Pre-yield non-affine fluctuations and a hidden critical point in strained crystals.

Tamoghna Das,Madan Rao,Saswati Ganguly,Surajit Sengupta

doi:10.1038/srep10644

Abstract

A crystalline solid exhibits thermally induced localised non-affine droplets in the absence of external stress. Here we show that upon an imposed shear, the size of these droplets grow until they percolate at a critical strain, well below the value at which the solid begins to yield. This critical point does not manifest in most thermodynamic or mechanical properties, but is hidden and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. Slow relaxation of stress and an-elasticity appear as observable dynamical consequences of this hidden criticality. Our results may be directly verified in colloidal crystals with video microscopy techniques but are expected to have more general validity.

Highlights

A crystalline solid exhibits thermally induced localised non-affine droplets in the absence of external stress
In Ref. 13 we studied the statistics of shape and size of non-affine clusters and their local thermodynamic properties using molecular dynamics (MD) simulations of an unstrained, two-dimensional Lennard-Jones (2D-LJ) solid[14,15]
We have unearthed a hidden mechanical critical point associated with the percolation of non-affine droplets which is intimately tied to the onset of complex mechanical response in a crystalline solid

Summary

Introduction

A crystalline solid exhibits thermally induced localised non-affine droplets in the absence of external stress. Pre-yield phenomena such as anelasticity, occurring at non-zero temperatures and below the yield stress, in both crystals[4] and metallic glasses[5,6] is somewhat less understood, Within this anelastic regime, a crystalline solid undergoes recoverable strain but with a long relaxation time and is accompanied by conspicuous production and reorganisation of lattice defects[7,8] marked by the onset of significant departure from instantaneous and linear, “Hooke’s law”, elasticity. We provide strong evidence associating the proliferation of crystalline defects during deformation at non-zero temperatures, with the critical behaviour of thermally generated non-affine droplets These non-affine displacements exist in crystalline solids even in the absence of an applied strain and have a purely thermal origin[12].

Methods

Results

Conclusion