1510.04708v5.pdf (952.48 kB)
Optimality of general lattice transformations with applications to the Bain strain in steel
journal contribution
posted on 2023-06-09, 04:55 authored by Konstantinos KoumatosKonstantinos Koumatos, Anton MuehlemannThis 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 SciencesISSN
1364-5021Publisher
Royal SocietyExternal DOI
Issue
2188Volume
472Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes