The Exit-Wave Power-Cepstrum Transform for Scanning Nanobeam Electron Diffraction: Robust Strain Mapping at Subnanometer Resolution and Subpicometer Precision

TL;DR

This paper introduces the exit wave power cepstrum (EWPC), a novel transform for analyzing nanobeam electron diffraction patterns, enabling highly precise strain mapping at subnanometer resolution and subpicometer accuracy despite sample imperfections.

Contribution

The paper presents the EWPC transform, a new analytical method that decouples lattice information from intensity variations, improving strain measurement robustness in complex samples.

Findings

Achieved sub-picometer strain measurement precision.

Demonstrated robustness to sample mistilts and orientations.

Enabled high-resolution strain mapping in practical applications.

Abstract

Scanning nanobeam electron diffraction (NBED) with fast pixelated detectors is a valuable technique for rapid, spatially resolved mapping of lattice structure over a wide range of length scales. However, intensity variations caused by dynamical diffraction and sample mistilts can hinder the measurement of diffracted disk centers as necessary for quantification. Robust data processing techniques are needed to provide accurate and precise measurements for complex samples and non-ideal conditions. Here we present an approach to address these challenges using a transform, called the exit wave power cepstrum (EWPC), inspired by cepstral analysis in audio signal processing. The EWPC transforms NBED patterns into real-space patterns with sharp peaks corresponding to inter-atomic spacings. We describe a simple analytical model for interpretation of these patterns that cleanly decouples lattice information from the intensity variations in NBED patterns caused by tilt and thickness. By tracking the inter-atomic spacing peaks in EWPC patterns, strain mapping is demonstrated for two practical applications: mapping of ferroelectric domains in epitaxially strained PbTiO3 films and mapping of strain profiles in arbitrarily oriented core-shell Pt-Co nanoparticle fuel-cell catalysts. The EWPC transform enables lattice structure measurement at sub-pm precision and sub-nm resolution that is robust to small sample mistilts and random orientations.