Mixing Properties and Crystallization Behaviour of the Scheelite

CRYSTAL GROWTH & DESIGN

Mixing Properties and Crystallization Behaviour of the Scheelite-Powellite Solid Solution A Ä ngeles Fernańdez-Gonza´lez,* A Ä ngel

Andara,#

2007 VOL. 7, NO. 3 545-552

and Manuel Prieto

Department of Geology, UniVersity of OViedo (Spain) ReceiVed October 2, 2006; ReVised Manuscript ReceiVed December 6, 2006

ABSTRACT: Different compositional members of the CaWO4-CaMoO4 (scheelite-powellite) solid solution were obtained using precipitation experiments and crystallization in a gel. The solids were characterized by X-ray diffraction (XRD), scanning electron microscopy-energy dispersive spectrometry (SEM-EDS), and electromagnetic pulse (EMP). XRD analyses of the crystals formed in the precipitation experiments show that the unit cell parameters (tetragonal, I41/a) vary with composition in a nonlinear way. Whereas the parameter a increases with the tungsten content, c decreases and the unit cell volume shows a minimum for intermediate compositions. From these crystallographic data, a negative excess volume of mixing has been determined. The excess enthalpy of mixing has been determined using solution calorimetry, resulting to be clearly negative for all compositions. The negative character of both parameters points toward a nonideal solid-solution with a tendency to ordering. On the basis of these data, a Guggenheim expansion series (a0 ) -1.422, a1 ) 0.213, and a2 ) -0.130) is proposed to describe the excess free energy of mixing. The solid phase activity coefficients obtained from this series have been used to calculate the Lippmann phase diagram and the equilibrium partitioning for the system CaWO4-CaMoO4-H2O. Finally, the crystallization behavior in gels and particularly the development of concentric compositional zoning of high gradient is explained on the basis of the proposed nonideal solid-solution model. Introduction The scheelite-powellite series (CaWO4-CaMoO4) constitutes an interesting example of anionic substitution. Both endmembers crystallize in the same space group (I41/a) and are isostructural.1 The solid solution is considered to be continuous from one end-member to the other,2 but this assumption still requires verification. On the one hand, the small difference in the cell parameters (less than 1%) suggests the possibility of a wide range of miscibility. On the other hand, whereas the unit cell parameter a () b) is larger in scheelite, c is larger in powellite and it has been observed that the c/a ratio is usually significantly larger for molybdates than for tungstates in scheelite-type compounds.3 Paradoxically, a number of structure determinations have shown that the tetrahedral units WO42- and MoO42- have essentially the same size, which means that the difference in c/a ratios cannot be due to dissimilarities in the configuration of these anionic units. Sleight3 explains this systematic difference between scheelite-type molybdates and tungstates assuming that MoO42- is more covalent than WO42-. Obviously, this difference can imply complexities in the WO42--MoO42- substitution. Hsu and Galli4 obtained different Ca(WO4,MoO4) compositional members by precipitation from aqueous solutions and observed that the angular separation (∆2θ) between the two XRD reflections 211 and 114 varies uniformly and considerably with the W/Mo ratio. However, to our knowledge, there is no systematic study of the variation of the unit cell parameters with composition. In nature, this solid solution occurs in a variety of geological settings (pegmatites, contact-metasomatic rocks, hydrothermal veins, etc.), the composition being controlled by the physicochemical environment during mineral formation. Scheelitepowellite specimens of metasomatic origin show a wide * To whom correspondence should be addressed. Department of Geology, University of Oviedo, C/ Jesu´s Arias de Velasco s/n 33005 Oviedo (Spain). Tel. (+34) 985 103 174. Fax. (+34) 985 103 103. E-mail mafernan@ geol.uniovi.es. # Present address: Nu ´ cleo Universitario “Pedro Rincoń Gutie´rrez”. Edificio de Ingenierıá, Me´rida (5101-A), Venezuela.

compositional range,5 but mineral samples from other occurrences rarely contain more than 4 mol % CaMoO4. According to Hsu and Galli4 this is because molybdenum forms molybdenite (MoS2) in many geological environments that are favorable to the formation of scheelite. Crystallization of scheelite-powellite solid solutions requires low S2 fugacities and/or oxidizing conditions. Natural scheelite-powellite crystals frequently show a compositional concentric zoning that has been interpreted as resulting from changes in physicochemical parameters during crystal growth.5 This work aims (i) to clarify the ideal or nonideal character of the scheelite-powellite solid solution, (ii) to propose a thermodynamic model for the CaWO4-CaMoO4-H2O system, and (iii) to study the nucleation and crystal growth behavior of this solid solution from aqueous solutions. To achieve these objectives, the thermodynamic mixing properties of the scheelitepowellite solid solution are estimated and the equilibrium Lippmann model6 is applied to the CaWO4-CaMoO4-H2O system. The research includes experimental work on crystallization of scheelite-powellite solid solutions from aqueous solutions. Finally, the crystallization behavior is discussed in light of the proposed equilibrium model. Thermodynamic Background. The Lippmann model6 has been widely used for the description of thermodynamic equilibrium in solid solution-aqueous solution (SS-AS) systems7-9 and has been demonstrated to be particularly useful in interpreting crystallization processes.10 Lippmann extended the solubility product concept to solid solutions by developing the concept of “total activity product” (∑∏). This parameter is defined as the sum of the partial solubility products contributed by each end-member of the solid solution. For the Ca(WO4,MoO4) solid solution, ∑∏ is given by

