NATIONAL BUREAU OF STANDARDS REPORT

10 062

Progress Report

on THE CRYSTALLOGRAPHY OF OTHER BIOLOGICALLY

SIGNIFICANT INORGANIC COMPOUNDS

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS REPORT

THE CRYSTALLOGRAPHY OF OTHER BIOLOGICALLY

SIGNIFICANT INORGANIC COMPOUNDS

by

Brian Dickens*

* Research Chemist, Dental Research Section, National

Bureau of Standards, Washington, D. C. 20234

This investigation is part of the dental research program

conducted by the National Bureau of Standards and is supported by the National Institute for Dental Research

Collaborative 0 ffice.

NBS PROJECT

3 11.05-1 1-31 1056 1 June 30, 1969

NBS REPORT

10 062

Progress Report

on

IMPORTANT NOTICE NATIONAL BUREAU OF ST/

for use within the Government. Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

s accounting documents intended objected to additional evaluation

listing of this Report, either in Office of the Director, National

i the Government agency for which

jpies for its own use.

and review. For this reason, the whole or in part, is not authori Bureau of Standards, Washingto

the Report has been specifically

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

THE CRYSTALLOGRAPHY OF OTHER

BIOLOGICALLY SIGNIFICANT INORGANIC COMPOUNDS

INTRODUCTION

Calcium and phosphate are present in. vivo mainly as

calcium hydroxyapatite (HA) , which is the prominent topic of

the symposium. Since hydroxyapatite is held together by

ionic bonds, the ions in the structure can readily be replaced

shape

by other ions of roughly the same size,/cind charge. Some

change in charge can be tolerated provided the crystal as a

whole is kept electrically neutral. In a simple example, substitution of Na+ for Ca 2+ could be compensated for electrically

by substituting SO4 for PO4. Thus compounds crystallizing in

ionic lattices, and in the apatite structure in particular, need

not be completely homogeneous as is well known. The apatite

structure is apparently so stable that it is not only common

among compounds with the same type of formula, but will also

form as layers in a crystal interleaved with layers of differing stoichiometry, e Q g., HA interlayered with octacalcium

phosphate (see later) 0 Substitutions in general, and in the

HA structure in particular, can be envisioned on three levels:

(i) interleaved layers (epitaxy)

(ii) parts of one or more unit cells of related compounds

replacing parts of the HA structure
- 2 -

(iii) substituted ions

It is therefore desirable to systematically study compounds

related to HA with a view to revealing how the apatite structure

can incorporate these substitutions or 'defects', and/or to

gain enough structural knowledge to allow us to make predictions

about the method of 'defect' incorporation.

The likelihood of epitaxy or other intergrowth can be

considered from examinations of the crystal structures of

appropriate compounds. Appropriate compounds, in turn, can

be suggested from an observation of the types of coordination

and bonding of ions. A formal evaluation of epitaxy has not

yet been accomplished. In fact, only recently has a least

squares computer program (Busing, 1968) been written to refine

the various parameters required in a calculation of lattice

energy from their initial estimates (by the method of steepest

descents, using determined crystallographic parameters such as

the cell dimensions and atomic positional parameters as observations) . It may be feasible to calculate an approximation

to the interfacial energy of two possibly epitaxial layers

if the various energetic parameters above are "known". This,

however, lies in the future.
-3-

Besides searching for structural features which may be

significant in the incorporation of defects or nonstoichiometry

into apparently homogeneous crystal structures, it is also

significant to examine appropriate structures, which will

probably be of hydrated salts (see below) , for features which

may be important in determining the identity of a precursor

phase during crystallization. Hydrated salts may be important

in the nucleation and growth of anhydrous species from aqueous

environments for the following reasons (Dickens and Brown,

1968 ) , mentioned briefly below:

(i) For small particles such as the nucleating

particles during crystallization, the surface

energy is a large factor in determining the

identity of the particles. The high energy

attractions between ions are reduced, and

the surface energy in an aqueous environment

hydrated salt.

is lowered when the nucleus is formed from a highly/

(ii) Because of kinetic factors, hydrated salts

often crystallize more rapidly than the anhydrous counterparts, even when the latter are

thermodynamically more stable.
-4-

(iii) Crystal growth poisons such as polyphosphates,

magnesium and sugar, all of which are present in

biological systems, apparently repress the growth

of anhydrous calcium carbonates, and perhaps of

HA, and allow hydrated forms to grow.

(iv) Most nucleation processes are thought to be

heterogeneous rather than homogeneous. In the

case of biological mineralization such nucleation

is thought to be on collogen and other proteins,

which, because of their hydrophilic nature, would

presumably reduce the surface energy of a hydrated

salt to a lower value than that of an anhydrous

salt.

In this chapter, we report on the comtemporary structural

knowledge of several compounds of interest. The structures

of some of these have not been determined; some others are

known except for the hydrogen atoms. In general much further

work needs to be done.

The compounds have been chosen to indicate the relationship of that particular structural type to HA 0 If a particular

compound or ion sounds unlikely as a biological agent, a more

acceptable compound with a high probability of having the

same or a related crystal structure can often be thought of by
-4ajuggling the identities of the constituent ions while keeping

the overall formula electrically neutral.

1. COMPOUNDS NOT ISOMORPHOUS WITH HYDROXYAPATITE BUT

POSSIBLY RELATED TO IT. These compounds are relevant to

hydroxyapatite in the context of possible ion substitution,

unit cell substitution or interlayer ing

-5-

(a) Na 2 M8 (Si04 ) 6 F s M = La, Pr, Nd

Rare earth compounds with the general formula Na 2 M8 (Si0 4 ) 6 F 2

have been prepared from molten fluxes by Ito (1967). The cell

dimensions (Bowen, 1967; Swanson, McMurdie, Morris and Evans,

1969) are seen (Table 1) to be very closely related to those

of HA (Posner, Perloff and Diorio, 1958) and fluorapatite (FA)

(Naray-Szabo, 1930) . The reciprocal lattice extinctions 000£ =

2n+l indicate the space groups P63 or P6 3 /m. The Ca ions in

FA and HA are in positions 4f and 6h of space group P63 /m

(Table 2) . The rare earth compounds probably have the space

group P63 , a subset of P63 /m a Six rare earth ions thus probably

occupy general positions in P6 3 in a configuration like that

of the 6 Ca ions in positions 6h of P63 /m for FA and HA. The

remaining two rare earth ions and the two Na ions probably occupy

the 2b positions in P63 , and thus lie in columns analogous to

the columns of Ca ions in the 4f positions in FA and HA. Since

the electrostatic repulsive energy of a chain of M

3+ ...M3+

...

Na +

. . .Na +

. . .M3

will be 9+3+1+3=16 units/unit cell

(Table 3) whereas that of a chain M3 +

. .

.

Na+ ...M3+ ...Na...M3+

will be 3+3+3+3=12 units/unit cell, these columns are

expected to have Na and rare earth ions alternating. This may

be relevant to the incorporation of foreign cations into

hydroxyapatite

.
Table 6

HA N| i—

i—i r—)i—

—1 TSC

rd <

Cm °c^—. ^ £ CM CM

-P

—

uo CO a| o CM i—l 00 r- CM 00 00

w r—l o O 00 00

r—

• • > • * i—1 r"- r-" C' cO CO

CDU

+J-HC ^ 

, V P CM CM *

* *—

CM

OO

Cm «J|O CO CM

cO 00 CO 1—r- CO „

CO in LO CO 'vt* • • • • • O Oc a> <r> cr> CTi •H

CO '—*CO S

CM

(d £

CM CM CM CM

<4M Cm Cm Cm ,—„ 0 cO cO CD £ ^—

,—„

CMO c P' 'vf '3* Cm -

0 O O O cO CD w H H H _—„

•H CO CO CO <ct P '

— — O O

rd CO 00 00 cm Oh a rd u b — —

g £ cm £ o O 0 CM CM CM i—

i—

u rd rd rd rd rd £ £ £ U U
-7-

Table 2

Comparison of Na 2Mg (Si04 ) 6 F

2 with Ca 10 (P04 ) 6 F

2

Space group P 63 Space group P 63/m

6c 1 x, y, z 6h m x, y, .25

X, y, 0 5+2 x, y, o 75

y, x-y, z y, x-y, 0 25

y, y-x, 0 5+z y, y-x, c 75

y-x, x, z y-x, x, 0 25

x-y, x , .5+z x-y, x, » 75

2b 3 O 33, o67, z 4f 3 0 33, 0 67, z

0 67, 0 33, 0 5+z 0 67, 0 33, e 5+z

2a 3 0, 0, z 0 0 0, z

^a 2^8 (Si04 ) gF 2

6 M in (6c) with x ; y =^= 0 o; z ^ . 25

,25

2 M in (2b) with z=Q=0 o 2 Na in (2b) with z 0 5

24 0 in general position (6c)

2 F in (2a) with z^ c 25

* Kay, Young and Posner (1964)

.

