Influence of KF and HF on the Selectivity of Zr and Hf Separation by

Dec 8, 2009 - North-West UniVersity, PriVate Bag X6001, Potchefstroom 2531, South Africa. For nuclear applications, zirconium metal (Zr) must adhere t...
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Ind. Eng. Chem. Res. 2010, 49, 797–808

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Influence of KF and HF on the Selectivity of Zr and Hf Separation by Fractional Crystallization of K2Zr(Hf)F6 Dawie J. Branken,*,† Gerhard Lachmann,† Henning M. Krieg,† and Dolf S. L. Bruinsma‡,§ School of Physical and Chemical Sciences and School of Chemical and Minerals Engineering, North-West UniVersity, PriVate Bag X6001, Potchefstroom 2531, South Africa

For nuclear applications, zirconium metal (Zr) must adhere to stringent specifications, where a low hafnium (Hf) content, i.e., zHf. Notice that by rearranging eq 3, the relative distribution coefficient can be written as βHf,Zr )

xZr /xHf zZr /zHf

(4)

Therefore, the relative distribution coefficient also equals Zr: Hf(aq)/Zr:Hf(s). Accordingly, Figure 5 shows the calculated Zr: Hf mole fraction ratios at equilibrium for both the solid (zZr/ zHf) and liquid phases (xZr/xHf). The error bars shown for each value represent the average experimental error calculated for the solid and liquid phases, respectively. The initial Zr:Hf ratio in K2Zr(Hf)F6 before recrystallization (i.e., the starting material) is also shown as reference at the left side of the chart. From the figure, it is evident that with increasing KF concentration,

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Figure 6. SEM micrographs of the crystalline products obtained by crystallization from aqueous KF solutions with concentrations of 0.25 (A), 0.3 (B), 0.35 (C), and 0.5 mol/L (D).

the ratio zZr/zHf (i.e., for the solid phase) decreased; therefore, the relative concentration of Hf in the crystalline product increased. The question is then, why does the selectivity increase with an increase in the KF concentration up to 0.25 mol/L when the product purity decreases? This may be elucidated by further inspection of Figure 5, where it is clear that the Zr:Hf ratio in the liquid phase (xZr/xHf) simultaneously decreased slightly up to a KF concentration of 0.25 mol/L. Therefore, the concentration of Hf relative to Zr in the liquid phase (xHf) also increased, or, in other words, at higher KF concentration more Hf remained in solution with respect to the Zr which led to better separation of the two species with respect to the two phases. The simultaneous increase of zHf and xHf seems to be erroneous; therefore, the additional experiments were performed to determine whether mass balance conditions were satisfied (Supporting Information, section 2). The results hereof (Supporting Information, section 3) have shown that the simultaneous decrease of both mole fraction ratios zZr/zHf (solid phase) and xZr/xHf (liquid phase) are justified, where the purity of the crystalline phase is also influenced by the product yield. Returning to Figure 5, it is evident that, with further increase in the KF concentration, i.e., beyond 0.25 mol/L KF, the ratio zZr/zHf continued to decrease while the ratio xZr/xHf increased. Therefore, xHf decreased with respect to xZr, and zHf increased with respect to zZr implying that more and more Hf was transferred to the solid phase with increasing KF concentration, be it by solid solution formation or cocrystallization. Finally, for crystallization from a KF solution with a concentration of 0.5 mol/L, the mole fraction ratios xZr/xHf and zZr/zHf were nearly equal, leading to the value for βHf,Zr of 0.76. Therefore, with

