| Citation: | CHEN Kaile, WANG Yuechao, XU Yuanji, LIU Yu, XIAN Jiawei, WANG Lifang, JIAN Dan, LIU Haifeng, SONG Haifeng. First-Principles Study on the Multiphase Equation of State of Tin[J]. Chinese Journal of High Pressure Physics. doi: 10.11858/gywlxb.20251054 |
| [1] |
余克章. 锡(Sn)——金属在现代军事上的应用(十四) [J]. 金属世界, 1996(3): 18–19.
YU K Z. The use of metals in modern military applications (14): tin (Sn) [J]. Metal World, 1996(3): 18–19.
|
| [2] |
BUTTLER W T, WILLIAMS R J R, NAJJAR F M. Foreword to the special issue on ejecta [J]. Journal of Dynamic Behavior of Materials, 2017, 3(2): 151–155. doi: 10.1007/s40870-017-0120-8
|
| [3] |
DEFFRENNES G, FAURE P, BOTTIN F, et al. Tin (Sn) at high pressure: review, X-ray diffraction, DFT calculations, and Gibbs energy modeling [J]. Journal of Alloys and Compounds, 2022, 919: 165675. doi: 10.1016/j.jallcom.2022.165675
|
| [4] |
CHEN T, YUAN F B, LIU J C, et al. Modeling the high-pressure solid and liquid phases of tin from deep potentials with ab initio accuracy [J]. Physical Review Materials, 2023, 7(5): 053603. doi: 10.1103/PhysRevMaterials.7.053603
|
| [5] |
CORNELIUS B, TREIVISH S, ROSENTHAL Y, et al. The phenomenon of tin pest: a review [J]. Microelectronics Reliability, 2017, 79: 175–192. doi: 10.1016/j.microrel.2017.10.030
|
| [6] |
SALAMAT A, BRIGGS R, BOUVIER P, et al. High-pressure structural transformations of Sn up to 138 GPa: angle-dispersive synchrotron X-ray diffraction study [J]. Physical Review B, 2013, 88(10): 104104. doi: 10.1103/PhysRevB.88.104104
|
| [7] |
LIU M, LIU L G. Compressions and phase transitions of tin to half a megabar [J]. High Temperatures High Pressures, 1986, 18(1): 79–85.
|
| [8] |
OLIJNYK H, HOLZAPFEL W B. Phase transitions in Si, Ge and Sn under pressure [J]. Journal de Physique Colloques, 1984, 45(C8): 153–156. doi: 10.1051/jphyscol:1984828
|
| [9] |
DESGRENIERS S, VOHRA Y K, RUOFF A L. Tin at high pressure: an energy-dispersive X-ray-diffraction study to 120 GPa [J]. Physical Review B, 1989, 39(14): 10359–10361. doi: 10.1103/PhysRevB.39.10359
|
| [10] |
SMIRNOV N A. Ab initio calculations of the phase diagrams of tin and lead under pressures up to a few TPa [J]. Journal of Physics: Condensed Matter, 2021, 33(3): 035402. doi: 10.1088/1361-648X/abbbc5
|
| [11] |
MABIRE C, HÉREIL P L. Shock induced polymorphic transition and melting of tin [J]. AIP Conference Proceedings, 2000, 505(1): 93–96. doi: 10.1063/1.1303429
|
| [12] |
CHAUVIN C, ZUCCHINI F, DE BARROS D P. Study on phase transformation in tin under dynamic compression [C]//2019 15th Hypervelocity Impact Symposium. Destin: American Society of Mechanical Engineers, 2019: V001T09A006.