67, o 33, z 33 67, 0 5-z

2a 6 0, 0, .25

0, 0, 0 75

Ca 10

(

po4)

6

F 2

6 Ca in (6h) with x = 0 2466,

y = o 0031

4 Ca in (4f) with z = o 0014

12 0 in general position

with x = .3433, y = 0 2579

z = o 0705

6 0 in (6h) with x = 0 3283

y = 0 4846, z = 0 25

6 0 in (6h) with x = 0 5876

y = 0 4652, z = 0 25

2 F in (2a)
ison

of

electrostatic

energies

differently

ordered

chains

-8 -

1—

i

rd rd +j +J 0 0

+j •P

CN

i—

i—

u

rd u

Cl O

e m-i ou

+

oo_£

+

rd

+

rd a

+

s

00

00

+

OO _ S

+

+

OO

+

+

00

00

rd £

00

00

rd !3

00
-9-

(b) CaK3 H (P04 ) g The structure of CaK3 H(P04 ) 2 (Frazier, Smith, Lehr and

Brown, 1962; Brown and Fowler, 1967) is very closely related

to that of NaK3 (S0 4 ) 2 (glaserite) . The formal relation between

the type structure

/NaK3 (S04 ) 2 /and HA has been discussed by Wondratschek (1963).

CaK3 H(P04 ) 2 is unusual in that although it contains a

phosphate group with an acid hydrogen, it is formed from

solutions with a pH of 10-11. Presumably the packing in the

structure is so efficient that the structure is able to remove

a proton from such an alkaline environment in order to achieve

the correct charge balance. In water, CaK3 H(P04 ) 2 hydrolyzes

to HA. It has not been found in physiological situations, but

here

is relevant/because of its structural relationship to HA.

The usual unit cells of CaK3 H(P04 ) 2 , NaK3 (S04 ) 2 and HA

are shown in Table 4 and are redefined in Table 5 to bring

out their close correspondence.

That CaK3 H(P04 ) 2 and NaK3 (S0 4 ) 2 must have similar

structures can be seen from

(1) the similarities of their formulae except for the H.
- 10 -

Table 4

The Unit Cell Dimensions of CaK3 H(P04 ) 2/

NaK3 (S04 ) 2 and HA

CaK3 H (P04 ) 2 NaK3

( S0 4 ) g Ca 5 0H(P04 ) a 9.93 & 5.66 A 9.43 &

b 5.72 5.66 9.43

c 7.44 7.33 6.88

a 90° 90° 90°

B 92.3 90 90

Y 90 120 120

z 2 1 2

.ce-group C

2 /m P 3ml P63 /m

3 (HA)
- 11 -

Table 5

The Unit Cells from Table 4, Redefined

C&3 Kg H3 (P04 ) 6 Na3 Kg (S04 )

1 6 Ca l0 (P04 ) 6 (OH)

a 9.93 & 9 o 80 & 9 0 43 A

b 9.92 9.80 9.43

c 7.44 7.33 6.88

a 91.6° 90° 90°

3 91.6 90 90

Y 120 120 120
- 12 -

(2) The similar dimensions of their ions

O Na ionic radius = 0.96 A

O Ca ionic radius = 0.99 A

O K ionic radius = 1.33 A

P-0 bond distance = 1 0 56 A

S-0 bond distance = 1.44 A

(3) CaK3 H(P04; ) 2 is pseudo-trigonal in morphology,

twinning, cell dimensions and in the intensities

of supposedly non-equivalent reflections on all

layers. The trigonal space-group which will

most easily accommodate one formula weight of

CaK3 H(P04 ) 2 is P3ml, which is the space-group of

NaK3 (S04 ) g . The actual space-group of CaK3 H(P04 ) 2 ,

C

2 /m, is a subgroup of P3ml.

(4) the x-ray intensities of CaK3 H(P04 ) 2 indicate

a subcell with the heavy atoms at the corners as

is found in NaK3 (S04,) 2

.

(5) the x-ray powder patterns of CaK3 H(P04 ) 2 and

NaK3 (S0 4 ) 2 are very similar.
-13-

Thus, the NaK3 (S0 4 ) 8 structure can be used as a first

approximation to the actual structure of CaK3 H(P04 ) 2 with

in CaK3 H (P04 ) s the exception of H, which is probably to be found/hcross the

0 0 close approach, i.e., across a center of symmetry in

NaKs (S04 ) 2 . This hydrogen bond will destroy the three-fold

axis of the P04 group, but will keep the mirror plane of

C

2 /m. By analogy with other structures containing an 0-H...O

hydrogen bond across a nominal center of symmetry, the hydrogen

is probably disordered about the center of symmetry. This

conclusion is supported by IR and NMR evidence (Brown and

Fowler , 1967)

.

In the NaKg(S04 ) s structure (Fig. 1) there are columns

of S04 groups and K ions related by a 3 axis. Thus, adjacent

columns have the S04 groups pointing "up" and "down". The

remaining ions, Na and K, are packed into columns designated

by small circles in Figure 1. The formula balance is kept

because there are twice as many S04 /K columns as there are

Na/K columns.
-14-

Figure 1 0 The crystal structure of glaserite, NaK3 (S0 4 ) 2

.

The columns with the dark dots may be considered to have the 0

of the S04 group above the S on the three- fold axis, the others

to the real unit

have the 0 below the S. The light line corresponds /-cell,

the heavy line is the refined cell. The small circles are

columns of Na and K ions. One of these columns may be considered to have replaced the OH” column in HA.
-15-

The effect of changing the sign of the ions in the central

column may be seen by comparing the structure of NaK3 (S0 4 ) s with that of HA (Fig. 2) . In HA the Ca ions have been pulled

in by the 0H“, and the P04 groups have moved out so that they

can coordinate to the Ca's through their oxygens while keeping

the repulsion with OH- within tolerance. Further, the P04

groups have tilted over about 35° which

puts two oxygens near the centers of two Ca triangles (Fig. 3) f

in the Ca/O configuration found in aragonite (Bragg, 1924) and

each of

puts/ the other two oxygens near the center of a Ca...Ca line in

the configuration found in calcite (Bragg, 1913)

.

CaK3 H(P04 ) 2 could exhibit epitaxial growth on HA or interchange with HA on a unit cell level and thus have relevance to

the mechanism of crystal growth, to the poisoning of crystal

growth and in the incorporation of impurities and defects.
-16-

Figure 2. The crystal structure of HA, Ca 10 (P04 ) s (OH) 2 , projected down the _c axis.
17
-18-

(c) Silico-carnotite Ca 5 (P04 ) 2 (Si04 )

Silico-carnotite , which is apparently named more after

its discoverer, Carnot, than by analogy with the mineral

carnotite, is found in basic slags rich in phosphorus. Since

it is readily soluble in dilute acids, it has been used for

has been reported to

many years directly as a plant fertilizer. It/exist over

a range of composition of about 55% to 83% Ca3 (P04 ) 2 by

weight at 1125°C (Nurse, Welch and Gutt, 1959) and has been

found in several high temperature investigations (Nurse, e_t

al , 1959; Berak and Woj ciechowska , 1956; Vol'fkovich, Illarionov,

Ozerov and Remen, 1960) of the Ca-P04 -Si04 system. Since

stoichiometric silico-carnotite is unstable below about 750°

(Nurse et _al_, 1959) it must be preserved by quenching.

Keppler (1968) has performed microprobe analyses on various

crystals of silico-carnotite and has concluded that it is a

definite compound.
-19 —

The crystallographic properties of a representative

specimen are given in Table 6 (Riley and Segnit, 1948; Tromel

Dickens and Brown, 1969)

and Zaminer, 1959; Keppler, 1968)/. There is good correspondence

dimensions

between the unit cell /of hydroxyapatite and silico-carnotite

,

and especially between the volumes of one formula weight (Table

7) . Although silico-carnotite has the same cation/anion ratio

(5/3) as the garnets (A 3 B 2 (X0 4 ) 3 where A and B are cations and

probably

X04 is an anion) , the garnet structure is/too dense for silicocarnotite since the garnets invariably have for B some small

O cation which can form B 0 distances of about 2 A. In the

garret Ca3 Al 2 (Si0 4 ) 3 (Abrahams and Geller, 1958) B is Al,

Ca...O distances are usually greater than 2.3 A.

which forms Al 0 distances of 1.95 A./
Table - 20 -

°rf;

CNOO•

+1

CNooi—

oI—

J0| II

oo

(U V\

<0 (Nc • a, rH o

54 o

II 0 •

fd > rd +1

4-> !3 s

fd 2 00 T3 cu o

b| LD

CL) = a • 4-i m cn p cn

•r4 LO a) 0 i-4 4J c£) -M 54 0 •'f • <d tJ> Q C O rH r-4 1 >4 *H Cl a) bl

td

w II

u o (V r—, fd •» 1 ^ cn i—

a i-4 0 « !3 o cn O u o o O

•H D-i - w-> - •

r-l U|

a • H if) = c H +1 w id i—

0 b u ^ e t"- <D TJ 0 00 • CD rC r- 1—

54

u • P 0 ^0

II cnb

rd 4-1 II

d <D 54 a e 0 rd|
-21 -

<D

4-> •H

x:

a,uoeou

>1

PU

OV Ov cvj 0

K\

><U

m

O 00 • • • CO o G\ OV t>- 1—1

VO

tn

>=<

-=r o

K\

n

CD H

rQ

fO Eh

4-1 rti <uc ^ -=r o p 1 <D •H 00

rd

O +> CO o C\J

u

O *H CO LO ro

<u •H 4-^ '—

r^—f

rd 4-J rH

O ^r • • •H •H C o in o

». X, CO ?4 Pu i—i rH

CL, Cti -—

ItM o in 0 cd 44 g o 0 0

S4

CO >1 K\

rH cu

—

rH -=r

QJ t o U c •H tro

4-4 CO 00 co

4J <u *>

— • • •H <u c CVJ rH rH C 4-> k rH rH i—1 D •H cd <

44 o m

CD 0 cd & C o

4-4 P

rd 44 u "—

0 i SC 0 O ><$ C u v—

0 •r4 m m

m

CO 1 1 -—•» •H •H -=f « • p C/D o G\ Ov

fO < p-.

