Thermodynamic Assessment of the AF–CrF3 (A = Li, Na, K) and CrF2–CrF3 Systems
Abstract
:1. Introduction
2. Literature Review
2.1. Structural Data
2.2. Thermodynamic Data
Compound | (298.15 K) | (298.15 K) | (T/K)/(J·K−1·mol−1) = a + b·T + c·T2 + d·T−2 + e·T3 | T(K) | Ref. | ||||
---|---|---|---|---|---|---|---|---|---|
(kJ·mol−1) | (J·K−1·mol−1) | a | b | c | d | e | |||
LiF(Cr) | −616.931 | 35.66 | 43.30898 | 0.016312168 | 5.0470398 × 10−7 | −569123.6 | 298.15−2500 | [30] | |
LiF(l) | −598.654 | 42.96 | 64.183 | - | - | - | - | 298.15–6000 | [30] |
NaF(Cr) | −576.650 | 51.21 | 47.630 | 0.01479 | - | −464300 | - | 298.15–2500 | [30] |
NaF(l) | −557.730 | 52.75 | 72.989 | - | - | - | - | 298.15–6000 | [30] |
KF(Cr) | −568.606 | 66.55 | 68.757414 | −0.057756882 | 7.5404856 × 10−5 | −766718.34 | −2.3885627 × 10−8 | 298.15−2000 | [30] |
KF(l) | −554.374 | 67.77 | 71.965 | - | - | - | - | 298.15–6000 | [30] |
CrF2(Cr) | −781.8 | 86.87 | 76.68345 | 0.0105410 | −1.386756 × 10−9 | −1338373 | - | 298.15–1167 | [26,27] |
CrF2(l) | −764.692 | 86.308 | 100 | - | - | - | - | 1167–4000 | [25,26,27] |
CrF3(Cr) | −1160.0 | 93.88 | 75.86301 | 0.0404446 | −4.20805 × 10−6 | −782870 | - | 298.15–1100 | [25,26,27] |
CrF3(Cr) | - | - | 226.552 | −0.0870137 | 2.020701 × 10−5 | −49199760 | - | 1100–1698 | [26,27] |
CrF3(l) | −1125.281 | 83.0567 | 130 | - | - | - | - | 1698–2500 | [26,27] |
Cr2F5(Cr) | −1950.8 | 181.0 | 152.54646 | 0.05098565 | −4.20944 × 10−6 | −2121243 | - | 298.15–6000 | [26], this work |
Li3CrF6(Cr) | −3070.0 | 210.6 | 205.78995 | 0.089381104 | −2.69393806 × 10−6 | −2490240.8 | - | 298.15–1100 | [26], this work |
Li3CrF6(Cr) | - | - | 356.47894 | −0.038077196 | 2.172112194 × 10−5 | −50907130.8 | - | 1100−3000 | [26], this work |
NaCrF4(Cr) | −1777.5 | 156.2 | 123.49301 | 0.0552346 | −4.20805 × 10−6 | −1247170 | - | 298.15–3000 | [26], this work |
α—Na3CrF6(Cr) | −2935.9 | 314.5 | 218.75301 | 0.0848146 | −4.20805 × 10−6 | −2175770 | - | 298.15–913 | [26], this work |
β—Na3CrF6(Cr) | −2925.4 | 326.3 | 218.75301 | 0.0848146 | −4.20805 × 10−6 | −2175770 | - | 913–3000 | [26], this work |
Na5Cr3F14(Cr) | −6545.65 | 584.2 | 465.739030 | 0.1952838 | −1.262415 × 10−5 | −4670110 | - | 298.15–3000 | [26], this work |
α—KCrF4(Cr) | −1772.8 | 181.9 | 144.620424 | −0.017312282 | 7.1196806 × 10−5 | −1549588.34 | −2.3885627 × 10−8 | 298.15–1066 | [26], this work |
β—KCrF4(Cr) | −1768.8 | 185.9 | 144.620424 | −0.017312282 | 7.1196806 × 10−5 | −1549588.34 | −2.3885627 × 10−8 | 1066–3000 | [26], this work |
