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

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.

SUBMITTER: Koumatos K

PROVIDER: S-EPMC4892280 | biostudies-literature | 2016 Apr

REPOSITORIES: biostudies-literature

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

Koumatos K K Muehlemann A A

Proceedings. Mathematical, physical, and engineering sciences 20160401 2188

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 t ...[more]

PMID: 27274692

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