A phenomenological model of anisotropic lattice vibrations is proposed, using a temperature-dependent spectral cutoff and varying Debye temperatures for the vibrational normal components. The internal lattice energy, entropy and Debye–Waller B factors of non-cubic elemental crystals are derived. The formalism developed is non-perturbative, based on temperature-dependent linear dispersion relations for the normal modes. The Debye temperatures of the vibrational normal components differ in anisotropic crystals; their temperature dependence and the varying spectral cutoff can be inferred from the experimental lattice heat capacity and B factors by least-squares regression. The zero-point internal energy of the phonons is related to the low-temperature limits of the mean-squared vibrational amplitudes of the lattice measured by X-ray and γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal close-packed zinc structure, including the temperature evolution of the B factors of zinc. In this case, the lattice vibrations are partitioned into axial and basal normal components, which admit largely differing B factors and Debye temperatures. The second-order B factors defining the non-Gaussian contribution to the Debye–Waller damping factors of zinc are obtained as well. Anharmonicity of the oscillator potential and deviations from the uniform phonon frequency distribution of the Debye theory are modeled effectively by the temperature dependence of the spectral cutoff and Debye temperatures.

中文翻译：

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非立方晶体中晶格振动的热力学：重新审视锌结构

提出了一种各向异性晶格振动的现象学模型，使用依赖于温度的光谱截止和振动法向分量的变化德拜温度。推导出非立方元素晶体的内部晶格能、熵和德拜-沃勒B因子。所开发的形式是非微扰的，基于正常模式的温度相关线性色散关系。各向异性晶体中振动法向分量的德拜温度不同；它们的温度依赖性和不同的光谱截止可以从实验晶格热容和B最小二乘回归的因素。声子的零点内能与 X 射线和 γ 射线衍射测量的晶格均方振幅的低温极限有关。讨论了一个具体的例子，六方密堆积锌结构的热力学变量，包括锌的B因子的温度演变。在这种情况下，晶格振动被划分为轴向和基础法向分量，它们承认有很大不同的B因子和德拜温度。二阶B还获得了定义对锌的 Debye-Waller 阻尼因子的非高斯贡献的因子。振荡器电位的非谐性和与德拜理论的均匀声子频率分布的偏差通过光谱截止和德拜温度的温度依赖性有效地建模。