The Debye–Waller factor explains the temperature dependence of the intensities of X-ray or neutron diffraction peaks. It is defined in terms of the B matrix whose elements B αβ are mean-square atomic displacements in different directions. These quantities, introduced in several contexts, account for the effects of temperature and quantum fluctuations on the lattice dynamics. This paper presents an implementation of the B factor (8π2 B αβ) in the thermo_pw software, a driver of Quantum ESPRESSO routines that provides several thermodynamic properties of materials. The B factor can be calculated from the ab initio phonon frequencies and displacements or can be estimated, although less accurately, from the elastic constants, using the Debye model. The B factors are computed for a few elemental crystals: silicon, ruthenium, magnesium and cadmium; the harmonic approximation at fixed geometry is compared with the quasi-harmonic approximation where the B factors are calculated accounting for thermal expansion. The results are compared with the available experimental data.

中文翻译：

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温度相关的原子 B 因子：从头计算

德拜-沃勒因子解释了 X 射线或中子衍射峰强度的温度依赖性。它的定义是乙矩阵，其元素乙 αβ是不同方向上的均方原子位移。这些在多种情况下引入的量解释了温度和量子涨落对晶格动力学的影响。本文提出了一个实现乙因数 (8π2 乙 αβ） 在里面热密码软件，驱动程序量子浓缩咖啡提供材料的几种热力学性质的例程。这乙系数可以由下式计算从头开始声子频率和位移，或者可以使用德拜模型根据弹性常数来估计，尽管不太准确。这乙计算一些元素晶体的因子：硅、钌、镁和镉；将固定几何形状下的调和近似与准调和近似进行比较，其中乙计算热膨胀系数。结果与现有的实验数据进行了比较。