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First-principle calculations of elastic, electronic and thermodynamic properties of TiC under high pressure

Wang Bin Liu Ying Ye Jin-Wen

First-principle calculations of elastic, electronic and thermodynamic properties of TiC under high pressure

Wang Bin, Liu Ying, Ye Jin-Wen
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  • First-principle investigations of the elastic, electronic and thermodynamic properties of TiC in NaCl structure under high pressure are conducted by using the plane-wave pseudopotential method and quasi-harmonic Debye model. The obtained lattice parameters, elastic constants and moduli at p=0 GPa and T=0 K are in very good agreement with the available experimental data and other theoretical results. According to the analysis of the density of states, the Ti-C bond becomes stronger with pressure increasing. The values of bulk modulus, thermal expansion coefficient, Debye temperature, entropy, Grüneisen parameter and heat capacity (CV) at different pressures and temperatures are obtained successfully by using the quasi-harmonic Debye model. The influence of pressure on bulk modulus, thermal expansion parameter and Debye temperature is greater than that of temperature. The CV decreases with the increase of pressure under the same temperature and tends to the Dulong-Petit limit at high temperature.
    • Funds: Project supported by the National Natural Science Foundation, China (Grant No. 51104103) and the Sichuan Provincial Science Research Program of China (Grant No. 2011GZ0114).
    [1]

    Gotoh Y, Fujimura K, Koike M, Ohkoshi Y, Nagura M, Akamatsu K, Deki S 2001 Mater. Res. Bull. 36 2263

    [2]

    Koc R 1998 J. Mater. Sci. 33 1049

    [3]

    Sen W, Xu B Q, Yang B, Dai Y N, Sun H Y, Ma W H, Wan H L 2010 Light Met. 12 44 (in Chinese) [森维, 徐宝强, 杨斌, 戴永年, 孙红燕, 马文会, 万贺利 2010 轻金属 12 44]

    [4]

    Holt J B, Munir Z A 1986 J. Mater. Sci. 21 251

    [5]

    Yamada O, Miyamoto Y, Koizumi M 1987 J. Am. Ceram. Soc. 70 C-206

    [6]

    Aeiji A, Wada T, Mihara T, Miyamoto Y, Koizumi M, Yamada O 1989 J. Am. Ceram. Soc. 72 805

    [7]

    Klerk J D E 1965 Rev. Sci. Instrum. 36 1540

    [8]

    Dodd S P, Cankurtaran M, James B 2003 J. Mater. Sci. 38 1107

    [9]

    Chang Y A, Toth L E, Tyan Y S 1971 Metall Trans. 2 315

    [10]

    Wolf W, Podloucky R, Antretter T, Fischer F D 1999 Philos. Mag. B 79 839

    [11]

    Dubrovinskaia N A, Dubrovinsky L S, Saxena S K, Ahuja R, Johansson B 1999 J. Alloys. Compd. 289 24

    [12]

    Ahuja R, Eriksson O, Wills J M, Johansson B 1996 Phys. Rev. B 53 3072

    [13]

    Winkler B, Juarez-Arellano E A, Friedrich A, Bayarjargal L, Yan J, Clark S M 2009 J. Alloy. Compd. 478 392

    [14]

    Winkler B, Friderich A, Bayarjargal L, Juarez-Arellano E A 2010 High-Pressure Crystallography from Fundamental Phenomena to Technological Applications in Boldyreva E, Derap (Pedl). (Netherlands Springer)

    [15]

    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condes. Matter 14 2717

    [16]

    Srivastava A, Chauhan M, Singh R K 2011 Phase Transitions 84 58

    [17]

    Li S N, Liu Y 2010 Acta Phys. Sin. 59 6882 (in Chinese) [李世娜, 刘永 2010 物理学报 59 6882]

    [18]

    Li X F, Liu Z L, Peng W M, Zhao A K 2011 Acta Phys. Sin. 60 076501 (in Chinese) [李晓凤, 刘中利, 彭卫民, 赵阿可 2011 物理学报 60 076501]

    [19]

    Marlo M, Milman V 2000 Phys. Rev. B 62 2899

    [20]

    White J A, Bird D M 1994 Phys. Rev. B 50 4954

    [21]

    Vanderbilt D 1990 Phys. Rev. B 41 7892

    [22]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [23]

