A general method to determine twinning elements

J Appl Crystallogr. 2010 Dec 1;43(Pt 6):1426-1430. doi: 10.1107/S0021889810037180. Epub 2010 Nov 9.

Abstract

The fundamental theory of crystal twinning has been long established, leading to a significant advance in understanding the nature of this physical phenomenon. However, there remains a substantial gap between the elaborate theory and the practical determination of twinning elements. This paper proposes a direct and simple method - valid for any crystal structure and based on the minimum shear criterion - to calculate various twinning elements from the experimentally determined twinning plane for Type I twins or the twinning direction for Type II twins. Without additional efforts, it is generally applicable to identify and predict possible twinning modes occurring in a variety of crystalline solids. Therefore, the present method is a promising tool to characterize twinning elements, especially for those materials with complex crystal structure.