94 citations · 414 across the 17 of their papers we have counts for
17 papers
The crossmetric tensor and the geometrical meaning of the imaginary numbers
Cyril Cayron
The product of two Cartesian quaternions can be written as a quadratic form based on a 4x4 matrix made of the symbols 1,i,j,k where i,j,k are imaginary numbers introduced by Hamilt…
The crystallographic quaternions and their product law
Cyril Cayron
Unit quaternions are widely used in science to encode rotations because the quaternion product is more efficient than matrix product and more stable than Rodrigues product to calcu…
A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bezout identities
Cyril Cayron
The paper explains the method to determine a short unit cell attached to any hyperplane given by its integer vector . Equivalently, it gives all the solutions of the $N…
Lattice reduction by cubification
Cyril Cayron
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmi…
Axial heterotwins
Cyril Cayron
The current theory of twin crystallography is based on the concept of invariant plane. The present paper extends the theory to encompass the cases of heterotwins in which the compo…
Solving constrained optimization problems without Lagrange multipliers
Cyril Cayron
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the La…
The transformation matrices (distortion, orientation, correspondence), their continuous forms, and their variants
Cyril Cayron
The crystallography of displacive phase transformations can be described with three types of matrices: the lattice distortion matrix, the orientation relationship matrix, and the c…
Evidence of new twinning modes in magnesium questioning the shear paradigm
Cyril Cayron, Roland Loge
Twinning is an important deformation mode of hexagonal close-packed metals. The crystallographic theory is based on the 150-years old concept of simple shear. The habit plane of th…
The (11-22) and (-12-16) twinning modes modelled by obliquity correction of a (58deg, a+2b) prototype stretch twin
Cyril Cayron
The {11-22} and {11-26} twinning modes were recently put in evidence by Ostapovets et al. (Phil. Mag, 2017)and interpreted as {101-2}-{101-2} double-twins formed by a simultaneous…
Over the shear paradigm
Cyril Cayron
Deformation twinning and martensitic transformations are displacive transformations; they are defined by high speed collective displacements of the atoms, the existence of a parent…
Crystallography of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56 deg, a) contraction twins in magnesium
Cyril Cayron
Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation of 56 deg around the a-axis. The classical theory of deformati…
Displacive model of deformation twinning in hexagonal close-packed metals. Case of the (90 deg, a) and (86 deg, a) extension twins in magnesium
Cyril Cayron
A crystallographic displacive model is proposed for the extension twins in magnesium. It is based on a hard-sphere assumption previously used for martensitic transformations. The a…
A crystallographic model of the {557} habit planes in low-carbon martensitic steels
Cyril Cayron, Annick Baur, Roland Loge
Low-alloy steels are constituted of twenty-four variants of lath martensite that exhibit gradients of orientations from Kurdjumov-Sachs (KS) to Nishiyama-Wassermann (NW). They are…
Comment on 'A new nanoscale metastable iron phase in carbon steels'
Cyril Cayron
We show that the selected area diffraction patterns presented in a recent paper (T. Liu et al. Sci. Rep. 2015 5, 15331) do not prove the existence of a new hexagonal phase in marte…
Continuous atomic displacements and lattice distortions during martensitic transformations in fcc-bcc-hcp systems
Cyril Cayron
This work generalizes our previous works on fcc-bcc martensitic transformations to the larger family of transformations in the fcc-bcc-hcp system and to fcc-fcc mechanical twinning…
Lattice distortion and atomic displacements during the fcc/bcc martensitic transformation
Cyril Cayron
From our previous models of martensitic transformation, the continuous matrices of atomic displacements and lattice deformations from face-centred-cubic (fcc) to body centred-cubic…
One-step theory of fcc-bcc martensitic transformation
Cyril Cayron
Martensitic transformation in steels is responsible for their very high strength and has thus been studied for more than one century since the first works of Martens. However, ther…