M. P. Gururajan

Wrinkling of atomic planes in ultrathin Au nanowires.

A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.

3D Growth Kinetics of Precipitates with Anisotropic Interfacial Free Energy: A Phase-Field Study

In this study, we report on the 3D growth kinetics of an isolated β precipitate growing from a supersaturated α matrix. The α-β interfacial energy is assumed to be cubic anisotropic; specifically, either (100) or (111) interfaces are preferred. The diffusivity is maintained a constant in our model; this constant diffusivity is achieved through a combination of Cahn–Hilliard and Allen–Cahn equations (with appropriate choice of model free energy parameters). Our results indicate that depending on the matrix supersaturation, the growth modes can either be shape preserving or non-shape preserving. In the case of shape preserving growth, we are able to verify, that as indicated by the earlier theoretical studies, the classical Zener-Frank theories can be used to predict the growth rates of precipitates.

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.

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.