Papers by Author: Turab Lookman

Abstract: We develop a phase field model that describes the elastic distortion of a ferroelastic material with cubic anisotropy due to an arbitrary dislocation network and a uniform external load. The dislocation network is characterized using the Nye tensor and enters the formulation via a set of incompatibility constraints for the internal strain field. The long-range elastic response of the material is obtained by minimization of the free energy that accounts for higher order terms of the order parameters and symmetry-adapted strain gradients. To demonstrate the performance of the model, a minimal version of continuum dislocation dynamics is used to investigate the simultaneous evolution of the network of geometrically necessary dislocations and the internal strain field.

Abstract: We explore the kinetics of a three-state strain pseudospin model for a square/rectangle ferroelastic transition, described by a temperature dependent hamiltonian without quenched disorder, using temperature quench Monte Carlo simulations. The model hamiltonian includes power law anisotropic long range interactions, which lock the domain walls in a symmetry breaking diagonal direction. In athermal parameter regime, there are fast conversions at the athermal transition temperature, but with delay tails above it, as in experiment. The conversion delay tails have a Vogel-Fulcher divergence at transition to austenite. The incubation delays and their insensitivity to elastic energy scales are attributed to entropy barriers. Temperature cycling shows hysteretic behavior in physical quantities.

Abstract: We review the description of ferroelastic transitions in terms of spin models. We show how one can systematically obtain a pseudo-spin Hamiltonian from the Landau energy describing the first order transition between Austenite/Martensite phases. It is shown that a Local Mean-field approximation predicts the same microstructure as the continuous Landau model in terms of strain variables. This method can be applied to a wide range of two and three dimensional transitions. We then demonstrate how quenched disorder in such pseudo-spin models yields the existence of a glass phase, characterized by the Edwards-Anderson order parameter. Our approach uses Mean-field approximation and Monte-Carlo simulations (using Zero Field Cooling/Field Cooling experiments) to study the influence of the long-range interactions. Although our model captures the salient features of a ferroelastic material in the presence of disorder, the influence of the disorder on the high symmetry austenite phase is not quite consistent with expected behavior. We examine different means of introducing disorder that can improve upon the results.

Abstract: The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.