Phonon-based thermal configurational forces: Definitions and applications in rupture of semiconductors

Abstract

A general framework encompassing spatial and material settings of atomistic crystalline systems is presented. Theoretical and computational analysis of configurational forces in the context of atomistic thermomechanics constitutes the central topic of the presented paper. We distinguish between atomistic configurational forces stemming from the changes in static energy density and the changes in vibrational energy density. To this end, we first propose a novel atomistic phonon-based thermal configurational forces rendering infinitesimal changes in vibrational energy density under configurational variations. Next, we employ pair and triplet configurational forces resulting from the changes in static energy density due to two-body stretch and three-body stretch-bending. Using thermal configurational forces, we study numerically the problem of temperature rise, bond stretching and bending occurring at the crack tip induced by brittle crack propagation in crystalline lattices. Energy release caused by large harmonic vibrations and deformations is estimated by the magnitude of configurational forces at the crack tip. The atomistic temperature is shown to be governed by atom-wise frequency through local entropy. Finally, we demonstrate suitability and versatility of atomistic configurational forces in analyzing fracture of silicon diamond lattice subjected to mode-I loading at different finite temperatures.