Arka Lahiri

Effect of Surface Energy Anisotropy on the Stability of Growth Fronts in Multiphase Alloys

Eutectic growth offers a variety of examples for pattern formation which are interesting both for theoreticians as well as experimentalists. One such example of patterns is ternary eutectic colonies which arise as a result of instabilities during growth of two solid phases. Here, in addition to the two major components being exchanged between the solid phases during eutectic growth, there is an impurity component which is rejected by both solid phases. During progress of solidification, there develops a boundary layer of the third impurity component ahead of the solidification front of the two solid phases. Similar to Mullins–Sekerka type instabilities, such a boundary layer tends to make the global solidification envelope unstable to morphological perturbations giving rise to two-phase cells. This phenomenon has been studied numerically in two dimensions for the conditions of directional solidification, by Plapp and Karma (Phys Rev E 66:061608, 2002) using phase-field simulations. While, in the work by Plapp and Karma (Phys Rev E 66:061608, 2002) all interfaces are isotropic, in our presentation, we extend the phase-field model by considering interfacial anisotropy in the solid–solid and solid–liquid interfaces and characterize the role of interfacial anisotropy on the stability of the growth front through phase-field simulations in two dimensions.

Finding the insphere of a convex polyhedron: an analytical approach

Recursive analytical formulation for calculating the insphere in an irregular convex polyhedron has been developed. Emphasis has been placed on using coordinate geometry so that the geometric theories can be used without much modification. The results have been compared with some simple geometries for which the analytical results are well known. In all cases the results are matched with analytical results up to eight decimal places. The result for one irregular prism is also presented.

Effect of epitaxial strain on phase separation in thin films

In epitaxially grown alloy thin films, spinodal decomposition may be promoted or suppressed depending on the sign of the epitaxial strain. We study this asymmetry by extending Cahn’s linear theory of spinodal decomposition to systems with a composition dependent lattice parameter and modulus (represented by Vegard’s law coefficients, and y, respectively), and an imposed (epitaxial) strain (e). We show analytically (and confirm using simulations) that the asymmetric effect of epitaxial strains arises only in elastically inhomogeneous systems. Specifically, we find good agreement between analytical and simulation results for the wave number of the fastest growing composition fluctuation. The asymmetric effect due to epitaxial strain also extends to microstructure formation: our simulations show islands of elastically softer (harder) phase with (without) a favourable imposed strain. We discuss the implications of these results to GeSi thin films on Si and Ge substrates, as well as InGaAs films on GaAs substrates.

Theoretical and Numerical Study of Growth in Multi-Component Alloys

In multi-component systems, during diffusion-controlled growth of a precipitate from a supersaturated matrix, differential diffusivities lead to a selection of tie-line compositions different from the thermodynamic tie-line containing the alloy composition. In this paper, we address the multi-component version of the growth problem by extending Zener’s theory, and derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar, cylindrical, and spherical precipitates for independent as well as coupled diffusion of solutes in the scaling regime. We confirm our calculations by sharp interface and phase-field simulations in a ternary setting, in which we also extend the tie-line and growth constant predictions for two well-known limiting cases, namely partition and negligible partition under local equilibrium (PLE and NPLE).

Theoretical and numerical investigation of diffusive instabilities in multi-component alloys

Diffusive instabilities of the Mullins-Sekerka type are one of the principal mechanisms through which microstructures form during solidification. In this study, we perform a linear stability analysis for the perturbation of a planar interface, where we derive analytical expressions to characterize the dispersion behavior in multi-component alloys under directional and isothermal solidification conditions. Subsequently, we confirm our calculations using phase-field simulations for different choices of the inter-diffusivity matrices. Thereafter, we highlight the characteristics of the dispersion curves upon change of the diffusivity matrix and the velocity. Finally, we also depict conditions for absolute stability of a planar interface under directional solidification conditions.

Interfacial free energy anisotropy driven faceting of precipitates

Abstract During solid–solid precipitation, interface free energy anisotropy is known to drive faceting of precipitates. In this paper, using a recently developed phase field formulation based on higher order tensor terms, we develop and implement a family of phase field models and indicate the parameter choices which lead to faceted precipitate morphologies. We also indicate how to choose the parameters given either the known precipitate morphology or the interfacial free energy anisotropy. Specifically, we study the faceting of precipitates in systems with cubic and hexagonal anisotropies; in 2 and 3D implementation of our phase field model, the precipitates do show facets in accordance with the Wulff plot – including cases where the Wulff plot predicts facets made up of more than one family of planes. We also indicate the possible extensions of our model to study other problems of interest.