increasing KF concentration, crystal growth became less selective due to the increased incorporation of Hf in the crystalline product relative to that of Zr. SEM images of the crystals obtained by crystallization from solutions with different KF concentrations are shown in Figure 6. According to the images, needle-shaped crystals were formed at KF concentrations up to 0.25 mol/L, where better separation was also obtained. With increasing KF concentration, i.e., where the selectivity decreased, the crystal size decreased significantly as shown in Figure 6B,C. The crystal morphology also changed, i.e., from thin needles to a more spherical shape which led to the formation of large agglomerates, shown in Figure 6D. The decrease in the crystal size with increasing KF concentration (above 0.25 mol/L) may be related to changes in the nucleation rate,23 although it has been shown that adsorption of the additive on the growing crystal surface can affect the growth process,22 which can then also lead to a decrease in the crystal size. Thus, the gradual decrease in the crystal purity (Figure 5) and selectivity (Figure 4) above a KF concentration of 0.25 mol/L could be caused by an increased nucleation rate, although in depth kinetic studies are required to further investigate this issue. Representative results of XRD analyses of the product crystals, with possible identifications (according to the 2007 Relational Database of the International Centre for Diffraction Data), are shown in Figure 7A,B. In Figure 7A, the sample pattern corresponds quite well with the low-angle peaks (10° < 2θ < 50°) of all the possible compounds, whereas the lowintensity peaks of the sample at higher angles might indicate the presence of orthorhombic K2ZrF6. The results therefore show that, in addition to the orthorhombic crystal structure that we

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Figure 8. Measured distribution coefficient during crystallization of K2Zr(Hf)F6 from aqueous solutions of KF with varying concentration with a constant HF concentration of 2.5 mol/L: ), crystallization from pure H2O solution.

Figure 7. Results of XRD analyses of the crystalline products obtained by crystallization from a 0.2 (A) and a 0.4 mol/L KF solution (B). The number codes represent the identification number of each compound according to the structural library that was used.

have used in our previous work to model solid solutions of K2Zr(1-z)HfzF6 to evaluate the role of the solid-state thermodynamics on the selectivity,18 occurrence of the monoclinic structures is also possible (Figure 7A). As shown in Figure 7B, occurrence of the cubic heptafluorides is possible at higher KF concentrations (sample peaks at 2θ values of 28, 44, and 50° correspond with that of K3ZrF7 and K3HfF7), which is probably the reason for the significant change in the appearance of the crystals shown in Figure 6D. The formation of the heptafluorides could therefore also be the reason for the drastic change in the selectivity (Figure 4) beyond a KF concentration of 0.3 mol/L. The possibility of heptafluoride formation (crystallization of K3Zr(Hf)F7 instead of K2Zr(Hf)F6), during crystallization from solutions with high KF concentrations, was investigated by ICPOES analysis (section 2.5.2), and the results thereof are discussed in section 3.3.2. In summary, it was shown from the ICP-OES analyses, SEM, and XRD results that the following two factors can influence the selectivity during crystallization of K2Zr(Hf)F6 from solution: solution chemistry and the crystallizing compound (i.e., hexafluoride vs heptafluoride). It was shown that at KF concentrations lower than 0.25 mol/L there is a gradual increase in the selectivity with increasing KF concentration wherein the addition of KF to the solution might therefore influence the formation of the elementary units (Zr(IV) and Hf(IV) species) of the solid. Furthermore, according to the SEM and XRD results, the formation of the heptafluorides could occur at high KF concentrations. The heptafluoride (K3ZrF7)

Figure 9. Mole fraction ratio of Zr:Hf in both the solid (s) and liquid phases (aq) at equilibrium during crystallization of K2Zr(Hf)F6 from aqueous solutions of varying KF concentration with a constant HF concentration of 2.5 mol/L: 0 (light and medium light gray), crystallization from pure H2O.

