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

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posted on 2023-06-09, 04:55 authored by Konstantinos KoumatosKonstantinos Koumatos, Anton Muehlemann
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

ISSN

1364-5021

Publisher

Royal Society

Issue

2188

Volume

472

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-25

First Open Access (FOA) Date

2017-04-17

First Compliant Deposit (FCD) Date

2017-01-24

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