∑∏ ) a(Ca2+)[a(WO42-) + a(MoO42-)]

(1)

where a(Ca2+), a(WO42-), and a(MoO42-) are the activities of the ions in the aqueous solution. At thermodynamic equilibrium,

10.1021/cg0606646 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/08/2007

546 Crystal Growth & Design, Vol. 7, No. 3, 2007

Fernańdez-Gonza´lez et al.

the total solubility product ∑∏eq can be expressed as a function of the solid composition, the solidus:

∑∏eq ) KSchXSchγSch + KPowXPowγPow

(2)

where K is the solubility product of the scheelite (Sch) or powellite (Pow) end-member, X is the mole fraction (XSch ) 1 - XPow) of the corresponding end-member in the solid solution, and γ is the solid-phase activity coefficient. ∑∏eq can also be expressed as a function of the aqueous solution composition, the solutus:

∑∏eq ) X(WO 2-) 4

KSchγSch

1 X(MoO42-) + KPowγPow

(3)

where X(WO42-) is the activity fraction of WO42- ions in the aqueous solution, given by

X(WO4 ) )

a(WO42-)

2-

a(WO42-) + a(MoO42-)

(4)

An analogous expression defines X(MoO42-), so that X(WO42-) ) 1 - X(MoO42-). Lippmann’s solidus and solutus relationships can be used to predict the solubility of any solid solution and the equilibrium partitioning of the substituting ions between the aqueous and the solid phases. Moreover, these functions can be plotted against two superimposed scales on the abscissa, XSch and X(WO42-), thereby outlining a Lippmann diagram that can be used in a similar way to binary solid-melt phase diagrams. In the case of nonideal solid solutions, the calculation of the solidus and solutus functions requires the solid-phase activity coefficients to be known, and this is the main difficulty in establishing thermodynamic equilibrium in SS-AS systems.11 The nonideal character of a solid solution can be evaluated in terms of “excess” thermodynamic parameters, such as the excess free energy of mixing (GE), the excess enthalpy of mixing (HE), the excess molar volume (VE), and the excess entropy of mixing (SE). These excess parameters are defined by the difference between the thermodynamic mixing parameters (GM, HM, VM, SM) of the actual solid solution and the corresponding parameters (GM,id, HM,id ) 0, VM,id ) 0, SM,id) of an equivalent ideal solid solution. The excess parameters govern the relationships between activity and composition for nonideal solutions. In the case of binary solid solutions, the activity coefficients are related to GE according to the Redlich and Kister expressions,12,13 which for the scheelite-powellite series are given by

( (

) )

∂GE /RT ln γSch ) GE + XPow ∂XSch

(5)

∂GE ln γPow ) GE - XSch /RT ∂XSch

(6)

In practice, experimental GE data can be fitted to a Guggenheim’s expansion series, which satisfies the required property that GE ) 0 at the end-member compositions:

GE ) XSchXPowRT[a0 + a1(XSch - XPow) + a2(XSch XPow)2 + ...] (7) where a0, a1, a2, ... are dimensionless fitting constants independent of the composition. Two or three of these parameters

are usually enough to define a suitable GE function. From this function, the solid-phase activity coefficients, the solidus, and the solutus can be calculated. A complete review of the thermodynamics of SS-AS sytems is given by Glynn and coworkers.7-9 Experimental Methods All of the experiments were performed in a thermostated (25 ( 0.5 °C) room using deionized water (MilliQ system), and all reagents were of analytical grade (Aldrich). Two methods were used to crystallize different compositions of the Ca(WO4,MoO4) solid solution: direct precipitation and crystallization in gels. The precipitation experiments were designed to produce micrometric, compositionally homogeneous crystals that could be analyzed by powder X-ray diffraction (XRD) to assess how the crystallographic parameters varied as a function of composition. The gel experiments were used to grow larger crystals allowing the qualitative study of the chemical evolution of the crystals during growth. Moreover, to estimate the enthalpy of mixing, a number of solution calorimetry experiments was carried out to measure the heat of precipitation of different Ca(WO4,MoO4) compositional members. In all cases, the activities of the aqueous ions were calculated using the geochemical speciation code PHREEQC.14 Precipitation Experiments. Micrometric crystals of the Ca(WO4,MoO4) solid solution were precipitated according to the reaction: The