has a different structure than the hexafluoride (K2ZrF6) and therefore a different morphology, which might explain the large particles seen in Figure 6D. The heptafluoride might be less selective toward rejection of the Hf impurity, which could help explain the poor selectivity obtained at high KF concentrations. 3.2.2. Crystallization of K2Zr(Hf)F6 from KF Solutions with HF Added. The results of crystallization from aqueous solutions with varying KF concentration with a constant HF concentration of 2.5 mol/L are shown in Figure 8. In comparison with the crystallization from pure H2O solution, the distribution coefficient decreased (selectivity improved) with increasing KF concentration, even beyond a concentration of 0.25 mol/L, when HF was present. With respect to the crystallization from only KF solutions, improved selectivity was therefore obtained, with an optimum selectivity of β ) 0.13 at a KF concentration of 0.45 mol/L. It seems that the negative effect of the high KF concentration as observed in Figure 4 is suppressed by HF. The corresponding mole fraction ratios are shown in Figure 9. Again, the errors associated with each value represent the average experimental error for the solid and liquid phases, respectively, and the initial Zr:Hf ratio in K2Zr(Hf)F6 before recrystallization (i.e., the starting material) is also shown as reference at the left side of the chart. The results show that the ratio xZr/xHf decreased with increasing KF concentration. Therefore, the Hf concentration in the liquid phase (xHf) increased relative to that of Zr (xZr). Thus, the Hf impurity is concentrated more effectively in the liquid phase with increasing KF concentration when HF is added. While the ratio zZr/zHf also

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Figure 10. SEM micrographs of the crystalline products obtained by crystallization from HF solutions (2.5 M) with KF concentrations of 0.2 (A), 0.4 (B), and 0.45 mol/L (C).

decreased with increasing KF concentration for the “KF crystallizations”, there was now an initial decrease with respect to the “H2O crystallzation”, while the ratio remained more or less constant with increased KF concentration. Thus, with HF as additive (in the presence of KF) less of the Hf impurity is incorporated into the solid phase, while its concentration in the liquid phase increased with respect to the Zr concentration as the KF concentration was increased. In comparison with crystallization from KF solutions, the addition of HF therefore causes the crystallization process to be more selective toward the desired compound (ZrF62-), whereby the Hf impurity is concentrated more effectively in the liquid phase as the KF concentration increased, leading to improved selectivity. Therefore, with the addition of HF, the relative degree of enrichment of the solid phase remained more or less constant with increasing KF concentration, which together with the improved retention of Hf in the mother liquor led to enhanced selectivity. SEM images of the crystals (Figure 10) indicate that there was no drastic change in crystal morphology during crystallization with increasing KF concentration in the presence of HF, contrary to the results obtained for crystallization in the absence of HF (see Figure 6). The crystal size did decrease slightly with increasing KF concentration, but not to the same extent as was observed for crystallization without HF (Figure 6). Results of XRD analysis of the crystalline product obtained by crystallization from a 2.5 mol/L HF solution with a KF concentration of 0.2 mol/L are shown in Figure 11, which serves as representative data for the crystallization of K2Zr(Hf)F6 from

Figure 11. Results of XRD analysis of the crystalline product obtained by crystallization from a 2.5 mol/L HF solution with a KF concentration of 0.2 mol/L. The graphs were modified to illustrate the peaks of lower intensity. The unmatched sample peaks below 2θ values of 10° may be attributed to noise that is displayed as peaks due to modification of the intensity axis.

2.5 mol/L HF solutions with increasing KF concentration. The cubic K3Zr(Hf)F7 were not detected with XRD analysis, although different modifications of both the monoclinic and orthorhombic structures of K2ZrF6 as well as K2HfF6 were again observed. The different monoclinic and orthorhombic possibilities are only small differences in the structures contained within the structural database which were matched to the acquired spectra by the system’s software. The fact that the cubic heptafluorides were not detected by XRD, even in the crystalline products obtained by crystallization

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Figure 12. Relative distribution coefficient for the crystallization of K2Zr(Hf)F6 from aqueous KF solutions with varying concentration at conditions of Σ ) 2.5 and Σ ) 5.

