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arXiv 1703.03212cond-mat.mtrl-sci
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在自洽谐波近似下的二阶结构相变、自由能曲率和温度依赖的非谐声子:理论和随机实现

Second order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: theory and stochastic implementation

Raffaello Bianco, Ion Errea, Lorenzo Paulatto, Matteo Calandra, Francesco Mauri

摘要:

自洽谐波近似是计算原子强非谐振动系统自由能的有效谐波理论,其随机实现已被证明是从第一性原理研究固体非谐性质的有效方法。作为平均原子位置(质心)的函数的自由能可以用于研究量子或热晶格不稳定性。特别地,质心是二阶结构相变中的序参量,例如,电荷密度波或铁电不稳定性。根据朗道的理论,关于高对称性构型中质心的自由能(即曲率)的二阶导数的知识允许识别相变和不稳定模式。本文导出了一般原子组态在自洽谐波近似下自由能二阶导数的精确解析公式。的解析导数表示的原子位移和力的形式,可以通过使用重要性抽样的随机技术进行评估。我们的方法特别适合于基于第一性原理密度泛函理论计算的应用,与总能量测定相比,原子上的力可以用微不足道的计算工作来获得。最后,我们提出了一个动力学扩展的理论来计算强非谐声子的光谱特性,探测非弹性散射过程。我们说明了我们的方法与玩具模型,模拟的铁电相变的岩盐晶体,如碲化锡或碲化锗的数值应用。

英文摘要:

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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