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Element bismuth (Bi) will experience complex phase transitions under high temperature and high pressure, which means significant changes in physical properties, such as density, energy, etc. Multiphase equations of states (EOSs) of both solid and liquid phases for Bi are presented. The EOSs are based on the three-term expression for Helmholtz free energy, where the ion vibration free energy is evaluated from the mean field potential model we recently proposed. The calculated results show that our multiphase EOSs can well reproduce the experimental data, including phase diagram, isotherms of solid phases, density measurements of liquid phase and shock-wave compression data, which proves the rationality of the parameter values and the universal nature of this model.
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Keywords:
- bismuth /
- multiphase equation of states /
- phase diagram /
- high temperature and high pressure
[1] Greeff C W 2005 Modelling Simul. Mater. Sci. Eng. 13 1015
[2] Pecker S, Eliezer S, Fisher D, Henis Z, Zinamon Z 2005 J. Appl. Phys. 98 043516
[3] Wang Y, Li L 2000 Phys. Rev. B 62 196
[4] Zhang L, Li Y H, Yu Y Y, Li X M, Ma Y, Gu C G, Dai C D, Cai L C 2011 Physica B 406 4163
[5] Pelissier J L, Wetta N 2001 Physica A 289 459
[6] Bundy F P 1958 Phys. Rev. 110 314
[7] Homan C G 1975 J. Phys. Chem. Solids 36 1249
[8] Tonkov E Yu 1992 High Pressure Transformations: A Handbook (1st Ed.) (London: Taylor-Francis) p109
[9] Aoki K, Fujiwara S, Kusakabe M 1982 J. Phys. Soc. Japan 51 3286
[10] Young D A 1991 Phase Diagrams of Elements (1st Ed.) (Berkeley: University of California Press)
[11] Akahama Y, Kawamura H, Singh A K 2002 J. Appl. Phys. 92 5892
[12] Yoneda A, Endo S 1980 J. Appl. Phys. 51 3216
[13] Chen J H, Iwasaki H, Kikegawa T, Yaoita K, Tsuji K 1994 High Pressure Science and Technology-1993 Colorado Springs, USA June 28-July 2, 1994 p421
[14] Chen J H, Iwasaki H, Kikegawa T 1996 High Press. Res. 15 143
[15] Gschneidner Jr K A 1964 Solid State Phys. 16 275
[16] Marsh S P 1980 LASL Shock Hugoniot Data (1st Ed.) (Berkeley: California University Press) p23
[17] Tan Y, Yu Y Y, Dai C D, Tan H, Wang Q S, Wang X 2011 Acta Phys. Sin. 60 106401 (in Chinese) [谭叶, 俞宇颖, 戴诚达,谭华,王青松,王翔 2011 60 106401]
[18] Asay J R 1977 J. Appl. Phys. 48 2832
[19] Cox G A 2007 Shock Compression of Condensed Matter Waikoloa, June 24-29, 2007 p151
[20] Pelissier J L, Wetta N 2001 Physica A 289 459
[21] Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2963
[22] Dugdale J S, MacDonald D K C 1953 Phys. Rev. 89 832
[23] Kittel C 2004 Introduction to Solid State Physics (8th Ed.) (New York: John Wiley and Sons) p131
[24] Degtyareva O, Mcmahon M I, Nelmes R J 2004 High Pressure Res. 24 319
[25] Hultgren R, Desai P D, Hawkins D T, Gleiser M, Kelley K K 1973 Selected Values of the Thermodynamic Properties of Binary Alloys (1st Ed.) (Ohio: ASM Metals Park) p41
[26] Klement Jr W, Jayaraman A, Kennedy G C 1963 Phys. Rev. 131 1632
[27] Bridegman P W 1935 Phys. Rev. 48 893
[28] Peerdeman S A G, Trappeniers N J, Schouten J A 1980 High Temp. High Pressures 12 67
[29] Chen J H, Kikegawa T, Shimomura O, Iwasaki H 1997 J. Synch. Rad. 4 21
[30] Degtyareva V F 2000 Phys. Rev. B 62 9
[31] Trunin R F, Zhernokletov M V, Kuznetsov N F, Shutov V V 1995 High Temp. 33 220