from solutions with high KF concentrations, confirms the SEM results, in that the formation of K3Zr(Hf)F7 is suppressed during crystallization from solutions of high KF concentration when HF is present in a sufficient amount. When HF is omitted, the formation of K3Zr(Hf)F7 is more likely, which is accompanied by a simultaneous decrease in the selectivity. This supports the hypothesis that the formation of the heptafluoride can lower the selectivity, as noted in the previous section. This inhibiting effect of HF toward the formation of K3Zr(Hf)F7 might be attributed to speciation effects, due to the excess amount of fluorine that is present when HF is added to the solutions, although more work is needed to better understand these chemical effects. The influence of KF and HF on the selectivity is investigated in more detail in the next section. 3.3. Cooling Crystallization Using a Controlled K2Zr(Hf)F6 Concentration. As explained in section 2.4, crystallization was performed using the conditions of Σ ) 2.5 and Σ ) 5 calculated according to eq 2. These values were chosen on the basis of the conditions that corresponded with the most efficient separation of the KF, and KF and HF series of crystallizations, i.e., at 0.25 mol/L KF (section 3.2.1) and 0.45 mol/L KF in the presence of 2.5 mol/L HF (section 3.2.2). The solubility of K2Zr(Hf)F6 at 15 °C in a solution of these compositions were calculated by extrapolation of the data presented in section 3.1. Using eq 2, the value of Σ was then calculated to be 5.29 for crystallization from a 0.25 mol/L KF solution, and Σ ) 5.52 was obtained for crystallization from a 0.45 mol/L KF with 2.5 mol/L HF solution, where in both cases a total K2Zr(Hf)F6 concentration of 20 g/(500 mL) was used. Because the most efficient separation was obtained by crystallization from a 0.25 mol/L KF solution and a 0.45 mol/L KF with 2.5 mol/L HF solution, it seems that optimum separation was obtained for Σ ) 5. For the crystallization of K2Zr(Hf)F6 from H2O; Σ is approximately equal to 2 (also for a K2Zr(Hf)F6 concentration of 20 g/(500 mL). Consequently, Σ ) 2.5 and Σ ) 5 was chosen for these controlled K2Zr(Hf)F6 concentration experiments (by varying the concentration according to the solubility), whereby the effect of the solvent composition and the relative excess amount of solute, as characterized by Σ, was evaluated in more detail, while simultaneously attempting, qualitatively, to eliminate kinetic effects on the crystallization process (as solvent composition is changed) and thus the selectivity, βHf,Zr. 3.3.1. Crystallization of K2Zr(Hf)F6 from KF Solutions. The results for crystallization from KF solutions with increasing concentration are shown in Figure 12 for Σ ) 2.5 and Σ ) 5 (which are abbreviated by Σ2.5 and Σ5). With crystallization from

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Figure 13. Results of XRD analysis of the crystalline product obtained by crystallization from a 0.5 mol/L KF solution with Σ ) 2.5.

solutions of low KF concentration, i.e., below 0.3 mol/L, it can be seen from the figure that the KF concentration has a relatively small influence on the selectivity. With an increased relative excess of the salt (Σ5), however, there seems to be an improvement in the selectivity as characterized by the decrease in the value of βHf,Zr. With crystallization from KF solutions of higher concentration, i.e., above 0.3 mol/L KF, the effect of Σ appears to be negligible and the KF concentration is evidently the determining factor. Therefore, for crystallization from KF solutions with increasing concentration for which a constant K2Zr(Hf)F6 concentration was used (section 3.2.1), the selectivity did not decline because of an increased relative amount of solute but, as these results show, was caused by the increased KF concentration. Furthermore, during the crystallization from the 0.5 mol/L KF solution, poor selectivity was obtained at both Σ2.5 and Σ5, which is comparable to the results obtained with the crystallization using a constant K2Zr(Hf)F6 concentration. Therefore, according to these results, the selectivity is partially controlled by the relative excess amount of solute, as characterized by the value of Σ. During crystallization from solutions with increased KF concentration, this effect is overshadowed by the high KF concentration which leads to poor selectivity. SEM micrographs of the crystals obtained from both the Σ2.5 and Σ5 experiments (not shown), indicated that the same transition in the appearance of the crystals that was observed for crystallization with a constant K2Zr(Hf)F6 concentration with increasing KF concentration, as shown in Figure 6, section 3.2.1, also occurred at these conditions. Therefore, the change in crystal size and structure is independent of the relative excess amount of solute, characterized by Σ, but is rather caused by the increased KF concentration of the solution. XRD results, of which representative data are shown in Figure 13, indicate that the formation of K3Zr(Hf)F7 is probable when the KF concentration is 0.5 mol/L. Therefore, the formation of the heptafluorides is also not determined by the relative excess amount of solute but is rather caused by the high KF concentration. The XRD results also indicate that the formation of an oxyfluoride is possible during crystallization from 0.5 mol/L KF solutions which also has a cubic crystal structure. Nevertheless, it is evident from these results that poor selectivity is obtained when crystallization of K3Zr(Hf)F7 occurs, which is induced by a high KF concentration of the solution and overshadows the effect of Σ at such high concentrations. The identification of the heptafluorides in the crystalline products, obtained by crystallization from KF solutions with high

