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Ca0.5Sr0.5TiO3弹性和热学性质的第一性原理研究

邵栋元 惠群 李孝 陈晶晶 李春梅 程南璞

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Citation:

Ca0.5Sr0.5TiO3弹性和热学性质的第一性原理研究

邵栋元, 惠群, 李孝, 陈晶晶, 李春梅, 程南璞

First-principles study on the elastic and thermal properties of Ca0.5Sr0.5TiO3

Shao Dong-Yuan, Hui Qun, Li Xiao, Chen Jing-Jing, Li Chun-Mei, Cheng Nan-Pu
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  • 利用能量最小原理, 确定了Ca0.5Sr0.5TiO3晶体中4c位置的Ca/Sr原子对称分布, 建立了Ca0.5Sr0.5TiO3稳定的晶体结构, 在此基础上利用基于密度泛函理论第一性原理的平面波超软赝势方法, 采用局域密度近似和广义梯度近似函数, 计算了Ca0.5Sr0.5TiO3的晶格参数、弹性常数、体弹模量、剪切模量、杨氏模量、泊松比, 并基于Christoffel方程的本征值研究了平面声波的特征, 基于Cahill和Cahill-Pohl模型研究了最小热导率的特征. 计算结果表明: Ca0.5Sr0.5TiO3晶格参数和实验值很接近, 体弹模量大于剪切模量, [100], [010], [001]晶向的杨氏模量、泊松比、普适弹性常数(AU)以及杨氏模量三维图均显示了弹性各向异性; 平面声波在(010), (001)平面呈现各向异性, 在(100)平面呈现各向同性, 平面声波大小与平均横波和平均纵波的数值很接近. Cahill模型最小热导率在各平面呈现各向同性, Cahill-Pohl模型最小热导率在高温时趋于恒定. 准谐德拜模型下Ca0.5Sr0.5TiO3 晶体的摩尔热容和热膨胀系数与CaTiO3晶体的接近, 并且高温下具有稳定的热膨胀性能. 计算所得禁带宽度为2.19 eV, 导带底主要是Ti-3d与O-2p态电子贡献; 由电荷布居和电荷密度图理论证实Ca0.5Sr0.5TiO3具有稳定的Ti-O八面体结构.
    In this paper, Ca/Sr atoms are confirmed to have symmetric distributions on 4c sites by using the minimum energy principle, and the stable crystal structure of Ca0.5Sr0.5TiO3 is built. The lattice parameters, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio of Ca0.5Sr0.5TiO3 (CST50) are investigated by the plane wave pseuedopotential method based on the first-principles density functional theory within the local density approximate (LDA) and generalized gradient approximation. The properties of planar acoustic velocity are studied by Christoffel equation, and the minimum thermal conductivity is investigated with Cahill and Cahill-Pohl models. The results show that the calculated lattice parameters are consistent with the corresponding experimental values. The larger calculated elastic constasnts C11, C22, and C33 suggest the incompressibility along the principle axes. The bulk modulus B is larger than the shear modulus G; G/BLDA = 0.5789 and G/BGGA = 0.5999, indicating that CST50 is a brittle material. The three-dimensional image of Young's modulus along [100], [010], and [001] crystal orientations shows the anisotropic elasticity of CST50. The planar projections of Young's modulus in (001) and (010) planes show the stronger anisotropy than in (100) plane and all the planar projections have two-fold symmetry. The Poisson's ratio exhibits the incompressbility of CST50. The universal elastic anisotropy indexes ALDAU = 0.0235 and AGGAU= 0.0341 indicate the weak anisotropy of CST50. The planar acoustic wave which has a branch of longitudinal wave and two branches of transverse wave is anisotropic along (010) and (001) planes and isotropic along (100) plane, and all the corresponding planar projections have two-fold symmetry. The minimum thermal conductivity calculated in Cahill model is isotropic in each plane, while the minimum thermal conductivity calculated in Cahill-Pohl model is proportional to the second power of T under low temperatures and reaches a constant at high temperatures. In the quasi harmonic Debye model, the molar heat capacity and thermal expansion coefficient of CST50 are close to those of calcium titanate, indicating that CST50 has the stable thermal expansion property at high temperatures. The direct band gap of CST50 is 2.19 eV and the bottom of the valence band is mainly determined by the electron orbitals of Ti-3d and O-2p. The analysis of the charge populations shows that the covalence of Ti–O is stronger than those of Sr–O and Ca–O, and the band length of Ti–O is shorter than those of Sr–O and Ca–O; (200), (110) and (002) planar contour charge densities indicate that Ti atoms interact strongly with O atoms. The charge population and contour charge density prove that CST50 has a stable Ti–O octahedral structure.
    • 基金项目: 国家自然科学基金(批准号: 51171156)和中央高校基本业务费(批准号: XDJK2014C008)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51171156) and the Fundamental Research Funds for the Central Universities, China (Grant No. XDJK2014C008).
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  • [1]

