  /*  (,**/)
 +  +1ῌ,- 
 




Application of High-temperature Calorimetric Measurements for Magmalogy
Toru SUGAWARA
\}

+







  

l:m:Bῌ6#5

I~ STY 95o Hart and Davis, +312 ; Taka-

hashi, +312 ; Snyder and Carmichael, +33,> J

 !

K  L MN%OeCc.M\ 95o"#$%&' ()*+ ,-./01234

 Nielsen and Dungan, +32- ; Beattie et al., +33+ ; 

56#578 9!:;#<% !:5=<%

+332>+ Fig. + > l : m : Bῌ6 # 5

?@ AῌLiq
 MgO     E DOl
MgO

OlῌLiq
FeO, MnO, NiO E 9DMO
, MFe, Mn, Ni> 

B CD+!EF"

PST7bc.M\GH  

@A+ PpOCSTI~Y\W%;

IJCK#C$% L&M'&C!:;#D PN06#5 EN(<%N(O@)P@*QR. 123456#5

 (pQR\K  L MN@GA+A,%STU-V./W%;&X\}  E @z=5Ap@Y-.Z+ [P !EY-.M\S^:{#c. RSC)pT]^@01 R. ,%W%;@2&R\(Jones, +32. ; Beattie et al., +33+)+ Fig. +7834_`5@6aR\Z+ CG,%
STU- P 7bc.M\p( Fe  Mn ETRZUcC8D

7

 +R Ni VMCE8@A+ \}

88d%Oe9- P:fg4

W%; Z.45W/l:m:B

CK hZ. ;7<= 9 ,**/> @i>R.

]X&W#@Y  l:m:Be7L

Z\jM\Z+ Fa Y

MnO yYR.

NiO  Z ¡[A5:¢@£R 95o Sato,,ῌ Ni  :5#k l:m:/nc.Z_op.G) \?q@eCrs/Atl:
m:B@uvZ+ l:m:BkD Fe,+311 ; ¤¥ +320> S¦ Atrs/0l:m:B\X( Ce7L@A 95o Tamura etal., ,*** ;  ,**->+§¨ Ni VMCE@AD© yª

Mg C  DR.N( EF ppm  Ni, Mn,

Pl:m:Bῌ6#5

Ca @uvG) uGwxdHe@Uy)typ^*@X} c¬C­#Cc.M\ 95R.

z={|@_`APM+ P* ±02,ῌ*+3- b²³cd´µefsg 2,1¶sV7 ·¸¹{:;%
Institute for Study of the Earth’s Interior, Okayama
University, Yamada 2,1, Misasa, Tottori 02,ῌ*+3-,
Japan.
e-mail : toru@misasa.okayama-u.ac.jp +/ "Khrs7º¸¹»ij¼j

 Ni ]xCJ«o Burns, +31* ; _® +313 ; Mysen, +32+>+ + ¯GHl:m:Bῌ6#5

 Ni, SiO. `L@7 %OeR E@)(°O@) (Sugawara and Akaogi, ,**-a) :

aA

²³ ¼

18

Fig. +. Plots of partition coe$cients of FeO, MnO
and NiO between olivine and liquid against thatof MgO. Data is from a compilation by
Sugawara (+332). The lines show partition
coe$cients predicted from calorimetric data
assuming  + (Sugawara and Akaogi,,**-a).



ln   DHDCpTTm
RT
DS DCp ῌ T ῎
ῌ
῎


ln
῍R
῏
R ῍ Tm῏
ln


 

 




ῌ,a῎
῍-῏

ln

 DH, DS, DCp

Fig. ,. Enthalpy,  , of liquid in thesystem An/* Di/*-Ni, SiO. and Ni, SiO. olivine(Sugawara and Akaogi, ,**-a). Solid circles
represent measured enthalpies and liquid compositions of starting materials, and open circles
show measured enthalpies and liquid compositions by heating and quenching experiments for +/ minutes. A straight line indicatesenthalpy of An/* Di/*-Ni, SiO. liquid calculatedby the least squares ﬁtting for the experimental
data assuming zero heat of mixing. A dottedcurve shows enthalpy calculated assuming
   -* kJ/mol,   /-..0/./ -****  (+ ).

