Classical and quantum concepts of probability applied to diffraction physics in perfect crystals

TL;DR

This paper presents a unified approach combining classical and quantum probability concepts to model diffraction in perfect crystals, deriving recursive equations for X-ray reflectivity that align with established dynamical theory.

Contribution

It introduces a novel probabilistic framework that reproduces diffraction phenomena and provides simple recursive formulas for X-ray reflectivity in crystals of varying thickness.

Findings

Recursive equations accurately predict X-ray reflectivity.

Method aligns with dynamical diffraction theory.

Applicable to crystals from a few atomic layers to infinite thickness.

Abstract

By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained. Diffraction phenomena in crystals are reproducible after assigning probability amplitudes to every classical outcome. When applied to X-ray diffraction in reflection geometry, this procedure has provided simple recursive equations to calculated the X-ray reflectivity of crystals with thickness varying since a few atomic layers to infinity. The results are in agreement with the dynamical theory of X-ray diffraction, even when absorption is considered.