Validating x-ray line-profile defect analysis using atomistic models of deformed material

Abstract

The population of dislocation defects in a crystalline material strongly influences its properties, so the ability to analyse this population in experimental samples is of great utility. As a complement to direct counting in the transmission electron microscope, quantitative analysis of x-ray diffraction line profiles is an important tool. This is an indirect approach to quantification and so requires careful validation of the physical models that underly the inferential process. Here we undertake to directly evaluate the ability of line profile analysis to quantify aspects of the dislocation and stacking fault populations by exploiting atomistic models of deformed copper single crystals. We directly analyse these models to determine exact details of the defect content (our "ground truth"). We then generate theoretical line profiles for the models and analyse them using the same procedures used in experimental analysis. This leads to inferred measures of the defect content which we are able to compare with the exact data. We show that line profile analysis is able to provide sound predictions of both dislocation density and stacking fault fraction across two orders of magnitude. We further show how the outer cut-off radius in the mean-square strain of a dislocation distribution invoked by Warren and Averbach corresponds to the cell size in an artificially constructed restrictedly-random distribution of dislocations according to the model of Wilkens. Overall, our results lend important new support to the use of line profile analysis for the quantification of line and planar defects in crystalline materials.