Cl, ffi *»—

g LTV O cd U o

[•" m

m

m • o

vo oO s -=?• 1—1• tn cn to m vo o CO

tm 00

m

00 in ><< • 0 • rH O CO CO tn Ov

rH OV t- o

VO CO 1—1

fA

m

CO

co oo o CO

-3" rH

><

in • cvj m • vo

VO 1—1

in tn CO <

Cd| 43 | O I >- o> N

>» -P

•H

COC

0) 'O

rH Pl, O> rH

Q<nO

CN

rd ro S>

°c

r-'-

in

with

permuted

axes
- 21aDickens and Brown (1969) have very recently determined

the crystal structure (R = 0.05) of silico-carnotite using

a crystal from sample D (British Museum sample 1919,64) in

Riley and Segnit's paper (1948). Silico-carnotite was expected

to follow in the HA-glaserite series as a member where the

structure is essentially the HA structure with an empty column

where the OH's are found in HA. The actual structure of silicocarnotite may be considered to be a distorted form of the above.

The column Ca '

in HA are represented by a Ca zig zag in silicocarnotite. The six Ca(2)/P04 chains along _c (surrounding the

OH column) in HA are represented by four Ca/P04 and two Ca/Si04 in silico-carnotite

chains. A further distortion/is that the Ca '

in the Si04

chain have been pulled in towards the OH site in HA to form

a central zig zag of cations. The structure of silico-carnotite

thus also approaches the NaK3 (SO 4) 2 structure and is intermediate

between HA and NaK3 (S0 4 ) 2

.

The structure principles found in silico-carnotite may

be used in an appropriate calcium phosphate (Ca4 Na(P04 ) 3 is

one possibility) to allow the stoichiometry and properties of

HA to change locally.
-21bPb B (P04 ) 2 Si04 (pyromorphite) has been reported by

Wondratschek (1963) from x-ray data to be hexagonal with cell

dimensions (Table 7) similar to those of hydroxyapatite. Presumably the lead atoms are in a hexagonal array perpendicular

to _c and either dominate the scattering so that deviations

from hexagonal symmetry because of the non-equivalence of the

P04 and Si04 groups are unnoticed, or the P04 and Si0 4 groups

are statistically disordered. The formula of Pb5 (P04 ) 2 Si0 4 relates it to silico-carnotite , and it may have a closely

related structure, perhaps made hexagonal or more nearly so by

the effect of the increased size (Pb2+ = l o 20 K, Ca = 0.99 K)

of the cation. The structure of Pb 5 (P04 ) 2 Si04 is of great

interest, and would be best determined by neutron diffraction,

(d) Tetracalcium phosphate, Ca 4 0(P04 ) 2 , TCP

Tetracalcium phosphate (Bookey, Richardson and Welch,

1952; Tromel, Fix and Fritze, 1961; Brown and Epstein, 1965)

or Hilgenstockite , is prepared at high temperatures in systems

free of water. It may not be found _in vivo but may have a

structural relationship to HA (Table 8) where it can be seen

that the cell volume of HA and the a and c axes and hence the

(010) faces of the two compounds are very closely related
of

the

Unit

Cells

of

22

<d +j

ro

4=1a

COo

rC

(h co

co HP

ro§•Ou< EPHU

i-

roU

fOPP

a)

E-i

T3C

rO

0) +J’HP

roa

rO>iXOP

TO

CM ,—„ o tN

m co

a cn CD CM o CO —* cn o 00 o • • • • H

ao rH I""- o in CM

(0 rH co cn a, u p" °-=t CO

cu P- o<< p CM 0 • in

cm cn rn i—i r-'

CD II II cn U , „ (0 HO LT)

ffi ’<

a • o CO rH rH

CM CN i—

cO CO ro CO o X

X

CO

O o • • • CM CO CO

O CO CD rH in < °*a! CU trj '— o o CO

1—

O HO

(0

O

UH • T3 i—

A

(0| -Q| o| > o>
_23_

Although the crystals are nearly always twinned, we have

collected x-ray data from an apparently untwinned single

crystal. Statistical tests on the quasi-unitary structure

factors indicate that the space group is non-centrosyrametric,

and must therefore be P2 X from the x-ray extinctions. We have

tried to solve the structure by superposition techniques,

son

using an unsharpened Patter/ map, but obtained a trial structure

for the Ca and P atoms which would not refine satisfactorily. This trial structure has four layers roughly

equally spaced along b. We plan further effort in the solution

of the structure using statistical methods on the quasinormalized structure factors (Dickinson, Stewart and Holden,

1966) .

TCP takes up C02 , especially at high temperatures when

o the 0= presumably becomes COJ . This is of considerable interest

to the problem of carbonate-apatites, and suggests that carbonation of apatite can take place by making an 0H“ into HC0“ or

CO^- and expelling water if necessary. Since two cells of TCP

can, on spatial considerations, readily replace three cells of

HA, TCP may fit easily into the HA lattice and thus substitution

of TCP for HA may provide a mechanism of defect incorporation

and/or carbonate incorporation in HA.
- 24-

(e) Sr6 H3 (P04 ) 5» 2Hs Q and Sr 3 (P04 ) 2

» 4H2 0

These two compounds (Collin , 1959, 1960, 1964, 1966) are

of interest because of the mechanism of incorporating Sr 90

in the body. Also, Sr6 H3 (P04 ) 2H2 0 has been shown to immediately precede the formation of SrHA in vitro and there is

evidence, quoted below, that the same may be true in. vivo .

Sr 3 P04 «4H2 0 may be related to the "amorphous phase" (Eanes,

Gillessen and Posner, 1965, 1967; Weber, Eanes and Gerdes,

1967) found in the precipitation of calcium phosphates from

aqueous solution.

In an examination (Johnson, Armstrong and Singer, 1966)

of the tooth enamel of rats fed on a strontium-rich diet,

the cell dimensions of the hydroxyapatite present were found

to have increased from a. = 9.47, jc = 6.86 & in enamel from Srpoor animals to a. = 9.48 K, _c = 6.91 & in Sr-rich animals.

Extra lines in the powder patterns of the tooth enamel could

Sr6 H3 £04 ) 5 -2H2 0

be attributed to Sr6 H3 (P04 ) 5

• 2H2 0 . otherwise has a

powder pattern very similar to HA and, because of its Sr /P

ratio of 1.2, could lower the apparent stoichiometry of

(Ca, Sr) HA by interlayered growth in the way suggested (Brown,

Smith, Lehr and Frazier, 1962) for octacalcium phosphate,

Ca8 H2 (P04 ) 6 «5H2 0, (OCP) » The formulae of Sr6 H3 (P04 ) 5

• 2H2 0
-25-

and OCP are compared in Table 9. The Sr salt is obviously

more acidic than OCP and contains less water. Sr6 H3 (P04 ) 5

• 2H2 0

is the sole solid phase formed (Collin, 1966) (at pH 7.7) when

2.3 equivalents of Sr (OH) 2 are added to 1 equivalent of H3 P04 .

It often forms as a disordered intergrowth of crystals from

aqueous solution.

Sr 3 P04 *4H2 0 is formed (Collin, 1966) when more than 2.6

equivalents of Sr(OH) 2 are added to 1 equivalent of H3 P04 ,

and is stable for many days at 0°C. At 25°C and 37°C it very

easily changes into SrHA (Collin, 1966) . Its high degree of

hydration make it of great interest. It has a variable water

content as does OCP. The strong reflection at 20 = 6° (CuKa

radiation) is dependant on the degree of hydration and suggests

that the structure has a layer structure with a repeat distance

of about 14 & (Collin, 1964) . OCP has a layer structure with

a repeat of about 18.7 A.
26.

63

m • m• o „—„

CNO

X CM -

X

ID

—

nm • CO ^—

• o—

CU

O 

CU in '—

CM

m • • ^

s X X

0^ '—«"i—

I—

cu rd

U

rH

U

C

A

fO ii II Eh o o

CN CN

EC ffi in CN • • i£> LO O o

CU cu >—

CM co

as

X

00 <o

ffl

u

u cn

CO •H

cuuo
-27-

Thus Sr 3 (P04 ) 2 *4H2 0 is of interest to biological mineralization both as a possible candidate for a direct analogy to

amorphous calcium phosphate , and as another structure which

can incorporate several water molecules with alkaline earth

and phosphate ions perhaps arranged in layers. Other examples

of the latter are CaHP04 *2H2 0 and Ca (H2 P04 ) 2 'HgO.

(f) Octacalcium phosphate, CaQ H2 (P04 ) 6

• 5H2 0, OCP

The possible importance of OCP in reducing the apparent

Ca/P ratio of CaHA and in the growth mechanism of HA has been

discussed by Brown (1966) . The unit cells of OCP and HA are

compared in Table 10. Since the b, _c and a dimensions are

very similar in the two compounds, their unit ceils can easily

share a common face.

The structure of OCP has been determined (Brown, 1962)

but the hydrogen atoms have not been located because the x-ray

data contain the effect of large corrections for absorption.

