 4 

9.3 

11.8 

11. 8 

2.5 

10. 7 

12. 0 

4.8 

12.8 

10. 5 

13.5 

5.2 

6.0 

14.0 

15.0 

42 

. 5 

22 

20. 7 

1.7

Si02

79.6 

77.7 

77.8 

76. 0 

73.5 

72. 1 

71.1 

69.0 

68.0 

67.7 

67. 5 

645 

64 1 

63.6 

57.3 

76.0 

57.0 

56.5 

53.5 

53.0 

52.0 

51.0 

45.3 

42 

30.9 

38.2

1 Tridymite is metastable.

K2O-CaO-Al2O3

The system K2O-CaO-Al2O3 was studied by Brownmiller (1935) with special reference to the effect of small 

amounts of K2O on portland cement. No ternary compound was found in the region investigated, and the 

field of K2O-A12O3 is adjacent to those of CaO, 

3CaO A12O3,5CaO 3A12O3, and CaO A12O3. The compound 5CaO -3A12O3 takes as much as 2 percent of K2O 

into solid solution. The phase-equilibrium diagram is 

shown in figure 29, and the invariant points are given in 

table 18.

K2O-CaO-SiO2

The system K2O-CaO-SiO2, shown in figure 30 and 

table 19, was worked out by Morey, Kracek, and Bowen 

(1930). There are five ternary compounds, the most 

siliceous of which is K2O2CaO9SiO2 . This compound is very difficult to crystallize in the dry way, 

and its fusion relations were worked out with the aid 

of hydrothermal crystallization. Its field, EFGrHIbCa, 

is far removed from its composition. The pure compound melts incongruently at 1052 °C with formation of 

a-K2O-3CaO6SiO2 , and a liquid of composition K2O 

12.6 percent, CaO 15.0 percent, SiO2 72.4 percent. On 

further heating, the K2O-3CaO-6SiO2 decomposes into 

CaO-SiO2 (wollastonite) and the liquid composition 

is K2O 13.2 percent, CaO 11.8 percent, SiO2 75.0 percent. The composition K2O-2CaO-9SiO2 melts completely at 1198°C. A second compound,

K2O-3CaO-6SiO2 ,

the K2O analog of devitrite (Na2O3 -3CaO-6SiO2 ), 

also melts incongruently, and exists in a high temperature, or fi-form, and a low temperature, or a-form, with

TABLE 18. Invariant points in the system K2O CaO A12O3

Invariant 

point on 

fig. 29

A.... ________

B _________

C_ -_ __-

Phase reaction

3CaO-Al2O3+K2O-Al2O3-^CaO+L___ ___ _ ___ _ ___ _____

3CaO.Al2O3+K2O.Al2O3+5CaO.3Al2O3-\L_ __ _ _ ___ _ __

5CaO.3Al2O3+ CaO- A12O3+ K2O- A12O3-"L_ 

Temperature (°C)

1475 

1425 

1430

Composition of liquid (percent 

by weight)

K2O

6.5 

4.8 

5.0

CaO

48.8 

48.0 

39.0

A12O3

447 

47.2 

56.0
K 2 0

PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

CaO

L47

To CaO

;3CaO-AI 203

CaO- 3AI203

90

WEIGHT PERCENT AI 203

FIGURE 29. The system KjO-CaO-AljCh. Modified ftom Brownmiller (1935).

AI203
L48 DATA OF GEOCHEMISTRY

70 I " 80 

"K20-4Si02

WEIGHT PERCENT Si02

F'IGUBE 30. The system KjO-CaO-SiO2. Modifled'from Morey, Kracek, and Bowen (1930,1931).

an inversion temperature of approximately 1000°C. 

The a-form melts incongmently at 1120°C with formation of CaO-SiO2 (wollastonite) and a liquid of composition, K2O 14.5 percent, CaO 16.5 percent, SiO2 69.0 

percent. There are two disilicate compounds:

4K2O-CaOlOSiO2 , 

which melts congruently at 946°C, and 

2K2O-CaO-6SiO2 ,

which melts congruently at 959°C. These disilicate 

compounds have no analogs in the Na2O system. There 

is also one ternary metasilicate compound,

2K2OCaO3SiO2,

which melts incongmently with formation of the orthosilicate, K2OCaOSiO2. The probably congruent 

melting point of this compound is approximately 

1630°C, but accurate work with mixtures high in K2C
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 19. Invariant points in the system K2O-CaO-SiO2

L49

Invariant 

point on 

fig. 30

B -------

C ------

E ---------

F -------

G ------

H -------

I............

&_____ .......

M- .........

N-. ---------

0 -------

P ------

R -------

S... .........

T .........

Phase reaction

<^K2O.3CaO.6SiO2 +SiO2 ^3-CaO-SiO2 +L____ __ ______

K2O.2CaO.9SiO2 ^K2O.3CaO.6SiO2 +Si02 +L_ ________________

SiO2 (o-quartz) k SiO2 (tridymite) ______ ___ ___ . _____ _ _

K2O-2CaO.9SiO2 +K2O-4SiO2 +SiO2 ^L __._____._______-.__..

K2O-2SiO2 +K2O.2CaO.9SiO2 +K2O.4SiO2^L_ ____ ___ .

K2O.2SiO2 +K2O.2CaO.9SiO2 ^4K2O.CaO-10SiO2 +L_. _________

4K2O-CaO.10SiO2 +K2O.2CaO.9SiO2 ^±2K2O.CaO-6SiO2 +L_.____

2K2O.CaO.6SiO2 +K2O.2CaO.9SiO2 -^/3-K2O-3CaO.6SiO2 +L..._.

j8-K2O-3CaO.6SiO2-"«-K2O-3CaO-6SiO2 __ _____ __ _ __ . __

2K2O-CaO.6SiO2 L_ __..._. ....___--_______-________-_____

4K2O.CaO.10SiO2^L_ _-___-___---__-___--_-_-_____-_-.____

i8-K2O-3CaO-6SiO2 -"a-K2O.3CaO-SiO2 _____ _ _ _ __ _ _ _ _ _ _ _ _

2K2O-CaO.6SiO2 +/3-CaO-SiO2^|8-K2O.3CaO-6Si02 +L ___ _ _

2K2O.CaO-3SiO2 + 4K2O-CaO- 10SiO2 + 2K2O-CaO.6SiO2 ^L_ _____

2K2O-CaO-3SiO2 +2K2O-CaO-6SiO2 +|8-CaO.SiO2 ^L___ ________

2K2O-CaO-3SiO2 + 0-CaO-SiO2 -"K2O-CaO-SiO2 + L ______ _ _

K2O.CaO-SiO2 +/3-CaO.SiO2 ^2CaO-SiO2 +L_ _________________

2K2O.CaO.3SiO2 +K2O.2SiO2 +4K2O-CaO.10SiO2 ^L___________

K2O.SiO2 +2K2O.CaO.3SiO2+K2O-2SiO2 ^L_____ ______________

K2O-CaO-SiO2 +K20.23CaO.12SiO2 +L_ _______ __ _____ ._

K2O.CaO-SiO2 -^L_ ________________________________________

Temperature (°C)

1080 

1050 

867 

720 

720 

740 

825 

910 

1000 

959 

946 

1000 

930 

890 

800 

830 

1180 

895 

770 

1598 

1630

Composition of liquid (percent by 

\\eight

K2O

13.3 

13.8 

20. 1 

25. J 

30. 8 

31.6 

28.8 

26.6 

23.6 

31.1 

36.5 

31. 1 

32.3 

37.2 

34.2 

34. 1 

22.5 

40.5 

54.7 

41.2 

44.8

CaO

10.8 

10.5 

5.2 

1.9 

.9 

2.3 

5.3 

7.8 

11.0 

9.3 

5.4 

13.4 

11.3 

10.2 

13.0 

13.7 

31.0 

7.7 

.2 

29.7 

26.7

Si02

75.9 

75.7 

74.7 

73.0 

68.3 

66. 1 

65.9 

65.6 

65.4 

59. 6 

58.1 

56.5 

56.4 

52.6 

52.8 

52.2 

46. 5 

51.8 

45. 1 

29. 1 

28.5

is difficult because of their hygroscopicity and the volatilization of K2O. The K2O glasses are more viscous 

than the corresponding Na2O glasses, and mixtures 

high in SiO2 are more difficult to crystallize.

Taylor (1941) studied mixtures along the join 

K2O-CaO-SiO2 and 2CaOSiO2 , and found the compound K2O 23CaO 12SiO2 , not shown on figure 30, 

which has a eutectic with K2OCaOSiO2 at 1598°C.

K2O-FeO-SiO2

Eoedder (1952) made a reconnaissance of liquidus 

relations in the partial system K2O2SiO2-FeO-SiO2 , 

with results shown in figure 31. The experiments were 

made in a nitrogen atmosphere, and iron foil was 

used for wrapping the quenching charges. Two new 

ternary compounds were formed: K2O FeO 3SiO2 , 

which melts congruently at about 900°±10°C, and 

K2O FeO 5SiO2 , which also melts congruently at about 

900°±10°C. A small region of liquid immiscibility 

may exist, possibly caused by the presence of some

K2O-Al2O;r-SiO2

The system K2O-Al2O3-SiO2 was studied by Schairer 

and Bowen (1955) and their results are given in figure 

32 and table 20. The ternary diagram has been modified in harmony with the congruent melting of mullite (Aramaki and Roy, 1959). The compound 

K2O A12O3 6SiO2 , corresponding to the pure potassium 

feldspar, which occurs as adularia, orthoclase, sanidine, 

or microcline, melts incongruently at 1150 °C (Morey

and Bowen, 1922) with formation of K2O A12O3 -4SiO2 

(leucite) and a more siliceous melt (point e, fig. 32). 

Mixtures on the line leucite-SiO2 , with liquidus temperatures below 1250°C, are practically impossible to crystallize by themselves, and are so viscous that even at 

temperatures near the liquidus the powdered glasses fail 

to flow together and barely frit in periods of several 

days or weeks; the isotherms crossing this line are extrapolated from mixtures nearer the side K2O-SiO2. 

The compound K2OAl2O3 -2SiO2 melts congruently 

probably near or above 1750 °C; the point, however, has 

not been determined accurately.

Five polymorphs of K2OAl2O3 -2SiO2 exist (Smith 

and Tuttle, 1957). Below 850°C, kalsilite (hexagonal) 

is the stable phase. Near 1000°C, synthetic kaliophilite 

(hexagonal) has been obtained but the remainder of the 

laboratory syntheses from 900° C to the liquidus have 

yielded orthorhombic K2OA] 2O3 -2SiO2. The synthetic kaliophilite is not identical with natural kaliophilite (hexagonal) but there is a remarkable similarity between their X-ray powder patterns. A second 

form of natural kaliophilite anomalous natural kaliophilite is also known.

Bowen (1917) found an enantiotropic inversion 

from a hexagonal to an orthorhombic form at about 

1540°C, and Tuttle and Smith (1953), in a preliminary 

report, found that hexagonal kalsilite is stable at atmospheric pressure up to 840°C, when an orthorhombic 

form appears. The compound K2O A12O3 SiO2 probably exists with a melting point well above 1700°C. 

The reactions along the boundary curves URSP offer
L50 DATA OF GEOCHEMISTRY

FeO

(Total iron oxides as FeO)

2FeO-SI02

K20-FeO-3Si02 

\

K20-4Si02 TRIDYMITE 

WEIGHT PERCENT Si02

FIGURE 31. The system KjO-FeO-SiOj. Modified from Roedder (1952). Isotherms are in degrees centigrade.

Si02

no special difficulties except those resulting from the 

hygroscopicity of the mixtures and the loss of K2O by 

volatilization.

Faust (1936) studied crystallization along the join 

K2O GSiO-j-FegOa which is not a binary system but an

arbitrary line through the ternary systems. A mixture 

of the composition K2O, 6SiO2 (79.3 percent SiO2 ) has 

a liquidus of 1133°C, and tridymite is the primary 

phase (Kracek, Bo wen, and Morey, 1929). On addition 

of Fe2O3 , the melting point is lowered and the mixture 

crosses the tridymite field until the boundary of the
PHASE-EQUILIBRIUM RELATIONS, ROCK -FORMING OXIDES EXCEPT WATER L51

CORUNDUM

20

 2Si02 

MULLITE

K20 AI2 03

70

90 CRISTOBALITE

r40 

K20-Si02

50 / 60 

K20- 2Si02

70 \ 80 

K20-4Si02

90

WEIGHT PERCENT Si02 

FIGURE 32. The system KjO-AljOs-SiOj. Modified from Sehairer and Bowen (1955).

K2O FesOa 6SiO2 field is reached at 13.5 percent Fe2O3 

and 725°C. These mixtures could only be crystallized 

hydrothermally and metastable tridymite appeared in 

the quartz field. The next field is that of the analog of 

orthoclase, K2O Fe2O3 6SiO2, which is difficult to crystallize and probably melts incongruently at 21 percent 

Fe2O3 and 921 °C with formation of an iron analogue of

leucite, K2O-FeO-4SiO2 , the composition of which is 

not on this join. It is the primary phase from 21 to 

24.75 percent Fe-jOa and 1050°C, where Fe2O3 (hematite), appears. The curve was not studied beyond 

1265 °C because of the increasing rate of dissociation of 

Fe2O3 . Faust and Peck (1938) measured the index of 

refraction of some glasses in this system.
L52 DATA OF GEOCHEMISTRY

TABLE 20. Invariant points in the system K2O-Al2O3-SiO2

Invariant 

point on 

fig. 32

b. ...........

M... ________

d__ __________

P............

N. __________

6

/______._____

A__--_______

S_-_-____._-_

#__._________

g __ ____ _

&____________

U. ..........

fc__i_-.____-_

#___________

Z

Phase reaction

SiO2 (tridymite)-J-SiO2 (cristobalite)-___ __ _ ____ __ _ __

K2O-Al2O3 -6SiO2 +SiO2 +3Al2O3 .2SiO2<^L- -__-----, _ ________

K2O.Al2O3 .6SiO2 +SiO2 ?±L_-_______________________-_-__-___

K2O.4SiO2 +SiO2 +K2O.Al2O3 -6SiO2 -^L________-__________.___

K2O.Al2O3 -6SiO2 +3Al 2O3 .2SiO2 ^K2O-Al2O3 .4SiO2 +L___ ________

K2O.Al2O3.6SiO2 ^K2O.Al2O3 -4SiO2 +L____________ _ _________

K2O.4SiO2 +K2O-Al2O3 .6SiO2 ^L_ ____________________________

K2O-Al2O3 .4SiO2 +3Al2O3 .2SiO2 ^Al2O3 +L_ _______-__--------_

K2O.2SiO2 +K2O.4SiO2 +K2O.Al2O3 .6SiO2 ^L_. ________________

K2O-2SiO2 + K2O.Al2O3 .6SiO2 ^K2O.Al2O3 .4SiO2 + L _ _________

K2O.2SiO2 +K2O.Al2O3 .4SiO2-^L________________-___________-

K2O-Al2O3 .4SiO2 -^L__ _ _ _ ____ _ _ _ _ ___ ____ _

K2O.Al2O3 -4SiO2 +Al2O3 ^L _ ______________________________

K2O-2SiO2 +K2O-Al2O3 -4SiO2 +K2O-Al2O3 -2SiO2 -^L_ _ _ _______

K2O.2SiO2 +K2O.Al2O3 .2SiO2 ^L_____________________________

K2O-A12O3 -4S1O2 (hexagonal) -^K2O-Al2O3 -4SiO2 (orthorhombic) _ _

K2O.Al2O3 -2SiO2 +K2O-Al2O3 -4SiO2 -^L_________ _ ____________

K2O- Al2O3 -2SiO2 + K2O- Al2O3 -4SiO2 + A12O3 -^L_ ________________

K2O-Al2O3 -4SiO2 (hexagonal) -^K2O-Al2O3 -4SiO2 (orthorhombic) __

K2O-Al2O3 -2SiO2 +Al2O3 -^L__ _______ __________ _ _ _ _______

Temperature (°C)

1470 

1470 

985 

990 

867 

710 

1140 

1150 

725 

1315 

695 

810 

918 

1686 

1588 

905 

923 

1540 

1615 

1553 

1540 

1680

Composition of liquid (percent 

by weight)

K2O

4.3 

2.4 

9. 5 

9.8 

17.0 

22.8 

12.2 

12.5 

26. 1 

13.9 

30.4 

32. 1 

36.9 

21.59 

19.9 

39.3 

40.6 

28.5 

24.8 

22. 1 

35.6 

27.4

A12 03

4.7 

7.3 

10.9 

10.7 

6.8 

3.7 

13.7 

13.5 

3.3 

18.5 

3.2 

5.3 

7.4 

23.36 

29.3 

7.8 

7.7 

22.0 

27.0 

31.3 

19.0 

37.7

SiO2

91 

90.3 

79.6 

79.5 

76.2 

73.5 

74.1 

74. 0 

70.6 

67. 6 

66.4 

62.6 

55.7 

55.05 

50.8 

52.9 

51.7 

49.5 

48.2 

46.6 

45.4 

34.9

MgO-CaO-Al2O3

Eankin and Merwin (1916) found that no ternary 

compounds were formed in the system

MgO-CaO-Al2O3 ,

and the fields are those of the components and the four

calcium aluminates. The invariant points, all near the 

side of CaO-Al2O3, are given in table 21. The melting 

surfaces for MgO, MgOAl2O3 , and CaO rise steeply 

from the invariant points, but the glasses could be obtained by quenching in the low-temperature region. 

The system CaO-Al2O3 has been revised since the publication of this work.

TABLE 21. Invariant points in the system MgO-CaO-Al2O3

Phase reaction

MgO+3CaO-Al2O3 ^CaO+L__ ____________________________________________

MgO + 5CaO.3Al2O3^L___________________________________________________

MgO+CaO.Al2O3 +5CaO-3Al2O3 ^L________________________________________

MgO+CaO.Al2O3 ^MgO.Al2O3 +L_ ________________________________________

MgO-Al2O3 +CaO-Al2O3 ;=±CaO-2Al2O3 +L ______ _ _ ____ _ __ __ ____ _

Temperature (°C)

1450 ±5 

1345 ±5 

1345 ±5 

1370±5 

1550 ±5

Composition (percent by weight)

MgO

6.2 

6.3 

6.7 

6.9 

3.5

CaO

51.5 

46.0 

41.5 

40.7 

33.3

A1203

43.3

47.7 

51.8 

52.4 

63.2

MgO-CaO-Fe2O3

The system MgO-CaO-Fe2O3 was studied by Hay 

and White (1940) and by Eait (1949). There is no 

evidence of a ternary compound, and the phase 

diagram is divided into sections by the joins 

MgO-2CaO-Fe2O3 , MgO Fe2O3-2CaO Fe2O3 , and 

MgOFe2O3-CaOFe2O3 . The effect of the partial 

pressure of oxygen was not considered.

MgO-CaO-SiO2

The system MgO-CaO-SiO2 has been studied by 

Alien and White (1909), who worked on the relation

of diopside to magnesium and calcium metasilicate; by 

Bo wen (1914), who worked on the partial system diopside-forsterite-silica; and by Ferguson and Merwin 

(1919b), who completed the system. Eevisions of the 

phase-equilibrium diagram were made by Bowen, 

Schairer, and Posnjak (1933b), Schairer and Bowen 

(1942), Osborn (1942, 1943), and Eicker and Osborn 

(1954). The revised diagram is figure 33, modified 

from Eicker and Osborn, and the invariant points are 

in table 22.

There are four ternary compounds in this system. 

CaO-MgO-2SiO2, the mineral diopside, melts congru-
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L53

CaO

aO'Si02

-2CaO-Si02

3CaO-2Si02

CaO-Si02

/3-CaOSi02

MgO 10 2MgO-Si02 MgO-Si02

WEIGHT PERCENT Si02 

FIGURE 33. The system MgO-CaO-SiOj. Modified from Ricker and Osborn (1954).

80 90 Si02

ently at 1391.5 °C and does not take any of its components into solid solution. Yoder (1952a) found that 

the increase in melting point with pressure can be represented by the expression

£OT =1391.5+ 0.01297 P

when tm is the melting temperature in °C, and P is the 

pressure in bars. Boyd and England (1958) extended 

the melting-point curve to 32,000 bars and 1740°C. 

The slope of the melting curve decreases with pressure; 

in the range 20,000 to 30,000 bars the average slope is 

10.3°C per 1,000 bars.

Wollastonite (0-CaO-SiO2 ) takes into solid solution 

as much as 21 percent diopside, but little or no diopside 

enters into solid solutions in a-CaG-SiO* (pseudowollastonite). The inversion temperature of wollastonite 

is raised by this solid solution from 1125 to 1368°C, so 

that it has a field on the liquidus surface of the ternary 

system.

The phase-equilibrium diagrams of the binary system 

CaO SiO2-CaO MgO 2SiO2 is figure 34. The inversion temperatures of /?-CaO-SiO2 (wollastonite) to 

a-CaO-SiO2 (pseudowollastonite) is raised by solid 

solution of diopside from 1125°C (point E) to 1368°C
L54 DATA OF GEOCHEMISTRY

1600

/3-CaO-Si02 ss +CaO-MgO'Si02

1100

1000

/ 

CaO-Si02 10 20 30 40 50 60 70 80 90 CaO-MgO-SK>2

WEIGHT PERCENT 

FIGURE 34. The binary system CaO-SiO2 (wollastonite)-CaO-MgO-2SiO2 (diopside). Modified from Ricker and Osborn (1954).

TABLE 22. Invariant points in the system MgO-CaO-Si02

Invariant 

point on fig. 33

a _____ ____

A.... ________

b. ...........

c _ _ __ ____

B.... ........

C____________

D...... ......

E... _________

F _________

/___-________

K. __________

L... .........

M. __________

Phase reaction

/3-CaO.SiO2ss + SiO2 ^a-CaO-SiO2 +L _ ____________ _ ______

/3-CaO.SiO2ss+SiO2 + CaO.MgO.2SiO2 ~^L..... _________ _______

CaO.MgO.2SiO2 -^L________________________________________

/3-CaO-SiO2ss + CaO.MgO.2SiO2 -\L____ _____-___-__-_ ____ __

/3-CaO-SiO2 ss-^a-CaO-SiO,+ !/_____ _____ ________________ _

/3-CaO-SiO.ss + CaO-MgO-2SiO2 + 2CaO-MgO-2SiO2 ^L__- _ _ _

a-CaO-Si02 +2CaO.MgO-2SiO2 -^/3-CaO-SiO2s.« + L_ ____________

2CaO-MgO.2Si02 + CaO.MgO-2SiO2 + 2MgO-SiO2 -^L___ _ _______

2CaO.MgO.2SiO2 +2MgO.SiO2 ^CaO.MgO.SiO2 +L-_______--_-

2CaO.MgO.2SiO2^L. __________________ __________________

2CaO.MgO.2SiO2 +CaO.MgO.SiO2 ^3CaO.MgO.2SiO2 + L-_-.__

CaO.MgO.SiO2 +2MgO.SiO2 ^MgO+L_ ---_____----__--_-- 1-

3CaO.MgO-32SiO2 +CaO.MgO.SiO2 ^MgO + L_._ _____________

3CaO.MgO.2SiO2 -^MgO+2CaO.SiO2 +L_ _____--___-_--------

2CaO.SiO2 + 2CaO.MgO-2SiO2 --3CaO.MgO.2SiO2 + L--_ ________

Temperatiire (°C)

1336 

1320 

1391. 5 

1358 

1368 

1350 

1360 

1357 

1430 

1454 

1436 

1502 

1490 

1575 

1400

Composition of liquid 

(percent by weight)

MgO

7.2 

8.0 

18. 62 

11. 5 

10. 8 

12.6 

12.3 

20. 2 

22.3 

14.79 

18.3 

26.4 

22.3 

18. 2 

6.8

CaO

31. 3 

30. 6 

25.9 

34.4 

35.3 

36 

36.7 

29.8 

33.3 

41. 14 

39 

32. 1 

37.3 

43. 0 

49; 5

SiO2

61.5 

61.4 

55.48 

54. 1 

53.9 

51.4 

51 

50 

44.4 

44. 07 

42.7 

41.5 

40.3 

38. 8 

43.7
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L55

at F, where the diopside content of the wollastonite is 

21 percent. The point B ( 1368°C, 58 percent diopside) 

is a binary reaction point at which liquid B is in equilibrium with a-CaO-SiO2 and 0-CaOSiO2 solid solutions. The solubility of diopside in pseudowollastonite, 

if any, is less than 5 percent. Liquids along the line 

BC are in equilibrium with wollastonite solid solutions 

along the line FG. The eutectic is at 1358°C and 62 

percent diopside, and the solid phases are a wollastonite 

solid solution G containing 22 percent diopside and 

pure diopside.

When a mixture containing 10 percent diopside, 

originally in the region 0-CaOSiO2 solid solution + 

diopside, in being heated meets the curve HG, the diopside goes into solid solution and a divariant region of 

wollastonite solid solution is entered. When the curve 

EF is met, some a-CaOSiO2 separates, and further 

heating the mixture causes a region of a-CaO SiO2 and 

0-CaOSiO2 solid solutions until the line IFB is 

reached, when the £-CaO SiO2 solid solutions disappear 

and liquid B is formed. There is no eutectic melting. 

If the original composition contained more diof side 

than point G, say 30 percent, the wollastonite solid solution would on heating increase in diopside content until 

1358°C when eutectic melting would begin, with formation of liquid G in equilibrium with crystals G. Temperature would remain constant at 1358°C until diopside was melted. When the field of solid solution and 

liquid would be entered, the solid solutions would 

change composition along the line GF, the liquid along 

the line BC.

The compound 2CaOMgO-2SiO2, which corresponds to the mineral akennanite, melts congruently at 

1454°C, and forms a binary eutectic with pseudowollastonite at 1402°C. There probably is no solid solution 

in this binary system. The compound

3CaOMgO-2SiO2

is the mineral merwinite and was first identified by Larsen and Foshag (1921). Later Phemister, Nurse, and 

Bannister (1942) identified it as a frequent constituent 

of blast-furnace slags. Its field in the ternary system 

was determined by Osborn (1943), who found it to melt 

incongruently at 1575°C with formation of liquid, 

2CaOSiO2, and MgO. The composition of the compound CaOMgO-SiO2 , corresponding to the mineral 

monticellite, lies within the field of MgO (periclase). 

Attempts to prepare the pure compound did not succeed: a glass of that composition crystallized to 

2CaO SiO2 and monticellite solid solution. The phaseequilibrium diagram of figure 33 shows a field of the 

binary compound 3CaO SiO2. This compound decomposes before its melting point in the binary system

CaO-SiO2 but Ricker and Osborn (1954) found that 

the liquidus surface in the ternary systems has a region 

of temperature low enough for 3CaO-SiO2 to be stable.

MgO-CaO-TiO2

Solid-state reactions in the system MgO-CaO-TiO2 

were studied by Coughanour, Roth, Marzullo, and Sennett (1955) by heating mixtures usually below the liquidus surface, but a mixture of molecular ratio 

MgO: CaO: TiO2 of 4:1:9 had melted at 1500°C, of 

3:2: 6 at 1550°C, of 4:1:4 at 1590°C, and of 4:1:2 at 

1672°C. No ternary compounds were found, and little 

or no solid solution, with the probable exception of the 

areas adj acent to 3CaO 2TiO2. The samples were studied by X-ray diffraction and by petrographic methods.

MgO-FeO-SiO2

The system MgO-FeO-SiO2 was studied by Bowen 

and Schairer (1935) by heating the mixtures in iron 

crucibles in a stream of nitrogen, and the equilibrium 

melts were analyzed for ferrous and ferric iron. The 

ferric iron increased in amount from almost zero with 

low FeO content to a maximum of more than 2 percent 

near the composition of Pe^SiO*. The phase-equlibrium 

diagram of the system, shown in figure 35, is dominated 

by several fields, one of which, BCED^ is the area of 

two liquid layers. There is a field of pyroxene solid 

solutions containing MgO-SiO2 and FeO-SiO2 . This 

metasilicate line, shown in figure 35, is complicated and 

only in part binary, owing first to the incongruent melting of MgO-SiO2, so that the first phase to separate 

along this line is an orthosilicate, 2MgO*SiO2 , and, 

second, to the field of tridymite spreading over the 

other end of the metasilicate line. The .pyroxenes are 

monoclinic at the liquidus, but are orthorhombic at 

lower temperatures, and the inversion temperature 

ranges from 1140°C at the MgO -SiO2 end of the series, 

to approximately 995°C at the extreme iron-rich member. There is a field occupied by the olivines, a complete 

series of solid solutions between 2MgO-SiO2 and 

2FeO SiO2 , and a large field occupied by the magnesiowiistites, a complete series of solid solutions between 

MgO and FeO. The invariant points are listed in 

table 23.

MgO-Al2O3-SiO2

The original study of the system MgO-Al2O3-SiO2 

was by Rankin and Merwin (1918). They found only 

one ternary compound, 2MgO 2A12O3 5SiO2, corresponding to the mineral cordierite, which melts incongruently at 1460 °C with formation of mullite and liquid. 

When a glass of the composition of cordierite is quickly 

cooled, it forms the mineral indialite (Miyashiro and

695-382 O - 64 - 5
L56 DATA OF GEOCHEMISTRY

FeO

10

20

30 FeO-Si02

40

:eO-Si02

50

70

80

MgO 10 20 30 3 40 \ 

2MgO S

50 

02

1

MgO- SiOa

70

1

80 90 Si02

WEIGHT PERCENT Si02 

FIGURE 35. The system MgO-FeO-SiO2. Modified from Bowen and Schairer (1935).

TABLE 23. Invariant points in the system MgO-FeO-SiO2

Invariant 

Point on 

fig. 35

G__. _________

L______._____

Phase reactions

SiO2 + olivine (Mg2SiO4 32, Fe2SiO4 68) + clinopyroxene (MgSiO3 

38, FeSiO3 62) ^L.

Temperature (°C)

1470 

1305

Composition of liquid (percent 

by weight)

MgO

23.5 

9

FeO

20 

46

SiO2

56. 5

45
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L57

liyama, 1954). Schreyer and Schairer (1959) found 

that there is no solid solution of MgO, A12O3 , or SiO2 

in cordierite, although indialite formed from a glass 

containing excess SiO2 at low temperatures may contain 

excess SiO2 in metastable solid solution. Yoder (1952) 

also believed that solid solution in cordierite is doubtful. 

Cordierite exists in three polymorphic forms, a high 

temperature or o-f orm, obtained by crystallization above 

about 950°C, a stable low temperature or /?-form, obtained by hydrothermal crystallization, and an unstable 

ju,-form, obtained by crystallizing the glass at about 

850°C (Yoder, 1952c; Karkhanavala and Hummel, 

1953). Foster (1950) deduced that a compound 

4MgO-5Al2O3 -2SiO2 corresponding in properties with 

the mineral sapphirine, should have a field of stability 

in the ternary system, and Keith and Schairer (1952) 

found such a field, which is shown in their phase-equilibrium diagram (figure 36). The small sapphirine 

field is the area NWX; the reaction points are included 

in table 24. Aramaki and Eoy (1959) revised the side 

Al2O3-SiO2 .

Pyrope, the garnet of the composition

3MgO-Al2O3 -3SiO2

is also in this system. It is not stable at the liquidus, 

but on heating decomposes to a mixture of 2MgO SiO2 , 

MgO A12O3 , and 2MgO 2A12O3 5SiO2. It is, however, 

stable at increased pressures, and Boyd and England 

(1959) gave a preliminary diagram of the stability field 

of pyrope (fig. 37).

At pressures above 23,000 atm and temperatures 

above 1200°C, pyrope forms rapidly from glass or from 

mixtures of anhydrous crystalline phases of its composition. Below 1100°C reactions involving pyrope become sluggish, and curve A of figure 37 has not been 

extended to lower temperatures. The reactions were 

accelerated by the presence of H2O. The phases stable 

for the pyrope composition below curve A are not the 

same as those stable at atmosphere pressure cordierite+forsterite+spinel. At the pressures indicated for 

the run below A, cordierite is unstable, and the stable 

assemblage for the pyrope composition is aluminous 

enstatite+sapphirine, and possibly sillimanite, but it 

is possible that the sillimanite may enter into solid solution in the sapphirine. The melting of pyrope must be 

incongruent at the lower temperature end of curve B. 

Curve C represents the approximate position of one of 

the melting curves of the assemblage enstatite+sapphirine (+sillimanite?), and probably is the solidus 

curve determined by the melting of enstatite in this 

assemblage. The invariant point at the intersection of 

curves A, B, and C is at 1510°C and 21,600 atm.

Boyd and England (1960) found evidence of the 

formation of a spinel-type structure in some runs on 

the join 2MgO SiO2-2FeO SiO2 at approximately 

75,000 atm and 1300°C. The mixture, 10 percent 

2MgOSiO2-90 percent 2FeO-SiO2, crystallized to a 

mixture of spinel and olivine.

Mixtures richer than 10 percent 2MgO-SiO2 yielded 

only olivine, and higher pressure would be necessary 

to convert it to the spinel structure. Boyd and England also found that when mixtures on the join 

MgSiO3-Al2O3 were crystallized at 1400°C and 18,200 

atm pressure, only a solid solution of A12O3 in enstatite, 

from 0 to 14 percent A12O3 , was formed; between 14 

and 22 percent A12O3 , sapphirine appeared but the 

composition of the enstatite continued to change; for 

compositions containing more than 22 percent A12O3 , 

sillimanite also is formed and the composition of the 

enstatite is invariant.

MgO-FeO-FejOs

Eoberts and Merwin (1931) studied the melting relations in the system MgO-FeO-Fe2O3 in air, hence at 

a partial pressure of oxygen of approximately 0.21 

atm. Two series of solid solutions are formed. One of 

these extends from MgO toward MgO-Fe2O3 and FeO 

to a liquid boundary curve at this oxygen pressure and 

1770°±20°C where the coexisting solid contains 73 percent Fe2O3 . The second solid solution extends, with increasing temperature, from MgO-Fe2O3 toward the 

iron oxide boundary, which it reaches at 1380° ±5 °C.

Paladino (1960) studied the system in the solid state 

at 1000°, 1100°, 1200°, and 1300°C, and at oxygen pressures of 1.0, 0.21 (air), and 0.01 atm. He found that 

the spinel field is at a higher MgO content than the 

join Fe3O4-MgFe2O4 near MgFe2O4, and a mixture of 

the composition Mg2Fe2O4 contains Fe2O3 and a spinel 

richer in MgO under all the experimental conditions 

chosen.

Gurry and Darken (1950) determined the compositions of some mixtures equilibrated in oxygen at 0.2 

atm and 1 atm oxygen pressure and in CO2 at 1 atm 

pressure and constructed a tentative diagram for the 

equilibrium at 1600°C.

CaO-FeO-SiO2

The system CaO-FeO-SiO2 is of importance not 

only in geology because of the insight it gives on the 

relationship between the pyroxenes and olivines, but 

also in metallurgy because of the insight it gives on 

the action of iron-bearing slags on silica refractories. 

Bowen, Schairer, and Posnjak (1933a) published a
L58 DATA OF GEOCHEMISTRY

AI203

SPINEL 

MgO-AI2 C>3

SAPPHIRINE 

4MgO-5AI 203 -2Si02

MgO

/ MgO I 

9°A I

L v v \/ \ v

//' ^ //s/ // #K CRISTOBALITE ^ \

/ 1^7 ^-***""^ ^"" -_. 

/ // / .X'^WO LIQUIDS ^^">^. 

/i/ \/ fiS/ / >X^ v v

10 20 30 440/' 50 [E F G 80 90 

FORSTERITE PROTOENSTATITE 

2MgO-Si02 MgO-Si02

10

^

//Si02

WEIGHT PERCENT Si02

FIGURE 36. The system MgO-AljOs-SiOj. Modified from Keith and Schairer (1952). 

TABLE 24. Invariant points in the system MgO-Al2Os-SiO2

Invariant 

point on 

fig. 36

«__.... ......

P_......_

V... __....._.

U. ..........

B- . .......

M. ..........

W...........

N. ..........

X.. .........

T- ..........

Phase reactions

MgO-SiO2 +2MgO-2Al2O3-5SiO2 +SiO2 ^L- _____ _____ ... _

3Al2O3 .2SiO2 +SiO2-"2MgO.2Al2O3 .5SiO2 +L... _._-----------.

2MgO.SiO2 +2MgO.2Al2O3 -5SiO2^MgO.Al2O3 +L__-_--------_-

MgO.SiO2 +2MgO-SiO2 +2MgO-2Al2O3 -5SiO2^L_. ____________ .

MgO+ MgO-Al2O3 +2MgO-SiO2^L_. _._.__. -__-------------.

MgO.Al2O3 +3Al2O3 .2SiO2-"Al2O3 +L___. __.-_-_._-_---.-.-..