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Figure 14. Relative distribution coefficient for the crystallization of K2Zr(Hf)F6 from aqueous KF solutions with varying concentration with a constant HF concentration of 2.5 mol/L, at conditions of Σ ) 2.5 and Σ ) 5.

concentrations, by XRD analysis are supported by ICP-OES analysis which is discussed in the next section (section 3.3.2). This leads one to believe that the heptafluoride crystal structure is less selective toward rejection of the Hf impurity. 3.3.2. Crystallization of K2Zr(Hf)F6 from KF Solutions with HF Added. The results of crystallization from KF solutions with increasing concentration with a constant HF concentration (2.5 mol/L), shown in Figure 14, indicate that, in comparison with the crystallization from H2O, the selectivity improved slightly. The KF concentration appears to have a negligible influence on the selectivity as the value of βHf,Zr remained constant, while the KF concentration was increased (Figure 14). The relative excess amount of solute however had a significant influence on the selectivity, where the separation improved noticeably with a 2-fold increase in Σ. In light of the crystallization from only KF solutions, it is evident that the addition of HF regulates the effects of the KF concentration. Thus, when HF is added, the selectivity is controlled mainly by the relative excess amount of solute, as characterized by the value of Σ, and not by the KF concentration. When crystallization was performed from 2.5 mol/L HF solutions with increasing KF concentration using a constant K2Zr(Hf)F6 concentration (section 3.2.2), Σ increased because of the decrease in the solubility of K2Zr(Hf)F6 with increasing KF concentration. It is by this effect that the selectivity improved for crystallization from 2.5 mol/L HF solutions with increasing KF concentration when a constant K2Zr(Hf)F6 concentration was used. It is possible that the relative excess amount of solute also controls the onset of the crystallization process, which could affect the growth process. Therefore, seeding could possibly be used as a method of crystallization to further regulate the selectivity of the crystallization process. The inhibiting effect of HF toward the decrease of the crystal size and the formation of K3Zr(Hf)F7 that is caused by a high KF concentration becomes apparent when studying the SEM and XRD results. First, SEM micrographs of the crystals obtained from both the Σ2.5 and Σ5 experiments (not shown) correlate with those presented in Figure 10, wherein the crystal size and morphology were retained, regardless of the increase in the KF concentration. Second, the XRD analysis of the product crystals of both the Σ2.5 and Σ5 experiments yielded the same results as those presented in Figure 11, confirming the SEM results in that none of the heptafluorides were detected, even for the crystals produced by crystallization from a solution of 0.5 mol/L KF with 2.5 mol/L HF at both Σ2.5 and Σ5. ICP-OES analyses were used to determine the potassium concentrations in the crystalline products (section 2.5.2) of the