    Zhang X D, Shi H F, Quan S Y 2011 Journal of Shenyang University of Technology 33 50 (in Chinese) [张旭东, 史海峰, 权善玉 2011 沈阳工业大学学报 33 50]

    [24]

    Slaughter W S 2002 The Linearized Theory of Elasticity (Basel: Birkhäuser Verlag)

    [25]

    Voigt W 1928 Lehrburch der Kristallphysik [Leipzig Teubner]

    [26]

    Reuss A, Angew Z 1929 Math. Mech. 9 49

    [27]

    Hill R 1952 Proc. Phys. Soc. London 65 350

    [28]

    Sin'ko G V, Smirnov N A 2002 J. Phys.: Condes. Matter 14 6989

    [29]

    Blanco M A, Francisco E, Luana V 2004 Comput. Phys. Commun. 158 57

    [30]

    Hao A, Zhou T, Zhu Y, Zhang X, Liu R 2011 Mater. Chem. Phys. 129 99

    [31]

    Huang Z, Feng J, Pan W 2011 Solid State Commun. 151 1559

    [32]

    Huang Z, Feng J, Pan W 2011 Comput. Mater. Sci. 50 3056

    [33]

    Blanco M A, Martín Pendás A, Francisco E, Recio J M, Franco R 1996 J. Molec. Struct. (Theochem) 368 245

    [34]

    Flórez M, Recio J M, Francisco E, Blanco M A, Pendás A M 2002 Phys. Rev. B 66 144112

    [35]

    Francisco E, Sanjurjo G, Blanco M A 2001 Phys. Rev. B 63 094107

    [36]

    Otero-de-la-Roza A, Abbasi-Pérez D, Luaña V 2011 Comput. Phys. Commun. 182 2232

    [37]

    Zhukov V P, Gubanov V A, Jepsen O, Christensen N E, Andersen O K 1988 J. Phys. Chem. Solids 49 841

    [38]

    Grossman J C, Mizel A, Côté M, Cohen M L, Louie S G 1999 Phys. Rev. B 60 6343

    [39]

    Dridi Z, Bouhafs B, Ruterana P, Aourag H 2002 J. Phys.: Condens. Matter 14 10237

    [40]

    Guemmaz M, Mosser A, Ahujab R, Johansson B 1999 Solid State Commun. 110 299

    [41]

    Yang Y, Lu H, Yu C, Chen J M 2009 J. Alloy. Compd. 485 542

    [42]

    Ji Z H, Zeng X H, Hu Y J, Tan M Q 2008 Acta Phys. Sin. 57 3753 (in Chinese) [季正华, 曾祥华, 胡永金, 谭明秋 2008 物理学报 57 3753]

    [43]

    Pugh S F 1954 Philos. Mag. 45 823

    [44]

    Haddadi K, Bouhemadou A, Louail L, Maamache M 2011 Intermetallics 19 476

    [45]

    SheinI R, Ivanovskii A L 2008 J. Phys.: Condens. Matter 20 415218

    [46]

    Minisini B, Roetting J, Tsobnang F 2008 Compu. Matter Sci. 43 812

    [47]

    Koster W, Franz H 1961 Metall Rev. 6 1

    [48]

    Ledbetter M H 1983 in: Reed R P, Clark A F (ed), Materials at Low Temperatures (Metals Park, OH American Society for Metals) p6

    [49]

    Chen K, Zhao L 2007 J. Phys. Chem. Solids 68 1805

    [50]

    Choy M M, Cook W R, Hearmon R F S, Jaffe H, Jerphagnon J, Kurtz S K, Liu T, Nelson D F 1979 Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology (vol 11) in: Hellwege K H, Hellwege A M. (ed) (Berlin: Springer)

    [51]

    Haines J, Leger J M, Bocquillon G 2001 Annu. Rev. Mater. Res. 31 1

    [52]

    Clerc D G, Ledbetter H M 1998 J. Phys. Chem. Solids 59 1071

    [53]

    Gilman J J, Roberts B W 1961 J. Appl. Phys. 32 1405

    [54]

    Jhi S H, Ihm J, Louie S G, Cohen M L 1999 Nature 399 132

    [55]

    Jhi S H, Louie S G, Cohen M L, Ihm J 2001 Phys. Rev. Lett. 86 3348

    [56]

    Murnaghan F D 1944 Proc. Natl. Acad. Sci. USA 30 244

  • [1]