+    #$ % &'()*+ gji

Di/*-Ni, SiO. \ Ni, SiO. /* molῐ \(i,

*/\^+ yz m-;<"-./ j 012)*/" a-34  abcd-!/#w(y56789 (SiO,, MgO, NiO, etc):0;<=!" T, Tm, R

 NiO >NiSi*./ O, -?@;<=?2)*+ ABAC0DEFGH- +.,ῑ+.0 Iz

CaO-MgO-Al, O- SiO, 

mn 43<\ op Navrotsky et al., +323 ; Kojitani and Akaogi, +331
 Tw( qr
yz\O4*+ }E&*/"J KL  M2) NO/ P QR!/
+ST;U M2)#$C0VWX(Y9-Z[\]^ 43<"

<O  \_=7I`!  abcde Ni \£ _&e¤ 3<¥¦-§S¨=/©\ª« /\¬; yz mx<"

fg-_=

 

7-34m ¡ ¢+;<"Fig. , -yz£`!" 

Ni, SiO. C0­®; I Liebenbergite Ni,

C0VWX(Y9\mn 4=< op Snyder

SiO.   / +11- K -and Carmichael, +33, ; Kinzler et al., +33* ; Hirschmann./¯(°7hi jX!/<O*/ kl 

and Ghiorso, +33."qr 

st!/<O;4 ,+.±,0 kJῌ

mol \ª« <" I

Forsterite +-2.3 kJῌmol ; ²- u#$v-+ Ni, SiO.  w( mx³ ,**/ Fayalite (23.- kJῌmol ; Stebbins and Car-< (Sugawara and Akaogi, ,**-a).

michael, +32.), Tephroite (23./ kJῌmol ; Mah, +30*) w(yz b{|}#$~m \ +./ῑ, ´_=l*/" ª« <*/" +11- K  #$ -34 µI 34 ¶·¸-3^,yz

;<U An/*

¹\ jº*/»(;4 (  











¯
+), 

 " .

*+/

19

Fig. +

 !" #$%$῍&'()
" &'( o EJ,-,01231


" 45 Ni, SiO. 6,.
89: Fe,;, Mn,;, Ni,;  7d < = >,?@AB$" C= DC EFGHI JFK " !L ,MN'OPQC 236 RGHIL
6,3" Ni,;

MN'OP" CFSES. C

Fe,;, Mn,;, Ni,;

/TUV

CFSE

 0 C 6, CFSE

Fig. -. Typical endothermic peak (example of An.,Di/2 sample) during melting reaction observed in
di#erential scanning calorimetry (Sugawara and
Akaogi, ,**-b). Solidus and liquidus temperatures are deﬁned by temperature Tp at
which the heat ﬂow falls from baseline (dottedline) and by onset temperature Te, respectively.

23  (Burns, +31*) WXY " , Z ?@[!\]^A(&'(_`%ab". C c# 723 

R$de" Jackson et al., +33- ; Farges and Brown, +330S

5 " #$%$%+ .M$f'gP 61
h3#$%$&'(/Ti&$kde" Ni, SiO.
M lA(

#$%$

j CFSE6,.

j Ni,;

!L ,GH¡" 2 D K ExPf ¢£K

IMN'OP mn 7!" 23#$%$o )n .p1

'(, Ni" diopside (Di)-anorthite (An)-akermanite (Ak), diopside-anorthite-forsterite

/F¥-ῌ ῏ῑ῎῍ῒῐ*+qr,**-b)  /F¥§G ¨]a]a)J©ª 2 «1" ¨]

Gibbs s,MN'OP3tu 1

9 vwK" xPf*+q36 R$de" -yz." +312

2{|S T }¤ diopside-silica (Qt) r¦ (Sugawara and Akaogi,a]a 6/36,ª"  v *+q~

6,937  diopside2n /73" 2 01K ¦L ® §&-  37 (+)  +  (SiO,-TiO,-Al,O--Fe,O--FeO-MgO-CaO-Na,OK,O-H,O)n2 + K" T K

%&Pfn2 T



H

35 ,K" ¬I­ 7+8

3

J

!" /F¥}6M 1!n¯°6,xPf32
3 "¡2 01 2+r&'(n§2  Di-An r $-

Fig.

2  !" An., Di/2, Di/2 Ak.,, An.0 Ak/.,

K" 2+r *+q xPf

Di2. Qt+0 R

 R$de" Hallstedt et al., +33. ; Ghiorso et al.," Ti³..-´,.0" ³-.0´,.-" ³3.2´/.1" /.*´,**,S" 

3

K



_x'

m4

©n wtῌS±²M$f'gP+.1 kJ ῌ mol 3 Di-An-Ak r3N±²M$f

w"  b v 235'gP 2" Ti %+3µ27 (,) *+q. 01]a MN'OP !L67+89&'( xPf3¶,2 d" (-) ]a* H &'(7Di-Qt r+ 

K " : &'(7+6xPf

35 2 ;,e" M$f'gP" M$(gP" <Ti " :7+68 =>?