MgO-Al2O3 + 2MgO-2Al2O3 .5SiO2-^4MgO-5Al2O3 .2SiO2^L ____

2MgO-2Al2O3 .5SiO2 +4MgO.5Al2O3 -2SiO2-"3Al2O3 -2SiO2 +L_ _ _._

4MgO.5Al2O3.2SiO2^MgO.Al2O3 +3Al2O3 .2SiO2 + L__-_.------_-

MgO.SiO2 +2MgO-2Al2O3 .5SiO2-"L__ __ ____ ___ _____

Temperature (°C)

1355 

1440 

1370 

1360 

1700 

1575 

1453 

1460 

1482 

1365

Composition of liquid 

(percent by weight)

MgO

20. 50 

9.25 

25.7 

25.0 

56.0 

15.2 

17.4 

16.3 

16.9

A12O3

17.50 

22.5 

22:8 

21.0 

16.0 

42.0 

33.5 

34.4 

36.8

SiO2

62.06 

68.25 

51.5 

54 

28.0 

42.8 

49. 1 

49.3 

46.3
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L59

cr

LU

x

Q_ 

C/5 

O

<

LJ_

o

Q

C/5

ID 

O

X

cr

ID 

C/5 

C/5 

LU

o: 

o_

45

40

-zc 35

30

10

3MgO-2AI203 -3Si02 

PYROPE

LIQUID

+ 

( CRYSTALS)

ALUMINOUS MgO-Si02 (ENSTATITE) 

+ 4MgO-5AI 203 -2Si02 (SAPPHIRINE) 

+ AI203 -Si02 (SILLIMANITE)

0

400 600 800 1000 1200 1400 1600 1800

TEMPERATURE, IN DEGREES CENTIGRADE

FIGUKE 37. The stability field of SMgO-AhOs-SSiOj (pyrope). Modified from Boyd and England (laay;.
L60 DATA OF GEOCHEMISTRY

FeO

90

.80

2FeO-Si02

80

CaO

3CaO'

30 \ 40 '\/ 50 

2CaO-Si02 3CaO-Si02

60 

CaO-Si02

WEIGHT PERCENT Si02 

FIGUBE 38. The system CaO-FeO-SiO2. Modified from Bowen, Schairer, and Poshjak (1933b). ss, solid solution.

study of the olivine solid solutions, and also (1933b) 

published a comprehensive study of the system, with a 

discussion of its applications and of the literature. The 

system actually has oxygen as a component, and even 

though the final melts were made in an iron crucible in 

an atmosphere of nitrogen, some Fe2O3 was present in 

all melts; small in amount in the high-silica part of the 

ternary diagram, more than 1 percent along the ironrich part of the metasilicate join, and more than 2 percent on the orthosilicate join near 2FeO SiO2. The 

phase-equilibrium diagram is figure 38, and the invariant points are listed in table 25. The silica-rich part of 

the phase-equilibrium diagram is occupied by a region 

of two liquid layers and the fields of cristobalite and 

tridymite.

The phase-equilibrium diagram of the binary system 

2CaOSiO2 (calcium orthosilicate)-2FeO-SiO2 (fayalite), determined by Bowen, Schairer and Posnjak 

(1933a) is given in figure 39. The results are expressed 

as a binary system by calculating all iron oxide as FeO, 

although some Fe2O3 was always present. The amount 

of Fe2O3 is indicated in the upper part of the diagram.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 25. Invariant points in the system CaO-FeO-SiO2

L61

Invariant 

point on 

fig. 38

A.... ........

M___________

B... .........

#____ ........

C... .........

F... .........

D. ..........

/........_...

Phase reactions

SiO2 +/3-CaO.SiO2ss (93CaSiO3)^±o-CaO.SiO2 +L_ __ .... ...

/3-CaO-SiO2ss (9lCaSiO3)^o-CaO.SiO2 +L. --_____-____---___

SiO2 +/3-CaO-SiO2ss (28 CaSiO3)+olivine (4Ca2SiO4, 96Fe2SiO4 ss)

o-CaO-SiOji+olivine (43Ca2SiO4, 57Fe2SiO4ss)^/3-CaO-SiO2ss 

(97CaSiO3) + L. 

o-CaO-SiO2 +olivine (58Ca2SiO4 , 42Fe2SiO4ss)^3CaO-2SiO2 +L. 

3CaO-2SiO2 +olivine (59 a2SiO4 , 4lFe2SiO4 ss)^2CaO-SiO2 +L_ 

0-CaO-SiO2ss (50CaSiO3)+oIivine (20Ca2SiO4, 80Fe 2SiO4ss);=±L_ 

CaO-FeO-SiO2 -iL. _ _____ _ _ _ ___ ... -_---_.

o-CaO-SiO2 +/3-2CaO-SiO2-*3CaO-2SiO2+L-. _ _ . _ . ....

Temperature f°C)

1272 

1285

1105 

1193

1120 

1227 

1093 

1208 

1420?

Composition of liquid 

(percent by weight)

CaO

26. 5

27.8

11.5 

30

36 

37 

17 

29. 83 

50

FeO

18.5 

23. 2

45. 5 

34

27 

28 

46 

38. 22

8

SiO2

55 

49

43 

36

37 

35 

37 

31. 95 

42

1500

1450

1400

o 1350

CO

LJ 

LJ

cr 

o

LJ

^ 1300

cr

1250

1200

I 150

WEIGHT PERCENT Fe 203

Liquid* fi- 2CaO Si02 ss

~£-2CaO-Si02 ss

1230°- -Liquid + CaO-FeO OLIVINES 

D

>0-2CaO-Si02 ss

+ 

CaO-FeO OLIVINES

2CaO-Si02 lo 20

CALCIUM ORTHOSILICATE

Liquid + CaO-FeO 

OLIVINES

30 50 " 60 

CaO-F( 0-Si02

WEIGHT PERCENT 2FeO-Si02

70 80 2FeO-Si02 

FAYALITE

FIGURE 39. The system 2CaO^SiOj (calcium orthosi]icate)-2FeO-SiOj (fayalite) expressed as a binary system by calculating all iron oxide as FeO. The actual 

amounts of FesOs are shown In the upper right-hand part of the diagram. Modified from Bowen, Schairer, and Posnjak (1933). ss, Solid solution.
L62 DATA OF GEOCHEMISTRY

2CaO-SiO2 and 2FeOSiO2 form a 1:1 compound 

CaOFeO-SiO2 (analogous in composition to monticellite, CaO-MgOSiO2 ), which melts congruently at 

1208°C. Between CaO-FeO-SiO2 and 2FeO-SiO2 (fayalite), there is a complete series of solid solutions with 

a minimum melting point at 81 percent 2FeO SiO2 and 

1117°C (#, fig. 39). The solid solution series continues 

throughout the composition of the compound

CaO-FeO-SiO2

up to point C. At this point, 1230 °C, a liquid C containing 46 percent of 2FeOSiO2 is in equilibrium 

with a solid solution #, an olivine containing 41 

percent of 2CaO-SiO2. With mixtures richer in 

2CaO SiO2, the olivine B is in equilibrium with

3CaO2SiO2

solid solution containing 90 percent 2CaO'SiO2 . The 

solid solutions of 2FeO SiO2 in /?-2CaO SiO2 along the 

curve AK decrease in 2FeO SiO2 content with decreasing temperature and at 1125 °C contains only 2 percent; 

the compositions of the olivines in equilibrium are given 

by the line BC.

On cooling, the /?-2CaO SiO2 solid solutions invert 

completely or partially to a-2CaOSiO2 solid solutions 

which have indices of refraction higher than those of 

pure a-2CaOSiO2. This probably is caused by solid 

solutions of 2FeO SiO2 in this form also, but the limits 

could not be determined.

The binary system CaO SiO2-CaO FeO SiO2 is of 

simple eutectic type, with the eutectic at 1203 °C, only 

5°C below the melting point of CaO FeO SiO2, and 80 

percent of CaO FeO SiO2.

The join CaO SiO2-FeO SiO2 is not a binary system, 

as shown in figure 40, because FeO SiO2 does not exist 

as a crystalline compound.

The inversion temperature of /?-CaO-SiO2 (wollastonite) to a-CaO-SiO2, (pseudowollastonite) is raised 

135°C, by solid solution of FeO-SiO2 to point B, 

1285°C, which contains about 9 percent FeO-SiO2 . At 

1285 °C some liquid of composition M is formed. There 

are now three phases, and the temperature remains constant until the reaction /?-CaO < SiO2ss=a-CaO < SiO2 + 

liquid M is complete. There is no solid solution in 

a-CaO-SiO2 .

When a mixture containing 40 percent FeO-SiO2 

is cooled from a high temperature, the liquid begins to 

crystallize at 1308 °C with separation of crystals of pure 

pseudowollastonite, which continues until 1285 °C. At 

that temperature the liquid has the composition M, and 

crystals of wollastonite solid solutions of composition B 

begin to form at the expense of the pseudowollastonite.

When the pseudowollastonite has entirely disappeared, 

further cooling occurs and the liquid changes in composition along MZ while the wollastonite solid solution 

changes in composition along BC. At 1160 °C the last 

solid has reached the composition C and the last true 

liquid, now of composition Z, vanishes. The mass then 

consists entirely of a solid solution of the composition 

C.

The liquid 0 has the highest content of FeO-SiO2 

of any liquid that behaves in this simple manner. All 

liquids between C and Z exhibit ternary equilibrium at 

some stage of their crystallization, and all between Z 

and FeO-SiO2 show ternary behavior at all stages of 

their crystallization, although some of these again become binary when all liquid has disappeared and 

crystallization is complete.

All liquids of composition between CaO SiO2 and B 

become completely crystalline at the temperature of 

the horizontal BM and then consist of pseudowollastonite and wollastonite solid solution B. With further 

cooling, the composition of the solid solution changes 

along the curve B A at the expense of the pseudowollastonite, which eventually disappears. In a mixture 

with 5 percent FeO-SiO2, for example, pseudowollastonite disappears at 1240 °C and the mass is then made 

up of crystals of wollastonite solid solution containing 

5 percent FeO SiO2 .

The behavior of solid solutions that show ternary 

relations may be seen by reference to figure 40. A 

liquid of the composition of CaO-FeO-2SiO2 (hedenbergite) begins to crystallize at 1207°C with the separation of crystals of /?-CaO-SiO2 (wollastonite) solid 

solution containing 25 percent FeO SiO2. As cooling 

proceeds both liquid and solid solutions change in composition until at 1160 °C the liquid has the composition 

Z, the solid, C. At this temperature tridymite begins 

to separate and thenceforth the composition of the 

phases present cannot be shown on a binary diagram. 

When the liquid has cooled to 1118° C both liquid and 

tridymite have disappeared and the mass consists entirely of a wollastonite solid solution having the composition of hedenbergite (CaO-SiO2 46.8 percent, 

FeO-SiO2 53.2 percent). A liquid of composition 

CaO SiO2 30 percent, FeO SiO2 70 percent begins to 

crystallize at 1240 °C with separation of tridymite. The 

liquid immediately departs from metasilicate composition and cannot be shown on the binary diagram. The 

diagram does show, however, that at 1125°C tridymite 

is joined by a wollastonite solid solution, but the composition of the solid solution cannot be shown on the 

binary diagram. Upon further cooling, liquid and 

tridymite finally disappear at 1106°C and the mass is
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER

Q 

< 

CE 

O

O 

C/5

QC 

O

z

LJ 

CL

<

LJ 

Q_

1550 

W

1500

1400

1300

1200

1100

1000

900

800

700

LIQUID+CRISTOBALITE

LIQUID* TRIDYMITE and OLIVINE

and 

a-CaO Si02

LIQUID*/3-CaO-Si02 ss 

TRIDYMITE

y#-CaO-Si02 ss 

(WOLLASTONITE)

£\ E

j8-CaO-Si02 ss

TRIDYMITE and 

OLIVINE

V

/ p -^uu-Si02 ss

* (WOLLASTONITE) 

and

HEDENBERGITE

X P 

\HEDENBERGITE ss

\TRIDYMITE and 

HEDENBERGITE ss \ OL|V|NE

N

R

TRIDYMITE

and 

OLIVINE

CaOSi02 

WOLLASTONITE

10 20 30 40 50 A 60

CaO-FeO-2Si02 

HEDENBERGITE

70 80 90 Fe0 . S i02

WEIGHT PERCENT FeO-Si02

FIGURE 40. Phase-equilibrium diagram for mixtures of CaO-SiOj and FeO-SiOj. Tbe heavy curves refer to binary equilibria, tbe ligbt ones to ternary equilibria. Tbese 

can be considered as binary and ternary only when tbe small amounts of ferric iron present are calculated to FeO. Modified from Bowen, Schairer, and Posnjak 

(1933b). ««, solid solution.

made up entirely of a wollastonite solid solution containing 70 percent FeO SiO2 .

The compound CaO-FeO-2SiO2 (hedenbergite), is 

stable at temperatures below 965°C (H on fig. 40). If it 

is heated above this temperature it changes to a stable 

homogeneous solid phase of the same composition. The

substance is no longer a compound, but is a member, 

in no way unique, of the wollastonite solid-solution series. When a solid phase or mixture of solid phases is 

transformed in this manner into a solid solution, the 

equilibrium diagram can assume any of the various 

forms that a melting-point diagram can assume. The
L64 DATA OF GEOCHEMISTRY

higher temperature phase is a solid solution but in most 

respects the possible forms of the diagram are the same. 

Thus, the curve VHNJ on figure 40, with its maximum 

at the composition of hedenbergite, is analogous to the 

liquidus curve of a melting-point diagram except that 

the phase above it is a solid solution instead of a liquid 

solution. All the phase changes incident to a change of 

temperature and the proportions of phases present at 

any temperature are read from the diagram in the same 

manner as in the more familiar melting-point diagram. 

The metasilicate and the orthosilicate solid solutions 

are the dominant solid phases of the ternary system and 

their relations to each other and to ternary liquids are 

the features of greatest interest in the system. The coexistence of two solid-solution series in rocks is a phenomenon of common occurrence which renders desirable 

a full discussion of their interrelations. They are best 

brought out with the aid of the series of isothermal 

planes of figure 41. The relations of phases of constant 

composition, such as tridymite, pseudowollastonite, and 

tricalcium disilicate, are so,simple that they require 

no special discussion. The first isothermal plane to be 

described will, therefore, be 1285°C, which is the maximum temperature at which crystals of one of the solidsolution series can exist. At this temperature only 

one liquid, M, can exist in equilibrium with a /?-CaSiO3 

(wollastonite) solid solution. The composition of the 

solid is B. The equilibrium is binary and the device 

is here adopted of indicating binary equilibrium by a 

brace. The point M corresponds with the point lettered 

M in figures 38 and 40, and point B with point B in 

figure 40. The liquids represented by points on the 

curves Ma and Md (except M itself) are in equilibrium 

only with a-CaSiO3 (pseudowollastonite) which has the 

fixed composition W. The liquid a is in equilibrium 

with both tridymite and CaOSiO2 and therefore corresponds with a point on the boundary curve GA of 

figure 38. The liquid d is in equilibrium with both aCaO-SiO2 and 3CaO-2SiO2 . The liquid c is in equilibrium with both 3CaO2SiO2 and 2CaO-SiO2 solid 

solution of composition b. As in metasilicate compositions, so in the orthosilicate compositions the binary 

equilibrium is indicated by a brace joining the liquid 

and solid in equilibrium. The point g therefore represents the composition of crystalline orthosilicate in equilibrium with liquid at 1285°C. All compositions in 

the triangle ObL are completely crystalline at this temperature (1285°C) and consist of two phases: one the 

compound 3CaO-2SiO2 , the other a £-2CaO-SiO2 solid 

solution of a composition between b and O. The only 

other compositions that are completely crystalline at 

1285 °C are those lying in the line WB and those lying 

in the line Og.

Many of the characters described for various points 

in the figure apply to similar points in the subsequent 

isothermal planes and will not be again discussed. 

Only the new features brought out by the successive 

planes will, in general, be mentioned.

At the next isothermal plane, 1280°C, which is only 

5°C lower, any one of the liquids lying on the curve by 

is in equilibrium with a wollastonite solid solution. 

There are now two liquids b and y that are in equilibrium with both <x-CaO-SiO2 and £-CaOSiO2 (wollastonite) solid solution. Moreover, the liquids b and y 

are in equilibrium with the same wollastonite solid solution and its composition is 3. This follows from the fact 

that only one wollastonite solid solution can be in equilibrium with pseudowollastonite at any given temperature and, the temperature being 1280°C, the point 0 

must represent the same composition as the point in the 

curve AB of figure 40 which lies at 1280°C.

The next isothermal plane is 127'20C, the temperature 

of the invariant point A of figure 38. There are again 

two liquids, H and Y, that are in equilibrium with both 

pseudowollastonite and a wollastonite solid solution, 

but here the liquid H is also in equilibrium with tridymite. The wollastonite solid solution has the composition 0, which is nearly the same as 2 at 1280°C and 

is fixed by the same considerations. The temperature 

1272 °C is the minimum temperature of existence of 

pseudowollastonite in contact with liquids containing 

silica in excess of the metasilicate ratio. In liquids containing less than the metasilicate ratio, pseudowollastonite continues to much lower temperatures.

At a temperature immediately below 127'20C, the join 

Wff disappears and is replaced by zT. All mixtures in 

the triangle WzT therefore become completely crystalline at 1272 °C and consist of the three solid phases, 

tridymite, a-CaO'SiO2 (pseudowollastonite), and 

/3-CaO-SiO2 (wollastonite) solid solution of composition 2. Further cooling of this mixture of three solid 

phases brings about a change of composition of the 

wollastonite solid solution which consists of its enrichment in CaO SiO2 at the expense of pseudowollastonite 

and which continues until the supply of pseudowollastonite is exhausted. The exact behavior is to be read 

from the curve AB of the (partially) binary figure 40, 

the tridymite present acting as a wholly neutral body 

with respect to these changes.

The next isothermal plane represents the relations at 

1250°C. There is now only one liquid, y, which is in 

equilibrium with both pseudowollastonite, and a wollastonite solid solution designated by 2. It lies much 

closer to W than it did in the isothermal planes for 

higher temperatures, a relation that is rendered necessary by the slope of the curve AB of figure 40. All
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L65

the liquids on the curve ya are in equilibrium with wollastonite solid solutions. The liquid a is also in equilibrium with tridymite and the particular wollastonite 

solid solution in equilibrium with it is x. All mixtures 

in the triangle WzT are completely crystalline at 

1250°C and consist of the three solid phases, tridymite 

(T7 ), pseudowollastonite (TF), and wollastonite solid 

solution (z}. All mixtures in the triangle zxT are also 

completely crystalline at 1250°C but they consist of 

only two solid phases, tridymite and a wollastonite solid 

solution of a composition, which may lie anywhere between z and a?, the exact position depending upon the 

total composition.

The next isothermal plane to be described shows 

phase relations at 1227°C, the temperature of the invariant point F of figure 38, and the same point is 

marked Q in this isothermal figure. There is again a 

series of liquids, ya, each of which is in equilibrium 

with a wollastonite solid solution. The liquid y is in 

equilibrium with the solid solution z and also with 

pseudowollastonite. The liquid a is in equilibrium with 

the solid solution x and with tridymite T. The triangles 

~WzT and zxT have the same qualities as the triangles 

so lettered in the 1250°C figure. WzT has become 

smaller and zxT larger. The liquid Q is joined with the 

three solid phases in equilibrium with it. These are 

3CaO-2SiO2 (Z), £-2CaO-SiO2 solid solution (6), and 

Ca-Fe olivine (c). The temperature 1227°C is the minimum temperature of existence of 2CaO-SiO2 solid 

solutions in contact with liquid. At a temperature immediately below 1227°C, the join bQ disappears and its 

place is taken by the join cL.

The next isothermal plane is for 1220°C, the temperature of the invariant point C of figure 38. The points 

«, y, a?, and z require no special discussion for this particular figure. The liquid P is joined with the three 

solid phases in equilibrium with it. They are pseudowollastonite (W), 3CaO-2SiO2 (Z), and Ca-Fe olivine 

(c) . The temperature 1220°C is the minimum temperature of existence of 3CaO-SiO2 in contact with liquid. 

At a temperature immediately below this, the join pL 

disappears and its place is taken by the join cW. The 

triangles that represent completely crystallized material 

may be mentioned. In the triangle dcL there are two 

solid phases, 3CaOSiO2 and a Ca-Fe olivine of composition between d and c. In the triangle dbL there 

are three solid phases, /?-2CaO-SiO2 solid solution (6), 

3CaO-2SiO2 (Z) and Ca-Fe olivine (d). In the triangle LOb there are two solid phases, 3CaO-2SiO2 (Z) 

and a /?-CaO SiO2 solid solution of composition between 

b and 0.

The next isothermal diagram is that for 1200°C. 

The points «, y, z, and x have their usual characters.

The point x is now much closer to TF, in correspondence 

with the fact that the wollastonite solid solution that is 

in equilibrium with pseudowollastonite at 1200 °C has 

only a very small content of FeSiO3 . The liquid I is 

joined to the two solid phases in equilibrium with it. 

They are pseudowollastonite (TF) and a Ca-Fe olivine 

(n) , a point a small distance to the right of the composition of the compound CaO-FeO-SiO2 . The triangle 

cnW represents completely crystalline material in two 

phases, pseudowollastonite (W) and a Ca-Fe olivine of 

composition lying between c and n. The triangle cWL 

represents completely crystalline material in three 

phases, TF, Z, and c, the last being a Ca-Fe olivine. 

The triangles adjacent to these have the characters already given under the preceding isotherm. Two-phase 

and three-phase triangles alternate. In this figure 

there appears for the first time a small area representing liquid and olivine very close to fayalite.

The next isothermal diagram presents phase relations at 1193°C, the temperature of the invariant point 

E of figure 38. The two points I and y of the preceding 

figure have now become the single point R. The liquid 

R is joined with the three solid phases in equilibrium 

with it: pseudowollastonite (W), wollastonite solid 

solution (z), and Ca-Fe olivine (n). The temperature 

1193°C is the minimum temperature of existence of 

pseudowollastonite in contact with liquid. At a temperature immediately below 1193°C the join RW disappears and is replaced by the join nz.

The next isothermal diagram shows phase relations 

at 1160°C, the temperature of the point Z of figure 38. 

The point Z is not an invariant point, but is merely the 

lower limit of the congruent melting of metasilicate 

solid solutions. At temperatures above 1160°C liquids 

on both sides of the metasilicate join are in equilibrium 

with wollastonite solid solutions. At temperatures below 1160°C only liquids with less silica than the metasilicate ratio are in equilibrium with wollastonite solid 

solutions. In the diagram for 1160°C, the points Z 

and C correspond with the points similarly lettered in 

figure 40. The point z represents the wollastonite solid 

solution in equilibrium with liquid (m) and with Ca-Fe 

olivine (n). It no longer represents a wollastonite 

solid solution in equilibrium with pseudowollastonite 

as it did in all previous isothermal figures. At temperatures above 1193°C the point z moved toward W 

with falling temperature; at temperatures below 1193°C 

it moves away from TF, and at 1160°C has attained the 

approximate position shown. All compositions in the 

quadrilateral AnzW consist of a wollastonite solid solution of composition between W and z and a Ca-Fe olivine of composition between A and n. All compositions 

in the triangle WAc consist of pure wollastonite (W)
L66 DATA OF GEOCHEMISTRY

CoO Si0 2 

5

B. I280"C

CaO-SiO? 

50,

CaO-SiO,

FeO-S!02

FIGUEE 41A-O. Isothermal planes showing phase-equilibrium relations in the system CaO-FeO-SiOj.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L67

CoO SiOg 

50,

2FeO-Si02

CaO SiO 

50,

40,

CaO FeOSi02" 

J. II30°C

2FeOSi02

K. II05°C

CaO-FeO Si02 

M. I093°C

CaO-Si02 

5

0. 700"C

ZFeO-Si02

Truncated SiOs apex= T in text. Modified from Bowen, Schairer, and Posnjak (1933b).
L68 DATA OF GEOCHEMISTRY

and a Ca-Fe olivine of composition between A and c. 

This diagram is the first of these isothermal figures on 

which a liquid appears that is in equilibrium with both 

tridymite and an olivine. It is represented by the 

point e.

The next isothermal plane shows phase relations at 

1130°C, which is not a unique point but may be taken 

as representative of the changing equilibrium between 

1160° and 1105°C. The liquids on the curve am, all 

of which have silica in less than the metasilicate ratio, 

are the only liquids in equilibrium with metasilicate 

(wollastonite) solid solutions. The triangle sFT represents mixtures that are completely crystalline at 

1130°C and consist of tridymite and olivine of composition between F and *. A triangle having these characteristics appeared on the preceding figure but there it 

was too small to assign letters to it. 

The next isothermal plane, 1105°C, is at the temperature of the invariant point B of figure 38. The liquid 

K is joined with the three solid phases in equilibrium 

with it, wollastonite solid solution (a), olivine (s), and 

tridymite (T). The point K lies nearly on a straight 

line joining the points s and a; in fact, experimental 

results do not prove conclusively that K does not lie in 

that line. If K lay above the join sa, it would be a 

eutectic point; if it lies below sa, it is a reaction point; 

and if it lies in the line, it is a neutral point, and tridymite is an indifferent phase and plays no part in the 

phase reaction. The general relations in the vicinity of 

K show that it is not a eutectic, but do not permit a 

decision as to whether it is a neutral point or a reaction 

point. In the figure it is shown slightly below the join 

sa and therefore as a reaction point, but there would be 

no important difference in the general relations if K lay 

in the join sa. The temperature 1105°C is the minimum 

temperature of existence of tridymite in contact with 

liquid. At a temperature immediately below 1105°C, 

the join KT disappears and is replaced by the join sa.

The next isothermal plane is for 1097°C, only 4°C 

above the minimum temperature of existence of liquid. 

The liquid & is in equilibrium with the wollastonite solid 

solution e and the olivine r, the liquid m with the wollastonite solid solution z and the olivine n. The quadrilateral WznA which appeared in higher isothermals 

has in this figure the companion quadrilateral easr, 

which represents mixtures that are completely crystalline and consist of a wollastonite solid solution between 

e and a and an olivine between r and s. The tie lines 

join the compositions in equilibrium. The triangle saT 

represents mixtures that are completely crystalline at 

1097°C and consist of three phases, tridymite T7, olivine 

s (96 percent 2FeOSiO2 ) and wollastonite solid solution a (72 percent FeO SiO2 ).

The next isothermal plane is for 1093°C, which is the 

minimum temperature of existence of liquid. At this 

temperature only one liquid can exist and it is represented by the point S which corresponds with the point 

similarly lettered in figure 38. This liquid is in equilibrium with the two solid phases O (and olivine with 

about 80 percent 2FeO-SiO2 ) and to (a wollastonite 

solid solution with 50 percent FeOSiO2 ), and wSo is a 

straight line. Only mixtures lying in this line are partly 

liquid at 1093 °C. All other mixtures are completely 

crystalline. The lines joining the solid phases in equilibrium with each other are readily pictured from the 

preceding figures. At a temperature immediately below 

1093 °C all mixtures are completely crystalline.

The next isothermal diagram represents relations at 

980°C, an invariant point where four solid phases (and 

vapor) are in equilibrium. The four phases are wollastonite solid solution j, hedenbergite solid solution JT, 

olivine ,§, and tridymite T. The points / and X correspond with the points similarly lettered in the metasilicate diagram (figure 40). Immediately above 980°C 

the triangle JsT represents the stable configuration. 

Immediately below 980°C Js and JT disappear and the 

triangle XsT represents the stable configuration.

The next isothermal plane shows the most probable 

relations at 700°C. At this temperature the compound, 

2CaO-FeO-2SiO2, is one of the phases participating in 

the equilibrium in mixtures of appropriate composition. The point a corresponds with a point at 700 °C 

on the curve HV of figure 40 and the point & with a 

point at 700 °C on the curve XR of figure 40.

The point m represents the composition of the olivine 

that is in equilibrium with hedenbergite at 700° C. Its 

position is not determined but is based on the assumption that this is the same olivine that is in equilibrium 

with hedenbergite at 965 °C and therefore with a wollastonite solid solution of the same composition as hedenbergite. Even at 965 °C the composition of this olivine is not determined, but again is based on the assumption that it is the same olivine that is in equilibrium with a wollastonite solid solution of the composition of hedenbergite at the still higher temperature 

somewhat above 1100°C, where liquid is present. The 

assumption is that the composition of the two phases 

in equilibrium at 1100°C is the same as the composition 

of the two phases in equilibrium at 700 °C. No doubt 

this is not strictly true but it is probably not far from 

the truth.

Some of the areas of the isothermal plane- at 700°C 

have the same significance as the similar areas in preceding planes and need not be discussed. Others may 

require special mention. The quadrilateral Hbsm includes all compositions that consist, at 700°C of two
PHASE-EQUILIBBIUM RELATIONS, BOCK-FORMING OXIDES EXCEPT WATER L69

A

90

CaO 10 20 30 40 

WEIGHT PERCENT Fe 2 03

50

2CoO-Fe 203 

FIGURE 42. The system CaO-AljOs-FejOj. Modified from Swayze (1946). ss, solid solution.

70 I 80 

CaO-Fe 203

phases: hedenbergite solid solution, H to &, and olivine, 

m to «. The triangle Hma includes all compositions 

that consist of three phases: pure hedenbergite, H, 

olivine, m, and wollastonite solid solution, a. The triangle Gam has the three phases, 2CaO-FeO-2SiO2, 

G, wollastonite solid solution, a, and olivine, m. The 

triangle Gem has the two phases, 2CaO FeO 2SiO2, 

G, and olivine, c to m. The triangle GcL has the 

three phases, 2CaOFeO2SiO2 , G, olivine, c, and 

3CaO 2SiO2 , L. The triangle GLW has the three solid 

phases, 2CaO FeO 2SiO2, 3CaO2SiO2, and pure 

wollastonite. The triangle GWa has only two solid 

phases, 2CaO FeO 2SiO2, G, and wollastonite solid 

solution, W to a.

C aO- Al2

The original study of this system, important in the 

cement industry, was by Hansen, Brownmiller, and 

Bogue (1928). McMurdie (1937) later worked on 

CaO-CaO-Al2O3^CaO-Fe2O3 , and Swayze (1946) 

made a further study of CaO-5CaO 3A12O3- 

2CaOFe2O3 . Swayze's results which also are given 

in Bogue (1955), are given preference in figure 42. 

In the, binary system CaO'-Al2O3-CaO-Fe2O3 , 

CaOAl2O3 takes as much as 15 percent of CaOFeaOs 

into solid solution, and CaOFe2O3 takes as much as 

19 percent of CaOAl2O3. There is a eutectic at 

1205°±5°C of composition CaO 28 percent, A12O3 13 

percent, Fe2O3 59 percent. Two ternary compounds are
L70 DATA OF GEOCHEMISTRY

AI203

2CaO-AI203 -Si02 

GEHLENITE

CaO 10 20 / 30 '\ 40 \ 50 \ 60 

3CaO-Si02 2CaO-Si02 3CaO-2Si02 CaO-Si02

WEIGHT PERCENT SiO,

FIGUKE 43. The system CaO-AliOa-SiOi. Based on Rankin and Wright (1915), Greig (1927a), Osborn (1942), and Schairer and Bowen (1947b). The diagram has not been 

corrected for the incongruent melting of 3CaO-SiO2 desciibed by Welch and Gutt (1959), and the field of 3CaO-SiO2 should extend to the side CaO-SiO2 instead of terminating at 7.

formed. The first, 4CaOAl2O3 -Fe2O3 was found by 

Hansen, Brownmiller, and Bogue to melt congruently 

at 1415°C. It forms a series of solid solutions on the 

line 4CaOAl2O3 -FeO3 which extends on both sides of 

the composition 4CaO A12O3 Fe2O3 . The second compound, 6CaO-2Al2O3-Fe2O3 , found by Swayze, in confirmation of previous observations by Yamauchi 

(1937#,5), melts incongruently at B (fig. 42) with 

formation of a solid solution on the join 

6CaO-2Al2O3 -Fe2O3-4CaO-Al2O3 -Fe2O3 and at the

temperature of complete melting, 1390°C, the residual 

solid phase had a molecular ratio (A12O3 : Fe2O3 ) 

of 0.72:1. The region between the join CaO-Al2O3- 

CaOFe2O3 and the fields of 3CaO-Al2O3 and the 

region of solid solution has not been clarified.

CaO-Al2O3-SiO2

Parts of this system have been studied by many investigators, chiefly because of the information it gives 

concerning the constitution of portland cement. This
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 26. Invariant points in the system CaO-Al2O3-SiO2

L71

Invariant 

point on 

fig. 43

A. ._. _______

B____________

C______ _-

&____________

£>____________

E- _--_-.----

F____. _______

(? __________

d____________

#-_-______-_

7 1 ___________

L____________

#_-___-_____

M_-________-

AT___. _______

<?___________.

P____-__._-__

Phase reactions

CaO-Al2O3 .2SiO2 -f SiO2 +3Al2O3 -2SiO2^±L__ ___ ___ ________

CaO -A12O3- 28102+8102-^ (50. 5 An). _ _________________ ___

CaO-SiOz+SiO^CaO-AlzOs^SiOz-^L. _______ ___ __ ___ __ _

CaO-Al2O3 -2SiO2 +3Al2O3-2SiO2^Al2O3 +L__ __ _____ __ ___

CaO-Si02 +CaO.Al2O3 .2SiO2^L___ _ ___ :__ ________ ______

CaO-Al2O3 -2SiO2^±L_ ______ __ _ __ _ ___ _ _ _____ _____

CaO-Si02 +CaO.Al2O3 -2SiO2 +2CaO.Al2O3 -SiO2L+_ _ _______ _

3CaO.2SiO2 + CaO-Al2O3 .2SiO2 ^CaO-SiO2 +L--__ __ __ _ _ _

3CaO-2SiO2 + 2CaO-Al2O3-SiO2 ^2CaO-SiO2 + L__ __ ___ _ ____

2CaO-Al2O3 .SiO2 +CaO-Al2O3 -2SiO2 -^L___ __ ___ __ ___ _ _

2CaO-Al2O3 .SiO2 +CaO.Al2O3 .2SiO2 +Al2O3^L_____ __ ___ _ _

2CaO-SiO2 +2CaO-Al2O3 -SiO2 ^L_ ______ ___ _ ___ _________

2CaO.Al2O3 -SiO2 +Al2O3-iCaO-2Al2O3+L____ ________________

3CaO.SiO2 -OaO+2CaO-SiO2 _ _ ____ _ ___ ________ __ __

2CaO.Al2O3 -SiO2 +CaO-2Al2O3 -iL______ _ ___ _ _ ___ ____

2CaO-SiO2 +CaO.Al2O3 ^2CaO-Al2O3 -SiO2 ^L_____ ______ ____

CaO- A12O3 + 2CaO.Al2O3 -SiO2 + CaO-2SiO2 ^L_ _ _ _ _ _________

2CaO-SiO2 +3CaO-Al2O3 ^3CaO-SiO2 +L___-__ _ _ ___ _____

3CaO-SiO2 +3CaO.Al2O3 ^CaO+L _ ________________________

5CaO-3Al2O3+ 2CaO-SiO2+ CaO-AliAr^L __ _ _ _ _ ___________

3CaO-Al2O3 + 2CaO-SiO2 + 5CaO-3Al2O3 ^L_. _ _ __ _ _ _ __

Temperature (°C)

1345 

1368 

1165 

1512 

1307 

1553 

1265 

1310 

1335 

1387 

1380 

1545 

1475 

1900 

1552 

1380 

1505 

1455 

1470 

1335 

1335

Composition of liquid 

(percent by weight

CaO

9.8 

10.2 

23. 25 

15. 6 

34.8 

20. 16 

38 

47.2 

48.3 

30.2 

29.2 

49.6 

31.2 

68.4 

35 

48.3 

37.5 

58.3 

59.7 

49.5 

52. 0

A1203

18.6 

18. 5 

14.75 

36.5 

17.6 

36.65 

20 

11.8 

11.8 

36.8 

39.0 

23.7 

44.5 

9.2 

50.8 

42 

53.25 

33. 0 

32.8 

43.7 

41. 2

Si02

71.6 

71.3 

62. 0 

47.9 

47.6 

43. 19 

42 

41 

39i9 

33 

31.8 

26.7 

24.3 

22. 4 

14. 2 

9.7 

9.25 

8.7 

7.5 

6.8 

6.8

The point 7 is in error since the field 3CaO-SiO2 extends to the side CaO-SiO2 .

literature has been critically reviewed by Bogue (1955) 

and by Lea and Desch (1956). The phase-equilibrium 

diagram of figure 43 is based on the work of Rankin 

and Wright (1915) as modified by Greig (1927a), 

Osborn (1942), Schairer and Bowen (1947b) and 

Aramaki and Roy (1959). The invariant points are 

summarized in table 26.

There are three ternary compounds. One of these is 

2CaO-Al2O3 -SiO2 , corresponding to the mineral gehlenite, which melts congruently at 1590 °C and crystallizes readily. The second compound,

CaOAl2O3 -2SiO2 ,

corresponds to the mineral anorthite, the CaO-rich end 

member of the plagioclase feldspars, and melts congruently at 1553°C. The third ternary compound, 

3CaO-Al2O3 -SiO2 , decomposes at 1335°C, below the 

liquidus surface, and hence does not have a field of stability in figure 43. It is an example of a, condition which 

may not be uncommon; and the fact that a compound 

is not stable at the liquidus is not proof that it does not 

exist at lower temperature. Since Welch and Gutt 

(1959) found that 3CaOSiO2 melts incongruently 

(see p. 18), the field of 3CaOSiO2 should extend to 

the side CaO-SiO2 instead of terminating in an invariant point /, which is in error.

