Corresponding States for Volumes of Elemental Solids at Their Pressures of Polymorphic Transformations
Abstract
:1. Introduction
2. Materials and Methods
3. Results
4. Discussion
4.1. Theoretical Explanation
4.2. Molecular Gap and Forbidden Zone
Phase | Ptr [GPa] | Vtr/L [Å3/at] | Vtr [Å3/at] | Reference(s) |
---|---|---|---|---|
Li-fcc | 7.5(1) | 7.6(1) | 15.2(2) | [33,34,35] |
Li-hR1 | 39.7(1.0) | 4.6(1) | 9.2(2) | [34,36] |
Li-c16 | 48(2) | 4.4 | 8.8(4) | [34,35] |
Li-oC40 | 67(2) | 3.4(1) | 6.8(2) | [35] |
Li-oC24 | 97(3) | 3.3(2) | 6.6(4) | [35] |
Na-fcc | 67(1) | 4.10(5) | 12.3(30) | [36] |
Na-cI16 | 115(2) | 3.26(1) | 9.77(3) | [3] |
Na-oP8 | 119(2) | 3.15(1) | 9.45(6) | [3] |
Na-h4p | 200(8) | 2.7(1) | 8.1(3) | [2] |
K-fcc | 11.0(5) | 8.4(1) | 33.74(4) | [37] |
K-III | 22(43) | 5.64(5) | 22.57(3) | [5] |
K-IIIb | 31(2) | 5.2(2) | 20.8(4) | [38] |
K-IV (oP8) | 54(2) | 3.69(1) | 14.78(4) | [39] |
Rb-II | 7.0(5) | 7.13(6) | 35.65(30) | [37] |
Rb-III | 14.3(2) | 6.95(1) | 34.77(5) | [5] |
Rb-IV | 16.7(1) | 5.56(1) | 27.8(15) | [5,40] |
Rb-V | 19.6(5) | 5.2(1) | 26.0(5) | [41] |
Rb-VI | 48.1(5) | 3.6(3) | 18.0(1.5) | [41] |
Rb-VII | >70 | 3.4(1) | 17(1) | [41] |
Rb-VIII | 220(15) | 2.4(1) | 12(1) | [41] |
Cs-II | 2.37(1) | 8.58(1) | 51.47(6) | [42] |
Cs-III | 4.20(2) | 8.37(1) | 50.22(6) | [5] |
Cs-IV | 4.30(2) | 5.83(1) | 32.28(6) | [43] |
Cs-V | 10(1) | 5.1(2) | 30.6(1.2) | [44] |
Cs-VI | 72(2) | 2.6(2) | 15.6(1.2) | [44,45] |
Mg-bcc | 47(2) | 4.63(3) | 13.9(2) | [46] |
Ca-II | 19.5(15) | 8.02(2) | 32.08(8) | [47,48] |
Ca-III | 35(3) | 5.0(1) | 19.9(4) | [49,50] |
Ca-IV | 124(10) | 3.0(2) | 12.0(8) | [50] |
Ca-V/VI | 155(15) | 2.5(2) | 10.0(8) | [50] |
Ca-VII | 170 * | 2.0 * | 8 | this work |
Sr-II | 3.5(2) | 8.30(8) | 41.5(4) | [48] |
Sr-III | 26.0(6) | 3.98(19) | 19.9(9) | [5,49] |
Sr-IV | 35(1) | 4.1(2) | 20.5(10) | [5,49,51] |
Sr-V | 46(3) | 3.5(1) | 17.5(5) | [5,49,51] |
Ba-II | 5.5(1) | 7.14(4) | 42.84(24) | [48] |
Ba-IV | 12.6(1) | 7.0(1) | 42.0(6) | [52] |
Ba-V | 45(2) | 3.5(1) | 21.0(6) | [53] |
Sc-II | 20(1) | 4.5(1) | 18.0(4) | [54] |
Sc-III | 104(5) | 3.02(2) * | 12.08(8) | [54] |
Sc-IV | 140(10) | 2.58(27) * | 10.3(1.1) | [54] |
Sc-V | 240(10) | 2.09(7) | 3.36(28) | [19] |
ω-Zr | 12.5(10) | 4.15(5) | 20.75(25) | [55] |
Zr-bcc | 35(2) | 3.5(10) | 17.5(50) | [55,56] |
Zr-bccII | 58–60 | 3.08(5) | 15.4(3) | [55] |
ω-Ti | 0(5) | 4.375(15) | 17.5(6) | [20] |
γ-Ti | 110(10) | 2.55(5) | 10.2(2) | [20,21] |
δ-Ti | 150(10) | 2.41(5) | 9.64(20) | [20,21] |
Ti-bcc | 243(10) | 2.07(3) | 8.28(12) | [21] |
Vrhombohedral | 250(20) | 2.02(5) | 8.08(20) | [57] |
Fe-hcp | 17.6(1) | 2.57(1) | 10.28(4) | [58] |
Os-hcpII | 140(10) | 1.88(10) | 11.28(60) | [22] |
Os-hcpIII | 440(20) | 1.5(1) | 9.0(6) | [22] |
Sn-bct | 10.8(1) | 4.60(1) | 23.00(5) | [59] |
Sn-bco | 32.5(10) | 3.93(1) | 19.65(5) | [59] |
Sn-bcc | 40.8(15) | 3.78(1) | 18.9(5) | [59] |
Pb-hcp | 14(1) | 6.95(10) | 41.7(6) | [60] |
Pb-bcc | 142(10) | 2.68(2) | 16.08(12) | [5,61] |
Ga-II | 2.0(2) | 4.52(8) | 18.08(32) | [5] |
Ga-III | 2.8(1) | 4.24(5) | 16.96(24) | [62] |
Ga-V | 10.5(2) | 4.358(5) | 17.432(24) | [5] |