Good large (0.1-0. 2 mm) single crystals of OCP are very difficult to grow. We are attempting to grow suitable single crystals

in order to recollect the data. We are also reprocessing the

photographic x-ray data collected earlier and plan to describe

the structure in much more detail when the fine details are

better known. The structure of OCP is shown in Figure 4 and

consists of apatitic layers between x = -.25 to +.25 interlayered by a hydrated layer with some Ca and P04 ions.
-28-

Table 10

A Comparison of the Unit Cells of OCP and HA

Ca8 H 2 (P0J S *5H2 0 (OCP) Ca 1 o (P04 ) 6 (OH)

a 19.87 A 9.42 A

b 9.63 9.42

_c 6.87 6.88

a 00 KD 0 H

-J 90°

3 92° 13' 90°

Y 108° 57' 120°

(HA)
OOo

-29-

Figure 4 The crystal structure of octacalcium phosphate
-30-

The corners of the two hexagons are the phosphorus and

calcium positions as they occur in projection in HA. (The

hexagon in HA is a trigonal antiprism in three dimensions.)

Two Ca ions and two P04 groups occur at each level of the

trigonal antiprism in OCP. The environments of the Ca ions are

very similar to those of the corresponding ions in HA. The OH

groups in columns in HA have been replaced by the 0(42) water

molecule and 0(35) of the P(14) P04 groups The 0(41) water

has replaced a Ca ion in HA and presumably hydrogen bonds to

the groups that Ca would have bonded to electrostatically with

roughly similar distances (Ca-0^2.4 A, O-H... O = 2.5... 2.8 A).

The Ca(l) and Ca(2) ions in OCP are almost exactly analogous

to the column Ca ' s in HA. The other column has been distorted

considerably with Ca(3) roughly in the same position as a column

with

of Ca's in HA but/Ca(4) moved by about 1.5 A along the b

axis to bond to 0(41) which has replaced a Ca ion in the HA

Ca

structure. The detailed atomic arrangement around theso^ ions

is part way between the environment of the Ca (5, 6, 7,8) ions

and the environment of the Ca(l,2) ions

. ^^Layer ed intergrowth

of OCP and HA has been observed directly and the crystal habit

of HA has been correlated with that of OCP by topotactic

change (Brown, Smith, Lehr and Frazier, 1962)

„
-31-

2. CALCIUM CARBONATES . The calcium carbonates are the

other great body of biological minerals. The anhydrous forms

have been found in the shells of marine life (K. M. Wilbur,

1964) and in humans in gallstones (Sutor and Wooley, 1968)

.

Bone can contain (Neuman and Neuman, 1958) up to 6% carbonate

ion.

(a) Calcite, CaCC3 Calcite is the most stable form of CaC03 at normal temperatures. It is abundant in nature in such forms as the shells of

several sea creatures, including oysters, and in gallstones, as

well as a mineral. It is the final form precipitated from

aqueous solutions at room temperature in the absence of crystal

growth poisons such as polyphosphates, Mg s+ and sugars. It

crystallizes in a hexagonal unit cell, a = 4.989, _c = 17.062 K,

spacegroup R3c, and the structure is well known (Bragg, 1913;

Sass, Vidale and Donohue, 1957) . The oxygens are hexagonally

closed packed and the Ca 1 s are in octahedral coordination. As

shown in Figure 5, each oxygen is coordinated to two Ca's.

Calcite is isomorphous with NaN0 3 and with the carbonates of

Mg, Mn, Fe, Zn, Cd and Co, which are all small ions with ionic

range of

radii in the / 0 o 65 to l o 0 A 0
-32-

A. C03 environment in calcite. B. C03 environment in aragonite.

From Bragg (1924)

Figure 5.
-33-

(b) Aragonite, CaC03 Aragonite is the next most stable form of CaC03 at room

temperature It is denser than calcite and presumably is more

stable than calcite at low temperatures and/or high pressures.

When heated it changes into calcite (Subba Rao and Yoganarashimhan

,

1965) with the [001] of aragonite becoming the [0001] of calcite

[ 0110 ] and [100] and [110] of aragonite being parallel to [1010) and /

respectively of calcite (Dasgupta, 1964) 0 Thus, during the

transition the C03 group in aragonite is rotated 30° about _c

and moved to halfway between the Ca layers. The Ca layers must

also change to become an ABCABC sequence in calcite instead of

the ABABAB sequence in aragonite. ; Aragonite is found in coral,

clams and gallstones, and is isomorphous with the carbonates

of Ba, Sr and Pb Q Aragonite is precipitated preferentially

to calcite from aqueous environments at temperatures above

about 40°C. The unit cell is compared to that of calcite in

Table 11 0 The structure (Fig 0 6) is known formally (Bragg, 1924)

but apparently not well by modern standards
-34-

Table 11

A Comparison of the Unit Cells of Calcite and Aragonite

Calcite Aragonite

a 4. 989 4. 959

b 4.989 7.968

_c 17.062 5.741

V 120° o O

CT>

4.989 x 1 0 7321 = 8.64 A ( or thohexagonal description of calcite

compare with b (aragonite = 7.968)

O 5.72 x 3 = 17.16 A (comparison of _c (aragonite) with _c calcite)

*ASTM card 5-0453
-35-

Figure 6. Crystal structure of aragonite perpendicular

to c (twinned on (110) . From Bragg (1924) .
-36-

In aragonite, the oxygens are coordinated equally to

three Ca ' s instead of two as in calcite (Fig. 5). Aragonite

twins easily in the way explained by Bragg and has been reported

(Hiragi, Kachi, Takeda and Nakanishi, 1966) to exist in fine

particles (0.5 - l o 0 u) which have, at least in part, a superstructure (Fig. 7) with space-group Pbca and cell dimensions

_a = 8.420, b = 9.385, _c = 5.741. The relationship of the

superstructure (As, Bs , Cs) to the normal structure (_a, b,

_c) of aragonite is As = a - b, Bs = 3/2_a + 1/2 b, _Cs = _c

(c) High pressure phases of CaC03 X-ray diffraction studies (Davis, 1964) at high pressures

on powdered calcite (calcite I) have indicated the existence

of two more phases of CaC03

. CaC03 (II), a modified calcite

type, is probably isos tructural with KN03 (III) (Davis, 1963)

apparently

which is/related to calcite (Table 12) but has only unidirectional order of the N03 ion (about the 3-fold axis)

Calcite I is considered to transform into Calcite II at

about 15.5 Kb pressure. Calcite III is stable at higher

pressures (about 17.6 Kb to 27 Kb) . Its powder pattern has

been indexed (Davis 1964) as a KN03 -IV aragonite type (Table

13) though this is still not certain.
-37-

Table 12

Comparison of the Proposed Unit Cells of the

High Pressure Forms KN03 (III) and CaC03 (II) With Calcite

Calcite (I) KN03 (III) CaC03 (II)

4.989 A 5.44 A 4.98 A

17.062 18.25 16.83
-38-

Table 13

Comparison of the High Pressure Forms

KN03 (IV) and Calcite (III) with Aragonite

Aragonite KN03

(IV) Calcite (III)

5.741 A 11.04 A 8.90 K

4.959 8.36 8.42

7.978 7.40 7.14
-39-

Figure 7. The (001) plane projection of the model for

the superstructure, including atoms from 0 to _c/2. The solid

lines show the unit cells of the superstructure, and the

structure

broken lines a unit cell of normal aragonite. The / is no

longer periodic within the broken lines.

From Hiragi, Kachi, Takada and Nakanishi (1966).
-40-

The structures of the disordered KN03 and CaC03 forms

are still not known 0 These disordered forms may be important

in understanding the mechanisms of defect incorporation in

calcium carbonates and in studying the kinetics of calcareous

reactions

(d) Vaterite, CaC03 Vaterite has been found as a mineral (McConnell, I960),

in the repaired part of mineralized tissue (Wilbur and

Watabe, 1964) and in gallstones (Meier and Moenke, 1961)

It has been recognized as the end member of the series of

rare earth fluoride carbonate-calcium carbonate series

bastnaesite-roentgenite-synchisite . . .vaterite (Donnay and

Donnay, 1953) . Structures have been given by Meyer (1959) and

Kahmi (1963) . Vaterite often grows in a spherulitic form;

spherulitic vaterite has been discussed by Donnay and Donnay

(1967) 0 Kahmi used crystals which under high magnification

could be seen to be aggregates of uniformly oriented hexagonal

plates o Meyer proposed a structure in an orthohombic space

a group witt/ primitive ortho-hexagonal unit cell. His space
-41-

group and structure are incompatible with the results of

other workers who have assigned vaterite to the hexagonal

crystal system.

Optical studies (Bunn, 1945) had shown that the _c axis

of the hexagonal system must be in the plane of the C03 group.

(This is presumably the major difference between vaterite and

calcite and aragonite. The C03 groups are perpendicular to

to

the hexagonal axis in the case of calcite and /the correspseudo hexagonal

ponding/c. axis in the case of aragonite.) The vaterite

structure can not exist in the cell _a = 4.13, c = 8.49 &

because this contains only two C03 groups, vertically arranged,

the

and with only two C03 groups in /unit cell the structure can

not accommodate a three-fold axis. McConnell (1960) found

evidence for the real cell a/ = /3a, c' = c. Kahmi found a_' =

/3a, c' = 2c (Table 14). Because most of the x-ray scattering

is from the psuedo-cell, Kahmi analyzed the structure in terms

of this cell in space group P63 /mmc and gave positions for

the carbon and oxygens in the C03 group which are the result

of averaging three orientations (Fig. 8). For Kahmi ' s structure R = 0.16 which is about the limit of the data. Single

crystals of vaterite good enough to extend Kahmi ' s averaged
- 42-

Table 14

Pseudo-Cell and "True"

Pseudo-Cell

a 4 0 13 A

c 8.49

z 2

Cell of Vaterite

"True" Cell (Kahmi)

/3 x 4.13 = 7.16 &

2 x 8.49 =16.98

12
-43-

Figure 8. Kahmi's structure for the vaterite

pseudo-cello From Kahmi (1963) .
- 44-

structure into a three-dimensional structure have not yet

been grown. Other routes to the vaterite structure may be

through the structure of an isomorph or by lattice energy

calculations on various models.