    Yang X, Fu J, Jin C, Chen J, Liang C, Wu M, Zhou W 2010 J. Am. Chem. Soc. 132 14279

    [2]

    van Benthem K, Elsässer C, French R H 2001 J. Appl. Phys. 12 6156

    [3]

    Souza A E, Almeida Santos G T, Silva R A, Moreira M L, Volanti E C, Teixeira S R, Longo E 2012 Int. J. Appl. Ceram. Technol. 9 186

    [4]

    Ouillon R, Pinan-Lucarre J P, Ranson P, Pruzan P, Mishra S K, Ranjan R, Pandey D 2002 J. Phys: Condens. Matter 14 2079

    [5]

    Bednorz J G, Mller K A 1984 Phys. Rev. Lett. 52 2289

    [6]

    Mishra S K, Ranjan R, Pandey D, Stokes H T 2005 J. Solid State Chem. 178 2846

    [7]

    Yamanaka T, Hirai N, Komatsu Y 2002 Am. Mineral. 87 1183

    [8]

    Qin S, Becerro A I, Seifert F, Gottsmann J, Jiang J 2000 J. Mate. Chem. 10 1609

    [9]

    Harrison R J, Redfern S A T, Street J 2003 Am. Mineral. 88 574

    [10]

    Ranjan R, Pandey D, Schuddinck W, Richard O, de Meulenaere P, van Landuyt J, van Tendeloo G 2001 J. Solid State Chem. 162 20

    [11]

    Carpenter M A, Howard C J, Knight K S, Zhang Z 2006 J. Phys: Condens. Matter 18 10725

    [12]

    Mishra S K, Ranjan R, Pandey D, Ranson P, Ouillon R, Pinan-Lucarre J P, Pruzan P 2006 J. Phys: Condens. Matter 18 1899

    [13]

    Hui Q, Dove M T, Tucker M G, Redfern S A, Keen D A 2007 J. Phys: Condens. Matter 19 335214

    [14]

    Pandech N, Sarasamak K, Limpijumnong S 2015 J. Appl. Phys. 117 174108

    [15]

    Sakhya A P, Maibam J, Saha S, Chanda S, Dutta A, Sharma B I, Thapa R K, Sinha T P 2015 Indian J. Pure Appl. Phys. 53 102

    [16]

    Walsh J N, Taylor P A, Buckley A, Darling T W, Schreuer J, Carpenter M A 2008 Phys. Earth Planet. In. 167 110

    [17]

    Ashman C R, Hellberg C S, Halilov S 2010 Phys. Rev. B 82 024112

    [18]

    Yang C Y, Zhang R 2014 Chin. Phys. B 23 026301

    [19]

    Perks N J, Zhang Z, Harrison R J, Carpenter M A 2014 J. Phys: Condens. Matter 26 505402

    [20]

    Aso R, Kan D, Shimakawa Y 2014 Cryst. Growth Des. 14 2128

    [21]

    Kovalevsky A V, Populoh S, Patricio S G, Thiel P, Ferro M C, Fagg D P, Weidenkaff A 2015 J. Phys. Chem. C 119 4466

    [22]

    Lima B S, da Luz M S, Oliveira F S, Alves L M S, Santos C A M, Jomard F, Sidis Y, Bourges P, Harms S, Grams C P, Hemberger J, Lin X, Fauque B, Behnia K 2015 Phys. Rev. B 91 045108

    [23]

    Wang J D, Dai J Q, Song Y M, Zhang H, Niu Z H 2014 Acta Phys. Sin. 63 126301 (in Chinese) [王江舵, 代建清, 宋玉敏, 张虎, 牛之慧 2014 物理学报 63 126301]

    [24]

    Kong X L, Hou Q Y, Su X Y, Qi Y H, Zhi X F 2009 Acta Phys. Sin. 58 4128 (in Chinese) [孔祥兰, 侯芹英, 苏希玉, 齐延华, 支晓芬 2009 物理学报 58 4128]

    [25]

    Hammer B, Hansen L B, Nørskov J K 1999 Phys. Rev. B 59 7413

    [26]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [27]

    Ceperley D M, Alder B J 1980 Phys. Rev. Lett. 45 566

    [28]

    Vanderbilt D 1990 Phys. Rev. B 41 7892

    [29]

