Calculation of the Debye–Waller factor of crystals using the n-dimensional Debye function involving binomial coefficients and incomplete gamma functions

Abstract

The objective of this work was to obtain a simpler and more accurate analytical expression to determine the Debye-Waller factor of crystals using an ndimensional Debye approximation involving binomial coefficients and incomplete gamma functions. The results obtained were compared with the corresponding experimental and theoretical results and, the calculated values were shown to be in excellent agreement with those obtained in the experimental and other previous studies.

Design and thermal modeling of a cold finger open cycle cryostat for Mössbauer spectroscopy

“…Cryogenics has been present in Mössbauer spectroscopy since the first Mössbauer spectra was obtained, by then Rudolf Mössbauer developed a cryostat to allow the recoilless resonance absorption in 191 Ir [1], by considering that the Debye-Waller factor gives a higher probability of having a zero phonon process as the temperature of the solid decreases [2]. In addition, cryogenics offers several advantages in Mössbauer spectroscopy, because in some materials containing Mössbauer nuclei, which exhibit paramagnetic or superparamagnetic behavior at room temperature, the reduction of temperature introduces magnetic ordered states in the structure [3], allowing measuring the magnetic hyperfine interaction in Mössbauer nuclei, as https://doi.org/10.1007/s10751-019-1554-2 Proceedings of the 16th Latin American Conference on the Applications of the Mössbauer Effect (LACAME 2018), 18-23 November 2018, Santiago de Chile, Chile Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10751-019-1554-2) contains supplementary material, which is available to authorized users.…”