Abstract

Using the ab initio molecular dynamics method, the dynamics of the bcc titanium lattice and its response to high temperature deformations are studied. The results of calculation of phonon spectra with use of the harmonic Hamiltonian and the Hamiltonian containing third-order force constants are compared. It is shown that the lattice dynamics of bcc titanium cannot be correctly described without taking into account the anharmonic terms. Stress–strain curves are calculated for specified deformation scheme η₁ = η₁₁ = η, η₆ = 2η₁₂= η. Analytical expressions of the dependence of the nonzero components of the stress tensor on the strain magnitude are given for this deformation scheme, which take into account the elastic constants up to the fourth order inclusive. All second-order elastic constants, three third-order elastic constants, and four fourth-order elastic constants of bcc titanium are calculated.

中文翻译：

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BCC 钛的晶格动力学及其对高温变形的非线性响应 从头算分子动力学

摘要

采用从头算分子动力学方法，研究了体心立方钛晶格的动力学及其对高温变形的响应。比较了使用谐波哈密顿量和包含三阶力常数的哈密顿量计算声子谱的结果。结果表明，如果不考虑非谐波项，就无法正确描述 bcc 钛的晶格动力学。针对指定的变形方案计算应力-应变曲线 η ₁ = η ₁₁ = η, η ₆  = 2η ₁₂= η。对于这种变形方案，给出了应力张量的非零分量对应变大小的依赖性的解析表达式，其中考虑了高达四阶的弹性常数。计算了体心立方钛的所有二阶弹性常数、三个三阶弹性常数和四个四阶弹性常数。