Various rare-earth borates apparently isostructur al

with vaterite have been studied (Battram and Felton, 196 2;

Newnham, Redman and Santoro, 1963; Bradley, Graf and Roth,

1966) and a structure for the high temperature form of YbB03

has been suggested (Bradley, Graf and Roth, 1966) which is

reported to be very close to Kahmi ' s for vaterite. Bradley,

et al give x = .39, y = .78 for oxygen and Kahmi gives x =

.38, y = .76, all for the vaterite subcell. Bradley _et_ ad

give the space group as probably being P63 22 for their "real"

O cell a_ = 6.99, c = 8.34 A, z = 6. Their suggested structure

for the YbB03 'isomorph' is given in Fig. 9. Since their

cell is only half the vaterite cell along _c, the structure

of vaterite may consist of layers of the proposed YbB03 struc

ture displaced perpendicular to c. to double the c_ translation
-45-

* E

The structure proposed by Bradley, Graf and Roth (1966) for

the

Figure 9 0 YbOs

. This is a form of/c-axis projection of edge-sharing nets of Yb06 octahedra. The profiles of triangular borate ions above this net

are indicated by heavy lines to the corners which they share

with octahedra, and the positions of ions below the net by

light lines.
-46-

(e) CaC03

• 6H2 0

CaC03 «6H2 0 may be an important compound in the

nucleation of calcium carbonates in precipitation from

aqueous solutions. It is the final form of calcium carbonate produced in an aqueous environment near 0°C in the

presence of polyphosphates, (Brooks, Clark and Thurston,

1951). The CaC03 *6H2 0 initially formed slowly redissolves

with concommitant formation of CaC03 »6H2 0. CaC03 -6H2 0

crystallizes in the unit cell a. = 8.87 ± .02 A, b = 8.23 ±

.01 A, c = 11.02 ± .02 A, 3 = 110.2 ± .1° (at about -120°C)

with space group 0.2 /c and four formula weights per cell. The

structure (R = 0.10, Figures 10 and 11) was determined (Dickens

and Brown, 1968a) from photographic x-ray data collected from

a crystal held at about -120°C. It is of great interest

because it contains discrete [CaC03 ] ion-pairs even though the

structure contains enough water to coordinate Ca octahedrally.

Each ion-pair is isolated from other ion-pairs by an envelope

of 18 water molecules. Such ion**pairs may have a significant

concentration in solutions saturated with respect to the calcium

carbonates and may be important in mechanisms of biological

transport. One factor preventing the formation of Ca(0H2 ) 6 "complexes" may be the difficulty in packing such complexes using

only C(T3 ions. However Ca does not have the afinity for water
*

Icr

-47-

environment in CaC03 »6H2 0. From Dickens and Brown (1968a).
-48 -
-49-

of the increased importance, relative to the Ca...O term,

of the Ca....H repulsion in the Ca...„0H2 electrostatic

compared with the corresponding terms in the

interaction when/Mg .... 0H2/

It is also noteworthy in this

interaction

respect that the highest stable hydrated Mg carbonate

presently recognized is MgC03 '5H2 0, where Mg is probably

coordinated to the five H2 0 molecules and either a C03

'apex' or 'edge'. Thus even Mg, with its many known

instances of complete water coordination, may preferentially

coordinate to CO;T in the presence of water molecules.

At atmospheric pressure, the reactions

(a) CaC03 (calcite) + 6H2 0 (liq.) = CaC03 ‘6H2 0 (solid)

(b) CaCC^( aragonite) + 6H2 0(liq.) = CaC03 *6H2 0 (solid)

(c) CaNa2 (C03 ) 2 (solid) + 5H2 0(liq.) = CaNa2 ( C03 ) 2

* 5H2 0 ( solid)

would be accompanied by 20, 18 and 13 percent decreases in

volume, respectively, suggesting that at high hydrostatic

pressures (such as those that occur in the abyssal layer
-50-

of the oceans or in hydrostatic vessels) CaC03 '6He 0 in

particular, and hydrated salts in general, may not only be

present as nucleating particles for the reasons mentioned

earlier, but may actually be the most stable forms. It is

1 ) noteworthy in this connection that/most deep sea animals have

little or no calcareous materials in their skeletons

(Svendrup, Johnson and Fleming, 1942) suggesting that anhydrous calcium carbonates are not easily formed at these

2 ) depths, and/that CaC03 is essentially absent from sediments

collected at depths greater than 5,000 m (Arrhenius, 1963)

and Laughton,

presumably because of its increased solubility (Heezen / 1963)

It has been suggested (Riedel, 1963 ) from an electron

microscopic examination that almost all the calcium carbonate in deep sea sediments is of organic origin and has

not been changed by recrystallization after deposition.

However, the possibility must be considered that at great

depths the calcium carbonates in such sediments can be

converted in part into hydrated forms which prevent the

formation of normal skeletons and which rapidly decompose

to the anhydrous forms at normal temperatures and pressures

(.i.e., during sample recovery).
- 51-

(f) CaC03 *H2 0

CaC03 *H2 0 usually has a spherulitic habit (Brooks,

Clark and Thurston, 1951) and its structure is unknown at

present. It is the first macroscopic phase obtained in the

preparation of CaC03*6H2 0 and CaNa2 (C03 ) 2

* 5H2 0 (gaylussite)

by precipitation from aqueous solution in gel form in the

presence of polyphosphates. CaC03 *H2 0 has been grown as

single crystals by Lippmann (1959) by hydrolysing KCNO in

aqueous solution with MgCl2 and CaCl2 in a closed vessel at

20°C. The structure has a pronounced pseudo-cell (Table 15)

.

CaC03 'H2 0 is of considerable interest since it is so readily

produced (in spherulitic form) in the presence of crystal

growth poisons which inhibit the formation of calcite. It

is stable for several months at 20°C in air.

(g) Gavlussite CaNa? (C03 ) P

* 5Ha 0

Gaylussite is found as a mineral and in the solid phase

eventually

formed/at room temperature from aqueous solution when a

large excess of Na2 C03 solution is added to CaCl2 solution

in the presence of polyphosphate. The unit cell has dimensions a = 14.361(2)A, b = 7.781(4) A, _c = 11.209(2) A and

3 = 127.84(1)°, with space group C2/c. The structure has

been determined (Dickens and Brown, 1968 b) , (R = 0.043),
- 52-

Table 15

The "True" and Pseudo Cells of CaC03 *H2 0

a. 10.62 A pseudo cell a_‘ = 6.13 A

c 7.54 c = 7 . 6

z 9 2

a = /3a

space-group D3 ^ P3,21 or D3

^ 3,5 ^P3,21

density 2.38 g/ml
"53"

and the hydrogen atoms have been located approximately.

Specific details are shown in Fig. 12 and 13. The structure

contains C03 -Ca-C03 ion triplets isolated from each other

but coordinated to Na ions and water molecules. These triplets could be of importance in biological transport.

The structure is more fully discussed by Dickens and Brown

(1968b)

.

(h) Pirssonite, CaNa? ( C03 ) g

• 2Ha 0

Pirssonite is found as a mineral and is the solid phase

formed instead of gaylussite when the reactants are maintained at 50°C. The cell data are given in Table 16. Its

structure has been determined from natural (Corazza and

Sabelli, 1967) and synthetic (Dickens and Brown, 1968 b)

material. For the latter determination R^. = 0.029. Despite

the resemblance of its cell dimensions to those of Na2 C03

'

NaHC03 *2H2 0, trona, it is not structually related. The

structure (Fig. 14, 15) contains ion triplets (Fig. 14) very

much like those in gaylussite except that the triplets are

further coordinated together (Fig. 14, 15) because there are

not enough water molecules in the structure to complete the
-54-

Table 16

Cell Data for Pirssonite

Evans

a = 11.32

b = 20.06

c = 6.00 A

Space group Fdd2

z = 8

density = 2.367 g/ml

Dickens and Brown

(196a?

)

11.340(4)

20.096(5)

6.034(2)
-55-

in CaNa s (C03 ) 2

. 5H2 0 (gaylussite) . From Dickens and Brown (1968b)
-56

cn|^-

Figure

13,

The

hydrogen

bonding

in

CaNa

2

(C0

3)

2

°

5H2

0

(gaylussite)

.

From

Dickens
Brown

(1968b)

.
-58'

Figure 15 « The detailed bonding in CaNa2 (C0S ) 2

• 2H2 0

(pirssonite) . From Dickens and Brown (1968b)
-59-

coordination round the Ca ions. Other features of the

coordination are shown in Fig. 14 and 15. The structure

is more fully discussed by Dickens and Brown (1968b).

