Optimality of general lattice transformations with applications to the Bain strain in steel.
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.
Gran Sasso Science Institute , Viale Fransesco Crispi 7 , 67100 L'Aquila, Italy.
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Koumatos
Mathematical Institute , University of Oxford , Woodstock Road, Oxford OX2 6GG, UK.
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0000-0002-8807-9686
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Muehlemann
Bain strain in steel; Bravais lattices; fcc to bcc; lattice transformation; least atomic movement; terephthalic acid