An algebraic description of screw dislocations in SC and BCC crystal lattices

TL;DR

This paper provides an algebraic framework for describing screw dislocations in SC and BCC crystal lattices, linking strain energy to special functions, which enhances understanding of dislocation behavior in these materials.

Contribution

It introduces an algebraic approach using free abelian groups and fibering structures to model screw dislocations in specific crystal lattices, connecting strain energy to Epstein-Hurwitz zeta functions.

Findings

Algebraic description of screw dislocations in SC and BCC lattices.

Strain energy approximated by Epstein-Hurwitz zeta function.

Framework facilitates analysis of dislocation properties.

Abstract

We give an algebraic description of screw dislocations in a crystal, especially simple cubic (SC) and body centered cubic (BCC) crystals, using free abelian groups and fibering structures. We also show that the strain energy of a screw dislocation based on the spring model is expressed by the Epstein-Hurwitz zeta function approximately.