Elastic, vibrational, and thermodynamic properties of Sr10(PO4)6F2 and Ca10(PO4)6F2 from first principles

doi:10.1088/1674-1056/26/8/086301

Abstract

The electronic, elastic, vibrational, and thermodynamic properties of Sr₁₀(PO₄)₆F₂(Sr-FAP) and Ca₁₀(PO₄)₆F₂(Ca-FAP) 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.

Keywords: Sr-FAP Ca-FAP TDOS elastic modulus thermodynamic properties

Received: 13 April 2017
Revised: 15 May 2017
Accepted manuscript online:

PACS:	63.20.dk	(First-principles theory)
	65.40.Ba	(Heat capacity)
	71.20.-b	(Electron density of states and band structure of crystalline solids)
	65.40.gd	(Entropy)

Fund:

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

Corresponding Authors: Tao Gao
E-mail: gaotao@scu.edu.cn

About author: 0.1088/1674-1056/26/8/

Cite this article:

Xianggang Kong(孔祥刚), Zhihong Yuan(袁志红), You Yu(虞游), Tao Gao(高涛), Shenggui Ma(马生贵) Elastic, vibrational, and thermodynamic properties of Sr₁₀(PO₄)₆F₂and Ca₁₀(PO₄)₆F₂ from first principles 2017 Chin. Phys. B 26 086301

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Elastic, vibrational, and thermodynamic properties of Sr10(PO4)6F2 and Ca10(PO4)6F2 from first principles

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Elastic, vibrational, and thermodynamic properties of Sr₁₀(PO₄)₆F₂and Ca₁₀(PO₄)₆F₂ from first principles