A new method for lattice reduction using directional and hyperplanar shearing.

A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called `basis rhombicity' which is the sum of the absolute values of the elements of the metric tensor associated with the basis. The levels of reduction are quite similar to those obtained with the Lenstra-Lenstra-Lovász (LLL) algorithm, at least up to the moderate dimensions that have been tested (lower than 20).

A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout's identities.

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them.

The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigenda.

Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411-437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.

The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants.

The crystallography of displacive/martensitic phase transformations can be described with three types of matrix: the lattice distortion matrix, the orientation relationship matrix and the correspondence matrix. Given here are some formulae to express them in crystallographic, orthonormal and reciprocal bases, and an explanation is offered of how to deduce the matrices of inverse transformation. In the case of the hard-sphere assumption, a continuous form of distortion matrix can be determined, and its derivative is identified to the velocity gradient used in continuum mechanics.

A one-step mechanism for new twinning modes in magnesium and titanium alloys modelled by the obliquity correction of a (58°, a + 2b) prototype stretch twin.

The \{ 11{\overline 2}2\} and \{ 11{\overline 2}6\} twinning modes were recently discovered by Ostapovets et al. [Philos. Mag.

Variant selection in surface martensite.

A significant variant selection is reported in isothermal martensite formed on the surface of an Fe-30% Ni sample. The selection phenomenon is modelled using different descriptions of the martensitic phase transformation. In particular, matrices based on the phenomenological theory of martensite crystallography, the Jaswon and Wheeler distortion, and the continuous face centred cubic-body centred cubic distortion are compared.

Hard-sphere displacive model of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56°, a) contraction twins in magnesium.

Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation (56°, a). The classical shear theory of deformation twinning does not specify the atomic displacements and does not explain why contraction twinning is less frequent than extension twinning. The paper proposes a new displacive model in line with our previous work on martensitic transformations and extension twinning.

{225} habit planes in martensitic steels: from the PTMC to a continuous model.

Fine twinned microstructures with {225} habit planes are commonly observed in martensitic steels. The present study shows that an equibalanced combination of twin-related variants associated to the Kurdjumov-Sachs orientation relationship is equivalent to the Bowles and Mackenzie's version of the PTMC for this specific {225} case. The distortion associated to the Kurdjumov-Sachs orientation relationship results from a continuous modeling of the FCC-BCC transformation.

Embedded layer of Ag nanoparticles prepared by a combined PECVD/PVD process producing SiOxCy-Ag nanocomposite thin films.

Structural properties of SiO(x)C(y)-Ag nanocomposite thin films prepared by a dual process PVD-PECVD in the same reactor have been investigated. The experimental results have demonstrated the influence of a PECVD process carried out at room temperature for the growth of a dielectric matrix on the size and the distribution density of Ag nanoparticles (NPs) deposited beforehand by magnetron sputtering. The plasma during the growth of the encapsulation SiO(x)C(y) layer caused a diffusion of silver from NPs through the SiO(x)C(y) matrix associated with a decrease in the average size of nanoparticles and an increase of their distribution density.

Odd electron diffraction patterns in silicon nanowires and silicon thin films explained by microtwins 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.

Growth of one-dimensional Si/SiGe heterostructures by thermal CVD.

The first results on a simple new process for the direct fabrication of one-dimensional superlattices using common CVD chambers are presented. The experiments were carried out in a 200 mm industrial Centura reactor (Applied Materials). Low dimensionality and superlattices allow a significant increase in the figure of merit of thermoelectrics by controlling the transport of phonons and electrons.

ARPGE: a computer program to automatically reconstruct the parent grains from electron backscatter diffraction data.

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.

GenOVa: a computer program to generate orientational variants.

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.

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Sigma3(n) grain boundaries.

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 Sigma3(n) 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 Sigma3(n) operators for any twinning order.

Groupoid of orientational variants.

Daughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants to be determined.