Wang Kun Lun, Huang Xian Bin, Li Jing, Xu Qiang, Dan Jia Kun, Ren Xiao Dong
Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
Acta Crystallogr A Found Adv. 2017 Mar 1;73(Pt 2):151-156. doi: 10.1107/S2053273317000912.
In an increasing number of cases the harmonic approximation is incommensurate with the quality of Bragg diffraction data, while results of the anharmonic Debye-Waller factor are not typically available. This paper presents a Monte Carlo computation of a Taylor expansion of an anharmonic Debye-Waller factor with respect to temperature up to the fourth order, where the lattice was a face-centred cubic lattice and the atomic interaction was described by the Lennard-Jones potential. The anharmonic Debye-Waller factor was interpreted in terms of cumulants. The results revealed three significant points. Firstly, the leading term of anharmonicity had a negative contribution to the Debye-Waller factor, which was confirmed by Green's function method. Secondly, the fourth-order cumulants indicated a non-spherical probability density function. Thirdly, up to the melting point of two different densities, the cumulants up to the fourth order were well fitted by the Taylor expansion up to T, which suggested that the Debye-Waller factor may be calculated by perturbation expansion up to the corresponding terms. In conclusion, Monte Carlo simulation is a useful approach for calculating the Debye-Waller factor.
在越来越多的情况下，简谐近似与布拉格衍射数据的质量不相符，而非简谐德拜 - 瓦勒因子的结果通常不可用。本文给出了一个蒙特卡罗计算，即非简谐德拜 - 瓦勒因子关于温度的泰勒展开式，展开到四阶，其中晶格为面心立方晶格，原子间相互作用由 Lennard - Jones 势描述。非简谐德拜 - 瓦勒因子用累积量来解释。结果揭示了三个要点。首先，非简谐性的首项对德拜 - 瓦勒因子有负贡献，这一点通过格林函数方法得到了证实。其次，四阶累积量表明概率密度函数是非球形的。第三，在两种不同密度的熔点之前，四阶累积量通过到 T 的泰勒展开式能很好地拟合，这表明德拜 - 瓦勒因子可以通过到相应项的微扰展开来计算。总之，蒙特卡罗模拟是计算德拜 - 瓦勒因子的一种有用方法。