|
| [13] |
HU J B, ZHOU X M, DAI C D, et al. Shock-induced bct-bcc transition and melting of tin identified by sound velocity measurements [J]. Journal of Applied Physics, 2008, 104(8): 083520. doi: 10.1063/1.3003325
|
| [14] |
XU L, BI Y, LI X H, et al. Phase diagram of tin determined by sound velocity measurements on multi-anvil apparatus up to 5 GPa and 800 K [J]. Journal of Applied Physics, 2014, 115(16): 164903. doi: 10.1063/1.4872458
|
| [15] |
HAFNER J. Ab initio calculation of the pressure-induced A4→A5→2 (distorted)→A3 phase transitions in tin [J]. Physical Review B, 1974, 10(10): 4151–4160. doi: 10.1103/PhysRevB.10.4151
|
| [16] |
IHM J, COHEN M L. Equilibrium properties and the phase transition of grey and white tin [J]. Physical Review B, 1981, 23(4): 1576–1579. doi: 10.1103/PhysRevB.23.1576
|
| [17] |
REDDY P J, SUBRAHMANYAM S V. Dependence on temperature of elastic moduli of tin [J]. Nature, 1960, 185(4705): 29. doi: 10.1038/185029a0
|
| [18] |
PRICE D L, ROWE J M, NICKLOW R M. Lattice dynamics of grey tin and indium antimonide [J]. Physical Review B, 1971, 3(4): 1268–1279. doi: 10.1103/PhysRevB.3.1268
|
| [19] |
CUI S X, CAI L C, FENG W X, et al. First-principles study of phase transition of tin and lead under high pressure [J]. Physica Status Solidi (b), 2008, 245(1): 53–57. doi: 10.1002/pssb.200743240
|
| [20] |
CHEN C C, APPLETON R J, NYKIEL K, et al. How accurate is density functional theory at high pressures? [J]. Computational Materials Science, 2025, 247: 113458. doi: 10.1016/j.commatsci.2024.113458
|
| [21] |
PERDEW J P, RUZSINSZKY A, CSONKA G I, et al. Restoring the density-gradient expansion for exchange in solids and surfaces [J]. Physical Review Letters, 2008, 100(13): 136406. doi: 10.1103/PhysRevLett.100.136406
|
| [22] |
KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects [J]. Physical Review, 1965, 140(4A): A1133–A1138. doi: 10.1103/PhysRev.140.A1133
|
| [23] |
PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)] [J]. Physical Review Letters, 1997, 78(7): 1396. doi: 10.1103/PhysRevLett.78.1396
|
| [24] |
CORKILL J L, GARCA A, COHEN M L. Theoretical study of high-pressure phases of tin [J]. Physical Review B, 1991, 43(11): 9251–9254. doi: 10.1103/PhysRevB.43.9251
|
| [25] |
AGUADO A. First-principles study of elastic properties and pressure-induced phase transitions of Sn: LDA versus GGA results [J]. Physical Review B, 2003, 67(21): 212104. doi: 10.1103/PhysRevB.67.212104
|
| [26] |
YU C, LIU J Y, LU H, et al. Ab initio calculation of the properties and pressure induced transition of Sn [J]. Solid State Communications, 2006, 140(11/12): 538–543. doi: 10.1016/j.ssc.2006.09.026
|
| [27] |
SHAHI C, SUN J W, PERDEW J P. Accurate critical pressures for structural phase transitions of group Ⅳ, Ⅲ-Ⅴ, and Ⅱ-Ⅵ compounds from the SCAN density functional [J]. Physical Review B, 2018, 97(9): 094111. doi: 10.1103/PhysRevB.97.094111
|
| [28] |
ZHANG L, LI Y H, YU Y Y, et al. General construction of mean-field potential and its application to the multiphase equations of state of tin [J]. Physica B: Condensed Matter, 2011, 406(22): 4163–4169. doi: 10.1016/j.physb.2011.01.018
|
| [29] |
KRESSE G, JOUBERT D. From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Physical Review B, 1999, 59(3): 1758–1775. doi: 10.1103/PhysRevB.59.1758
|
| [30] |
DONG W, KRESSE G, FURTHMÜLLER J, et al. Chemisorption of H on Pd(111): an ab initio approach with ultrasoft pseudopotentials [J]. Physical Review B, 1996, 54(3): 2157–2166. doi: 10.1103/PhysRevB.54.2157
|
| [31] |