xNa2WO4 (aq) + (1 - x)Na2MoO4 (aq) + CaCl2 (aq) w Ca (WO4)x(MoO4)(1-x) (s) + 2NaCl (aq) (8) experiments were carried out by adding 10 mL of 1 M CaCl2 to a polypropylene beaker containing 100 mL of a vigorously stirred solution with different ratios of Na2WO4 and Na2MoO4. The precipitates were then separated from the aqueous phase using 0.65 µm Millipore filters, washed using ethanol, and dried in an oven at 40 °C. The initial concentrations of Na2WO4 and Na2MoO4 are shown in Table 1. To determine the relative W/Mo content and the homogeneity of the solid phase produced, the precipitates were examined in a JEOL JMS-6100 scanning electron microscope (SEM) equipped with an INCA Energy 200 microanalysis system (EDS). The precipitates were also studied by powder XRD. The diffractograms were obtained using Cu KR radiation on a Phillips X’PertPro diffractometer in the 2θ range 5°< 2θ < 80°. Between analyses, the diffractometer was calibrated using an external silicon standard with the help of X’PERT PLUS.15 The peak positions of the standard were compared by X’PERT PLUS to their theoretical values, and a polynomial correction curve was calculated. This polynomial was then used to correct the peak positions of the solid-solution sample. The diffractograms were then studied using X’PERT PLUS to index the main reflections and to calculate the unit cell parameters of each precipitate. Moreover, the peak widths were investigated by considering the full width at half-maximum (fwhm) of the main reflections. This was done to identify peak broadening effects that could be a result of compositional inhomogeneities of the precipitating solid solutions. Although it is a complicated task to separate the broadening effects due to crystallite size from those due to composition inhomogeneities in a sample, a rough estimation can be obtained by comparing fwhm values measured for the precipitates of the pure end-members with the values obtained from equivalent reflections of intermediate precipitates. With this aim, the “Scherrer calculator” of X’PERT PLUS was used to estimate the crystallite size of the end-members since in this case any potential peak broadening will be basically a size effect. The instrumental broadening was previously determined using a powdered powellite standard. Finally, the EDS composition of the precipitates was correlated with the angular separation (∆2θ) between the two reflections 211 and 114, which has been established to vary in a uniform way with the XSch molar fraction.4 It is worth noting that, in the present context, the crystallite size is an XRD term that indicates the size of a coherently diffracting domain and thus does not necessarily coincide with the particle size. Here, the determination of the crystallite size of the end-members is part of a protocol in which the important point is to determine whether peak broadening changes in a linear way with composition (from one endmember to the other) or if there is some “excess” peak broadening

Mixing Properties of the Scheelite-Powellite Series

Crystal Growth & Design, Vol. 7, No. 3, 2007 547

Table 1. Unit Cell Parameters and Precipitate Compositions parent solutions (M) Na2WO4

Na2MoO4

a ) b (Å)

c (Å)

Vcell (Å3)

∆2θ (°) 211-114

XEDS Sch ((0.02)

XXRD Sch

0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

5.243(1) 5.241(1) 5.240(2) 5.238(2) 5.234(2) 5.228(1) 5.224(2) 5.228(2) 5.227(2) 5.226(1) 5.226(1)

11.373(3) 11.376(4) 11.379(6) 11.387(6) 11.391(6) 11.397(5) 11.406(7) 11.418(6) 11.426(6) 11.433(4) 11.442(4)

312.6(2) 312.5(2) 312.4(4) 312.4(4) 312.1(4) 311.5(3) 311.3(4) 312.1(4) 312.2(4) 312.3(2) 312.5(2)

0.724 0.705 0.684 0.664 0.651 0.631 0.602 0.576 0.543 0.515 0.504

1.00 0.89 0.81 0.74 0.69 0.59 0.48 0.36 0.22 0.12 0.00

1.00 0.90 0.81 0.73 0.68 0.60 0.48 0.37 0.22 0.08 0.00

that could be attributed to compositional heterogeneities in intermediate members of the solid solution. Solution Calorimetry. The excess enthalpies of mixing (HE ) HM) were evaluated at 25 °C by direct calorimetric measurements of the heat of precipitation of different compositional members of the scheelite-powellite series. With this aim, a solution calorimeter (PARR6775) controlled by precision thermometer (PARR-6772) was used. The Dewar flask was filled with 100 mL of an aqueous solution of Na2WO4 and Na2MoO4, and a 10 mL sample of 1 M CaCl2 was introduced in a rotating glass cell sealed with a polytetrafluoroethylene (PTFE) dish. After thermal equilibrium had been established, the glass cell was opened within the Dewar, and the change of enthalpy was measured. The heat of dilution of 1 M CaCl2 was previously measured, and the result was used to calculate enthalpies of precipitation at full dilution. The heats of dilution (from 100 to 110 mL) of the Na2WO4 and Na2MoO4 parent solutions were estimated to be negligible. The enthalpy of mixing was then estimated according to the expression: ppt ppt HM ) ∆Hppt SS - (XSch∆HSch + XPow∆HPow)

(9)

where ∆Hppt stands for the measured enthalpy of precipitation of a solid solution (SS) with composition XSch, pure scheelite (Sch), and pure powellite (Pow). As can be deduced from eq 9, the enthalpy of precipitation itself is not of interest, but the difference between the enthalpy of precipitation of the solid solution and the enthalpy of precipitation of a mechanical mixture of the end-members gives the enthalpy of mixing. This has the advantage that many systematic errors involved in the determination of precipitation enthalpies cancel mutually in calculating HM since their contribution can be assumed to be virtually the same in all three heats of precipitation involved in eq 9. The precipitates formed in these calorimetry experiments were separated from the aqueous phase and confirmed to be members of the scheelite-powellite series by powder XRD. The solid composition (XSch) was determined by SEM-EDS. Finally, the remaining solution was analyzed for Mo and W using ICP-AES (Perkin-Elmer-Optima3300-DV) to quantify the amount of precipitate. Each experimental run was conducted in quintuplicate; thus, the values reported in Table 2 are the average of five analogous experimental runs. The variation (relative standard deviation) in ∆Hppt from replicate experiments was around (6%. Although this relative error is small, the result (HM) of subtraction according to eq 9 is a smaller number with a larger relative error (RSD ≈ 20-30%). Crystallization in Gels. The experimental device consisted of a U-shaped tube6 in which two reactant reservoirs are separated by a column (length 18 cm; diameter 1 cm) of silica hydrogel. The gel was prepared by acidification of a sodium silicate solution (Merck; density: 1.059 g cm-3; pH 11.2) with 1 N HCl to a pH ) 5.5. This acidified solution was poured into the horizontal branch of the U-tube where it polymerizes to form a hydrogel with about 96.5 wt % water within interconnecting pores. One of the reservoirs was then filled with 10 mL of 0.5 M CaCl2 and the other was filled with 10 mL of an aqueous solution with different ratios of Na2WO4 and Na2MoO4. The compositions of the parent solutions used in these experiments are shown in Table 4. The silica hydrogel is a porous medium that suppresses convection and advection only allowing counter diffusion of the reactants, which eventually meet and precipitate in a narrow region of the diffusion column. While the composition of the interstitial solution at the nucleation event can be estimated according to procedures widely described in previous papers,10,17,18 monitoring the aqueous phase

