IMX Colloquium - Martensite, twins and math

Metallurgists spend part of their time trying to modify the chemical compositions and thermomechanical parameters of the alloys to improve their mechanical properties by forming complex microstructures. Understanding these microstructures requires curiosity, efforts and … math. Let me give two examples. 1) Martensite forms complex intricate assemblies of laths or plates that can be very hard, as in the steels used for sharp knives, or very soft, as in shape memory alloys. Twenty years ago, I understood that martensite variants can be defined from the parent and martensite symmetries by a mathematical structure called groupoid. The groupoid composition table is a kind of signature of the phase transformation; it can be used to reconstruct the parent grains from EBSD maps, with many applications in metallurgy and beyond. 2) Deformation twinning is a lattice shear deformation that may compete with usual dislocation plasticity at low temperatures or high deformation rates, or at room temperature in hexagonal alloys and TWIP steels. Four years ago, I realized that a deep link exists between deformation twinning and three math problems: lattice reduction, Bézout’s identity and integer relations. Thinking these problems in terms of hyperplanar lattice shears allowed me to develop new algorithms that, surprisingly, showed better performances than the usual LLL and PLSQ methods implemented in Mathematica.

Bio: Dr Cyril Cayron is as senior scientist at EPFL in the Laboratory of Thermo Mechanical Metallurgy (LMTM). His domains of research cover metallurgy, microscopy and crystallography. He earned his Ph.D in 2000 at EPFL in the Interdepartmental Center for Electron Microscopy (CIME) on the study by TEM of the interfacial reactions and precipitation in aluminum matrix composites. He worked for fourteen years at Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA) in Grenoble, France, on projects aiming at developing or improving materials for nuclear, aerospace, microelectronic, photovoltaic, hydrogen and Li-battery industries. He came back to EPFL in 2014 to join LMTM. Since then, he has participated to the development of new alloys for watch industries, and helped the students in their works on additive manufacturing. He is also in charge of the SEM Gemini microscope equipped with STEM, EDS and EBSD. He continues his research on martensite and twins thanks to SNSF subsidies and some collaborations with other research groups.