Pirssonite may be important in the otoliths of benthic

which are found

fishes (Morris and Kittleman, 1967) /to be well

stratified into distinct species in the sea. The otoliths

are strongly piezo-electric and it has been suggested that

this may be the mechanism by which the fishes perceive

their depth, since they do not have gas bladders. The major

inorganic component of the otoliths is aragonite, which,

being centrosymmetric, cannot be piezo-electric. Pirssonite,

however, is non-centrosymmetric and consists of ions commonly present in sea water, although it is not normally

formed under conditions expected in sea water (Bury and Redd,

1933) . Organic components in the otoliths also may be

responsible for the piezo-electricity, however, as has been

Lavine and Shamos, 1963

suggested for bone (Shamos / ) . Other possible candidates

are shortite and Na2 C03 *H2 0. Using a crude apparatus we

have found both pirssonite and shortite to exhibit piezoelectricity. Our sample of small plates of Na2 C03 *H2 0 did

not give a positive test under these conditions, although

Harper (1936) observed such an effect.
-60

( i) Short it e Cag Nap ( 00^)3

Shortite is found mainly as a mineral and, because it

is non-centrosymmetric, may, like pirssonite, be of importance in generating the piezo-electricity of some otoliths.

Its structure has been determined (Wickman, 1949) but there

are some large discrepancies between the calculated and the

qualitatively observed structure factors and the structure

needs refining.
- 6L3. OTHER STRUCTURES OF INTEREST

(a) Brushite CaHP04 .2H2 0

Brushite was first found in 1865 by G 0 E. Moore (1865)

in druses in phosphate rock from Avis Island in the Caribbean

Sea. It frequently occurs as encrustations on ancient human

and animal bones (Frondel, 1943) and is found in human urinary

calculi

/(Lonsdale, Sutor and Wooley, 1968), The structure is

related to that of gypsum, CaS0 4 «2H2 0 (Atoji and Rundle, 1958),

and was first refined (Beevers, 1958) in the same centrosymmetric space group 12/a. Chemical considerations and the

observance of a pronounced piezoelectric effect prompted

refinement to (R = 0.164) in the non-centrosymmetr ic space group

la (Jones and Smith, 1962). The refinement used Beever's original data which was uncorrected for what must have been

appreciable absorption. More recent work (Jones, 1968) using

an incomplete set of neutron data collected from a large single

crystal of brushite retains the overall structural similarity

of CaHP04“2H20 to CaS04 -2H2 0, including the hydrogen bonding

of the water molecules, although the detailed atomic distances in the two cases are different 0 The 'acid' hydrogen

in CaHP04 »2H20, which presumably distorts the space group

from 12/a to I/a, is suggested to be located between 0(1) and

0(4') (Jones, 1968), i.e., in the CaP04 layer. The positions
-62-

of the heavy atoms have not yet been refined from those in

Jones and Smith (1962) . Further refinment with new data is

necessary. The structure (Figure 16) consists of CaP04 sheets

like those which have been found in several other calcium

phosphate structures (in gypsum there are similar CaSC>4 sheets) .

The sheets consist of neighboring chains of alternating Ca and

P04 ions and are linked together by interleaved layers of water

molecules. The water molecules hydrogen bond to the oxygens

cf the P0

4

ions on the surfaces of the CaP04 sheets and are electro'

statically bonded to the Ca's. The structure may be rationalized

from Figure 17 which is the monetite (CaHP0

4

) structure idealized into a tetragonal structure. Figure 17 is also essentially

Hohne, 1962?

the anhydrite (CaS04

) structure (£heng and Zussman, 1963).

In CaS04 , the structure is orthorhombic with

a_ = 6.991, b .= 6„996. c = 6.238 (Swanson, Fugat and Ugrinic,

If A I^fentfal Ca/P04 in CaHP04 -2H2 0

1955). • B and C are

CaHP04 chains and D and E are water molecules .

Similarly, in CaHP0

4 »2H2 0 the Ca's in the B and C chains are

coordinated to water molecules on the side away from the A

chain so that the layer in both brushite and gypsum is a zigzag

interlocking of chains. In brushite, presumably there is distortion of the chain by the hydrogen bonding between P04 groups.
-63-

Figure 16. Projection of the structure of brushite on

to a plane perpendicular to [101], From Beevers (1958).
D

i

- 64-

E

1

Figure

Ca (H) PO4
-65-

(b) Monetite CaHP04 The crystal structure of monetite has been determined

(MacLennan and Beevers, 1955; Jones and Cruickshank, 1961)

with moderate precision (R = 0.15) from photographic x-ray

data uncorrected for what must have been appreciable absorption. The hydrogen positions have been determined (Curry,

Denne and Jones, 1968) using neutron data and are consistent

with observed P-0 lengths and NMR data. The heavy atom

positions have not been refined from the positions reported in

Jones and Cruickshank (1961). Further work (Curry, Denne

and Jones, 1968) is continuing on monetite.

The structure (Figure ]8) contains sheets of CaHP04 which

are bonded to one another by Ca...O electrostatic bonds and

by hydrogen bonds. The shortest O. . .0 distance in the

structure is 0(7). ..0(7') = 2.44 ± .03 A across the center of

symmetry. The hydrogen is disordered about this center of

symmetry so that the bond contains half a hydrogen on average

on each side of the center. The reamaining "half" hydrogen

is similarly disordered in the 0(1). ..0(5) region, where the
66-4

Figure 18 0 Monetite: projection of one layer of the

crystal structure on to the plane perpendicular to [001]

the other layer (of which only 07

' and 08

' is shown) is related to this by a center of symmetry. The smallest circles

represent probable hydrogen sites*

From Jones and Cruickshank (1961).
67

interatomic distance is 2.58 ± .02 A. The remaining hydrogen

in the unit cell is on 0(6) and forms an essentially linear

hydrogen bond to 0(8) with 0(6)... 0(8) = 2.66 ± .02 A a

The structure of monetite is essentially the structure

given in Figure 17 distorted to triclinic by the hydrogen

bonding and perhaps by the lack of fit of the 0 'cage 1 and the

Ca ionic radius.

(c) Ca(He P04 ) 2 -H 2 0

The structure of Ca (H

2 P04

) 2 *H2 0 (Figures 19, 20) has

been determined (MacLennan and Beevers, 1956; Jones and

Cruickshank, 1961) with moderate precision (R = 0.16) from

photographic x-ray data uncorrected for absorption. The

hydrogens have been placed (Jones and Cruickshank, 1961)

provisionally from considerations of the P-0 bond lengths in

the P04 group and of 0...0 distances in the structure. In

the P (1) PO4 group, two statistically disordered hydrogens

have been suggested, from 0(1) to 0(1') (2.67 ± .05 A) across

the center of symmetry and (a little less likely) from 0(4)

to 0(9) (0(4). ..0(9) = 2.60 ± .03 A). 0(3) is assigned a

hydrogen which is hydrogen bonded to 0(5) (0(3) .. .0(5) =

2.48 ± .03&) . In the P (2) PC>

4 group, the P-0 distances suggest

the assignment of one hydrogen to 0(6), forming a hydrogen

bond to 0(8) (0(6).. .0(8) = 2.72 ± .04 A), and one hydrogen
-68-

Figure 19 0 Four unit cells of Ca (H^PC^) 2 'H^O, projected

down the _a axis. From MacLennan and Beevers (1956)
-69-

«*

Figure 20. Projection of the crystal structure of

Ca (H2 P04 ) 8 aH2 0 onto the plane perpendicular to [100].

From Jones and Cruickshank (1961).
70

to 0(7), forming a hydrogen bond to 0(8) (0(7). ..0(8) =

2.58 ± o 04 A). The hydrogens of the water molecules hydrogen

bond to 0(4) (0(9). ..0(4) = 2.60 ± .03 A) and to 0(8)

(0(9). ..0(8) = 2.74 ± .03 A). Neutron data on a twinned

crystal of Ca (H 2 P04

) 2

.

2 0 are being collected (Curry, Denne

and Jones, 1968). The CaP04 layer structure for Ca (HP04 ) 2 .H2 0

is very similar to that for CaHP04 -2H2 0, if the hydrogen atoms

E

are ignored. One of the water molecules, say position/lh

Figure 17, in CaHP04 *2Hs 0 is the oxygen 0(5) of a P04 group

which is hydrogen bonded to its centro-symmetr ically related

partner (Figures 19,20). Successive sheets in Ca (H2 P04 ) o

• 2 H2 O

crystallographically

are not/related by a rotation about 180° as they are in gypsum

and brushite and the occasional crystallization of layers

rotated by 180° explains the observed twinning of Ca (H

2 P0

4

) 2 -H2 0

The fact that there are similar

(MacLennan and Beevers, 1956). /Sheets in the above compounds account for their observed intergrowths (Lehr, Smith

and Brown, 1952)
-71-

The structure of Ca (H2P04 ) 2 *H2 0 is also related (Brown,

Smith, Lehr and Frazier, 1958) to several other calcium phosphate compounds as shown in Table 17.

(d) Ca 2 P04 Cl chlorospodiosite

The crystal structures of Ca

2 P04 Cl (Figure 21) and its

analog Ca 2 Cr04 Cl have recently been determined (Greenblatt,

Banks and Post, 1967) with R = 0.043 and 0.041, respectively.