Table 2. Experiments of Solution Calorimetry: Excess Enthalpy of Mixinga parent solutions (M) Na2WO4

Na2MoO4

XSch (( 0.04)

∆Hppt KJ mol-1

HM KJ mol-1

0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

1.00 0.88 0.80 0.73 0.67 0.58 0.48 0.35 0.24 0.11 0.00

-4.68 ( 0.18 -4.16 ( 0.16 -3.79 ( 0.19 -3.46 ( 0.20 -2.91 ( 0.18 -2.43 ( 0.17 -2.46 ( 0.20 -0.87 ( 0.20 -0.004 ( 0.21 1.35 ( 0.17 2.35 ( 0.13

-0.35 ( 0.23 -0.55 ( 0.24 -0.72 ( 0.25 -0.67 ( 0.23 -0.84 ( 0.21 -1.51 ( 0.23 -0.84 ( 0.23 -0.77 ( 0.24 -0.34 ( 0.21

a The standard deviations are shown with the ( symbol. Errors in HM were calculated as the accumulation of errors in ∆Hppt for the end and intermediate members of the series.

Table 3. Precipitation behavior (in All Cases a(Ca2+) ) 2.47 × 10-2) parent solutions (M) Na2WO4

Na2MoO4

a(WO42-) × 103

a(MoO42-) × 103

X (WO42-)

XSch ((0.02)

0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

10.9 9.81 8.72 7.63 6.54 5.45 4.36 3.27 2.18 1.09 0.00

0.00 1.01 2.01 3.02 4.03 5.04 6.04 7.05 8.06 9.07 10.1

1.00 0.90 0.81 0.72 0.62 0.52 0.42 0.32 0.21 0.11 0.00

1.00 0.89 0.81 0.74 0.69 0.59 0.48 0.36 0.22 0.12 0.00

Table 4. Compositional Evolution during Crystal Growth in Gels parent solutions (M)a Na2WO4

Na2MoO4

XSch (max) ((0.05)

XSch (min) ((0.05)

grad (XSch) (µm-1) ((0.001)

0.5 0.5 0.5 0.3 0.1

0.1 0.3 0.5 0.5 0.5

0.83 0.77 0.72 0.60 0.11

0.42 0.25 0.26 0.09 0.03

0.014 0.009 0.007 0.006 0.002

a

The calcium parent solution was 0.5 M CaCl2 in all the experiments.

during the growth process is virtually impossible in this kind of “black box” SS-AS system. A quantitative description of the nucleation and growth behavior in these experiments is, however, beyond the scope of the present work. Here the gel experiments are used in a qualitative way, and the growth scenario is approximated from indirect observations. The experiments were monitored to know the position in the gel column of the first nuclei and the waiting time for nucleation (the time taken for the first crystallites to become visible under magnification ×500). One month after nucleation, the crystals were extracted from



Figure 1. Typical diffractogram (XSch ≈ 0.36) of the spherulitic aggregates obtained in the precipitation experiments. the gel and confirmed to be members of the scheelite-powellite series by XRD. The crystal morphologies were studied by polarizing microscopy and SEM. To characterize the compositional evolution during the growth process, fresh crystals of each sample were embedded in a resin, cut, polished, carbon coated, and studied by backscattered electron imaging (SEM-BSE). Moreover, detailed quantitative analyses of the crystals were obtained using a CAMEBAX SX-100 electron microprobe (EMP).

Figure 2. Variation of the unit cell parameters with the solid-solution composition.

Results and Discussion Precipitation Experiments: Lattice Parameters vs Composition. Figure 1 shows a typical diffractogram and a SEM image representative of spherulites formed in the precipitation experiments. All the diffractograms were indexed in the tetragonal space group I41/a. The unit cell parameters determined from the XRD data are listed in Table 1 with the standard deviation (affecting the corresponding decimal place) in parentheses. Table 1 also shows the composition of the parent solutions used in the precipitation experiments, the angular separation (∆2θ) between 211 and 114 reflections, the composition (XEDS Sch ) measured using SEM-EDS, and the composition (XXRD Sch ) of the solids that can be obtained from ∆2θ(211-114). Each data in the XEDS Sch column is the average of the microanalyses of 10 spherulites, and in all cases there is no variation above 0.04XSch and the standard deviation is no greater than 0.02XSch. The precipitates were checked for compositional homogeneity by considering the broadening of main reflections. Working with 101 (the peak corresponding to the largest d-spacing), the observed fwhm was 0.263 (°2θ) for pure powellite and 0.566 (°2θ) for pure scheelite. Since the pure end-members are obviously homogeneous in composition, these values can be used to calculate crystallite sizes, which result to be 120 and 26 nm for powellite and scheelite, respectively. Working with 112 (the highest intensity peak), the observed fwhm was 0.298 (°2θ) for powellite and 0.570 (°2θ) for scheelite, which confirms a smaller crystallite size in the case of scheelite. The diffractograms of the precipitates with intermediate compositions show intermediate peak broadenings. The fwhm values change in a nearly linear way with composition, and thus compositional inhomogeneities can be considered irrelevant for the present purposes. The only diffractogram that shows some “excess” broadening is the one corresponding to XSch ) 0.48, with FWHM112 ) 0.546. This value is still intermediate between those of the end-members but clearly deviates from linearity.

