Geochemical Processes at Mineral Surfaces - American Chemical

coprecipitation they follow the Doerner-Hoskins law, where the ... with 0 £ χ £ 1, i f AX and BX form a continuous series of solid solutions. ...
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25 Ionic Solid Solutions in Contact with Aqueous Solutions Ferdinand C. M. Driessens Catholic University, Nijmegen, the Netherlands The knowledge that ionic solutions are mostly regular, if not ideal (1-3) was used to describe their solubility behavior in water. It appears that Roozeboom's class I solid solutions are ideal. In coprecipitation they follow the Doerner-Hoskins law, where the distribution coefficient is a simple func­ tion of the solubility products of the pure components. Class II and class III solid solutions were found to be regular, having a positive and a negative heat of mixing respectively. Substitutional disorder in ideal solid solutions gives rise to class II solid solutions, whereas ordering related to a negative value for the heat of mixing gives rise to type III solid solutions. An i o n i c compound has a f i x e d c o m p o s i t i o n . I t may c o n s i s t o f s e v e r a l c a t i o n s ( A , B, ...) and s e v e r a l a n i o n s ( X , Y, ...) so t h a t i t s g e n e r a l formula i s g i v e n b y : Ak B i . . . X

m

Y

n

0>

i n such a way t h a t k, 1, m and η a r e s i m p l e i n t e g e r s . An i o n i c s o l i d s o l u t i o n , on t h e o t h e r hand, i s o f v a r i a b l e c o m p o s i t i o n . I t s c h e m i c a l formula c a n n o t be w r i t t e n i n s i m p l e i n t e g e r r a t i o numbers. A t h e o r e t i c a l example i s t h a t o f two compounds AX and BX which form a s o l i d s o l u t i o n o f t h e g e n e r a l formula: Al-x

B

x

X

(2)

w i t h 0 £ χ £ 1, i f AX and BX form a c o n t i n u o u s s e r i e s o f s o l i d solutions. The e q u i l i b r i u m between an i o n i c compound l i k e t h a t o f f o r m u l a (1) and an aqueous s o l u t i o n c a n be d e s c r i b e d by a s o l u b i l i t y product defined b y :

0097-6156/86/0323-0524$10.25/0 © 1986 American Chemical Society

25.

DRIESSENS

Ionic Solid Solutions

(a )k A

(ae)

...

1

(a ) X

and Aqueous

(a )

m

Y

n

= K

525

Solutions

s p

(3)

which i s a c o n s t a n t under g i v e n t e m p e r a t u r e and p r e s s u r e . In E q u a t i o n ( 3 ) , a^ r e p r e s e n t s the a c t i v i t y i n t h e aqueous s o l u t i o n o f the i o n i . For s i m p l i c i t y , the charge o f the i o n s i s omitted i n E q u a t i o n (3) and subsequent e x p r e s s i o n s . However, e q u i l i b r i u m between a s o l i d s o l u t i o n l i k e t h a t o f F o r m u l a (2) and an aqueous s o l u t i o n i s not c h a r a c t e r i z e d by a c o n s t a n t s o l u b i l i t y p r o d u c t . In t h a t c a s e the f o l l o w i n g two E q u a t i o n s a p p l y (4): AX < A)

(ax)

= K

(a )

(a )

= K

a

s p

a x,

s

(4)

a x,

s

(5)

A

and, BX B

x

s p

B

where a x and agx , r e s p e c t i v e l y , r e p r e s e n t t h e a c t i v i t i e s o f t h e components A^ and BX i n t h e s o l i d s o l u t i o n o f F o r m u l a ( 2 ) , whereas and a r e t h e s o l u b i l i t y p r o d u c t s o f pure AX and BX, respectively. In most c a s e s t h e s t u d y o f e q u i l i b r i a between s o l i d s o l u t i o n s and aqueous s o l u t i o n s c o n t a i n i n g t h e i r i o n s i s e x t r e m e l y d i f f i c u l t , s i n c e s o l i d s t a t e d i f f u s i o n i s v i r t u a l l y absent at o r d i n a r y t e m p e r a t u r e s . Most i o n i c s o l i d s o l u t i o n s can be made homogeneous o n l y at t e m p e r a t u r e s above 500°C, where s o l i d s t a t e d i f f u s i o n i s relatively fast. Only i n c e r t a i n c a s e s (a r e l a t i v e l y h i g h s o l u b i l i t y o f b o t h components) i s i t p o s s i b l e t o o b t a i n e q u i l i b r i u m between a s o l i d s o l u t i o n o f known c o m p o s i t i o n and an aqueous s o l u t i o n , because the s o l i d s o l u t i o n i s homogenized by a r e l a t i v e l y f a s t r e c r y s t a l l i z a t i o n . In o t h e r i n s t a n c e s , e q u i l i b r i u m d e v e l o p s between t h e s u r f a c e o f t h e p a r t i c l e s o f t h e s o l i d s o l u t i o n and t h e aqueous solution. The p r e s e n t paper i s i n t e n d e d t o r e v i e w t h e most i m p o r t a n t l i t e r a t u r e i n t h i s f i e l d and t o extend the t h e o r y from the w i d e l y a c c e p t e d i d e a l s o l i d s o l u t i o n s t o the more g e n e r a l models o f r e g u l a r s o l i d s o l u t i o n s Ç 5 ) , w i t h and w i t h o u t o r d e r i n g (6) or s u b s t i t u t i o n a l d i s o r d e r (2^ 3^, 1). A

) S

s

The Roozeboom C l a s s i f i c a t i o n Roozeboom (J3) c l a s s i f i e d s y s t e m s o f two isomorphous s a l t s , forming s o l i d s o l u t i o n s l i k e t h o s e o f Formula (2) which v a r y i n r e s p e c t t o o n l y one i o n , such t h a t t h e y c o n s t i t u t e t e r n a r y systems ( i n c l u d i n g w a t e r ) . Three t y p e s were d i s t i n g u i s h e d , depending on t h e r e l a t i v e d i s t r i b u t i o n o f t h e s a l t s between t h e aqueous and s o l i d p h a s e s , as shown s c h e m a t i c a l l y i n F i g u r e 1 a . T h i s d i a g r a m , commonly known as a Roozeboom d i a g r a m , g i v e s t h e mole f r a c t i o n o f one o f t h e s a l t s i n the aqueous phase ( d i s r e g a r d i n g the water i n t h i s p h a s e ) , e . g .

526

G E O C H E M I C A L PROCESSES AT M I N E R A L SURFACES

B(aq) A(aq)+B(aq)

F i g u r e l a . Roozeboom* s c l a s s i f i c a t i o n f o r t h e d i s t r i b u t i o n o f t h e i o n i c compounds AX and BX o v e r t h e s o l i d phase and t h e aqueous phase.

H 0

H

2

AX

BX T y p e I]

2

0

AX

BX T y p e III

F i g u r e l b . R e p r e s e n t a t i o n o f t y p e I I and t y p e I I I systems i n t h e u s u a l t e r n a r y phase diagram.

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

BX aq AX

a

q +

527

Solutions

(6)

BX

a

q

as a f u n c t i o n o f i t s mole f r a c t i o n χ i n t h e s o l i d p h a s e . (i) q r e p r e s e n t s the molar c o n c e n t r a t i o n o f t h e s p e c i e s i i n t h e aqueous solution. The meaning o f t y p e s II and III can a l s o be v i s u a l i z e d on a G i b b s t r i a n g u l a r diagram (See F i g u r e 1 b ) . The l i n e s o f t y p e II would t e n d t o c o n v e r g e on t h e aqueous s o l u t i o n c u r v e , l e a d i n g i n extreme c a s e s , t o the f o r m a t i o n o f an i s o t h e r m a l l y and i s o b a r i c i n v a r i a n t aqueous p h a s e , i n e q u i l i b r i u m w i t h two s o l i d p h a s e s , meaning d i s c o n t i n u i t y i n t h e s o l i d s o l u t i o n . The l i n e s o f t y p e III s y s t e m s would t e n d to c o n v e r g e on t h e s o l i d s o l u t i o n c u r v e , l e a d i n g f i n a l l y t o the f o r m a t i o n o f a s o l i d compound w i t h a d e f i n i t e c o m p o s i t i o n l y i n g between the two components. a

D i s t r i b u t i o n Laws F o r S i m p l e I d e a l s o l i d s o l u t i o n s . I f a s o l i d s o l u t i o n o f Formula (2) i s i n e q u i l i b r i u m w i t h an aqueous phase (aq), the d i s t r i b u t i o n o f A and Β i o n s between the aqueous phase and the s o l i d phase (s) can be r e p r e s e n t e d b y : AX and i s

(s)

+ B(aq)

described a

J A(aq)

+ BX (s)

(7)

by:

BX,s

a

B

= D _ a

AX,s

a

(8) A

p r o v i d e d t h a t t h e s o l i d phase i s homogeneous. The s o l i d s o l u t i o n Formula (2) i s i d e a l when t h e i r heat o f m i x i n g i s z e r o and when t h e i r e n t r o p y o f m i x i n g i s g i v e n by t h e r e l a t i o n S = 2.303R fx In t h a t

log χ +

(1-x)

log

(1-x)J

of

(9)

case, a

AX,s

=

1

~

x


s

(10b)

= x

apply (2, 3 ) . Assuming that the a c t i v i t y c o e f f i c i e n t s of the A and Β ions do not d i f f e r s i g n i f i c a n t l y , Equation (8) transforms t o : [b>J

CBJaq

s

= D

(11)

