Statistical and image analysis for characterizing simulated atomic-scale damage in crystals

Abstract

While molecular dynamics simulations have been used for decades to study structure and formation mechanisms of plastic damage in crystals, the analytical tools needed to characterize collections of plastic defects have been limited. Here we demonstrate the use of two methods, spatial cross-correlations (CC) and Linear Discriminate Analysis (LDA), to analyze and compare plastic damage profiles among molecular dynamics simulations in which damage was created by straining bi-crystals containing symmetric tilt grain boundaries with different tilt angles. Two potentials were used, one representing Cu and one representing Ag, and two coarse-grained descriptors for different types of crystal damage were used, averaged central symmetry parameters (CSP) and atomic hydrostatic stress (HS). We find that in general the CSP is a more accurate descriptor than HS for both analysis methods, and for data base sizes of about 30 or more simulations per tilt angle, the LDA does considerably better in predicting angle and material than the CC method. For example, at the largest data base size of 50 simulations per tilt angle and using the average CSP values, the LDA predicts the exact initial tilt angle and material type for 92% of the simulations, while the CC approach drops to 58%. If the average HS is used instead of the average CSP, the LDA and CC predictions drop to 63% and 32%, respectively. These results point to a number of possible applications of this method, for example in quantifying how the range of damage for a set of strained systems may depend on strain rate or temperature, or quantifying similarities between complex damage from processes such as indentation and energetic ion bombardment.

Using spatial cross-correlation image analysis to characterize the influence of strain rate on plastic damage in molecular dynamics simulations

“…We show in this paper that the strain-rate dependence of plastic damage for the case of uni-axial straining of three copper crystals can be clearly quantified using the cross-correlation image analysis reported earlier [52,53]. One of the crystals is strained along the [011] direction, while the other two have two complementary grain boundaries with a tilt angle of 45°and a tilt angle of 15°with respect to the [001] direction (the equivalent angle for the [011] direction is 90°).…”

“…In two recent studies we showed that MD simulations of bi-crystal straining at a single strain rate of 10 9 s −1 can produce distinctly different damage configurations, even when started from ostensibly the same grain boundary structure [52,53]. This is largely due to different thermal fluctuations during the simulations.…”

“…This is largely due to different thermal fluctuations during the simulations. We also showed that image and statistical analysis can be used to quantify similarities in damage configurations among a data base of atomic configurations that were generated by MD simulation using different initial grain boundary tilt angles and inter-atomic potentials [52,53].…”

An enhanced method for the identification of ferritic morphologies in welded fusion zones based on gray-level co-occurrence matrix: A computational intelligence approach

“…Li et al. 19 presented results from a more comprehensive set of analysis using the set of atomic systems of strained bicrystal based on previous results. Ortegon et al.…”

“…Seita et al 18 used a custom-made apparatus that controls the light source of orientation and analyzes the collected optical micrographs using MATLAB. Li et al 19 presented results from a more comprehensive set of analysis using the set of atomic systems of strained bicrystal based on previous results. Ortegon et al 20 used scanning electron microscopy images as the source of information about the structure of random heterogeneous materials.…”