|
|
Equation of state for solids with considering cohesive energy and anharmonic effect and its application to MgO |
Zhang Da (张达)a, Sun Jiu-Xun (孙久勋 )a b |
a Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, China; b Laboratory for Shock Wave and Detonation Physics Research, Southwest Institute of Fluid Physics, Mianyang 621900, China |
|
|
Abstract A simple equation of state (EOS) in wide ranges of pressure and temperature is constructed within the Mie-Grüneisen-Debye framework. Instead of the popular Birch-Murnaghan and Vinet EOS, we employ a five-parameter cold energy expression to represent the static EOS term, which can correctly produce cohesive energy without any spurious oscillations in extreme compression and expansion region. We developed a Padé approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in low temperature region. The anharmonic effect is taken into account by using a semi-empirical approach. Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature, and tends to ideal-gas limitation at high temperature, which is physically correct. Besides, based on this approach, the anharmonic thermal pressure can be expressed in the Grüneisen form, which is convenient for applications. The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions, and the results are very satisfactory as compared with the experimental data.
|
Received: 05 December 2011
Revised: 06 January 2012
Accepted manuscript online:
|
PACS:
|
05.70.Ce
|
(Thermodynamic functions and equations of state)
|
|
64.30.Jk
|
(Equations of state of nonmetals)
|
|
62.50.-p
|
(High-pressure effects in solids and liquids)
|
|
Fund: Project supported by the Joint Fund of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant No. 10876008). |
Corresponding Authors:
Sun Jiu-Xun
E-mail: sjx@uestc.edu.cn
|
Cite this article:
Zhang Da (张达), Sun Jiu-Xun (孙久勋 ) Equation of state for solids with considering cohesive energy and anharmonic effect and its application to MgO 2012 Chin. Phys. B 21 080508
|
[1] |
Rose J H, Smith J R and Ferrante J 1983 Phys. Rev. B 28 1835
|
[2] |
Rose J H, Smith J R, Guinea F and Ferrante J 1984 Phys. Rev. B 29 2963
|
[3] |
Vinet P, Smith J R, Ferrante J and Rose J H 1987 Phys. Rev. B 35 1945
|
[4] |
Baonza V G, Cáceres M and Núñez J 1995 Phys. Rev. B 51 28
|
[5] |
Baonza V G, Taravillo M, Cáceres M and Núñez J 1996 Phys. Rev. B 53 5252
|
[6] |
Holzapfel W B 2003 Phys. Rev. B 67 026102
|
[7] |
Li J H, Liang S H, Guo H B and Liu B X 2005 Appl. Phys. Lett. 87 194111
|
[8] |
Li J H, Liang S H, Guo H B and Liu B X 2007 J. Alloy. Compd. 431 23
|
[9] |
Qin T, Drautz T and Pettifor D G 2008 Phys. Rev. B 77 220103(R)
|
[10] |
Qin T, Drautz T and Pettifor D G 2008 Phys. Rev. B 78 214108
|
[11] |
Sun J, Wu Q, Cai L and Jing F 2006 Physica B 371 257
|
[12] |
Hu J, Sun J X, Chen X M and Cai L C 2010 Acta Phys. Sin. 59 3384 (in Chinese)
|
[13] |
Tian R G and Sun J X 2011 Chin. Phys. B 20 080508
|
[14] |
Zhang D, Sun J and Zhao Y 2011 Physica B 406 1276
|
[15] |
Jin K, Li X, Wu Q, Geng H, Cai L, Zhou X and Jing F 2010 J. Appl. Phys. 107 113518
|
[16] |
Anderson O L and Zou K 1990 J. Phys. Chem. Ref. Data 19 69
|
[17] |
Matsui M, Parker S C and Leslie M 2000 Am. Mineral. 85 312
|
[18] |
Karki B B, Wentzcovitch R M, de Gironcoli S and Baroni S 2000 Phys. Rev. B 61 8793
|
[19] |
Oganov A R and Dorogokupets P I 2003 Phys. Rev. B 67 224110