KRESSE G, FURTHMÜLLER J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set [J]. Computational Materials Science, 1996, 6(1): 15–50. doi: 10.1016/0927-0256(96)00008-0
|
| [32] |
MONKHORST H J, PACK J D. Special points for Brillouin-zone integrations [J]. Physical Review B, 1976, 13(12): 5188–5192. doi: 10.1103/PhysRevB.13.5188
|
| [33] |
BLÖCHL P E. Projector augmented-wave method [J]. Physical Review B, 1994, 50(24): 17953–17979. doi: 10.1103/PhysRevB.50.17953
|
| [34] |
SUN J W, RUZSINSZKY A, PERDEW J P. Strongly constrained and appropriately normed semilocal density functional [J]. Physical Review Letters, 2015, 115(3): 036402. doi: 10.1103/PhysRevLett.115.036402
|
| [35] |
METHFESSEL M, PAXTON A T. High-precision sampling for Brillouin-zone integration in metals [J]. Physical Review B, 1989, 40(6): 3616–3621. doi: 10.1103/PhysRevB.40.3616
|
| [36] |
WANG Y. Classical mean-field approach for thermodynamics: ab initio thermophysical properties of cerium [J]. Physical Review B, 2000, 61(18): R11863–R11866. doi: 10.1103/PhysRevB.61.R11863
|
| [37] |
WANG Y, LI L. Mean-field potential approach to thermodynamic properties of metal: Al as a prototype [J]. Physical Review B, 2000, 62(1): 196–202. doi: 10.1103/PhysRevB.62.196
|
| [38] |
WANG Y, AHUJA R, JOHANSSON B. Mean-field potential approach to the quasiharmonic theory of solids [J]. International Journal of Quantum Chemistry, 2004, 96(5): 501–506. doi: 10.1002/qua.10769
|
| [39] |
WANG Y, AHUJA R, JOHANSSON B. Melting of iron and other metals at Earth’s core conditions: a simplified computational approach [J]. Physical Review B, 2001, 65(1): 014104. doi: 10.1103/PhysRevB.65.014104
|
| [40] |
SLATER J C. Introduction to chemical physics [M]. New York: McGraw-Hill, 1939.
|
| [41] |
DUGDALE J S, MACDONALD D K C. The thermal expansion of solids [J]. Physical Review, 1953, 89(4): 832–834. doi: 10.1103/PhysRev.89.832
|
| [42] |
VASHCHENKO V Y, ZUBAREV V N. Concerning the Grüneisen constant [J]. Soviet Physics-Solid State, 1963, 5: 653–655.
|
| [43] |
SONG H F, LIU H F. Modified mean-field potential approach to thermodynamic properties of a low-symmetry crystal: beryllium as a prototype [J]. Physical Review B, 2007, 75(24): 245126. doi: 10.1103/PhysRevB.75.245126
|
| [44] |
SONG H F, TIAN M F, LIU H F, et al. Theoretical study on equation of state of porous Mo and Sn [J]. Chinese Physics Letters, 2014, 31(1): 016402. doi: 10.1088/0256-307X/31/1/016402
|
| [45] |
WANG W Y, ZHANG S Y, LI G N, et al. Artificial intelligence enabled smart design and manufacturing of advanced materials: the endless Frontier in Al+ era [J]. Materials Genome Engineering Advances, 2024, 2(3): e56. doi: 10.1002/mgea.56
|
| [46] |
YU W, CHONG X Y, LIANG Y X, et al. Discovering novel γ-γ′ Pt-Al superalloys via lattice stability in Pt3Al induced by local atomic environment distortion [J]. Acta Materialia, 2024, 281: 120413. doi: 10.1016/j.actamat.2024.120413
|
| [47] |
HAFNER J. Materials simulations using VASP—a quantum perspective to materials science [J]. Computer Physics Communications, 2007, 177(1/2): 6–13. doi: 10.1016/j.cpc.2007.02.045
|
| [48] |
ZHANG Q L, ZHANG P, SONG H F, et al. Mean-field potential calculations of high-pressure equation of state for BeO [J]. Chinese Physics B, 2008, 17(4): 1341–1348. doi: 10.1088/1674-1056/17/4/031
|
| [49] |
陈惠发, SALIPU A F. 弹性与塑性力学 [M]. 余天庆, 王勋文, 刘再华, 译. 北京: 中国建筑工业出版社, 2004.
CHEN H F, SALIPU A F. Elasticity and plasticity [M]. Translated by YU T Q, WANG X W, LIU Z H. Beijing: China Architecture Publishing & Building Press, 2004.
|
| [50] |
简单. 铀和二氧化铀状态方程与弹性模量计算 [D]. 绵阳: 中国工程物理研究院, 2020.
