A Themostatistical Model for Cell Formation in Two Dimensions

A new thermostatistics based approach to describe the conditions leading to the formation of cells is presented. The objective of this study is to develop a theoretical framework that minimizes the free energy for different dislocation arrangements, contributing to the understanding of cellular dislocation structures in metals. The methodology involves employing thermostatistic approaches to obtain equilibrium cell structures, which are characterized by regions of low dislocation density separated by dense dislocation entanglements. The results indicate that a transition from a homogeneous dislocation distribution to cell structures can be achieved through the minimization of Helmholtz free energy by considering the self and interaction energy between dislocations along with their entropic contribution. This framework potentially provides insights into the driving forces behind dislocation patterning and cell structure formation in two-dimensional systems. The findings emphasize the importance of free energy minimization in understanding the behavior of dislocations during plastic deformation.