Ionic Solid Solutions in Contact with Aqueous Solutions - American

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


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


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


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


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


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


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


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


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


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


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 .


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


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


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


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


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


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


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.


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


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


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


25.

D R IESS E N S


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

+


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


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


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


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


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 )

Ionic Solid Solutions in Contact with Aqueous Solutions - American

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