JIAN D. Calculation of equations of state and elastic modulus of uranium and uranium dioxide [D]. Mianyang: China Academy of Engineering Physics, 2020.
|
| [51] |
SWENSON C A. Equation of state of cubic solids; some generalizations [J]. Journal of Physics and Chemistry of Solids, 1968, 29(8): 1337–1348. doi: 10.1016/0022-3697(68)90185-6
|
| [52] |
WANG Y, WANG J J, ZHANG H, et al. A first-principles approach to finite temperature elastic constants [J]. Journal of Physics: Condensed Matter, 2010, 22(22): 225404. doi: 10.1088/0953-8984/22/22/225404
|
| [53] |
VOIGT W J T L. A determination of the elastic constants for beta-quartz lehrbuch de kristallphysik [J]. Terubner Leipzig, 1928, 40: 2856–2860.
|
| [54] |
REUSS A. Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals [J]. Zeitschrift fur Angewandte Mathematik und Mechanik, 1929, 9: 49–58. doi: 10.1002/zamm.19290090104
|
| [55] |
谭华. 实验冲击波物理导引 [M]. 北京: 国防工业出版社, 2007.
TAN H. Introduction to experimental shock-wave physics [M]. Beijing: National Defense Industry Press, 2007.
|
| [56] |
经福谦. 实验物态方程导引 [M]. 2版. 北京: 科学出版社, 1999.
JING F Q. Introduction to experimental equation of state [M]. 2nd ed. Beijing: Science Press, 1999.
|
| [57] |
CHEN S, SUN Y, DUAN Y H, et al. Phase stability, structural and elastic properties of C15-type Laves transition-metal compounds MCo2 from first-principles calculations [J]. Journal of Alloys and Compounds, 2015, 630: 202–208. doi: 10.1016/j.jallcom.2015.01.038
|
| [58] |
FENG J, XIAO B, WAN C L, et al. Electronic structure, mechanical properties and thermal conductivity of Ln2Zr2O7 (Ln=La, Pr, Nd, Sm, Eu and Gd) pyrochlore [J]. Acta Materialia, 2011, 59(4): 1742–1760. doi: 10.1016/j.actamat.2010.11.041
|
| [59] |
BIRCH F. Finite elastic strain of cubic crystals [J]. Physical Review, 1947, 71(11): 809–824. doi: 10.1103/PhysRev.71.809
|
| [60] |
BARRETT C S, MASSALSKI T B. Structure of metals: crystallographic methods, principles and data [M]. 3rd ed. Oxford: Pergamon, 1980.
|
| [61] |
KITTEL C. Introduction to solid state physics [M]. New York: Wiley, 1976.
|
| [62] |
BRANDES E A, BROOK G B. Smithells metals reference book [M]. 7th ed. Oxford: Butterworth-Heinemann, 2013.
|
| [63] |
CHEONG B H, CHANG K J. First-principles study of the structural properties of Sn under pressure [J]. Physical Review B, 1991, 44(9): 4103–4108. doi: 10.1103/PhysRevB.44.4103
|
| [64] |
TONKOV E Y, PONYATOVSKY E G. Phase transformations of elements under high pressure [M]. Boca Raton: CRC Press, 2005.
|
| [65] |
BARNETT J D, BEAN V E, HALL H T. X-ray diffraction studies on tin to 100 kilobars [J]. Journal of Applied Physics, 1966, 37(2): 875–877. doi: 10.1063/1.1708275
|
| [66] |
REHN D A, GREEFF C W, BURAKOVSKY L, et al. Multiphase tin equation of state using density functional theory [J]. Physical Review B, 2021, 103(18): 184102. doi: 10.1103/PhysRevB.103.184102
|
| [67] |
SALAMAT A, GARBARINO G, DEWAELE A, et al. Dense close-packed phase of tin above 157 GPa observed experimentally via angle-dispersive X-ray diffraction [J]. Physical Review B, 2011, 84(14): 140104. doi: 10.1103/PhysRevB.84.140104
|
| [68] |
RAMBERT N, SITAUD B, FAURE P. Equation d’état multiphase et courbe de fusion de l’étain sous pression: une nouvelle approche expérimentale: rapport CEA A-22F00-00-10 [R]. Gif-sur-Yvette: CEA, 2003.
