Factors determining crystal–liquid coexistence under shear

The interaction between an imposed shear flow and an order–disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter1,2,3,4 is observed to spontaneously form bands characterized by different local order—for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour5. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear6 and lubrication7,8. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures9, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments10,11, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.