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高压下TiC的弹性、电子结构及热力学性质的第一性原理计算

王斌 刘颖 叶金文

高压下TiC的弹性、电子结构及热力学性质的第一性原理计算

王斌, 刘颖, 叶金文
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  • 利用基于密度泛函理论的第一性原理平面波赝势方法 并结合准谐徳拜模型研究了NaCl结构的TiC在高压下的弹性性质、电子结构和热力学性质. 计算所得零温零压下的晶格常数、体弹模量及弹性常数与实验值符合得很好. 零温下弹性常数和弹性模量随压强增大而增大. 通过态密度和电荷密度的分析, Ti-C键随压强增大而增强. 运用准谐德拜模型, 成功计算了TiC在高温高压下的体弹模量、熵、热膨胀系数、徳拜温度、 Grüneisen参数和比热容. 结果表明压强对体弹模量、热膨胀系数和徳拜温度的影响大于温度对其的影响. 热容随着压强升高而减小, 在高温高压下, 热容接近Dulong-Petit极限.
    • 基金项目: 国家自然科学基金( 批准号: 51104103)和四川省科学研究项目(批准号: 2011GZ0114)资助的课题.
    [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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  • 收稿日期:  2011-02-01
  • 修回日期:  2012-03-19
  • 刊出日期:  2012-09-20

高压下TiC的弹性、电子结构及热力学性质的第一性原理计算

  • 1. 四川大学材料科学与工程学院, 成都 610065;
  • 2. 先进特种材料及制备加工技术教育部重点实验室, 成都 610065
    基金项目: 

    国家自然科学基金( 批准号: 51104103)和四川省科学研究项目(批准号: 2011GZ0114)资助的课题.

摘要: 利用基于密度泛函理论的第一性原理平面波赝势方法 并结合准谐徳拜模型研究了NaCl结构的TiC在高压下的弹性性质、电子结构和热力学性质. 计算所得零温零压下的晶格常数、体弹模量及弹性常数与实验值符合得很好. 零温下弹性常数和弹性模量随压强增大而增大. 通过态密度和电荷密度的分析, Ti-C键随压强增大而增强. 运用准谐德拜模型, 成功计算了TiC在高温高压下的体弹模量、熵、热膨胀系数、徳拜温度、 Grüneisen参数和比热容. 结果表明压强对体弹模量、热膨胀系数和徳拜温度的影响大于温度对其的影响. 热容随着压强升高而减小, 在高温高压下, 热容接近Dulong-Petit极限.

English Abstract

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