Figure 3. Angular separation (∆2θ) between 211 and 114 reflections as a function of XEDS Sch . The dashed curve represents a third-order polynomial (A + B1x + B2x2 + B3x3) fitting the experimental data. The fitting parameters, the coefficient of determination (R2), and the standard deviation (SD) are also displayed.

As can be observed in Table 1, the dimensions of the unit cell change in an unusual way with composition. Whereas a () b) increases with the scheelite content, c decreases with increasing XSch. Figure 2 shows that the decrease of c with XSch is almost linear, the correlation coefficient being higher than 0.99. In contrast, the parameter a exhibits a significant minimum around XSch ) 0.5, and the unit cell volume varies in a nonlinear way with composition. Hsu and Galli4 report the existence of a “definite” relationship between ∆2θ(211-114) and composition. On this basis, they construct a determinative curve to assess solid compositions but do not determine a fitting function. Figure 3 displays the correlation between ∆2θ(211-114) and XEDS Sch obtained in the present work. As can be observed, the experimental data have been fitted to a third-order polynomial that exhibits a slightly sinuous shape. The figure also shows the fitting equation, the coefficient of determination, and the standard deviation. The column labeled XXRD Sch in Table 1 shows the compositions obtained using this equation. A linear fit results also in a very good coefficient of



Figure 4. Variation of the excess molar volume as a function of the solid solution composition.

determination (R2 > 0.99) but obviates the deviation from linearity observed in the proximities of the end-members. Clearly, the ∆2θ(211-114) method is not enough to allow a sensitive determination of the composition but may be suitable for many purposes. Excess Volume of Mixing. The excess volume (VE ) VM since VM,id ) 0) of the solid solution can be calculated from the unit cell volume according to

VE ) VSS - VMM

(10)

where VMM is the molar volume of a mechanical mixture of the two end-members and VSS is the molar volume of the solid solution, given by

1 VSS ) VcellNAvogadro 4

(11)

since the unit cell contains 4 formula units. The end-member molar volumes (VSch and VPow) can also be calculated from the corresponding cell volumes according to eq 11 and are in good agreement with the available macroscopic values;19 thus

VMM ) VSchXSch + VPowXPow

(12)

The difference between the molar volumes of scheelite and powellite is very small, but the values corresponding to intermediate compositions are clearly smaller than those of the end-members, and so the excess molar volume is negative. Figure 4 shows the values of VE calculated for the precipitates obtained in these experiments. As can be observed, all the data points corresponding to intermediate compositions fall below VE ) 0, which points toward a negative excess volume of mixing. Excess Enthalpy of Mixing. Table 2 displays the concentration of the parent solutions used in the calorimetry experiments, the mean composition of the solids, the enthalpy of precipitation at full dilution, and the excess enthalpy of mixing (HE ) HM since HM,id ) 0) computed according to eq 9. In spite of the unavoidable experimental error, the enthalpy of mixing appears to be clearly negative, with a sharp minimum for compositions close to XSch ) 0.5. This finding is in agreement with the data obtained by Kiseleva et al.,20 who determined a negative enthalpy of mixing by high-temperature calorimetry of the dissolution of different members of the series in an oxide melt at 700 °C. Moreover, this result agrees with the negative values of VE determined from the present XRD study. The negative character of both parameters indicates that we are dealing with a nonideal solid solution with a tendency to ordering.

Figure 5. Experimental values of HM obtained from solution calorimetry experiments. The solid line represents a Guggenheim’s expansion series fitting all of the experimental data except that corresponding to XSch ) 0.48. The text box shows the Guggenheim’s fitting parameters. The dash-dot line illustrates the “cuspidal” aspect of the series when the value corresponding to XSch ) 0.48 is also considered.

