Modeling SolidâSolution Reactions in Low-Temperature Aqueous

Chapter 6

Modeling Solid—Solution Reactions in Low-Temperature Aqueous Systems Downloaded by EAST CAROLINA UNIV on November 5, 2016 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch006

Pierre D. Glynn U.S. Geological Survey, 432 National Center, Reston, VA 22092

The effect of substitutional impurities on the stability and aqueous solubility of a variety of solids is investigated. Stoichiometric saturation, primary saturation and thermodynamic equilibrium solubilities are compared to pure phase solubilities. Contour plots of pure phase saturation indices (SI) are drawn at m i n i m u m stoi chiometric saturation, as a function of the amount of substitution and of the excess-free-energy of the substitution. SI plots drawn for the major component of a binary solid-solution generally show little deviation from pure phase solubility except at trace component fractions greater than 1%. In contrast, trace component SI plots reveal that aqueous solutions at minimum stoichiometric saturation can achieve considerable supersaturation with respect to the pure trace-component end-member solid, i n cases where the major component is more soluble than the trace. F i e l d or laboratory observations of miscibility gaps, spinodal gaps, critical mixing points or distribution coefficients can be used to estimate solid-solution excess-free-energies, when experimental measurements of thermodynamic equilibrium or stoichiometric saturation states are not available. As an example, a database of excess-free-energy parameters is presented for the calcite, aragonite, barite, anhydrite, melanterite and epsomite mineral groups, based on their reported compositions in natural environments. Past studies of solid-solution aqueous-solution (SSAS) systems have focused on measuring the partitioning of trace components between solid and aqueous phases. The effect of solid-solution formation on mineral solubilities was rarely studied. Recently however, Lippmann (1,2), Thorstenson and Plummer (3) and Plummer and Busenberg (4) have enriched our understanding of SSAS systems with their theoretical and experimental descriptions of solid-solution dissolution and component distribution reactions. The objectives of this paper are: 1) to describe and to compare the concepts presented by the above authors, 2) to present some techniques which may help estimate the effect of SSAS reactions on the chemical evolution of natural waters. DEFINITIONS A N D REPRESENTATION OF T H E R M O D Y N A M I C STATES Several thermodynamic states are of interest in the study of SSAS systems. The following sections discuss the concepts of thermodynamic equilibrium, primary saturation and stoichiometric saturation states. This chapter not subject to U.S. copyright Published 1990 American Chemical Society

Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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Modeling Solid—Solution Reactions in Low-Temperature Systems

Thermodynamic E q u i l i b r i u m States Thermodynamic e q u i l i b r i u m in a system with a binary solid-solution B ^ C ^ A can be defined by the law-of-mass-action equations: [B*)[A-]

=K a

=K x y

( I )

BA

[C*][A-]

=K a

=K

( 2 )

CA

BA

CA

BA

BA

BA

ycA

CAXcA

-

where [ A ] , [B+] and [C+] are the activities of A " , B+ and C + i n the aqueous-solution. a ^ and a , * and * , and f and f A are the activities, mole fractions and activity coefficients of components B A ana C A in the e q u i l i b r i u m solid-solution. K and K are the solubility products of pure B A and pure C A solids. Using equations 1 and 2, phase diagrams can be constructed which display the series of possible e q u i l i b r i u m states for any given binary SSAS system. By analogy to the pressure versus mole fraction diagrams used for b i n a r y - l i q u i d vapor systems, Lippmann ( I , 2, 5) defines a variable E l l = [A~] ([B+] + [C+]), such that adding together equations 1 and 2 yields the following relation, known as the "solidus" equation: BA

C A

Downloaded by EAST CAROLINA UNIV on November 5, 2016 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch006

B

A

B A

C

C A

B A

C

A

^

E

^

Q

^BAXBA^BA^

(

^CAXCA^CA

3

)

where £ I I is the value of the EII variable at thermodynamic e q u i l i b r i u m . To completely describe thermodynamic e q u i l i b r i u m , a second relation must be derived from equations 1 and 2 (2; G l y n n and Reardon, A m . L Sci.. i n press). The "solutus" equation expresses E I I as a function of aqueous solution composition: e q

eq

X b

iu =\/(

'

eq

q q

+

X c

'

a q

\K y BA

)

