Stretched-exponential stress dynamics in chain of springs and masses model of crystals: analytical results and MD simulations

TL;DR

This paper develops an analytical model and confirms through MD simulations that the dynamics of layered crystalline materials under pressure follow stretched-exponential behavior, revealing scaling relations in time and size.

Contribution

An extended analytical model of the chain of springs and masses for crystal layers, validated by MD simulations across various alloys and conditions.

Findings

Dynamics follow stretched-exponential functions

Model applies to multiple alloys and potentials

Scaling relations in time and sample size

Abstract

The model of a chain of springs and masses (CSM), originating from the works of Schr\"odinger (1914), and Pater (1974), is found suitable as an analytical description of the dynamics of layers in orientated FCC crystals. An analytical extension of that model has been developed for the case of linear-in-time ramp pressure applied to a sample surface. Examples are provided of molecular dynamics (MD) simulations, confirming the usefulness of the model in the description of dynamic effects on steel 310S under pressure. Qualitatively the same results have been obtained by us for several other medium-entropy alloys CoNiCr (with EAM and MEAM inter-atomic potentials), and CoNiV (with MEAM potential). For studies of dynamic stability on large sizes of samples and for long times, the proposed earlier table-style harmonic interlayer potential has been used. The results of MD simulations suggest that the dynamics of the CSM model of perfectly ordered matter is described by stretched-exponential time functions, and it is characterised by simple scaling relations in time and size of the sample.