Optimality of general lattice transformations with applications to the Bain strain in steel

Koumatos, Konstantinos and Muehlemann, Anton (2016) Optimality of general lattice transformations with applications to the Bain strain in steel. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2188). ISSN 1364-5021

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Abstract

This article provides a rigorous proof of a conjecture by E. C. Bain in 1924 on the optimality of the so-called Bain strain based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a graphical user interface to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body- centred cubic, applications include the face-centred cubic to body-centred tetragonal transition as well as the transformation between two triclinic phases of terephthalic acid.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Depositing User: Konstantinos Koumatos
Date Deposited: 25 Jan 2017 10:23
Last Modified: 25 Apr 2017 21:03
URI: http://sro.sussex.ac.uk/id/eprint/66434

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