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.