[32] Donohue J 1982 The Structures of the Elements (1st Ed.) (Florida: Robert E. Krieger Publishing Company)
[33] Greenberg Y, Yahel E, Caspi E N, Benmore C, Beuneu B, Dariel M P, Makov G 2009 Euro. Phys. Lett. 86 36004
[34] Alchagirov B B, Mozgovoi A G, Shamparov T M 2004 High Temp. 42 493
[35] Li J, Zhou X M, Li J B, Li S N, Zhu W J, Wang X, Jing F Q 2007 Acta Phys. Sin. 56 6557 (in Chinese) [李俊, 周显明, 李加波, 李赛男, 祝文军, 王翔, 经福谦 2007 56 6557]
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[1] Greeff C W 2005 Modelling Simul. Mater. Sci. Eng. 13 1015
[2] Pecker S, Eliezer S, Fisher D, Henis Z, Zinamon Z 2005 J. Appl. Phys. 98 043516
[3] Wang Y, Li L 2000 Phys. Rev. B 62 196
[4] Zhang L, Li Y H, Yu Y Y, Li X M, Ma Y, Gu C G, Dai C D, Cai L C 2011 Physica B 406 4163
[5] Pelissier J L, Wetta N 2001 Physica A 289 459
[6] Bundy F P 1958 Phys. Rev. 110 314
[7] Homan C G 1975 J. Phys. Chem. Solids 36 1249
[8] Tonkov E Yu 1992 High Pressure Transformations: A Handbook (1st Ed.) (London: Taylor-Francis) p109
[9] Aoki K, Fujiwara S, Kusakabe M 1982 J. Phys. Soc. Japan 51 3286
[10] Young D A 1991 Phase Diagrams of Elements (1st Ed.) (Berkeley: University of California Press)
[11] Akahama Y, Kawamura H, Singh A K 2002 J. Appl. Phys. 92 5892
[12] Yoneda A, Endo S 1980 J. Appl. Phys. 51 3216
[13] Chen J H, Iwasaki H, Kikegawa T, Yaoita K, Tsuji K 1994 High Pressure Science and Technology-1993 Colorado Springs, USA June 28-July 2, 1994 p421
[14] Chen J H, Iwasaki H, Kikegawa T 1996 High Press. Res. 15 143
[15] Gschneidner Jr K A 1964 Solid State Phys. 16 275
[16] Marsh S P 1980 LASL Shock Hugoniot Data (1st Ed.) (Berkeley: California University Press) p23
[17] Tan Y, Yu Y Y, Dai C D, Tan H, Wang Q S, Wang X 2011 Acta Phys. Sin. 60 106401 (in Chinese) [谭叶, 俞宇颖, 戴诚达,谭华,王青松,王翔 2011 60 106401]
[18] Asay J R 1977 J. Appl. Phys. 48 2832
[19] Cox G A 2007 Shock Compression of Condensed Matter Waikoloa, June 24-29, 2007 p151
[20] Pelissier J L, Wetta N 2001 Physica A 289 459
[21] Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2963
[22] Dugdale J S, MacDonald D K C 1953 Phys. Rev. 89 832
[23] Kittel C 2004 Introduction to Solid State Physics (8th Ed.) (New York: John Wiley and Sons) p131
[24] Degtyareva O, Mcmahon M I, Nelmes R J 2004 High Pressure Res. 24 319
[25] Hultgren R, Desai P D, Hawkins D T, Gleiser M, Kelley K K 1973 Selected Values of the Thermodynamic Properties of Binary Alloys (1st Ed.) (Ohio: ASM Metals Park) p41
[26] Klement Jr W, Jayaraman A, Kennedy G C 1963 Phys. Rev. 131 1632
[27] Bridegman P W 1935 Phys. Rev. 48 893
[28] Peerdeman S A G, Trappeniers N J, Schouten J A 1980 High Temp. High Pressures 12 67
[29] Chen J H, Kikegawa T, Shimomura O, Iwasaki H 1997 J. Synch. Rad. 4 21
[30] Degtyareva V F 2000 Phys. Rev. B 62 9
[31] Trunin R F, Zhernokletov M V, Kuznetsov N F, Shutov V V 1995 High Temp. 33 220
[32] Donohue J 1982 The Structures of the Elements (1st Ed.) (Florida: Robert E. Krieger Publishing Company)
[33] Greenberg Y, Yahel E, Caspi E N, Benmore C, Beuneu B, Dariel M P, Makov G 2009 Euro. Phys. Lett. 86 36004
[34] Alchagirov B B, Mozgovoi A G, Shamparov T M 2004 High Temp. 42 493
[35] Li J, Zhou X M, Li J B, Li S N, Zhu W J, Wang X, Jing F Q 2007 Acta Phys. Sin. 56 6557 (in Chinese) [李俊, 周显明, 李加波, 李赛男, 祝文军, 王翔, 经福谦 2007 56 6557]
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