Figure 5 shows the experimental values of HM and a solid line fitting the data to a Guggenheim expansion series (eq 7). As can be observed, disregarding the value for XSch ) 0.48, the data fit reasonably well (R2 ) 0.98) to a Guggenheim series of three terms. However, the sharp fall of HM around XSch ) 0.5 would require a function type with a more acute sketch. In fact, the assumption GE ) HM implies that we assume a completely random mixing in the solid solution and absence of nonconfigurational contributions to the entropy of mixing, i.e., a negligible excess entropy (SE) of mixing. This assumption is, however, very questionable in the case of solid solutions with a negative enthalpy of mixing in which departures from complete randomness and formation of partially ordered microdomains could be expected, particularly at XSch ≈ 0.5. Here the arrangement of the HM datapoints around XSch ) 0.5 forms a “cuspidal” minimum, which could be due to a certain ordering of the substituting ions in the solids with this composition. However, although some “excess” peak broadening has been detected, the diffractograms corresponding to these solids do not show incipient extra reflections that could be attributed to ordering schemes. This is not surprising since, in solid solutions with a tendency to be ordered, local ordered domains can exist within the nominally disordered solid solution. The final outcome will be the separation of a completely random distribution, which will further reduce the enthalpy of mixing. Such local ordering effects will also decrease the entropy of mixing, which will become lower than that corresponding to ideal disorder. Therefore, in fitting the experimental data to a Guggenheim expansion series one should disregard the value for XSch ) 0.48 since, for this intermediate composition, the excess entropy of mixing does not seem to be negligible and, consequently, GE * HM. Moreover, these deviations of enthalpy and entropy could balance to some extent, and the value of GE for this composition may not be very different from that corresponding to the Guggenheim curve calculated from the rest of the HM data. Equilibrium Behavior in the CaWO4-CaMoO4-H2O System. The Lippmann diagram calculated for the system CaWO4-CaMoO4-H2O is shown in Figure 6a. Solidus and solutus have been computed at 25 °C, assuming a nonideal solid solution model (a0 ) -1.422, a1 ) 0.213, and a2 ) -0.130) and using 8.67 and 7.95 as end-member pK’s for scheelite and powellite, respectively. On the Lippmann diagram, horizontal tie lines can be drawn between the solidus and solutus curves,



Figure 6. (a) Lippmann’s diagram calculated for the Ca(WO4,MoO4)H2O system assuming a nonideal solid solution with a0 ) -1.422, a1) 0.213, and a2 ) -0.130. The dashed lines connect a particular fluid composition with the corresponding equilibrium composition of the solid. (b) Roozeboom diagram (solid line) computed using the same parameters. The dash-dot line connects (0,0) and (1,1) and corresponds to a distribution coefficient equal to unity.

thereby giving the aqueous phase, X(WO42-), and solid phase, XSch, compositions for the series of possible thermodynamic equilibrium states. By combining solidus and solutus (eqs 2 and 3), the following expression can be deduced (Prieto et al., 1997):

XSch )

KPowγPowX(WO42-) (KPowγPow - KSchγSch)X(WO42-) + KSchγSch

(13)

This expression can be used to construct a Roozeboom, X(WO42-)-XSch, plot (Figure 6b), which describes the coexisting compositions of aqueous and solid solution under equilibrium conditions. This diagram illustrates the preferential partitioning for WO42- toward the solid phase: the Roozeboom curve plots above the dash-dot line joining the points (0,0) and (1,1), which means that X(WO42-) < XSch for all the compositions. Ideal versus Nonideal Behavior. While the values of a0, a1, and a2 used here are an approximation and the precise shape of the Lippmann diagram could be to a degree different, some firm conclusions can be achieved by comparing the diagram in Figure 6a with an analogous diagram computed for an equivalent ideal solid solution. As can be observed in Figure 7a, the negative excess free energy lowers the position of the solutus curve relative to the position of an ideal solutus. This means that the solubility of intermediate members of the solid solution is significantly smaller than that of an equivalent ideal solid solution. The general shape of the diagrams is also rather

Figure 7. (a) Comparison between the Lippmann diagram calculated using a0 ) -1.422, a1 ) 0.213, and a2 ) -0.130 (solid lines) and that calculated assuming an ideal solid solution (dashed lines). The inset shows the Roozeboom diagram calculated assuming an ideal solid solution. (b) Variation of the equilibrium distribution coefficient as a function of the solid solution composition (solid line). The dash-dot line represents the equilibrium distribution coefficient for an equivalent ideal solid solution.

different, which affects the partitioning of the substituting ions between the solid and the aqueous phase. At equilibrium, the degree of preferential partitioning is usually expressed in terms of the equilibrium distribution coefficient (Deq), which for this solid solution is given by

{ }{

}

XSch a(WO42-) Deq ) / . XPow a(MoO 2-) 4

(14)

In addition, the two conditions (one for each end-member) describing equilibrium in this system are

a(Ca2+)a(WO42-) ) KSchXSchγSch

(15)

a(Ca2+)a(MoO42-) ) KPowXPowγPow

(16)

Therefore, combining eqs 14-16 gives an expression for Deq in terms of the solid-phase activity coefficients:

Deq )

KPowγPow KSchγSch

(17)

Since both γPow and γSch change in agreement with eqs 5 and 6, Deq is not a constant but a function that depends on the solid composition. This function is shown in Figure 7b, which also displays the distribution coefficient (Deq,id) for an equivalent ideal solid solution. For an ideal solid solution γPow ) γSch ) 1 and, consequently, the distribution coefficient is a constant,



Figure 8. Experimental X(WO42-)-XSch pairs (open diamonds) corresponding to the precipitation experiments. The solid line represents the equilibrium Roozeboom diagram.