CaO-Fe2O3-SiO2

Burdick (1940) made a survey of this system which 

is of importance in the making of portland cement. No 

ternary compounds were found, and the fields of SiO2 ,

CaO-SiO2 , 2CaO-SiO2 , and CaO occupy most of the 

phase-equilibrium diagram, with small fields of 

3CaO 2SiO2 , 3CaO SiO2, and 2CaO Fe2O3. The ternary eutectic

3CaO-SiO2 +2CaO-SiO2 +2CaO-Fe2O3 =Z

is at 1414° C, and the eutectic

CaO + 3CaO SiO2 + 2CaO FeA = L

at 1411 °C. Compositions are not given, but are not 

far from the composition 46 percent CaO, 50 percent 

Fe2O3 , 4 percent SiO2 , the only mixture studied in the 

field of 2CaO-FeO3 . The study did not extend to the 

field of CaO-Fe2O3 or of Fe2O3 , and the composition 

of the liquid at the reaction

3CaO SiO2 = CaO + 2CaO SiO2

was not determined.

Phillips and Muan (1959) studied this system by the 

quenching method in air. The results are shown in 

table 27 and in figure 44 which is the projection onto 

the plane CaO-Fe2O3-SiO2 of the irregularly curved 

isobaric surface in air through the quaternary system 

CaO-FeO-Fe2O3-SiO2 . The composition of the liquids 

are within the subvolume CaO-Fe3O4-Fe2O3-SiO2 . 

The temperature along the hematite-magnetite boundary increases from 1358 °C when no SiO2 is present to 

1390° C at invariant point B in the diagram, indicating 

that magnetite takes some CaO into solid solution.

695-382 O - 64 - 6
L72 DATA OF GEOCHEMISTRY

CaO-Si02 

50

3CaO-2Si02

6Q 

2CaO-Si02

3CaO-Si02

sa

/

90

CaO 10 20 30 40 50 2CaO-Fe 203 

WEIGHT PERCENT Fe 203

CaO-2Fe203

FIGURE 44. Phase relations in the system CaO-FejOa-SiOj in air (Poj-0.21 atm). The system is not truly ternary, and this text figure represents an irregularly curved 

isobaric surface through the quaternary system CaO-FeO-Fe2O3-SiOs. Heavy lines are boundary curves with arrows pointing in the direction of falling temperatures; 

lines with stippling on one side are approximate outlines of composition areas where two immiscible liquids form above liquidus temperature. Boundary curves 

and isotherms are dashed in regions where their locations are uncertain. Modified from Phillips and Muan (1050).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER 

TABLE 27. Invariant points in the system CaO-Fe.Os-Si02

L73

Invariant 

point on 

fig. 44

A.. ..........

B ... .........

C............

D. ..........

E ---------

F .........

G..... .......

H. ..........

I............

Phase reactions

CaO.Si02 +Si02 +Fe203 ^L__-_ _ _ _ _--_. _ __________ __

SiO-j+Fe-A+FeaO^L---. ____ _____ ___ _ ______ ______

3Ca0.2Si02 +CaO.Si02 +Fe203^L-----------------_---------

3Ca0.2SiO_+Fe2 03 -^L+2CaO.Si02 _ ___ __ ____________ __

2CaO-Si02 +Ca0.2Fe2 03 +Fe203 ^L_. _ _ _ ____ ____________

2CaO-Si02 +Ca0.2Fe203^L + CaO.Fe203 --- __ ----- _ - ____

2CaO-Si02 +CaO.Fe203 ^L+2CaO.Fe2 03 -- ____ . _ _ _ __

3CaO.Si02 +2CaO.Fe2 03 -^L+CaO__ _______ _ _ ___ _ _____

3CaO.Si02 +2CaO.Si02 +2CaO.Fe203 ^L. _---___-_________--_

MAXIMUM ON BOUNDARY CURVES

CaO-Si02 +Fe203 -*L______ ___ ______ _ ______ __ _____

2CaO-Si02 +Fe2 03 ^L ______ ______ _ ___ ___ _ _ ___

2CaO.SiO_+Ca0.2Fe203 -^L____ _ _ _ _ _ _______ ___ _

Temperature (°C)

1204 

1390 

1214 

1230 

1216 

1192 

1195 

1412 

1405

1280 

1315 

1242

Composition of liquid (percent 

by weight)

CaO

24.0 

11.0 

345 

35. 0 

25.0 

26.5 

29. 0 

47. 0 

45.5

30.5 

245 

26.0

Fe208

28.5 

55.0 

38. 5 

39. 0 

65.0 

66.0 

66.0 

48.0 

48.0

37.0 

62.5 

66.0

Si02

47.5 

340 

27.0 

26. 0 

10.0 

7.5 

5.0 

5.0 

6.5

32. 5 

13.0 

8.0

CaO-SiO_-TiO2

The latest study of this system is by DeVries, Roy, 

and Osborn (1955). The phase-equilibrium diagram is 

figure 45, and the invariant points are in table 28. The 

ternary compound, CaO SiO2 TiO2, which corresponds 

to the mineral sphene, melts congruently at 1382 °C, and 

forms binary systems with CaO SiO2 , SiO2 , TiO2, and 

CaO TiO2 (perovskite). There is a large area in which

two liquid layers are formed. This sweeps from the 

side CaO-Si02 , with cristobalite as solid phase, to the 

boundary curve NN', where rutile becomes solid phase, 

and extends to the side SiO2-TiO2 . The compound 

3CaO-SiO2 has a small field of stability, ABD, in the 

ternary system, and the compounds 3CaO-2SiO2 and 

3CaO-2TiO2 , each of which melts incongruently, also 

have small stability fields.

TABLE 28. Invariant points in the system CaO-Si02-Ti02

Invariant 

point on 

fig. 45

A.. ..........

B-. ..........

C.-. .........

D. ..........

E. ..........

F..... .......

d... .........

H. .........

£.:::::::::::

h............

L...... ......

k... ........

P...........

N. ..........

N' --------

Phase reactions

3CaO.Si02 +3CaO-2Ti02 ^CaO + L_ _________________________

3CaO.Si02 +2CaO-Si02 +3CaO-2Ti02 -\L_---_- ___________ __

2CaO-Si02 +3CaO-2Ti02 ^CaO.Ti02 + L_-___ _-__ -----_-_-----

3CaO.Si02 -^CaO+2CaO.Si02+L - _____--___-_- ___________

3Ca0.2Si02 +CaO.Ti02 -k2CaO.Si02 +L___-------_-_--__-_-_-

3Ca0.2Si02 +CaO.Si02 +CaO.Ti02^L.___ _______ ____________

CaO.Si02 +CaO.Ti02 ^L_-_____-----__---_- -----___----__--

CaO-Si02 +CaO-Ti02 -Si02 + CaO-Ti02 ^L_ ___________ __ ____

CaO-Si02 +CaO-Ti02 -Si02 ^L--__- __ _ ___________ _ _ _ _

CaO-Si02 -|rSi02 +CaO.Ti02 -Si02 ^L- _________________ _______

CaO-TiOz-Si02+Si02^L_ _____________________ ___ _________

Si02 +Ti02 +CaO.Ti02 -SiO_-*L- ___--____-__-_ ____ _______

CaO-Ti02 -Si02 +Ti02 ^Z,-_____--_---____-----____- _________

CaO.Ti02 +CaO-Ti02 -Si02 +Ti02 ^L-___-----_ ___ _______ ___

Si02 (cristobalite) + Ti02 +Li__- ___ _ _ _________ ___ ____

Si02 (cristobalite) + Ti02 +L2 -_- ___ ___ _ _ _ ___ ----- _ -

Temperature (°C)

1670? 

1650 

1670? 

1900 

1403 

1398 

1424 

1348 

1353 

1318 

1373 

1365 

1375 

1365 

1535 

1535

Composition of liquid (percent 

by weight)

CaO

62.0 

61.0 

60.0 

65. 5 

52.3 

51.5 

46.6 

36.8 

36.7 

33.1 

25.8 

22.2 

23.0 

24.5 

15.5 

1.5

Si02

16.0 

17.5 

18.0 

26.5 

38.6 

39.2 

39.3 

37.0 

39.3 

49.4 

32.6 

29.0 

24.6 

18.0 

31.5 

88.0

Ti02

22.0 

21. 5 

22.0 

8.0 

9. 1 

9.3 

14 1 

26.2 

24.0 

17.5 

36.6 

48.8 

52.4 

57.5 

53 

10. 5
L74 DATA OF GEOCHEMISTRY

20 80

30

TWO-LIQUID 

BOUNDARY

CaO

50

3CaO-2SiO£ 

60

2CaO-S 102-7^2 CaO-Si O 

70

i02

/ 

80

90 10

10 20 30 40 X/50 ,H60 70 80

3CaO-2Ti02 CaO-Ti02

WEIGHT PERCENT Ti02 v 

FIGUEE 45. The system CaO-SiO»-TiOj. Modified from DeVrles, Roy, and Osborn (195s).

90 Ti02

The effect of temperature on the solid solution between FeOFe2O3 (magnetite) and FeOAl2O3 (hercynite) was studied by Turnock (1959) with results 

shown in figure 46. The work was done by the hydrothermal method, with />totai =.PH2o+.PH2) using a solid 

buffer to control the partial pressure of oxygen. Complete solid solution exists above 858°±8°C. Below this 

temperature the solid solution unmixes, and the amount 

of unmixing increases with decreasing temperature.

The reactions are sluggish, the effect of pressure on the 

solvus cannot be detected in the range from 1 to 4,000 

atmospheres, and H2O is not a component.

The effect of changes in the partial pressure of oxygen are oxidation and reduction reactions that change 

the species and bulk composition of the solid phases, 

as is shown by the diagram of figure 47. The tie lines 

connecting equilibrium assemblages in regions of two 

solid phases are also contour lines of the partial pressure of oxygen, with values increasing up to the 

hematite-corundum join.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L75

800

£5 500

3

Spinel solid solution

Fe 3 04 FeO-AI 2 03 

Magnetite ss + Hercynite ss

0 

Fe304

20 40 60 

WEIGHT PERCENT HERCYNITE

80 100 

FeO-AI203

FIGURE 46. The effect of temperature in limiting the amount of solid solution in the 

spinel series, FeaO4 to FeO-AhOs (hercynite). An isobaric section with a water 

pressure of 2,000 atm. Modified from Turnock (1959). ss, solid solution.

The system FeO-Al2O3-SiO2 was studied by Schairer 

and Yagi (1952) by heating the final mixtures in iron 

crucibles in a current of nitrogen. All mixtures contained Fe2O3 ; some contained as much as 9 percent. 

They state that while their results properly belong in 

the quaternary system Fe-Fe2O3-Al2O3-SiO2 , they are 

more conveniently and lucidly presented by neglecting 

the amount of Fe2O3 in the liquid, and calculating the 

total iron as FeO. Only one ternary compound is 

formed, 2FeO-2Al2O3 -5SiO2, called iron cordierite in 

analogy with the corresponding compound in the magnesia system. The phase-equilibrium diagram (fig. 48) 

and table 29 show iron cordierite to melt incongruently,

and to have a small narrow field, KLMNf The composition of the garnet almandine (3FeO'Al2O3 '3SiO2 ) 

is in the field of FeO-Al2O3 , and material of this composition becomes completely crystalline at the point M. 

Attempts to crystallize almandine, including hydrothermal methods, failed. Experiments with natural 

garnet high in almandine showed that the dissociation 

temperature is at least as low as 900°C and the dissociation is very sluggish. The side Al2O3-SiO2 was revised 

by Aramaki and Koy (1959).

FeO-Fe2O3-SiO2

Greig (1927b) gave an incomplete equilibrium diagram showing the extension of the region of immiscibility in the binary system FeO-SiO2 with the addition of 

Fe2O3 . The two-liquid surface was lowered from 1690° 

to 1665° C and the compositions of the two liquids in 

equilibrium with cristobalite at 1665°C were: FeO 2.38 

percent, Fe2O3 2.05 percent, and SiO2 95.6 percent; and 

FeO 31.7 percent, Fe2O3 36.7 percent, and SiO2 31.6 

percent. This is not an invariant point. Gurry and 

Darken (1950) published a tentative diagram for the 

equilibrium at 1600°C and 1 atm of oxygen, and at 0.2 

atm CO2 . Muan (1955) studied this system with varying oxygen pressures, obtained with oxygen at 1 atm, 

air, or mixtures of CO2 and H2, and the equilibrium 

constants used in the calculation of oxygen pressures 

are given. Kesults are shown in figure 49. At the 

eutectic J., the phase reaction is

SiO2 +2FeO SiO2 +Fe3O4 =Z 

at an oxygen partial pressure of 10"9 atm and 1140°C.

Fe 3°4

G +

Hematite ss-tMagnetite ss + 

Corundum ss

/ G+Fe+Wiistite 

/ + Hercynite ss

FeO

To Fe 

900°

FeO-AI203 AI203

Fe203

F*3°4

6 +

Hematite ss + 

Magnetite ss + 

Corundum ss

G+ 

Magnetite ss

+ Hercynite ss 

+ WUstite ss

G+Fe+Wiistite + 

Hercynite ss

FeO ToFe 2W 3

WEIGHT PERCENT AI 2 0 3

700°

G +

Magnetite ss + 

Hercynite ss + 

Corundum ss

FIGURE 47. Subsolidus relations in the system FeO-FejOr-AhOz. Isothermal sections at 900° and 700° C at a total water pressure of 2,000 atm. Modified from Turnock

(1959). ss, solid solution.
L76 DATA OF GEOCHEMISTRY 

TABLE 29. Invariant points in the system FeO-AljOa-SiOj

Invariant 

point on 

fig. 48

K. ..........

L ---------

N. ..........

M... ________

«/----__.___-_

a_____ ______

Phase reactions

2FeO.2Al2O3-5SiO2 ^SiO2 +3Al2O3-2SiO2 +L- ------------------

FeO-Al2O3+2FeO-2Al2O3-5SiO2 -i3Al2O3-2SiO2 +I,--------- _ __

2FeO.SiO2 +SiO2 +2FeO.2Al2O3 -5SiO2 -^L_----__------_-------

2FeO.SiO2 +2FeO-2Al2O3-5SiO2 -^FeO.Al2O3+L----------------

FeO.Al2O3+3Al2O3-2SiO2 ^Al2O3+L_____-__--___-_-------_-_.

2FeO.SiO2 + FeO.Al2O3-^L-:------_-_---_-------------------

Temperature (°C)

1210 

1205 

1083 

1088 

1380 

1150

Composition of liquid 

(percent by weight)

FeO

33.3 

33.9 

47.5 

47.7 

38.0 

67.4

A12O3

20 

20. 1 

12.0 

12.6 

27.0 

6.3

SiO2

46.7 

46.0 

40.5 

39.7 

35.0 

26.3

2FeO-2AI203-5Si02 

TRIDYMITE

90

WEIGHT PERCENT Si02 

FIGURE 48. The system FeO-AhOs-SiOz. Modified from Schairer and Yagi (1952).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L77

Fe 2 0 3

FeO 10 20 / 30 

2FeO-Si02

40 50 60 70

WEIGHT PERCENT Si02

FIGURE 49. The system FeO-FezOs-SiOs. Modified from Muan (19S5).

80 90 Si02

The liquid composition is: FeO 54 percent, Fe2O3 11 

percent, and SiO2 35 percent. At the eutectic B the 

phase reaction is Fe3O4 +2FeO-SiO2 + FeO=Z at 

Po2 =10-9- 9 atm, 1150°C. The FeO phase, a wiistite 

solid solution, contains 35 percent Fe2O3 and the liquid 

contains FeO 64 percent, Fe2O3 14 percent, and SiO2 22 

percent. A third eutectic 6r, Fe3O4 + Fe2O3 + SiO2 =Z, 

was inferred to be located at an oxygen pressure of 

slightly more than 1 atm and 1455°C, FeO 16 percent, 

Fe2O3 69 percent, and SiO2 15 percent.

Al2O3-SiOz-TiO2

Agamawi and White (1952) studied a part of the 

system Al2O3~SiO2-TiO2 by a survey determining cone 

fusion points, followed by quenching studies. The resulting diagram is figure 50. The field of cristobalite is 

adjacent to that of mullite, the compound Al2O3 'TiO2 

and TiO2 (rutile). The point R, at 1480°C is a reaction point, SiO2 + Al2O3 -TiO2 =3Al2O3 -2SiO2 +7;, 

with the liquid composition 8.2 percent A12O3 ,79.4 percent SiO2, and 12.4 percent TiO2. Point E at 1470°C
L78 DATA OF GEOCHEMISTRY

AI203 40 T

WEIGHT PERCENT Ti02 

FIGURE 50. The system AljOs-SiO»-TiOj. Modified from Agamawi and White (1952).

90 TiOg

is a eutectic, SiO2 +Al2O3 -TiO2 +TiO2 =Z, with the 

liquid composition A12O3 7.5 percent, SiO2 79.0 percent and TiO2 13.5 percent. The melting point of 

A12O3 TiO2 was not determined nor was the boundary 

between the fields of mullite and corundum. The join 

SiO2-Al2O3 TiO2 is not binary, since it crosses the field 

of mullite.

Galakhov (1958) confirmed the congruent melting of 

Al2O3 -TiO2 .

QUATERNARY SYSTEMS

Systems containing four components are usually represented by a regular tetrahedron, with each apex representing one component. Such a tetrahedron is composed of four or more primary phase volumes, each of 

which represents the compositions of all liquids which 

can coexist in equilibrium with a given solid phase. 

The boundaries between the volumes are surfaces representing the coexistence of two solid phases with 

liquid, and the meeting of four surfaces gives rise to a 

quaternary invariant point at which a liquid coexists 

with four solid phases. When the composition of the 

liquid at an invariant point lies within the tetrahedron 

formed by the compositions of the four solid phases, 

the invariant point is a quaternary eutectic; when the 

liquid is outside of that tetrahedron, the invariant point
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L79

is a reaction point. A special case is that of a phase 

inversion where a solid phase undergoes a polymorphous change without a change in composition. From 

a quaternary invariant point at constant pressure proceed four curves representing the change with temperature of a univariant equilibrium between a liquid and 

three solid phases.

Four-component systems usually are studied by means 

of sections through the tetrahedron produced by planes 

cutting the tetrahedron into triangles. Morey (1930d) 

has discussed the calculation of mixtures lying in a plane 

determined by any three compositions in the four-component system. The intersection of a plane with a primary phase volume gives rise to an area in the triangle ; 

the boundary surfaces between phase volumes give rise 

to traces of the boundary curves; and the univariant 

equilibrium between a liquid and three solid phases give 

rise to piercing points in the triangle. When the components of the plane have been so chosen that the composition of all phases in the triangle can be represented 

by positive amounts of these components, the piercing 

point becomes a eutectic and is a point of maximum 

temperature on the curve representing the change of 

composition with temperature of the univariant reaction 

in question. Such a section is a ternary system.

Details of the method of working out a quaternary 

system and of the interpretation of the planes 

through a tetrahedron and their relationship to each 

other are exemplified by the discussion of the system 

K2O-MgO-Al2O3-SiO2 .

The representation of this system is a tetrahedron is 

figure 51, in which is shown the plane

Na2O A12O3-K2O Al2O3-SiO2

which includes most of the known compounds. The 

compositions of the dehydrated micas, paragonite and 

muscovite, which do not lie in this plane, are shown by 

crosses. The position of the system Na2O A12O3 2SiO2 

(carnegieite, nepheline) -K2O A12O3 2SiO2 (kaliophilite)-SiO2 , published by Schairer (1950), is indicated. 

This diagram is reproduced as figure 52. The join 

Na2O A12O3 2SiO2-K2O A12O3 2SiO2

was studied by Bowen (1917). The composition 

Na2OAl2O3 -2SiO2

crystallizes as carnegieite, and takes into solid 

solution excess of both K2O A12O3 2SiO2 and 

Na2O-Al2O3 -6SiO2 , giving rise to a field of solid 

solutions which are terminated on the albite side by 

formation of a nepheline solid solution at 1280°C, on 

the K2OAl2O3 -2SiO2 side by formation of a Na-K

nepheline solid solution at 1404 °C. The inversion 

temperature of nepheline to carnegieite is raised 

by solid solution from 1250 °C in the pure compound 

to the intersection of the field of the Na-K nepheline 

with that of the field of the carnegieite solid solution. 

The field of the Na-K nephelines is terminated on the 

K2O side by a field of orthorhombic Na-K solid solutions. The complicated relationships in the solid' 

solutions in this binary system, both at and below the 

liquidus, have been discussed by Smith and Tuttle 

(1957). 

The alkali feldspars,

Na2O A12O3 6SiO2-K2O A12O3 6SiO2,

form a complete series of solid solutions, and this join 

is only in part binary, owing to the formation of leucite 

from 0 to 51 percent of Na2O-Al2O3 -6SiO2 . At this 

point the temperature is 1078°C. There is a minimum 

on the melting and freezing curves of these feldspars at 

1063°C and 35 percent K2O-Al2O3 -6SiO2 . Each of 

these ternary fields will have phase spaces in the quaternary system, but these regions have not been studied. 

The eutectic K2O-Al2O3 -4SiO2 + a Na-K nepheline+a 

Na-K feldspar=L is at 1020 °O and about 48 percent 

NaaO-AUVGSiOa, 20 percent K2O-Al2O3 -6SiO2 , and 

32 percent SiO2 .

The complex interrelationship among the alkali feldspars is yet to be explained. Tuttle and Bowen (1950) 

showed that there are two distinct modifications of 

Na2O-Al2O3 -6SiO2 , which they described as high-temperature and low-temperature albite. X-ray studies 

of albite (MacKenzie, 1957) crystallized in the presence 

of water at 450° to 1000°C, and at pressures ranging 

from 14,000 to 88,000 psi suggested that at each temperature there is a stable crystalline form of Na^O' 

Al2O3 -6SiO2 which is intermediate between high-temperature albite, stable only above 1000°C, and low-temperature albite, stable only below about 450°C. Bowen 

and Tuttle (1950) used bombs under a water pressure 

of 1000 to 2000 atm and found that solid solutions of the 

two feldspars unmixed at temperatures below the liquidus, and they determined the equilibrium curve for 

this unmixing. Smith and MacKenzie (1958) revised 

the equilibrium curve and discussed the crystallization 

history of some natural feldspars.

NazO-MgO-CaO-SiOz

Morey (1930b) studied the effect of MgO on the liquidus relationships of a glass of the mole composition 

1.15 Na2O-0-0.84CaO-6SiO2 , or 14.86 percent Na,O, 

9.83 percent CaO, 75.2 percent SiO2, liquidus 1085°C, 

primary phase tridymite. When 2.4 percent MgO was
L80 DATA OF GEOCHEMISTRY

KoO

Na20

:20-2Si02

90,

10

Na20-2Si02

WEIGHT PERCENT Si02 

FIGURE 51. Projection of the tetrahedron NasO-K^O-AljOs-SiOj on base Na2O-KsO-SiOj showing the position of the plane NajO-AljOs-KjO-AlsOj-SiOj.

added, the melting point was lowered to 895 °C with 

tridymite as primary phase. On further addition of 

MgO the glass passes into a narrow region of 

Na2O 3CaO 6SiO2 (devitrite) with a slight rise in temperature, after which the mixture passes into the region 

of CaO-MgO-2SiO2 (diopside) with rapid rise in liquidus temperature to 1218°C, at a glass composition of 

Na2O 12.4, MgO 16.7, CaO 8.2, SiO2 62.7. In contrast, 

when CaO was replaced by MgO, mole per mole, the

mixture remained in the tridymite field with much 

smaller lowering of the melting point. When MgO 

was completely replaced by CaO, giving a glass of the 

composition Na2O 16.1, CaO 7.1, SiO2 76.8, the liquidus 

was 1013°C. When a mixture of the composition 

(Na2O, MgO, CaO, 3SiO2 ) was crystallized, it gave a 

mixture of 50 percent CaO-MgO-2SiO2, some 

2MgO-SiO2 , and an unknown compound, hence this 

composition is not a stable compound at the liquidus.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER

Si02

LSI

K20-AI 203 -4Si02 

80

«<-Na20-AI2 03 -2Si02 

CARNEGIEITE

K20-AI203 -6SiO; 

K FELDSPAR

Na20-AI203 -6Si02

ALBITE

ORTHORHOMBIC 

(K20,Na20)-AI2 03 -2Si02

SOLID SOLUTIONS

K20-AI203 2Si02 

KALIOPHILITE

10 20 30 40 50 60 70 80 90

WEIGHT PERCENT Na2 0- - 2Si 02

No20-AI203 -2Si0 2

CARNEGIEITE 

NEPHELINE

FIOUBE 32. The system NajO-AljO3-2SiO» (carnegieite, nepheline)-KjO-AljO3-2SiOj (kaliophilite)-SiO2. Modified from Schairer (1950).

C, Gr, and /, respectively. Point 7 is a ternary eutectic 

at which the solid phases are albite, cordierite, and 

tridymite, and hence is a point of maximum temperature on the 4-component univariant curve along which 

these phases coexist with liquid. Mixtures near the 

binary eutectic F, between cordierite and albite, are 

viscous and require several weeks to reach equilibrium. 

The side albite-cordierite is not a binary system, since 

the field of spinel cuts across it, and cordierite melts 

incongruently with formation of mullite.

A study of the system Na2O-MgO-Al2O3-SiO2 was 

begun by Schairer (1957b), who studied three planes 

through the tetrahedron representing this system. One 

of these planes (fig. 53) is the system Na2O A12O3 6SiO2 

(albite) -2MgO 2A12O3 5SiO2 (cordierite) -SiO2 . 

This plane cuts the phase volumes of 

3Al2O3 -2SiO2 (mullite), cordierite, MgO2 -Al2O3 

(spinel), albite, tridymite, and cristobalite. Three lines 

of univariant equilibrium pierce this plane at the points
L82 DATA OF GEOCHEMISTRY

Si02 

SILICA

10,

171315°

,90

I470±IO°

40

50

I470±IO°

fl

60

1448+5°

80

1062 ±3° 

30

20

90

2MgO 2AI203 -5Si02 

CORDIERITE

10 20 30 40 50

WEIGHT PERCENT ALBITE

80 

1265+5°

90

10

1098+3°

1118+3°

Na20-AI203 -6Si02 

ALBITE

FIQUEE 53. The system NaiO-AliOs-6SiOj (albite)-2MgO-2AljOj-5SiOa (cordierite)-SiOj. This is part of the plane NajO-AljOs-MgO-AljOs-SiOa through the tetrahedron

NajO-MgO-AljOs-SiOj. Modified from Schairer (1957b).

Figure 54 is the system Na2O A12O3 6SiO2 (albite)- 

2MgOSiO2 (forsterite)-2MgO2Al2O3 -5SiO2 (cordierite) and is represented by part of a plane passing 

through the tetrahedron, and cutting the phase volume 

of forsterite, spinel, mullite, albite, and twice through 

the cordierite volume. N, O, and P are piercing points 

of univariant equilibria, and P is a ternary eutectic at 

which the solid phases are albite+forsterite+cordierite. The side forsterite-albite is a binary system, but 

neither of the other sides is binary because of the incongruent melting of cordierite.

Figure 55 is the system Na2OAl2O3 -6SiO2 (albite)- 

MgOSiO2 (enstatite)-2MgO-2Al2O3 -5SiO2 (cordierite) , and it also is part of a plane through the tetrahedron. This plane cuts the phase volumes of 

2MgOSiO2 (forsterite), MgOSiO3 (protoenstatite), 

albite, cordierite, spinel, and mullite, and there are 

three piercing points of univariant equilibria, at £7, 

F, and W. None of the sides of this triangle is a 

binary system. Schairer and Yoder (1959) studied the 

system Na2O A12O3 2SiO2 (carnegieite, nepheline)- 

MgO A12O3 (spinel )-SiO2 , with results shown in figure
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L83

2MgO-2AI203 -5Si02 

CORDIERITE

146812°

3AI2 03 -2Si02 

MULLITE

1890120°

40 

137413°

126515°

A 109813° 

|095±3VA ALBITE

A

2MgO-Si02

FORSTERITE

V

10

V

20

V

30

V

40

WEIGHT

V

50

PERCENT

V

60

ALBITE

v \

70 80

\ \ f M 11813°

90 ^109813°

No20-AI203-6Si02

ALBITE

FIGURE 54. The system ^O-AhOa-BSiOj (albite)-2MgO-SiOs (forsterite)-2MgO-2AhO3-5SiOj (cordierite). This is part of a plane through the tetrahedron NajO-MgOAljOs-SiOj. Modified from Schairer (1957b).

56. This plane through the tetrahedron cuts the phase 

volumes of carnegieite and nepheline, which are the 

high- and low-temperature forms of Na2O Al2O32SiO2 , 

of spinel, mullite, cordierite, albite, and the two forms 

of silica, tridymite and cristobalite. There are six 

piercing points of univariant equilibrium, C, G, /, K, L, 

and O, temperatures of which are shown in a tabular 

insert in the figure. The side MgO Al2O3-SiO2 is not 

a binary system because of the appearance of a field of 

mullite.

All compositions in the triangle nepheline-spinelalbite become completely crystalline at the ternary 

eutectic L ; those in the triangle albite-spinel-cordierite 

become completely crystalline at the ternary reaction 

point K; those in the triangle albite-cordierite-silica 

become completely crystalline at /. Since Z, K, and / 

are near the side nepheline-silica, residual liquids from 

crystallization are poor in spinel or corundum or both 

and rich in albite or nepheline or both. Compositions 

on the silica side of the line albite-spinel which are in
L84 DATA OF GEOCHEMISTRY

2MgO-2AI203 -5Si02 

CORDIERITE

40 

136313° ,CS

1397+5°,

90

MgO-Si02 

ENSTATITE

10 20

WEIGHT PERCENT ALBITE

I098±3° 

ALBITE 

III8±3°

109713°

Na20-AI203 -6Si02 

ALBITE

FIGURE 65. The system NajO-AhOa-eSiCh (albite)-MgO-Si02 (enstatite)-2MgO-2Alz03-5SiOj (cordierite). This is part of a plane through the tetrahedron NajO-MgOAlzOs-SiOj. Modified from Schairer (1957b).

the triangle albite-spinel-cordierite have a residual 

liquid at K, which lies on the nepheline side of albitespinel. If the residual liquid were separated from 

early-formed crystals, it would give a nepheline-bearing product of crystallization.

Schairer and Yoder (1960a) have published a preliminary diagram of the system Na2OAl2O3 -6SiO2 

(albite)-2MgO-SiO2 (forsterite)-SiO2 (fig. 57).,

Heavy lines are the boundary curves between the several solid and liquid phases. The tieline albite-enstatite 

divides the system into two parts. All compositions in 

the triangle albite-forsterite-enstatite become completely crystalline at the temperature of the point H 

(1098°rfclO°C). Those in the triangle albite-enstatitesilica become completely crystalline only at the temperature of the eutectic /, which has not been determined.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L85

B =

c -- G =

H =

/ =

J =

K --

L = 

M =

N =

0 =

P =

MgO-AI203 

SPINEL

2I35±20£

10 90

A = I448±5°

1526+2°,

1470 ±10°

I438±5°

I345±5°

106213°

I045±IO°

I470±IO°

109515°

105515°

I068±5°

12801°

12801°

About 1490°

2MgO-2AI203 -5Si02 

CORDIERITE

B

80, 20

90 10

171315°

10 80 J 90

Na20-AI203 -2Si02 

NEPHELINE

Si02 

SILICA

40 \ 50 

Na20-AI203 -6Si02

ALBITE 

111813°

WEIGHT PERCENT Si02

FIGURE 56. The system NasO-AljOj^SiOz (carnegieite nephelineJ-MgO-AhOa (spinel)-SiO2. This is part of a plane through the tetrahedron NajO-MgO-AljOs-SiOz

Modified from Schairer and Yoder (1958).

Na2O-CaO-Al2 O3-Fe2O3

Planes through the system Na2O-CaO-Al2O3-Fe2O3, 

which are indicated in figure 58, were studied by Eubank and Bogue (1948). One plane, the pseudoternary

system CaO-the arbitrary composition (Na2O,3Al2O3 )- 

4CaOAl2O3 -Fe2O3 is shown as an equilateral triangle 

in figure 59. No invariant points appear in this plane, 

but rather piercing points of univariant equilibrium in
L86 DATA OF GEOCHEMISTRY

2MgO-SI02 

FORSTERITE

189012O*

[MgO-Si02

IENSTATITE [PROTOENSTATITE

±2°

I543i2"

WEIGHT PERCENT Si02

FIGURE 67. Preliminary diagram of the system NajO-AljOs-6SiOj (albite)- 

2MgO-SiOj (forsterite)-SiOz. Modified from Schairer and Yoder (1960a).

the quaternary system. Point Z, at 1390°±10°C is the 

piercing point of the univariant equilibrium

CaO+4CaO A12O3 Fe2O3 +Na2O 8CaO 2 A12O3 =L.

The composition of the liquid is 2.3 percent Na2O, 48.4 

percent CaO, 26.8 percent A12O3, and 22.3 percent 

Fe2O3 ; or 17 percent CaO, 67 percent 

4CaO-Al2O3 -Fe2O3 and 16 percent (NaASAUX). 

The composition of the compound Na2O 8CaO 3A12O3 

is not in this plane. The solid phases at point H, 

1399°±5°C are 4CaO A12O3 Fe2O3ss, 5CaO-3Al2O3 , 

and Na2O-8CaO-3Al2O3 . The composition is 4.7 percent Na2O, 44 percent CaO, 34.2 percent A12O3 , and 

17.1 percent Fe2O3 ; or 20 percent CaO, 52 percent 

4CaO A12O3 Fe2O3 and 28 percent (Na2O,3Al2O3 ). At 

point K the solid phases are Na2O 8CaO 3A12O3 + 

5CaO-3Al2O3 +2Na2O-3CaO-5Al2O3 , the composition 

of which is not in the plane. The temperature is 

1410°±10°C, the composition 7.8 percent Na2O, 48.2 

percent CaO, 32.8 percent A12O3 , and 7.2 percent FeaOs; 

or 32 percent CaO, 22 percent 4CaO-Al2O3-Fe2O3, and 

46 percent (Na2O,3Al2O3 ).

There is a small field of A12O3 extending over the 

composition (Na2O, 3A12O3 ). In the plane CaO-

(A12O3 -FeaOsJ-AlaOs there is a region of 3CaO-Al2O3 , 

which has been replaced in the plane

CaO- (Na2O 3A12O3 ) -4CaO A12O3 Fe2O8 

by the region of Na2O 8CaO 3A12O3, so between these 

planes will be an invariant point. To locate this point, 

a series of planes were explored by adding increasing 

amounts of Na2O to the ternary system CaO5CaO-3Al2O3-2CaO-Fe2O3 shown in figure 58. The 

planes containing 2 and 4 percent Na2O did not show 

Na2O'8CaO-3Al2O3 as primary phase, but planes containing 6, 5, and 4.5 percent Na2O did cut its primaryphase region, the section of which at 6 percent was 

narrow and elliptical, extending from about 3 to 22 

percent 2CaO Fe2O3 . At the invariant point the Na2O 

content is taken as about 4.2 percent.

Na2O-CaO-Al2O3-SiO2

The first study of the system Na2O-CaO-Al2O3-SiO2 

was the classic one by Day and Alien (1905) of the 

plagioclase feldspars, which was the first paper published by the Geophysical Laboratory of the Carnegie 

Institution of Washington. This work, started in the 

laboratories of the U.S. Geological Survey, led to the 

establishment of the Geophysical Laboratory and demonstrated that exact physiochemical methods could be 

applied to the study of problems in geology. The paper 

by Day and Alien was followed by the work of Bowen 

(1913) who applied the newly developed quenching 

method. Figure 60 is by Bowen, modified by some unpublished results by J. F. Schairer. The position of the 

line CaO-Al2O3 -2SiO2-Na2O-Al2O3 -6SiO2 is indicated 

by a broken line in figure 61.

This system, of fundamental importance in geochemistry, is a classic example of a complete solid-solution series showing neither a maximum nor a minimum. 

When, for example, a molten mixture of 60 percent of 

albite and 40 percent anorthite is cooled, at about 

1420 °C, crystals of plagioclase feldspar separate of 

composition given by the point on the lower or solidus 

curve at 1420 °C, approximately 25 percent albite and 

75 percent anorthite. On further cooling, the composition of the liquid follows the upper or liquidus curve, 

and the composition of the solid follows the solidus 

curve. At about 1200 °C the mixture solidifies completely to a solid solution of composition 60 percent 

albite and 40 percent anorthite.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L87

3CaO 5AI2

5CaO-3AI20.

3CaO-AI203

CaO 2CaO-Fe203

FIGURE 58. The system NajO-CaO-AljOs-FejOs, showing the position of planes which have been studied.

Fe2°3

The pioneering work of Day and Alien and Bowen 

was followed much later by several studies which have 

given a comprehensive knowledge of the phase equilibrium relationships in this system. Figure 61 indicates the relation of each of these studies to the system 

as a whole.

Foster (1942) studied the system

 A12O3 2SiO2-CaO SiO2-Na2O A12O3 6SiO2

with results indicated in figure 62. This is a plane 

through the tetrahedron of figure 61, and shares a side, 

CaO-SiO2-Na2O-Al2O3 -2SiO2 , with the two following 

systems. The side CaO - SiO2-Na2O A12O3 2SiO2 is a 

binary system, with a eutectic at 1164°±2°C, 59 percent Na2OAl2O3 -2SiO2 (7.0 percent Na2O, 20.2 percent CaO, 11.5 percent A12O3 , and 61.3 percent SiO2 ). 

