Abstract
Solubility of HfO2(am) was determined as a function of KHCO3 concentrations ranging from 0.001 mol·kg−1 to 0.1 mol·kg−1. The solubility of HfO2(am) increased dramatically with the increase in KHCO3 concentrations, indicating that Hf(IV) makes strong complexes with carbonate. Thermodynamic equilibrium constants for the formation of Hf-carbonate complexes were determined using both the Pitzer and SIT models. The dramatic increase in Hf concentrations with the increase in KHCO3 concentrations can best be described by the formation of Hf(OH−)2(CO3)22− and Hf(CO3)56−. The log10K0 values for the reactions [Hf4++2CO32−+2OH−⇌Hf(OH)2(CO3)22−] and [Hf4++5CO32−⇌Hf(CO3)56−], based on the SIT model, were determined to be 44.53±0.46 and 41.53±0.46, respectively, and based on the Pitzer model they were 44.56±0.48 and 40.20±0.48, respectively.
Acknowledgments
The experiments were conducted at Pacific Northwest National Laboratory (PNNL), Richland, WA. The authors acknowledge financial support from Japan Atomic Energy Agency to interpret the experimental data and draft this article. We thank Mr. Yuanxian Xia for help with the experimental work.
Appendix
Concentrations of different elements in 0.0036 μm filtrates from HfO2(am) suspensions equilibrated for 4 days in KHCO3 solutions.
| Sample | pH | log10 [Mi]((mol·dm−3)a | ||
|---|---|---|---|---|
| KHCO3 (initially added) | C | Hf | ||
| 601–4 | 9.328 | −3.000 | −3.072 | −9.336 |
| 602–4 | 8.855 | −2.398 | −2.471 | −8.268 |
| 603–4 | 8.715 | −2.000 | −2.002 | −7.413 |
| 604–4 | 8.440 | −1.699 | −1.727 | −6.052 |
| 605–4 | 8.317 | −1.398 | −1.475 | −4.494 |
| 606–4 | 8.254 | −1.155 | −1.288 | −3.676 |
| 607–4 | 8.249 | −1.000 | −1.061 | −3.184 |
| 608–4b | 8.298 | −0.699 | −0.781 | −2.675 |
| 609–4b | 8.385 | −0.398 | NV | −2.553 |
| 610–4b | 8.436 | −0.222 | NV | −2.534 |
| 611–4b | 8.422 | −0.097 | NV | −2.540 |
| 612–4b | 8.455 | 0.000 | NV | −2.536 |
aMi stands for KHCO3, C, or Hf concentrations. NV, no value.
bAll of the HfO2(am) solid that was initially added dissolved completely in these samples. Therefore, these samples cannot be used for thermodynamic analyses of data.
M4+ (where M=Th, U, Np, Pu, Zr, or Hf) 8-coordinate apparent cation radius (A°) and the values of equilibrium constants for the formation of M(CO3)56− and M(CO3)44− (data plotted in Figure 5).
| M4 + | Cation radius (r)a | 1/r2 | log10 β50b | log10 β40c | Reference |
|---|---|---|---|---|---|
| Th(IV) | 1.05 | 0.9070 | 31.00±0.7 | NV | [10] |
| U(IV) | 1.00 | 1.0000 | 34.00±0.9 | 35.12±0.93 | [8] |
| Np(IV) | 0.98 | 1.0412 | 35.62±1.07 | 38.91±0.55 | [8] |
| Pu(IV) | 0.96 | 1.0851 | 35.65±1.13 | 37±1.0 | [8] |
| Zr(IV) | 0.84 | 1.4172 | ~43d | 42.9±1.0e | [26] |
| Hf(IV) | 0.83 | 1.4516 | 41.53±0.46 | 40.16±0.24 | This study |
aM4+ 8-coordinate apparent cationic radii in A° from Shannon [25].
bEquilibrium constant for the reaction M4++5CO32−=M(CO3)56−.
cEquilibrium constant for the reaction M4++CO32−=M(CO3)44−. NV, No value.
dThe log10K0 value we calculate from the relationship in Figure 5a for the Zr reaction in this column is 41.3 as compared to an approximate value (~43) for this reaction reported by Pouchon et al. [26].
eValue calculated by Brown et al. [7] from the quoted reference.
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