K2CrF5(Cr) | −2378.6 | 251.0 | 213.377838 | −0.075069164 | 1.4660166 × 10−4 | −2316306.68 | −4.7771254 × 10−8 | 298.15–3000 | [26], this work |
K2Cr5F17(Cr) | −7067.5 | 632.8 | 516.829878 | 0.086709236 | 1.2976946 × 10−4 | −5447786.68 | −4.7771254 × 10−8 | 298.15–3000 | [26], this work |
α—K3CrF6(Cr) | −2941.2 | 338.5 | 282.135252 | −0.132826046 | 2.2200652 × 10−4 | −3083025.02 | −7.1656881 × 10−8 | 298.15−499 | [26], this work |
β—K3CrF6(Cr) | −2925.0 | 371.3 | 282.135252 | −0.132826046 | 2.2200652 × 10−4 | −3083025.02 | −7.1656881 × 10−8 | 499–3000 | [26], this work |
2.3. Phase Diagram Data
2.3.1. CrF2−CrF3 System
2.3.2. AF−CrF3 (A = Li, Na, K) Binary Systems
3. Thermodynamic Modelling
3.1. Gibbs Energies of Pure Compounds
3.2. Solid Solutions
3.3. Liquid Solution
4. Results and Discussion
4.1. CrF2–CrF3
4.2. AF–CrF3 (A = Li, Na, K)
4.2.1. LiF−CrF3
4.2.2. NaF−CrF3
4.2.3. KF−CrF3
4.3. Excess Properties
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Compound | Symmetry | Space Group | a(Å) | b(Å) | c(Å) | (°) | Ref. |
---|---|---|---|---|---|---|---|
α—Li3CrF6 | Monoclinic | C2/c | 14.4058(10) | 8.6006(4) | 10.0122(6) | 94.714(5) | [9,10] |
β—Li3CrF6 | Orthorhombic | Pna21 | 9.5796(1) | 8.4071(1) | 4.9793(7) | 90 | [9,10] |
α—NaCrF4 | Monoclinic | P2/c | 7.862(2) | 5.328(2) | 7.406(2) | 101.65(4) | [11] |
β—NaCrF4 | Tetragonal | P4/mmm * | 15.330(5) | 5.330(5) | 6.279(3) | 90 | [12] |
Na3CrF6 | Monoclinic | P2/c | 5.46(1) | 5.68(1) | 7.88(1) | 90 | [13] |
α—Na5Cr3F14 | Monoclinic | P2/c | 10.5096(3) | 7.2253(2) | 7.2713(2) | 90.6753(7) | [14] |
β—Na5Cr3F14 | Orthorhombic | C222 | 10.49(1) | 10.19(1) | 10.21(1) | 90 | [15] |
γ—Na5Cr3F14 | Tetragonal | P422 | 7.32(2) | 7.32(2) | 10.24(2) | 90 | [15] |
KCrF4 | Orthorhombic | Pnma | 15.761(10) | 7.448(5) | 18.361(11) | 90 | [16,17] |
K2CrF5 | Orthorhombic | Pbcn | 7.334(2) | 12.804(4) | 20.151(5) | 90 | [18] |
K2Cr5F17 | Orthorhombic | Pmmm * | 12.56(1) | 7.25(1) | 7.36(1) | 90 | [19,20] |
γ—K3CrF6 | Cubic | 8.66(1) | 8.66(1) | 8.66(1) | 90 | [19] |
A | B | |||
---|---|---|---|---|
Li+ | Li+ | 6 | 6 | 3 |
Na+ | Na+ | 6 | 6 | 3 |
K+ | K+ | 6 | 6 | 3 |
Cr2+ | Cr3+ | 6 | 6 | 2.4 |
Li+ | Cr3+ | 2 | 6 | 2 |
Na+ | Cr3+ | 4 | 6 | 2.7 |
K+ | Cr3+ | 6 | 6 | 3 |
Equilibrium | Invariant Reaction | This Study (calc.) | Sturm et al. [23] | ||
---|---|---|---|---|---|
X(CrF3) | T/K | X(CrF3) | T/K | ||
Eutectic | CrF2(cr) + Cr2F5(cr) = L | 0.115 | 1104 | 0.14 * | 1103 ± 5 |
Peritectic | Cr2F5(ss) = CrF3(cr) + L | 0.28 | 1271 | 0.29 | 1272 ± 5 |
Equilibrium | Invariant Reaction | This Study (calc.) | De Kozak [15] | Yin et al. (calc.) [29] | |||