528

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

where BX and AX r e p r e s e n t t h e c o n c e n t r a t i o n o f BX and AX, r e s p e c t i v e l y , i n the s o l i d p h a s e . E q u a t i o n (10) i s known as the B e r t h e l o t - N e r n s t d i s t r i b u t i o n law f o r c o p r e c i p i t a t i o n ( 9 ) . It r e p r e s e n t s type I s o l i d s o l u t i o n s a c c o r d i n g to the c l a s s i f i c a t i o n o f Roozeboom. T h i s i s i l l u s t r a t e d i n F i g u r e 2 f o r two v a l u e s o f D. The c o r r e s p o n d i n g r e l a t i v e amounts o f AX and BX c o p r e c i p i t a t e d a r e g i v e n i n F i g u r e 3 which i s m o d i f i e d from Gordon ( 1 0 ) . I f the e q u i l i b r i u m e x p r e s s e d i n E q u a t i o n (7) i s a t t a i n e d o n l y between the c r y s t a l s u r f a c e and t h e aqueous s o l u t i o n , the e q u i l i b r i u m i s described by: s

a

a

s

BX,cs AX,cs

ae aA

=

(12)

where a n ^ c s and a /\χ r e p r e s e n t t h e a c t i v i t i e s o f components BX and AX, r e s p e c t i v e l y , i n t h e c r y s t a l s u r f a c e l a y e r . In t h e c a s e o f i d e a l s o l i d s o l u t i o n s , d BX and d AX , the increments o f the components i n t h e p r e c i p i t a t e d s u b s t a n c e i n t h e s u r f a c e l a y e r , are p r o p o r t i o n a l t o t h e i r r e s p e c t i v e s o l u t i o n c o n c e n t r a t i o n , i.e. c

s

c

d BX

c

s

b

0

-

b

a

0

-

a

s

= d AX

c

c

s

(13)

s

p r o v i d e d t h a t the a c t i v i t y c o e f f i c i e n t s o f t h e A and Β i o n s i n t h e aqueous s o l u t i o n do not d i f f e r s i g n i f i c a n t l y . In E q u a t i o n (13) b and a r e p r e s e n t t h e i n i t i a l q u a n t i t i e s o f BX and AX, r e s p e c t i v e l y , i n t h e aqueous s o l u t i o n . The symbols b and a r e p r e s e n t t h e q u a n t i t i e s o f BX and AX, r e s p e c t i v e l y , which have been d e p o s i t e d i n t h e s o l i d . I n t e g r a t i o n o f E q u a t i o n (13) y i e l d s : 0

0

log

Baq>i

-

Baq>f

log

^aq»i

(14)

Aaq>f

where t h e s u b s c r i p t s i and f denote t h e i n i t i a l and f i n a l c o n c e n t r a t i o n s i n t h e aqueous s o l u t i o n ( 1 0 ) . E q u a t i o n (14) i s known as t h e D o e r n e r - H o s k i n s d i s t r i b u t i o n law TT2) for c o p r e c i p i t a t i o n , a l t h o u g h i t was d e r i v e d f i r s t by K r o e k e r TT2). It a l s o represents o n l y Roozeboom's t y p e I s y s t e m s . The n u m e r i c a l v a l u e s o f the d i s t r i b u t i o n c o e f f i c i e n t s λ and D have been d e r i v e d from e x p e r i m e n t a l d a t a f o r a l a r g e number o f systems ( e . g . (J_0, J M , _13). From the c o n s t a n c y o f e i t h e r λ or D v a l u e s i t can be d e t e r m i n e d whether or not t h e system y i e l d e d homogeneous p r e c i p i t a t e s . In e i t h e r c a s e , the n u m e r i c a l v a l u e o f λ or D s h o u l d be e q u a l t o : AX ^sp λ = D = _ BX Ksp

(15)

25.

D R IESS E N S

Ionic Solid Solutions

and Aqueous

529

Solutions

B(aq) A(aq)+B(aq)

Figure

2.

Distribution of

solid

components

phase

for

different

the

assumption

the

solid

values

that

phase

the

ionic

AX and BX over

i s

of

components

the

solid

AX a n d BX o v e r

phase

and the

the d i s t r i b u t i o n parameter

AX and BX form

ideal

solid

the

aqueous

solutions

D

under

and

that

homogeneous.

100BX(s) BX(s) + BX(aq)

AX(s) + AX(aq) Figure

3.

aqueous solid

Percent

solution

solutions.

coprecipitation under

of

the assumption

Modified

from

Gordon

AX v s . that et

that

of

BX from

AX a n d BX form

a l .

(10).

an ideal

530

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

which i s e a s i l y d e r i v e d from E q u a t i o n (4) and ( 5 ) . By c h a n g i n g t h e e x p e r i m e n t a l c o n d i t i o n s some systems can be made t o obey e i t h e r E q u a t i o n (11) or E q u a t i o n (14) ( 1 0 ) . In most c a s e s , however, t h e b e h a v i o r o f a system w i l l be somewhere between t h a t d e s c r i b e d by E q u a t i o n (11) or E q u a t i o n ( 1 4 ) .

D i s t r i b u t i o n Laws F o r Complex I d e a l S o l i d S o l u t i o n s . L e t A X and B X be two i o n i c compounds which form a s e r i e s o f s o l i d s o l u t i o n s o f the Formula: n

n

And-χ) In t h a t c a s e

B

n x

X

(16)

the entropy o f mixing

S = 2.303 Rn {x

so

is:

l o g χ + (1-x)

log

(1-x)}

(17)

that:

and, a

B X

,

as l o n g as t h e i s random ( 2 ) . c o n d i t i o n s , so these systems.

s

= x

(19)

n

d i s t r i b u t i o n o f A and Β i o n s o v e r t h e i r s u b l a t t i c e E q u a t i o n s (8) t h r o u g h (14) remain v a l i d under t h e s e t h a t o n l y t y p e I s o l i d s o l u t i o n s a r e found among I t i s e a s i l y shown t h a t i n t h i s c a s e

1/n

AX ^sp

(15a) BX ^sp

which i s

a more g e n e r a l

expression

o f E q u a t i o n (15)

(14).

D i s t r i b u t i o n Laws And R e g u l a r S o l i d S o l u t i o n s . F o r s o - c a l l e d r e g u l a r s o l i d s o l u t i o n s (J_5), E q u a t i o n (9) s t i l l h o l d s but by d e f i n i t i o n the expression for t h e i r enthalpy o f mixing i s :

H

m

= χ (1-x)

W

(20)

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

Solutions

531

i n which W i s t h e parameter f o r A - Β i o n i n t e r a c t i o n ( 2 ) . The a c t i v i t i e s o f t h e components AX and BX i n t h e s o l i d s o l u t i o n o f Formula (2) t h e n becomes:

a

A X , s = (1-x)

exp { 2w/(2.303 RT)}

a

B X , s = x exp {(1-x)2w/2.303 RT)}

(21)

X

and (22)

In t h a t c a s e a p l o t o f l o g ( a x ) / ( 1 - x ) v e r s u s x o r o f l o g a x / x v e r s u s ( 1 - x ) must y i e l d s t r a i g h t l i n e s w i t h t h e same s l o p e , from which W c a n be c a l c u l a t e d . Under t h e s e c o n d i t i o n s E q u a t i o n (8) t r a n s f o r m s t o : A

B

2

) S

2

) S

B X

s

AX s

B

= D

aq

exp { - ( 1 - 2 x )

W/(2.303 RT)}

(23)

A q a

so t h a t t h e apparent d i s t r i b u t i o n c o e f f i c i e n t (D i n E q u a t i o n ( 1 0 ) , i s no l o n g e r c o n s t a n t but depends on x . K i r g i n t s e v and T r u s h n i k o v a (16) have p u b l i s h e d a g e n e r a l method t o d e r i v e a x and ββχ from e x p e r i m e n t a l d i s t r i b u t i o n d a t a , and t h e y have'shown t h a i a number o f systems obey E q u a t i o n (23) i n systems w i t h h i g h r a t e s o f r e c r y s t a l l i z a t i o n . F i g u r e s 4 and 5 g i v e an example o f d i s t r i b u t i o n s i n a system w i t h v a r y i n g v a l u e s f o r W and D . Both t y p e I I and t y p e I I I s o l i d s o l u t i o n s o f Roozeboom s c l a s s i f i c a t i o n a r e found i n such s y s t e m s , depending on whether W has a p o s i t i v e o r a n e g a t i v e v a l u e , respectively. The v a l u e s chosen f o r W/(2.303 RT) i n o r d e r t o c o n s t r u c t F i g u r e s 4 and 5 a r e r e a l i s t i c ; f o r most r e g u l a r i o n i c s o l i d s o l u t i o n s t h e s e v a l u e s range from 1 t o - 2 Ç3).Due t o t h e d i f f e r e n c e s i n s o l u b i l i t y p r o d u c t s o f t h e components o f such s o l i d s o l u t i o n s , however, t h e v a l u e o f t h e d i s t r i b u t i o n c o e f f i c i e n t D can d e v i a t e s e v e r a l o r d e r s o f magnitude from u n i t y ( s e e E q u a t i o n ( 1 4 a ) ) . By e x t r a p o l a t i o n from F i g u r e s 4 and 5 i t c a n be shown t h a t type II and t y p e I I I systems a r e i n d i s t i n g u i s h a b l e from type I systems when t h e d i s t r i b u t i o n c o e f f i c i e n t D d i f f e r s by one o r d e r o f magnitude o r more from u n i t y . In t h o s e c a s e s , e x p e r i m e n t a l d a t a f o r the d i s t r i b u t i o n o f i o n s between t h e s o l i d s o l u t i o n and aqueous s o l u t i o n are not s u i t a b l e t o d e r i v e the nature o f the s o l i d s o l u t i o n s , as has been proposed by K i r g i n t s e v and T r u s h n i k o v a ( 1 6 ) . A t v e r y s m a l l o r v e r y l a r g e v a l u e s o f D, even m i s c i b i l i t y gaps i n s o l i d s o l u t i o n s c a n n o t be d e t e c t e d by t h i s method. A

1

s

s

532

G E O C H E M I C A L PROCESSES AT M I N E R A L SURFACES

B(aq) A(aq)+B(aq)

F i g u r e 4. D i s t r i b u t i o n o f t h e i o n i c compounds AX and BX o v e r t h e s o l i d phase and t h e aqueous phase f o r d i f f e r e n t v a l u e s o f t h e d i s t r i b u t i o n parameter D under t h e assumption t h a t AX and BX form homogeneous r e g u l a r s o l i d s o l u t i o n s w i t h a n e g a t i v e v a l u e f o r t h e i n t e r a c t i o n parameter W.