Ga-IV | 120(10) | 2.3(1)* | 9.2(4) | [62,63] |
Tl-fcc | 3.5(5) | 4.3(2) | 25.8(1.2) | [64] |
Ge-II | 10.6 | 4.28(8) | 17.12(32) | [65] |
Ge-hp | 75(3) | 3.18(10) | 17.72(40) | [18,66] |
Ge-Cmca | 140(120–160) * | 2.68(7) | 10.72(28) | [66] |
Ge-hcp | >170 | 2.4(1) | 9.6(4) | [18] |
Diamond | 2.0(1) | 2.837(1) | 5.674(2) | [67] |
Si-II | 12(1) | 4.3(1) | 12.9(3) | [68] |
Si-V | 16(2) | 4.43(2) | 13.29(6) | [69] |
Si-VI | 38(2) | 3.83(1) | 11.49(3) | [69] |
Si-VII | 42(2) | 3.71(2) | 11.13(6) | [69] |
N, cg-phase | 110(7) | 2.58(3) | 5.16(6) | [28] |
P-A7 | 4.5(1) | 5.03(5) | 15.09(15) | [70] |
P-sc | 10(1) | 4.54(2) | 13.62(6) | [70] |
P-ph | 140(8) | 2.8(1) | 8.4(3) | [70] |
P-bcc | 280(20) | 2.4(1) | 7.2(3) | [70] |
As-sc | 25(1) | 4.1(1) | 16.4(4) | [18] |
As-III | 46(3) | 3.5(1) | 14.0(4) | [18] |
As-IV | 125(10) | 2.84(2) | 11.36(8) | [18] |
Sb-II | 8.6(2) | 4.42(20) | 22.1(1) | [71] |
Sb-V | 28(3) | 4.05(6) | 20.25(30) | [71] |
Bi-II | 2.55(1) | 5.30(2) | 31.80(12) | [8] |
Bi-III | 2.70(1) | 4.48(9) | 26.88(54) | [8] |
Bi-V | 7.7(1) | 4.57(10) | 27.42(60) | [8] |
S-II | 3.0(2) | 7.0(1) | 21.0(3) | [72] |
S-III | 38(2) | 4.6(1) | 13.8(3) | [72] |
S-IV | 103(6) | 3.3(1) | 9.9(3) | [72] |
S-V | 150(10) | 2.8(1) | 8.4(3) | [72] |
Se-VII | 14(1) | 4.5(1) | 18.0(4) | [72] |
Se-III | 26(1) | 4.25(7) | 17.0(3) | [72] |
Se-IV | 35(1) | 3.8(1) | 15.2(4) | [72] |
Se-V | 77(2) | 4.0(1) | 16.0(4) | [72] |
Se-VI | 136(7) | 2.87(7) | 11.48(28) | [18] |
Te-II | 4.0(1) | 5.56(1) | 27.80(5) | [5,73] |
Te-III | 7.4(1) | 5.40(1) | 27.00(5) | [5,73] |
Te-V | 29.2(7) | 4.25(2) | 21.25(10) | [5,73] |
Te-VI | 102(5) | 3.3(2) | 16.5(1) | [74] |
I-bct | 43(3) | 3.9(1) | 19.6(1) | [75,76] |
I-fcc | 55(4) | 3.78(2) | 18.9(1) | [75,76] |
Th-bct | 100(30) | 2.51(1) | 17.57(7) | [77] |
γ-Ce | 0.5(1) | 4.70(1) | 28.20(6) | [78] |
PrtI2 | 180(10) | 23.90(14) | [79] | |
Sm-dhcp | 0.4(1) | 5.51(1) | 33.06(6) | [80] |
Sm-hR9 | 13(1) | 4.2(1) | 25.2(6) | [81] |
Sm-oF8 | 90(10) | 2.45(8) | 14.70(48) | [81] |
Nd-oF8 | 100(10) | 2.30(4) | 13.80(24) | [82] |
Eu_IV | 31.5(20) | 3.32(2) | 19.9(1) | [83] |
Gd-dhcp | 9(3) | 4.3(1) | 26 | [84] |
Gd-fcc | 26(2) | 3.7(1) | 22.2(6) | [85] |
Gd-dfcc | 33(2) | 3.43(10) | 20.5(6) | [85] |
Gd-VIII | 60.5(3) | 2.86(10) | 17.15(61) | [85] |
Dy-hR9 | 2.5(2) | 4.79(1) | 28.74(6) | [86] |
Cl-IV | 266(10) | 2.77(6) | 8.31(18) | [29] |
Ir-II | 59 | 1.63(2) * | 9.78(12) | [5,87] |
5. Conclusions
Supplementary Materials
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Tschauner, O. Corresponding States for Volumes of Elemental Solids at Their Pressures of Polymorphic Transformations. Crystals 2022, 12, 1698. https://doi.org/10.3390/cryst12121698
Tschauner O. Corresponding States for Volumes of Elemental Solids at Their Pressures of Polymorphic Transformations. Crystals. 2022; 12(12):1698. https://doi.org/10.3390/cryst12121698
Chicago/Turabian StyleTschauner, Oliver. 2022. "Corresponding States for Volumes of Elemental Solids at Their Pressures of Polymorphic Transformations" Crystals 12, no. 12: 1698. https://doi.org/10.3390/cryst12121698