Elastic,vibrational,and thermodynamic properties of Sr(10)(PO4)6F2 and Ca(10)(PO4)6F2 from first principles  

作　　者：孔祥刚 袁志红 虞游 高涛 马生贵 

机构地区：[1]Institute of Atomic and Molecular Physics,Sichuan University,Chengdu 610065,China [2]College of Optoelectronic Technology,Chengdu University of Information Technology,Chengdu 610225,China [3]Key Laboratory of High Energy Density Physics and Technology of Ministry of Education,Sichuan University,Chengdu 610064,China

出　　处：《Chinese Physics B》2017年第8期337-345,共9页中国物理B（英文版）

基　　金：supported by the National High Technology Research and Development Program of China(Grant No.2015AA034202);the National Natural Science Foundation of China(Grant No.11305147)

摘　　要：The electronic, elastic, vibrational, and thermodynamic properties of Sr_（10）（PO_4）_6F_2（Sr-FAP） and Ca_（10）（PO_4）_6F_2（CaFAP） are systematically investigated by the first-principles calculations. The calculated electronic band structure indicates that the Sr-FAP and Ca-FAP are insulator materials with the indirect band gap of 5.273 eV and 5.592 eV, respectively. The elastic constants are obtained by the “stress–strain” method, and elastic modulus are further evaluated and discussed. The vibrational properties, including the phonon dispersion curves, the phonon density of states, the Born effective charge, and associated longitudinal optical and transverse optical（LO–TO） splitting of optical modes, as well as the phonon frequencies at zone-center are obtained within the linear-response approach. Substitution of Ca by Sr causes phonon frequencies to shift to lower values as expected due to the mass effect. Additionally, some phonon-related thermodynamic properties, such as Helmholtz free energy F, internal energy E, entropy S, and specific heat C_V of Sr-FAP and Ca-FAP are predicted with the harmonic approximation. The present calculated results of two apatites are consistent with the reported experimental and theoretical results.The electronic, elastic, vibrational, and thermodynamic properties of Sr_（10）（PO_4）_6F_2（Sr-FAP） and Ca_（10）（PO_4）_6F_2（CaFAP） are systematically investigated by the first-principles calculations. The calculated electronic band structure indicates that the Sr-FAP and Ca-FAP are insulator materials with the indirect band gap of 5.273 eV and 5.592 eV, respectively. The elastic constants are obtained by the “stress–strain” method, and elastic modulus are further evaluated and discussed. The vibrational properties, including the phonon dispersion curves, the phonon density of states, the Born effective charge, and associated longitudinal optical and transverse optical（LO–TO） splitting of optical modes, as well as the phonon frequencies at zone-center are obtained within the linear-response approach. Substitution of Ca by Sr causes phonon frequencies to shift to lower values as expected due to the mass effect. Additionally, some phonon-related thermodynamic properties, such as Helmholtz free energy F, internal energy E, entropy S, and specific heat C_V of Sr-FAP and Ca-FAP are predicted with the harmonic approximation. The present calculated results of two apatites are consistent with the reported experimental and theoretical results.

关 键 词：Sr-FAR Ca-FAR TDOS elastic modulus thermodynamic properties 

分 类 号：O469[理学—凝聚态物理]