Tomaschitz Roman
Sechsschimmelgasse 1/21-22, Vienna, 1090, Austria.
Acta Crystallogr A Found Adv. 2021 Sep 1;77(Pt 5):420-432. doi: 10.1107/S2053273321005507. Epub 2021 Jul 29.
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.
提出了一种各向异性晶格振动的唯象模型，该模型使用温度依赖的谱截止和不同的德拜温度来描述振动的法向分量。推导了非立方元素晶体的内部晶格能、熵和德拜-瓦勒B因子。所发展的形式体系是非微扰的，基于法向模式的温度依赖线性色散关系。在各向异性晶体中，振动法向分量的德拜温度不同；它们的温度依赖性和变化的谱截止可以通过最小二乘法回归从实验晶格热容和B因子中推断出来。声子的零点内能与通过X射线和γ射线衍射测量的晶格平均平方振动振幅的低温极限有关。讨论了一个具体例子，即六方密堆积锌结构的热力学变量，包括锌的B因子的温度演化。在这种情况下，晶格振动被划分为轴向和基面法向分量，它们具有很大不同的B因子和德拜温度。还得到了定义锌的德拜-瓦勒阻尼因子中非高斯贡献的二阶B因子。通过谱截止和德拜温度的温度依赖性有效地模拟了振子势的非谐性以及与德拜理论中均匀声子频率分布的偏差。
