Anomalous extra spots visible in electron diffraction patterns of silicon nanowires and silicon thin films are explained by the presence of micro- and nanotwins.

Odd electron diffraction patterns (EDPs) have been obtained by transmission electron microscopy (TEM) on silicon nanowires grown via the vapour–liquid–solid method and on silicon thin films deposited by electron beam evaporation. Many explanations have been given in the past, without consensus among the scientific community: size artifacts, twinning artifacts or, more widely accepted, the existence of new hexagonal Si phases. In order to resolve this issue, the microstructures of Si nanowires and Si thin films have been characterized by TEM, high-resolution transmission electron microscopy (HRTEM) and high-resolution scanning transmission electron microscopy. Despite the differences in the geometries and elaboration processes, the EDPs of the materials show great similarities. The different hypotheses reported in the literature have been investigated. It was found that the positions of the diffraction spots in the EDPs could be reproduced by simulating a hexagonal structure with c/a = 12(2/3)1/2, but the intensities in many EDPs remained unexplained. Finally, it was established that all the experimental data, i.e. EDPs and HRTEM images, agree with a classical cubic silicon structure containing two microstructural defects: (i) overlapping Σ3 microtwins which induce extra spots by double diffraction, and (ii) nanotwins which induce extra spots as a result of streaking effects. It is concluded that there is no hexagonal phase in the Si nanowires and the Si thin films presented in this work.

This computer program calculates the orientational variants, the operators and the composition table of a groupoid.

A computer program called GenOVa, written in Python, calculates the orientational variants, the operators (special types of misorientations between variants) and the composition table associated with a groupoid structure. The variants can be represented by three-dimensional shapes or by pole figures.

A computer program has been written to reconstruct the parent grains from EBSD data of phase transition materials.

A computer program called ARPGE written in Python uses the theoretical results generated by the computer program GenOVa to automatically reconstruct the parent grains from electron backscatter diffraction data obtained on phase transition materials with or without residual parent phase. The misorientations between daughter grains are identified with operators, the daughter grains are identified with indexed variants, the orientations of the parent grains are determined, and some statistics on the variants and operators are established. Some examples with martensitic transformations in iron and titanium alloys were treated. Variant selection phenomena were revealed.

Multiple twinning in cubic crystals is represented geometrically by three-dimensional fractals and algebraically by groupoids. The groupoid composition table can be used to identify the Σ3n grain boundaries in EBSD maps.

Multiple twinning in cubic crystals is represented geometrically by a three-dimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the Σ3n operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of variants and the number of Σ3n operators for any twinning order. Different substructures of this groupoid (free group, semigroup) can be equivalently introduced to encode the operations with strings. For any coding substructure, the operators are expressed by sets of equivalent strings. The composition of two operators is determined without any matrix calculation by string concatenations. It is multivalued due to the groupoid structure. The composition table of the operators is used to identify the Σ3n grain boundaries and to reconstruct the twin related domains in the electron back-scattered diffraction maps.