Twinned crystals and how to describe them

Abstract

Twinned crystals are the subject of intensive investigation since the dawn of crystallography, because of their peculiar, eye-catching morphology. The occurrence of twins affects the physical properties of materials and can be a serious hindrance to the solution and refinement of the crystal structure. In this review, we present basic definitions and terminology, a brief survey of the formation mechanism of twins, the reticular and structural approach to explain their occurrence and a few examples. The presence of a substructure shared by the twinned crystals is considered the key feature for the formation of twins. This common substructure can be found by determining first of all a common sublattice, and then by identifying those crystallographic orbits which possess, in their eigensymmetry, operations whose linear part coincide with the twin operation. The orientation and location of the composition surface play, however, a fundamental role in determining the degree of structural restoration which defines the common substructure. Examples in staurolite, feldspars and an organic co-crystal composed of N-iodosaccharin and pyridine, all taken from the literature, are presented.

Keywords:

• Twins
• twinning
• domain structures
• oriented crystal associations

Acknowledgments

Critical remarks by two anonymous reviewers are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here we follow Müller [18], who uses the term misorder instead of the more common disorder, claiming that the phenomenon is not a real disorder but rather ‘order with faults’.

2 Diffusion-controlled civilian transformations correspond to discontinuous transformations.

3 Using the letter $\text{t}$ for the twin operation has a long tradition in the literature on twinned crystals. We trust that this does not lead to any confusion with the conventional usage of t for translation vectors, since in the present article translations play basically no role.

4 We trust that the notation ${\mathcal{H}}^{\ast }$ often used in connection with reciprocal space does not lead to confusion, since the reciprocal space is not relevant in the current context.

Additional information

Notes on contributors

Massimo Nespolo

Massimo Nespolo got an MSc degree in Chemistry from the University of Torino, Italy, and a DrSc degree in Mineralogy from the University of Tokyo, Japan. After a post-doc at the National Institute for Materials Science in Tsukuba, Japan, he got a position at the Université de Lorraine in France, where he is now distinguished professor of crystallography and mineralogy. He is also adjoint lecturer at the University of Graduate Studies in Japan, where he is responsible of a training course in symmetry and group theory taught every Summer at the High Energy Accelerator Research Organization in Tsukuba. Founder and former chair of the Commission on Mathematical and Theoretical Crystallography of the International Union of Crystallography, he serves also in the Commission on Inorganic and Mineral Structures as member and in the Commission on Crystallographic Nomenclature as consultant. He is a former member of the Executive Committee of the European Crystallographic Association, where he served as Education Coordinator, Editor in Chief of the SpringerBriefs in Crystallography, book review editor for the IUCr journals, associate editor of the European Journal of Mineralogy, member of the advisory board of Crystal Research and Technology and member of the IUCr/Oxford University Press (OUP) Book Series Selection Committee. His research currently focuses on twins and modular structures.

Bernd Souvignier

Bernd Souvignier got a Diploma and a PhD in Mathematics, both from RWTH Aachen, Germany. After a post-doc in Sydney, Australia, he worked on automatic speech recognition at the Man-Machine-Interfaces Group at Philips Research Aachen, before getting a position at the Radboud University Nijmegen, The Netherlands, where he is currently associate professor. He has been member of the Commission on Mathematical and Theoretical Crystallography of the International Union of Crystallography, where he now serves as a consultant, and co-author of the sixth edition of Volume A of the International Tables for Crystallography. His research interests span from algorithmic group theory and representation theory and, more generally, various aspect of computer algebra to mathematical crystallography. He co-authored a number of articles on twinned crystals.