The nepheline-carnegieite inversion is raised 13°C by 

between 5 and 10 mol percent solid solution in nepheline,

695-382 O - 64 - 7
L88 DATA OF GEOCHEMISTRY

CaO

90

Na20, 3AI 203 10 20 30 40 50 60 70 80 4CaO-AI2 03 -Fe 2 03

WEIGHT PERCENT 

FIGUEE 59. The pseudoternary system CaO-the composition NajO^AljOs-the compound 4CaO-AlsO3-Fe2Oa. Based on Eubank and Bogue (1948).

practically none in carnegieite. The join CaO-SiO2- 

Na2O A12O3 6SiO2 is not binary. Pseudowollastonite 

crystallizes out with lowering liquidus temperatures 

until at 1125°C and about 89 percent albite a plagioolase feldspar of undetermined composition separates. 

The boundary between the fields of a- and /?-CaO-SiO2 

(pseudowollastonite and wollastonite) is the line of constant temperature 1125°C, since there is no solid solution. The fields of a- and jff-Na2OAl2O3 -2SiO2 are 

separated by an inversion line, but solid solution in 

nepheline raises the inversion to 1267 °C in the binary 

system Na2O Al2O32SiO2-CaO SiO2 , and 1280°C in 

Na2O A12O3 2SiO2-Na2O A12O3 6SiO2 . The composition Na2O -Al2O3 -6SiO2 is surrounded by an almost flat 

field of plagioclase feldspar, and the points at which 

these fields of wollastonite, plagioclase, and nepheline
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L89

1600

1500

1400

1300

1200

II 18 

1100

1000

LIQUID

PLAGIOCLASE

EXPLANATION

Points by Bowen

OD 

Points by Schairer

Lower Curve

First indication of glazed grain

O 

First indication of fritted grain

1553°

20 30 40 50 60 70 80 90

Na^O-Al20 3 -6Si02 

ALBITE

CaO-AI2 03-2SI02 

ANORTHITE

WEIGHT PERCENT ANORTHITE

FIGURE 60. The system Na»O-AljOs-6SiOj (albite)-CaO-Al2O3 -2SiOj (anorthite). Based on Bowen (1913) with additional points by J. F. Schairer (written communication,

1960).

solid solutions meet is not an invariant point, but the 

piercing point in this plane of the invariant equilibrium 

containing these three solids and a liquid.

A second plane through this quaternary system is 

NaO A12O3 2SiO2-CaO SiO2-CaO A12O3 2SiO2 (fig. 

63) studied by Gummer (1943). This shares a side, 

Na*O-Al2O3 -2SiO2-CaO-SiO2 , with the preceding and 

following diagrams. The primary phase fields occuring in the plane are: (1) CaOSiO2 , as a-CaOSiO2 

(pseudowollastonite); (2) plagioclase feldspar, largely

anorthite (CaO-Al2O3 -2SiO2 ), but containing some 

Na2O A12O3 6SiO2 in solid solution; (3) the two forms 

of Na2O A12O3 2SiO2 (carnegieite and a nepheline solid 

solution) with the inversion temperature ranging from 

1267° to 1352° C; (4) a field indicated as ^-alumina, 

resulting from a decomposition reaction which makes 

this section no longer ternary; and (5) a field indicated 

as 2CaO A12O3 SiO2 (gehlenite), which has a primary 

phase field in the boundary system CaO-Al2O3-SiO2 . 

There is a maximum on the boundary curve between the
L90 DATA OF GEOCHEMISTRY

CaO

2CaO-Si02

CaO-Si02

Na,0

Na20-AI20

Na20-AI203 -2Si02

'AI 2 03 -Si02 

'3AI203 -2Si02

(Na 2 0-3AI203

AI 2 03 

FIGURE 61. The tetrahedron representing the system NaaO-CaO-AlsOs-SiOj showing the numerous planes which have been studied.

Si02
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L91

CaO-Si02 

WOLLASTONITE

Na2 0-AI203 -2Si0 2

CARNEGIEITE 

NEPHELINE WEIGHT PERCENT

Na2 0-AI203-6Si02 

ALBITE

FGURE 62. The plane NajO-AljOs-2SiOj (carnegieite, nepheline)-CaO-SiOj (wollastoniteJ-NajO-AhOa-eSiOs (albite) through the tetrahedron ^O-CaO-AhOs-SiOj.

Modified from Foster (1942). ss solid solution.

the fields of pseudowollastonite and nepheline solid solutions. Since there is no solid solution in the CaO SiO2 , 

the composition of the nepheline solid solution in equilibrium with pseudowollastonite at this point of maximum temperature must be on the line passing through 

CaO SiO2 and this point.

A third section, Na2O SiO2-CaO SiO2- 

Na2O-Al2O3 -2SiO2 (fig. 64), through the tetrahedron 

Na2O-CaO-Al2O3-SiO2 studied by Spivak (1944), 

shares the side Na2O-Al2O3 -2SiO2-CaO-SiO2

with the two preceding sections, and the side 

Na2O SiO2-CaO SiO2 was worked out by Morey and 

Bowen (1925). No new compounds are formed and the 

system is ternary except that the compositions of some 

of the nepheline solid solutions require the inclusion of 

CaO A12O3 2SiO2 , which is outside of this section. The 

field of CaO-SiO2 is entirely pseudowollastonite, and 

is bounded by the fields of Na2O 2CaO2 3SiO2 and 

nepheline solid solutions. The ternary eutectic, E^ 

Na2O 2CaO 3SiO2 + CaO SiO2 + nepheline solid solutions containing 8 percent CaO-Al2O3 -2SiO2 =Z
L92 DATA OF GEOCHEMISTRY

CaO-SiOg 

WOLLASTONITE 

, 1544°

30.

20 30 40

CARNEGIEITE 

NEPHELINE

50

WEIGHT PERCENT

60 70 80 90

CaO-AI203 -2Si02 

ANORTHITE

FIGURE 63. The plane NazO-AUO8-2SiOz (carnegieite, nepheline)-CaO-SiOz (wollastonite)-CaO-AhO8 -2SiO> (anorthite) through the tetrahedron NajO-CaO-AljOs-SiOs

Modified from Gummer (1943). ss solid solution.

is at 1120° ±3°C, 13.6 percent Na2O-SiO2 , 39.4 percent 

CaO SiO2 , and 47.0 percent Na2O A12O3 2SiO2 . The 

field of Na2O t 2CaO t 3SiO2 occupies a large part 

of the phase triangle, and spreads over the composition of 2Na2OCaO3SiO2 . At point R, 985°d=8°C, 

the reaction is 2Na2OCaO-3SiO2 +nepheline solid 

solution containing 5 percent CaO < Al2O3 t 2SiO2 := 

Na2O-2CaO3SiO2 + £ and the liquid is 47.8 percent 

Na2OSiO2 , 8.8 percent CaO-SiO2 , and 42.5 percent

Na2OAl2O3 -2SiO2 . The join Na2O2CaO3SiO2- 

Na2O-Al2O3 -2SiO2 is not a binary system because of 

solid solution, and the maximum on the boundary 

curve at 1128°C is not on the join but at 35.5 percent CaO-SiO2 . The narrow field of the incongruently melting 2Na2O CaO 3SiO2 falls to a eutectic, #2 , Na2O-SiO2 + 2Na2O-CaO-SiO2 + nepheline 

solid solution containing approximately 1 percent 

CaOAl2O3 -2SiO2 =Z, at 892°±2°C, 51.8 percent
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L93

CoO-SiOg 

WOLLASTONITE

40

80

10 30 40 50 

WEIGHT PERCENT

60 70 80 90

Na20-AI203 -2Si02

CARNEGIEITE 

NEPHELINE

FIGURE 64. The plane NajO-SiO2-CaO-SiOs (wollastonite)-Na2O-A)2O3-2SiO} (carnegieite, nepheline) through the tetrahedron NasO-CaO-AljOs-SiOz. Modified from

Spivak (1944). sn solid solution.

Na2O-SiO2, 2.8 percent CaOSiO2, and 45.4 percent 

Na2O Al2O3 2SiO2. The temperature of the inversion 

of nepheline to carnegieite is lowered in the system 

Na2O-SiO2-Na2O-Al2O3 -2SiO2 because of the solid 

solution in carnegieite, and in the system CaO-SiO2- 

Na2O-Al2O3 2SiO2 it is raised by solid solution in 

nepheline.

The join Na2OAl2O3 -2SiO2 (carnegieite, nepheline )-2CaO-Al2O3 -SiO2 (gehlenite) was studied by 

Smalley (1947) and the plane Na2OAl2O3 -2SiO2 

(carnegieite, nepheline) -CaO SiO2 (wollastonite) - 

2CaO-Al2O3 -SiO2 (gehlenite) by Juan (1950). This 

plane is not a ternary system because both carnegieite 

and nepheline form solid solutions of composition out-
L94 DATA OF GEOCHEMISTRY

lOCaO AI,0,-2SiO,

10 20 

90CaO-Si02 

IOCaO-AI2Ov2Si02

30 40 50/60 70 

1179°

WEIGHT PERCENT IOCaO-AI203 -2Si02

FIGURE 65. The plane obtained by adding 10 percent CaO -AljO3-2SiO2 to the 

plane Na2O-Al2Os-2SiO2-CaO-SiO2-2CaO-Al2O3-SiO2 through the tetrahedron 

Na2O-CaO-Al2Os-SiO2. Modified from Yoder (1952b). ss, solid solutionSide of this plane, and the phase spreading out from 

2CaO-Al2O3 -SiO2 is not gehlenite but a melilite solid 

solution. The piercing point of the univariant equilibrium a-CaOSiO2 (pseudowollastonite) + nepheline 

solid solutions + melilite solid solutions + liquid is at 

1174°C and the composition of the liquid is approximately 54 percent Na2O A12O3 2SiO2 , 37 percent 

CaOSiO2 , 9 percent 2CaO-Al2O3 -SiO2 . There is a 

maximum temperature on the trace of the boundary between the phase volume of CaOSiO2 and nepheline 

solid solutions at 1182°C and about 6 percent of 

2CaO-Al2O3 -SiO2 .

A similar maximum was found by Gummer (1943) in 

his study of the plane

CaO SiO2-Na2O A12O3 2SiO2-CaO A12O3 2SiO2 .

Yoder (1952b) added 10 percent CaOAl2O3 -2SiO2 to 

this plane,

Na2O A12O3 2SiO2-CaO SiO2-2CaO A12O3 SiO2 , 

and located the piercing point of the equilibrium 

a-CaO-SiO2 (pseudowollastonite) + nepheline solid 

solution + melilite solid solution + liquid at 1173°C. 

His results are shown in figure 65, in which are shown 

the boundaries of the fields of pseudowollastonite, 

melilite solid solutions, nepheline solid solutions, and 

carnegieite solid solutions. The temperature maximum 

on the trace of the pseudowollastonite-nepheline solid 

solution boundary found by Juan and by Gummer 

has disappeared on the addition of 10 percent of 

CaO-Al2O3 -2SiO2 .

Goldsmith (1947) studied the plane

CaO A12O3 2SiO2-2CaO A12O3 SiO2-

Na2O-Al2O3 -2SiO2.

The phase-equilibrium diagram (fig. 66) is not 

ternary. The plane cuts the primary-phase volumes 

of a calcic plagioclase feldspar extending from 

CaO A12O3 2SiO2 , of a melilite solid solution extending 

from 2CaO-Al2O3 -SiO2 , and of carnegieite and nepheline solid solutions extending from Na2O-Al2O3 -2SiO2 . 

There is a slight maximum on the trace of the 

boundary surface between melilite and nepheline 

solid solutions, and the piercing point of the 

univariant-equilibrium plagioclase feldspar (melilite), 

nepheline solid solutions, and liquid is at 1266°C, 

39.5 percent CaO A12O3 2SiO2 , 27.5 percent 

2CaO-Al2O3 -SiO2 , and 33 percent Na2O-Al2O3 -2SiO2 . 

There is another piercing point, at which the phases are 

plagioclase feldspar, a nepheline solid solution, and 

/?-Al2O3 . Goldsmith also located the piercing point of 

the univariant-equilibrium plagioclase feldspar+melilite solid solution+nepheline solid solution + liquid in 

the plane obtained by adding 10 percent CaO SiO2 to 

the plane

CaO A12O3 2SiO2-2CaO A12O3 SiO2-

Na2O-Al2O3 -2SiO2 .

The temperature is 1248 °C and the composition of the 

liquid is 35.7 percent CaO-Al2O3 -2SiO2 , 17.8 percent 

2CaO-Al2O3 -SiO2 , 36.5 percent Na2O-Al2O3 -2SiO2 , 

and 10 percent CaO SiO2.

Schairer (1957a) published a preliminary diagram 

of the section

Na2O A12O3 2SiO2-CaO A12O3 2SiO2-SiO2

(fig. 67). This is not a ternary system because of the 

occurrence of a field of alumina in the diagram. The 

section is dominated by the large field of plagioclase 

feldspar.

Morey (1930c) replaced CaO by A12O3 , mole for 

mole, in a glass of the composition 1.15 Naj>O, 0.84 CaO, 

6SiO2 and found that the liquidus fell from 1075°C 

with tridymite as solid phase, to 990°C, where 

Na2O-3CaO-6SiO2 (devitrite) became a solid phase, 

after which it rose to a maximum of about 1030°C with 

about 8 percent A12O3 , then fell to about 1000°C at 12 

percent A12O3 , when CaO-SiO2 became a solid phase, 

after which temperatures rose uniformly until at about 

1060°C, 17 percent A12O3, when Na2O-Al2O3 -6SiO2 

became a solid phase. When A12O2 was added to the
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L95

ANORTHITE

2CaO-AI203 -Si02 10 

GEHLENITE

20 30 40 50 60 

WEIGHT PERCENT CARNEGIEITE 

NEPHELINE

FIGTTBE 66. The plane CaO-Al2O3 -2SiO2 (anorthite)-2CaO-Al2O3 -SiO2 (gehlenite)-Na2O-AhO3-2SiO2 (carnegieite, nepheline) through the tetrahedron Na2O-CaO-Al2O3-SiO2.

Modified from Goldsmith (1947). ss, solid solution.

above glass, a narrow field of devitrite was met, followed 

by a field of CaO-SiO2 , The final mixture of this series 

had the composition 13 percent Na2 0, 10.0 percent CaO, 

9.1 percent A12O3 , 67.9 percent SiO2 , liquidus 1156°C 

with CaO SiO2 as primary phase.

Greene and Bogue (1946) studied two planes high in 

CaO. One was the plane

CaO-2CaO SiO2-

and in it appear the compounds 

and 2Na2O -3CaO 5A12O3 . The field of

Na2O-8CaO-3Al2O3

O3 ) ,

 8CaO 3A12O

is very narrow, and the univariant reaction point 

2CaO-SiO 2 , 3 C a O A1 2 O 3 , 5CaO-3Al 2 O 3 , 

Na2O-8CaO-3Al2O3 , and liquid is slightly outside the 

plane of this diagram, at 3.5 percent Na2O, 50.2 percent 

CaO, 37.6 percent A12O3 ,8.7 percent SiO2 ; 1365°±10°C. 

The phase 2Na2O 3CaO 5A12O3 is probably a member 

of a solid-solution series, which occupies a larger area in 

the section CaO-2CaO SiO2- (Na,O+3A12O3 ). 

From results in this section it is estimated that the 

liquid at the univariant point CaO, 3CaO'SiO2 , 

Na2O-8CaO-3SiO2 has the composition 50 percent 

Na2O, 54.1 percent CaO, 28.6 percent A12O3 , 12.3 percent SiO2 , at 1445°=blO°C. Another reaction point out-
L96 DATA OF GEOCHEMISTRY

CaO-AI203 -2Si02 

ANORTHITE

I553±2°

90 10

80 20

30

.40

I368±2° 

50

1470110°

1526+2

CARNEGIEITE 

NEPHELINE

I7I3±5C

1470+10° 90

Na20-Al203 -6Si02 

ALBITE

WEIGHT PERCENT Si02

Si02 

SILICA

FIGURE 67. The plane Na2O-AljO3-2SiOs (carnegieite, nepheline)-CaO-AUO3-2SiOz (anorthite)-SiOz through the tetrahedron NazO-CaO-AljOs-SiC^. Modified from preliminary diagram by Schairer (1957a).

side this plane is at 1440°±10°C and the solid phases 

are 2CaO-SiO2 , 3CaO-SiO2 , 3CaO-Al2O3 and 

Na2O-8CaO-3Al2O3 , and the liquid, 3.5 percent Na2O, 

55.2 percent CaO, 31 percent A12O3 , 10.3 percent SiO2. 

Another plane studied was CaO-2CaO SiO2- 

Na2O-Al2O3 . Na2O-Al2O3-2CaO-SiO2 is a binary 

system with a eutectic at 1405° ±10° C, and 61 

percent 2CaO-SiO2 , or 14.7 percent Na2O, 39.7 

percent CaO, 24.3 percent A12O3 , 21.3 percent 

SiO2 . This section is essentially ternary, with

the exception of a small amount of solid solution 

in 2CaO-SiO2 and probably in Na2O-Al2O3 . The ternary eutectic CaO+2CaOSiO2 +Na2O-Al2O3 =Z is at 

1355°±10°C and the liquid composition is 28 percent 

Na2O-Al2O3 , 16 percent CaO, 56 percent 2CaO-SiO2 , 

or 11 percent Na2O, 52 percent CaO, 17 percent A12O3 , 

20 percent SiO2 . This part of the quaternary system 

contains much solid solution and is difficult to work 

with because of the volatilization of Na^O at the high 

temperature necessary to melt the mixtures.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L97

Eubank and Bogue (1948) explored a plane in this 

system, obtained by adding 5 percent Na2O to the system CaO-2CaO SiO2-CaO Fe2O3 . No ternary compounds were found. Compositions near the 

2CaOSiO2-CaOFe2O3 join near 2CaOSiO2 were 

very refractory and showed little liquid at 1550° C. 

As the composition contained increasing amounts of 

2CaOFe2O3 , the amount of liquid increased, and a 

mix containing 31.5 percent CaO was completely liquid 

at!320°C. No 3CaOSiO2 was found.

Bo wen and Schairer (1936, 1938) studied the system 

Na2O-Al2O3 -2SiO2-FeO-SiO2-SiO2 , which is part of

the plane Na2OAl2O3 -2SiO2-FeO-SiO2 through the 

tetrahedron Na2O-FeO-Al2O3-SiO2 , and this is a part 

of the larger plane Na2O A12O3 + FeO+SiO2 . The relations in the ternary section Na2OAl2O3 -2SiO2-FeOSiO2 are shown in figure 68, which is only in part ternary because of the apperance of a field of FeOAl2O3 

(hercynite). Moreover, the melts always contained 

some Fe2O3 , in amount determined by analysis, but the 

amount is small and the presentation of the results is 

greatly facilitated by calculating all the iron as FeO. 

The largest field in the diagram of figure 68 is that of 

2FeOSiO2 (fayalite), which forms a binary system 

with Na2O A12O3 6SiO2 (albite), with a eutectic at 

1050 °C and 84 percent albite. The ternary eutect>

No 2 0 AI2 03 -6Si02 

ALBITE ~~~~

Na2 0-AI203-2Si02

CARNEGIEITE

NEPHELINE

40 50 60 

WEIGHT PERCENT FeO

90 FeO

FIGURE 68. The plane NajO-AlsOa-28iOi (carnegjeite, nephelineJ-FeO-SiOj through the tetrahedron NajO-FeO-AlsOs-SiOs. Modified from Bowen and Schairer (1938).
L98 DATA OF GEOCHEMISTRY

Na2O-Al2O3 -6SiO2 + SiO2 +2FeO-SiO2 =Z is at 34 

percent Na2O-Al2O3 -2SiO2, 4.5 percent FeO, 61.5 percent SiO2 , and 980°C, and the eutectic

Na2O A12O3 2SiO2 +Na2O A12O3 6SiO2

+2FeO-SiO2 =Z

at 60.5 percent Na2O-Al2O3 -2SiO2 , 9.0 percent FeO, 

30.5 percent SiO2 , and 990°C. The point in this diagram at which the fields of nepheline, fayalite, and 

hercynite meet, which is a piercing point for the univariant equilibrium in the quaternary system, is at about 

56.5 percent Na2OAl2O3 -2SiO2 , 23 percent FeO, 20.5 

percent SiO2 , and 1090°C. The join

is not binary because 

of the crystallization of hercynite and wiistite.

K2O-MgO-Al2Og-SiO2

Schairer (1954) studied the phase-equilibrium relations in four planes in the tetrahedron representing the 

system (fig. 69), and in a later paper, Schairer (1955) 

gave results of the study of two additional planes.

The plane 2MgO SiO2 (forsterite)- 

K2O-Al2O3 -4SiO2 (leucite)-SiO2 through the tetrahedron K2O-MgO-Al2O3-SiO2 is shown in figure 70. 

This is a ternary system, since the composition of all

KoO

MgO 2MgO-Si02 MgO-SiOg Si02 

FIGURE 69. Diagrammatic representation of the tetrahedron KjO-MgO-A^Os-SiOj, showing planes through it which have been studied.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L99

2MgO-Si02 

FORSTERITE

1890 ±20e

MgO-SiOa 

ENSTATITE 

I557±2°

154312°

169515°

I686±5°

TWO 

LIQUIDS

I493±5°

4O C E 990±20° 70 

FELDSPAR FIELD TRIDYMITE FIELD

90

1695+5° 

1713+5°

LEUCITE

SILICA 

WEIGHT PERCENT 

FIGURE 70. The plane K2O AljOs -4SiO8 (leucite)-2MgO SiO8 (forsterite)-SiOj through the tetrahedron KiO-MgO-AhOj-SiOa. Modified from Schalrer (1954).

the phases which appear in crystallization may be expressed in terms of positive amounts of the components 

and hence any of the quaternary univariant curves 

which pierce it will have a point of maximum temperature in this plane. Accordingly, this plane is a barrier which no quaternary liquid can cross during 

crystallization. Seven primary phase volumes are cut 

by this plane: leucite, forsterite, the two forms of 

MgO-SiO2 (protoenstatite and enstatite), potassium 

feldspar (KaO-AlaCVGSiCX), tridymite, cristobalite, 

and a region of two immiscible liquids. The fields 

of potassium feldspar and enstatite in figure 70 are 

narrow. Two compositions studied which were near

these fields but contained only 1 percent MgOSiO2 

were in the field of protoenstatite, with liquidus temperatures around 1200°C. The points G and D must 

be very close together both in temperature and composition, as must also points E and F. The heavy 

lines of fig. 70 are not only the traces of boundary 

curves between primary phase volumes in the tetrahedron representing the four-component system, but 

since this is a ternary system they also are boundary 

curves. The points of intersection of these boundary 

curves, data for which are given in table 30, are univariant points in this ternary system and also piercing 

points for univariant curves in the quaternary system.
L100 DATA OF GEOCHEMISTRY

The relation of the invariant points and boundary 

curves in the ternary system to the quaternary system 

are shown in (fig. 71).

The three points B, D, and F (fig. 70) not only lie, 

respectively, on three invariant lines, but each is a maximum of temperature on one of these curved lines because the plane leucite-forsterite-silica is a composition

plane for the crystalline phases along each of these 

three lines. A composition plane in a quaternary system 

is the equivalent of a tieline in a ternary system, and 

has at its apices the composition of the three crystalline 

phases which may coexist in equilibrium with liquid. 

Such a composition plane, when and if this plane (or 

sometimes this plane extended) cuts the quaternary in-

(MgO-AI2 03 -Si02 )

460±5°

-

(MgO-AI 203-Si02) SAp

b* - Qp * '

(K2 0-AI2 03 -Si02 ) '

LC 

17 SP

(LC-SP-COR) °

(MgO-AI203 -Si02 ) «

f

> 1315110°

LC

COR

MU

LC

SP

MU

/CORD LC 

A MU * ' SP " '

COR

MU 131813° -

SP

. 157515° LC 

r « 1 > F0 (

(LC'FO-SP) SP

(MgOAI203-Si02) F0 

PR

'* CORD *

1360+5°

MU

CORD

SAP

MU

SP

SAP

CORD MU (MgO-AU^CySiOg) (MgO-ALCVSiOJ 

^ ^ SAP *d y 2 3 2'

SP I482±3°£ f

(K20-AI203 -Si02)'

MU

CORD

SP

LC

SP

MU

^CORD 

_./ LC

C MU ,. ,

.CORD

LC

CORD

SP

FO 

SP

.^CORDpo 137015°

F SP 

CORD ' 

(MgO-AI203-Si02)

LC

FO

CORD

FO

PR <

LC

CORD 

/ LC

G PR

' CORD

FO

PR

LC

.1200+20°

^(LC-FO-Si02)

40+20° <

C

EL

U

LC

FEL

MU

/ ° FEL

MU

144315°

CORD

MU

TR

FEL

CORD

MU

_ -^TR FEL (K^O'AI2CVSi02 ) 

* . TR..,...^

CORD ^ MU 98g± 20o

\ CORD

\ FEL

c V TR

EL 970 + 20° \ EN

ORD A TR

\ FEL \ TD T*J**^P

30120° V FEL 985120° * 

/ \

/EN \ EN

/ FEL \ TR

/CORD \ CORD

LC /PR \ PR

FEL /EN \ EN

PR / FEL \ TR

CORD / CORD \ CORD 

X PR /,/ PR \ ,/ PR 

H FEL // EN \J EN

CORD

LC

PR

FEL

. 1140120°

CORD TR

PR

EN

FEL

PR

TR

(LC-FO-Si02) u UUKU

134515°

1470+10° 

/ 

CR 

TR

(MgO-AI203 -Si02)

MU

1470 + 10° 

 m

1470 + 10° CR 

TR I470±IO° (MgO-AI203-Si02)

(MgO-AI 203-Si02)

PR

FIGUBB 71. The system KjO-MgO-AljOj-SiOj. Diagram showing univariant lines and their relation to ternary invariant points (small black dots and lowercase letters a 

through o) in limiting systems and to quaternary invariant points (large black dots and capital letters). These lines and points do not lie in a plane. Only their relations to one another are shown in this diagram, which is not intended to show their angular or spatial relations. The lengths of the lines and the position of a temperature 

maximum on a line are arbitrary and without significance. Arrows indicate the direction of falling temperatures. Abbreviations for crystalline sohd phases along the 

lines and at the points: iC=leucite, COR=corundum, AfC7=mullite, SP=spinel, CO«D=cordierite, SXP=sapphirine, F£i=potassium feldspar, Tfi=tridymite, 

Cfi=eristobalite, FO=forsterite, PJS=protoenstatite, JBAT=enstatite. Reprinted from Schatrer (1954).
PHASE-EQUILIBRIUM BMLATTONS, ROCK-FORMING OXIDES EXCEPT WATER L101

variant line along which these three crystalline phases 

coexist with liquid, defines a temperature maximum on 

the curved invariant line where it cuts it.

The phase assemblages along each of the six invariant 

lines (curved lines within the tetrahedron, K_O-MgOAl2O3-SiO2 ) which pierce the plane leueite-forsteritesilica are as follows:

1. Leucite + forsterite + protoenstatite + liquid. 

Point B (fig. 70) lies on this line and is a temperature maximum on it. This line is sCr of figure 71 

and B of figure 70 is the maximum shown on sG.

2. Leucite + protoenstatite + potassium feldspar 

+ liquid. Point Z> (fig. 70) lies on this line and 

is a temperature maximum on the line tH (fig. 71).

3. Enstatite + potassium feldspar + tridymite + liquid. Point F lies on this line and is the point of 

maximum temperature of pK of figure 71.

4. Protoenstatite + enstatite + potassium feldspar 

+ liquid. Df of figure 70 lies on this line, which is 

ul of figure 71.

5. Protoenstatite + enstatite + tridymite + liquid. Fr 

(fig. 70) lies on this line, which is vJ of figure 71.

6. Protoenstatite + cristobalite + tridymite + liquid. 

Point H (fig. 70) lies on this line, which is no of 

figure 71, and joins the points H of figure 36 and K 

of figure 28.

With the exception of protoenstatite + cristobalite 

+ tridymite + liquid, which ends at two ternary invariant points in different faces of the tetrahedron, each 

of these invariant lines connects two quaternary invariant points. Four invariant lines meet at each 

quaternary invariant point (fig. 71). The points 5, Z?, 

and F as temperature maxima on their respective invariant lines are significant because they locate three 

maxima of temperature, below which the temperature 

of each of the three pairs of quaternary invariant point 

must lie. The positions of 5, Z), and F in the plane and 

the position of this plane leucite-forsterite-silica hi the 

tetrahedron set some limits to the possible locations six 

quaternary invariant points.

TABLE 30. Significant points in the system K2O-MgO-Al_O3-SiO2 

[Locations of significant points in the five joins on univariant lines of figure 71. Based on Schairer, 1954]

Letter (significant 

point)

B. ...........

D. ........ ..

D'. ..........

Ff..... .......

F. ...........

H... ....

M... .........

P............ P'

P". ..........

V.........

W..... .......

X.........

Y...

Z. ...........

B'. ..........

C' .........

Ff ...... ......

H'. ....... .

H".... _______

H'"__________

K'. ..........

M'. __________

Figure on which 

point is shown

70

70

70

70

70

70

72

72

72

72

73

73

73

737°.

74

74

74

74

74

74

75

75

Temperature (°C)

19ftO J-9O

1140 ±20

1125+0, -25

1125 + 0, -25

985 ±20

1470 ±10

1445 ±5

1450 ±5

1458 ±5

1 4-fiO 4- ^

1435 ±5

1440 ±3

1318±3

1130 ±20

O7ft i on

1405±5

1370 ±5

1 5 KQ _U K

1455 ±5

1458 ±5

14.^0-4- <*

1478 ±3

iQ7ft i o

Three solid phases

Leucite + feldspar + protoenstatite- __________ _

Tridymite + protoenstatite + enstatite 1 - _ ._ .__ ________

Cordierite + mufiite + sapphirine- _ ___ _-_ -- ---- _____

Leucite + cordierite + spinel 1 _______ ___________

Leucite + forsterite + spinel. ______ _ _ _____ __ ___ _____

Mullite + sapphirine + cordierite -- ______ _ _ __. ----- -

Cordierite + sapphirine + spinel.. ._.. .__-. -_- -- ---

Line (fig. 71) on 

which letter point 

lies

sG

tH

ul

vJ

pK

no

rF

bB

dB

cB

fE

BC

CF

DH

EK

rF

JF

iG

cB

dB

bB

kA

qA

1 Following are the compositions of the liquids at their ternary invariant points within the quaternary system, in weight percent:

Letter point

B.... ... . _ ... ...

D-- - .- . .

&. .................

F...... ......... ..

*" . ._..--.....

X... ...............

Y ........... .....

Z.. ................

Leucite

58.8

57.7

57.8

45.5

44.8

62.0

55.0

44 5

Forsterite

0

0

.2

.2

Cordierite

16.0

2.5

*> ft

SiOi

40 4

42.1

A.O ft

64.3

55.0

no A

42.5

53.5
L102 DATA OF GEOCHEMISTRY

2MgO-2AI2 03 -5Si02

^ CORDIERITE 

I468±2

^MULLITE 3AI 2 0,-2Si02 

CORDIERITE^L \<k\ -M458+5o

'l460±5°

4MgO-5AI 203 -2Si02 

SAPPHIRINE

1890120°,

2MgO-Si02 

FORSTERITE

FIGURE 72. The plane

I686±5°

10 30 40 50 60 

WEIGHT PERCENT

70 A

1493+3° 90

K20-AI2 03 -4Si02 

LEUCITE

(leucite)-2MgO-SiO8 (forsterite)-2MgO-2Al2O3 -5SiOj (cordierite) through the tetrahedron KjO-MgO-AUOs-SiOz. Modified 

from Schairer (1954).

The plane K2OAl2O3 -4SiO2 (leucite )-2MgO-SiO2 

(forsterite)-2MgO-2Al2O3 -5SiO2 (cordierite) through 

the tetrahedron K2O-MgO-Al2O3-SiO2 is shown in 

figure 72. It shows the side

2MgO SiO2-K2O A12O3 -4SiO2

in common with figures 70 and 77. This plane cuts 

the primary phase volumes of forsterite, leucite, spinel, 

cordierite, mullite, and 4MgO 5A12O3 2SiO2 (sappliirine). This is not a ternary system, since cordierite melts 

incongruently to mullite, and there are fields of spinel 

and sapphirine, the compositions of which are not in 

this plane.

The nine curves AM, NM, SM, RP, OP", PP', PP", 

P'P", and QP' of figure 72 are traces of curved surfaces,

along which two adjacent phase volumes meet in the 

plane forsterite-cordierite-leucite. The points M, P'', 

P", and P are piercing points in the plane of four univariant lines in the tetrahedron and each of these points 

is a point on one of the four univariant lines in the plane. 

Along each of these curved univariant lines three crystalline phases are in equilibrium with liquidus of compositions in the plane forsterite-cordierite-leucite. The 

phase assemblages on each of the four univariant lines 

which pierce this plane are:

1. Fosterite+leucite+spinel+liquid. Point M (fig. 

72) is on this line, and the plane enstatite-cordierite-leucite cuts this line at Bf of figure 74. 

This is the line rF of figure 71.

2. Spinel+mullite+sapphirine+liquid. P" (fig. 72)
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L103

lies on this line, and the plane enstatite-cordieriteleucite cuts it at H" (fig. 74). This line is dB of 

figure 71.

3. Mullite+cordierite+sapphirine+liquid. P' (fig. 

72) is on this line and the plane enstatite-cordierite-leucite cuts it at H' (fig. 74). This line is 

cB of figure 71.

4. Cordierite+sapphirine+spinel+liquid. Point P 

(fig. 72) is on this line, and the plane enstatitecordierite-leucite cuts it at H'" (fig. 74). This 

line is dB of figure 71. 

The plane K2OAl2O3 -4SiO2 (leucite)- 

2MgO-2Al2O3 -5SiO2(cordierite)-SiO2,which is part of 

the larger plane K2O-Al2O3 -4SiO2-MgO-Al2O3-SiO2 

through the tetrahedron K2O-MgO-Al2O3-SiO2 , is

shown in figure 73. It also is not a ternary system since 

neither mullite nor spinel is in this plane. It shares 

the side cordierite-leucite with figure 74.

The point U in the side line cordierite-silica is the 

point where the tieline cordierite-silica in the limiting 

ternary system MgO-Al2O3-SiO2 cuts QP^ the boundary curve between the fields of mullite and tridymite 

(fig. 36). The 11 heavy curves, or heavy dashed curves 

where the data are insufficient to locate them accurately, 

are traces of curved surfaces along which two adjacent 

primary phase volumes meet in the tetrahedron 

K2O-MgO-Al2O3-SiO2 . The points V, W, X, Y, and 

Z are piercing points in the plane cordierite-leucitesilica of five univariant lines within the tetrahedron. 

At three of the five piercing points the compositions of

990±20°

FELDSPAR 

FIELD

K20-AI203 -6Si02 

20

10

I686±5°

2MgO-2AI203 -5Si02 

CORDIERITE

20 30 40 50 60

WEIGHT PERCENT Si0 0

1498 ±5° 80 90

LEUCITE

FIGURE 73. The plane K2O-Al2O3-4SiO2 (leucite)-2MgO-2Al2O3 -5SiO2 (cordierite)-SlO2 through the tetrahedron K^O-MgO-AlsOs-SiOz. Modified from Schairer (1954).

695-382 O - 64 - 8
L104 DATA OF GEOCHEMISTRY

all the phases in equilibrium lie in the plane of the diagram or in this plane produced (cordierite-leucite-silica 

is a part of the larger plane spinel-silica-leucite) . 

Thus, T (fig. 73) is the piercing point of the univariant 

line leucite 4- potassium feldspar 4- cordierite 4- liquid, 

and since the composition plane leucite-potassium feldspar-cordierite lies in this plane, T is a temperature 

maximum on this univariant line. Similarly, Z (fig. 

73) is the piercing point of cordierite 4- potassium feldspar 4- tridymite 4- liquid and a temperature maximum 

on this invariant line. Similarly, X (fig. 73) is the 

piercing point of the univariant line leucite + cordierite 4- spinel 4- liquid, and since cordierite-silica-leucite is a portion of the larger plane spinel-silica-leucite, 

the point X is a temperature maximum on this univariant line.

The phase assemblages along each of the five univariant lines which pierce the plane cordierite-leucite-silica 

are as follows :

1. Mullite 4- cordierite 4- tridymite 4- liquid. Point V 

(fig. 73) lies on this line, which is fE of figure 71. 

The point P of figure 36 is one terminus of this 

line.

2. Mullite 4- cordierite 4- spinel + liquid. Point W 

lies on this line, which is BC of figure 71.

3. Cordierite + spinel + leucite 4- liquid. Point X 

lies on this line and is the temperature maximum 

on it. This line is CF of figure 71 and point X is 

the maximum on CF.

4. Leucite 4- potassium feldspar 4- cordierite + liquid. 

Point T is on this line and is a point of maximum 

temperature. This line is DH of figure 71, and T 

is the maximum shown on it.

5. Cordierite + potassium feldspar + tridymite + 

liquid. Point Z of figure 73 is on this line and is a 

temperature maximum both on it and on line EK 

of figure 71.