---|---|---|---|---|---|---|---|
X(CrF3) | T/K | X(CrF3) | T/K | X(CrF3) | T/K | ||
Eutectic | LiF(cr) + Li3CrF6(cr) = L | 0.136 | 1008 | 0.15 | 1003 | 0.148 | 1003 |
Congruent melting | Li3CrF6(cr) = L | 0.25 | 1111 | 0.25 | 1129 | 0.25 | 1125 |
Eutectic | Li3CrF6(cr) + CrF3(cr) = L | 0.363 | 1062 | 0.35 | 1059 | 0.354 | 1058 |
Equilibrium | Invariant Reaction | This Study (calc.) | De Kozak [15] | Yin et al. (calc.) [29] | |||
---|---|---|---|---|---|---|---|
X(CrF3) | T/K | X(CrF3) | T/K | X(CrF3) | T/K | ||
Eutectic | NaF(cr) + Na3CrF6(cr) = L | 0.106 | 1175 | 0.123 | 1166 | 0.114 | 1162 |
Congruent melting | Na3CrF6(cr) = L | 0.25 | 1385 | 0.25 | 1413 | 0.25 | 1416 |
Eutectic | Na5Cr3F14(cr) + Na3CrF6 = L | 0.371 | 1145 | - | - | 0.367 | 1142 |
Congruent melting | Na5Cr3F14(cr) = L | 0.375 | 1145 | - | - | 0.375 | 1142 |
Eutectic | Na5Cr3F14(cr) + NaCrF4 = L | 0.381 | 1144 | - | - | 0.383 | 1141 |
Peritectic | NaCrF4(cr) = L + CrF3(cr) | 0.5 | 1232 | 0.5 | 1234 | 0.5 | 1239 |
Equilibrium | Invariant Reaction | This Study (calc.) | De Kozak [15] | Yin et al. (calc.) [29] | |||
---|---|---|---|---|---|---|---|
X(CrF3) | T/K | X(CrF3) | T/K | X(CrF3) | T/K | ||
Eutectic | KF(cr) + K3CrF6(cr) = L | 0.041 | 1108 | 0.048 | 1115 | 0.045 | 1113 |
Congruent melting | K3CrF6(cr) = L | 0.25 | 1553 | 0.25 | 1553 | 0.25 | 1548 |
Peritectic | K2CrF5(cr) = K3CrF6(cr) + L | 0.333 | 1130 | 0.333 | 1133 | 0.333 | 1135 |
Eutectic | K2CrF5(cr) + KCrF4(cr) = L | 0.432 | 1112 | 0.45 | 1112 | 0.426 | 1107 |
Peritectic | KCrF4(cr)= K2Cr5F17(cr) + L | 0.50 | 1191 | 0.50 | 1200 | 0.50 | 1195 |
Peritectic | K2Cr5F17(cr) = L + CrF3(cr) | 0.714 | 1390 | 0.714 | 1390 | 0.714 | 1388 |
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Dumaire, T.; Konings, R.J.M.; Smith, A.L. Thermodynamic Assessment of the AF–CrF3 (A = Li, Na, K) and CrF2–CrF3 Systems. Thermo 2021, 1, 205-219. https://doi.org/10.3390/thermo1020014
Dumaire T, Konings RJM, Smith AL. Thermodynamic Assessment of the AF–CrF3 (A = Li, Na, K) and CrF2–CrF3 Systems. Thermo. 2021; 1(2):205-219. https://doi.org/10.3390/thermo1020014
Chicago/Turabian StyleDumaire, Thomas, Rudy J. M. Konings, and Anna Louise Smith. 2021. "Thermodynamic Assessment of the AF–CrF3 (A = Li, Na, K) and CrF2–CrF3 Systems" Thermo 1, no. 2: 205-219. https://doi.org/10.3390/thermo1020014
APA StyleDumaire, T., Konings, R. J. M., & Smith, A. L. (2021). Thermodynamic Assessment of the AF–CrF3 (A = Li, Na, K) and CrF2–CrF3 Systems. Thermo, 1(2), 205-219. https://doi.org/10.3390/thermo1020014