(4)

K y J

BA

CA

CA

where the aqueous activity fractions * and x are defined as * = [B+]/([B+]+[C+J) and x , = [C+]/([B+]+[C% Solid-solution activity-coefficients can be fitted using the following equations (6), derived from Guggenheim's expansion series for the excess-free-energy of mixing (7): B a a

c a a

B a a

q

c

a q

l

n

Y ^ = xL[ o-ai(3x^-X J

l

n

Y ^

a

=

xL[ o a

+

c

+

a i ( 3 x ^ - X ^ )

+

a 2 ( X ^ - X c J ( X ^ - X c J 5

a (x 2

C / 4

-X

f i

+

-"]

J(5x^-X^) -...] 4

( 5 )

( 6 )

The first two terms of equations 5 and 6 are generally sufficient to accurately represent the dependence of f a n d IQA composition (Glynn and Reardon, A m . J. Sci.. in press). Indeed, in the case of a solid-solution with a small difference in the size of the substituting ions (relative to the size of the non-substituting ion), the first parameter, a , is usually sufficient (8). Equations 5 and 6 then become identical to those of the "regular" solid-solution model of H i l d e b r a n d (9). For the case where both a and aj parameters are needed, equations 5 and 6 become equivalent to those of the "subregular" solid-solution model of Thompson and Waldbaum (10), a model much used in high-temperature work. Equations 5 and 6 can also be shown equivalent to Margules activity coefficient series (11). Lippmann's solidus and solutus curves can be plotted and used to predict the solubility of any binary solid-solution at thermodynamic e q u i l i b r i u m , as well as the distribution of components between solid and aqueous phases, i f solid-phase and aqueous-phase activity coefficients are known. Figure 1 shows an example of a Lippmann phase diagram for the Ag(Cl,Br) - H 0 system, modeled using the distribution coefficient data of Vaslow and Boyd (12) for trace A g B r in A g C l and trace A g C l i n A g B r . Aqueous solutions which plot below the solutus curve are undersaturated with respect to all solid phases, including the pure end-member solids, while solutions plotting above the solutus are supersaturated w i t h respect to one or more solid-solution compositions. o

n

B A

0

0

2


75

76

CHEMICAL MODELING O F AQUEOUS SYSTEMS II


Ag(CI,Br) - H

-1 3 00 0.00

'

1

'

1

i

2

0 System

i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i

i i i i

0.20

0.40 x

AgBr

0.60 r X

0.80

1.00

Br,aq

Figure 1. L i p p m a n n diagram (with stoichiometric and pure-phase saturation curves) for the Ag(Cl,Br) - H 0 system at 30° C. Calculated a and a values are 0.30 and -0.18 respectively. p K = 9.55 (16). p K = 12.05 (12). T l and T2 give the aqueous and solid phase compositions, respectively, of a system at thermodynamic e q u i l i b r i u m with respect to an A g C l B r solid. PI and P2 describe the state of a system at primary saturation w i t h respect to the same solid. M S I gives the composition of an aqueous phase at congruent stoichiometric saturation w i t h respect to that solid. 2

0

A g C 1

A g B r

5

5


x

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Modeling Solid-Solution Reactions in Low- Temperature Systems


Primary Saturation States Primary saturation is the first state reached during the congruent dissolution of a solid-solution, for which the aqueous-solution is saturated w i t h respect to a secondary solid-phase (13, 14, G l y n n and Reardon, A m . L Sci.. i n press). This secondary solid w i l l usually have a composition different from that of the dissolving solid. A t primary saturation, the aqueous phase is at thermodynamic e q u i l i b r i u m with respect to this secondary solid but remains undersaturated w i t h respect to the primary dissolving solid. The series of possible primary-saturation states for a given SSAS system is represented by the solutus curve on a L i p p m a n n diagram. In the specific case of a "strictly congruent" dissolution process occurring i n an aqueous phase with a [B+]/[C+] activity ratio equal to the B+/C+ ratio i n the solid, primary-saturation can be approximately found by drawing a straight vertical line on the L i p p m a n n diagram from the solid-phase composition to the solutus (see figure 1). F o r an exact calculation, the following relations may be used to determine the primary saturation state: =