Figure 15. K/Zr concentration ratios as determined by ICP-OES analyses of the solid products obtained by crystallization from KF solutions with increasing concentration at Σ2.5 (A) and crystallization from 2.5 mol/L HF solutions with increasing KF concentration (B) at Σ5: black, precrystallized K2Zr(Hf)F6 (Sigma-Aldrich); dark gray, crystallization from H2O solution; light gray, crystallization from solutions with increasing KF concentration with and without HF with a concentration of 2.5 mol/L.

varying K2Zr(Hf)F6 concentration experiments. From this data the K/Zr concentration ratios (mg · L-1/mg · L-1) were calculated and compared to the XRD results. The results for crystallization from KF solutions with increasing concentration at Σ2.5 and crystallization from 2.5 mol/L HF solutions with increasing KF concentration at Σ5 are shown in Figure 15A,B, respectively. The solid and dashed lines represent the theoretical K/Zr ratios (mass ratios) for K2ZrF6 and K3ZrF7, respectively, which were calculated using the molecular weights of the two elements. The results indicate that the formation of the heptafluoride may have occurred for the crystallization from KF solutions with concentrations equal to and larger than 0.3 mol/L (Figure 15A). In the presence of HF, however, the heptafluorides do not seem to form irrespective of the KF concentration, since the observed K/Zr ratios remained below the threshold which corresponds to the heptafluorides (Figure 15B). These results therefore support the XRD results with respect to the inhibition of the formation of the heptafluorides by HF during crystallization from aqueous solutions of high KF concentrations. It is therefore clear that the addition of HF to an unsaturated solution of K2Zr(Hf)F6 and KF restricts the influence that KF has on the crystallization process. Furthermore, during crystallization of K2Zr(Hf)F6 from KF solutions (wherein a constant salt concentration was used despite the increase in the KF concentration), the addition of HF caused a gradual increase in the relative excess amount of solute with increasing KF concentration. In light of the results presented in this section and section 3.3.1, the increased relative excess amount of solute resulted in improved selectivity. Therefore, in accordance with the results presented in section 3.3.1, the relative distribution

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coefficient, and therefore the selectivity, is dependent on the relative excess amount of solute, as characterized by the value of Σ. It should be noted that the relative distribution coefficient measured in this study (eq 3) is an effective, or average, distribution coefficient, because the composition of the crystals at the growing interface, as well as the solution, changes during the course of crystallization, and here only the ratio of the compositions of the liquid and crystalline phases for the completed crystallization process was measured. The value of βHf,Zr (effective distribution coefficient) is, in principle, influenced by the degree of crystallization (degree to which the solution is depleted of nutrients), which is related to Σ and therefore also contributes to the dependence of the selectivity of Zr and Hf separation on Σ. 4. Conclusions It was shown experimentally that Zr enrichment can be obtained by fractional crystallization of K2Zr(Hf)F6 from aqueous solutions and that the selectivity of Zr-Hf separation is influenced by various factors that are in turn affected by the solution composition. The selectivity is still relatively poor, however, which could be attributed to solid solution formation, as discussed in our previous work. SEM results have shown that crystallization from KF solutions of high concentrations resulted in a decrease in the crystal size and a change in the crystal shape and appearance (i.e., formation of large rounded particles), which also correlated with a decrease in the selectivity. Using XRD analysis, it was shown that the formation of the large agglomerates at the high KF concentrations was likely caused by the crystallization of K3Zr(Hf)F7 instead of K2Zr(Hf)F6. However, with the addition of HF (2.5 mol/L) to the crystallization solution, it was found, based on the XRD results, and confirmed by ICP-OES analyses, that the formation of K3Zr(Hf)F7 was inhibited at high KF concentrations, which correlated with the SEM results that showed that the crystal size and morphology remained nearly unchanged with increasing KF concentration. Consequently, the use of HF as additive, together with KF, resulted in improved selectivity in comparison with crystallization from solutions of high KF concentrations without HF, as well as crystallization from only an H2O solution. By controlling the relative excess amount of solute (thus also the supersaturation), as characterized by the value of Σ, for crystallization of K2Zr(Hf)F6 from KF solutions of varying concentration, it was shown by the SEM and XRD results that the change in crystal size and structure could be attributed to the increased KF concentrations and not the relative excess amount of solute. The results of these experiments also confirmed the inhibiting effect of HF toward the formation of small crystallites and the heptafluoride structure during crystallization from aqueous KF solutions. Due to its apparent influence on the crystal size, the KF concentration may also influence the kinetics of crystallization, although further research is needed to elucidate this phenomenon. Nevertheless, it is clear that the formation of small crystallites and the crystallization of K3Zr(Hf)F7, when high KF concentrations are used, are suppressed by the addition of HF, which evidently also promotes improved selectivity with regard to Zr and Hf. Most importantly, however, it was shown that improved selectivity could be obtained when using a higher relative excess amount of solute, i.e. higher value of Σ, for crystallization from KF solutions with varying concentration both