B(aq) A(aq)+B(aq)

0-f 0 AX

1 0.2

1 0.4

1 0.6 x ^

1 0.8

1 1.0 BX

F i g u r e 5 . D i s t r i b u t i o n o f t h e i o n i c compounds AX and BX o v e r t h e s o l i d phase and t h e aqueous phase f o r d i f f e r e n t v a l u e s o f t h e d i s t r i b u t i o n parameter D under t h e assumption t h a t AX and BX form homogeneous r e g u l a r s o l i d s o l u t i o n s w i t h a p o s i t i v e v a l u e f o r t h e i n t e r a c t i o n parameter W.

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

533

Solutions

DISTRIBUTION LAWS AND SUBSTITUTIONAL DISORDER D r i e s s e n s (2) has d i s c u s s e d the consequences o f s u b s t i t u t i o n a l d i s o r d e r on component a c t i v i t i e s i n s o l i d s o l u t i o n s . F o r example, s o l i d s o l u t i o n s o f the F o r m u l a :

M n

2(1-x)

C o

2x

S i 0

4

(24)

w i t h the o l i v i n e s t r u c t u r e obeyed

0.5

In a

C

o

2

S

i

0

In a

M

n

2

S

i

o

4

>

s

= in a

C o

= In a

M n

the

relations:

Si . 02,s

= In x -

Si . 0 ,s

=

0

5

0.2

(1-x)

2

(25)

and 0.5

4

>

s

0

5

2

l

n

( -x) 1

- ° ·

2

χ 2

< ) 26

w i t h i n t h e l i m i t s o f e x p e r i m e n t a l e r r o r , and t h u s , t h e s e s o l i d s o l u t i o n s appeared t o be r e g u l a r . However, exchange o f C o and Mn *** can o c c u r between l a t t i c e s i t e s (4a) and ( 4 c ) , r e s u l t i n g i n e q u i l i b r i u m a c c o r d i n g t o the reaction: 2 +

Co + (4a) 2

2

+ Mn + (4c) t

Co + (4c)

2

2

+ Mn + (4a) 2

(27)

L e t the d i s o r d e r parameter be z . Then the s t r u c t u r a l Formula o f t h e s e o l i v i n e s can be w r i t t e n a s :

Co

x + z

Mni_x_

z

(Co _ x

z

Μη _ Ί

χ + ζ

)

(28)

S1O4

I f t h e law o f mass a c t i o n a p p l i e s t o E q u a t i o n ( 2 7 ) , t h e parameter can be e s t i m a t e d t o a f i r s t a p p r o x i m a t i o n b y :

ζ = χ (1-x)

(1-K

2 7

(1+K

)

2 7

(29)

H

where K i s the e q u i l i b r i u m c o n s t a n t f o r E q u a t i o n ( 2 7 ) . F u r t h e r m o r e , the f o l l o w i n g f o r the a c t i v i t i e s o f the components: 2 7

a

Co Si04,s

= ( +ζ)

a

Mn Si0 ,s

= O-x+z)

2

χ

(x-z)

=

x

disorder

the r e a c t i o n i n e x p r e s s i o n s are o b t a i n e d

(30)

2

and 2

4

From t h e s e e x p r e s s i o n s ,

one can

O - x - z ) = (1-x)2 derive

z

2

(31)

534

0.5

G E O C H E M I C A L PROCESSES AT M I N E R A L SURFACES

In a

C

o

9

S

i

.

0

= In χ + 1/2 { V ( 1 - x )

s

- 1/2 V

2

2

(1-x)

4

+ ...}

4

+

...}

and 0.5

In a

M n 2 S i

Q

= In (1-x)+1/2 ( V x - 1 / 2 2

4 > s

V

2

x

(33)

where V w i l l be d e f i n e d below i n E q u a t i o n ( 3 4 ) . E q u a t i o n s (32) and (33) a g r e e t o a f i r s t a p p r o x i m a t i o n w i t h t h e e x p e r i m e n t a l c u r v e s g i v e n by Formulas (25) and ( 2 6 ) . In t h i s way and by n u m e r i c a l e v a l u a t i o n , D r i e s s e n s (2) proved t h a t t h e e x p e r i m e n t a l a c t i v i t i e s c o u l d be e x p l a i n e d on t h e b a s i s o f s u b s t i t u t i o n a l d i s o r d e r , according to Equation (27), within the l i m i t s o f e x p e r i m e n t a l e r r o r . I t seems, t h e r e f o r e , t h a t measurements o f d i s t r i b u t i o n c o e f f i c i e n t s and t h e r e s u l t i n g a c t i v i t i e s c a l c u l a t e d by t h e method o f K i r g i n t s e v and T r u s h n i k o v a (16) do not d i s t i n g u i s h between the r e g u l a r c h a r a c t e r o f s o l i d s o l u t i o n s and t h e p o s s i b i l i t y o f s u b s t i t i o n a l d i s o r d e r . However, the l a t t e r c a n be d i s c e r n e d by X - r a y o r n e u t r o n d i f f r a c t i o n o r by NMR o r magnetic measurements. I t can be shown t h a t s u b s t i t u t i o n a l d i s o r d e r always r e s u l t s i n n e g a t i v e v a l u e s o f t h e i n t e r a c t i o n parameter W due t o t h e f a c t t h a t W(2.303 R T ) "

1

= - 1/2 V = - 1/2 ( 1 - K 7 ) 2

2

O+K27)

2

(34)

T h i s i s a l s o v a l i d f o r t h e more complex s p i n e l s o l i d s o l u t i o n s o f Fe3Û4, Mn3Û4 and CO3O4, i n which e l e c t r o n exchange o c c u r s i n a d d i t i o n to s u b s t i t u t i o n a l disorder (2).

S u b s t i t u t i o n a l D i s o r d e r I n R e g u l a r S o l i d S o l u t i o n s . Most s i m p l e i o n i c s o l u t i o n s i n which s u b s t i t u t i o n o c c u r s i n one s u b l a t t i c e o n l y a r e n o t i d e a l , but r e g u l a r (2^, 2). Most complex i o n i c s o l i d s o l u t i o n s i n which s u b s t i t u t i o n o c c u r s i n more t h a n one s u b l a t t i c e a r e n o t o n l y r e g u l a r i n t h e sense o f H i l d e b r a n d ' s d e f i n i t i o n (15) but a l s o e x h i b i t s u b s t i t u t i o n a l d i s o r d e r . The E q u a t i o n s d e s c r i b i n g t h e a c t i v i t i e s o f t h e components as a f u n c t i o n o f t h e c o m p o s i t i o n o f t h e i r s o l i d s o l u t i o n s a r e r a t h e r complex (_7, W), and t h e s e can be e v a l u a t e d b e s t f o r each i n d i v i d u a l c a s e . Both type II and t y p e I I I d i s t r i b u t i o n s c a n r e s u l t from t h e s e c o n d i t i o n s .

O r d e r i n g . New compounds which i n c l u d e t h e i o n i c components AX and BX may be formed by o r d e r i n g o f t h e s o l i d s o l u t i o n (6_). In t h a t c a s e , t h e e n t r o p y o f m i x i n g may s t i l l be g i v e n by E q u a t i o n 1 7 , whereas t h e e n t h a l p y o f m i x i n g i s g i v e n b y : H

m

= x

n

(1-x)

n

W

(35)

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

Solutions

535

in which W has a negative value. In t h i s expression η i s the minimum number of units of AX and BX which unite to form a nucleus of the new compound Α Β Χ 2 · The s o l u b i l i t y behavior of s o l i d solutions of CaCO.3 and MgCu*3 could be explained with t h i s Equation under the assumption that η = 3 for dolomite, the new compound which forms between C a C Û 3 and MgC03. This value of η i s i n agreement with the content of a l a t t i c e c e l l i n the dolomite structure ( 6 ) . The appropriate expressions for the a c t i v i t i e s of the components become: η

a

η

η

AX,s = (1-x) βχρ{χη(1-χ)η-1/Ί-η+(2η-1)χ7ν^}/(2.303 RT)

(36)

and, a

(37)

BX,s = * exp{(1-x)n χη-1/η-(2n-1)xJW}/(2.303 RT)

Such systems belong to type III d i s t r i b u t i o n s because the value of W i s always negative. The system CaCû*3 - MgCu*3 - Η 0 i s given as an example i n Figure 6 . 2

Comparison With L i t e r a t u r e Data The d i s t r i b u t i o n of components of binary s o l i d solutions over the s o l i d phase and the aqueous phase has been studied for a number of systems. Table I contains a summary of some of these systems with references. This l i t e r a t u r e review i s not complete; more data are available e s p e c i a l l y for rare earth and actinide compounds, which primarily obey type I Equations to a good approximation. In the following sections, the theory above w i l l be applied to some special systems which are relevant to the f i e l d s of a n a l y t i c a l chemistry, inorganic chemistry, mineralogy, oceanography and biominerals.