6K" @A,%&Pf BC v 236

·¸O3JF2
±²M$f'gP3º,9,&'(
¹ w
72" 2

r3»*PµQ  (Schairer and Bowen, +3-2) 2
RQ7
Fig. . "¡±²M$f'gP

¼S %+ xPf J]aRS *+q &7 \]^A(&'(

»¼ *

20

Fig. .. Comparisons of liquidus temperatures in thesystem (a) diopside-anorthite, (b) diopsideakermanite and (c) anorthite-akermanite. Solidcircles show phase equilibrium experiments(Osborn, +3., ; Ferguso and Merwin, +3+3 ; De
Wys and Foster, +3/0). Solid and dotted lines
represent liquidus temperatures calculated using
calorimetric excess enthalpes and assuming ideal
solutions, respectively. Two-lattice model for
conﬁgurational entropy are assumed in both
calculations.



  +** !"#"$% &Fig. . '() "*" + ,-./
01234567 8.9:;<=+<>



ln



{








 

 

  




\ln


+
\ 

.

&-(

BB DHEq)&,(
DSEq)&,(= ..v &,( 23T
T?@A BC* DEFGH5G+

456723G67o) Carmichael -=I*-J K +L 1BMN#OP.

+32* 

,VW

X,H5GK ,`  Fe-\ῌFe,\/)  , "/ &_9 Sack et al., +32* ;.ῌ ῏῎῏῍῔ῐῑῒ῕ΐ

Kilinc et al., +32- ; Lange and Carmichael, +323 ; Kress

QRSTUTVW X= DNNO &Y Ni-NiOand Carmichael, +33+ 1() -=H5G,"#




buffer  logfO, Z( [- *-\/ ],^8_

5  "# ln ( )-.#` (Carmichael and Ghiorso, +33*)) VW X=

74, ¡!¢"*-  (-)

Fe-\

abcd e fg_/N 

X,h1TUTijk) l"}k"o/N|£H74  "/) 1¤",8¥=¦§¨©"#C.#ª &_9

#mn43Vocp6q5 a$1`TUT=Tangeman et al., ,**+ ; Gaillard et al., ,**-( «¬*-

Vorstu=DEFGH5GVorsvwx­®¬$¯`],^74°!P.

yz7P. :±±)+FeO+./&liquid({FeO&liquid(\ O,&gas(.

B. |}~ %,1 :&,(B.-² ³#´µ #¶$·% %1 (-) @& /N,= |£H74
%¸'(, g ¹,ºN#ªB)a¼dC

Fig. /. Enthalpy, H+-1- (L)H,32 (S), in the system
Na, SiO-Fe, O- (Sugawara and Akaogi, ,**.).

 

 Na, SiO--Fe, O--SiO,

 Na, SiO--NaFeSi, O0   +-1- K 

21

Fig. 0. A plot of ln () vs. +***/T (K)at logfO,/*.01. Data is from a compilation
by Sugawara and Akaogi (,**.). The line
shows the ln () predicted from
calorimetric data assuming  /+.

  (Sugawara and Aka, x. MXOFe, O--FeO-SiO,  M/K=Naogi, ,**.).

!"#$%#&'() Fe-* +),.( (/*.,+) - Fe 0 1-+*῍/*ῌ + Fe,* 2+

3 Na,O-Fe,

O--SiO, 456 7&' (89 Fe-*ῌFe,* + :;=Ca 

Fe-* ῌ Fe,* +tu

-;

M


"OeO %+sr; Ig  +),>?/+/,+Mrg  &e&d !"#$%# X Fe,*  Fe-* 0 (<+-1- K)  . NaῌFe =+ >?@ opk( - 1 2H,+:   FeO  + A B C D-*E

(Lange and Carmichael, +323) 3FFe ,G - HIJ+:J3 Na,
SiO--Fe, O- KL Fig. /

῏

῎

M,

3 a45  6+%a

$%#NOP%QR Fe, O- SET' 7 I8R

Hematite NOP%QRUVW +-1- K

, 9Wi :;<X

Fe, O- YZ[ 2-.-\+*./ kJῌmol :S = ¡¢ a£¤xa¥¦ a ]!^_"#Y`$%a§¨©  fghg' 7

bRPcVW&d (,) NOP%QRNO#D

ª>6AV 6+«J

QR'e fghg +/1- K
kJῌmol i D

 D

/+*/.,/.3.. JῌK-mol jS gW k($%#Rlm)nbRP opqrg:- +*<-*ῌ sr3

tu op   vWg.( X$%# Fe-*ῌFe,* 7 Fig. 0

fgW

M, bRP

op; Fe-*ῌFe,* *w>?ABx+FeaA5¯B° ±Navrotsky  Wi²³%´µ

a  A.

