Prediction of Debye-Scherrer diffraction patterns in arbitrarily strained samples

TL;DR

This paper derives a general formula to predict Debye-Scherrer diffraction patterns in arbitrarily strained samples, extending beyond the small strain approximation and validated through computational simulations.

Contribution

It introduces a new comprehensive formula for diffraction patterns in highly strained samples, surpassing previous small strain limitations.

Findings

The formula aligns with ray-traced diffraction in simulations.

Deviations from small strain solutions are significant at large strains.

The approach applies to arbitrary sample geometries and strain conditions.

Abstract

The prediction of Debye-Scherrer diffraction patterns from strained samples is typically conducted in the small strain limit. Although valid for small deviations from the hydrostat (such as the conditions of finite strength typically observed in diamond anvil cells) this assertion is likely to fail for the large strain anisotropies (often of order 10% in normal strain) such as those found in uniaixally loaded dynamic compression experiments. In this paper we derive a general form for the (\theta_B, \phi) dependence of the diffraction for an arbitrarily deformed sample in arbitrary geometry. We show that this formula is consistent with ray traced diffraction for highly strained computationally generated polycrystals, and that the formula shows deviations from the small strain solutions previously reported.