The plane K2O -AlsA^SKX (leucite) -MgO-SiO2 

(enstatite)-2MgO. 2Al2O3 -5SiO2 (cordierite) through 

the tetrahedron K2O-MgO-Al2O3-SiO2 is shown in 

figure 74. It shares the side K2O A12O3 4SiO2- 

2MgO-2Al2O3 -5SiO2 with figure 73. The section cuts the seven primary phase volumes of 

the three components and of 2MgO-SiO2 (forsterite), 4MgO 5A12O3 2SiO2 (sapphirine), mullite, 

and spinel, but, since the compositions of these last 

four phases cannot be represented by the components 

chosen, it is not a ternary system. Because of the incongruent melting of MgO SiO2 (enstatite) , it does not 

appear on the phase-equilibrium diagram, but the field

of f orsterite extends over the metasilicate composition 

and sweeps over the field until it meets the field of leucite. The side leucite-cordierite is not binary due to 

the formation first of spinel, then of mullite, and because 

of the incongruent melting of cordierite. The heavy 

curves are traces of curved surfaces along which two 

adjacent primary phase volumes meet in the tetrahedron, in the plane MgO SiO2-cordierite-leucite. The 

points B', C', Ff, H"f, H", and Hf are piercing points 

of six univariant lines within the tetrahedron. Along 

each of these curved univariant lines, three crystalline 

phases are in equilibrium with liquids whose compositions lie on this curved line. The phase assemblages 

along each of these six lines are as .follows:

1. Leucite+forsterite4-spinel+liquid. Point B' is on 

this line and the plane forsterite-cordierite-leucite 

cuts it at M (fig. 72). This line is rF in figure 71.

2. Forsterite 4- spinel 4- cordierite 4- liquid. Point G' lies 

on this line, which is jF of figure 71.

3. Forsterite 4- protoenstatite 4~ cordierite+liquid.

Point F' (fig. 74) is on this line, and U (fig. 36) 

is one terminus. This line is iG of figure 71.

4. Spinel 4-mullite 4-sapphirine+liquid. Point H" 

lies on this line, and the plane forsterite-cordieriteleucite cuts it at P" of figure 72. It is dB of figure 71.

5. Mullite+cordierite 4-sapphirine+liquid. H' is on 

this line, and the plane forsterite-cordierite-leucite 

cuts it at P' of figure 72. This line is cB of figure 71.

6. Cordierite 4-sapphrine 4-spinel+liquid. Point H'" 

lies on this line and the plane forsterite-cordieriteleucite cuts it at P of figure 72. It is fiB of figure 71.

The plane 2MgO2Al 2 O3 -5SiO 2 (cordierite)- 

3A12O3 2SiO2 (mullite) -K2O A12O3 6SiO2 (potassium 

feldspar) through the tetrahedron K2O-MgO-Al2O3- 

SiO2 shown in figure 75, cuts the primary phase volumes 

of mullite, corundum, spinel, and leucite. This again is 

not a ternary system, since each of the components 

melts incongruently.

The point /' lies at the intersection of the tieline 

cordierite-mullite and the boundary curve JM of figure 

36. The side line cordierite-mullite lies in the plane 

cordierite-leucite-silica (fig. 73). The five heavy 

curves are traces of curved surfaces along which two 

adjacent primary phase volumes meet within the tetrahedron in the plane cordierite-mullite-potassium feldspar. The point Kf and M' are piercing points of two
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L105

CORDIERITE 

2MgO'2AI203-5Si02

20/ ^0 f \^I490±3°

wW >x4MgO-5AI203 -2Si02 

H /I450±5° |\> SAPPHIRINE

136413° 

PROTOENSTATITE

I398±2°

|498±5C

168615°

MgO-Si02 

ENSTATITE

10 20 30 40 50 60

WEIGHT PERCENT

70 .480 ±5° 8° 90

LEUCITE

FIGURE 74. The plane K»O-AljO!-4SlOi neucite)-MgO-SiOi (enstatite)-2MgO-2AliOs-5SiOj (cordierite) through the tetrahedron KiO-MgO-AliO»-SiOj. Modified from

Schairer (1954).

univariant lines within the tetrahedron. The phase assemblages along each of these two lines are as follows:

1. Corundum+mullite+spinel+liquid. Point Kf is on 

this line, and point M (fig, 36) is one terminus. 

This line is kA of figure 71.

2. Leucite+corundum+spinel+liquid. Point Mf is on 

this line, which is qA of figure 71.

The plane K2O-Al2O3 -4SiO2 (leucite)-MgO-Al2O3 

(spinel)-Al2O3 (corundum) (fig. 76) is a ternary system 

and the maximum temperature of the univariant equilibrium leucite-corundum-spinel (line qA, fig. 71) is

a ternary eutectic in this plane. The ternary eutectic 

(point D of fig. 76) is at 1543° ±5°C and 88 percent 

leucite, 1.5 percent A12O3 , 10.5 percent MgOAl2O3. 

The binary eutectic spinel+leucite=L is at 1553° ±5°C 

and 88.5 percent leucite (point A).

The plane K2O-Al2O3 -4SiO2 (leucite)-2MgO-SiO2 

(forsterite)-MgO-Al2O3 (spinel) (fig. 77) also is a 

ternary system, and the maximum temperature of the 

univariant equilibrium leucite+forsterite+spinel=L 

(line rF of fig. 71) is the eutectic G of figure 77 at 

1473°±:50C, 74.0 percent leucite, 18.5 percent forsterite, 

7.5 percent spinel.
L106 DATA OF GEOCHEMISTRY

3AI203 '2Si02 

MULLITE

20

30 70

40 60

50 50

60

70

80 20

90

2MgO-2AI203 -5Si02 

CORDIERITE

70

WEIGHT PERCENT

1460 ±10°

80 L 90 

1370 ±10° K20-AI203-6Si02

POTASSIUM FELDSPAR

FIGURE 75. The plane 2MgO-2AlaO3-581O2 (cordierite)-3AljO3-2SiO8 (mulllteJ-KjO-AljOa-eSiOj (potassium feldspar) through the tetrahedron EjO-MgO-AljOs-SiOj.

Modified from Schairer (1954).

Figure 71 gives in diagrammatic form the interrelations of the significant points in the quaternary system, 

and table 30 lists these points, their location and temperature, the coexisting solid phases, and in some cases 

the composition of the liquid. From the information 

obtained in studying the above planes, it was deduced 

that the liquid at the reaction point A must be in 

the volume feldspar-cordierite-mullite-SiO2, not far 

from the ternary invariant point a in the ternary system 

K2O-Al2O3-SiO2, at which the solid phases are leucite, 

corundum, and mullite. The liquid composition at A 

is 13.9 percent K2O, 18.5 percent A12O3 , 67.6 percent 

SiO2 and the temperature is approximately 1300°C. 

The reaction point B must be near point H'" of figure 

74 in composition, and at 1445° ±5°C. Reaction point C

must be in the volume feldspar-cordierite-mullite-silicate, at approximately 1290°C. Reaction point D must 

be near in composition to the invariant point N in the 

ternary system K2O-Al2O3-SiO2 (point e of figure 71) 

and near point Y of figure 73, and at 1120°±20°C. 

Point E is a eutectic, hence must be within the tetrahedron feldspar-cordierite-mullite-SiO2 . It must be near 

point M in the system K3O-Al2O3-SiO2 (g of fig. 71) 

and near Z of figure 73, and at 960°±20°C. Reaction 

point F is in the volume leucite-MgO SiO2-cordieriteSiO2, not far in composition from X of figure 73, and 

not far from 1318°C, the temperature maximum on the 

line OF. Reaction point Cr is near B of figures 73 in 

both composition and temperature, 1200°C. Reaction 

point H must be near in temperature and composition
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L107

AI 2 03 

CORUNDUM

1925140°

CA

2050120°

2135120°

158815° 

168615°

MgO-AI2 03 

SPINEL

FIGUBE 76. The plane

10 20 30 70 80 A 90 

155315°

40 50 60 

WEIGHT PERCENT 

-MgO-AlaO3 (spinel)-AljO3 (corundum) through the tetrahedron KjO-MgO-AljOs-SiOj. Modified from Schairer (1966).

7/ K20-AI203 -4Si02 

LEUCITE LEUC|TE

to both D of figure 70 and Y of figure 73. Points / and 

-7 are inversion points of enstatite and protoenstatite in 

the quaternary system, and unless there is some solid 

solution the temperature is 1125°C. The composition of 

points / and / are near to each other and to point H 

of figure 71. Point K is a quaternary eutectic, at 

960°±20°C, and in composition it is near to Z of figure 

73 and to F of figure 70.

K2O-CaO-Al2O3-SiO2

Schairer and Bowen (1947b) studied the ternary 

system K2OAl2O3 -4SiO2 (leucite)-CaOAl2O3 -2SiO2 

(anorthite )-SiO2 (figure 78). This is that part richer 

in SiO2 than the join leucite-anorthite of the plane 

K2OAl2O3-CaOAl2O3-SiO2 through the tetrahedron 

representing the quaternary system. The side leuciteanorthite is a simple binary system with a eutectic at 45 

percent anorthite and 1413° ±5°C. Because of the incongruent melting of K2OAl2O3 -6SiO2 (potassium 

feldspar), the join potassium feldspar-anorthite is not 

a binary system. Anorthite is the primary phase from 

its melting point down to the point #, at 1348 °C, 78 percent K2OAl2O3 -6SiO2 , 22 percent CaOAl2O3 -2SiO2 . 

The field of anorthite occupies the largest area in the 

ternary diagram, extending down to the reaction 

point R; K2O-Al2O3 -6SiO2 +CaO-Al2O3 -2SiO2 == 

K2OAl2O3 -4SiO2 +Z at 1040°±20°C, and to the eutectic V; K2O-Al2O3 -6SiO2 + CaO-Al2O3 -2SiO2 + SiO2 = 

L at 950°±20°C. Melts near the curve RV are so exceedingly viscous that the composition relations have not 

been accurately determined, but the anorthite content 

is less than 5 percent.
L108 DATA OF GEOCHEMISTRY

MgO-AI2 03 

SPINEL

2135120°

18901 20°

1725125°,

80 20

90

155315°

I 

10

168615°

2MgO-Si02 

FORSTERITE

10 20 30 40 50 60 70 E 80 

149315°

90 K2 0-AI2 03 -4Si02 

LEUCITE

WEIGHT PERCENT

FIGURE 77. The plane KjO-Al2O3-4SiOs (leucite)-2MgO-SiOi (forsterlteJ-MgO-AljOs (spinel) through the tetrahedron KjO-MgO-AliOa-SiOj. Modified from Schairer

(1055).

Roedder (1951b) published a preliminary study of 

the section K2OAl2O3 -4SiO2 (leucite)-2FeOSiO2 

(fayalite)-SiO2 , which is part of the plane K2O A12O3- 

FeO-SiO2-SiO2 , with results shown in figure 79. This 

section of the plane cuts the phase volumes of leucite, 

fayalite, cristobalite, tridymite, and two-phase regions in 

which two immiscible liquids are formed within the quaternary system. The line A A' gives the compositions of 

two immiscible liquids, in equilibrium with each other 

and with fayalite and tridymite, and the points AA'', 

are conjugate piercing points for the univariant equilibrium Li + Lz + tridymite+ fayalite. In later publications Roedder (1953a,b) describes this immiscibility 

volume as roughly ellipsoidal, flattened parallel to and 

approximately astride the 1:1 K2OA12O3 mole-ratio 

plane, with its longest axis subparallel to the FeOSiO2 edge. The compositional limits are roughly 8 to 

52 percent FeO and 5 to 16 percent of the sum of K2O 

plus A12O3 . The closest portion of the immiscibility 

volume to either of the limiting ternary systems K2OFeO-SiO2 or FeO-Al2O3-SiO2 contains about 2 percent of the fourth component in each case. The divariant equilibrium surface between the phase volumes 

of fayalite and tridymite cuts through this immiscibility volume. No quaternary compounds have been
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L109

CaO AU.03 -2Si02 

I553±2°A ANORTHITE

IOA *> ft £ A %

1470110° 

\60

I686±5

K20-AI203-4Si02 10 20 \ 30 

LEUCITE K20 -Af^-eS^ 

POTASSIUM FELDSPAR

171315°

| 5o 990±20°60 

POTASSIUM FELDSPAR

WEIGHT PERCENT SiO

70 I470±l0e 90 Si02 

SILICA

FIGURE 78. The system K»O-Al»O3-4SiOj (leucite)-CaO-AlaO3-2SiO2 (anorthite)-SiOj, a part of a plane through the tetrahedron K2O-CaO-Al2O3-SiO2. Modified from

Schairer and Bowen (1947b).

found, but evidence points toward at least partial solid 

solutions between

K2O A12O3 2SiO2 and K2O FeO 3SiO2 

and between

K2O-Al2O3 -4SiO2 and K2O-FeO-5SiO2 .

MgO-CaO-FeO-SiO2

Schairer and Osborn (1950) studied the system 

CaOSiO2 (wollastonite)-CaO-MgO-SiO2 (monticellite)-FeO (%. 80), which is part of the plane passing

through CaO SiO2 , MgO, and FeO in the tetrahedron 

MgO-CaO-FeO-SiO2 . Monticellite melts incongruently with formation of MgO, and the area monticellite- FsO-H-C-D is a section cut by the plane through 

the phase volume of the magnesiowustite solid solutions. In this triangle there is a section EBCD through 

the phase volume of 3CaO MgO 2SiO2 (merwinite), 

the composition of which is outside this plane. The 

area BCHGrA is a trace of the phase volume of olivine 

solid solutions intermediate between monticellite and 

its iron analog CaO FeO 2SiO2 . There is also a section 

through the phase volume of melilite solid solutions
LI 10 DATA OF GEOCHEMISTRY

2FeO SiOz 

FAYALITE

I205±2°

II78±2°

I470±5°

Approximate Temperatures

A and A' ||40°C 

Band B' 1150° 

C 1270° 

D

1690110°

TWO 

LIQUIDS

1690+10°

K20-AI203-4Si02 

LEUCITE 

1686+5°

^\ KgO-AlgOs-SSiOg / 990±20° 

POTASSIUM FELDSPAR '

I470±5° Si02 

171315°

WEIGHT PERCENT

FIGURE 79. A preliminary study of the section K2O-Al2O3-4SiOa (leucite)-2FeO-SiOs (fayalite)-SiOs, which is part of the plane I&O-AlsOr^FeO-SiOr-SiOz through the

tetrahedron K8O-FeO-Al2O3-SiO2 . Modified from Roedder (1951b).

intermediate between akermanite and iron-akermanite, 

area FEE A. The join akermanite-Fe akermanite may 

be considered as binary up to its intersection with the 

curve FAG, the trace of the boundary curve between 

the phase volumes of a-CaO-SiO2 (pseudowollastonite) and melilite. Beyond this point pseudowollastonite is formed, which does not form solid solutions containing either MgO or FeO. When mixtures in this 

region are cooled below the inversion temperature, the 

/?-OaO-SiO2 (wollastonite) formed contains some solid 

solution, and at subsolidus temperatures on this join the 

phases are £-CaO-SiO2 , melilite, and olivine.

MgO-CaO-Al2 C>3-Fe2 C>3

Hansen and Brownmiller (1928) and Insley and McMurdie (1938) found the system

MgO-4CaO A12O3 Fe2O3

to be binary with a eutectic at 1347°±3°C, at 6.5 percent MgO, 93.5 percent 4CaO A12O3 Fe2O3 . No indication of solid solution was found.

MgO-CaO-Al2OHSiO2

Many planes through the tetrahedron representing 

the system MgO-CaO-Al2O3-SiO2 have been studied.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER Llll

CaO-MgO-Si02 

MONTICELLITE

3CaO-MgO-2Si02 

MERWINITE

2CaO-MgO 2Si02 

AKERMANITE

1454°

50

40

1400° 

30

10 

CaO-SiC>2 

WOLLASTONITE 

1544°

20 \ 30^o;

2CaO-FeO-2Si02 

Fe-AKERMANITE

3o A40 H 50 60 70

CaO-FeO-Si02 

Fe- MONTICELLITE

80 90

FeO

I370°±

WEIGHT PERCENT FeO

FIGURE 80. Phase-equilibrium diagram of the area CaO-SiOa (wollastonite)-CaO-MgO-SiOj (monticellite)-FeO, a part of the plane CaO-SiOr-MgO-FeO, through the

tetrahedron MgO-CaO-FeO-SiO2 . Modified from Schairer and Osborn (1950).

No quaternary compounds are formed, and each of the 

planes is a triangular section, having its corners at an 

apex, or a side, or in one of the limiting triangles. The 

various compounds are shown in figure 81 in which 

the base of the tetrahedron is the system MgO-CaOSiO2 , and two of the sides, CaO-Al2O3-SiO2 and MgOAl2O3-SiO2 , are laid out flat. The side MgO-CaOA12O3 is omitted because none of the compounds used as 

components lie in it.

Prince (1951) found that the join 2CaO-SiO2- 

MgO-Al2O3 is a binary system, with a eutectic at 

1418°C, 65.6 percent 2CaO-SiO2 , 34.5 percent MgO. 

A12O3 , or 9.8 percent MgO, 24.7 percent A12O3 , 65.5 percent 2CaOSiO2 . This line divides the plane MgOAl2O3-2CaOSiO2 (fig. 82) into two ternary systems. 

The piercing point T of the equilibrium

MgO + MgO A12O3 +2CaO SiO2 +liquid, 

at 1417°C, 10.4 percent MgO, 23.9 percent A12O3 , 65.7
L112 DATA OF GEOCHEMISTRY

CaO 5CaO-3AI203 

 

AI203 -SiO,

02CaO-Alo03 -Si02 

(GEHLENITE)

OMgO-2CaO-2Si02 

(AKERMANITE) CaO 

(ANORTHITE) O MgO-CaO-2Si02 

(DIOPSIDE)

AI 2 03

AI 2 03

FIOUBE 81. The tetrahedron MgO-CaO-Al2Oj- SiOs, represented by the base MgO-CaO-SiO2, and two of the triangular sides, CaO-AljOs-SiOj and MgO-AUOs-SiOs, which

terminate at the AljOs-apex, laid out flat.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L113

A

2CaO-AI203 -Si02 

GEHLENITE

90,

80 90

2CdOSi02

WEIGHT PERCENT

FIOUBE 82. The plane MgO-AljOs-2CaO -Sid through the tetrahedron MgO-CaO-AljOj-SiOz. Modified from Prince (1951).

percent 2CaO SiO2 is a eutectic, as is also the piercing 

point Q of the equilibrium

MgOAl2O3 + 2CaOAl2O3 -SiO2 (gehlenite)+ 

2CaO-SiO2 + liquid, at 1414°C, 9.3 percent MgO, 

24.8 percent A12O3 , 65.9 percent 2CaOSiO2 . 

Point R is the eutectic between 2CaO-SiO2 and 

2CaOAl2O3 *SiO2 , at 1545°C, 24.9 percent A12O3 , 75.1 

percent 2CaO-SiO2. Point P is a binary eutectic be-- 

tween MgO-Al2O3 and 2CaO A12O3 SiO2 , at 152T°C, 

4.4 percent MgO, 42.5 percent A12O3, 53.1 percent 

2CaOSiO2.

The system MgO-Al2O3-CaO A12O3 2SiO2 (anorthite), figure 83, was studied by DeVries and Osborn 

(1957). The sides Al2O3-anorthite and MgO-Al2O3 are 

binary systems previously considered, but the side 

MgO-anorthite is not binary because it intersects the 

phase volume of MgO-Al2O3 (spinel). The join 

anorthite-spinel is not binary because it cuts the phase 

volume of corundum. The field of anorthite in this section is bounded by the trace of the boundary anorthiteA12O3 on which the temperature falls from. 1551 °C in 

the binary system to 1485 °C at the piercing point in
L114 DATA OF GEOCHEMISTRY

CORUNDUM 

2050°

1925°

2135°

MgO-AI 2 0 3 

SPINEL

2030°

1553'

CaO-AI203-2Si02 

ANORTHITE

1448° 1800° 

WEIGHT PERCENT MgO

2800°

MgO 

PERICLASE

FIGUEE 83. The plane MgO (periclaseJ-AljOs (corundum)-CaO-Ah03-2Si02 (anorthite) through the tetrahedron MgO-CaO-AhOs-SiOj. Modified from DeVries and

Osborn (1957).

this section of the equilibrium anorthite-corundumspinel-liquid. The trace of the boundary between 

CaO-Al2O3 -2SiO2 and MgO-Al2O3 then falls to its intersection with the join MgO-anorthite, at 1448°C. 

This section thus cuts the primary phase volumes of 

anorthite, corundum, spinel, and periclase.

The plane MgO (periclase) -2MgOSiO2 (forsterite )-CaO-Al203 -2SiO2 (anorthite) (fig. 84), studied 

by DeVries and Osborn (1957), cuts the phase volumes 

of MgO (periclase), forsterite, spinel, and anorthite, 

and since the composition of spinel does not lie in this, 

plane, the system is not ternary. The piercing point of 

the univariant equilibrium periclase + forsterite 4- spinel +liquid is at 1610°C, but the exact composition was 

not determined.

The system

MgO-SiO2 (enstatite)-CaO-A!2O3 -2Si02 (anorthite)- 

CaO-MgO-2SiO2 (diopside) was studied by Hytonen 

and Schairer (1960) and the results are shown 

in the preliminary diagram figure 85. Heavy 

curves are traces of boundary surfaces between the 

primary-phase volumes of the several solid phases that 

appear on the liquidus surface. The subliquidus crystallization is complex and the details have not been 

worked out. Three polymorphic modifications of 

MgO-SiO2 (protoenstatite, clinoenstatite, and ortho-
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L115

CaO-AI203 -2Si02 

ANORTHITE 

1553°

1448°

1444

1800°

1466

1890

2MgO-Si02 

FORSTERITE

1870°

2800°

WEIGHT PERCENT MgO

MgO 

PERICLASE

FIGURE 84. The plane MgO (periclase)-2MgO-8iOs (forsterite)-CaO-AhO3-2SiO2 (anorthite) through the tetrahedron MgO-CaO-AbOs-SiOz. Modified from DeVries

and Osborn (1957).

enstatite), each as solid solutions, appear at various 

temperatures during crystallization or as quenching 

products. Small amounts of free silica (present as 

metastable cristobalite) were observed in some of the 

compositions rich in diopside at and below solidus 

temperatures.

The plane, MgO-2CaO SiO2-5CaO 3A12O3 , was 

studied by Hansen (1928) with special reference to the 

constitution of portland cement. The plane cuts the 

primary-phase volume of MgO, which occupies most of 

the section of 2CaO-SiO2 and of 5CaO3Al2O3 . The 

piercing point of the equilibrium

MgO + 2CaO SiO2 + 5CaO r 3A12O3 + liquid

is a eutectic, at 1315°±5°C, 5 percent MgO, 12 percent 

2CaO-SiO2 , 76 percent 5CaO-3Al2O3.

The plane CaO A12O3 2SiO2 (anorthite) -MgO A12O3 

(spinel)-2MgO-SiO2 (forsterite) (fig. 86), studied by 

DeVries and Osborn (1957), is not a ternary system. In 

addition to the phase volumes of the components, it 

intersects the phase volume of corundum, and on the 

side anorthite-forsterite there is a region in which spinel is the primary phase, and the composition of the 

liquid in equilibrium with spinel, anorthite, and forsterite lies outside of this triangle at 1420°C. The 

piercing point of the equilibrium anorthite+corundum -f spinel+ liquid is at 1480°C.
L116 DATA OF GEOCHEMISTRY

CaO'AI203-2Si02 

ANORTHITE 155312°

10 .90

20

30

130712° 

40

1274 ±2°

.40

ENSTATITE

70 T 80

1392 + 2° 

WEIGHT PERCENT DIOPSIDE

DIOPSIDE

FIGURE 85. Phase-equilibrium diagram for the plane MgO-SiOs (enstatite)-CaO-AhO3 -2SiOj (anorthite)-CaO-MgO-2SiO! (diopside). Modified from Hyttaen and Schaiier

(1960).

The plane, 2CaO A12O3 SiO2 (gehlenite)-Al2O3 corundum )-MgO-Al2O3 (spinel), represented by figure 

87, was studied by DeVries and Osborn (1957). The 

field of spinel, MgO-Al2O3 , occupies the largest part of 

this diagram, but the plane also cuts the primary-phase 

volumes of 2CaO A12O3 SiO2 , A12O3 , CaO -2A12O3 , and 

CaO 6A12O3 , and since the compositions of the two calcium aluminates are not in this triangle, the section is 

not a ternary system. There are three piercing points: 

2CaO A12O3 SiO2 + CaO 2A12O3 + spinel+liquid, at 

1515°C; CaO 2A12O3 + CaO 6A12O3 + spinel+liquid, at 

1640°C; and CaO-6 A12O3 +spinel, at 1775°C.

The plane 2CaO A12O3 SiO2 (gehlenite)- 

CaO-Al2O3 -2SiO2 (anorthite )-MgO-Al2O3 (spinel) 

shown in figure 88, was studied by DeVries and Osborn 

(1957). It cuts the primary phase volume of spinel, 

gehlenite, anorthite, corundum, and also of 

CaO-6Al2O3 , a composition outside of the component 

triangle. Liquids in equilibrium with anorthite, gehlenite, and spinel are represented by points outside this 

triangle.

The plane 2MgO SiO2 (f orsterite) -CaO MgO 2SiO2 

(diopside) -CaO A12O3 2SiO2 (anorthite) through the 

tetrahedron was studied by Osborn and Tait (1952)
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L117

SPINEL

MgO-AI2 03

2135°

I7IO

1590

CORUNDUM

1553 I890e

1444

ANORTHITE

1466° 

WEIGHT PERCENT FORSTERITE

2MgO-Si02 

FORSTERITE

FIGURE 86. The plane MgO-AhOs (spinel)-2MgO-SiO8 (forsterite)-CaO-Al2O3-2SiO2 (anorthite) through the tetrahedron MgO-CaO-AhOs-SiC^. Modified from DeVries

and Osborn (1957).

and their phase-equilibrium diagram is figure 89. It 

is not a ternary system because it cuts the phase volume of spinel, and because the diopside contains some 

A12O3 . Point Z>, at 1317° ±5°C is the piercing point 

of the equilibrium CaO-Al2O3 -2SiO2 + MgO-Al2O3 + 

2MgO-SiO2 +liquid. The minimum temperature of 

the system is at point E, 1270° ±5°C, at the composition 

7.5 percent 2MgO-SiO2 , 49 percent MgO CaO 2SiO2 , 

43.5 percent CaO A12O3 2SiO2 . It is the piercing point 

of the equilibrium 2MgO SiO2 + CaO MgO 2SiO2

solid solution+ CaO Al2O3 -2SiO2 + liquid, and would 

be eutectic were it not for the small amount of solid 

solution in the diopside.

The section 2MgO-SiO2 

CaOAl2O3 -2SiO2 (anorthite )-SiO2 

tetrahedron CaO-MgO-Al2O3-SiO2

(forsterite)-

through the

was the first

plane to be studied (Andersen, 1915). It is not a 

ternary system, for the plane cuts the phase volume 

of MgO-Al2O3 (spinel) on the side 2MgO-SiO2-
L118 DATA OF GEOCHEMISTRY

AI 203

CORUNDUM 

2050°

1925°

CaO'6AI 2 03

CaO- 2AI 2 Q3

1590

2CaO-AI203-Si02 

GEHLENITE

1527

WEIGHT PERCENT SPINEL

2135°

MgO-AI203 

SPINEL

FIGURE 87. The plane 2CaO-AljO8 -SiOs (gehlenite)-AljO3 (corundumJ-MgO-AljOa (spinel), through the tetrahedron MgO-CaO-AhOs-SiOs. Modified from DeVries

and Osborn(1957).

CaO A12O3 2SiO2 . In figure 90 the traces of the boundaries between the various phase volumes are shown, 

with their intersections at the piercing points. K is 

the piercing point for the univariant equilibrium 

2MgO SiO2 +MgO A12O3 + CaO A12O3 2SiO2 +liquid, 

at 1320°C, and the liquid has the composition 61 percent CaO-Al2O3 -2SiO2 , 29.5 percent 2MgO-SiO2 , 9.5 

percent SiO2 . Point M corresponds to the equilibrium

MgO SiO2 + 2MgO SiO2 +CaO A12O3 2SiO+liquid, 

at 1260°C, 25.5 percent 2MgO-SiO2, 55 percent 

CaO-Al2O3 -2SiO2 19.5 percent SiO2 . Piercing point 

N is a eutectic, since the liquid lies within the triangle determined by the solid phases MgO-SiO2 , 

CaO-Al2O3 -2SiO2 , and SiO2 . The temperature is 

1222°C, the composition 16.4 percent 2MgO-SiO2 , 50.6 

percent CaO-Al2O3 -2SiO2 , 33.0 percent SiO2 . The
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L119

CaOAI203 -2Si02

ANORTHITE 

1553°

1513°

1590°

CaO-6AI2 03

1590' 2135°

2CaO-AI203 -Si02 

GEHLENITE

1527'

WEIGHT PERCENT SPINEL

MgO-AI 203 

SPINEL

FIGUKE 88. The plane 2CaO-Al2O3 -SiOj (gehlenite)-CaO-AhO3-2SiOs (anorthite)-MgO-AljOs (spinel) through the tetrahedron MgO-CaO-AljOs-SiOj. Modified from

DeVries and Osborn (1957).

plane also cuts a section through the region of two immiscible liquid layers, but the location of the boundary 

has not been determined.

The plane MgO SiO2-CaO SiO2-Al2O3 through the 

tetrahedron was studied by Segnit (1956) with results 

shown in figure 91. The section is not a ternary system, 

and it cuts the primary-phase volumes of corundum, 

spinel, enstatite solid solutions, pyroxene solid solutions,

wollastonite solid solutions, pseudowollastonite, melilite, and anorthite.

The section

CaOSiO2 (wollastonite) -CaO- MgO -2SiO2 (diopside)-CaO-Al2O3 -2SiO2 (anorthite) (fig. 92), studied 

by Osborn (1942), is part of a plane through the 

tetrahedron passing through the points MgOSiO2 , 

CaO SiO2, and A12O3 SiO2 . It is not a ternary system

695-382 O 64 - 9
L120 DATA OF GEOCHEMISTRY

CoO-AI2 03 -2Si02 

ANORTHITE

1553

10

1391.5°

90

1890°

1387

CaO-MgO-2Si02 

DIOPSIDE

30 40 50 60 70 80 90

WEIGHT PERCENT FORSTERITE

2MgO-Si02 

FORSTERITE

FIGURE 89. The plane 2MgO-SiOj (forsterite)-CaO-MgO-2SiOj (diopside)-CaO-AhO3-2SiOi (anorthite) through the tetrahedron MgO-CaO-AljOs-SiOj. Modified from

Osbom and Tait (1952).

because the diopside (CaOMgO2SiO2 ) contains a 

small amount of A12O3 . The boundary between the 

phase volumes of a-CaOSiO2 (pseudo wollastonite) and 

0-CaO-SiO2 (wollastonite) solid solutions is the curve 

ZR, and is not a line of constant temperature because 

of solid solution in 0-CaO-SiO2 . The piercing-point 

R of the equilibrium between a-CaO-SiO2 and 

0-CaO-SiO2 solid solutions, anorthite, and liquid is at 

1245° ±3°C, 36 percent CaOSiO2, 25.5 percent

CaO-MgO-2SiO2, 38.5 percent CaO-Al2O3 -2SiO2, and 

the wollastonite solid solution contains 91 percent 

CaO SiO2, 9 percent CaO MgO 2SiO2. The phases at 

the piercing point E, at 1236° ±3°C, are the wollastonite 

solid solution containing 89 percent CaOSiO2 and 11 

percent CaO-MgO-2SiO2 ; diopside; anorthite; and 

the liquid of the composition 32 percent CaO-SiO2, 

30 percent CaOMgO-2SiO2, and 38 percent 

CaO-Al2O3 -2SiO2.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L121

CoO-AI203 -2Si02 

ANORTHITE

2MgO-Si02

FORSTERITE

10

MgO-Si02 

ENSTATITE

WEIGHT PERCENT Si02 

FIGURE 90. The plane 2MgO-SiOj (forsterite)-CaO-AljO3-2SiOj (anorthite)-SiOi through the tetrahedron MgO-CaO-AhOj-SiOj. Modmed from Andersen (1915).

The system CaO-SiO2 (wollastonite)- 

2CaO A12O3 SiO2 (gehlenite) -2CaO MgO 2SiO2 

(akermanite) is part of the plane

MgO-CaO SiO2-CaO A12O3

through the tetrahedron MgO-CaO-Al2O3-SiO2 (fig. 

81). It was studied by Osborn and Schairer (1941) and

their phase-equilibrium diagram is figure 93. The side 

akermanite-gehlenite is a solid-solution series with a 

minimum at 1390°C, 73 percent akermanite; the side 

CaO-SiO2-gehlenite has a eutectic at 1318°C, 36.7 percent gehlenite; the side CaO SiO2-akermanite a eutectic 

at 1400 °C and 53 percent akermanite. There are but 

two fields, one of a-CaO-SiO2 (pseudowollastonite) in
L122 DATA OF GEOCHEMISTRY

CoO-SiOg 

WOLLASTONITE

MgOSi02 

ENSTATITE

10 20 / 30 

3MgO-AI203 -3Si02 

PYROPE

40 50 60 70 80 90

AUO,

WEIGHT PERCENT AI 2 03

FIGURE 91. The plane MgO-SiOa (enstatite)-CaO-SiOj (wollastoniteJ-AljOs through the tetrahedron MgO-CaO-AljOs-SiOj. Modified from Segnit (1956). aa, Solid

solution.

which there is no solid solution, and a complete series 

of solid solutions between gehlenite and akermanite. 

The minimum along the boundary between these two 

fields is at 1302°C and 51.1 percent CaOSiO2 , 

20±2 percent 2CaOMgO-2SiO2 , 29±1 percent 

2CaOAl2O3 -SiO2 .

DeWys and Foster (1956) found that 

CaO Al2O3 -2SiO2 (a n o r t h i t e)-2CaO-MgO-2SiO2 

(akermanite) form a binary system, with a eutectic at 

1234°C and 54 percent akermanite. DeWys and Foster 

(1958) found the system CaO-MgO2SiO2 (diopside)- 

CaO A12O3 2SiO2 (anorthite)-2CaO MgO 2SiO2
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L123

CaO-AI 2 03 '2Si02 

ANORTHITE 

1553°

10

1544

CaO-Si02

WOLLASTONITE

1307

1274"

10

1391.5°

10 20 30 40 50 '368° 60 1358° 70 80 

WEIGHT PERCENT DIOPSIDE

90

CaOMgO-2Si02 

DIOPSIDE

FIGURE 92. The section CaO-SiOs (wollaston.te)-CaO-MgO-2SiOs (diopside)-CaO-AhO3-2SiOj (anorthite), part of a plane through the tetrahedron MgO-CaO-AljOs-SiOj

Modified from Osborn (1942). ss, Solid solution.

(akermanite) to have a ternary eutectic at 1226 °C, 9 

percent diopside, 44 percent anorthite, 47 percent akermanite.

Prince (1954) studied the plane through the tetrahedron MgO-CaO-Al2O3-SiO2 parallel to the side 

CaO-Al2O3-SiO2 and containing 10 percent of MgO. 

Figure 94 and table 31 give his results. The plane cuts

the primary phase volumes of MgO (periclase), CaO, 

3CaO-SiO2 , 2CaO-SiO2 , 3CaOMgO-2SiO2 (merwinite), 2CaO-Al2O3 -SiO2-2CaO-MgO-2SiO2 solid solution (melilite), a-CaOSiO2 (pseudowollastonite), 

0-CaO-SiO2 (wollastonite), CaOMgO2SiO2 (diopside) solid solutions, CaO-Al2O3 -2SiO2 (anorthite), 

MgO-Al2O3 (spinel), A12O3 , 3Al2O3 -2SiO2 (mull-
L124 DATA OF GEOCHEMISTRY

GEHLENITE 

1590°

80

70 30

1544

BINARY

MINIMUM

1390°

I454«

CaO-SiC-2 

WOLL ASTON ITE

10 20 30 40 50 1400° 60

WEIGHT PERCENT

70 80 90

2CaO-MgO-2Si02 

AKERMANITE

FIGURE 93. The section CaO-SiOj (wollastonite)-2CaO-AljO3-SiO» (gehlenite)-2CaO-MgO-2SiO» (akermanite) of the plane MgO-CaO-AhOj-CaO-SiOj through the tetrahedron MgO-CaO-AljOs-SiOi. Modified from Osborn and Schaiier (1941). ss, Solid solution.

ite), 2MgO2Al2O3 -5SiO2 (cordierite), tridymite, cristobalite, and a volume of immiscibility. The heavy lines 

outlining the traces of the intersection of this plane with 

the boundaries between these phase volumes intersect 

at 11 lettered points in figure 94, which are the piercing 

points of the various univariant equilibria.

The join 3CaO -AUVSSiC^ (grossularite)- 

3MgOAl2O3 -3SiO2 (pyrope) is always quaternary, 

since each of the end members melts incongruently. 

