A model for predicting critical size for dislocation formation in phase transforming planar particles of energy storage intercalation materials

Abstract

Defect formation has been widely observed to occur in phase transforming intercalation materials of critical importance to many technological applications. In this work, relying on energy balance argument, we develop a planar particle model to investigate critical conditions for spontaneous dislocation formation in a single-crystalline phase transforming material. Dislocations self-energy is calculated assuming isotropic elasticity, and the work done by the background stress field during dislocation formation is examined based on bilayer and core-shell models of solute distribution. Considering well-known slip systems in cubic crystals, critical sizes are derived, as a function of transformation strain, below which dislocation formation is predicted to remain energetically suppressed throughout complete phase transformation, resulting in completely coherent phase transformation. Effect of the surface flux on the critical size is also examined using a moving interphase model. Minimum dislocation spacing is derived for an array of dislocations which could spontaneously form at the phase boundary when particle size exceeds the critical size. Numerical estimates of the critical size are presented for several materials systems, and the results are discussed with reference to the available experiments. Results of this work could have potentially important implications in terms of designing phase changing materials resistant against cyclic damage.