Anharmonic correlated Debye model is derived for Debye-Waller factors of bcc (bodycentered cubic) crystals presented in terms of cumulant expansion up to the fourth order. The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. | VNU Journal of Science: Mathematics – Physics, Vol. 33, No. 1 (2017) 22-28 Anharmonic Correlated Debye Model high-order Expanded Debye-Waller Factors of BCC Crystals: Application to Metallic Wolfram Nguyen Van Hung*, Trinh Thi Hue, Nguyen Bao Trung, Nguyen Cong Toan Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Hanoi, Vietnam Received 15 January 2017 Revised 16 February 2017; Accepted 20 March 2017 Abstract: Anharmonic correlated Debye model is derived for Debye-Waller factors of bcc (bodycentered cubic) crystals presented in terms of cumulant expansion up to the fourth order. The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS (X-ray absorption fine structure) cumulants of bcc crystals have been derived using the many-body perturbation approach. Numerical results for W are found to be in good agreement with experiment. Keywords: Debye-Waller factor, effective potential, correlated Debye model, bcc crystals. 1. Introduction X-ray Absorption Fine Structure (XAFS) has developed into a powerful technique for providing information on local atomic structure and thermal effects of the substances [1-14]. The formalism for including anharmonic effects in XAFS is often based on the cumulant expansion approach [1] from which the expression for anharmonic XAFS is given by [2] (k ) F k e 2 R / ( k ) kR 2 (2ik ) n ( n ) Im ei ( k ) exp 2ikR n! n (1) where is net phase shift, λ is mean free path, k is wave number of photoelectron, R r with r being the instantaneous bond length between absorber and backscatterer atoms, and σ(n) (n