The structure of Ca

2 P04 Cl contains CaPC>

4 layers which are easily

constructed from Figure 17 by taking a planar sheet consisting of

the ABC chains and replacing those oxygens in chains

by Cl” ions

D and E which are coordinated to the Ca in the A chain/ The

Cl ions are in turn coordinated to another planar sheet on thier

far side. The voids left between adjacent CaP04 sheets and

in the Cl” layer are filled by Ca ions. The whole structure

undergoes some slight rearrangement, seemingly based on the

second type of Ca being coordinated most efficiently to the two

P04 edges in the six oxygen atoms in its coordination environment . The other two oxygens in this environment are PCt

apices. These six oxygens from a cyclo-hexane shaped boat

with the Ca just above the 'deck' and with two Cl ions at right

angles to the prow-stern line completing the Ca coordination

as a 'sail'. The oxygen 'boats' share a common side and

adjacent ones are inverted. The CaPO chains, apart from being
Cell

Data

of

Several

Compounds

Related

to

Ca(H2

P04 )

-72-

O

CV E

cv

O

cv e

cv ^—* tO i—

r--

O l—

in

(X • 0 0 o 0 0 •

tv

m r^ CO

O OO o 00 E rH GO rH OO o

rd oo

cv e

CMOe

CD E

cv rd u

CM 1 1 rH rH <To tO OO LO r-1 m OO 00 • • t O 0 0 • LO rH v£) 00 00 oo m 1—

OO rH

rH

CO

CN

O

cv e

(NoE

t- E

W*

O 2A

00 to 'st' o

rH "sf rH uo 00 • 0 • o O o • U0 ON] to 00 CO U0 uo i—

OO rH

rH

OO

cv fd u

-pHcD

<D 43

Eh

O

cv E

CM “ — O OO 0\J o U0 » OO rH E r~- uo uo uo o OO '— • 9 • O' o o • uo Ovj to r" t"- 00 U0 E rH OO rH OO ,—„

rH

>1 rH E -P f—

E H 0) W u

cvC

X (d fd| rQl D|

(D 5 U d CD. > TO E
.-73

o o o

°

o

o O b

oO° OoO° C

o Q

d

O

o

«b

b

0 o

C^ofes#’ «b

o

O

o

O

O

o

O

o

O

o

O

O

O

Figure 21 0 The unit<=cell contents of Cas P04 Cl viewed

along a. D Large open circles. Cl; atoms shaded up and down, P;

double circles, Ca; smaller open circles, 0 o Bonds between

the atoms in P04 3 ” tetrahedra are represented by broken lines 0

From Greenblatt, Banks and Post (1967).
-74-

slightly rotated about their axis by coordination to interlayer

Ca ions, are regular because no hydrogens are present to distort

them through hydrogen bonding.

(e) a-Ca3 (P04 )

a-Ca3 (P04 ) 2 is the form of Ca3 (P04 ) 3 stable above 1180°C

MacKay (1953) assigned to it the monoclinic cell a_ = 12.86 ±

.02, b = 9.11 ± .01, c = 15.23 ± .02, p = 125.3 ± .2° and the

space group P2 1 /a with z = 8. A pseudo-orthorhombic cell

a_ = 15.22, b = 20.71, _c = 9.109 A has been reported (DeWolff) .

MacKay noted considerable hexagonal pseudo-symmetry in the hkO

layer of the reciprocal lattice, i.e., in the projection of the

structure along c.. In three dimensions the structure is not

pseudo-hexagonal. From two-dimensional Patterson syntheses he

suggested the structure contained 12 columns of Ca and PO4 ions

parallel to _c, the columns being spaced about 3 & apart with

O the heavy atoms Ca and P about 3.8 A apart in the columns. More

recently, Epstein (1968) has found that the b axis is invariably

tripled in samples he has examined, and we have confirmed this.

He found trial positions for the heavy atoms but could not find

positions for the light atoms which would allow the structure

to refine. He considered two structures with packings similar

to the chains of Ca and P04 ions in structures such as CaHP0„

% 4
-7 5

( f ) PCa3 (P0

4

) s 3Ca2 (P04 ) 2 is the form of Ca3 (P04

) 2 stable at temperatures below 1180° and is trigonal (Frondel 1941, 1943; Mac ay,

1952) with _a = 10.32 A, _c = 37.0 A, space group R3c and z = 7.

It exists as the mineral whitlockite and is often a pathological calcified deposit in the body. There is an anomaly

in that 21 Ca ' s (in 7 formula weights of Ca 3 (P04 ) 2 ) cannot

fit in space group R3c without statistical disordering. Brown

and Wallace have recently (1968) shown by heating mixtures of

CaC03 and CaHP04 »2H2 0 to form 3Ca 3 (P04 ) 2 and Ca4 P 2 07 and subsequently analyzing for P 2 07 4 “ that the ratio of Ca/P in

3Ca 3 (P04 ) 2 is 21/14 and not 20/14 (which would fit in space

group R3c) . The structure of 3Ca 3 (P04 ) 2 is not yet known.

(g) Ca 4 Mg 5 (P04) 6 The structure of Ca 4 Mg5 (P04 ) 6 has recently been determined

by Dickens and Brown to the point of final refinement (R = 0.08)

.

The formula is really Ca3<B Mg4#B (Ca, Mg) (P04 ) 6 . Ca and Mg

are present in the variable site in about equal amounts in

our crystal, making the empirical formula Ca 4 Mg5 (P0 4 ) 6 .

When the structure is reviewed along [201] an approximate h
-76

axis can be discerned if small shifts in the atomic positions

and the difference between Ca and Mg are ignored. A pseudohexagonal cell a.' = 6.86 A, b' = 9.99 and _c ' = 14.88 A can

be defined. Similarities between this cell and that of

NaK3 (S0 4 ) 2 (glaserite) can be seen. As in glaserite, there

are cation columns and cation-anion columns in Ca 4 Mg 5 (P0 4 ) 6

.

The cation-anion columns in Ca 4 Mg5 (P0 4 ) s have every other

cation site vacant.

One of the main objectives in our study of Ca 4 Mg5 (P04 ) 6

is to find relationships between it and the two better known

tricalcium phosphates, (3-Ca 3 (P04 ) 2 , and a-Ca3 (P04 ) 2 , neither

of which has a known structure. The dimensions of the pseudoorthohexagonal cell of Ca 4 Mg B (P04 ) s strongly suggest that there

are relationships between it and the two tricalcium phosphates.

For example, whitlockite is known to have a prominent repeat

of c/10 (i.e., 3.74 A) in its cell structure. The pseudoorthohexagonal described above has a similar repeat of c'/4

(i.e., 3.72 A). The _a axis of whitlockite, 10.43 A, is quite

similar to b' of Ca4 Mg5 (P04 ) 6 , 9.99 A. The dimensions of the

pseudo-orthorhombic cell of a-Ca 3 (P04 ) 2 , a_ = 15.23, b = 20.71
-77

and _c = 9.11 A, are also similar to those of the pseudoorthohexagonal cell of Ca 4 Mg5 (P04 ) 6 . It now appears that

no two of these compounds are isostructural , but it is likely

that they will share important structural features. The unit

cell and related data of Ca 4 Mg5 (P04 ) s are compared with those

of aCa3 (P04 ) 2 , BCa 2 (P04 ) 2 and NaK3 (S04 ) 2 (glaserite) in

Table 18.

(h) Calcium Oxalates

Other important constitutents of human urinary calculi

are the compounds Ca(C00) 2 «H 2 0 (whewellite) and Ca(COO) 2 -2-

2«2Hs O (weddellite) , which are also found as minerals. The

structures of both have been determined. Whewellite is monoclinic, _a = 6.24, b = 14.58, _c = 9.89, B = 107°, z = 8 with

space group P2 l /c, R = .13-. 15. Its structure (Cocco and

Carobbi, 1961; Cocco and Sabelli, 1962) is shown in Figure 22.

The Ca 1 s are coordinated by the longer edge of the oxalate

anion, which presumably allows each oxygen to coordinate to

two Ca's more easily. Apparently the hydrogen atoms were

not located.
-78-

Table 18

A Comparison of the Unit Cell Data of

a and (3Ca 3 (P04 ) 2 , and Ca4 Mg 5 (P04 ) 6 and

Na 3 Kg (S0 4

) 6 ( glaserite) aCa3 (P04 ) 2 Monoclinic

cell)

pseudoorthorhombic 6Ca 3 (P04 )

g

Ua3 Kg ( S0 4 ) 6 Ca 4 Mg5 (P04 ),

a 12.86 A

cell)

20.71* 10.32 A 9.80 A 22.84 A

b 27.33 9.109 10.32 9.80 9.994

c 15.23 15.22 37.0 7.33 17.09

3 125°20 1 y: 120° y : 120 0 6:99.96°

space group P2 x /a

R3c or

R3c P^ml C2/c

Vol . 4367 A

3 3412 A

3 610 A 3841

density 2.81 g/ml 3.12 g/ml 3.13 g/ml

Fwt/cell 24 21 1 8

Vol. M3 (X04 ) 3 182.0 A

3 162.5 A

3 203 A

3 160 A

3

* 2 x 12.86 cos (125 °20 ' ) = 20.98 A
-79

Figure 22. Projection of half of the structure of whewellite

on a plane roughly normal to [010],
80-

Weddellite is tetragonal with a. = 12.30 ± .02, _c = 7.34 ±

.02 and space group I 4/m. Its structure (Sterling, 1965)

is shown in Figure 23. For this structure, R = 0.13. The

Ca... oxalate coordination is similar to that in whewellite

An unusual feature in the structure is the 0(7) water, which is

not in a position to form well defined hydrogen bonds and which

is held in a zeolitic manner to a variable extent. The refinement suggests (Sterling, 1965) 0.4 of a water in this

position, which in turn suggests the formula Ca (COO) 2

• 2 . 2H 2 0,

close to the measured value of 2.17H2 0. Crystallographically

,

the maximum amount of water the structure can hold is 2.5H2 0,

which agrees with the suggestion of Philipsborn (1952). The

hydrogen positions were not determined but possible hydrogen

bonds have been suggested from inter-oxygen distances and

angles

(i) Newberyite MgHP04 »3H2 0

Newberyite is often found with struvite, of which it may

be a decomposition product. It is found in various types of

guano and in urinary calculi. The structure has been determined (Sutor, 1967) (R = 0.044) and is shown in Figure 24.