Application In A n a l y t i c a l And Inorganic Chemistry Knowledge about d i s t r i b u t i o n c o e f f i c i e n t s i s used i n a n a l y t i c a l chemistry to determine the f e a s i b i l i t y of quantitative separation by p r e c i p i t a t i o n . Therefore, D and λ are also c a l l e d separation factors. In order to p r e c i p i t a t e 99.8% or more of the primary substance, λ must be 3 . 2 χ 10~4 or smaller. For larger values of λ more than one p r e c i p i t a t i o n step i s necessary, and the number of steps can be calculated when λ i s known. This straightforward application i s obvious for type I systems only, f o r which c o p r e c i p i t a t i o n diagrams l i k e Figure 3 can be calculated and experimentally v e r i f i e d . As can be seen from Figures 4 and 5, the apparent d i s t r i b u t i o n c o e f f i c i e n t , λ , for systems of

536

G E O C H E M I C A L PROCESSES AT M I N E R A L SURFACES

Table

I.

E v a l u a t i o n o f some systems o f s o l i d s o l u t i o n s to t h e i r s o l u b i l i t y behavior

AX

BX

Type

D( )*

according

Reference

NaCl

NaBr

II

KC1 NH4CI

KBr

RbCl CsCl RbBr

RbBr CsBr KBr

II II II II II (II)** (ID I ( ? ) 104 I I 0.9

K i r g i n t s e v and T r u s h n i k o v a (16) K i r g i n t s e v and T r u s h n i k o v a K i r g i n t s e v and T r u s h n i k o v a K i r g i n t s e v and T r u s h n i k o v a K i r g i n t s e v and T r u s h n i k o v a Durham e t a l (19) F l a t t and B u r k h a r d t (20) F l a t t and B u r k h a r d t Yutzy and K o l t h o f f (21) Vaslow and Boyd (22) H i l l e t a l (13)

I I I (II)

H i l l et a l H i l l et a l H i l l et a l Driessens

ΝΗ4ΒΓ

KC1

NH4CI

KBr AgCl TICI

NH Br AgBr AgCl KA1 ( S 0 4 ) KCr ( S 0 ) T1A1 ( S 0 ) T1A1 ( S 0 ) Ca5(P04) F 4

NH4AI (S04)2 NH Cr (SG*4) 4

2

4

2

NH4AI ( S 0 4 ) KA1 ( S 0 ) Ca5(P04)3 OH 2

4

2

2

4

2

Zu(NH4)2(S04)2 Cu(NH ) (S04) Mg(NH4) (504) CuK (S04) CoK (S04) RaCr04 2

2

2

2

2

2

2

RaS04 RaC03 SrS04 RaBr 2

RaCl Ra(N0 ) 2

3

2

2

4

2

1.6 2.5 2.5

BX

Cu(NH4) (S0 )

2

4

3

AX

4

2

Zn(NH ) (S04) 4

2

Type 2

Ni(NH4)2(S04)2 Ni(NH4) (S04) 2

2

Cu(NH4)2(S04)2 NiK2(S04)2 CuK2(S04)2 BaCr04 BaS04 BaC03 BaS04 BaBr2 BaCl2 Ba(N0 ) 3

2

D(

)*

Reference

4

Hill Hill

e t a l (13) et a l

I (?) 16 II

Hill Hill

et a l et a l

II II

I I (?) I I

5.5 1.2 0.18 0.030 9.8 5.0

H i l l et a l H i l l et a l Gordon e t a l ( 1 0 , 2 3 ) Gordon e t a l Gordon e t a l Gordon e t a l Gordon e t a l Gordon e t a l

I

2.0

Gordon e t a l

II I

I I

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

537

Solutions

Table I . (Continued)

AX

BX

Pb(N03) BaSO.4 PbCr0

2

4

CaCU3 BaHP0

4

MgNH4P04 Sm-oxalate Nd-oxalate Sm-oxalate Gd-oxalate Ce(III)-oxalate Am-oxalate Yb-oxalate Fe(I04) Th(I0 )4 3

4

Type

I

Ra(N0 )2 PbSO.4

I

(?)

PbMo04

I

(?)

MgC0

(Ill)

3

3

SrHP04 MgNH4As0 Nd-oxalate Pr-oxalate Gd-oxalate Dy-oxalate Nd-oxalate La-oxalate Nd-oxalate Y(I0 ) La(I0 ) 4

4

3

3

3

D(

I I I I I I I I I I

**

(?)

(?)

)*

3 0.08 250

****

Reference

Ratner

(9)

Kolthoff (24)

and

Noponen

Kolthoff (25)

and

Eggertsen

0.31 5.7 1.65 1.37 1.66 2.09 1.75 5.85 0.69 0.001

D r i e s s e n s and Verbeeck (6) S p i t s y n et a l (26) K o l t h o f f and C a r r (27) Weaver (22) Weaver Weaver Weaver Gordon e t a l (10, 23) Gordon et a l Gordon e t a l Gordon e t a l

6.5

Gordon et

al

The c a s e o f t y p e I were D i s c o n s t a n t r a t h e r t h a n are r a r e . In t h i s c a s e r e l a t i o n (13) i s not v a l i d . A more a p p r o p r i a t e r e l a t i o n was d e r i v e d by Gordon et a l (10). (II) means t h a t the i n t e r a c t i o n parameter W i s so s t r o n g l y p o s i t i v e t h a t a m i s c i b i l i t y gap o c c u r s i n t h e s e r i e s o f s o l i d solitions. (III) means t h a t η i s so h i g h and W i s so n e g a t i v e t h a t a new compound i s formed under t h e s i m u l t a n e o u s development o f two m i s c i b i l i t y gaps i n t h e s e r i e s o f s o l i d s o l u t i o n s .

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

538

Mg(aq) Ca(aq)+Mg(aq) 1.0

F i g u r e 6. D i s t r i b u t i o n o f t h e i o n i c compounds C a C 0 and MgCO^ o v e r t h e s o l i d phase and t h e aqueous p h a s e . O r d e r i n g o c c u r s i n t h e s o l i d s o l u t i o n s around χ = 0.5. I t i s assumed t h a t t h e s o l i d phase i s homogeneous. 3

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

Solutions

539

r e g u l a r s o l i d s o l u t i o n s or w i t h s u b s t i t u t i o n a l d i s o r d e r or o r d e r i n g depends on t h e i n i t i a l molar r a t i o o f the components i n the aqueous s o l u t i o n . Thus, the c a l c u l a t i o n o f c o p r e c i p i t a t i o n diagrams for t y p e II and t y p e I I I systems i s m e a n i n g l e s s , e x c e p t f o r t h e o r e t i c a l purposes. There i s e v i d e n c e t h a t the v a l u e o f λ f o r t y p e I systems depends on t h e degree o f s u p e r s a t u r a t i o n d u r i n g t h e p r e c i p i t a t i o n p r o c e s s w i t h a somewhat b e t t e r s e p a r a t i o n b e i n g r e a c h e d at lower r a t e s o f p r e c i p i t a t i o n , and h e n c e , at lower d e g r e e s o f s u p e r s a t u r a t i o n ( 2 9 ) . T h i s may mean t h a t the e v e n t s at the i n t e r f a c e o f s o l i d phase and l i q u i d phase a r e not c o m p l e t e l y d e s c r i b e d by E q u a t i o n ( 1 2 ) , e . g . a d s o r p t i o n might a l s o be i n v o l v e d . The i m p o r t a n c e o f a d s o r p t i o n i s e s p e c i a l l y c l e a r from s t u d i e s o f i o n e n t r a p m e n t , a phenomenon whereby o c c l u s i o n o f adsorbed f o r e i g n i o n s o c c u r s by overgrowth o f a p r e c i p i t a t e ( 3 0 ) . O c c l u s i o n o f c h l o r i d e i n a BaSO^ p r e c i p i t a t e can be d i m i n i s h e d by a d d i n g barium c h l o r i d e t o t h e s u l f a t e s o l u t i o n r a t h e r than t h e r e v e r s e . I t i s w e l l known t h a t t h e amount o f o c c l u s i o n g e n e r a l l y i n c r e a s e s w i t h t h e speed o f f o r m a t i o n o f a p r e c i p i t a t e . However, t h e r a p i d l y formed c r y s t a l s produced from r e l a t i v e l y c o n c e n t r a t e d s o l u t i o n s have a h i g h e r r a t e o f r e c r y s t a l l i z a t i o n d u r i n g a g i n g due t o t h e i r s m a l l p a r t i c l e s i z e . Thus, i t i s a d v i s a b l e i n a n a l y t i c a l procedures t o p r e c i p i t a t e r a p i d l y at room t e m p e r a t u r e f o l l o w e d by a g i n g at s l i g h t l y higher temperatures (31). As has been o b s e r v e d by many a u t h o r s and as seen from T a b l e I , t h e r e are o n l y a few t y p e I systems f o r which the d i s t r i b u t i o n c o e f f i c i e n t D i s c o n s t a n t . U s u a l l y λ i s c o n s t a n t which means t h a t p r e c i p i t a t e s a r e not homogeneous but c o n t a i n l o g a r i t h m i c c o n c e n t r a t i o n g r a d i e n t s . T a k i n g i n t o a c c o u n t t h a t f o r t y p e II and III systems the s i t u a t i o n i s even more complex, one comes t o the c o n c l u s i o n t h a t , i n g e n e r a l , the p r e c i p i t a t e o f a s o l i d s o l u t i o n w i l l not be homogeneous, u n l e s s t h e c o n c e n t r a t i o n s o f t h e i o n s i n t h e aqueous s o l u t i o n a r e h e l d c o n s t a n t d u r i n g t h e p r e c i p i t a t i o n p r o c e s s . The g r a d i e n t s i n the s o l i d s o l u t i o n w i l l be more pronounced f o r more extreme v a l u e s o f D and W. As o b s e r v e d by D r i e s s e n s (2, 3_, 7), i d e a l s o l i d s o l u t i o n s a r e an e x c e p t i o n r a t h e r t h a n a r u l e among i o n i c s o l i d s o l u t i o n s . T h e r e f o r e , p r e p a r a t i o n o f homogeneous i o n i c s o l i d s o l u t i o n s by p r e c i p i t a t i o n from aqueous s o l u t i o n s can i n g e n e r a l o n l y be r e a c h e d by t e d i o u s i t e r a t i v e p r o c e d u r e s , p r o v i d e d t h a t t e c h n i q u e s are d e v e l o p e d t o keep the c o n c e n t r a t i o n o f a l l i o n s i n t h e aqueous s o l u t i o n c o n s t a n t d u r i n g the p r e c i p i t a t i o n p r o c e s s . For obvious reasons, the d i s t r i b u t i o n c o e f f i c i e n t D must not d i f f e r much from u n i t y i f one aims t o p r e p a r e such s o l i d s o l u t i o n s o v e r a wide range o f χ v a l u e s . F o r t u n a t e l y , high-temperature t e c h n i q u e s , i . e . hydrothermal or s o l i d - s t a t e c h e m i c a l methods, can p r o v i d e more d i r e c t methods t o p r e p a r e homogeneous i o n i c s o l u t i o n s f o r many s y s t e m s , because they may be o p e r a t e d at t e m p e r a t u r e s at which d i f f u s i o n i n t h e s o l i d s o l u t i o n s becomes s u f f i c i e n t l y f a s t .

540

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

The System CaCO-^ - MqCQ-s In t h e system CaC03-MgC03-H2Û s e v e r a l s o l i d phases can o c c u r . The compound CaC03 e x i s t s i n t h r e e polymorphs under a t m o s p h e r i c p r e s s u r e : c a l c i t e , a r a g o n i t e and v a t e r i t e . V a t e r i t e i s the l e a s t s t a b l e and w i l l not be c o n s i d e r e d f u r t h e r h e r e . C a l c i t e i s s l i g h t l y more s t a b l e t h a n a r a g o n i t e (32) at most e a r t h s u r f a c e c o n d i t i o n s . F o r MgCÛ3, m a g n e s i t e i s t h e s t a b l e s o l i d p h a s e , e x c e p t at low p a r t i a l p r e s s u r e s o f COo where h y d r o m a g n e s i t e (Mg4(C03)3(0H)2.3H20) becomes s t a b l e ( 3 3 ) . Between t h e extreme c o m p o s i t i o n s d o l o m i t e ( C a 5 M g o 5 C 0 3 ) i s found as a s t a b l e s o l i d phase ( 3 3 ) . The s t r u c t u r e o f d o l o m i t e i s t h a t o f an o r d e r e d c a l c i t e , whereas magnesite i s i s o s t r u c t u r a l w i t h c a l c i t e ( 3 4 ) . N a t u r a l d o l o m i t e s c o n t a i n between 40 and 51 mol-?o MgCÛ3 ( 3 5 - 3 8 ) . In c a l c i t e s e d i m e n t s , up t o about 6 mol-% MgCÛ3 i s f o u n d , whereas a r a g o n i t e s e d i m e n t s c o n t a i n v e r y l i t t l e MgCÛ3 ( 3 7 , 38). 0e

e

The s o l u b i l i t y o f d o l o m i t e i s l e s s than t h a t o f e i t h e r c a l c i t e o r magnesite ( 3 9 ) . E q u i l i b r i u m o f d o l o m i t e w i t h aqueous s o l u t i o n s , w i t h no added M g i o n s , l e a d s u l t i m a t e l y t o the f o r m a t i o n o f a t h i n c a l c i t e l a y e r onto t h e d o l o m i t e p a r t i c l e s ( 4 0 ) , whereas e q u i l i b r a t i o n o f c a l c i t e w i t h aqueous s o l u t i o n s c o n t a i n i n g M g i o n s r e s u l t s i n t h e f o r m a t i o n o f a t h i n l a y e r o f d o l o m i t e on t h e c a l c i t e p a r t i c l e s ( 4 1 , 4 2 ) . In b o t h c a s e s t h e s e s u r f a c e l a y e r s become t h e c o n t r o l l i n g s o l i d phase i n s o l i d - l i q u i d phase e q u i l i b r i a ( 4 3 ) . Under c e r t a i n c o n d i t i o n s c a l c i u m - r i c h d o l o m i t e appears t o be more s o l u b l e t h a n c a l c i t e ( 4 4 ) . The most s o l u b l e seems t o be a s o l i d s o l u t i o n c o n t a i n i n g c o n t a i n i n g between 20 and 30 mol-?o MgCÛ3 ( 4 5 ) . Aqueous s o l u t i o n s e q u i l i b r a t e d w i t h c a l c i u m - r i c h d o l o m i t e s can become s u p e r s a t u r a t e d w i t h a r a g o n i t e , which can t h e n p r e c i p i t a t e and become the s o l i d phase c o n t r o l l i n g t h e s o l u b i l i t y of Ca + (46). 2 +

2 +

2

In p r e c i p i t a t i o n s t u d i e s (47, 49) i t has been shown t h a t , below a c e r t a i n Mg/Ca c o n c e n t r a t i o n r a t i o i n t h e aqueous s o l u t i o n , t h e r a t e o f n u c l e a t i o n o f c a l c i t e was f a s t e r t h a n t h a t o f a r a g o n i t e . Above t h a t Mg/Ca r a t i o the o r d e r was r e v e r s e d . T h i s was e x p l a i n e d by t h e e f f e c t o f Mg2+ i o n s on t h e i n t e r f a c i a l t e n s i o n between t h e s o l u t i o n and p r e c i p i t a t e , which a p p a r e n t l y i s l a r g e r f o r c a l c i t e t h a n f o r a r a g o n i t e ( 4 9 ) . At s t i l l h i g h e r Mg/Ca r a t i o s d o l o m i t e can be formed ( 5 0 ) . Such low t e m p e r a t u r e p r e c i p i t a t e s o f d o l o m i t e c o n t a i n o r d e r i n g d e f e c t s . The number o f d e f e c t s i n c r e a s e s when p r e c i p i t a t i o n p r o c e e d s i n a s h o r t e r t i m e i n t e r v a l or at lower temperatures (51). The s o l u b i l i t y , d i s s o l u t i o n and p r e c i p i t a t i o n b e h a v i o r system CaC03-MgC03~H20 can be d e s c r i b e d by t h e f o l l o w i n g m o d e l . L e t t h e g e n e r a l Formula o f t h e C a - M g - c a r b o n a t e be represented by: C

a i

_ Mg x

x

C0

3

i n the

(38)

25.

DRIESSENS

Ionic Solid Solutions

The f r e e energy GM = G -

(1-x)

and Aqueous

o f m i x i n g o f such a s o l i d s o l u t i o n GO

C

a

C

{

]

3

- χ o G

M

g

C

0

541

Solutions i s given by: (39)

3

i n which G and G? r e p r e s e n t t h e f r e e energy o f t h e s o l i d s o l u t i o n and t h a t o f t h e pure component i r e s p e c t i v e l y . On t h e o t h e r hand, the f r e e energy o f m i x i n g a l s o e q u a l s :

GM = ( 1 - x )

GcaC0

+ x %

3

C

0

(*0)

3

i n which G^ i s t h e p a r t i a l f r e e energy o f m i x i n g o f component i . When a s o l i d s o l u t i o n o f F o r m u l a (38) i s i n e q u i l i b r i u m w i t h an aqueous s o l u t i o n o f i t s i o n s , i t s s o l u b i l i t y b e h a v i o r i s c o m p l e t e l y d e s c r i b e d by t h e r e a c t i o n s : 2_ CaC0 (ss) t

Ca2+(aq) + C 0

3

(aq)

3

(41)

and C a C 0 ( s s ) + Mg2+(aq) Z

MgC0 (ss) + Ca +(aq)

3

(42)

2

3

where ( s s ) r e p r e s e n t s t h e s o l i d s o l u t i o n . The e q u i l i b r i a (42) a r e d e f i n e d by t h e r e s p e c t i v e r e l a t i o n s :

(41) and

M GCaC0

= 2.303 RT ( l o g I

3

C a C

o

3

-

log K

C a

C0 )

(^)

3

and a

Ca

log

G

M CaC0

3

-

G

M MgC0

a

K

3

=

CaC0

3

+ log

Mg

2.303

RT

(44) K

MgC0

3

where Irj co a

(

1 0

-8.42)

and g

i s the i o n a c t i v i t y product

3

Kr»rn-* L

a

L

U

(arj )

(aco3)>

a

i s the s o l u b i l i t y

product

o f pure

calcite

i s the s o l u b i l i t y

product

o f pure

magnesite

3

KMgC0

3

D r i e s s e n s and Verbeeck e x p r e s s i o n f o r G^:

(£) derived

the following

analytical

542

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

GM = 2.303 R l / ( 1 - x ) l o g ( 1 - x )

