Koumatos K, Muehlemann A
Gran Sasso Science Institute , Viale Fransesco Crispi 7 , 67100 L'Aquila, Italy.
Mathematical Institute , University of Oxford , Woodstock Road, Oxford OX2 6GG, UK.
Proc Math Phys Eng Sci. 2016 Apr;472(2188):20150865. doi: 10.1098/rspa.2015.0865.
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.
本文基于最小原子运动准则，对E. C. 贝恩在1924年提出的关于所谓贝恩应变最优性的猜想给出了严格证明。引入并运用了一个探索多种此类最优性准则的通用框架，以证明任意两个布拉维晶格之间存在最优变换。提供了一种确定此最优变换的精确算法和图形用户界面。除了关于面心立方到体心立方转变的贝恩猜想外，应用还包括面心立方到体心四方转变以及对苯二甲酸两个三斜相之间的转变。