Chinner and Schairer (1959, 1960) determined the 

subsolidus assemblages and temperatures of crystallization shown in figure 95. By combining these data with 

that of previous investigations in this system, they 

were able to deduce the relationship of the quaternary

invariant points and univariant lines in the silica-rich 

portions of this system. Compositions lying between 

grossularite and approximately Gro78Py22 are represented in the subsolidus region by the assemblage pseudowollastonite + pyroxene + melilite + 

anorthite, which melts at 1235°C. Between about 

Gro78Py22 and Gro45I^y55 the subsolidus assemblage pyroxene + melilite + anorthite + forsterite melts at 

1225 °C. The proportion of pyroxene is very small and 

cannot always be identified either optically or by means 

of X-rays. At 1238 °C these compositions pass through 

a quaternary reaction point at which the phases are 

liquid + melilite + anorthite + forsterite + spinel. In 

a very narrow range of compositions between Gro45Py55
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L125

Si02-90 PERCENT 

MgO-10 PERCENT

WOLLASTONITEC VVWOLLASTONIT

CoO-90 PERCENT 

MgO-10 PERCENT

AI203 -90 PERCENT 

MgO- 10 PERCENT

WEIGHT PERCENT

FIGURE 94. The plane through the tetrahedron MgO-CaO-AljOj-SiOj parallel to the side CaO-Al»Oj-SiO» and containing 10 percent MgO. Modified from Prince (1964).

»», Solid solution.

TABLE 31. Temperatures and compositions of piercing points in the 10 percent MgO plane

Point on 

fig. 94

A... ........

B. ..........

C. ..........

D... ________

E. __________

F. __________

G. ..........

H... _______

J. ..........

K _________

L. __________

Temperature 

(±5°C)

1230 

1245 

1330 

1235 

1250 

1345 

1370 

1485 

1425 

1410 

1410

Crystalline phases

Tridymite, diopside, anorthite _ ___ _______ ________ __ _ _

Tridymite, cordierite, anorthite. ____ _____ _____________ __

Anorthite, cordierite, spinel________ _____ _____ __________

2CaO-SiO2, melilite, spinel. ______ ____ _____ ______________

Periclase, 2CaO-SiO2, spinel _ __ _ ________ __ -______-

Composition of liquid 

(weight percent)

MgO

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10

CaO

10 

8.5 

35. 5 

29 

29 

9 

8 

45 

43 

43 

43

A1203

18 

18.5 

45 

17 

19 

28 

30 

37 

19.5 

23.5 

25. 5

SiO2

62 

63 

50 

44 

42 

53 

52 

48. 5 

27. 5 

23.5 

21. 5
L126 DATA OF GEOCHEMISTRY

1600

sp+an+l

sptmeltan+l / mel+an+fo+l

o

pyrox +other phases

10 

3Si02

GROSSULARITE

3CaO-AI203

WEIGHT PERCENT PYROPE

3MgO-AI203 -3Si02 

PYROPE

FIGURE 95. The join SCaO-AljOs-SSiOj (grossulariteJ-SMgO-AUOs-SSiOj (pyrope). Modified from Chinner and Schairer (1960).

and Gro36Py6 4, the subsolidus assemblage melilite + 

anorthite + forsterite + spinel melts at the temperature of this reaction point. Between Gro36 and pyrope 

the assemblage anorthite + forsterite + spinel + 

cordierite melts at 1280°C.

MgO-FeO-Fe203-Si02

In the study of the system MgO-FeO-Fe2O3-SiO2 

by Muan and Osborn (1956), the partial pressure of 

oxygen was held constant at 1 atm obtained by passing commercial tank oxygen through the special quenching furnace at 0.21 atm, by using air, and at smaller 

partial pressures obtained by using mixtures of carbon dioxide and hydrogen in the ratios of 40:1, 24:1, 

and 19:1. The system is not truly quaternary because 

of the formation of metallic iron. For the purpose of 

simple illustration the phase relation can be represented 

as projections of irregularly curved surfaces in the tetrahedron onto triangular diagrams with FeOFe2O3 as 

one component. The most complete data were obtained 

in an air atmosphere, under which conditions the

mixtures fall reasonably close to the plane 

MgO-FeO Fe2O3-SiO2 . The phase-equilibrium diagram in air is figure 96. The primary phase volumes 

met are those of the magnesiowiistite, magnesioferrite 

(magnesioferrites are solid solutions of MgO-Fe2O3 

with magnetite), olivine, pyroxene solid solutions; 

tridymite; cristobalite; and a region of two immiscible 

liquid layers; and where three of these phase volumes 

meet is a piercing point of univariant equilibrium. The 

primary phase volumes shift with changing partial 

pressure of oxygen, from an inferred condition at a 

sufficiently high pressure of oxygen to keep essentially 

all the iron in the ferric condition over to the reducing 

condition of melts that are in contact with metallic iron 

(fig. 97).

CaO-FeO-Al2O3-SiO2

Schairer (1942) published the results of quenching 

experiments on five planes in this quaternary system. 

Because of the presence of FeO as a component, meltings were made in iron crucibles in an atmosphere of
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L127

Si02

10 90

80

MgO-SiOe

50

2MgO-Si02-

TRIDYMITE

MgO 10 20 30 40 50 60 70 80 90 FeO-Fe203

FIGURE 96. Phase-equilibrium relations in air of the system MgO-FeO-FejOs-SiOj represented as projected on the plane MgO-SiOj-FeO-FejOs. Points of approximately 

the same Fe2Ch/FeO ratio lie on the light dash-triple dot curves; lines with stippling on one side indicate the limits of the region of two liquid layers. Modified from Muan 

and Osbom (1956).

purified nitrogen, thus keeping the content of ferric 

iron to the minimum imposed by the equilibrium conditions. All melts were analyzed for ferrous and ferric 

iron. In general, the amount of Fe2O3 was small, and 

the results are presented with all the iron calculated 

to FeO, instead of the quinary system including both 

FeO and Fe2O3 as components. The amount of Fe2O3 

ranged from nearly zero in liquids that contained little

iron to 11.56 percent at the Fe-apex of the tetrahedron. 

The planes studied are shown in figure 98, each of 

which cuts several primary phase volumes within the 

tetrahedron. Where the plane cuts the curved boundary surface between the primary phase volumes it results in a curved line which is not a boundary curve, 

as in a ternary system, but the traces of the bounding 

surface in the plane.
L128 DATA OF GEOCHEMISTRY

SiO, SiO,

1543' 

1557 

PYROXENE

MgO FeO

FIGTJEE 97. Diagrams to show changes in phase-equilibrium relations in the system MgO-FeO-FejOs-SiOj with change in oxygen pressure. Diagram CA) shows the inferred 

relations at sufficiently high oxygen pressure to keep essentially all the iron in the ferric state; (B) the phase relations in air; (C), (D), and (JB) at constant COj:Hj 

ratios of 40:1,24:1, and 19:1 respectively; (F) extreme reducing conditions of melts in contact with metallic iron. Modified from Muan and Osborn (1956).

The traces of the intersection of the plane 

SiO2-CaO A12O3 2SiO3 (anorthite) -FeO with the 

curved contacts of two primary phase volumes, 

determined by Schairer (1942), are shown in. figure 

99. The points of intersection of these lines are not 

ternary invariant points but are piercing points of 

lines within the tetrahedron representing univariant 

equilibrium between three solid phases and liquid. 

Point /, 1070° ±4°C, is the point at which the liquid 

of the reaction CaO Al2O3 -2SiO2 ( anorthite ) + 

2FeO SiO2 (fayalite) + SiO2 =L lies in this . plane, 

and the composition of the liquid is 28 percent An, 

39.4 percent FeO, 32.5 percent SiO2 . Each of these 

solid phases is in this plane. At point /, 1108 °C, one 

of the phases, FeO-Al2O3 (hercynite), lies outside of 

this plane; the univariant reaction is

CaO A12O3 2SiO2 + 2FeO SiO2 =FeO A12O3 +L 

and the composition of the liquid is 27.7 percent An,

50.3 percent FeO, 22.0 percent SiO2. At the piercing 

point F, at 1120° ±4°C, the phase reaction is

+ FeO-Al2O3 +FeO=Z

and the composition of the liquid is approximately 14 

percent An, 77 percent FeO, 9 percent SiO2 .

Figure 100 gives in diagrammatic form the relations 

among the various invariant lines, ternary univariant 

points (small letters) , and quaternary univariant points. 

Schairer discussed in detail the location of the probable 

phase volume within these quaternary invariant points 

and their temperature relationships. On several of the 

univariant lines appear temperature maxima for example, at the composition plane anorthite-tridymitef ayalite on the line EG. The maxima on EC and FI 

separate the five invariant points H, G, Z>, E, and F 

from the rest of the quaternary invariant points. Table 

31 gives the locations of significant points on the several 

lines of figure 100.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L129

AI 2 03

CaO-2A! 2 03

CaO-AI2 03

5CaO-3AI2 03

3CaO-AI2 03

FeO-AI2 03

CaO FeO

FIGURE 98. The tetrahedron CaO-FeO-AljOs-SiO^ showing the position of the several planes on which phase-equilibrium studies have been made. Modified from Muan

and Osbom (1951).

A second plane, CaO-Al2O3 -2SiO2 (anorthite)- 

Al2O3-FeO, is almost entirely taken up by intersections 

with the primary phase volumes of A12O3 and 

FeO-Al2O3 . There is a small region of FeO, not exactly located, and one of anorthite. The piercing point, 

N, of the univariant reaction anorthite+hercynite 

=A12O3 f Z is at 1393° ±4°C, and the liquid has the 

composition 74.5 percent An, 4.5 percent A12O3 ,11.0 percent FeO. This point is a maximum on the univariant 

curve AK of figure 100, because it lies in the plane anorthite-Al2O3-FeO.

A third plane passes through CaO-SiO2- 

CaO-Al2O3 -2SiO2-FeO and the traces of the boundary 

curves are in figure 101. The primary-phase volumes 

cut by this plane are: anorthite; hercynite, whose composition is outside of this plane; wiistite (FeO); meli-
L130 DATA OF GEOCHEMISTRY

CdO 'AI203 2Si02 

ANORTHITE

15521 2e

60 CaO-AI203 -2Si02 

ANORTHITE

136812°

I470±5°

I290±IO°

10

1713110°

10 20 30 40 # 50 C QQ>D FAYALITE E QQ

120512°

90 FeO

WEIGHT PERCENT FeO

FIGURE 99. The plane SiO2-CaO-Al2O3-2SiO2 (anorthite)-FeO through the tetrahedron CaO-FeO-AhOs-SiOz. Modified from Schairer (1942).

lite, a phase outside this plane which consists of a solid 

solution of an unknown amount of iron-akermanite 

(2CaO-FeO-2SiO2 ) in 2CaOAl2O3 -SiO2 (gehlenite); 

olivine; probably solid solutions of CaOFeOSiO2 and 

2FeOSiO2 ; «-CaO-SiO2 ; and y3-CaOSiO2 solid solutions. Piercing point R'', at 1186° ±5°C, is the intersection of this plane with the univariant equilibrium 

a-CaOSiO2 , /3-CaO-SiO2 solid solutions, anorthite, and 

liquid of composition 47 percent CaO SiO2 ,35.5 percent

CaO-Al2O3 -2SiO2 , 17.5 percent FeO. Point R, 

1125°±5°C, is that of the equilibrium: y3-CaOSiO2 

solid solutions, anorthite, melilite, and liquid of composition 46.2 percent CaO SiO2 , 30.6 percent An, 23.2 percent FeO. Point V, 1188°±5°C, is the piercing point 

of the equilibrium a-CaO'SiO2 , /3-CaO-SiO2 solid solutions, olivine solid solutions, and liquid of composition 

64 percent CaO - SiO2 , 6 percent An, 30 percent FeO. 

This equilibrium terminates at the invariant point
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT -WATER L131

CaOAI203 Si02 

9 I345±5°

CaOAI203 -Si02 

rf 116515°

CaOFeO-Si02 

e 110513°

FeO-AI 203 Si02 

/ |073±5°

CaO FeO-Si02 

I272±3°c

126515° b

1193*3° a.

PWOL

AN

TRID

^2 PWOL

WOL

 > i 

TRID

ON PLANE

5 -FeSi03 -AN

3i02 pwOL

AN ,

 » i MEL

PWOL

WOL 

MEL

>i02 PWOL '

. WOL , « OLIV

PWOL

OLIV

MEL

PWOL WOL

WOL OLIV

AN TRID

TRID

' / WOL

D AN

TRID

PWOL

WOL

AN pwoL

WOL 

/MEL

/WOL 

G AN 1 - > , ., 4

MEL /

WOL OLIV 0

AN, TRID T

/COMPOSITION PLANE h

/ AN-TRID-FAY

E AN TRID I

OLIV ' TZ

WOL

OLIV

AN

AN 

WOL HER

OLIV OLIV 

/r/AN J 

^ MEL

/ "^-^_ AN

/ ^"v^OLIV

WOL / MEL^^ 

OLIV/ ^^^^^

/MPI ^^

/ 

' / /

/ AN

7/ HER \ OLIV

' \ MEL

PWOL

WOL

OLIV

MEL

OLIV

COMPOSITION PLANE 

AN-HER-FAY

FeO 

'138015°

CaO AI203 -Si02 

V'l5l2t5°

COMPOSITION PLANE 

COR-AN-HER

CaOAI203-SI02 

..A-1380 ±5°

FIGCEE 100. Diagram showing relations between univariant lines, ternary invariant points in the Ihniting systems (small letters), and quaternary invariant points (capital 

letters;. These lines and points do not lie in a plane. Only their relations to one another aie shown in this diagram which is not intended to depict their spatial or 

angular relations. The lengths of the univariant lines of this figure are arbitrary and without significance. Abbreviations for solid phases along the lines and at the points: 

AN anorthite; COR, corundum; FAY, fayalite; OEH, gehlenite; HER, heicynite; MEL, melilite; MULL, mullite; OLIV, olivine; PWOL, pseudowollastonite; TRID, 

tiidymite; WOL, wollastonite; and WUS, wustite. Reprinted from Schairer (1942).

TABLE 32. Significant points in the system CaO-FeO-Al2O3-SiO2 

[Locations of significant points in the five joins on univariant lines of figure 100]

Letter (significant point)

F

/-._._.....___._

J. .............

Rf . ............

R.. ............

S^. ...........

T ____________

U.. ............

V. ____________

V..............

Z. .............

A..............

D. .............

E. .............

N 1 __________

Figure on 

which 

point is 

shown

99 

99 

99 

101 

101 

101 

101 

101 

101 

101 

102 

102 

103 

103

Temperature (°C)

1120±4 

1108±4 

1070±4 

1186±5 

1125±5 

1130±5 

1188±5 

1118±5 

1188±5 

1145±5 

1320 ±5 

1263 ±10 

1178±4 

1180±5 

1393 ±4

Three solid phases

Line (fig. 100) 

on which 

letter point 

lies

IJ 

CI 

EC 

DG 

GF 

IK 

IJ 

IJ 

aH 

HF 

IK 

oj 

PH 

nJ 

AK

» Point Nrefers to the plane CaO.
L132 DATA OF GEOCHEMISTRY

CoO-AI203-2Si02 

ANORTHITE 

155212°

90,

«Xl37014°

10

CaO-Si02 

WOLLASTONITE

CaO-AI203 -2Si02 

ANORTHITE

WOLLASTONI 

SOLID SOLUTIONS

P-WOLLASTONITE 

<>£--CaO-Si02

30,

20

1290110'

W \40 

1203 ±3

2CaO-FeO-2Si02 

STABLE BELOW 775125°

FeO

WEIGHT PERCENT FeO

FIGURE 101. The plane CaO-SiOj (wollastonite)-CaO-AljO3-2SiOj (anorthite)-FeO through the tetiahedron CaO-FeO-AljOs-SiOj. Modified from Schairer (1942).

SiO2 +/8-CaO-SiO2 solid solutions + olivine solid solutions =L in the limiting ternary system CaO-FeO-SiO2 . 

Point F, 1145° ±5 °C, is the piercing point for 

the equilibrium /8-CaO SiO2 solid solutions, olivine solid 

solutions, melilite, and liquid of composition 54 percent

CaOSiO2, 16.5 percent anorthite, 29.5 percent FeO.

Point $, 1130° ±5°C, is the piercing point for the equilibrium anorthite, FeOAl2O3 , melilite, and liquid of 

composition 34.3 percent CaO-SiO2 , 35.5 percent anorthite, 30.2 percent FeO. Point T 1118°±5°C, is the
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L133

CaO-AI 2 03 -2Si02 

ANORTHITE

1552*2°

90

80

// I370±4°

70

60

2CaO AI2 03 Si02 

GEHLENITE

FeO

WUSTITE 

£l263±IO°

138 7 +3 

50

40

30

20

1290'

10,

2CaO-AI 203-Si02 I0 30 40 50 60 70 BOB 90 

I280±5e

FeO

GEHLENITE 

I590t2° WEIGHT PERCENT FeO

FIGURE 102. The plane 2CaO-AljOa-SiOj (gehlenite)-CaO-AliOj-2SiO» (anorthite)-FeO through the tetrahedlon CaO-FeO-AljOa-SiOj. Modified from Schairei (1942).

piercing point for FeO-Al2O3, olivine solid solution, 

melilite, and liquid of composition 37 percent 

CaO-SiO2, 25 percent anorthite, 38 percent FeO. 

Point Z7, 1118° ±5°C, is the piercing point for the 

equilibrium olivine solid solutions, FeO-Al2O3 , FeO, 

and liquid of composition 36 percent CaO-SiO2 , 25 

percent anorthite, 39 percent FeO.

A fourth plane is shown in figure 102, with components 2CaO A12O3 SiO2 (gehlenite), CaO A12O3 2SiO2 

(anorthite), and FeO. The primary phase volumes cut 

are those of FeO (wiistite), FeO-Al2O3 (hercynite), 

anorthite, and gehlenite, and the crystals formed in 

the gehlenite area may be melilite solid solutions of 

2CaO-Al2O3 -SiO2 and 2CaO-FeO-SiO2 (iron-aker-
L134 DATA OF GEOCHEMISTRY

2CaO-AI203 -Si02 

GEHLENITE 

.1590°

2CaO-FeO-2Si02 CaO-FeO 310^1208

1544

CaO-Si02 

WOLLASTONITE

I380 C

FeO

WEIGHT PERCENT FeO 

FIGURE 103. The plane CaO-SiO2 (wollastonite)-2CaO-Al2O3 -SiO2 (gehlenite)-FeO through the tetrahedlon CaO-FeO-AhOs-SiOs. Modified from Muan and Osborn (1951).

manite). At the piercing point A, 1263°±5°C, the 

phases are gehlenite solid solutions, FeO-Al2O3 , FeO, 

and liquid of the approximate composition 17.8 percent 

gehlenite, 1.4 percent anorthite, 80.8 percent FeO. At 

Z, 1320°±5°C, the reacting phases are gehlenite solid 

solution, anorthite, FeO-Al2O3 , and liquid of composition 37.3 percent gehlenite, 49.6 percent anorthite, 13.1 

percent FeO.

A fifth plane, CaO-SiO2-2CaO-Al2O3 -SiO2-FeO, 

was studied by Schairer (1942) and revised by Muan 

and Osborn (1951). The revised diagram is figure 103. 

The primary phase volumes intersected are a-CaO SiO2 ,

melilite solid solutions, olivine solid solutions, and wiistite. At the piercing point of the equilibrium 

a-CaO-SiO2 + melilite solid solution + olivine solid 

solution + liquid, point Z>, the temperature is 

1178° ±4°C, the liquid composition 59.8 percent 

CaO-SiO2 ,13.4 percent 2CaO-Al2O3 -SiO2 , 26.8 percent 

FeO. At the piercing point of the equilibrium olivine 

solid solution + melilite solid solution + wiistite + 

liquid, point E, the temperature is 1180°±5°C, the 

liquid composition 46.1 percent CaO SiO2, 15.7 percent 

2CaO-Al2O3 -SiO2 , 38.2 percent FeO. Muan and 

Osborn redetermined the binary (negelecting Fe2O3 )
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L135

2CaO-AI2 03 Si02 

GEHLENITEA , 590»

1545

1280°

2CaO-Si0 2 

2130°

WEIGHT PERCENT FeO

FIGURE 104. The plane 2CaO-SiO2-2CaO-Al2O3-SiOz (gehlenite)-FeO through the 

tetrahedron CaO-FeO-AhOs-SiOz. Modified from Muan and Osborn (1951).

system 2CaO A12O3 SiO2-FeO, and found the eutectic 

to be at 1280°C, 62 percent FeO, and they relocated the 

position of the trace of the boundary between wiistite 

and melilite.

Muan and Osborn (1951) studied this quaternary 

system in an interior tetrahedron whose base is the triangle 2CaO-SiO2-2CaO-Al2O3 -SiO2-CaO-SiO2 in the 

system CaO-Al2O3-SiO2 , and whose apex is FeO. The 

plane 2CaO SiO2-2CaO A12O3 SiO2 (gehlenite)-FeO 

is shown in figure 104. The primary phase volumes 

cut are 2CaO-SiO2, 2CaO-Al2O3 -SiO2 solid solution 

(melilite), and wiistite. At 1250 °C, where the 

boundaries of these phase spaces meet, is the piercing 

point of the equilibrium of these phase with a liquid 

of composition 21.3 percent 2CaO-SiO2 , 21.3 percent 

2CaO A12O3 SiO2 , and 57.4 percent FeO. The "FeO" 

component at this point is actually 48.9 percent FeO, 

8.5 percent Fe-jOs. In this interior tetrahedron appears 

a narrow primary phase volume of 3CaO-2SiO2 (fig. 

98). There are 3 invariant points in this interior 

tetrahedron. One of these is at 1195°±10°C, and the 

phases are 2CaO-SiO2 , olivine solid solution, melilite 

solid solution, wiistite, and liquid of composition 7 percent 2CaO-SiO2, 41 percent CaO-SiO2 , 17 percent 

2CaO-Al2O3 -SiO2 , or 32 percent CaO, 35 percent FeO, 

6 percent A12O3 , 27 percent SiO2 . This invariant point 

is connected with the piercing point mentioned above 

in the plane 2CaO-SiO2-2CaO-Al2O3 -SiO2-FeO. A 

second invariant point is at 1200°±10°C, and the 

phases are 2CaO-SiO2 , 3CaO-2SiO2 , olivine, melilite,

and liquid of composition 10 percent 2CaO2 -SiO2 , 51 

percent CaO-SiO2 , 17 percent 2CaO-Al2O3 -SiO2 , or 

37.5 percent CaO, 25 percent FeO, 5.5 percent 

A12O3 , 33 percent SiO2 . At a third invariant point, 

1175°±5°C, the phases are 3CaO-2SiO2 , CaO-SiO2 , 

olivine, melilite, and liquid of composition 5 percent 

2CaO-SiO2, 61 percent CaO-SiO2 , 12 percent 

CaO-Al2O3 -SiO2 , 22 percent FeO, or 37.5 percent CaO, 

22 percent FeO, 4.5 percent A12O3 , 36 percent SiO2. 

This is connected with the line pH of figure 100 by the 

equilibrium a-CaO SiO2 + olivine + melilite + L.

The system CaO-Al2O3-Fe2O3-SiO2, which is of importance in the portland cement industry, has been 

studied by Lea and Parker (1934) and by Swayze 

(1946) and a full discussion is given by Rait (1949) 

and by Bogue (1955). The region of most interest in 

cement technology is included in the tetrahedron with 

apex at CaO, with the base

2CaO SiO2-4CaO A12O3 Fe2O3-5CaO 3 A12O3 

shown in figure 105. One side of this tetrahedron 

CaO-2CaO-SiO2-5CaO-3Al2O3 was determined by 

Rankin and Wright (1915) in their study of the system 

CaO-Al2O3-SiO2 ; the side

CaO-5CaO 3Al2O3-4CaO A12O3 Fe2O3

by Hansen, Brownmiller, and Bogue (1928) and is included in figure 43. The side

CaO-2CaO SiO2-4CaO A12O3 Fe2O3

was worked out by Lea and Parker. The system 

CaO-4CaO'Al2O3 -Fe2O3 is binary, with a eutectic at 

1350°±10°C and 49.6 percent CaO, 17.1 percent A12O3 , 

26.8 percent Fe2O3 , 6.5 percent SiO2 . There is a narrow 

field of 3CaO-SiO2 , terminating at the ternary eutectic, CaO + 3CaO-SiO2 + 4CaO-Al2O3 -Fe2O3 =Z, at 

1347° ±5°C, and the composition of the liquid is 

52.8 percent CaO, 16:2 percent A12O3 , 25.4 percent 

Fe2O3 , 5.6 percent SiO2 . There is also a reaction point,

3CaO SiO2 + 4CaO A12O3 Fe2O3 = 2CaO SiO2 + Z, 

at 1348° ±5°C, and the composition of the liquid is 52.4 

percent CaO, 16.3 percent A12O3 , 25.5 percent Fe2O3 , 

5.8 percent SiO2 . The invariant point

CaO + 3CaO SiO2 + 2CaO SiO2 + L

was not located, but it is on the CaO-side of the join 

3CaO SiO2-4CaO A12O3 Fe2O3 . 

The base of this inside tetrahedron,

2CaO SiO2-4CaO A12O3 Fe2O3-5CaO 3A12O3 , 

was studied by Lea and Parker. There is a ternary 

eutectic at 1280° ±5°C, with a liquid of composition 

50.0 percent CaO, 34.5 percent A12O3 , 9.9 percent 

Fe2O3 , 5.6 percent SiO2 . The quaternary system was

695-382 O - 64 - 10
L136 DATA OF GEOCHEMISTRY

To Fe2 03

CoO Fe 2 0

2CoO-Fe 2Oj

CaO

To Si02

3CaO-AI 2 03 5CoO-3AI2 03 CoO-AI 203

TO AI203

FIGURE 105*. Diagrammatic representation of part of the tetrahedron CaO-AljOj-FesOs-SiOj showing the regions studied.

studied by means of planes through the tetrahedron 

containing 2, 5, 10, and 20 percent Fe2O3, respectively. 

In considering the crystallization relations the quaternary system is divided into three sections. One of 

these is the smaller tetrahedron

CaO-3CaO SiO2-4CaO A12O3 Fe2O3-3CaO A12O3 ,

and these phases form a quaternary eutectic at 1341 °C, 

55 percent CaO, 22.7 percent A12O3 ,16.5 percent A12O3 , 

5.8 percent SiO2 Within the wedge-shaped tetrahedron 3CaO SiO2-2CaO SiO2-4CaO A12O3 Fe^CX3CaO-Al2O3, crystallization leads to an invariant point 

at 1338° ±3°C, at which the liquid composition is 54.8 

percent CaO, 22.7 percent A12O3 ,16.5 percent FeaOs, 6.0 

percent SiO2 . The third tetrahedron is 2CaO-SiO2- 

4CaO A12O3 Fe2O3-5CaO 3Al2O3-3CaO A12O3, and 

the invariant point is at 1280° ±5°C, 50 percent CaO,

34.4 percent A12O3 , 10 percent Fe2O3 , 5.6 percent SiO2. 

Swayze (1946) extended the study to 2CaO-Fe2O3, that 

is, to the tetrahedral section

CaO-2CaO SiO2-2CaO Fe2O3-5CaO 3A12O3, 

and located the position of two invariant points. One 

of these, at which the solid phases are CaO, 

3CaO-SiO2 , 3CaO-SiO2 , 3CaO-Al2O3 , and the solid solution 6CaO-a?Al2O3 -2/Fe2O3 , is at 1342°C, and the 

liquid has the composition 53.9 percent CaO, 21.2 percent A12O3, 19.1 percent Fe2O3, 5.8 percent SiO2. At 

the other, solid phases are 3CaO-SiO2 , 2CaO-SiO2 , 

3CaO-Al2O3, and the solid solution

6CaO aA!2O3 2/Fe2O3 ;

the liquid has the composition 53.5 percent CaO, 22.3 

percent A12O3,18.2 percent FeaOs, 6.0 percent SiO2 , and 

the temperature is 1338 °C.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L137

SiO

3AI203 -2Si02 

MULLITE

90 Z MAGNETITE ss

FeO-F:e203 10 20 90 AI 203

WEIGHT PERCENT AI 2 03

FIGURE 106. The system iron oxide-AljOj-SiOa in air. Modified from Muan (1957a). st Solid solution.

CaO-Al2O3-SiO2-TiO2

Iwase and Nisioka (1936) studied the ternary 

system CaOSiO2-CaOAl2O3 -2SiO2 (anorthite)- 

CaO-SiO2 -TiO2 and found a eutectic at 1240°C, 37.5 

percent CaOSiO2 , 37.5 percent CaO-Al2O3 -2SiO2 , 25 

percent CaO SiO2 TiO2 , with these compounds as solid 

phases. Nisioka (1935) found a single eutectic relationship between CaO A12O3 2SiO2 and CaO TiO2 .

Greig (1927b) , following his study of liquid immiscibility in the system FeO-Fe2O3-SiO2, studied the effect

of addition of A12O3, and expressed his results by the 

intersection of the curved surface of two immiscible 

liquids with planes at 1, 2, 3, 4, 5, and 6 percent A12O3 . 

Between 2 and 3 percent of A12O3 sufficed to make the 

liquids miscible. 

Muan (1957a) studied the system

FeO-Fe2O3-Al2O3-SiO2

by the quenching method in air (Po2 =0.21). The results in air are shown in figure 106. The crystalline 

phases existing in equilibrium with a liquid are: tridymite and cristobalite; a spinel, which is a solid solu-
L138 DATA OF GEOCHEMISTRY

Si02

80

9Q

FeO-Fe203 10 20 30 40 50 60 70 80 90 AI203

WEIGHT PERCENT AI2 03

FIGURE 107. The system iron oxide-AhOs-SiOj at 1 atm oxygen pressure. Modified from Muan (1957b). ss Solid solution.

tion between FeOFe2O3 (magnetite) and FeOAl2O3 

(hercynite) with some excess A12O3 and (or) Fe2O3 in 

solid solution; 3A12O3 -2SiO2 (mullite) containing some 

Fe2O3 ; corundum with some Fe2O3 in solid solution; 

two immiscible liquid layers, which become miscible 

with more than 6 percent A12O3 . There are two quaternary piercing points: at 1460°C and 0.21 atm O2 the 

phases are liquid of composition 17 percent FeO, 38 

percent Fe2O3 , 25 percent A12O3 , and 20 percent SiO2 , 

cristobalite; tridymite; mullite solid solution; spinel 

solid solution; and corundum solid solution. At 

1380°C and 0.21 atm O2 the phases are liquid of composition 17 percent FeO, 38 percent Fe2O3 , 25 percent 

A12O3 , and 20 percent SiO2 . The liquid immiscibility 

gap in the system iron oxide-SiO2 is removed by the 

addition of 6 percent A12O3 .

In another paper, Muan (1957b) worked chiefly at 

Po2 =l atm but also made runs at pressures ranging 

from 0.9 atm to 1Q-12 - 5 atm. The results at 1 atm are 

shown in figure 107. The crystalline phases are the 

same as in air, with variations in the limits of solid 

solution; and Fe2O3 -Al2O3 with some variation in the 

Fe2O3 /Al2O3 ratio. The tabulation below shows the 

six quaternary piercing points found at _Po2=l atm.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER

CoO-AI 203-2Si02

ANORTHITE

,1553 ±2°

L139

10 90

30

1118 ±.3

 1150° 

 1100°-

70

90

Na2 0-AI2 03-6Si02 10 

ALBITE

20 30 40 1078 ±3° 60 

WEIGHT PERCENT

70 80 90 K20-AI2 03 -6Si02 

POTASSIUM FELDSPAR

FIGURE 108. Crystallization of mixtures of three feldspars. This triangular diagram is a section through the tetrahedron Na2O-Al2O3-6SiO2-KzO-Al2O3-6SiOi>-CaO-Al2O3-

2SiO2-SiO2 . Modified from Franco and Schairer (1951).

Quaternary piercing points at = l aim

Temperature (°C)

1390 ....

1452-.. ....

1440...... .

1445-.. ....

1470.......

1495-......

Reaction phase

Tridymite, mullite ««, hematite ** _ 

Tridymite, hematite ss, spinel ss. _ 

Mullite ss, hematite ss, hercynite ss. 

Hematite ss, hercynite ss, spinel ss.. 

Mullite ss, hercynite ss, corundum 

ss. 

Hercynite ss, spinel ss, corundum ss.

Composition of liquid 

(percent by weight)

FeO

13 

15 

15 

16 

15

15

FejO3

27 

65 

40 

41 

39

43

AUOa

20 

2 

29 

24 

32

31

SiO2

40 

18 

21 

19 

21

11

QUINARY SYSTEMS

Systems containing five components may formally be 

considered as represented by a pentahedroid or pentatope, the analog in four-dimensional space of a tetrahedron in three-dimensional space. The pentatope 

ABODE may be considered as resulting from the fusing

together in four-dimensional space of the two tetrahedra ABCD and ABCE, each of which has the same 

base, ABC, and D and E remain on the same side of 

the plane ABC. Morey (1930d) discussed the calculation of mixtures in a tetrahedral section of a pentatope, 

and of the triangular intersection of two tetrahedra. 

The few quinary systems which have been worked on 

have been composed of three stable compounds; they 

could therefore be represented by triangular diagrams.

The study by Franco and Schairer (1951) of liquidus 

temperature in mixtures of the potassium, sodium, and 

calcium feldspars was an exploration of a part of this 

quinary system. Their results are shown in the triangular diagram of figure 108, which is not a ternary sys-
L140 DATA OF GEOCHEMISTRY

CoO-MgO-2Si02 

DIOPSIDE

1350' .1350°

1300s

1300

1300°

I350 C

1250 1400°

|450 C

1200°,

1500s

1085 

i

Na20-AI203 '6Si02 

ALBITE

ANORTHITE

-2SJ02

WEIGHT PERCENT ANORTHITE 

FIGURE 109. Crystallization of mixtures of NasO-AlsOs-BS^ (albite)-CaO-MgO-2SiO2 (diopside)-CaO-AhO3-2SiO! (anorthite). Modified from Bowen (1915).

tern. The feldspars which separate over most of the diagram presumably can be represented in terms of the 

three components, but since K2O A12O3 6SiO2 melts incongruently there is an area in which K2O A12O3 -4SiO2 

(leucite) is the primary phase; hence, the more siliceous 

liquid formed is outside the component triangle. The 

melting relations probably could be represented by a 

plane through the tetrahedron Na2OAl2O3 -6SiO2- 

K2O A12O3 6SiO2-CaO A12O3 2SiO2-SiO2 .

Na2O-MgO-C aO-A!2O3- SiO2

Bowen (1915) studied the system Na2OAl2O3 6SiO2

(albite)-CaO-MgO-2SiO2 (diopside)- 

CaOAl2O3 -2SiO2 (anorthite), which is part of the

quinary system Na2O-MgO-CaO-Al2O3-SiO2. The 

results are shown in figure 109. The triangular diagram is divided into two parts by the curve DE. 

On one side is a field of diopside, on the other 

a field of plagioclase feldspars, solid solutions of 

albite and anorthite. The curve DE rises from 

the albite-diopside eutectic, D, near 1085 °C and 

97 percent albite, to the anorthite-diopside eutectic 

E, at 1270 °C and 42 percent anothite. The side 

Na2O A12O8 2SiO2-CaO -MgO 2SiO2 is not binary because of the field of forsterite, 2MgOSiO2.

In the discussion of this system Bowen gave a clear 

example of the methods for the determination of 3- 

phase boundaries. In figure 110, in which DFE is the
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L141

CaO-MgO-ZSiOg 

DIOPSIDE

££'

Na20-AI203 -6Si02 

ALBITE ANORTHITE

FIGURE 110. Phase relations at 1230°C (solid lines) and 1250°C (broken lines) in the system NazO-AhOs-eSiCh (albite)-CaO-MgO-2SiO» (diopside)-CaO-AhO3-2SiO2 (anorthite). Modified from Bowen (1915).

isotherm at 1230° C, the phases present in the various 

areas are:

Area DFEB, all liquid

Area EFG, liquid E-F and plagioclase K-G 

Area ADF, liquid D-F and diopside 

Area AFG, liquid F, plagioclase G, and diopside 

Area AGC, plagioclase G-C and diopside 

This line FG which bounds the field AFG is called a 

3-phase boundary (Bowen, 1915). AF and AG likewise bound the 3-phase field, but they are merely lines 

radiating from A, their position being completely determined by the points F and G. To predict the phases

present at 1230 °C in a given mixture it is necessary to 

know the position of the line FG^ the 3-phase boundary 

for that temperature, or at 1250 °C, on line F'G' and so 

on for other temperatures.

The determinations of the 3-phase boundaries can be 

accomplished in a number of ways, the principles of 

which are discussed with reference to figure 110. For 

a given position of the isotherm DFE that is, a known 

temperature it is only necessary to note that G represents the composition of the plagioclase which is in 

equilibrium with both liquid and diopside. If a mixture which gives all three phases is held at the desired
L142 DATA OF GEOCHEMISTRY

temperature, and the composition of the plagioclase is 

determined by optical methods, then the point G is determined and the figure for that temperature can be 

drawn. This may be called a composition method since 

it depends on the composition of the mix-crystal.

