Retrieval of the atomic displacements in the crystal from the coherent x-ray diffraction pattern

TL;DR

This paper presents a method to improve the reconstruction of atomic displacements in crystals from coherent x-ray diffraction patterns by constraining displacement derivatives, demonstrated on silicon structures.

Contribution

It introduces a novel approach that enhances phase retrieval convergence by limiting displacement derivative variations, enabling accurate atomic displacement mapping.

Findings

Improved convergence of phase retrieval algorithms.

Successful displacement reconstruction in silicon structures.

Enhanced accuracy in atomic displacement imaging.

Abstract

We investigate the retrieval of spatially resolved atomic displacements via the phases of the direct(real)-space image reconstructed from the strained crystal's coherent x-ray diffraction pattern. We demonstrate that limiting the spatial variation of the first and second order spatial displacement derivatives improves convergence of the iterative phase retrieval algorithm for displacements reconstructions to the true solution. Our approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.