Phase transitions of binary alloys with elastic inhomogeneity

Curvature-driven feedback on aggregation-diffusion of proteins in lipid bilayers

Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn-Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane-protein interactions.

Sharp Phase Field Method

Phase field modeling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretization scheme with a grid spacing small enough to preserve the continuous character of the theory. We present here a new formulation, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method. We show that interfacial kinetic properties are reproduced with a high accuracy. Finally, we apply the model to a situation where conserved and nonconserved fields are coupled.

Effect of elastic interactions on coarsening in elastically inhomogeneous multiphase systems

We investigate the effect of interactions between inclusions on the coarsening behavior of elastically inhomogeneous multiphase systems with lattice misfit using a recently introduced two-dimensional multiscale model based on the classical time-dependent density-functional theory. We show that spontaneous shape changes are very efficient in limiting the impact of the interactions on the chemical potential of inclusions. For this reason, the interactions between isolated pairs of inclusions are unable to significantly affect coarsening. At higher volume fraction, the efficiency of shape changes drops and major shifts of the chemical potential are observed; these are shown to be strong enough to counteract capillarity. For example, we show that sufficient confinement by neighboring inclusions causes inverse coarsening and we provide illustrations of this. We also examine the effect of interface elasticity in the presence of interactions. We demonstrate that elasticity induces kinetic faceting and gives rise to oscillations in the chemical potential of the inclusions. This is shown to lead to the stabilization of microstructures composed of inclusions of various sizes. Finally, we propose a simple modified Lifshitz-Slyozov-Wagner model for assessing the effect of interactions on coarsening. The results are shown to be in excellent agreement with experiment.

Kinetic faceting and anomalous coarsening in elastically inhomogeneous multiphase systems

With a view of finding a route toward microstructural stability in alloys, we numerically study the impact of elastic inhomogeneities on the growth of inclusions in multiphase systems. We show that growth can proceed either continuously at rough interfaces, or in a layer-by-layer fashion following an elastically induced kinetic faceting process. In the former case, the chemical potential of the inclusions is a smooth function of size, while in the latter case, elasticity increases the barrier for nucleation of new terraces on the facets, leading to an oscillatory behavior of the chemical potential and hence a strong resistance against coarsening, opening up the possibility to stabilize the structure.

Interface properties and microstructural stabilization in elastically inhomogeneous multiphase systems

Using a two-dimensional multiscale model based on the classical time-dependent density-functional theory for lattice systems we recently introduced, we numerically study the impact of elastic inhomogeneities on the growth of isolated inclusions in multiphase alloys. We demonstrate that the coupling between the overall interface structure (as determined by the shape of the inclusions) and the local, atomic-scale structure can be very large, and is able to significantly affect the behavior of inclusions during growth. Elasticity is shown to have a strong influence on the local energetics at interfaces, leading to shape modulations and kinetic faceting. Morphological and energetic changes induce oscillations in the chemical potential of the inclusions, opening the way to the stabilization of multi-inclusion microstructures, consistent with experiment. We demonstrate that the interface elastic misfit is a key parameter for controlling the strength of elastic effects.

Multiscale model for microstructure evolution in multiphase materials: Application to the growth of isolated inclusions in presence of elasticity

We present a multiscale model based on the classical lattice time-dependent density-functional theory to study microstructure evolution in multiphase systems. As a first test of the method, we study the static and dynamic properties of isolated inclusions. Three cases are explored: elastically homogeneous systems, elastically inhomogeneous systems with soft inclusions, and elastically inhomogeneous systems with hard inclusions. The equilibrium properties of inclusions are shown to be consistent with previous results: both homogeneous and hard inclusions adopt a circular shape independent of their size, whereas soft inclusions are circular below a critical radius and elliptic above. In all cases, the Gibbs-Thomson relation is obeyed, except for a change in the prefactor at the critical radius in soft inclusions. Under growth conditions, homogeneous inclusions exhibit a Mullins-Sekerka shape instability [W. Mullins and R. Sekerka, J. Appl. Phys. 34, 323 (1963)], whereas in inhomogeneous systems, the growth of perturbations follows the Leo-Sekerka model [P. Leo and R. Sekerka, Acta Metall. 37, 3139 (1989)]. For soft inclusions, the mode instability regime is gradually replaced by a tip-growing mechanism, which leads to stable, strongly out-of-equilibrium shapes even at very low supersaturation. This mechanism is shown to significantly affect the growth dynamics of soft inclusions, whereas dynamical corrections to the growth rates are negligible in homogeneous and hard inclusions. Finally, due to its microscopic formulation, the model is shown to automatically take into account phenomena caused by the presence of the underlying discrete lattice: anisotropy of the interfacial energy, anisotropy of the kinetics, and preferential excitation of shape perturbations commensurate with the rotational symmetry of the lattice.

Interplay between diffusive and displacive phase transformations: time-temperature-transformation diagrams and microstructures

Materials which can undergo extremely fast displacive transformations as well as very slow diffusive transformations are studied using a Ginzburg-Landau framework. This simple model captures the essential physics behind microstructure formation and time-temperature-transformation diagrams in alloys such as steels. It also predicts the formation of mixed microstructures by an interplay between diffusive and displacive mechanisms. The intrinsic volume changes associated with the transformations stabilize mixed microstructures such as martensite-retained austenite (responsible for the existence of a martensite finish temperature) and martensite-pearlite.