THE ROLE OF COMPOSITIONAL STRAIN IN THE INSTABILITY OF SOLID-FLUID THIN FILM INTERFACES

Consider a binary substitutional solid solution not in equilibrium with a fluid rich in either solid component. At the interface, depending on the chemical energy, the solid may selectively lose or gain atoms from the fluid. Any atom exchange upsets the nominal composition; thereby stresses are generated in the solid by simultaneous action of lattice dilation and interdiffusion. As stresses build up, the local changing volume tends to split up into islands in an effort to escape from stresses, while curvature tends to amalgamate the islands in an effort to minimize surface energy. This competition could lead to substantial corrugations of the solid-fluid interface. These corrugations and the thresholds for noticeable competition between stresses and curvatures had an old tradition in chemo-mechanical models of sharp interfaces beginning with Srolovitz (1989). However, stresses were generally considered as a mere cause of external loads, so a pure solid was tacitly asserted. This paper couples elasticity with a conserved-phase field model to mainly investigate the effect of compositional strain on the interface instability process between a binary solid selectively interacting with a fluid. The chemical energy barrier is considered, however, uncoupled from stress, and the mobility quadratically dependent on the gradient of composition. Under initial enforced sinusoidal perturbations, results of simulations showed that the compositional strain parameter can dramatically alter the effect of the chemical energy barrier on the critical wavelength of perturbations that trigger interface instability.

A Phase-Field – Finite Element Model for Instabilities in Multilayer Thin Films

ABSTRACTCahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C0 interpolation functions for the displacement, and C1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model.Using the PF – FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface.Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and metastable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.

On the origin of anomalous birefringence in grandite garnets

The origin of anomalous birefringence of grossular–andradite (grandite) garnets from skarns in Mali and Russia was considered. The crystals had complex superposition of two phenomena: mismatch compositional strain (stress birefringence) and growth ordering of atoms (growth dissymmetrization). Study of the crystals using several experimental techniques (optical microscopy, microprobe analysis, X-ray diffraction topography and X-ray single crystal diffraction) as well as calculations of anomalous birefringence has confirmed this hypothesis. Depending on the crystal composition and growth conditions, the relative magnitude of each phenomenon controls the various optical effects. As a result one can see two groups of crystals which are found to have fundamentally different anomalous optical properties: crystals with low (<0.001) and high (0.001–0.015) values of birefringence. The spatial distribution of birefringence within each group is different and this fact is related to different mechanisms causing optical anomalies: stress birefringence and growth dissymmetrization for these two groups, respectively.