Deq,id )KPow/KSch) 5.25. As can be observed, for XSch < 0.46, Deq is considerably higher than the ideal value, reaching a limit of ≈30.7 as XSch approaches zero. In contrast, for increasing values of XSch the distribution coefficient decreases gradually to reach values near 1. It is worth noting that, although the Roozeboom function (eq 13) illustrates the distribution of the substituting ions between the aqueous and the solid phase, it is not equivalent to the equilibrium distribution coefficient (eq 14). The Roozeboom diagram represents XSch as a function of X(WO42-). In contrast, the equilibrium distribution coefficient represents the proportion between two ratios, one corresponding to the solid mole fractions, XSch/XPow, and the other corresponding to the aqueous activity fractions, X(WO42-)/X(MoO42-). In Figure 7b this proportion is represented on the ordinate versus XSch on the abscissa. For an ideal solid solution, the Roozeboom diagram becomes symmetric (see inset of Figure 7a) with respect to the straight line joining the points (0,1) and (1,0), whereas the equilibrium distribution coefficient becomes a constant (see Figure 7b). In a similar way, the Lippmann diagram corresponding to an ideal solid solution is symmetric with respect to a 2-fold axis located at its center (see Figure 7a). Effective Partitioning in the Precipitation Experiments. Table 3 shows the concentrations of the parent solutions and the activities of WO42- and MoO42- ions in the aqueous solution. The activity of the aqueous Ca2+ ions is virtually the same in all cases since the initial concentration of CaCl2 was always the same. To calculate these activities, both the concentrations of the parent solutions and their pH were input into PHREEQC.14 Table 3 also displays the aqueous activity fraction of WO42- and the mole fraction of the precipitating solids. Obviously, in these experiments the supersaturation and the precipitation rate are very high, and the substituting ions tend to incorporate in a stoichiometric proportion close to that of the aqueous solution. The effect can be explained on a kinetic basis,21 and it is shown in Figure 8, which displays the experimental points on a Roozeboom diagram. As can be observed, all the datapoints plot below the equilibrium curve, but they are still above the line (0,0)-(1,1), which means that there is a slight preferential partitioning of the less soluble scheelite into the solid phase. In spite of the high supersaturation used in these experiments, the effective distribution coefficient reaches values around 1.4, a quantity that is still significant.

Figure 9. (a) Backscattered electron image of the central section of a typical Ca(WO4,MoO4) spherulite obtained in gel. The brighter regions are richer in tungsten. (b) Compositional profile: the solid diamonds correspond to data measured by EMP along the black line drawn on the image. The solid line represents the profile estimated using “gray levels”. The minimum and maximum XSch values and the overall compositional gradient observed in the outer zone are also shown. Parent solutions: 0.5 M CaCl2 and 0.5 M Na2WO4 + 0.3 M Na2MoO4.

Compositional Evolution of the Solids during Growth in Gels. Figure 9a shows the backscattered electron image of the central section of a typical Ca(WO4,MoO4) spherulite obtained in the gel experiments. In this image, the brightness of the different zones is proportional to the tungsten content. Figure 9b displays a compositional profile in which the solid diamonds correspond to data measured by EMP along the black line drawn on the image. Obviously, these EMP analyses represent the mean composition of a region of ≈2 µm of diameter and are insufficient to reveal compositional details of smaller size. A better spatial resolution can be obtained using the intensities of pixels (the irregular solid line in Figure 9b) after a gray scale calibration relative to composition. As can be observed, the spherulites exhibit a marked concentric compositional zoning. This indicates that during the growth process the substituting ions are not incorporated into the solid in the same stoichiometric proportion as in the aqueous solution. As a consequence, solid and aqueous solution compositions tend to vary as growth proceeds. Moreover, the solid grows in such a way that the layers growing on the surface block the inner zones from contact with the solution, which results in a compositional heterogeneity from core to rim in the spherulites. The cores are always relatively W-rich because CaWO4 is less soluble than CaMoO4 and therefore is preferentially incorporated into the solid phase at nucleation. This rapidly depletes the solution in WO42-, so the next stage of growth is molybdenum rich. Finally, as more WO42- diffuses from the reservoir into the crystallization zone, the spherulites enrich in tungsten again. These main compositional regions have been observed in all of the experiments performed in gels, the only difference being


the specific W/Mo content and the magnitude of the compositional gradients. Moreover, the presence of compositional oscillations superimposed to this general gradient becomes evident in the gray scale profile. Table 4 displays the minimum and maximum XSch values measured in the spherulites (mean values obtained from 10 different individuals of the same precipitate) and the average compositional gradient observed in the outer zone (see Figure 9b). The amplitude and wideness of the superimposed oscillations are, however, very variable and difficult to assess. Whereas the whole compositional gradient is similar in all the spherulites of the same experiment, there is no clear correlation among the superimposed zoning patterns. This behavior is common to all the gel experiments in which oscillatory zoning has been previously observed.10,22,23 The absence of correlation indicates that these minor compositional variations do not correspond to global changes in the bulk solution but to instabilities inherent to the growth process that occur at (or in close proximity to) the interface. Different models have been proposed in the literature to interpret oscillatory zoning in minerals,24-27 most of them based on the coupling of at least two time-dependent variables through some sort of feedback mechanism. However, proposing a specific feedback mechanism (and a dynamic model based on it) is beyond the scope of this work. Here, we only wish to remark that, during crystallization in gels, the development of oscillatory zoning has only been observed in SS-AS systems in which the endmember solubility products differ by two or more orders of magnitude. In these kinds of systems, there is a strong preferential partitioning of the less soluble end-member toward the solid phase. As a consequence, both the solid and the aqueous solution composition tend to vary dramatically during the growth process, which results in a sharp concentric zoning. Moreover, any cause that provokes small fluctuations in the fluid composition implies significant changes in the solid composition,10 resulting in oscillatory zoning with compositional waves of high amplitude. In contrast, solid solutions with close end-member solubility products grow usually rather homogeneous since the substituting ions tend to incorporate into the solid in the same stoichiometric proportion as in the aqueous phase, particularly at high supersaturations. This behavior has been observed10 in solid solutions such as (Sr,Ba)CO3, in which the end-member solubility products (10-9.27 for SrCO3 and 10-8.56 for BaCO3) differ less than 1 order of magnitude. In this system, the equilibrium distribution coefficient for strontium is 5.13, and the crystals grow homogeneously at the supersaturation level usually maintained during crystal growth in gels. Something similar could be expected for the Ca(MoO4,WO4)-H2O system, in which the end-member solubility products differ in a similar amount. In fact, the equilibrium distribution coefficient (Deq,id) calculated using an ideal solid solution model is 5.25 (see section 4.4). In spite of this, the crystals develop sharp gradients (see Table 4) and compositional waves of high amplitude (up to 0.2XSch). Such atypical behavior could be, however, explained as an effect of the negative enthalpy of mixing of this solid


