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Course# MSE-651: Crystallography of structural phase transformations

Summary

The microstructure of many alloys and ceramics are constituted of very fine intricate domains (variants) created by diffusive or displacive phase transformations. The course introduces the crystallographic tools required to define, calculate and predict the different configurations of variants.

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Instructor

Related courses (7)

Related MOOCs (11)

Related concepts (140)

Cyril Cayron

1992-1995 Engineering School. Ecole des Mines de Nancy.
1994-1995 Master's degree in Materials Science (rank = 1st)
1995-1996 Military Service
1996-2000 PhD at EPFL-CIME. Precipitation in 6xxx alloys and composites.
2000-2014 Researcher, Engineer and Group leader on materials for new energies at CEA-Grenoble, France.
2012 Habilitation to supervise researches (HDR)
2014-now Senior Scientist at EPFL-LMTM
Creator of the computer programs GenOVa and ARPGE (in Python).
I currently work on crystallographic models of martensitic transformations and deformation twinning.

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

Ce cours permet l'acquisition des notions essentielles relatives à la structure de la matière, aux équilibres et à la réactivité chimique en liaison avec les propriétés mécaniques, thermiques, électri

The aim of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

This is an introduction to modern algebra: groups, rings and fields.

This course covers the metallurgy, processing and properties of modern high-performance metals and alloys (e.g. advanced steels, Ni-base, Ti-base, High Entropy Alloys etc.). In addition, the principle

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Diffusionless transformation

Diffusionless transformations, also referred to as displacive transformations, are solid-state changes in the crystal structure that do not rely on the diffusion of atoms over long distances. Instead, they occur due to coordinated shifts in atomic positions, where atoms move by a distance less than the span between neighboring atoms while maintaining their relative arrangement. An illustrative instance of this is the martensitic transformation observed in steel.

Symmetry (physics)

In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries.

Transformation matrix

In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.

Crystallographic database

A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules. They are characterized by symmetry, morphology, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.

Rigid transformation

In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space.