title: Monte Carlo simulation of an anharmonic Debye-Waller factor to the T4order.
abstract: 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 T4, 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.
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Kun Lun
authors.initials: KL
authors.lastname: Wang
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Xian Bin
authors.initials: XB
authors.lastname: Huang
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Jing
authors.initials: J
authors.lastname: Li
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Xu
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Jia Kun
authors.initials: JK
authors.lastname: Dan
authors.affiliation: Key Laboratory of Pulsed Power Technology IFP CAEP, Mianyang 621900, People's Republic of China.
authors.forename: Xiao Dong
authors.initials: XD
authors.lastname: Ren
keywords: Debye–Waller factor; Monte Carlo simulation; X-ray diffraction; temperature measurement