Crystallographic description of coincidence-site lattice interfaces in homogeneous crystals

On three-dimensional misorientation spaces

Determining the local orientation of crystals in engineering and geological materials has become routine with the advent of modern crystallographic mapping techniques. These techniques enable many thousands of orientation measurements to be made, directing attention towards how such orientation data are best studied. Here, we provide a guide to the visualization of misorientation data in three-dimensional vector spaces, reduced by crystal symmetry, to reveal crystallographic orientation relationships. Domains for all point group symmetries are presented and an analysis methodology is developed and applied to identify crystallographic relationships, indicated by clusters in the misorientation space, in examples from materials science and geology. This analysis aids the determination of active deformation mechanisms and evaluation of cluster centres and spread enables more accurate description of transformation processes supporting arguments regarding provenance.

Merohedral twins revisited: quinary twins and beyond

A twin is defined as being an external operation between two identical crystals that share a fraction of the atomic structure with no discontinuity from one crystal to the other. This includes merohedral twins, twins by reticular merohedry as well as coherent twins by contact where only the habit plane is shared by the two adjacent crystals (epitaxy). Interesting and original cases appear when the invariant substructure is built with positions belonging to the same {\bb Z}-module as, for example, the quinary twin structure first drawn by Albrecht Dürer [(1525). The Painter's Manual: a Manual of Measurement of Lines, Areas and Solids by Means of Compass and Ruler. Facsimile Edition (1977), translated with commentary by W. L. Strauss. New York: Abaris Books]. This paper will show that the Dürer twins, once defined in five-dimensional space, are simple merohedral twins, in the sense of Georges Friedel, leaving the five-dimensional lattice invariant. This analysis will be generalized to some other higher-order {\bb Z}-modules.

Crystallography of embedded particles in Al–Mg–Zn alloys. Symmetry analysis

Following a proper heat treatment, the alloy system Al–Mg–Zn shows a great wealth of precipitate particles forming coherent (η′ crystals) and incoherent (η crystals) boundaries with the Al matrix. Both the matrix crystal and the precipitate crystals are holohedral, as their point groups correspond to their metric symmetries (m\overline{3}m and 6/mmm). On the basis of published orientational relationships for a principal variant of every known precipitate family, the full sets of orientational variants are deduced by the concepts of intersection groups,Hβ, and variant generating sets,Vβ. The intergrowth symmetry principle has been visualized by stereographic projections. Special attention has been given to patterns of superimposed lattice nodes in reciprocal space and the implications of overlap in terms of observable reflections. It has been uncovered, by artificially reducing the point group symmetry of the coherent η′ phase, whereVβis a proper subgroup of the matrix holohedral, that twin laws for merohedry are revealed whenVβis factorized into a weak direct product.

Anti-Site Bonds and the Structure of Interfaces in SiC

High resolution electron microscopy has been used to study the structure of the 3C/6H interface, Σ,=3 {111}and Σ.=3 {112}grain boundaries in 3C-SiC. In SiC, as in other compound semiconductors, anti-site bonds occur in a variety of defects. These are high energy bonds comparable to that of dangling bonds. But, while dangling bonds at the grain boundaries may be eliminated by reconstruction just as in elemental semiconductors, it may not be possible to avoid anti-site bonds.These problems are discussed for the Σ=3 {112} grain boundary, where the structures proposed for Ge and Si are used as starting models for SiC.

Characterization of interface structures in nanocrystalline germanium by means of high-resolution electron microscopy and molecular dynamics simulations

The atomic structure of nanocrystalline particles formed by vapor deposition and subsequent annealing of amorphous thin films of germanium was studied by high resolution electron microscopy (HREM). The HREM images revealed a strongly varied multiply twinned structure. In some regions of adjacent twins contrast features were detected which were caused by an overlapping of twin lamellae. It will be shown by HREM contrast simulations that these interface types can be described by Σ = 3 n boundaries. The influence of lattice relaxations is taken into consideration by molecular dynamics simulations of the structure models.