|
| [69] |
FRÉVILLE R, DEWAELE A, GUIGNOT N, et al. High-pressure-high-temperature phase diagram of tin [J]. Physical Review B, 2024, 109(10): 104116. doi: 10.1103/PhysRevB.109.104116
|
| [70] |
KIEFER B, DUFFY T S, UCHIDA T, et al. Melting of tin at high pressures [EB/OL]. [2025-04-05]. https://www.researchgate.net/publication/267709650_Melting_of_Tin_at_High_Pressures.
|
| [71] |
MARSH S P. LASL shock Hugoniot data [M]. Berkeley : University of California Press, 1980.
|
| [72] |
BORN M. On the stability of crystal lattices. I [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1940, 36(2): 160–172. doi: 10.1017/S0305004100017138
|
| [73] |
BORN M, HUANG K. Dynamical theory of crystal lattices [M]. New York: Oxford University Press, 1996.
|
| [74] |
MOUHAT F, COUDERT F X. Necessary and sufficient elastic stability conditions in various crystal systems [J]. Physical Review B, 2014, 90(22): 224104. doi: 10.1103/PhysRevB.90.224104
|
| [75] |
PRICE D L, ROWE J M. The crystal dynamics of grey (α) tin at 90 °K [J]. Solid State Communications, 1969, 7(19): 1433–1438. doi: 10.1016/0038-1098(69)90318-4
|
| [76] |
BUCHENAUER C J, CARDONA M, POLLAK F H. Raman scattering in gray tin [J]. Physical Review B, 1971, 3(4): 1243–1244. doi: 10.1103/PhysRevB.3.1243
|
| [77] |
BRIDGMAN P W. The compressibility of thirty metals as a function of pressure and temperature [J]. Proceedings of the American Academy of Arts and Sciences, 1923, 58(5): 165–242. doi: 10.2307/20025987
|
| [78] |
BRIDGMAN P W. The viscosity of liquids under pressure [J]. Proceedings of the National Academy of Sciences of the United States of America, 1925, 11(10): 603–606. doi: 10.1073/pnas.11.10.603
|
| [79] |
PRASAD S C, WOOSTER W A. The study of the elastic constants of white tin by diffuse X-ray reflexion [J]. Acta Crystallographica, 1955, 8(11): 682–686. doi: 10.1107/S0365110X55002119
|
| [80] |
MASON W P, BÖMMEL H E. Ultrasonic attenuation at low temperatures for metals in the normal and superconducting states [J]. The Journal of the Acoustical Society of America, 1956, 28(5): 930–943. doi: 10.1121/1.1908524
|
| [81] |
HOUSE D G, VERNON E V. Determination of the elastic moduli of tin single crystals, and their variation with temperature [J]. British Journal of Applied Physics, 1960, 11(6): 254–259. doi: 10.1088/0508-3443/11/6/308
|
| [82] |
CARDINAL L C. NRL problem No: F03-01 [R]. Washington D C, USA: Naval Research Laboratory, 1963: 31.
|
| [83] |
KRAMER W, NÖLTING J. Anomale spezifische wärmen und fehlordnung der metalle indium, zinn, blei, zink, antimon und aluminium [J]. Acta Metallurgica, 1972, 20(12): 1353–1359. doi: 10.1016/0001-6160(72)90070-3
|
| [84] |
DU X P, ZHAO J C. Facile measurement of single-crystal elastic constants from polycrystalline samples [J]. NPJ Computational Materials, 2017, 3(1): 17. doi: 10.1038/s41524-017-0019-x
|
| [85] |
RAYNE J A, CHANDRASEKHAR B S. Elastic constants of beta tin from 4.2 K to 300 K [J]. Physical Review, 1960, 120(5): 1658–1663. doi: 10.1103/PhysRev.120.1658
|
| [86] |
KAMMER E W, CARDINAL L C, VOLD C L, et al. The elastic constants for single-crystal bismuth and tin from room temperature to the melting point [J]. Journal of Physics and Chemistry of Solids, 1972, 33(10): 1891–1898. doi: 10.1016/S0022-3697(72)80487-6
|
| [87] |
FURNISH M D, THADHANI N N, HORIE Y. Shock compression of condensed matter 2001 [C]//Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter. Melville: American Institute of Physics, 2002.
|