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

PDF - Accepted Version Download (975kB)

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:	22 Jan 2018 09:16
URI:	http://srodev.sussex.ac.uk/id/eprint/66434

View download statistics for this item

📧 Request an update