|
[20] |
Liu Z J, Cheng X L, Zhang H and Cai L C 2004 Chin. Phys. B 13 384
|
[21] |
Wang Y, Liu Z K, Chen L Q, Burakovsky L and Ahuja R 2006 J. Appl. Phys. 100 023533
|
[22] |
Dorogokupets P I and Oganov A R 2007 Phys. Rev. B 75 024115
|
[23] |
Wu Z Q, Wentzcovitch R M, Umemoto K, Li B S, Hirose K and Zheng J C 2008 J. Geophys. Res. 113 B06204
|
[24] |
Sun X W, Liu Z J, Chen Q F, Song T and Wang C W 2009 Chin. Phys. B 18 5001
|
[25] |
Tange Y, Nishihara Y and Tsuchiya T 2009 J. Geophys. Res. 114 B03208
|
[26] |
Dorogokupets P I 2010 Phys. Chem. Mineral. 37 677
|
[27] |
Duffy T S, Hemley R J and Mao H K 1995 Phys. Rev. Lett. 74 1371
|
[28] |
Zha C S, Mao H K and Hemley R J 2000 Proc. Natl. Acad. Sci. USA 97 13494
|
[29] |
Fei Y W 1999 Am. Mineral. 84 272
|
[30] |
Dewaele A and Fiquet G 2000 J. Geophys. Res. 105 2869
|
[31] |
Speziale S, Zha C S and Duffy T S 2001 J. Geophys. Res. 106 515
|
[32] |
Zhang L and Gong Z 2006 Chin. Phys. Lett. 23 3049
|
[33] |
Jacobsen S D, Holl C M, Adams K A, Fischer R A, Martin E S, Bina C R, Lin J F, Prakapenka V B, Kubo A and Dera P 2008 Am. Mineral. 93 1823
|
[34] |
Hirose K, Sata N, Komabayashi T and Ohishi Y 2008 Phys. Earth Planet. Inter. 167 149
|
[35] |
Gillet P, Matas J, Guyot F and Ricard Y 1999 Microscopic Properties and Processes in Minerals, NATO Science Series C Vol. 543 (Dordrecht: Kluwer) p. 71
|
[36] |
Oganov A R and Dorogokupets P I 2004 J. Phys.: Condens. Matter 16 1351
|
[37] |
Holzapfel W B 2002 J. Phys.: Condens. Matter 14 10525
|
[38] |
Shukla R C and Cowley E R 1985 Phys. Rev. B 31 372
|
[39] |
Lacks D J and Shukla R C 1996 Phys. Rev. B 54 3266
|
[40] |
Al'tshuler L V, Brusnikin S E and Kuzmenkov E A 1987 Zh. Prikl. Mekh. Tekh. Phys. 161 134
|
[41] |
Vorobev V S 1996 High Temp. 34 391
|
[42] |
Grover R 1971 J. Chem. Phys. 55 3435
|
[43] |
Xu X and Zhang W 1986 Practical Introduction to Equation of State (Beijing: Science Press) P. 340 (in Chinese)
|
[44] |
Beg M M 1976 Acta Cryst. A32 154
|
[45] |
Cohen A J and Gordon R J 1976 Phys. Rev. B 14 4595
|
[46] |
Zerr A and Boehler R 1994 Nature 371 506
|
[47] |
Fei Y, Li J, Hirose K, Minarik W, Van Orman J, Sanloup C, van Westrenen W, Komabayashi T and Funakoshi K 2004 Phys. Earth Planet. Inter. 143-144 515
|
[48] |
Vassiliou M S and Ahrens T J 1981 Geophys. Res. Lett. 8 729
|
[49] |
Duffy T S and Ahrens T J 1993 Geophys. Res. Lett. 20 1130
|
[50] |
Marsh S P 1980 LASL Shock Hugoniot Data (Berkeley: University of Califonia Press)
|
[51] |
Ponkratz U and HolzapfeL W B 2004 J. Phys.: Condens. Matter 16 S963
|
[52] |
Anderson O L 1995 Equations of State of Solids for Geophysics and Ceramic Science (Oxford: Oxford University Press)
|
[53] |
Touloukian Y S, Kirby R K, Taylor R E and Desai P D 1975 Thermophysical Properties of Matter Vol. 12 (New York: Plenum)
|
[54] |
Simmons G and Wang H 1970 Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (Cambridge MA: MIT Press).
|
[55] |
Touloukian Y S, Kirby R K, Taylor R E and Lee T Y R 1977 Thermophysical Properties of Matter Vol. 13 (New York: Plenum)
|
[56] |
Fiquet G, Richet P and Montagnac G 1999 Phys. Chem. Miner. 27 103
|
[57] |
Chase M W Jr 1998 NIST-JANAF Thermochemical Tables, J. Phys. Chem. Ref. Data Monograph, No. 9, Am. Chem. Soc., Am. Inst. Phys., Nat. Inst. Stand. Tech.
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|