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with and without HF. The selectivity is therefore related to the degree of crystallization, because the crystallization medium is exhausted of nutrients to a larger degree, due to the decreased solubility of K2Zr(Hf)F6 when KF and HF are used as additives. Without measurement of the purecomponent solubilities of K2ZrF6 and K2HfF6, it could not be deduced whether the use of KF and HF as additives influences the solubility ratio of Zr(IV) and Hf(IV), which would affect the degree of solid solution formation and therefore selectivity, as shown in previous studies of other isomorphic systems. Following the favorable change in selectivity when using the appropriate KF and HF concentrations, it would seem, however, that solid solution formation might indeed be limited to some degree by varying the solution composition. It can be concluded, however, that KF and HF can be used together to affect the solution composition such that the total solubility of K2Zr(Hf)F6 decreases, leading to an increased relative amount of solute and a higher degree of crystallization that causes a noticeable increase in the selectivity with increasing KF concentration. Also, an increased relative amount of solute might cause a shift in the onset of crystallization that could affect the crystallization equilibria. Therefore, seeding could possibly be used to further regulate the selectivity of the crystallization process. Acknowledgment We greatly acknowledge the financial support received from The New Metals Development Network (NMDN) of the Advanced Metals Initiative (AMI), funded by the South African Department of Science and Technology (DST), as coordinated by Dr. J.T. Nel and Dr. E. Snyders from the South African Nuclear Energy Corporation Limited (Necsa). We also thank Dr. R.J. Kriek for coordinating the ICP analytical facilities, Dr. L.R. Tiedt at the Laboratory for Electron Microscopy, NorthWest University for taking SEM images, Mr. J.H. Broodryk, Instrument-making, North-West University, for constructing the crystallization vessels, and Mrs. B. Venter, at the XRD laboratory of the Geology department, North-West University, for performing the XRD analyses. Supporting Information Available: (1) Sample preparation for ICP-OES analyses, (2) experimental method used for testing mass balance conditions, and (3) results of mass balance experiments, including a mathematical derivation for an appropriate equation. This information is available free of charge via the Internet at http://pubs.acs.org. Nomenclature c ) solute concentration, g/(100 mL of solvent) csat. ) saturation concentration (solubility) of component, g/(100 mL of solvent) csat.(T1) ) total solubility of impure solute at temperature T1, g/(500 mL of solvent) c(T2) ) concentration of the dissolved solute at temperature T2, g/(500 mL of solvent) T ) temperature, K or °C xi ) mole fraction of component i in the liquid phase zi ) mole fraction of component i in the solid phase Greek Symbols βHf,Zr ) relative distribution coefficient of Hf(IV) relative to Zr(IV) σ ) relative supersaturation Σ ) relative excess amount of solute at T2 relative to T1

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ReceiVed for reView May 8, 2009 ReVised manuscript receiVed October 28, 2009 Accepted November 17, 2009 IE900747K