XB,aq

f BXBA

^

X c , a q

=

f c X c A

^

where f and f are factors correcting for a possible difference i n the aqueous speciation and activity coefficients of B+ and C+ The equation used to calculate the value of E n at primary saturation as a function of solid composition, for a strictly congruent dissolution process, may be found by combining the Lippmann solutus equation (4) with equations 7 and 8: B

c

-r—r z

n

,

.(

X BA f B

XCAI

C

it—— ir^— +

P * =

1

7

\ ^

BAY BA,y

^CAXCA.y

where B A , y CA,y secondary solid B ^ y C y A with respect to which the aqueous solution (at primary saturation) is i n temporary thermodynamic equilibrium. E r L refers to the value of the EII variable as specifically defined at primary saturation. The composition of the B j X y A phase w i l l generally not be known. B y equating EII (x) (equation 9) to EII (y) (equation 3), the relation between the i n i t i a l solid composition B _ C A and the secondary solid Bj.yCyA may be obtained: 7

a

n

d

7

8

ps

eq

, 1

,[ 7

X

XBAIB ~V v \ & BAY BA.y

X

X C A I C )

X

/ \ = XcA,yYcA,yKcA

+

(

XBA,yYBA,yKBA

1

I

\

N 0

)

K

CAYcA,yJ

In the case of a non-ideal solid-solution series, equation 10 must be solved graphically or by an iterative technique, because BA,y d c A , y typically exponential functions of cA,y7

a n

7

a

r

e

x

Stoichiometric Saturation States Stoichiometric saturation was formally defined by Thorstenson and Plummer (3). These authors argued that solid-solution compositions typically remain invariant during solid aqueous-phase reactions i n low-temperature geological environments, thereby preventing attainment of thermodynamic equilibrium. Thorstenson and Plummer defined stoichiometric saturation as the pseudoe q u i l i b r i u m state which may occur between an aqueous-phase and a multicomponent solid-solution, "in situations where the composition of the solid phase remains invariant, owing to kinetic restrictions, even though the solid phase may be a part of a continuous compositional series". The stoichiometric saturation concept assumes that a solid-solution can under certain circumstances behave as i f it were a pure one-component phase. In such a situation, the dissolution of a solid-solution B ^ C ^ A can be expressed as:


77

78


+

Bi- C A-* X

+

(1 -x)B

X

A p p l y i n g the law of mass action stoichiometric saturation states:

+ xC then

gives

the

defining

condition

for

where x and (1-x) are equal to * and x respectively and where A G ° is the standard free energy change of reaction 11. A c c o r d i n g to Thorstenson and Plummer's (2) d e f i n i t i o n of stoichiometric saturation, an aqueous-solution at thermodynamic e q u i l i b r i u m w i t h respect to a solid B ^ C x A w i l l always be at stoichiometric saturation w i t h respect to that same solid. The converse statement, however, is not necessarily true: stoichiometric saturation does not necessarily imply thermodynamic e q u i l i b r i u m . Stoichiometric saturation states can be represented on L i p p m a n n phase diagrams (figure 1) by relating the total solubility product variable E n (defined specifically at stoichiometric saturation with respect to a solid B _ C A ) to the K constant (equation 12) and to the aqueous activity fractions * , a q and c , a q C A


(11)

+ A'

B A

r

s 8

X

X

X

s g

x

:

B

£n

s s

=—

—

—

X B,aqX

d3)

C,aq

In contrast to thermodynamic e q u i l i b r i u m , for which a single ( B , a q > ^ e q ) point satisfies equations 1 and 2, stoichiometric saturation w i t h respect to a given solid composition is represented by a series of ( * B , a q > ) points, a l l defined by relation 13. As shown in figure 1, stoichiometric saturation states never plot below the solutus curve. This is consistent with the fact that stoichiometric saturation can never be reached before primary saturation in a solid-solution dissolution experiment. The unique point at which a stoichiometric saturation curve (for a given solid B ^ C x A ) joins the L i p p m a n n solutus represents the composition of an aqueous solution at thermodynamic e q u i l i b r i u m with respect to a solid B x - C x A . Saturation curves for the pure B A and C A end-member solids can also be drawn on L i p p m a n n diagrams (2,5): x

n

s n

9 S

TU

= - ^ -

BA

X

(14)

T

U

C

= J ^ ±

A

X

B,aq

x

sn

a

n

x

(15)

C,aq

N

These equations define the families of ( B A > B A ) d ( c A ^ C A ) conditions for which a solution containing A~, B+ and C + i o n s w i l l be saturated with respect to pure B A and pure C A solids. Thermodynamic e q u i l i b r i u m with respect to a mechanical mixture of the two pure B A and C A solids, i n contrast to a solid-solution of B A and C A , w i l l be represented on a L i p p m a n n diagram by a single point, namely the intersection of the pure B A and pure C A saturation curves. The coordinates of this intersection are: i n t Y

=

Hi* ^ BA

(16)

int

in

=K

CA

+K

BA

( 1 7 )

^ CA

COMPARISON OF SOLID-SOLUTION A N D P U R E PHASE SOLUBILITIES In predicting solid-solution solubilities, one of two possible hypotheses must be chosen. In the first, the solid-solution is treated as a one-component or pure-phase solid, given that the equilibration time is sufficiently short, the solid to aqueous-solution ratio is sufficiently high and the solid is relatively insoluble. These requirements are needed to ensure that no significant recrystallisation of the i n i t i a l solid or precipitation of a secondary solid-phase occurs. For such situations, the stoichiometric saturation concept may apply.


6.

GLYNN



The second hypothesis considers the solid as a multi-component solid-solution, capable of adjusting its composition i n response to the aqueous solution composition, given the long equilibration period, the relatively high solubility of the solid and relatively low solid to solution ratio. In this case, the assumption of thermodynamic e q u i l i b r i u m may apply. If the equilibration period is too short for thermodynamic e q u i l i b r i u m to have been achieved, but i f an outer surface layer of the solid has been able to recrystallise (because of the high solubility of the solid), the concept of primary saturation may apply. There are currently insufficient data to determine the exact conditions for w h i c h each of these assumptions may apply, especially i n field situations. In many instances, neither one of these assumptions w i l l explain the observed solubility of a solid-solution, which may lie between the "maximum" stoichiometric saturation solubility and the "minimum" primary saturation solubility. Nonetheless, these solubility limits can often be estimated. Stoichiometric Saturation Solubilities The case of stoichiometric saturation states attained after "strictly congruent" dissolution is examined here. The hypothetical B _ C A solid-solutions considered are 1) calcite ( p K = 8.48, 15) with a more soluble trace N i C 0 component ( p K = 6.87,16) and 2) calcite with a less soluble trace C d C 0 component ( p K = 11.31, 17). Contour plots of saturation indices (SI=log[IAP/K ]) w i t h respect to major and trace end-member components are drawn i n figure 2 as a function of the a value (assuming a regular solid-solution model) and of the log of the molefraction of the trace component (where 1 0 < * < 0.5). SI values are calculated for major ( B A ) and trace ( C A ) components using the relations: 1

X

X

8 p

3

8 p

3

s p

8p

0

-6

C A

- l o g C t f ^ + log

SI A

log(K

=

C

C Y L

) + log

X

B,ct(

(18)

Xc,ai X

(1-x)" C, ac,

(19)