IPGP  P. Richet  ¶^ !"#$%#%a
I·;6:S ¸. ¹;

,*?¬VW@­®6 S, a¥¦*w>?
 Fe

-*

!"#$%#+,yz{|}I~-º»+S,ῌ ῑ ῐ ῍
Beattie, P., Ford, C. and Russell, D. (+33+) Partition
coe$cients for olivine-melt and orthopyroxene-meltsystem. Contrib. Mineral. Petrol., +*3, ,+,῍,,..

22

78 9

Burns, R. G. (+31*) Mineralogical Applications of Crystal
Field Theory. Cambridge Univ. Press.
Carmichael, I. S. E. and Ghiorso, M. S. (+33*) The e#ect ofoxygen fugacity on the redox state of natural liquids andtheir crystallizing phases. Reviews in Mineralogy, ,.,Modern Methods of Igneous Petrology : Understanding
Magmatic Processes, +3+ῌ,++.
De Wys, E. C. and Foster, W. R. (+3/0) The binary systemanorthite (CaAl, Si, O2) akermanite (Ca, MgSi, O1). J.
Am. Ceram. Soc., -3, -1,ῌ-10.
Farges F. and Brown G. E. Jr (+330) An empirical modelfor the anharmonic analysis of high-temperature XAFS
spectra of oxide compounds with applications to thecoordination environment of Ni in NiO, -Ni, SiO. andNi-bearing Na-disilicate glass and melt. Chem. Geol.,+,2, 3-ῌ+*0.
Ferguson, J. B. and Merwin, H. E. (+3+3) The ternary
system CaO-MgO-SiO,. Am. J. Sci., .2, 2+ῌ+,-.
Gaillard, F., Pichavant, M. and Scaillet, B. (,**-) Experimental determination of activities of FeO and Fe,Ocomponents in hydrous silicic melts under oxidizing conditions. Geochim. Cosmochim. Acta, 01, .-23ῌ..*3.
Ghiorso, M. S., Hirschmann, M. M., Reiners, P. W. andKress, V. C. (,**,) The pMELTS : a revision of MELTS
for improved calculation of phase relations and major
element partitioning related to partial melting of the
mantle to - GPa. Geochem. Geophys. Geosyst., - (/), OI+*.+*,3/,**+GC***,+1.
Hallstedt, B., Hillert, M., Selleby, M. and Sundman, B.
(+33.) Modelling of acid and basic slags. Calphad, +2,-+ῌ-1.
Hart, S. R. and Davis, K. E. (+312) Nickel partitioning
between olivine and silicate melt. Earth Planet. Sci. Lett.,.*, ,*-ῌ,+3.
Hirschmann, M. M. and Ghiorso, M. S. (+33.) Activities
of nickel, cobalt, and manganese silicates in magmatic
liquids and applicaitons to olivine/liquid and to silicate/
metal partitioning. Geochim. Cosmochim. Acta, /2, .+*3ῌ
.+,0.
Jackson, W. E., Mustre de Leon, J., Brown, Jr. G. E.,
Waychunas, G. A., Conradson, S. D. and Combes, J.-M.
(+33-) High-temperature XAS study of Fe, SiO. liquid :reduced coordination of ferrous iron. Science, ,0,, ,,3ῌ,--.
Jones, J. H. (+32.) Temperature- and pressure-independent
correlations of olivine/liquid partition coe$cients andtheir application to trace element partitioning. Contrib.
Mineral. Petrol., 22, +,0ῌ+-,.
Kilinc, A., Carmichael, I. S. E., Rivers, M. L. and Sack, R.
O. (+32-) The ferric-ferrous ratio of natural silicate
liquids equilibrated in air. Contrib. Mineral. Petrol., 2-,+-0ῌ+.*.
Kinzler, R. J., Grove, T. L. and Recca, S. I. (+33*) An
experimental study on the e#ect of temperature and melt
composition on the partitioning of nickel between olivine
and silicate melt. Geochim. Cosmochim. Acta, /., +,//ῌ
+,0/.

