Statistical theory of structures with extended defects

TL;DR

This paper develops a statistical approach to describe the overall properties of materials containing nanoscale extended defects, using a method that averages over heterophase configurations and simplifies the problem to effective homogeneous models.

Contribution

It introduces a novel statistical method for modeling materials with extended nanosize defects by averaging heterophase configurations and deriving effective Hamiltonians.

Findings

Method successfully reduces complex defect structures to effective homogeneous models.

Illustrated using a lattice model with random disorder regions.

Provides a framework for predicting material properties with nanoscale defects.

Abstract

Many materials contain extended defects of nanosize scale, such as dislocations, cracks, pores, polymorphic inclusions, and other embryos of competing phases. When one is interested not in the precise internal structure of a sample with such defects, but in its overall properties as a whole, one needs a statistical picture giving a spatially averaged description. In this chapter, an approach is presented for a statistical description of materials with extended nanosize defects. A method is developed allowing for the reduction of the problem to the consideration of a set of system replicas representing homogeneous materials characterized by effective renormalized Hamiltonians. This is achieved by defining a procedure of averaging over heterophase configurations. The method is illustrated by a lattice model with randomly distributed regions of disorder.