XB,ac,

K values are evaluated from Thorstenson and Plummer's (3) equation 22, modified assuming a regular solid-solution model: 8 8

l l

x)

x

i

x)

x

K =K ; K (l- y - x exp[a x(l-x)] ss

B

CA

X

^

0

Assuming that the dissolution to stoichiometric saturation takes place i n i n i t i a l l y pure water and that the aqueous activity ratio of the major and minor ions is equal to their concentration ratio, the relation B,aq/ c,aq U ~ ) / will apply. Using this relation, applicable only at "minimum stoichiometric saturation" ( G l y n n and Reardon, A m . J. Sci.. i n press), the following equations may be derived from equations 18, 19 and 20: x

f K

CA

SI

= X\OQ[

BA

\K J

\

Ulog(l-x) +

BA

SI

C A

= (\-x)\oq[

(K \ BA

x

=

a x( 1-x) ° ; ln(10)

— + logx + U c J

0

a x(l-x) 0

^ ln(10)

x

X

(21) (22)

The SI contour plots drawn using equations 21 and 22 show the miscibility gap and spinodal gap lines separating intrinsically stable, metastable and unstable solid-solutions (11). In natural environments, while metastable solid-solution compositions may in some cases persist on a geological timescale (depending on the solubility of the solid), unstable solid-solutions formed i n low-temperature environments are not likely to do so. Busenberg and Plummer (18) in their study of magnesian calcite solubilities observed that the highest known magnesium contents in modern natural biogenic calcites correspond to the predicted spinodal composition. Metastable compositions w i l l probably not persist, however, i n solid-solutions with higher solubilities or which have been reacted for a longer


79

80

CHEMICAL MODELING OF AQUEOUS SYSTEMS II


Calcite SI values

C d C 0 SI Values

g

3

Log X c d C 0 3

Log C d C 0 3 x

C -5.0

Calcite SI Values -4.0 -3.0 -2.0 -1.0

Log X

N i C

D

NICO3 SI Values -5.0 -4.0 -3.0 -2.0

03

Log X

N i C

-1.0

03

Figure 2. Major and trace component saturation index values (in solid lines) for ( C a , C d ) C 0 (insets A , B) and ( C a , N i ) C O (insets C, D) solids at congruent stoichiometric saturation. M i s c i b i l i t y gap lines (short-dashed) and spinodal gap lines (long-dashed) are also shown. 3

?


6.

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Modeling Solid-Solution Reactions in Low- Temperature Systems

period of time (or at higher temperatures) than the biogenic magnesian calcites. While intrinsically unstable solid-solutions, formed at low-temperatures, may not be found i n geologic environments, they can often be synthesized i n the laboratory (eg. strontian aragonites (4); barian strontianites, G l y n n , unpublished). Figures 2 A and 2B show the case of a solid-solution series, ( C a , C d ) C 0 , w i t h a much less soluble trace end-member. If the mole-fraction of trace component is sufficiently high ( c d C 0 3 > 10 - ), the aqueous phase at stoichiometric saturation w i l l be supersaturated with respect to the trace end-member (except at unrealistic negative a values not shown on the plot). The lower solubility of the trace component w i l l generally cause negative SI values for the major component, except at high a values (higher than 7.5 i n the (Ca,Cd)CO^ case) for which the solidsolutions w i l l generally be metastable or unstable. Calcite SI values drawn i n figure 2A show that the mole-fraction of trace component must be sufficiently high ( C d C 0 3 > 10 - ) for this effect to be measurable i n the field (typical uncertainty * 0.01) or in the laboratory. A laboratory example of the above principle is given by the "strictly-congruent" dissolution experiment of Denis and M i c h a r d ( M ) on a 3.5% Sr-anhydrite. Analysis of their results shows that maximum S I and S l g ^ ^ values of 0.37 and -0.04 respectively were attained after 4 days. Their last sample (after 6 days) gave SI and SIgypgum values of 0.35 and -0.04 respectively. While these results show that stoichiometric saturation was not obtained with respect to the original anhydrite phase (probably because of back-precipitation of a gypsum phase), supersaturation d i d occur with respect to the less soluble celestite component. In the case of solid-solutions with a more soluble trace component, aqueous solutions at "minimum stoichiometric saturation" w i l l generally be supersaturated with respect to the major component and undersaturated with respect to the more soluble trace end-member (figures 2C and 2D). Aqueous solutions at minimum stoichiometric saturation with respect to ( C a , N i ) C 0 solid-solutions w i l l be supersaturated with respect to pure calcite at a values greater than -2.7. S I a k i values greater than +0.01, however, w i l l only be found at mole fractions of N i C 0 greater than approximately 10~ - . In contrast, Sl^ico? values w i l l exhibit significant undersaturation even at high *NiC03 mole tractions (-2 < S I 0 3 < "1 3