+ xlog

+ x (1-x)

xj

3

3

W

(45)

i n which the most a p p r o p r i a t e v a l u e f o r t h e i n t e r a c t i o n parameter W i s - 858 k J m o l e " ' ' , when the o r d e r i n g o f the Ca and Mg i o n s i n t h e s t r u c t u r e i s i d e a l . T h i s i s based on t h e s t a b i l i t y ranges f o r t h e s o l i d s o l u t i o n s mentioned above and on the e x p e r i m e n t a l f o r m a t i o n energy o f w e l l - o r d e r e d d o l o m i t e . The g r a p h i c a l form o f GM as a f u n c t i o n o f χ i s g i v e n i n F i g u r e 7 . F o r 0 < χ < x^j, c a l c i t e i s s t a b l e , whereas f o r Χ1 < χ < X2 c a l c i t e i s m e t a s t a b l e . S o l i d s o l u t i o n s between X2 and X3 are u n s t a b l e . In t h e range X3 < χ < X4 and X4 < χ < ( I - X 4 ) d o l o m i t e s are m e t a s t a b l e , and s t a b l e , r e s p e c t i v e l y . T h i s model f o r t h e system CaCÛ3-MgC03 a p p l i e s o n l y f o r i d e a l o r d e r i n g o f Mg and Ca i o n s i n t h e d o l o m i t e s t r u c t u r e . I d e a l o r d e r i n g o c c u r s o n l y i n p r e c i p i t a t e s o f d o l o m i t e formed at t e m p e r a t u r e s above about 250°C. S t u d i e s i n t h e l a b o r a t o r y (_52) show t h a t d o l o m i t i z a t i o n ( t h e development o f o r d e r i n g i n the Mg and Ca d i s t r i b u t i o n i n t h e c a l c i t e s t r u c t u r e ) i s a v e r y slow p r o c e s s at o r d i n a r y t e m p e r a t u r e s . T h e r e f o r e , a s o l i d - s t a t e c h e m i c a l model more a p p l i c a b l e to p r e c i p i t a t e d dolomites i s : G

M

= 2.303 R T f ( 1 - x ) l o g ( 1 - x )

where 0 t o 1.

xj+

+ χ log

i s an o r d e r i n g parameter The r e s u l t i n g e x p r e s s i o n

x

(1-x)

3

3

aW

(46)

which t h e o r e t i c a l l y can v a r y for ^ becomes: G

CaC0

from

3

M G

CaC0

= 2.303

3

R T

l o

9

C-x)

+ x (1-x) (5 3

x-2)

2

aW

(47)

whereas M

G

CaC03"

9,

M

G

MgC03 = 2.303 RT l o g

In t a b l e II t h e v a l u e s v a l u e s o f the o r d e r i n g Table

x-logO-x)

x9,

+ 3 x ( 1 - x K ( 1 + 2 x ) aW (48 ) z

o f x , t h r o u g h X4 are g i v e n parameter α .

for

certain

II.

V a l u e s o f x>j t h r o u g h X4 as a f u n c t i o n o f t h e o r d e r i n g parameter α f o r s o l i d s o l u t i o n s o f the c o m p o s i t i o n Ca>j_ Mg C03 at 25°C x

α χι

0.5

1 7.6

χ

ΙΟ"

7

4.3

χ 10-4

0.25 1.2

2

0.03

0.06

0.10

X3

0.28

0.28

0.27

X4

0.38

0.37

0.31

x

x

χ 10-2

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

Solutions

543

F i g u r e 7 . Proposed form f o r t h e c u r v e o f t h e f r e e energy o f m i x i n g i n t h e system CaCO^ - MgCO^. The c u r v e was c a l c u l a t e d w i t h t h e i n d i c a t e d v a l u e s f o r t h e parameters η and W a c c o r d i n g t o t h e p r o p o s e d model o f s u b r e g u l a r s o l i d s o l u t i o n s .

544

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

According to Equation 48 c a l c i t e s h o u l d p r e c i p i t a t e from waters h a v i n g a Mg/Ca r a t i o below a c e r t a i n v a l u e , w h i l e d o l o m i t e s h o u l d p r e c i p i t a t e from w a t e r s h a v i n g a Mg/Ca r a t i o above t h a t c r i t i c a l v a l u e . T h i s r u l e i s obeyed under c o n d i t i o n s o f p r e c i p i t a t i o n from v e r y s l i g h t l y s u p e r s a t u r a t e d aqueous s o l u t i o n s l i k e t h o s e o c c u r r i n g i n c e r t a i n a r e a s o f the o c e a n . Ocean water i s c l o s e t o e q u i l i b r i u m w i t h b o t h c a l c i t e and d o l o m i t e (53). When p r e c i p i t a t i o n o c c u r s under c o n d i t i o n s o f h i g h s u p e r s a t u r a t i o n , k i n e t i c f a c t o r s become i m p o r t a n t as w e l l . Then c a l c i t e , a r a g o n i t e and d o l o m i t e can form from s o l u t i o n s h a v i n g Mg/Ca r a t i o s i n i n c r e a s i n g o r d e r o f m a g n i t u d e . T h i s i s the main r e a s o n why not o n l y c a l c i t e and d o l o m i t e , but a l s o a r a g o n i t e i s found among b i o l o g i c a l l y induced carbonatations (53). I n t e r e s t i n g i n t h i s r e s p e c t i s t h a t c a l c i u m and pH h o m e o s t a s i s i n s n a i l s (54, 55) and f r o g s (56) was shown t o r e f l e c t a c o n s t a n t i o n i c p r o d u c t f o r c a l c i t e , which a f t e r p r o p e r c o r r e c t i o n f o r a c t i v i t y c o e f f i c i e n t s was e q u a l t o t h a t o f the s o l u b i l i t y p r o d u c t .

The System H y d r o x y a p a t i t e - F l u o r a p a t i t e Most c a l c i u m , c o n t a i n i n g a p a t i t e s i n n a t u r e are h e a v i l y c a r b o n a t e d . The o n l y e x c e p t i o n i s formed by the m i n e r a l i n the s u r f a c e o f t o o t h enamel which c o n s i s t s m a i n l y o f h y d r o x y a p a t i t e ( C a 5 ( P 0 4 ) 3 0 H ) . Most foods and d r i n k i n g w a t e r s c o n t a i n enough f l u o r i d e t o r e s u l t i n t h e i n c o r p o r a t i o n o f s i g n i f i c a n t amounts o f f l u o r i d e i n t o t h i s m i n e r a l whereby t h e s o l u b i l i t y d e c r e a s e s . T h e r e f o r e , t h e system h y d r o x y a p a t i t e - f l u o r a p a t i t e i s p r i m a r i l y o f importance for the p r e v e n t i o n o f d e n t a l c a r i e s . However, i n t h i s c o n t e x t i t s t h e o r e t i c a l t r e a t m e n t i s i m p o r t a n t f o r g e o c h e m i s t s who may be confronted with s o - c a l l e d subregular s o l i d s o l u t i o n s . The l o g a r i t h m o f the s o l u b i l i t y p r o d u c t f o r h y d r o x y a p a t i t e i s - 5 8 . 6 and t h a t o f f l u o r a p a t i t e ( C a 5 ( P 0 4 ) F ) i s - 6 0 . 6 (57), and t h u s , D = 0.01 i n f a v o u r o f f l u o r i d e i n c o r p o r a t i o n i n t o t h e s o l i d a p a t i t e p r e c i p i t a t e . A c c o r d i n g l y , i t s h o u l d be d i f f i c u l t t o p r e p a r e s o l i d s o l u t i o n s o f t h e s e compounds by p r e c i p i t a t i o n from aqueous s o l u t i o n and i f p r e p a r e d b a t c h w i s e , they are e x p e c t e d t o contain logarithmic gradients i n t h e i r i n t e r n a l composition. Yet, Moreno e t a l . ( 5 8 ) r e p o r t l i n e a r changes i n the l a t t i c e parameters o f such s o l i d s o l u t i o n s . They a l s o d e t e r m i n e d t h e i r s o l u b i l i t y behavior. Given the formula a s : 3

(49)

Ca5(P04)30 x 1-x H

F

t h e i r s o l u b i l i t y behavior s o l u b i l i t y products

Κ (χ)

=

a Ca

has been e v a l u a t e d

(58)

a.1-x

5

2 +

PO4

F-

by u s i n g

the

(50)

DRIESSENS

25.

Ionic Solid Solutions

and Aqueous

Solutions

545

On the other hand, Wier et a l (59) have shown that fluoride ions react with the surface of hydroxyapatite p a r t i c l e s so that a state of equilibrium i s reached as i f the aqueous solution i s i n equilibrium with pure fluorapatite, provided that enough fluoride ions occur i n the aqueous s o l u t i o n . Therefore, one should expect, that p a r t i c l e s of s o l i d solutions of hydroxyapatite and fluorapatite w i l l react s i m i l a r l y with fluoride ions from an aqueous solution, and that a surface layer i s formed which has a composition closer to that of pure fluorapatite than that of the o r i g i n a l s o l i d solution. This s o l i d solution s t i l l makes up the bulk of the s o l i d p a r t i c l e s after e q u i l i b r a t i o n i n an aqueous solution (59), since s o l i d state d i f f u s i o n i s n e g l i g i b l e at room temperature i n these apatites (60), which have a melting point around 1500°C. These considerations and controversial results j u s t i f y a thermodynamic analysis of the s o l u b i l i t y data obtained by Moreno et a l (58). We s h a l l consider below whether the data of Moreno et a l (58) i s consistent with the required thermodynamic relationships for 1) an ideal s o l i d s o l u t i o n , 2) a regular s o l i d s o l u t i o n , 3) a subregular s o l i d solution and 4) a mixed regular, subregular model for s o l i d solutions. In that study (58), the average of the logarithms of the s o l u b i l i t y products for pure hydroxyapatite (log K Q H ^ ) and pure fluorapatite (log Kp/\) appeared to be - 59.16 and - 60.52 respectively, both with an uncertainty of about + 0.30. In the present study the s o l u b i l i t y data found for e q u i l i b r a t i o n of s o l i d solutions are expressed as the negative logarithms for the ionic products of hydroxyapatite and fluorapatite, i . e . 1 ο

9

!θΗΑ =

5 1

° 9 Ca + + a

2

3 1 o

9

a

P0l - +

l o

9

a

0H~

( ) 51

and log Ifβ + 51og a£ 2+ + 31og apgf_ + log apa

(52)

Subsequently, the apparent a c t i v i t i e s of the quasibinary components hydroxyapatite OHA and fluorapatite FA were derived as follows: l o

9

a

0HA = log IoHA - 1°9 0HA K

( ) 53

and log ap/\ = log Ip/\ - log Kp/\

(54)

It i s assumed that i n t h i s experiment (58), stable or metastable equilibrium had been reached between the aqueous solution and a surface layer of the apatite p a r t i c l e s .