Kojitani, H. and Akaogi, M. (+331) Melting enthalpies ofmantle peridotite : calorimetric determinations in thesystem CaO-MgO-Al, O--SiO, and application to magma
generation. Earth Planet. Sci. Lett., +/-, ,*3ῌ,,,.
Kress, V. C. and Carmichael, I. S. E. (+33+) The compressibility of silicate liquids containing Fe, O- and the e#ect ofcomposition, temperature, oxygen fugacity and pressure
on their redox states. Contrib. Mineral. Petrol., +*2, 2,ῌ
3,.
Lange, R. A. and Carmichael, I. S. E. (+323) Ferric-ferrous
equilibria in Na, O-FeO-Fe, O--SiO, melts : e#ects ofanalytical techniques on derived partial molar volumes.
Geochim. Cosmochim. Acta, /-, ,+3/ῌ,,*..
Mah, A. D. (+30*) Thermodynamic properties of manganese and its compounds. U.S. Bur. Mines Report.
Investig., /0**.
 (+313)    . ῍ !" +0/ῌ+23.
Mysen, B. (+32+) Partitioning of Ni between olivine andsilicate melt : the “Henry’s law problem” reexamined :discussion. Geochim. Cosmochim. Acta, .0, ,31ῌ,32.
#$%& '()* (+312) +*,-, ./ - .
/0123   - 
ῌ456 ,,3ῌ,.1.
Navrotsky, A., Ziegler, D., Oestrike, R. and Maniar, P.
(+323) Calorimetry of silicate melts at +11- K : measurement of enthalpies of fusion and of mixing in the systems
diopside-anorthite-albite and anorthite-forsterite. Contrib. Mineral. Petrol., +*+, +,,ῌ+-*.
Nielsen, R. L. and Dungan, M. A. (+32-) Low pressuremineral-melt equilibria in natural anhydrous maﬁc systems. Contrib. Mineral. Petrol., 2., -+*ῌ-,0.
Osborn, E. F. (+3.,) The system CaSiO--diopside-anorthite.
Am. J. Sci., ,.*, 1/+ῌ122.
Sack, R. O., Carmichael, I. S. E., Rivers, M. and Ghiorso,
M. S. (+32*) Ferric-ferrous equilibria in natural silicate
liquids at + bar. Contrib. Mineral. Petrol., 1/, -03ῌ-10.
Sato, H. (+311) Nickel content of basaltic magmas : identiﬁcation of primary magmas and a measure of the degreeof olivine fractionation. Lithos, +*, ++-ῌ+,*.
Schairer, J. F. and Bowen, N. L. (+3-2) The system leucitediopside-silica. Am. J. Sci., -/A, ,23ῌ-*3.
Snyder, D. A. and Carmichael, I. S. E. (+33,) Olivine-liquid
equilibria and the chemical activities of FeO, NiO,
Fe, O-, and MgO in the natural basic melts. Geochim.
Cosmochim. Acta, /0, -*-ῌ-+2.
Stebbins, J. F. and Carmichael, I. S. E. (+32.) The heat offusion of fayalite. Am. Mineral., 03, ,3,ῌ,31.
78 9 (+332) :;<;ῌ=>? @ABCῌ=>?D .E FG HIJK4LM N .-+2+ῌ,*+.
78 9 (,**-) :;<;ῌ=>?*, OPQRSTUTVWXYZ ,**- [\]^N_`abc +.1.
78 9 (,**/) TUTdefg : hijk4lmLM N nob#p

 !"#
Sugawara, T. and Akaogi, M. (,**-a) Calorimetric measurements of fusion enthalpies for Ni, SiO. and Co, SiO.
olivines and application to olivine-liquid partitioning.
Geochim. Cosmochim. Acta, 01, ,02-ῌ,03-.
Sugawara, T. and Akaogi, M. (,**-b) Heats of mixing ofsilicate liquid in the systems Diopside-Anorthite-Akermanite, Diopside-Anorthite-Forsterite and DiopsideSilica. Am. Mineral., 22, +*,*ῌ+*,..
Sugawara, T. and Akaogi, M. (,**.) Calorimetry of
liquids in the system Na, O-Fe, O--SiO,. Am. Mineral., 23,+/20ῌ+/30.
Takahashi, E. (+312) Partitioning of Ni,, Co,, Fe,,

$% &'
,

,

23

Mn and Mg between olivine and silicate melts : compositional dependence of partition coe$cient. Geochim.
Cosmochim. Acta, .,, +2,3ῌ+2...
 (+320)      ,  -* S+1ῌS.*
Tamura, Y., Yuhara, N. and Ishii, T. (,***). Primary arc
basalts from Daisen volcano, Japan : equilibrium crystal
fractionation versus disequilibrium fractionation during
supercooling. J. Petrol., .+, .-+ῌ..2.
Tangeman, J. A., Lange, R. and Forman, L. (,**+) Ferricferrous equilibria in K, O-FeO-Fe, O--SiO, melts.
Geochim. Cosmochim. Acta, 0/, +2*3ῌ+2+3.