Wave-packet numerical investigation of thermal diffuse scattering: A time-dependent quantum approach to the Debye method

TL;DR

This paper introduces a time-dependent quantum method using wave packets to study thermal diffuse scattering, naturally accounting for diffraction attenuation without extra factors, applied to electrons in aluminum films.

Contribution

It presents a novel wave-packet numerical approach incorporating the frozen phonon approximation for thermal diffuse scattering analysis.

Findings

Increased temperature leads to greater incoherence among electron wave functions.

Diffraction features become blurred as atomic vibrations increase with temperature.

The method effectively models thermal effects without additional experimental parameters.

Abstract

The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the time-dependent Schr\"odinger equation. Unlike other methods in the related literature, in this approach the attenuation of diffraction features arises in a natural way by averaging over a number of wave-packet realizations, thus avoiding any additional experimentally obtained Debye-Waller factors or artificial modulations. Without loss of generality, the method has been applied to analyze the transmission of an electron beam through a thin Al film in two dimensions, making use of Einstein's model to determine the phonon configuration for each realization at a given temperature. It is shown that, as temperature and hence atomic vibration amplitudes increase, incoherence among different electron wave-function realizations gradually increases, blurring the well-defined diffraction features characterizing the zero-temperature intensity.