546

G E O C H E M I C A L PROCESSES AT M I N E R A L SURFACES

The r e s u l t s o f t h e c a l c u l a t i o n s u s i n g E q u a t i o n s (51) t h r o u g h (54) a r e g i v e n i n T a b l e I I I , which i n c l u d e s t h e pH v a l u e s o f t h e o r i g i n a l e q u i l i b r a t i o n s . In a d d i t i o n , mass b a l a n c e c a l c u l a t i o n s were c a r r i e d out t o see whether the s o l i d p a r t i c l e s had accumulated f l u o r i d e i n t h e i r s u r f a c e l a y e r from t h e aqueous s o l u t i o n s . The mass b a l a n c e showed t h a t an a c c u m u l a t i o n o f f l u o r i d e had o c c u r r e d i n t h e e q u i l i b r a t i o n o f a l l s o l i d s o l u t i o n s . T h i s d i s c o u n t s an i n t e r p r e t a t i o n o f t h e s o l u b i l i t y d a t a as c a r r i e d out by Moreno e t a l . (58). A thermodynamically acceptable explanation for the s o l u b i l i t y b e h a v i o r o f s o l i d s o l u t i o n s a t χ = 0.868 i s needed. F i r s t , we s h a l l assume t h a t OHA-FA s o l i d s o l u t i o n s a r e i d e a l . I f t h e c o m p o s i t i o n o f the s u r f a c e l a y e r o f t h e s o l i d p a r t i c l e s i s g i v e n by E q u a t i o n ( 4 9 ) , then t h e f o l l o w i n g e q u a t i o n s can be d e r i v e d ( 2 ) : log

3QHA

= log

χ

(55)

and l o g apA = l o g ( 1 - x )

(56)

The d a t a o f T a b l e I I I show t h a t t h e s u r f a c e l a y e r o f t h e s o l i d p a r t i c l e s i s i n d i s t i n g u i s h a b l e from pure f l u o r a p a t i t e i n a l l e q u i l i b r a t i o n s a t χ = 0 . 1 1 0 , 0.190 and 0.435 and 0 . 5 9 5 . However, some e q u i l i b r a t i o n s a t χ = 0.763 and a l l a t χ = 0.868 do d e v i a t e s i g n i f i c a n t l y from t h e b e h a v i o r o f pure f l u o r a p a t i t e . A p e c u l i a r a s p e c t i s t h a t the a c t i v i t y o f f l u o r a p a t i t e becomes s i g n i f i c a n t l y l a r g e r than 1. S i m u t a n e o u s l y , t h e a c t i v i t y o f h y d r o x y a p a t i t e approaches u n i t y . T h i s would mean t h a t a t a l l v a l u e s o f χ b o t h a c t i v i t i e s would become s m a l l e r than 1, and t h u s an i d e a l b e h a v i o r o f t h e s o l i d s o l u t i o n s would not e x p l a i n t h e o b s e r v e d s o l u b i l i t y behavior. Next l e t us assume t h a t t h e s o l i d s o l u t i o n s a r e Then t h e f o l l o w i n g r e l a t i o n s h o l d (_3, 7 )

regular.

1

W 1 ο

9

a

0HA = ( 1 - x )

2

2.303 RT

+

l

o

9

x

< ) 57

and

W l o g apA = x

2

2.303 RT + log(1-x)

(58)

where W i s a parameter f o r t h e i n t e r a c t i o n energy between h y d r o x y l and f l u o r i d e i o n s w i t h i n t h e a p a t i t e l a t t i c e . F o r W/2.303 RT< 0 . 8 8 , t h e a c t i v i t i e s as a f u n c t i o n o f χ a r e s i m i l a r t o t h o s e o f i d e a l s o l i d s o l u t i o n s ( F i g u r e 8 ) . However, f o r W/2.303 RT > 0 . 8 8 , a s o l u b i l i t y gap o c c u r s which i s s y m m e t r i c a l w i t h r e s p e c t t o χ = 0 . 5 . Under such c o n d i t i o n s , t h e f r e e e n t h a l p h y c u r v e a t a g i v e n t e m p e r a t u r e shows two minima and one maximum as a f u n c t i o n o f x .

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

547

Solutions

Table III. A p p a r e n t a c t i v i t i e s o f h y d r o x y a p a t i e (OHA) and f l u o r a p a t i t e a f t e r e q u i l i b r a t i o n o f s o l i d s o l u t i o n s o f the formula Ca5(P04)3F _ 0H 1

X

0.110

0.190

0.435

pH

x

(FA)

x

l o

9

a

0HA

log

apA

3.587 3.604 3.960 4.354 4.746 5.181 6.078

-8.33 -8.32 -7.76 -7.08 -6.41 -5.66 -4.27

0.10 0.06 -0.01 -0.01 -0.01 -0.04 -0.07

3.596 3.985 4.400 4.850 5.261 5.746 5.823 3.637 4.202 4.433 4.838 5.257 5.750 6.062

-7.98 -7.61 -6.77 -5.87 -5.27 -4.59 -4.52 -7.84 -7.12 -5.94 -5.78 -5.04 -4.48 -4.30

0.11 0.07 0.09 0.26 0.10 0.17 0.15 0.26 0.11 0.17 0.21 0.28 0.06 -0.23

X

pH

l o g aoHA

log

apA

0.595

4.334 5.057 5.495 5.956 6.150

-5.04 -4.25 -3.50 -2.83 -2.86

0.88 0.29 0.28 0.81 0.51

0.763

4.858 5.305 5.676 6.276

-3.38 -2.45 -2.15 -2.17

0.93 1.35 1.11 0.60

0.868

4.894 5.223 5.630 5.876

-0.84 -0.78 -0.66 -0.57

2.67 2.39 1.88 1.63

American Chemical Society Library 1155 16th St., N.W. Washington, D.C. 20036

548

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

25.

D R IESS E N S

Ionic Solid Solutions

and Aqueous

549

Solutions

An example i s i l l u s t r a t e d i n F i g u r e 8 f o r W/2.303 RT = 1.4. Two ranges o f χ v a l u e s o c c u r near the b o r d e r s at χ = 0 and χ = 1, where t h e s o l i d s o l u t i o n s are s t a b l e . The range o f s t a b i l i t y end at the χ v a l u e s which a p p l y t o the minima i n the e n t h a l p h y c u r v e , which are known as the l i m i t s o f s o l i d s o l u b i l i t y X 5 Q . The two ranges o f χ v a l u e s between the minima and the p o i n t s o f i n f l e c t i o n i n t h e e n t h a l p h y c u r v e p e r t a i n t o m e t a s t a b l e s o l i d s o l u t i o n s . The p o i n t s o f i n f l e c t i o n o c c u r at t h e s o - c a l l e d s p i n o d a l c o m p o s i t i o n s X$p ( 6 1 ) . Between the two s p i n o d a l c o m p o s i t i o n s any s o l i d s o l u t i o n i s u n s t a b l e and w i l l d i s p r o p o r t i o n a t e i n t o two s o l i d s o l u t i o n s o f the c o m p o s i t i o n s Xgg. W i t h i n t h e two m e t a s t a b l e ranges one o f the b i n a r y components can have an apparent thermodynamic a c t i v i t y l a r g e r than 1. The maximum w i l l be reached at χ = χ ς ρ . In t h i s s t u d y xgp was d e r i v e d as a f u n c t i o n o f W/2.303 RT by i t e r a t i v e p r o c e d u r e s u s i n g the r e l e v a n t e q u a t i o n s g i v e n by M e y e r i n g (61_). S u b s e q u e n t l y , t h e thermodynamic a c t i v i t i e s o f t h e two components were c a l c u l a t e d at the extremes which can be reached f o r v a r i a b l e xgp ( F i g u r e 9 ) . A p p a r e n t l y , such h i g h v a l u e s as l o g a p - 2 are reached o n l y f o r χ > 0 . 9 3 . T h u s , the assumption o f a r e g u l a r b e h a v i o r o f the s o l i d s o l u t i o n s o f OHA and FA does not e x p l a i n the o b s e r v e d s o l u b i l i t y b e h a v i o r either. A

Freund and Knobel (62) have found e v i d e n c e from i n f r a r e d s t u d i e s t h a t complexes o f the form F - O H - F are o f i m p o r t a n c e i n s o l i d s o l u t i o n s o f OHA and FA, which were s y n t h e s i z e d by us ( 6 3 ) . In t h a t c a s e , t h e e n t h a l p h y o f m i x i n g H s h o u l d be o f a form t y p i c a l f o r s u b r e g u l a r b e h a v i o r such a s : m

H

m

= x(1-x) W

(59)

2

whereas the f o l l o w i n g

expressions

are

derived

for

the

activities:

W log

agnA

= (1-2x)(1-x)

2

2.303 RT +

l o

9

x

( °) 6

and W l o g apA = 2 x ( 1 - x ) 2.303 RT log(1-x) (61) C a l c u l a t i o n o f t h e extreme v a l u e s o f t h e a c t i v i t i e s at t h e s p i n o d a l c o m p o s i t i o n s xgp f o r v a r i a b l e v a l u e s o f W/2.303 RT r e s u l t s i n t h e d a t a p r e s e n t e d i n F i g u r e 10. I t appears t h a t v a l u e s as h i g h as l o g apA = 2 are reached i n t h e range xgp > 0 . 6 3 . T h u s , the assump­ t i o n o f a s u b r e g u l a r b e h a v i o r o f t h e s o l i d s o l u t i o n s o f OHA and FA e x p l a i n s the o b s e r v e d s o l u b i l i t y b e h a v i o r q u a l i t a t i v e l y . I t follows f u r t h e r from t h e c a l c u l a t i o n s t h a t W/2.303 RT > 8 so t h a t W > 4 . 6 10 J mol-1. 2

4

+

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

F i g u r e 9. U l t i m a t e a c t i v i t i e s o f ΟHA and FA a t t h e s p i n o d a l compositions χ i n t h e model o f r e g u l a r s o l i d s o l u t i o n s .