solution, which (whatever the exact value of a0, a1, and a2 were) results in a significantly higher preferential partitioning of W toward the solid, at least for certain compositional ranges. Acknowledgment. This work was supported by the Ministry of Education and Science of Spain (Grant CGL2004-02501). The helpful comments of Roger Davey and three anonymous reviewers substantially improved the manuscript. References (1) Hazen, R. M.; Finger, L. W.; Mariathasan, J. W. E. J. Phys. Chem. Solids 1985, 46, 253-263. (2) Tyson, R. M.; Hemphill, W. R.; Theisen, A. F. Am. Miner. 1988, 73, 1145-54. (3) Sleight, A. W. Acta Crystallogr. 1972, B28, 2899-2902. (4) Hsu, L. C.; Galli, P. E. Econ. Geol. 1973, 68, 681-696. (5) Brugger, J.; Giere´, R.; Grobe´ty, B.; Uspensky, E. Am. Miner. 1998, 83, 1100-1110. (6) Lippmann, F. Neues Jahrb. Mineral., Abh. 1980, 139, 1-25. (7) Glynn, P. D. In Modelling in Aqueous Systems II; Melchior, D. C., Bassett, R. L., Eds.; ACS Symposium Series 1990, 416, 74-86. (8) Glynn, P. D.; Reardon, E. J. Am. J. Sci. 1990, 290, 164-201. (9) Glynn, P. D. In Sulfate Minerals, Crystallography, Geochemistry and EnVironmental Significance; Alpers, C. N., Jambor, J. L., Nordstrom, D. K. Eds.; Mineralogical Society of America: Washington, DC, 2000; Chapter 10, pp 481-511. (10) Prieto, M.; Fernandez-Gonza´lez, A.; Putnis, A.; Fernańdez-Dıáz, L. Geochim. Cosmochim. Acta 1997, 61, 3383-3397. (11) Prieto, M.; Fernańdez-Gonza´lez, A., Becker, U.; Putnis, A. Aquat. Geochem. 2000, 6, 133-146. (12) Redlich, O.; Kister, A. T. Ind. Eng. Chem. 1948, 40, 345-348. (13) Plummer, L. N.; Busenberg, E. Geochim. Cosmochim. Acta 1987, 51, 1393-1411. (14) Parkhurst, D. L.; Appelo, C. A. J. User’s Guide to PHREEQC (Version 2) - A Computer Program for Speciation, Batch-Reaction, One-dimensional Transport and InVerse Geochemical Calculations; U. S. Geological Survey Water Resources Investigations Report; U.S. Geological Survey: Washington, DC, 1999. (15) X’Pert Plus v.1.0. Program for Crystallography and RietVeld Analysis; Philips Analytical B.V.: Almelo, 1999. (16) Henisch, H. K. In Crystal Growth in Gels and Liesegang Rings; Cambridge University Press: Cambridge, 1988. (17) Andara, A. J.; Heasman, D. M.; Fernańdez-Gonza´lez, A.; Prieto, M. Cryst. Growth Des. 2005, 5, 1371-1378. (18) Henisch, H. K.; Garcia-Ruiz J. M. J. Cryst. Growth 1986, 75, 195202. (19) Robie, R. A.; Hemingway, B. S. Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 bar Pressure and at Higher Temperatures; U. S. Geological Survey Bulletin 2131; U. S. Geological Survey: Washington, DC, 1995. (20) Kiseleva, I. A.; Ogorodova, L. P.; Topor, N. D. Int. Geochem. 1980, 5, 764-768. (21) Pina, C.; Putnis, A. Geochim. Cosmochim. Acta 2002, 66, 185-192. (22) Putnis, A.; Fernańdez-Dıáz, L.; Prieto, M. Nature 1992, 358, 743745. (23) Fernańdez-Gonza´lez, A.; Prieto, M.; Putnis, M.; Lo´pez-Andre´s, S. Miner. Mag. 1999, 63, 331-343. (24) Reeder, R. J.; Fagioly, R. O.; Meyers, W. Earth Sci. ReV. 1990, 29, 39-46. (25) Wang, Y.; Merino, E. Geochim. Cosmochim. Acta 1992, 56, 587596. (26) Shore, M.; Fowler, A. D. Can. Mineral. 1996, 34, 1111-1126. (27) L’Heureux, I.; Kastev, S. Chem. Geol. 2006, 225, 230-243.

CG0606646

Mixing Properties and Crystallization Behaviour of the Scheelite

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