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 )