x

-2

8

0

0

-2


x

5

c e l e s t i t e

c e l e 8 t i t e

3

0

C

te

3

2

5

N i C

at * i C 0 3 = N

0.5).

Primary Saturation and Thermodynamic E q u i l i b r i u m Solubilities A detailed discussion of solid-solution solubilities at primary saturation states and at thermodynamic e q u i l i b r i u m states is given by G l y n n and Reardon ( A m . J. Sci.. in press). The fundamental principles governing these thermodynamic states are given below. A n aqueous solution at primary saturation or at thermodynamic e q u i l i b r i u m with respect to a solid-solution w i l l be undersaturated w i t h respect to a l l endmember component phases of the solid-solution (see figure 1). A positive excess-free-energy of m i x i n g (that is a positive a value i n the case of a regular solid-solution) w i l l raise the position of the solutus curve relative to that of an ideal solid-solution system. A positive excess-free-energy of m i x i n g w i l l therefore increase the solubility of a solid-solution at primary saturation or at thermodynamic equilibrium. The pure end-member saturation curves on a L i p p mann diagram offer a upward limit on the position of the solutus. Conversely, a negative excess-free-energy of mixing w i l l lower the position of the solutus relative to that of an ideal solid-solution series. The solutus curve, in binary SSAS systems with ideal or positive solid-solution free-energies of mixing and with large differences (more than an order of magnitude) in end-member solubility products, w i l l closely follow the pure-phase saturation curve of the least soluble end-member (except at high aqueous activity fractions of the more soluble component, e§. figure 1). In contrast, ideal solidsolutions with very close end-member solubility products (less than an order of magnitude apart) w i l l have a solutus curve up to 2 times lower i n £11 than the pure end-member saturation curves. The factor of 2 is obtained for the case where the two end-member solubility products are equal and can be derived from equations 4, 16 and 17. 0


81

82


The composition of a SSAS system at primary saturation or at stoichiometric saturation w i l l be generally independent of the i n i t i a l solid to aqueous-solution ratio, but w i l l depend on the i n i t i a l aqueous-solution composition existing prior to the dissolution of the solid. In contrast, the f i n a l thermodynamic e q u i l i b r i u m state of a SSAS system attained after a dissolution or recrystallisation process w i l l generally depend not only on the i n i t i a l composition of the system but also on the i n i t i a l solid to aqueous-solution ratio ( G l y n n et al., submitted to Geochim. Cosmochim. Acta).


ESTIMATION OF THERMODYNAMIC MIXING PARAMETERS There are two main applications for SSAS theory i n the chemical modeling of aqueous systems: 1) the prediction of solid-solution solubilities, 2) the prediction of the distribution of trace components between solid and aqueous phases. Currently, a big problem with both types of predictions is the lack of lowtemperature data on solid-solution excess-free-energy functions, and therefore on solid-phase a c t i v i t y coefficients. The two-parameter Guggenheim expansion series (the "subregular" model) has been successfully used to f i t laboratory solubility data for the ( S r , C a ) C 0 - H 0 (4), ( B a , S r ) C 0 - H 0 ( G l y n n , unpublished data), ( C a , M g ) C 0 - H 0 (18) and K ( C l , B r ) - H 0 systems ( G l y n n et al, submitted to Geochim. Cosmochim. Acta). The one-parameter Guggenheim series (the "regular" model) has also been frequently used (2, J_9). More laboratory determinations of thermodynamic m i x i n g parameters are needed, not only to acquire data on binary and multi-endmember solid-solutions, but also to further confirm the v a l i d i t y of the regular and sub-regular models, and to compare them w i t h other excessfree-energy models. In the meantime, as a better approximation than the commonly used assumption of "ideal" solid-solutions, a and a parameters can often be estimated. A computer code has been written (Glynn, unpublished), which uses either observed or estimated 1) miscibility gap data, 2) spinodal gap data, 3) critical temperature and c r i t i c a l mole-fraction of m i x i n g data, 4) distribution coefficient data, 5) alyotropic point data (2) or 6) activity coefficient data to calculate a and a! parameters. Depending on whether one or two datum points are given, the program assumes either a regular or subregular model. 3