The acid hydrogen has been assigned on the basis of the P-0

bond lengths and the 0...0 distances; the remaining hydrogens

have not been assigned unequivocally.
-81

Figure 23. Cell of weddellite. Atoms of primitive cell have

bolder outlines or are solid. Smallest atoms are calcium, next

larger ones are carbon, and largest are oxygen. Atoms of oxalate groups are connected with solid lines. Broken lines connect

calcium ions in primitive cell with the oxygen atoms which they

are coordinated. Solid oxygen atoms represent water molecules,

5 and 6 lying in the mirror plane (001) . The solid calcium

atoms also lie in (001)
-82

Figure 24 0 Bounded projection of the structure of

MgHP04 °3H2 0 from y

= 0 -* 0.5 on (010), showing the magnesium

coordination. The magnesium atoms which are approximately

coplanar are sandwiched by two planes of phosphorus atoms.

In the bounded projection from y = 0.5 - 1.0 which completes

the structure, the atoms are related to these by 1/2 - x,

1/2 + y, z.
-83-

(j) Struvite MgNH4 P04

• 6H2 0

Struvite is apparently almost ubiquitous , having been

found in canned crabmeat, shrimp, lobster, in peat bogs,

in a mammoth's tooth and in bat guano. Its structure has been

determined (Whitaker, 1965). The magnesium ion is coordinated

by water molecules only, as one would expect from the similar

situation in MgS04 *7H2 0 (Baur, 1964).- Struvite may be produced

in vivo by bacterial action (Palache, 1923; Ayres, 1942). It

seems probable that most or all of the newberyite found in

calculi results from the decomposition of struvite (Lonsdale

and Sutor, 1966)

.

(k) Calcium Arsenates

We have seen earlier that hydrated salts may be important

in general as precursors in precipitation from aqueous

solution. In the case of calcium phosphate hydrates, the

calcium arsenates are a rich source of structural information

by analogy.

Various hydrated calcium arsenates are thought to

(See for example, Pierrot (1964) and references therein.)

exist./ While several are related to known hydrated calcium

phosphates, other have no analogy among the stable calcium

phosphates o The structures of these arsenates may shed light

on the possible composition of the highly hydrated amorphous

phase (or on other possible precursors in the calcium/phosphate/

water system.
-84-

Table 19

Hydrated Calcium Arsenates

Ca(H2 As04 ) 2 «nH2 0 n = 0 , 1, 2 ,

CaHAs04 »nH2 0 n = 0 , 1, 2 ,

Ca5 H2 (As0 4 ) 4 *nH2 0 n = 4,5,9

Ca3 (As0 4 ) 2 -nH2 0 n o

i

—

00

s. CN o

II

Caio (OH) 2 (As04 ) 6

Ca2 (OH) As04 .2Hs O
Cell

Data

on

Some

Hydrated

Calcium

Arsenates

-85-

Go

p

o

<DU

rd&

W

rtJ H

b

C

oa

u

O \ \CN CN U CL.

0\H

CMa

m in

CN CM CO 0

0 CTi

t-- <*> rH

CO iH CN * rH •» * * CO rH * * o

ID - • • • ID ID - ID

i—

1

in O CN [> in on • % • ro «• rH CN • • in CO 0 c * vo LO O %

CO in r1

% r—

1

rH rH (Ti o o

5-1 • • o • CD rH LO CTi r- CO

0) in ID 1—1 O • • • ID % 9 -P i—

i

• rH • * rH <T> o ro • — CM rH <D CO VO * - % rH - rH - t" CO 1—

1

in

i—

1

rH ID O CT> in C *> rH * in 00 %

<L> § O 0 "sf 00 rH i—

1

r-- rH V0 rH 0 o 0 o 0 U 5-1 O <T> <T> rH o • o • 0 CO O 0 o CO CM ID o

rd • i—

1

• • • 0H CO • CM ro o • i—

1

• o

a ID rH ID i"- r- Ci <M c rH cn LO CO rH rH in rH in 1—

1

rH

rd g

-p (L) co 4J >i co

5-1 >1 u w

g o rd g +> g g g 6 « g

+>•Hca

0) CD •p •P •H •H

iH 5-1 0 0 H o Cn CL) rd CD rd G 4-> SH £ g •H H

CD ro 5H TO rH G S rd H •rH H jG rd <U 2 a a 3=

03o

ro O

O U O

<D

4-> (1) <D

•rl •p -P

i—

1

•H •H

rd t P

45 rH •rH +J 0 g

G 4H H

<D G T3 3 •rH rd 0 rd

1 a CO >

o o

TO ro O ffi ffi TO in a o • •

'Z? TO • *. TO o H1 1—

1

o O

• CO CO o H* < <

CO o —

< CO TO cu < a a

n n in in rd rd rd rd U O U O

CD

rHO

u| cd d) P -p

-P rd a) -h 0) •rl a -P C0 -p G •H CO •rH •H o > CD rH P p o g (L) 0) CJ i

1

1

—

i

CO G •H CD rd 0

0 a a £h a

o

TO O a O

ro CD ro a • a , . cn ro CN on

• • 2 O

H1 TO •• TO o s o a

H* CO H1 u CN O 6

o

CO CO TO TO < n < , s .

, .

'

O H*

TO tP tp u o

a s 2 % CO

in (o ro rd C

rd O rd U —

CJ — O — rtf

' n

cf

CaHP0

4

•

2HaO

(brushite)

Structure:

Binas,

1966;

Cassien,

Herpin

and

Permingeat,

1966.
-86-

Acknowledgments

Use of the following figures is acknowledged: Figure 4

from Brown (1962) ; Figures 5 and 6 from Bragg (1924) ; Figure

7 from Hiriagi, Kachi, Takeda and Nakanishi (1966) ; Figure 8

from Kahmi (1963) ; Figure 9 from Bradley, Graf and Roth (1966)

Figure 16 from Beevers (1958) ; Figures 18 and 20 from Jones

and Cruickshank (1961) ; Figure 19 from MacLennon and Beevers

(1956) ; Figure 21 from Greenblatt, Banks and Post (1967)

Figure 22 from Cocco and Carobbi (1961) ; Figure 23 from

Sterling (1965) ; and Figure 24 from Sutor (1967) . W. E. Brown

is thanked for helpful discussions.
References

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structure of a grossularite garnet. Acta Crvst . 11 , 437-441.

Arrhenius, G. 1963. Pelagic sediments. In: The Sea.

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Atoji, M. and Rundle, R. E. 1958. Neutron diffraction

study of gypsum, CaS0

4 *2H2 0. J. Chem. Phys. _29, 1306-1311.

Ayres, V. L. 1942. Struvite in canned lobster. Amer .

Min . 27 , 387-388.

Battram, S. F. and Felton, E. J. 1962. The crystal

structure of the "vaterite" type rare-earth borates.

Rare Earth Research Proc . 2nd Conf . 1961. (Edited by

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and Breach, New York.

Baur, W. H. 1964. On the crystal chemistry of salt hydrates.

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(Epsomite) . Acta Cryst . 17 , 1361-1369.

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. Roczniki Chemii 30, 757-771.
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4

-H2 0.

_Z . Anorg. Ang. Chem. _6, 156.

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spectrometer. Proc . Roy . Soc . 89A , 468-489.

Bragg, W. L. 1924, The structure of aragonite. Proc . Roy .

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Brooks, R., Clark, L. M. and Thurston, E. F. 1951.

Calcium carbonate and its hydrates. Phil . Trans . Roy .

Soc . A243 , 145-167.

Brown, W. E. 1962. Crystal structure of octacalcium

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Brown, W. E. 1966. Crystal growth of bone mineral. Clin.

Orth . 44, 205-220.

Brown, W. E. and Epstein, E 0 F. 1965. Crystallography

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1958. Crystallography of hydrated monocalcium phosphates

containing potassium or ammonium. J. Phys . Chem . 62 ,

625-627.

Brown, W. E. , Smith, J. P., Lehr, J. R. and Frazier, A. WQ

1962. Crystallographic and chemical relations between

octacalcium phosphate and hydroxyapatite. Nature 196 , 1050-1055.

Bunn, C. W. 1945. Chemical crystallography. p. 285.

Oxford Press, New York.

Bury, C. R. and Redd, R. 1933. The system sodium

carbonate-calcium carbonate-water, J. Chem . Soc . 1160-1162.

Busing, W. R. 1968. An aid to the analysis

Ml.

of interionic and intermolecular forces in crystals. Abstract/

American Crystallographic Association winter meeting,

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Cassien, M., Herpin, P. and Permingent, F. 1966.

Structure cristalline de la haidingerite. Bull. Soc .

Franc. Miner . Crist . 84 , 18-22.

Cheng, G. C. H. and Zussman, J. 1963. The crystal structure

of anhydrite (CaS0 4

) . Acta Cryst . 16 , 767-769.
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whewellite. Rend . Sc . Fis . Mat . _e Nat . 31 , 292-298.

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