The 3-phase boundaries may be located by starting 

with a mixture of known composition and determining 

the temperature at which the 3-phase area is entered 

either from above or below. Any point on the line AG, 

such as P, lies on the border of the 3-phase area for 

1230°C, and at this temperature, as at all lower temperatures it consists entirely of diopside and plagioclase, but if the temperature is raised a little the point 

enters the 3-phase area for this higher temperature 

(note that the point P lies well within the 3-phase area 

for 1250°C, AF'G'} that is, liquid is added to the 

phases already present. A 3-phase boundary, then, can 

be located by determining the temperature of beginning 

of melting for any mixture. Thus if any mixture of 

diopside with plagioclase of composition G is taken 

and the temperature of beginning of melting determined it will be found at 1230°C. If the isotherm for 

1230°C as previously determined is drawn, then the join 

FG is the 3-phase boundary for 1230°C.

The 3-phase boundary may also be determined by 

entering the 3-phase region from a higher temperature. 

The point R lies within the field of liquid and plagioclase, E'F'G', at 1250°C, and is in the border of the 

3-phase area at 1230°C, and if the temperature is 

lowered a little it enters the 3-phase area for this lower 

temperature, and liquid and plagioclase are joined by 

diopside. By determining the temperature (approached 

from above) at which the liquid and plagioclase are 

joined by diopside, the 3-phase boundary passing 

through the composition of the mixture can be determined. Thus, if the mixture R is taken it is found that 

diopside just appears at 1230°C, and if the isotherm 

of 1230°C, DEF, is drawn, FR joined and produced to 

G, then FG is the 3-phase boundary.

Determination of the crystallization paths can be 

quantitatively described when the 3-phase boundaries 

are known. Thus in figure 111 the mixture F (Ab: A^5 

50 percent, diopside 50 percent) begins to crystallize at 

1275°C, diopside separating and the liquid changing 

composition along the straight line AFG toward G. At 

1235 °C when the liquid has the composition G, plagioclase of composition H (Ab: J.n4 ) begins to crystallize; 

the point H is determined by the 3-phase boundary, GH, 

through G. As the temperature is lowered the composition of the liquid follows the boundary curve DE 

toward M. At 1218°C when the liquid has the composi-

'This means that the composition of the plagioclase is 1 part albite, 1 part 

anorthite.

tion /T, plagioclase has changed in composition from H 

(Abi An*) to L (Abt An2 ). Finally at 1200°C the 

liquid is used up, the last minute quantity having the 

composition M, the plagioclase has the composition Z 

(Abt Ani) the intersection of the line AF with the side 

albite-anorthite. The composition X (Ab2 An! 60 percent diopside 40 percent) begins to crystallize at 

1252 °C with the separation of diopside, meets the curve 

DE at 1218°C at K with separation of plagioclase of 

composition L (Ab^ An2 ) , and solidifies completely at 

1176°C to a mixture of diopside and plagioclase of composition T (Ab2 A-&I).

For all mixtures in the diopside field, the change of 

composition of the liquid is represented by a straight 

line until the boundary curve DE is reached. For mixtures in the plagioclase field the liquid follows a curved 

course in reaching the boundary curve. In order to 

find the composition of liquid in equilibrium with solid 

it is necessary to determine the index of refraction of 

the quenched glass. This fixes its position on a series 

of curves of equal index of refraction called isofracts. 

The composition of the glass must also be on the isotherm of the temperature at which the liquid was held. 

It must, therefore, be at the point of intersection of the 

isof ract and the isotherm.

The crystallization paths of two mixtures in the 

plagioclase field are shown on figure 112. The mixture 

(AbiAni 85 percent-diopside 15 percent) (Z), fig. 112) 

begins to crystallize at 1375 °C with separation of 

plagioclase of composition AbiAn^. As the temperature falls the plagioclase increases in amount and 

changes in composition until at 1300°C the liquid has 

the composition P and plagioclase the composition 

AbiAn3 . When the temperature has fallen to 1261 °C 

diopside begins to crystallize and the liquid has the composition M, the plagioclase the composition S 

(Ab±An2 ), and SM is the 3-phase boundary through D. 

With further lowering of temperature the liquid follows the boundary, with simultaneous crystallization 

of diopside and plagioclase, until at 1200 °C the mixture solidifies completely. The plagioclase has the composition F (AbiAni), on the line ADF, and FH is a 

3-phase boundary.

In the liquid E (Ab18An82 90 percent-diopside 10 

percent), crystallization begins at 1480°C with separation of Ab5An95, and the composition of the liquid follows the curve ERN. At 1245 °C diopside begins to 

crystallize. The composition of the plagioclase is 

T (Ab15An85 ), and NT is the 3-phase boundary. The 

mixture freezes completely at 1237°C, the composition 

of the liquid is 0, the feldspar (Abi8An82 ).

The crystallization curves, DPM and ERN apply to 

the liquids D and E, respectively, and to no other
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L143

CoO-MgO-ZSiOg 

DIOPSIDE

Na0 H

ALBITE

CaO-AI203 -2Si02 

ANORTHITE

FIGURE 111. Crystallization paths of mixtures in the diopside field ha the system NasO-AljOs-eSiOz (albite)-CaO-MgO-2SiOs (diops>ide)-CaO-Al2O3-2SiO2 (anorthite).

Modified from Bowen (1915).

liquids. Thus, the crystallization curve of the liquid P 

is not the curve PM but the new curve PL, that is, a 

liquid of composition P free from crystals follows the 

curve PL. Only when the liquid P contains the crystals formed during the change from D to P does the 

further course of the liquid coincide with PM. Moreover, the liquid P when originally free from crystals 

becomes completely crystalline on cooling, not at 

1200°C (H) as before, but at a lower temperature.

Several sections through the quaternary system 

Na2OAl2O3 -2SiO2 (nepheline)-2MgOSiO2 (forsterite)-CaO -MgO -2SiO2 (diopside)-SiO2 have been studied (fig. 113). This quaternary system is a part of 

the quinary system Na2O-MgO-CaO-Al2O3-SiO2.

Schairer (1957a) published the phase-equilibrium diagram of the system nepheline-diopside-silica (fig 114). 

Schairer and Morimoto (1958) studied the system 

Na2O-Al2O3 -6SiO2 (albite)-2MgO-SiO2 (forsterite)- 

CaOMgO-2SiO2 (diopside), and found an initial 

falling of the liquidus temperature toward the point 

where sodium-rich plagioclase and diopside coexist with 

liquid at the side line albite-diopside, which is not binary. The diopside crystals may contain some A12O3 . 

The relation of this system to the quaternary system 

nepheline-forsterite-diopside-silica is shown in figure 

113, and the phase-equilibrium diagram is figure 115. 

Schairer and Morimoto (1959) extended this work by 

a study of the plane albite-protoenstatite-diopside.
L144 DATA OF GEOCHEMISTRY

CaO MgO-2Si02 

DiOPSIDE

No20-AI203 -6Si02 

ALBITE

CaOAI203-2Si02 

ANORTHITE

FIGURE 112. Crystallization paths of mixtures in the plagioclase field in the system NajO-AljO3-6SiOj (albite)-CaO-MgO-2SiO» (diopside)-CaO-AlsO3-2SiOj (anorthite).

Modified from Bowen (1915).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L145

2MgO- Si02 

FORSTERITE

NEPHELINE

CaO-MgO-2Si02 

DIOPSIDE

FIGURE 113. The quaternary system Na»0-Ah08-2SiOj (nepheline)-2MgO-S10» (forsterite)-CaO-MgO-2SiO» (diopside)-SiOj, showing the ternary sections which have been

studied.
L146 DATA OF GEOCHEMISTRY

CaO-MgO-2Si02 

DIOPSIDE

1391.6°,

90 10

|362±3°

I295°± 20 

1470110°

30

169715°

40

TW9 LIQUIDS 

70

\ 

80

90

152612 

Na20-AI203 '2Si02 

CARNEGIEITE 

NEPHELINE

10 1280° / 106815° 40 

Na20'AI2 03 -4Si02

JADEITE

\ 50 Na20-AI2 03 -6Si02

ALBITE 

111813°

106212° 70

169715° 

171315°

Si02 

SILICA

WEIGHT PERCENT Si02

FIGURE 114. The ternary system NasO.AljO3-2SiO2 (nepheline)-CaO-MgO-2SiOs (diopside)-SiOs. Modified from Schairer (1957a).

The relation of this plane to the system nephelineforsterite-diopside-silica is indicated by a plane in figure 113 and the phase-equilibrium diagram is figure 

116. Since forsterite, the composition of which does 

not lie in this plane, is a primary phase, the liquid also 

cannot lie in this plane, the composition range enstatitealbite-diopside is not a ternary system, and the crystallization sequence on cooling is not simple.

Schairer and Yoder (1960b) have published a preliminary diagram for the system 2MgO SiO2 (forsterite)- 

Na 2OAl2O3 -2SiO2 (nepheline)-CaO-MgO-2SiO2 (diopside) (fig. 117). The primary phases forsterite,

spinel, carnegieite solid solutions, nepheline solid solutions, and diopsidic pyroxenes appear on the liquidus 

surface. During crystallization the spinel disappears 

by reaction with liquid at 1245° ±5°C. Melilites, 

which probably contain some sodium, in addition to 

akermanite and gehlenite, appear at subliquidus temperatures as crystalline solid phases.

K2O-MgO- CaO-Al2O3-SiO2

The system K2OAl2O3 -4SiO2 (leucite)- 

CaOMgO-2SiO2 (diopside), studied by Bowen and 

Schairer (1929a), and the system K2O-Al2O3 -4SiO2-
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L147

IB90±2° ,1391.5°

2MgO-SI02 10 20 30 

FORSTERITE

TO 80x^90 CaO-MgO-2SIOz

WEI6HT PERCENT D.OPS.DE

FIGURE 115. The ternary system Na!O-AhOj-6SiO2(albite)-2MgO-SiO2(.forsterue)- 

CaO-MgO-2SK>2 (diopside). Modified from Schairer and Morimoto (1958).

CaO-M;gO-2SiO2-SiO2 , studied by Schairer and 

Bowen (1938), represent portions of the 

five-component system K2O-MgO-CaO-Al2O3-SiO2 . 

Leucite and diopside form a binary system, with a 

eutectic at 1300°±2°C, and 61.5 percent-diopside. The 

ternary system is shown in figure 118. The field of 

diopside drops down so close (to less than 2 percent 

diopside) to the leucite-silica side, that the field of 

potassium feldspar in the ternary system is very small, 

and the compositions in this low-temperature region are 

so very viscous as to be impossible or almost impossible to crystallize. The ternary reaction point 

K2O A12O3 2SiO2 + K2O A12O3 6SiO2 + liquid is 

below 1100°C; the eutectic K2O A12O3 6SiO2 + 

MgO-CaO-2SiO2 + tridymite=Z is below 900°C. 

These liquids contain little diopside, but their composition could not be precisely determined.

MgO-CaO-Al2O3-Fe2 O3-SiO2

Swayze (1946) studied the effect of adding 5 percent 

of MgO to the quaternary system

CaO-2CaO SiO2-5CaO 3Al2O3-2CaO Fe2O3 . 

The invariant point at which the solid phases are CaO, 

3CaO-SiO2 , 3CaO-Al2O3 , and the solid solution 

6CaO-ajAl2Os-yFe2Oa at 1342°C is lowered to 1305°C, 

and the composition of the liquid changed to: 5 percent 

MgO, 50.9 percent CaO, 22.7 percent A12O3 , 15.8 percent Fe2O3 , 5.6 percent SiO2 . At the other invariant 

point, at which the solid phases are 3CaO-SiO2 ,

2CaO-SiO2 , 3CaO-Al2O3, and the solid solution 

6CaO-a?Al2O3 -yFe2O3, at 1338°C, the temperature is 

lowered to 1301 °C, and the liquid changed to 5 percent 

MgO, 50.5 percent CaO 23.9 percent A12O3, 14.7 percent 

Fe2O3 , 5.9 percent SiO2 . The addition of MgO raised 

the A12O3 content at each invariant point, and diminished the Fe2O3 and CaO content more than the corresponding amount, thus lengthening the field of the 

iron-containing solid solution.

Prince (1943) studied the system

Na2O-Al2O3 -6SiO2 (albite)-CaO-A!2O3 -2SiO2 (anorthite) -CaO- SiO2 -TiO2 (sphene), with results shown 

in figure 119. The side albite-sphene is not a binary 

system, because the feldspar separating is not pure 

albite but a plagioclase containing some CaO. On the 

side anorthite- sphene there is a binary eutectic at 

1301°C, 37 percent anorthite (point E, fig. 119). The 

triangular diagram shows a large area of plagioclase 

feldspars, bounded by the line EF, and there are no 

invariant points.

PETROGENY'S RESIDUA SYSTEM 

Bowen (1937) called the system

Na2O A12O3 2SiO2-K2O A12O3 2SiO2-SiO2

"petrogeny's residua system." He showed that the association of alkalic lavas of the region of the Great Rift 

Valley in Africa has those chemical characters of residual liquids that one is led to expect from the experimental studies of a number of relatively simple systems 

combining one of the early-crystallizing minerals in 

rocks with late-crystallizing alumino-silicates. The relations of these simple systems to petrogeny's residua 

system are shown in figure 120, reprinted from Schairer 

and Bowen (1956). Petrographic evidence indicates 

that an olivine, a solid solution of 2MgO-SiO2 (forsterite) and 2FeO-SiO2 (fayalite), is one of the earliest minerals to crystallize from rocks. One of the 

next minerals to crystallize is a pyroxene, and 

CaO-MgO-SiO2 (diopside) is a simple pyroxene. 

Another early mineral to crystallize is a plagioclase 

feldspar rich in CaO < Al2O3 -2SiO2 (anorthite). 

By combining the four early-crystallizing minerals 

forsterite, fayalite, diopside, and pyroxene with 

the potassium and the sodium aluminosilicates, we get 

a series of eight simple systems. In the system leuciteforesterite-silica (fig. 70), the lowest melting liquid 

is the ternary eutectic between potassium feldspar, tridymite, and enstatite, which is nearly coincident in temperature and composition with the binary eutectic be-
L148 DATA OF GEOCHEMISTRY

ALBITE III8±3° 

SOD 1C PLAGIOCLASE

II30±2°

20

40

60

80 20

90 10

1391.5°

MgO-SiOg

PROTOENSTATITE

ENSTATITE

10 20 70 -"±2° T 80 

I392±J

30 40 50 60 90

WEIGHT PERCENT DIOPSIDE

FIGURE 116. The system MgO-SiO2 (protoenstatite)-NazO-AljOj-6SiOj (albite)-CaO-MgO-2SiOj (diopside). Modified from Schairer and Morimoto (1969).

CaO-MgO-2Si02 

DIOPSIOE

tween potassium feldspar and tridymite. The system 

leucite-fayalite-silica (fig. 79) shows a similar lowmelting liquid, as do also the systems leucite-diopsidesilica (fig. 118) and leucite-anorthite-silica (fig. 78).

In each case the lowest melting mixture is rich in 

aluminosilicates and lies close in temperature and composition to the binary eutectic between potassium feldspar and tridymite. The same general relationship is
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L149

NEPHELINE

7 x 152612° 

14331

CARNEGIEITES

80

1260 ±5° 

124515°

70

NEPHELINES

119312* 

60

50

1890120°

2MgO Si02 

FORSTERITE

40

126012° 

30

20

90

DIOPSIOIC 

PYROXENES

10

1391.5°

10 CaO-MgO-2Si0230 40 50 60

i-zp^-f-po ^

WEIGHT PERCENT DIOPSIDE

FIGURE 117. The system 2MgO-SiOj (forsterite)-NajO-AljOs-2SiOz (nepheline)-CaO-MgO-2SiOj (diopside). Modified from Schairer and Yoder (1960b).

true in the simple systems with nepheline and silica, as 

will be seen by inspection of figures 67, 68, and 114. All 

these simple systems yield residual liquids from crystallization which are rich in aluminosilicates, and crystallization even of complex mixtures leads to the low-temperature trough in petrogeny's residua system. All 

these experimental systems lead to the conclusion that 

a granitic liquid is the goal toward which crystallization 

proceeds, and Bowen's discussion indicates that similarly a granitic liquid is the goal in magmatic processes.
L150 DATA OF GEOCHEMISTRY

CaO-MgO-2Si02 

DIOPSIDE

1391

90

1686

K20-AI 2 03-4Si02 I0 

LEUCITE

20 \ 30 40 / 50 60 

K20-AI203-6Si02 POTASSIUM FELDSPAR

POTASSIUM FELDSPAR

WEIGHT PERCENT SiO,

80 1470° 90 Si02

FIGURE 118. The ternary system KiO-AliOj-4SiOj (leucite)-CaO-MgO-2SiOi (diopside)-SiOi. Modified from Schairer and Bowen (1938).
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L151

CaO-Si02 -Ti02 

SPHENE

Na20-AI2 03 -6Si02 

ALBITE

WEIGHT PERCENT ANORTHITE

CaO-AI203 -2Si02 

ANORTHITE

FIGUKE 119. The triangular section NajO-AljOs-eSiOj (albite)-CaO-AljOa-2SiOj (anorthite)-CaO-SiOa-TiOj (sphene) showing isotherms. Modified fiom Prince (1943).

695-382 O - 64 - 11
L152 DATA OF GEOCHEMISTRY

FORSTERITE 

FAYALITE 

DIOPSIDE ~~ 

ANORTHITE

Si02

NaAISiO KAISify 

NEPHELINE.CARNEGIEITE KALSILITE.KALIOPHILITE

FIGUBE 120. Petrogeny's residua system. Reprinted from Schairer and Bowen (1956).

FORSTERITE 

FAYALITE 

'DIOPSIDE 

ANORTHITE

REFERENCES

Adams, L. H., 1953, A note on the stability of jadeite: Am. Jour.

Sci., v. 251, p. 299-308. 

Agamawi, Y. M., and White, J., 1952, The system AljOs-TiOrSiO2 : British Ceramic Soc. Trans., v. 51, p. 293-325. 

Alien, E. T., and White, W. P., 1909, Diopside and its relation

to calcium and magnesium metasilicates: Am. Jour. Sci.,

4th sen, v. 27, p. 1-47. 

Andersen, Olaf, 1915, The system anorthite-forsterite-silica:

Am. Jour. Sci., 4th ser., v. 39, p. 407-454. 

 1919, The volatilization of lead oxide from lead silicate

melts: Am. Ceramic Soc. Jour., v. 2, p. 784-789. 

Aramaki, Shigeo, and Roy Rustum, 1959, Revision of equilibrium

diagram for the system AhOa-SiO:,: Nature, v. 184, p. 631-

632. 

Aruja, E., 1959, The unit cell of pentacalciumtrialuminate,

5CaO-3Al2O3 : Acta Cryst., v. 10, p. 337-341. 

Atlas, Leon, 1952, The polymorphism of MgSiO3 : Jour. Geology,

v. 60, p. 125-147. 

Bakhuis Roozeboom, H. W. 1901-13, Die heterogenen Gleichgewichte von Standpunkte der Phasenlehre: v. 1 Systeme

aus einer Komponente, 1901; v. 2 Systeme aus zwei Komponenten, 1904; v. 3 Die ternaren Gleichgewichte, by

F. A. H. Schreinmakers, pt. 1, Systeme mit nur einer Flussigkeit ohne Mischkristalle und ohne Dampf, 1911; pt 2,

Systeme mit zwei und mehr Flussigkeiten und ohne Dampf,

1913: Braunschweig, F. Vieweg und Sohn. 

Bates, Frederick, and Phelps, F. P., 1927, A new base point on

the thermometric scale and the «;±0 inversion of quartz:

U.S. Natl. Bur. Standards, No. 557, Sci. Papers v. 22, p.

315-327. 

Beevers, C. A., and Ross, M. A. S., 1937, The crystal structure

of "Beta-alumina," Na»O 11A12O3 : Zeitschr. Kristallographie, v. 97, p. 59-66. 

Bernal, J. D., 1936, Geophysical discussion: Observatory, v. 59,

268 p. 

Birch, Francis, and LeComte, Paul, 1960, Temperature-pressure

plane for albite composition: Am. Jour. Sci., v. 258, p. 209-

217.

Bogue, R. H., 1955, The chemistry of Portland cement: New 

York, Reinhold Publishing Co., 572 p.

Botvinkin, O. K., and Popova, T. A., 1937, The melting diagram 

of the system Na2SiO3-Mg2 SiO4-SiO2 : 2d Conf. Experimental Mineralogy, Petrog., Moscow 1936, p. 87-93. Pub. by 

Akad. Nauk SSSR, Geol. Gruppa i Petrograf. Inst Imeni 

F. Yu. Levinson-Lessing (in Russian).

Bowen, N. L., 1912, The binary system Na2Al2 Si2O8 (nepheline, 

carnegiete)-CaAl2Si2O8 (anorthite) : Am. Jour. Sci., 4th 

ser., v. 33, p. 551-573.

 1913, Melting phenomenon of plagioclase feldspar: Am. 

Jour. Sci., 4th ser., v. 35, p. 577-599.

 1914, The ternary system : diopside-forsteritensilica: Am. 

Jour. Sci., 4th ser., v. 38, p. 207-264.

 1915, The crystallization of haplobasaltic, halplodioritic, 

and related magmas: Am. Jour. Sci., 4th ser., v. 40, p. 161- 

185.

 1917, The sodium-potassium nephelites: Am. Jour. Sci., 

4th ser., v. 43, p. 115-132.

 1922, The reaction principle in petrogenesis: Jour. Geology, v. 30, p. 177-198.

 1937, Recent high-temperature research on silicates and 

its significance in igneous geology: Am. Jour. Sci., 5th ser., 

v. 33, p. 1-21.

1956, The evolution of the igneous rocks, with a new introduction by J. F. Schairer: New York, Dover Publications, 332 p.

Bowen, N. L., and Anderson, Olaf, 1914, The binary system 

MgO-SiO2 : Am. Jour. Sci., 4th ser., v. 37, p. 487-500.

Bowen, N. L., and Greig, J. W., 1924, The system Al2Os-SiO2 : 

Am. Ceramic Soc. Jour., v. 7, p. 238-254.

 1925, The crystalline modifications of NaAlSiO4 : Am.

Jour. Sci., 5th ser., v. 10, p. 204-212. 

Bowen, N. L., and Schairer, J. F., 1929a; The system: Leucitediopside: Am. Jour. Sci., v. 18, p. 301-312.

 1929b, The fusion relations of acmite: Am. Jour. Sci., v. 

18, p. 365-374.

 1932, The system FeO-SiO2 : Am. Jour. Sci., v. 24, p. 177- 

213.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L153

Bowen, N. L., and Schairer, J. F., 1935, The system MgO-FeOSiO2 : Am. Jour. Sci., v. 29, p. 151-217.

 1936, The system, albite-fayalite: U.S. Natl. Acad. Sci. 

Proc., v. 22, p. 345-350.

 1938, Crystallization equilibrium in nepheline-albitesilica mixtures with fayalite: Jour. Geology, v. 46, p. 397- 

411.

Bowen, N. L., Schairer, J. F., and Posnjak, E., 1933a, The system, 

Ca2 SiO4-Fe2SiO4: Am. Jour. Sci., 5th ser., v. 25, p. 273-297.

 1933b, The system, CaO-FeO-SiO2 : Am. Jour. Sci., 5th 

ser., V. 26, p. 193-284.

Bowen, N. L., Schairer, J. F., and Willems, W. V., 1930, The 

ternary system, NasSiOa-FeaOs-SiOz: Am. Jour. Sci., 5th 

ser., v. 20, p. 405-455.

Bowen, N. L., and Tuttle, O. F., 1950, The system NaAlSiaOsKAlSisOs: Jour. Geology, v. 58, p. 489-511.

Boyd, F. R., Jr., and England, J. L., 1956, Phase equilibria at 

high pressures, in P. H. Abelson, Ann. Kept. Director Geophysical Laboratory: Carnegie Inst. Washington Year Book 

55, p. 154-157.

 1958, Melting of diopside under high pressure, in P. H. 

Abelson, Ann. Kept. Director Geophysical Laboratory: 

Carnegie Inst. Washington Year Book 57, p. 173.

 1959, Pyrope, in P. H. Abelson, Ann. Kept. Director 

Geophysical Laboratory: Carnegie Inst. Washington Year 

Book 58, p. 83-87.

 1960, Minerals of the mantle, in P. H. Abelson, Ann. Kept. 

Director Geophysical Laboratory: Carnegie Inst. Washington Year Book 59, p. 47-52.

 1961a, Melting of enstatite, in P. H. Abelson, Ann. Kept. 

Director Geophysical Laboratory: Carnegie Inst. Washington Year Book 60, p. 115-117.

 1961b, Melting of silicates at high pressure, in P. H.

Abelson, Ann. Bept. Director Geophysical Laboratory: 

Carnegie Inst. Washington Year Book, 60, p. 118-119.

Bozorth, R. M., 1927, Structure of a protection coating of iron 

. oxide: Am. Chem. Soc. Jour., v. 49, p. 969-976.

Bragg, W. L., Gottfried, C., and West, J., 1931, The structure 

of jS-alumina: Zeitschr. Kristallographie, v. 77, p. 255-274.

Bredig, M. A., 1945, High-temperature crystal chemistry of 

AmBXm compounds with particular reference to calcium 

orthosilicate: Jour. Phys. Chemistry, v. 49, p. 537-553.

 1950, Polymorphism of calcium orthosilicate: Am. Ceramic Soc. Jour., v. 33, p. 188-192.

Brewer, Leo, and Margrave, John, 1955, The vapor pressures of 

lithium and sodium oxides: Jour. Phys. Chemistry, v. 59, 

p. 421.

Bridgman, P. W., 1939, The high-pressure behavior of miscellaneous minerals: Am. Jour. Sci., v. 237, p. 7-18.

Brownmiller, L. T., 1985, A study of the system lime-potashalumina: Am. Jour. Sci., 5th ser., v. 29, p. 260-277.

Brownmiller, L. T., and Bogue, R. H., 1932, The system CaONa2O-Al2O3 : U.S. Natl. Bur. Standards Jour. Research, v. 8, 

p. 289^307.

Budnikov, P. P., Tresvyatskii, S.G., and Kushnakovskii, V. I., 

1953, The refinement in the ALOs-SiOs phase diagram: Akad. 

Nauk SSSR Doklady, v. 93, p. 281-283 (in Russian).

Budnikov, P. P., and Mateev, M. A.,1956, Synthesis of crystalline 

Na2O-3SiO2 and its properties: Akad. Nauk SSSR Doklady, 

v. 107, p. 547-550 (in Russian).

Bunting, E. N., 1931, Phase equilibrium in the system Cr2OrA12O3 : U.S. Natl. Bur. Standards Jour. Research, v. 6, p. 947.

 1933, Phase equilibria in the system TiO2,

and TiOa-AUOs: U.S. Natl. Bur. Standards Jour. Research,

v.. 11, p. 719-725. 

Burdick, M. D., 1940, Studies in the system lime-ferric oxidesilica: U.S. Natl. Bur. Standards Jour. Research, v. 25, p.

475-488. 

Biissem, W. and Eitel, A., 1936, Die Struktur des Pentacalciumtrialuminats : Zeitschr. Kristallographiej v. 95, p. 175-188. 

Carter, P. J., and Ibrahim, M., 1952, The ternary system Na^OFeO-SiO2 : Soc. Glass Technology Jour., v. 36, p. 142-163. 

Chao, E. C. T., Fahey, J. J., and Littler, Janet, 1961, Coesite

from Wabar, near Al Hadida, Arabia : Science, v. 133, no.

3456, p. 882-883. 

Chao, E. C. T., Fahey, J. J., Littler, Janet, and Milton, D. J.,

1962, Stishovite, SiO2, a very high pressure new mineral

from Meteor Crater, Arizona : Jour. Geophys. Research, v.

67, p. 419-421. 

Chao, E. C. T., Shoemaker, E. M., and Madseh, B. M., 1960, The

first natural occurrence of coesite from Meteor Crater,

Arizona : Science, v. 132, p. 220. 

Chinner, G. A., and Schairer, J. F., 1959, The join grossularitepyrope at atmospheric pressure, in P. H. Abelson, Ann.

Rept. Director Geophysical Laboratory: Carnegie Inst.

Washington Year Book, 58, p. 107-109. 

 1960, The join grossularite-pyrope at atmospheric pressure and its bearing on the system CaO-MgO-Al2Os-SiO2,

in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory: Carnegie Inst. Washingon Year Book 59, p. 72-76. 

Clark, S. P., Jr., 1960, Kyanite-sillimanite equilibrium, in P. H.

Abelson, Ann. Rept. Director Geophysical Laboratory : Carnegie Inst. Washington Year Book 59, p. 52-54. 

Clark, S. P., Jr., Robertson, E. C., and Birch, Francis, 1957, Experimental determination of kyanite-sillimanite equilibrium

relations at high temperatures and pressures: Am. Jour.

Sci., v. 255, p. 628-648. 

Clarke, F. W., and Washington, H. S., 1922, The average chemical composition of igneous rocks: U.S. Natl. Acad. Sci. Proc.,

v. 8, p. 108-115. 

Coes, L., Jr., 1953, A new dense crystalline silica : Science, v.

118, p. 131-132. 

Cohen, A. J., 1959, Origin of Libyan desert silica glass : Nature,

v. 183, p. 1548-1549. 

Coughanour, L. W., and DeProsse, V. A., 1953, Phase. equilibria

in the system MgO-TiO2 : U.S. Natl. Bur. Standards Jour.

Research, v. 51, p. 87-91. 

Coughanour, L. W., Roth, R. S., and DeProsse, V. A., 1954,

Phase-equilibrium relations in the system lime-titania and

zirconia-titania : U.S. Natl. Bur. Standards Jour. Research,

v. 52, p. 37^3. 

Coughanour, L. W., Roth, R. S., Marzullo, D., and Sennett, F. E.,

1955, Solid-state reactions and dielectric properties in the

system magnesia-lime-tin oxide-titania : U.S. Natl. Bur.

Standards Jour. Research, v. 54, p. 149-162. 

Coughlin, J. P., 1954, Contribution to the data of theoretical

metallurgy : XII, Heats and free energies of formation of

inorganic oxides : U.S. Bur. Mines Bull. 542, 80 p. 

D'Ans, J., and Loeffler, J., 1930, Untersuchung im System

Na2O-SiO2-ZrO2 : Zeitschr. anorg. allg. Chemie, v. 191, p.

1-35.
L154 DATA OF GEOCHEMISTRY

Darken, L. S., and Gurry, R. W., 1945, The system iron-oxygen: 

I, the wiistite field and related equilibria: Am. Chem. Soc. 

Jour., v. 67, p. 1398-1412.

 1946, The system iron-oxygen: II, Equilibrium and thermodynamics of liquid oxide and other phases: Am. Chem. 

Soc. Jour., v. 68, p. 798-816.

 1953, Physical chemistry of metals: New York, McGrawHill Book Co., 535 p.

Day, A. L., and Alien, E. T,, 1905, The isomorphism and thermal 

properties of the feldspars: Carnegie Inst. Washington, 

Pub. 31, 95 p.

Day, A. L., and Shepherd, E. S., 1908, The lime-silica series of 

minerals: Am. Chem. Soc. Jour., v. 28, p. 1089-1114.

Day, A. L., Shepherd, E. S., and Wright F. E., 1906, The limesilica series of minerals: Am. Jour. Sci., 4th ser., v. 22, 

p. 265-302.

Day, A. L., Sosman, R. B., and Hostetter, J. C., 1914, The determination of mineral and rock densities at high temperatures : Am. Jour. Sci., 4th ser., v. 37, p. 1-39.

DeVries, R. C., and Osborn, E. F., 1957, Phase equilibria in the 

high-alumina part of the system CaO-MgO-Al2Oj-SiO2 : Am. 

Ceramic Soc. Jour., v. 40, p. 6-15.

DeVries, R. C., Roy, Rustum, and Osborn, E. F., 1954a, The 

system TiO2 -SiO2 : British Ceramic Soc. Trans., v. 53, p. 

525-540.

 1954b, Phase equilibria in the system CaO-TiO2 : Jour. 

Phys. Chemistry, v. 58, p. 1069-1073.

1955, Phase equilibria in the system CaO-TiO2-SiO2 :

Am. Ceramic Soc. Jour., v. 38, p. 158-171. 

DeWys, E. C., and Foster, W. R., 1956, The binary system 

anorthite (CaAl2 Si2O8 )-akerinanite (Ca2MgSi2O7 ) : Am. 

Ceramic Soc. Jour., v. 39, p. 372-376.

 1958, The system diopside-anorthite-akennanite: Mineralog. Mag., v. 31, p. 736-743.

Edwards, J. D., and Tosterud, M., 1933, The oxides and hydrates 

of alumina: Jour. Phys. Chemistry, v. 37, p. 483H188.

Ervin, Guy, Jr., 1952, Structural interpretation of the diasporecorundum-boehmite-7-Al 2O3 transitions: Acta Cryst. v. 5, p. 

103-108.

Eubank, W. R., and Bogue, R. H., 1948, Preliminary study on 

portions of the systems Na2O-CaO-Al2O3-Fe2O3 and 

Xa2O-CaO-Fe2Os-SiO2 : U.S. Natl. Bur. Standards Jour. Research, v. 40, p. 225-234.

Eugster, H. P., Reduction and oxidation in metamorphism, in 

P. H. Abelson, ed., Researches in geochemistry: New York, 

John Wiley & Sons, p. 397-426.

Faust, G. T., 1936, The fusion relations of iron orthoclase, with 

a discussion of the evidence for the existence of an ironorthoclase molecule in feldspars: Am. Mineralogist, v. 21, 

p. 735-763.

Faust, G. T., and Peck, A. B., 1938, Refractive indices of some 

glasses in the ternary system K2O^SiO2-Fe2O3-SiO2 : Am. 

Ceramic Soc. Jour., v. 21, p. 322-324.

Fenner, C. N., 1913, The stability relations of the silica minerals: Am. Jour. Sci., 4th ser., v. 36, p. 331-384.

Ferguson, J. B., and Merwin, H. E., 1918, The melting points of 

cristobalite and tridymite: Am. Jour. Sci., 4th ser., v. 46, 

p. 417-426.

 1919a, The ternary system CaO-MgO-SiO2 : Am. Jour. 

Sci., 4th ser.. v. 48, p. 81-123.

 1919b, Wollastonite and related solid solutions in the 

ternary system lime-magnesia-silica: Am. Jour. Sci., 4th 

ser., v. 48, p. 165-189.

Filonenko, N. E., and Lavrov, I. V., 1953, The melting of mullite: Akad. Nauk SSSR Doklady, v. 89, p. 141-142 (in

Russian). 

Findlay, Alexander, 1951, The phase rule and its applications,

9th ed., revised by A. N. Campbell and N. O. Smith: New

York, Dover Publications, 494 p. 

F-orke, O. W., 1955, Strukturanomalien beim Tridymit und

Kristobalit: Deutsche Keram. Gesell. Ber., v. 37, p. 369-

381. 

Foster, W. R., 1942, The system NaAl3SiOg-CaSiOg-NaAlSiO4:

Jour. Geology, v. 50, p. 152-173.

 1950, Synthetic sapphirine and its stability relations in 

the system MgO-Al2O3- SiO2 : Jour. Geology, v. 58, p. 135- 

151.

 1951, High temperature X-ray diffraction study of the 

polymorphism of MgSiO3 : Am. Ceramic Soc. Jour., v. 34, 

p. 255-259.

Franco, R. R., and Schairer, J. F., 1951, Liquidus temperatures 

in mixtures of the feldspars of soda, potash, and lime: 

Jour. Geology, v. 59, p. 259-267.

Galakhov, F. Ya., 1958, Alumina regiona for ternary aluminosilicate systems: III, The system TiOsr-AbOs-SiCh: Akad. Nauk 

SSSR, Izv. Otdel. Khim. Nauk, p. 529-534 (in Russian).

Geller, R. F., and Yavorsky, P. J. 1945, Melting point of alphaalumina : U.S. Natl. Bur. Standards Jour. Research, v. 34, 

p. 395-401.

Gibbs, J. W., 1906, On the equilibrium of heterogeneous substances : The Scientific papers of J. Willard Gibbs, v. 1, p. 

85-349, New Haven, Conn., Yale Univ. Press.

Gibson, R. E. 1928a, The influence of pressure on the high-low 

inversion of quartz: Jour. Phys. Chemistry, v. 32, p. 1197- 

1205.

 1928b, A note on the high-low inversions of quartz and 

the heat capacity of low quartz at 573 ° C.: Jour. Phys. 

Chemistry, v. 32, p. 1206-1210.

Goldsmith, J. R., 1947, The system CaAl2Si2Ofr-Ca2Al2SiOrNaAlSiO4 : Jour. Geology, v. 55, p. 381-404.

 1948, The compound CaO-2Al2O3 : Jour. Geology, v. 56, 

p. 80-81.

Goranson, R. W., and Kracek, F. C., 1932, An experimental investigation of the phase relations of KsShOs under pressure : Jour. Phys. Chemistry, v. 36, p. 913-926.

Greene, K. T., and Bogue, R. H., 1946, Phase equilibrium relations in a portion of the system Na2O-CaO-Al2O3-SiO2 : 

U.S. Natl. Bur. Standards Jour. Research, v. 36, p. 185-207.

Greig, J. W., 1926, Formation of mullite from kyanite, andalusite, and sillimanite: Am. Jour. Sci. 5th ser., v. 11, p. 1-26.