D R IESS EN S

Ionic Solid Solutions

and Aqueous

Solutions

Figure 1 0 . Ultimate a c t i v i t i e s of OHA and FA at the spinodal compositions χ i n the model of subregular s o l i d solutions.

GEOCHEMICAL PROCESSES AT MINERAL SURFACES

552

Freund and K n o b e l (62) have found t h a t i n a d d i t i o n t o F - O H - F c o m p l e x e s , F-OH p a i r i n t e r a c t i o n s a r e i m p o r t a n t . T h e r e f o r e , a mixed t y p e r e g u l a r and s u b r e g u l a r model o f t h e s o l i d s o l u t i o n s s h o u l d be more a p p r o p r i a t e . To a f i r s t a p p r o x i m a t i o n , t h e e n t h a l p y o f m i x i n g s h o u l d then have t h e form: H

m

= x(1-x)Wi

+ x(1-x) W 2

(62)

2

I f one assumes W-j = W2 = W i n o r d e r t o m i n i m i s e t h e number o f parameters i n t r o d u c e d i n t h e m o d e l , one o b t a i n s t h e f o l l o w i n g expressions f o r the a c t i v i t i e s : W l o g aQHA = 2 ( 1 - x )

+ log χ

3

(63)

2.303 RT and W log a

F

A

= χ2(3-2χ)

+ log(1-x)

(64)

2.303 RT C a l c u l a t i o n o f t h e extreme v a l u e s o f t h e a c t i v i t i e s a t t h e s p i n o d a l c o m p o s i t i o n s x$p f o r v a r i a b l e v a l u e s o f W/2.303 RT y i e l d s t h e d a t a p r e s e n t e d i n F i g u r e 11. I t appears t h a t v a l u e s as h i g h a s l o g apA = 2 a r e reached i n t h e range xgp > 0.83. A c c o r d i n g l y , t h e v a l u e o f l o g ag^A i s about - 0 . 5 , which i s c l o s e t o t h e e x p e r i m e n t a l v a l u e a t χ = 0.868. T h u s , t h e assumption o f a m i x e d - t y p e r e g u l a r and s u b r e g u l a r s o l i d s o l u t i o n w i t h W-j = W2 = W e x p l a i n s t h e o b s e r v e d s o l u b i l i t y b e h a v i o r a t χ = 0.868. However, i t does not e x p l a i n t h e h i g h a c t i v i t i e s o f f l u o r a p a t i t e found i n some o f t h e e q u i l i b r a t i o n s a t χ = 0.763. I n t h i s model W/2.303 RT.> 2.0 so t h a t W >1.17 . 10 J m o l . F u r t h e r r e f i n e m e n t o f t h i s model i s p o s s i b l e by independent v a r i a t i o n o f W-j and W . In t h e s u b r e g u l a r model t h e absence o f a s o l u b i l i t y gap a t 1000°C would mean W/2.303 RT < 0.92 and t h u s W < 2.3 . 10 J mol"^ ( s e e F i g u r e 3 ) . On t h e o t h e r hand t h e s o l u b i l i t y d a t a i n d i c a t e a v a l u e o f W i 4.6 . 10^ J m o l " ' ' . In t h e m i x e d - t y p e r e g u l a r and s u b r e g u l a r model w i t h W-j = W = W t h e absence o f a s o l u b i l i t y gap a t 1000°C would mean W/2.303 RT 0.46 s o t h a t W < 1.17 . 10^ J m o l " . F o r t h a t m o d e l , t h e s o l u b i l i t y d a t a i n d i c a t e a v a l u e o f W > 1.17 . 10^ J m o l " ^ . T h e r e f o r e , a mixed t y p e r e g u l a r and s u b r e g u l a r s o l i d s o l u t i o n s i s t h e most a c c e p t a b l e model, and t h e most p r o b a b l e v a l u e f o r t h e i n t e r a c t i o n parameter i s W =1.17 . 10^ J m o l - 1 . W i t h i n t h e scope o f t h i s c o n c l u s i o n one should consider the increased a c t i v i t i e s o f f l u o r a p a t i t e at χ = 0.763 and 0.595 as p r o b a b l y b e i n g caused by t h e f a c t t h a t t h e i r c o m p o s i t i o n s a r e found beyond t h e maximum i n t h e f r e e e n t h a l p y c u r v e . Hence, t h e i r t r a n s f o r m a t i o n i n t o f l u o r a p a t i t e may be v e r y s l o w , u n l e s s t h e c o n c e n t r a t i o n o f f l u o r i d e i o n s i n t h e aqueous solution i s high. 4

- 1

2

4

2

1

25.

DRIESSENS

I

Ionic Solid Solutions

1

1

0

0,2

1

and Aqueous

1

1

1

0,6

0,4 x

553

Solutions

1

1

0,8

1

1

1,0

sp

F i g u r e 1 1 . U l t i m a t e a c t i v i t i e s o f OHA and FA a t t h e s p i n o d a l compositions x i n the model o f mixed-type r e g u l a r and s u b r e g u l a r solid solutions. s p

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

554

The previous paper (63) also studied the disintegration of s o l i d solutions and for that purpose samples were heated for 300 hours at 250°C, but no signs of disintegration were detec­ ted i n an X-ray diffractogram. This might be due to the fact that s o l i d state d i f f u s i o n i s s t i l l too slow at that temperatu­ re. This i s supported by the low d i f f u s i o n c o e f f i c i e n t c a l c u l a ­ ted i f one extrapolates from the experimental values determined at high temperature (60). In conclusion, the s o l u b i l i t y data indicate that upon pre­ c i p i t a t i o n from aqueous solutions which have a F/OH molar r a t i o less than a c e r t a i n value, s l i g h t l y fluoridated hydroxyapatites w i l l be formed (x ^ 0 . 1 5 ) , and above that r a t i o nearly pure f l u o r - a p a t i t e w i l l be formed. Usually the F/OH r a t i o varies so that intimate mixtures of hydroxyapatite and fluorapatite w i l l result (64). The e f f e c t of fluoride on teeth and bones are d i s ­ cussed elsewhere (5»3, 57).

The System Calciumhydroxyapatite - Strontiumhydroxyapatite. From a study of the cation d i s t r i b u t i o n over the two cation s u b l a t t i c e s i n s o l i d solutions of calciumhydroxyapatite and strontiumhydroxy-apatite (65) i t was shown that such s o l i d so­ l u t i o n s are i d e a l . Verbeeck (66) found that the s o l u b i l i t y behavior could be ex­ plained by assuming i d e a l i t y ; his value for the logarithm of the s o l u b i l i t y product of pure strontiumhydroxyapatite was -52.3. Hence, the value of D i s 18 i n favour of Ca incorpora­ t i o n and against Sr incorporation i n mixed p r e c i p i t a t e s . This seems to be i n agreement with discrimination against strontium in the bones and teeth of l i v i n g organisms.

The System Calciumhydroxyapatite - Leadhydroxyapatite. In t h i s system there i s at least one and presumably two m i s c i b i l i t y gaps around 1200°C (66). At room temperature there i s one large m i s c i b i l i t y gap. The s o l u b i l i t y product for leadhydroxyapatite (67) i s about 10~ so that for t h i s system D i s about 30000 i n favour of lead incorporation into the a p a t i t e . This means that upon p r e c i p i t a t i o n , p r a c t i c a l l y a l l the lead w i l l p r e c i p i ­ tate before any calcium coprecipitates. 81

Calcium Phosphates And C a l c i f i e d Tissues. P r e c i p i t a t i o n i n the system C a ( 0 H ) 2 - H 3 P O 4 - Η 0 can lead to the formation of several calcium phosphates (shown i n Table IV), of which hydroxy-apatite OHA i s the most stable above a pH of about 4.1. The r e l a t i v e s t a b i l i t i e s are i l l u s t r a t e d i n Figure 12. 2

25.

DRIESSENS

Ionic Solid Solutions

and Aqueous

555

Solutions

Table IV. P e r t i n e n t c a l c i u m phosphates r e l e v a n t t o aqueous s y s t e m s , t h e i r f o r m u l a , s t r u c t u r e and n e g a t i v e l o g a r i t h m o f t h e s o l u b i l i t y p r o d u c t pK

Mineral name

Ca/P

Nota­ tion

Formula

Space group

1

DC Ρ

CaHP04

P1

6.90

monetite

1

DCPD

CaHP04.2H 0

C2/c

6.59

brushite

1.33

OCP

Ca8(HP04)2(P04)4- 2°

PT

68.6

1

1.43

WH

Ca (HP04)(P04)

R3c

81.7

1

whitlockite

1.67

OHA

Ca

1.50

DOHA

Ca (HP04)(P04) (0H)

1

hydroxy­ apatite defective hydroxy­ apatite

2

5 H

1 0

1 0

(P0 ) (0H) 4

6

9

6

P6 /m

117.2

P6 /m

85.1

3

2

5

pK

3

-

1 Estimate

Once c a l c i u m d e f i c i e n t h y d r o x y a p a t i t e DOHA (between pH 6 . 8 and 8 . 2 ) i s formed, a m e t a s t a b l e e q u i l i b r i u m i s c r e a t e d w i t h t h e aqueous s o l u t i o n which may l a s t i n d e f i n i t e l y a t room o r body t e m p e r a t u r e . I f carbonate ions are present i n a d d i t i o n the a p a t i t e preferably formed i s Ca

9

(PO4M.5 (C0 )