Coarse-graining atomic displacements in a solid produces both local affine strains and non-affine fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show ho
w a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {it experimentally realisable} external field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal crystals using commonly available holographic laser tweezer and video microscopy techniques, and may lead to simple ways of controlling the defect density of a colloidal solid.
We study the phase ordering dynamics of a two dimensional model colloidal solid using molecular dynamics simulations. The colloid particles interact with each other with a Hamaker potential modified by the presence of equatorial patches of attractive
and negative regions. The total interaction potential between two such colloids is, therefore, strongly directional and has three-fold symmetry. Working in the canonical ensemble, we determine the tentative phase diagram in the density-temperature plane which features three distinct crystalline ground states viz, a low density honeycomb solid followed by a rectangular solid at higher density, which eventually transforms to a close packed triangular structure as the density is increased further. We show that when cooled rapidly from the liquid phase along isochores, the system undergoes a transition to a strong glass while slow cooling gives rise to crystalline phases. We claim that geometrical frustration arising from the presence of many crystalline ground states causes glassy ordering and dynamics in this solid. Our results may be easily confirmed by suitable experiments on patchy colloids.
We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and {em
non-affine} degrees of freedom. Non-affineness, $phi$, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of $phi$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({hv I}, {hv II} and {hv III}) for the structure of the product droplet depending on the scaled mobilities of $phi$ parallel and perpendicular to the parent-product interface and the stress threshold. In {hv I}, $phi$ is vanishingly small, {hv II} involves large $phi$ localized in regions of high stress within the parent-product interface and {hv III} where $phi$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $lproptosqrt{W}$ in solution {hv I}, this relation does not hold for {hv II} or {hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.
Nucleation of a solid in solid is initiated by the appearance of distinct dynamical heterogeneities, consisting of `active particles whose trajectories show an abrupt transition from ballistic to diffusive, coincident with the discontinuous transitio
n in microstructure from a {it twinned martensite} to {it ferrite}. The active particles exhibit intermittent jamming and flow. The nature of active particle trajectories decides the fate of the transforming solid -- on suppressing single particle diffusion, the transformation proceeds via rare string-like correlated excitations, giving rise to twinned martensitic nuclei. These string-like excitations flow along ridges in the potential energy topography set up by inactive particles. We characterize this transition using a thermodynamics in the space of trajectories in terms of a dynamical action for the active particles confined by the inactive particles. Our study brings together the physics of glass, jamming, plasticity and solid nucleation.
We study the nucleation dynamics of a model solid state transformation and the criterion for microstructure selection using a molecular dynamics (MD) simulation. Our simulations show a range of microstructures depending on the depth of quench. We clo
sely follow the dynamics of the solid and find that transient {em non-affine zones} (NAZ) are created at and evolve with the rapidly moving transformation front. The dynamics of these plastic regions determines the selection of microstructure. We formulate an {it elastoplastic model} which couples the elastic strain to the non-affine deformation, and recover all the qualitative features of the MD simulation. Using this model, we construct a dynamical phase diagram for microstructure selection, in addition to making definite testable predictions.