 1927a, Immiscibility in silicate melts: Am. Jour. Sci., 

5th ser., v. 13, p. 1-44.

 1927b, On liquid immiscibility in the system FeO-FfeOaAl2O,r-SiO2 : Am. Jour. Sci., 5th ser., v. 14, p. 473-484.

 1932, The existence of the high-temperature form of

cristobalite at room temperatures and the crystallinity of

opal: Am. Chem. Soc. Jour., v. 54, p. 2846-2849. 

Greig. J. W., and Earth, T. F. W., 1938, The system,

Na 2O-Al2Os -2SiO2 (nephelite, carnegieite)-Na2O-Al2Oj-6SiO2

(albite) : Am. Jour. Sci., v. 35A, p. 93-112. 

Greig, J. W., Posnjak, E., Merwin, H. E., and Sosman, R. B., 1935,

Equilibrium relationships of Fe3O4, FezOs, and oxygen: Am.

Jour. Sci., v. 30, p. 239-316. 

Grieve, J., and White, J., 1939, The system FeO-TiO2 : Royal

Tech. Coll. (Glasgow) Jour., v. 4, p. 441-448.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L155

Griggs, D. T., and Kennedy, G. C. 1956, A simple apparatus for 

high pressures and temperatures: Am. Jour, ScL, v. 254, 

p. 722-735.

Gummer, W. K., 1943, The system CaSiO8-CaAl2Si2O8-NaAlSiO4: 

Jour. Geology, v. 51, p. 503-530.

Gurry, R. W., and Darken, L. S., 1950, The composition of 

CaO-FeO-Fe2O3 and MnO-FeO-Fe2O3 melts at several oxygen pressures in the vicinity of 1600° C.: Am. Chem. Soc. 

Jour., v. 72, p. 3906-3910.

Hansen, W. C., 1928, Phase equilibria in the system

20aO-SiO2-MgO-5CaO-3Al2O3 : Am. Chem. Soc. Jour., v. 50, 

p. 2155-2160.

Hansen, W. C., and Brownmiller, L. T., 1928, Equilibrium studies on alumina and ferric oxide, and on combinations of 

these with magnesia and calcium oxide: Am. Jour. Sci., 

5th ser., v. 15. p. 225-242.

Hansen, W. 0., Brownmiller, L. T., and Bogue, R. H., 1928, 

Studies on the system calcium oxide-alumina-ferric oxide: 

Am. Chem. Soc. Jour., v. 50, p. 396-406.

Hay, R., and White, J., 1940, Slag systems: W. Scotland Iron 

and Steel Inst. Jour., v. 47, p. 87-92.

Hill, V. G., and Roy, Rustum, 1958a, Silica structure studies: 

VI, Tridymites: British Ceramic Soc. Trans., v. 57, p. 

496-510.

 1958b, Silica structures: V. The variable inversion in

cristobalite: Am. Ceramic Soc. Jour., v. 41, p. 532-537. 

Hytonen, Kai, and Schairer, J. F., 1960, The system enstatiteanorthite-diopside, in P. H. Abelson, Ann. Rept. Director

Geophysical Laboratory Carnegie Inst. Washington Year

Book 59, p. 71-72. 

Insley, H., and McMurdie, H. E., 1938, Minor constituents of

Portland cement clinker: U.S. Natl. Bur. Standards Jour.

Research, v. 20, p. 173-184. 

Iwase, K., and Nisioka, U., 1936, The equilibrium diagram of the

ternary system CaO-Al2Cv2SiCv-CaOSiO2: Tohoku Imp.

Univ. Sci. Repts., 1st ser., K. Hondra Anniv. Vol., p. 44-451. 

Juan, V. C., 1950, The system CaSiOg-Ca2Al2SiO7-NaAlSiO4:

Jour. Geology, v. 58, 1-15. 

Kammermeyer, K., and Peck, A. B., 1933, High temperature

preparation and the optical properties of sodium aluminate: Am. Ceramic Soc. Jour., v. 16, p. 363-366. 

Kanolt, C. W., 1914, Melting points of some refractory oxides:

U.S. Natl. Bur. Standards Bull., v. 10, p. 295-313. 

Karkhanavala, M. D., and Hummel, F. A., 1953, The polymorphism of cordierite: Am. Ceramic Soc. Jour., v. 36, p.

389-392. 

Keat, P. P., 1954, A new crystalline silica: Science, v. 120, p.

328 -330. 

Keith, M. L., and Schairer, J. F., 1952, The stability field of sapphirine in the system MgO-Al2O3-SiO2 : Jour. Geology, v. 60,

p. 181-186. 

Keith, M. L., and Tuttle, O. F., 1952, Significance of variation in

the high-low inversion of quartz: Am. Jour. Sci., Bowen

Volume, p. 203-280. 

Kennedy, G. C., Wasserburg, G. J., Heard, H. C., and Newton,

R. C., 1962, The upper three-phase region of the system

SiO2-H2O: Am. Jour. Sci., v. 260, p. 501-521. 

Korzhinskii, D. S. 1959, Physicochemical basis of the analysis of

the paragenesis of minerals: Consultants Bureau, New

York. 

Kracek, F. C., 1930, The system sodium oxide-silica: Jour.

Phys. Chemistry, v. 34, p. 1583-1589.

 1932, The ternary system K2SiOs-Na2SiO3-SiO2 : Jour. 

Phys. Chemistry, v. 36, p. 2529-2542^

Kracek, F. C., 1939, Phase-equilibrium relations in the system 

NasSiO^LiaSiOs-SiOs: Am. Chem. Soc. Jour., v. 61, p. 2863- 

2877.

Kracek, F. C., Bowen, N. L., and Morey, G. W., 1929, The system potassium metasilicate-silica: Jour. Phys. Chemistry, 

v. 33, p. 1857-1879.

 1939, Equilibrium relations and factors influencing their 

determination in the system K2 SiOr-SiO2 : Jour. Phys. 

Chemistry, v. 41, p. 1183-1193.

Kracek, F. C., Neuvonen, K. J., and Burley, G., 1951, A thermodynamic study of the stability of jadeite: Washington 

Acad. Sci. Jour., v. 41, p. 378-383.

Larsen, E. S., Jr., and Foshag, W. F., 1921, Merwinite, a new 

calcium magnesium orthosilicate from Crestmore, Calif.: 

Am. Mineralogist, v. 6, p. 143-148.

Lea, F. M., and Desch, C. H., 1956, The chemistry of cement 

and concrete, 2d ed.: London, Edward Arnold and Co., 

690 p.

Lea, F. M., and Parker, T. W., 1934, Investigations on a portion 

of the quaternary system CaO-AWV-SiOsr-FesOs: The 

quaternary system CaO-2CaO-SiO2-5CaO-3Al2O3- 

4CaO-Al2O3 -Fe2O3 : Royal Soc. London Trans., v. 234, p. 1-42.

Levin, E. M., McMurdie, H. F., and Hall, F. P., 1956, Phase 

diagrams for ceramists: Columbus, Ohio, Am. Ceramic 

Soc., 286 p.

Levine, I., and Ott, Emil, 1932, The crystallinity of opals, and 

the existence of high-temperature cristobalite at room temperature: Am. Chem. Soc. Jour., v. 54, p. 828-829.

MacChesney, J. B., and Muan, A., 1959, Studies in the system 

iron-oxide-titanium oxide: Am. Mineralogist, v. 44, p. 926- 

945.

McConnell, J. D. C., and McKie, Duncan, 1960, The kinetics 

of the ordering process in triclinic NaAlSisOs: Mineralog. 

Mag., v. 32, p. 436-454.

MacDonald, G. J. F., 1956, Quantz-coesite stability relations 

at high temperatures and pressures: Am. Jour. Sci., v. 254, 

p. 713-721.

M'lntosh, A. B., Rait, J. R., and Hay, R., 1937, The binary 

system FeO-Al2O8 : Royal Tech. Coll. (Glasgow) Jour., v. 

4, p. 72-76.

MacKenzie, W. S., 1957. The crystalline modifications of 

NaAlSisOs: Am. Jour. Sci., v. 255, p. 481-516.

McMurdie, Howard, 1937, Studies on a portion of the system: 

CaO-Al2O3-Fe2O3 : U.S. Natl. Bur. Standards Jour. Research, v. 18, p. 475-484.

Manuilova, N. S., 1937, Crystalline phases in the system 

Na2O-MgO-SiO2 : 2d Conf. Experimental Mineralogy, 

Petrog., Moscow 1936, p. 96-101, Pub. by Akad Nauk SSSR, 

Geol. Gruppa i Petrograf Inst. Imeni F. Yu Levinson-Lessing 

(in Russian).

Matignon, C., 1923, Action des temperatures elevees sur quelques substances refractaires: Acad. Sci. (Paris) Comptes 

rendus, V. 177, p. 1270-1273.

Miyashiro, A., and liyama, T., 1954, Mineral indialite, polymorphic with cordierite: Japan Acad. Proc., v. 30, p. 746- 

751.

Morey, G. W., 1914, New crystalline silicates of potassium and 

sodium, their preparation and general properties: Am. 

Chem. Soc. Jour., v. 36, p. 215-230.

 1923, A comparison of the heating-curve and quenching 

methods of melting-point determinations: Washington 

Acad. Sci. Jour., v. 13, p. 326-329.

 1930a, The devitrification of soda-lime-silica glasses:

Am. Ceramic Soc. Jour., v. 13, p. 683-713.
L156 DATA ON GEOCHEMISTRY

Morey, G. W., 1930b, The effect of magnesia on the devitrification 

of a soda-lime-silica glass: Am. Ceramic Soc. Jour., v. 13, 

p. 714-717.

 1930c, The effect of alumina on the devitrification of a 

soda-lime-silica glass: Am. Ceramic Soc. Jour., v. 13, p. 

718-724.

 1930d, Analytical methods in phase-rule problems: Jour. 

Phys. Chemistry, v. 34, p. 1745-1750.

 1936, The phase rule and heterogeneous equilibrium. A

commentary on the scientific writing of J. Willard Gibbs: 

New Haven, Conn., Yale Univ. Press, p. 233-293. 

Morey, G. W., and Bowen, N. L., 1922, The melting of potash 

feldspar : Am. Jour. Sci., 5th ser., v. 4, p. 1-21.

 1924, The binary system sodium metasilicate-silica : Jour. 

Phys. Chemistry, v. 28, p. 1167-1179.

 1925, The ternary system sodium metasilicate-calcium

metasilicate-silica: Soc. Glass Tech. Trans., v. 9, p. 262-264.

 1931, Devitrite: Glass Indus., v. 12, p. 133.

Morey, G. W., and Fenner, C. N., 1917, Ternary system

H2O-K2 giOit-SiO2 : Am. Chem. Soc. Jour., v. 39, p. 1173-1229. 

'Morey, G. W., and Ingerson, Earl, 1937, The pneumatolytic and

hydrothermal alteration and synthesis of silicates: Econ.

Geology, supp. to v. 32, no. 5, p. 607-761.

 1941, Solubility of solids in "gases" or "vapors" [abs.] :

Geol. Soc. America Bull., v. 52, p. 1924. 

Morey, G. W., Kracek, F. C., and Bowen, N. L., 1930, The ternary

system K2O-CaO-SiO2: Soc. Glass Tech. Trans., v. 14, p.

149-187.

 1931, The ternary system K2O-CaO-SiO2 : a correction: 

Soc. Glass Tech. Trans., v. 15, p. 57-58.

Morey, G. W., Kracek, F. C., and England, J. L., 1953, Polymorphism of sodium disilicate, Na2Si2O5 ; in G. W. Morey, Ann. 

Kept. Director of Geophysical Laboratory: Carnegie Inst. 

Washington Year Book 52, p. 58-59.

Mosesman, M. A., and Pitzer, K. S., 1941, Thermodynamic properties of the crystalline forms of silica: Am. Chem. Soc. 

Jour., v. 63, p. 2348-2356.

Muan, Arnulf, 1955, Phase equilibria in the system

FeO-Fe2Os-SiO2 : Am. Inst. Metals Trans., v. 203, p. 965-976.

 1957a, Phase equilibria at liquidus temperatures in the 

system iron oxide-A!3O3-SiO2 in air atmosphere: Am. 

Ceramic Jour., v. 40, p. 121-133.

 1957b, Phase-equilibria relationships in the system, 

FeO-Fe2Os-Al3O3-SiO2 : Am. Ceramic Soc. Jour., v. 40, p. 

420-^31.

 1958a, Phase equilibria at high temperatures in oxide 

systems involving changes in oxidation states: Am. Jour. 

Sci., v. 256, p. 171-207.

 1958b, On the stability of the phase Fe2O3 -Al2O3 : Am.

Jour. Sci., v. 256, p. 413-422. 

Muan, Arnulf, and Gee, C. L., 1956, Phase equilibrium studies

in the system iron oxide-Al2O3 in air and 1 atm. O2 pressure :

Am. Ceramic Soc. Jour., v. 39, p. 207-214. 

Muan, Arnulf, and Osborn, E. F., 1951, Phase relations in the

system 2CaO SiCVCaO SiOo-2CaO Al2Oa-SiO-2-FeO : Am.

Iron and Steel Inst., Year Book, p. 325-361.

 1956, Phase equilibria at liquidus temperatures in the 

system MgO-FeO-Fe2O3-SiO3 : Am. Ceramic Soc. Jour. v. 

39, p. 121-140.

Niggli, P., 1913, The phenomena of equilibrium between silica 

and the alkali carbonates: Am. Chem. Soc. Jour., v. 35, p. 

1693-1727.

Nisioka, U., 1935, The equilibrium diagram of the system

CaO-Al2O3 -2SiO2-CaO-TiO3 : Tohoku Imperial Univ. Sci.

Repts., v. 24, p. 708-717. 

Nurse, R. W., 1962, Phase equilibria and constitution of Portland

cement clinker, in Chemistry of Cement, Proc. 4th Internat.

Symposium, Washington, 1960: [U.S.] Natl. Bur. Standards

Mon. 43, v. 1, sess. 2, paper 21, p. 9-37. 

Osborn, E. F., 1942, The system CaSiOs-diopside-anorthite: Am.

Jour. Sci., v. 240, p. 751-788.

 1943, The compound merwinite (3CaO-MgO-2SiO2 ) and

its stability relations in the system CaO MgO-SiO2: Am.

Ceramic Soc. Jour., v. 26, p. 321-332. 

Osborn, E. F., and Schairer, J. F., 1941, The ternary system

pseudowollastonite-akermanite-gehlenite: Am. Jour. Sci., v.

239, p. 715-763. 

Osborn, E. F., and Tait, D. B., 1952, The system diopside-forsterite-anorthite: Am. Jour. Sci., Bowen Volume, pt. 2, p.

413-433.

Ostrovskii, I. A., 1956, Study of mineral formation in some silicate melts under pressure of water vapor and hydrogen:

Inst. Geol. Rudnykh Mestorozhdennii, Petrog. i. Geochemii,

Trudy, p. 3-199. [Russian.] 

Pablo-Galan, L. E. de, and Foster, W. R., 1959, Investigations of

the role of beta-alumina in the system, Na2O-Al2Os-SiO2:

Am. Ceramic Soc. Jour., v. 42, p. 491-498. 

Paladino, A. E., 1960, Phase equilibrium in the ferrite region of

the system FeO-MgO-SiO2 : Am. Ceramic Soc. Jour., v. 43,

p. 183-191. 

Pecora, W. T., 1960, Coesite craters and space geology: Geotimes,

v. 5, no. 2, p. 16-19, 32. 

Phemister, James, Nurse, R. W., and Bannister, F. A., 1942,

Merwinite as an artificial mineral: Mineralog. Mag. v. 26,

p. 225-230. 

Phillips, B., and Muan, Arnulf, 1958, Phase equilibria in the

system CaO-iron oxide in air and in 1 atm. O2 pressure: Am.

Ceramic Soc. Jour., v. 41, p. 445-454.

 1959, Phase equilibria in the system CaO-iron oxide-SiO2 

in air: Am. Ceramic Soc. Jour., v. 42, p. 413-423.

Prince, A. T., 1943, The system albite-anorthite-sphene: Jour. 

Geology, v. 51, p. 1-16.

 1951, Phase relations in a portion of the system 

MgO-Al2Os-2CaO-SiO2: Am. Ceramic Soc. Jour., v. 34, p. 44- 

51.

1954, Liquidus relationships on 10 percent MgO plane of

the system lime-magnesia-alumina-silica: Am. Ceramic Soc. 

Jour., v. 37, p. 402^08.

Rait, J. R., 1949, Basic refractories their chemistry in relation 

to their performance: Iron and Steel, v. 22, p. 189, 289, 493, 

623.

Ralston, O. C., 1929, Iron oxide reduction equilibria: a critique 

from the standpoint of the phase rule and thermodynamics : 

U.S. Bur. Mines Bull. 296, 326 p.

Rankin, G. A., and Merwin, H. W., 1916, The ternary system 

CaO-ALOs-MgO: Am. Chem. Soc. Jour., v. 38, p. 568-588.

 1918, The ternary system MgO-Al2Os-SiO2 Am. Jour. 

Sci., 4th ser., v. 45, p. 301-325.

Rankin, G. A., and Wrijrht. F. E., 1915. The ternary system 

CaO-Al2Os-SiO3 : Am. Jour. Sci., 4th ser., v. 39, p. 1-79.

Ricci, J. E., 1951, The phase rule and heterogeneous equilibrium: Princeton, N.J., D. Van Nostrand Co., 505 p.

Ricker. R. W., and Os>iorn, E. F., 1954, Additional phaseequilibrium data of the system CaO-MgO-SiO2 : Am. 

Ceramic Soc. Jour., v. 37, p. 133-139.
PHASE-EQUILIBRIUM RELATIONS, ROCK-FORMING OXIDES EXCEPT WATER L157

Ridgeway, R. R., Klein, A. A., and O'Leary, W. V., 1936, Preparation and properties of so-called "beta-alumina" : Electrochem. Soc. Trans., v. 70, p. 71-87. 

Ringwood, A. E., 1958, The constitution of the mantle : II, Further data on the olivine-spinel transition : Geochem. et Cosmochim. Acta, v. 15, p. 18-29. 

Roberts, H. S., and Merwin, H. E., 1931, The system MgO-FeOFesOs in air at one atmosphere: Am. Jour. Sci., v. 21, p.

145-157. 

Robertson, E. C., Birch, Francis, and MacDonald, .G. J. F., 1955,

Fields of stability of jadeite, kyanite, and pyrope [abs.] :

Geol. Soc. America Bull., v. 66, p. 1608. 

Roedder. E. W., 1951a, The system K2O-MgO-SiO2 : Am. Jour.

Sci., v. 249, p. 89-130, 224-248.

 1951b, Low-temperature liquid mimiscibility in the system KoO-FeO-ALO^SiOo : Am. Mineralogist, v. 36, p. 282- 

286.

 1952, A reconnaissance of liquidus relations in the system 

K2O-2SiO2-FeO-SiO2: Am. Jour. Sci., Bowen Volume, p. 

435-456.

 1953a, Liquid immiscibility in the system K2O-FeOALO.-SiO:! [abs.] : Geol. Soc. America Bull., v. 64, p. 1466.

 1953b, High silica portion of the system Kz

SiO2 [abs.] : Geol. Soc. America Bull., v. 64, p. 1554.

1959, Silicate melt systems, in Ahrens, L. H, and others,

eds., Physics and chemistry of the earth, v. 3, p. 224-297,

London, Pergamon Press, 464 p. 

Roeksby, H. P., and Rooymans, C. J. M., 1961, The formation

and structure of delta-alumina: Clay Minerals Bull., v. 4, p.

234-238. 

Roth, R. S., 1958, Revision of the phase-equilibrium diagram of

the binary system calcia-titania, showing the compound

Ca,Ti3Oio: U.S. Natl. Bur. Standards Jour. Research, v. 61,

p. 437-440. 

Roy, D. M., 1954, Hydrothermal synthesis of andalusite: Am.

Mineralogist, v. 39, p. 140-143. 

Roy, D. M., and Roy, Rustum, 1955, Synthesis and stability of

minerals in the system: MgO-Al2O3-SiO2-H2O: Am. Mineralogist, v. 40, p. 147-178. 

Roy, Rustum, 1959, Silica O, a new common form of silica:

Zeitschr. Kristallographie. v. Ill, p. 185-189. 

Ruff, O., and Schmidt, P., 1921, Die Dampfdrucke der Oxyde

des Siliciums, Aluminums, Calciums, und Magnesiums:

Zeitschr. anorg. allg. Chemie, v. 117, p. 172-190. 

Saalfeld, H., 1958, Dehydration of gibbsite: Clay Minerals Bull.,

v. 3, p. 249-257. 

Schairer, J. F., 1942, The system CaO-FeO-AhOa-SiOa: I, Results

of quenching experiments on five joins: Am. Ceramic Soc.

Jour., v. 25, p. 241-274.

 1950, The alkali-feldspar join in the system NaAlSiO*- 

KAlSiO4-SiO2 : Jour. Geology, v. 58, p. 512-517.

 1954, The system K2O-MgO-Al2Os-SiO2 : I, Results of 

quenching experiments on four joins in the tetrahedron 

cordierite-forsterite-leucite-silica and on the join cordieritemullite-potash feldspar: Am. Ceramic Soc. Jour., v. 37, 

p. 501-533.

 1955, The ternary systems leucite-corundum-spinel and 

leucite- forsterite-spinel: Am. Ceramic Soc. Jour., v. 38, p 

153-158.

 1957a, Melting relations of the common rock-forming 

oxides: Am. Ceramic Soc. Jour., v. 49, p. 215-235.

Schairer, J. F., 19571), The crystallization of rock-forming minerals from magmas and the nature of the residual liquid; 

in P. H. Abelson, Ann. Kept. Director Geophysical Laboratory : Carnegie Inst. Washington Year Book 56, p. 217-222.

Schairer, J. F., and Bowen, N. L., 1935, Preliminary report on 

equilibrium relations between feldspathoids, alkali-feldspars 

and silica: Am. Geophys. Union Trans., 16th Ann. mtg., p. 

323-328.

 1938, The system, leucite-diopside-silica: Am. Jour. Sci., 

v. 35A, p. 289-309.

 1942, The binary system CaSiOs-diopside and the relations between CaSiOs and akermanite: Am. Jour. Sci., v. 

240, p. 725-742.

 1947a, Melting relations in the systems Na2O-Al2Os-SiOj 

and K2O-Al2Os-SiO2 : Am. Jour. Sci., v. 245, p. 193-204.

 1947b, The system anorthite-leucite-silica: Soc. Geol. Finland Bull., v. 20, p. 67-87.

 1955, The system K2O-Al2Os-SiO2 : Am. Jour. Sci., v. 253, 

p. 681-746.

 1956, The system Na2O-Al2Oir-SiO2 : Am. Jour. Sci., v. 

254, p. 129-195.

Schairer, J. F., and Morimoto, N., 1958, Systems with rockforming olivines, pyroxenes, and feldspars: in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory: Carnegie 

Inst. Washington Year Book 57, p. 212-213.

 1959, The system forsterite-diopside-silica-albite, in P. H. 

Abelson, Ann. Rept. Director Geophysical Labortory: Carnegie Inst. Washington Year Book 58, p. 113-118.

Schairer, J. F., and Osborn, E. F., 1950, The system

CaO-MgO-FeO-SiO2 : 1, Preliminary data on the join 

CaSiOs-MgO-SiO2 : Am. Germanic Soc. Jour., v. 33, p. 160- 

167.

Schairer, J. F., and Yagi, K., 1952, The system FeO-AhOa-SiO.: 

Am. Jour. Sci., Bowen Volume, p. 471-512.

Schairer, J. F., and Yoder, H. S., Jr., 1958, The quaternary 

system Na2O-MgO-Al2Oa-SiO2, in P. H. Abelson, Ann. Rept. 

Director Geophysical Laboratory: Carnegie Inst. Washington Year Book 57, p. 210-212.

 1960a, The system albite-forsterite-silica, in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory: Carnegie 

Inst. Washington Year Book 59, p. 69-70.

 1960b, The system forsterite-nepheline-diopside, in P. H.

Abelson, Ann. Rept. Director Geophysical Laboratory: 

Carnegie Inst. Washington Year Book 59, p. 70-71. 

Schairer, J. F., Yoder, H. S., Jr., and Keene, A. G., 1953, The 

system Na2O-MgO-SiO2, in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory: Carnegie Inst. Washington 

Year Book 52, p. 62-64.

 1954, The systems Na2O-MgO-SiO2, and Na2O-FeO-SiO2, 

in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory : Carnegie Inst. Washington Year Book 53, p. 123-125.

Schreyer, W., and Schairer, J. F., 1959, Anhydrous cordierites 

and the system MgO-Al2Os-SiOs, in P. H. Abelson, Ann. 

Rept. Director Geophysical Laboratory: Carnegie Inst. 

Washington Year Book 58, p. 98-100.

 1960, Metastable quartz solid solutions in the system: 

MgO-AhOa-SiOa, in P. H. Abelson, Ann. Rept. Director 

Geophysical Laboratory: Carnegie Inst. Washington Year 

Book 59, p. 97-98.

Schroder, A., 1928, Beitrage zur Kentnis des Feinbaus des 

Brookits und des physikalischen Verhalten sowie der 

Zustandsanderung der drei naturalichen Titandioxyde: 

Zeitschr. Kristallographie, v. 67, p. 485-542.
L158 DATA ON GEOCHEMISTRY

Segnit, E. R., 1953, Further data on the system Na2O-CaO-SiO2 ; 

Am. Jour. Sci., v. 251, p. 586-601.

 1956, The section CaSiOs-MgSiOs-AUOs: Mineralog. Mag., 

v. 31, p. 255-264.

Shepherd, E. S., Rankin, G. A., and Wright, F. E., 1909, The 

binary systems of alumina with silica, lime, and magnesia: 

Am. Jour. Sci., 4th ser., v. 28, p. 293-333.

Shropshire, Joseph, Keat, P. P., and Vaughan, P. A., 1959, The 

crystal structure of keatite, a new form of silica: Zeitsehr. 

Kristallographie, v. 112, p. 409-413.

Smalley, R. G., 1947, The system NaAlSiO^-CaaAlaSiOr: Jour. 

Geology, v. 55, p. 27-37.

Smith, J. V., and MacKenzie, W. S., 1958, The alkali feldspars: 

IV, The cooling history of high-temperature soda-rich feldspars : Am. Mineralogist, v. 43, p. 872-889.

Smith, J. V., and Tuttle, O. F., 1957, The nepheline-kalsilite system : 1, X-ray data for the crystalline phases: Am. Jour. 

Sci. v. 25, p. 282-305.

Smits. A. and Endell, K., 1919, Eine Notiz zu der Abhandlung des 

Systems SiO2 : Zeitsehr. anorg. allg. Chemie, v. 106, p. 143- 

148.

Sosman, R. B., 1927, The properties of silica: New York, Chemical Catalog Co., 856 p.

 1952, Temperature scales and silicate research: Am. 

Jour. Sci., Bowen Volume, p. 517-528.

 1954, New high-pressure phases of silica: Science, v. 119,

p. 738-739.

Sosman, R. B., Hostetter, J. C., and Merwin, H. E., 1915, The 

dissociation of calcium carbonate below 500°C: Washington Acad. Sci. Jour., v. 5, p. 563-569.

Sosman, R. B., and Merwin, H. E., 1916, Preliminary report on 

the system lime-ferric oxide: Washington Acad. Sci. Jour., 

v. 6, p. 532-537.

Spivak, J., 1944, The system NaAlSiOi-CaSiOg-NasSiOs: Jour. 

Geology, v. 52, p. 24-52.

Stewart, D. B., 1960, Silicate phase equilibria, in Encyclopedia 

of Science and technology, v. 12: New York, McGraw-Hill 

Book Co., p. 312-317.

Stishov, S. M., and Popova, S. V., 1961, A new dense modification of silica: Geokhimiya, no. 10, p. 837-839. [Russian.]

Swayze, M. F., 1946, A report of studies of: 1, The ternary system CaO-CsHs-CzF; 2, The quaternary system 

CaO-C5As-C2F-C2S; 3, The quaternary system as modified 

by 5 percent magnesia. Pt. 1: Am. Jour. Sci., v. 244, p. 1-31.

Taylor, W. C., 1941, The system 2CaO-SiOr-KaO-SiO2 and other 

phase-equilibrium studies involving potash : U.S. Natl. Bur. 

Standards Jour. Research, v. 27, p. 311-323.

Tilley, C. E., 1933, The ternary system, Na2SiOs-Na2Si2OirNaAlSiOi: Mineralog. petrog. Mitt., v. 43, p. 406-421.

Tilley, C. E., and Vincent, H. C. G., 1948, The occurence of an 

orthorhombic high-temperature form of Ca^SOi (bredigite) 

in the Scawt Hill contact zone and as a constituent of slags: 

Mineralog. Mag., v. 28, p. 255-271.

Tornebohm, A. E., 1897, Die Petrographie des Portlandzements: 

Tonindustrie-Zeitung, v. 21, p. 1148-1151, 1157-1159.

Toropov, N. A., and Arakelyan, O. I., 1950, New calcium and 

sodium orthosilicates: Akad. Nauk SSSR Doklady, v. 72, 

p. 365-368 (in Russian).

Toropov, N. A. and Galakhov, F. Ya., 1951, The mullite problem: Akad. Nauk SSSR Doklady, v. 78, p. 299-302 (in 

Russian).

Tromel, G., Obst., K. H., Konopicky, K., Baver, H., and Patzek, 

I., 1957, Untersuchungen im System SiO2-Al2O3 : Deutsche 

keram. Gesell. Ber., v. 34, p. 397-402.

Turnock, A. C., 1959, Spinels, in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory. Carnegie Inst. Washington 

Year Book 58, p. 134-137.

Tuttle, O. F., and Bowen, N. L., 1950, High temperature albite 

and contiguous feldspars: Jour. Geology, v. 58, p. 572-583.

 1958, Origin of granite in the light of experimental studies in the system NaAlSisOs-KAlSiaOs-SiOs-H-O: Geol. Soc. 

America Mem. 74, 153 p.

Tuttle, O. F., and Smith, J. V., 1953, The system KAlSiOrNaAlSiOi, in P. H. Abelson, Ann. Rept. Director Geophysical Laboratory: Carnegie Inst. Washington Year Book 52, 

p. 118.

 1958, The nepheline-kalsilite system: II, Phase relations : Am. Jour. Sci., v. 256, p. 571-589.

Wartenberg, H. von, and Prophet, E., 1932, Schmelzpunktdiagramme hochstfeuerfester Oxyde, V: Zeitsehr. anorg. allg. 

Chemie, v. 207, p. 373-379.

Wartenberg, H. von, and Reuseh, H. J., 1932, Schmelzpunktdiagramme hochstfeuerfester Oxyde, IV: Zeitsehr. anorg. allg. 

Chemie, v. 207, p. 1-20.

Wartenberg, H. von, Reusch, H. J., and Saran, E. 1937, Sehmelzpunktdiagramme hochstf euerf ester Oxyde, VII: Zeitsehr. 

anorg. allg. Chemie, v. 230, p. 257-276.

Washburn, E. W., and Bunting, E. N., 1934, Note on phase equilibria in the system Na2O-TiO2 : U.S. Natl. Bur. Standards 

Jour. Research, v. 12, p. 239.

Weiss, Alarich, and Weiss, Armin, 1954, Siliziumchalkogenide 

VI. Zur Kentniss der faserigen Siliziumdioxyd-modification: Zeitsehr. anorg. allg. Chemie, v. 276, p. 95-112.

Welch. J. H., and Gutt, W., 1959, Tricalcium silicate and its stability within the system CaO-SiO2 : Am. Ceramic Soc. Jour., 

v. 42, p. 11-15.

Wyckoff, W. G., and Morey, G. W., 1926, X-ray diffraction measurements on compounds in the system soda-lime-silica: 

Am. Jour. Sci., v. 12, p. 419-440.

Yamauchi, Ti., 1937a, Celite system 3CaO-Al2O3-2CaO-Fe2O3 : 

Japan Ceramic Assoc. Jour., v. 45, p. 433.

 1937b, Celite. IV. The system 5CaO-Al2O3-2CaO-Fe2O3 : 

Japan Ceramic Assoc. Jour., v. 45, p. 614-631.

Yoder, H. S., Jr., 1950, High-low quartz inversion up to 10,000 

bars: Am. Geophys. Union Trans., v. 31, p. 827-835.

 1952a, Change of melting point of diopside with pressure : Jour. Geology, v. 60, p. 364-374.

 1952b, The 10 percent CaAl2 Si2Os plane in the system 

CaSiOs-CaoAlSiO-NaAlSiOr-CaALSisOs: Jour. Geology, v. 

60, p. 586-593.

 1952c, The MgO-Al2Os-SiO2-H2O system and related metamorphic f acies: Am. Jour. Sci., Bowen Volume, p. 569-627.

Yoder, H. S., and Weir, C. E., 1951, Change of free energy with 

pressure of the reaction nepheline+albite=2 jadeite: Am. 

Jour. Sci., v. 249, p. 683-694.

Zernike, J., 1955, Chemical phase theory: Deventer, Netherlands, Kl-uwer's Publishing Co,, 493 p.
INDEX

Page

Acmlte ..__.__________________________ 43 

Akermanite___________.___________________55,110,121-123 

Albite (see also Plagioclase)....-.._.--_-...._._._____.._.38-43, 79-84, 97,140,143

Almandine. __________________________________._ 75 

Andalusite.-. ... .... ... ._ 22

Anorthite (see also Plagioclase) .-. ..............71, 92-96,107,113-134,137,140

Bredlgite. 16

................................................................. 14

SCaO-AljOs.- _....................._ 11

2CaO-SiOj._....................................................16, 123, 125, 135, 147

3CaO-SiOi..-. .....................................................16,18,123,147

Carnegieite... ... . . .-....-.... ..__ ..._...39-43, 79-97,146

Clinoenstatite..__________________________________ 114 

Coesite._____________________________________ 2-6 

Cordierite 55-58, 81,84,100-106, 124-125

Corundum - . .. . .6-7, 100-101, 105-106, 113-119, 125, 131, 138-139 

Cristobaiite... .. ..... ..........2-6, 46, 52, 56, 99, 101,108, 124-126, 137-138

Devitrite .................................... 31-32, 95

Diopside .......................... . 52-55, 80, 117-125, 140, 143, 147

Enstatite .... _.......................... 11, 84, 99-101, 107, 114, 119

Fayalite (see also Olivine)__. .. . 21, 60-69, 76, 97-98, 108, 128

Feldspar. See Plagioclase, Potassium feldspar

Forsterite (see also Olivine) . 11, 57-58, 82, 98-108,114,118,124,126,140,143,146

Gehlenite ........ 71,89,93,95,113,116,118,121,122,130-135

Grossularite.. .......__........_._.__.....___. ..... 124,126

Hedenbergite. _______________________________ 60-69 

Hematite-. . ... -__.._..... 24,43,74,139 

Hereynite. _....... 24,74,97-^98,128-134,138-139

ImmisdbUity.................................................. 18,21,99,108,124,126

Indialite _____......_..__.___ 55-56

Iron-akermanite______________________________ 110,130,134 

Iron-cordierite _______________________________ 75-76 

Iron-orthoclase__________________________________ 51

Jadeite. 43

Page 

Kaliophilite.-.. .................. ............................... 49,52

Kalsilite.. 49

Keatite.... . .. .. 2-6

Kuanite.... . ........ --.-. ... .. . 22

Larnite.______..___-___-_---- ______ __-_ 18 

Leucite 49,98,99-108,140,147

Magnesioferrite_ . 126 

Magnesiowustite---- -- - --------- 9,55,109,126

Magnetite. - -- . - 19,126,138

Melilite (seealso Akermanitc, Gehlenite)-- - 94,109-110,119,123-135,146 

Merwinlte. 55,123

Monticellite 109

Mullite - 21,77,81,100-106,123,125,138-139

Nepheline 39-43,79,82-98,143,146

Olivine (see also Forsterite, Fayalite)... 55-56,60-69,109,110,126,130-135,147

Peridase----. ----- ---------------------------------------- 2,55,114,123,125

Plagioclase (see also Albite, Anorthite).. 86-90,94,140-144,147

Potassium feldspar.. _ ......... .......... 49,79,99-107,140,147

Protoenstatlte. . 11,82,99,101,104,107,114

Pseudowollastonite ____... .....__... 16,36,53-55,60-69,88,91,94,119-125,130,131

Pyrope 57-59,124,126

Pyroxene (see also Acmite, Clinopyroxene, Enstatite, Diopside, Hedenbergite,

Jadeite, Protoenstatite) 56,119,124,126,146-147

Quartz-.. 2-6,44,49

Rankinite. ............ ................................ .... 16,135

Sapphirine.... ................. ... 57,100-104

Silica (see also Cristobalite, Quartz, Tridymite).. . 2-6 

Silica, crystalline modifications 2 

Sillimanite_____________________________-_____ 22 

Sphene _.... 73,137,147

Spine..__ . ' ... 9,57-58,82-85,100-105,113,119,123-126,138-139,146 

Stishovite 2-6

Tridymite 2-6,44,46,49,52,56,99-104,108,124-126,131,137-139,147

Wollastonite. ...... 16,36,48,53-55,60-69,88,92-93,110,119-120,123,125,130-13

Wustite (see also Magnesiowustite) 19,21,129,131-13g

L 159

O