    Gotoh Y, Fujimura K, Koike M, Ohkoshi Y, Nagura M, Akamatsu K, Deki S 2001 Mater. Res. Bull. 36 2263

    [2]

    Koc R 1998 J. Mater. Sci. 33 1049

    [3]

    Sen W, Xu B Q, Yang B, Dai Y N, Sun H Y, Ma W H, Wan H L 2010 Light Met. 12 44 (in Chinese) [森维, 徐宝强, 杨斌, 戴永年, 孙红燕, 马文会, 万贺利 2010 轻金属 12 44]

    [4]

    Holt J B, Munir Z A 1986 J. Mater. Sci. 21 251

    [5]

    Yamada O, Miyamoto Y, Koizumi M 1987 J. Am. Ceram. Soc. 70 C-206

    [6]

    Aeiji A, Wada T, Mihara T, Miyamoto Y, Koizumi M, Yamada O 1989 J. Am. Ceram. Soc. 72 805

    [7]

    Klerk J D E 1965 Rev. Sci. Instrum. 36 1540

    [8]

    Dodd S P, Cankurtaran M, James B 2003 J. Mater. Sci. 38 1107

    [9]

    Chang Y A, Toth L E, Tyan Y S 1971 Metall Trans. 2 315

    [10]

    Wolf W, Podloucky R, Antretter T, Fischer F D 1999 Philos. Mag. B 79 839

    [11]

    Dubrovinskaia N A, Dubrovinsky L S, Saxena S K, Ahuja R, Johansson B 1999 J. Alloys. Compd. 289 24

    [12]

    Ahuja R, Eriksson O, Wills J M, Johansson B 1996 Phys. Rev. B 53 3072

    [13]

    Winkler B, Juarez-Arellano E A, Friedrich A, Bayarjargal L, Yan J, Clark S M 2009 J. Alloy. Compd. 478 392

    [14]

    Winkler B, Friderich A, Bayarjargal L, Juarez-Arellano E A 2010 High-Pressure Crystallography from Fundamental Phenomena to Technological Applications in Boldyreva E, Derap (Pedl). (Netherlands Springer)

    [15]

    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condes. Matter 14 2717

    [16]

    Srivastava A, Chauhan M, Singh R K 2011 Phase Transitions 84 58

    [17]

    Li S N, Liu Y 2010 Acta Phys. Sin. 59 6882 (in Chinese) [李世娜, 刘永 2010 物理学报 59 6882]

    [18]

    Li X F, Liu Z L, Peng W M, Zhao A K 2011 Acta Phys. Sin. 60 076501 (in Chinese) [李晓凤, 刘中利, 彭卫民, 赵阿可 2011 物理学报 60 076501]

    [19]

    Marlo M, Milman V 2000 Phys. Rev. B 62 2899

    [20]

    White J A, Bird D M 1994 Phys. Rev. B 50 4954

    [21]

    Vanderbilt D 1990 Phys. Rev. B 41 7892

    [22]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [23]

    Zhang X D, Shi H F, Quan S Y 2011 Journal of Shenyang University of Technology 33 50 (in Chinese) [张旭东, 史海峰, 权善玉 2011 沈阳工业大学学报 33 50]

    [24]

    Slaughter W S 2002 The Linearized Theory of Elasticity (Basel: Birkhäuser Verlag)

    [25]

    Voigt W 1928 Lehrburch der Kristallphysik [Leipzig Teubner]

    [26]

    Reuss A, Angew Z 1929 Math. Mech. 9 49

    [27]

    Hill R 1952 Proc. Phys. Soc. London 65 350

    [28]

    Sin'ko G V, Smirnov N A 2002 J. Phys.: Condes. Matter 14 6989

    [29]

    Blanco M A, Francisco E, Luana V 2004 Comput. Phys. Commun. 158 57

    [30]

    Hao A, Zhou T, Zhu Y, Zhang X, Liu R 2011 Mater. Chem. Phys. 129 99

    [31]

    Huang Z, Feng J, Pan W 2011 Solid State Commun. 151 1559

    [32]

    Huang Z, Feng J, Pan W 2011 Comput. Mater. Sci. 50 3056

    [33]

    Blanco M A, Martín Pendás A, Francisco E, Recio J M, Franco R 1996 J. Molec. Struct. (Theochem) 368 245

    [34]

    Flórez M, Recio J M, Francisco E, Blanco M A, Pendás A M 2002 Phys. Rev. B 66 144112

