On Cyclical Phase Transformations in Driven Alloy Systems

Cyclical phase transformations occurring in driven materials syntheses such as ball milling are described in terms of a free energy minimization process of participant phases. The oscillatory flow behavior of metals with low stacking fault energies during hot working is taken as a prototype in which a ductile crystalline phase sustains undulation in its free energy, due to the alternate succession of work-hardening and work-softening mechanisms. A time-dependent, oscillatory free energy function is then obtained by solving a delay differential equation (DDE), which accounts for a time lag due to diffusion. To understand cyclical transitions on an atomistic scale, work is extended to molecular dynamics simulations. Under shear deformation, a two-dimensional nanocrystal shows cyclical transitions between an equilibrium rhombus and a nonequilibrium square phase. Three-dimensional simulations show crystalline-to-glass transitions at high strain rates, but very high shear strain rates are found to lead to a latticelike network structure in the plane perpendicular to the shear direction, with strings of atoms parallel to the shear direction.