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

    [30]

    Goldfarb D 1970 Math. Comput. 24 23

    [31]

    Shanno D F 1970 Math. Comput. 24 647

    [32]

    Wu Z, Zhao E, Xiang H P, Hao X F, Liu, X J, Meng J 2007 Phys. Rev. B 76 054115

    [33]

    Hill R 1952 Proc. Phys. Soc. A 65 349

    [34]

    Pugh S F 1954 Philos. Mag. 45 823

    [35]

    Ranganathan S I, Ostoja-Starzewski M 2008 Phys. Rev. Lett. 101 055504

    [36]

    Nye J F 1964 Physical Properties of Crystals (Oxford: Clarendon Press) pp130-145

    [37]

    Foley B M, Brown-Shaklee H J, Duda J C, Cheaito R, Gibbons B J, Medlin D, Medlin D, Ihlefeld J F, Hopkins P E 2012 Appl. Phys. Lett. 101 231908

    [38]

    Wang Y, Fujinami K, Zhang R, Wan C, Wang N, Ba Y, Koumoto K 2010 Appl. Phys. Express 3 031101

    [39]

    Cahill D G, Watson S K, Pohl R O 1988 Ann. Rev. Phys. Chem. 39 93

    [40]

    Wong J, Krisch M, Farber D L, Occelli F, Xu R, Chiang T C, Clatterbuck D, Schwartz A J, Wall M, Boro C 2005 Phys. Rev. B 72 064115

    [41]

    Costescu R M, Bullen A J, Matamis G, O'Hara K E, Cahill D G 2002 Phys. Rev. B 65 094205

    [42]

    Yang H Y, Ohishi Y J, Kurosaki K, Muta H, Yamanaka 2010 J. Alloys Compd. 504 201

    [43]

    Yamanaka S, Kurosaki K, Maekawa T, Kobayashi S I, Uno M 2005 J. Nucl. Mater. 344 61

    [44]

    Webb S, Jackson I, Gerald J F 1999 Phys. Earth Planet. In. 115 259

    [45]

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

    [46]

    Boudali A, Khodja M D, Amrani B, Amrani B, Bourbie D, Amara K, Abada A 2009 Phys. Lett. A 373 879

    [47]

    Boudali A, Abada A, Driss Khodja M D, Amrani B, Amara K, Khodja F D, Elias A 2010 Phys. B: Condens. Matter 405 3879

    [48]

    Souza J A, Rino J P 2011 Acta Mater. 59 1409

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出版历程
  • 收稿日期:  2015-03-27
  • 修回日期:  2015-06-16
  • 刊出日期:  2015-10-05

Ca0.5Sr0.5TiO3弹性和热学性质的第一性原理研究

  • 1. 西南大学材料与能源学部, 重庆 400715
    基金项目: 国家自然科学基金(批准号: 51171156)和中央高校基本业务费(批准号: XDJK2014C008)资助的课题.

摘要: 利用能量最小原理, 确定了Ca0.5Sr0.5TiO3晶体中4c位置的Ca/Sr原子对称分布, 建立了Ca0.5Sr0.5TiO3稳定的晶体结构, 在此基础上利用基于密度泛函理论第一性原理的平面波超软赝势方法, 采用局域密度近似和广义梯度近似函数, 计算了Ca0.5Sr0.5TiO3的晶格参数、弹性常数、体弹模量、剪切模量、杨氏模量、泊松比, 并基于Christoffel方程的本征值研究了平面声波的特征, 基于Cahill和Cahill-Pohl模型研究了最小热导率的特征. 计算结果表明: Ca0.5Sr0.5TiO3晶格参数和实验值很接近, 体弹模量大于剪切模量, [100], [010], [001]晶向的杨氏模量、泊松比、普适弹性常数(AU)以及杨氏模量三维图均显示了弹性各向异性; 平面声波在(010), (001)平面呈现各向异性, 在(100)平面呈现各向同性, 平面声波大小与平均横波和平均纵波的数值很接近. Cahill模型最小热导率在各平面呈现各向同性, Cahill-Pohl模型最小热导率在高温时趋于恒定. 准谐德拜模型下Ca0.5Sr0.5TiO3 晶体的摩尔热容和热膨胀系数与CaTiO3晶体的接近, 并且高温下具有稳定的热膨胀性能. 计算所得禁带宽度为2.19 eV, 导带底主要是Ti-3d与O-2p态电子贡献; 由电荷布居和电荷密度图理论证实Ca0.5Sr0.5TiO3具有稳定的Ti-O八面体结构.

English Abstract

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