    [35]

    Francisco E, Sanjurjo G, Blanco M A 2001 Phys. Rev. B 63 094107

    [36]

    Otero-de-la-Roza A, Abbasi-Pérez D, Luaña V 2011 Comput. Phys. Commun. 182 2232

    [37]

    Zhukov V P, Gubanov V A, Jepsen O, Christensen N E, Andersen O K 1988 J. Phys. Chem. Solids 49 841

    [38]

    Grossman J C, Mizel A, Côté M, Cohen M L, Louie S G 1999 Phys. Rev. B 60 6343

    [39]

    Dridi Z, Bouhafs B, Ruterana P, Aourag H 2002 J. Phys.: Condens. Matter 14 10237

    [40]

    Guemmaz M, Mosser A, Ahujab R, Johansson B 1999 Solid State Commun. 110 299

    [41]

    Yang Y, Lu H, Yu C, Chen J M 2009 J. Alloy. Compd. 485 542

    [42]

    Ji Z H, Zeng X H, Hu Y J, Tan M Q 2008 Acta Phys. Sin. 57 3753 (in Chinese) [季正华, 曾祥华, 胡永金, 谭明秋 2008 物理学报 57 3753]

    [43]

    Pugh S F 1954 Philos. Mag. 45 823

    [44]

    Haddadi K, Bouhemadou A, Louail L, Maamache M 2011 Intermetallics 19 476

    [45]

    SheinI R, Ivanovskii A L 2008 J. Phys.: Condens. Matter 20 415218

    [46]

    Minisini B, Roetting J, Tsobnang F 2008 Compu. Matter Sci. 43 812

    [47]

    Koster W, Franz H 1961 Metall Rev. 6 1

    [48]

    Ledbetter M H 1983 in: Reed R P, Clark A F (ed), Materials at Low Temperatures (Metals Park, OH American Society for Metals) p6

    [49]

    Chen K, Zhao L 2007 J. Phys. Chem. Solids 68 1805

    [50]

    Choy M M, Cook W R, Hearmon R F S, Jaffe H, Jerphagnon J, Kurtz S K, Liu T, Nelson D F 1979 Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology (vol 11) in: Hellwege K H, Hellwege A M. (ed) (Berlin: Springer)

    [51]

    Haines J, Leger J M, Bocquillon G 2001 Annu. Rev. Mater. Res. 31 1

    [52]

    Clerc D G, Ledbetter H M 1998 J. Phys. Chem. Solids 59 1071

    [53]

    Gilman J J, Roberts B W 1961 J. Appl. Phys. 32 1405

    [54]

    Jhi S H, Ihm J, Louie S G, Cohen M L 1999 Nature 399 132

    [55]

    Jhi S H, Louie S G, Cohen M L, Ihm J 2001 Phys. Rev. Lett. 86 3348

    [56]

    Murnaghan F D 1944 Proc. Natl. Acad. Sci. USA 30 244

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  • Received Date:  01 February 2011
  • Accepted Date:  19 March 2012
  • Published Online:  05 September 2012

First-principle calculations of elastic, electronic and thermodynamic properties of TiC under high pressure

  • 1. School of Materials Science and Engineering, Sichuan University, Chengdu 610065, China;
  • 2. Key Laboratory of Advanced Special Material and Technology, Ministry of Education, Chengdu 610065, China
Fund Project:  Project supported by the National Natural Science Foundation, China (Grant No. 51104103) and the Sichuan Provincial Science Research Program of China (Grant No. 2011GZ0114).

Abstract: First-principle investigations of the elastic, electronic and thermodynamic properties of TiC in NaCl structure under high pressure are conducted by using the plane-wave pseudopotential method and quasi-harmonic Debye model. The obtained lattice parameters, elastic constants and moduli at p=0 GPa and T=0 K are in very good agreement with the available experimental data and other theoretical results. According to the analysis of the density of states, the Ti-C bond becomes stronger with pressure increasing. The values of bulk modulus, thermal expansion coefficient, Debye temperature, entropy, Grüneisen parameter and heat capacity (CV) at different pressures and temperatures are obtained successfully by using the quasi-harmonic Debye model. The influence of pressure on bulk modulus, thermal expansion parameter and Debye temperature is greater than that of temperature. The CV decreases with the increase of pressure under the same temperature and tends to the Dulong-Petit limit at high temperature.

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