3

2

3

2

2

2

0

x

0

M i s c i b i l i t y Gap Data M i s c i b i l i t y gaps, determined from mineral compositions observed i n the field, can be used to estimate thermodynamic mixing parameters i n the absence of more accurate laboratory data. This approach suffers from several problems. The maximum mole-fraction of trace component found may not correspond to the miscibility gap fraction. In this case, i f the solid-solution composition is stable, then the excess-free-energy calculated w i l l be overestimated. If the mineral was formed at much higher temperatures than the temperature of interest and i f the mineral is f a i r l y unreactive at the lower temperature, the maximum solid-solution mole-fraction observed may well be metastable or even unstable. The temperature of formation (and of equilibration) of the solid-solution may not be known. If a lower temperature is assumed, the excess-free-energy w i l l be underestimated. The extrapolation to 25° C of excess-free-energies estimated at higher temperatures w i l l introduce an additional error, because of the lack of excess enthalpy and excess entropy data. A partial solid-solution series may not be isomorphous (i.e. the end-members may not have the same structures). In that case the excess-free-energy parameters should be calculated only on a single side of the miscibility gap. On the other side of the miscibility gap, a different model w i l l apply. Despite the above problems, mixing parameters estimated from m i s c i b i l i t y gap information w i l l still be an improvement over the assumption of an ideal solidsolution model. a parameters estimated from data i n Palache et al. (20) and Busenberg and Plummer (21) are presented i n table I for a few low-temperature mineral groups. Because of the large uncertainties in the data and i n the estimation procedure, a sub-regular model is usually unwarranted. A s a result, these estimated a values presented should be used only for solid-solution compositions on a single side of the miscibility gap, i.e. only up to the given m i s c i b i l i t y fraction. 0

0


6.

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Table I. Estimated M i x i n g Parameters for Binary Solid-Solutions at 25° C System (main, trace)

Misc. Frac. ( trace) ÎMg,Ni)S0 .7HoO complete M g , Z n ) S 0 . 7 I T 0 complete Mg,Fe)SO>f.7HoO 16.7% Mg,Mn)Sa4.7H2p 28.6% Z n , C u ) S 0 * 7 H O 22.2% Zn,Fe)SO;.7HoO 22.4% Z n , M n ) S ( J 7 H p 25.6%? Ni,Fe)S0 .7H26 16.7% Ni,Cu)S0 .7IT20 2% ÎFe,Cu)SOi.7H20 65.4%

Temp. CO 25 25 25 25 25 25 25 25 25 25

ÎFe,Mn)S0 .7H2P F e , C o ) S 0 7ΗοΌ [Fe,Mg)S0 .7IT20

8.2% complete 58%

25 25 25

(Fe Z n ) S 0 . 7 H 0 AsfcLér) K(Cl,èr )

30.7% complete complete

25 25 25

Ba,Pb)S04 Ba,Sr)S04 Ba,Ca)S04 Sr,Ca)S04 Ca, M n ) C 0 Ca, F e ) C 0 Ca, Z n ) C 0 Ca, C o ) C 0 Ca, M g ) C O Ca, M g ) C 0 Ca, M g ) C 0 Ca,Ca,Mg )Cp non-deTective (Ça C a . M g ) C 0 defective fCa, P b ) C 0 Mg,Fe)CO, Mg,Mn)C

Modeling SolidâSolution Reactions in Low-Temperature Aqueous

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