The martensitic phase transition is one in which there is a transformation path defined by a shear strain. Typically the low temperature "martensite" phase is a symmetry subgroup of the high temperature "austenite" phase. But sometimes the martensite has additional symmetry.
Martensites should be a nice target for molecular dynamics, but in fact they are rather painful on account of finding potentials which undergo the transition, and applying appropriate boundary conditions.
Many of the interesting features of martensites are already present in two dimensions, and a binary Lennard-Jones potential can be constructed to give the transition. The austenite is a square structure(C), and the martensite is a hexagonal structure(H). There are four possible variants of the martensite, depending on how the transformation goes.
If we set the system up as a bar with free boundary conditions, care must be taken because the surface energy per atom is much larger than the transformation energy. Indeed, for small systems surface tension leads to a significant contraction of the bar.
In the first movie, we see a bar clamped at one end and set up in the bulk (C) structure. The surface tension causes the bar to contract. Once it is in equilibrium with its own surface tension we cool the sample, inducing the C-H transition which propogates right to left across the bar. the latent heat raises the temperature, but it is then cooled again by the thermostat. The transformation strain causes a shear and rotation, but because of the clamping (and inertia) rotation to a single variant is impossible. Thus the bar comprises successive twins. A feature of this model is that the variant boundary has zero energy (!): this arises because of the additional symmetry of the H phase..
Movie ; GIF ; Movie ; GIF ; GIF
The animated GIF show fiducial lines with traces around the C unit cell. These pick out the variant boundaries (i.e. where the direction of transformation shear changed)
In the second movie we see a bar stabilised in the C structure being cooled through the transition. Here the atoms at each end are held fixed. On cooling the temperature drops, but then the transition releases latent heat into the system warming it. The transition begins at the boundary (bottom right) and a spear-shaped region of H is formed, which then spreads along the bar. The interface between this and the C is on a "habit" plane which is defines by the geometry of the transition to be 45 degrees. The expanded region shows the pre-transition elastic straining and the final twinned microstructure with occasional stacking fauls where a single plane has sheared the "wrong" way. Overall the total shear is zero (fixed ends) so the amounts of reddish and yellowish variants must be equal. Note the surface roughness: unlike the mathematical theory of martensite based on affine deformations, the twinned structure here forms to accommodate the strains, not to fit the boundaries. Details of twin and point defects are shown in close-up.
All these simulations are still affected by the free surfaces, in that every twin appears to extend to the surface. To eliminate this effect requires still larger simulations. In the next simulation we use a wider bar free at both ends set up in the C phase but cooled to be unstable with respect to the transition. The spear-shaped H region is nucleated in the middle of the free surface, but now the spread perpendicular to the needle happens reasonable far from the free surface. This region must then transform while strain-compensating, which it does by creating a finely-twinned structure.
Despite the free surfaces, there is no body-rotation of the sample. Presumably this is a kinetic effect in that new variants are nucleated locally before the inertia of the body can relax the shear to the boundary.
A detail cut from the centre of such a run shows the effecte. Movie
Finally, a square sample shows coarse twins at the surface and fine microtwins in the centre. GIF
This page showcases work by Oliver Kastner from an HPC-Europa visit. Movies are in AVI format
