Evolution of the correlation functions in 2D dislocation systems

TL;DR

This paper derives and analyzes evolution equations for spatial correlation functions of 2D dislocation systems, revealing their equivalence to density fields and confirming findings through simulations.

Contribution

It introduces a novel approach to model dislocation correlations using the Kirkwood superposition approximation and links these to screening phenomena.

Findings

Correlation functions evolve similarly to density fields.

Simulation results confirm the approximation's validity.

Dislocation correlations relate to Debye screening.

Abstract

In this paper spatial correlations of parallel edge dislocations are studied. After closing a hierarchy of equations for the many-particle density functions by the Kirkwood superposition approximation, we derive evolution equations for the correlation functions. It is found that these resulting equations and those governing the evolution of density fields of total as well as geometrically necessary dislocations around a single edge dislocation are formally the same. The second case corresponds to the already described phenomenon of Debye screening of an individual dislocation. This equivalence of the correlation functions and screened densities is demonstrated also by discrete dislocation dynamics simulation results, which confirm the physical correctness of the applied Kirkwood superposition approximation. Relation of this finding and the linear response theory in thermal systems is also discussed.