Grain growth in thin films with a fibre texture studied by phase-field simulations and mean field modelling

'Grain growth in thin films with a fibre texture studied by phase-field simulations and mean field modelling', This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. The evolution of fibre textured structures is simulated in two dimensions using a generalised phase field model assuming two forms for the misorientation dependence of the grain boundary energy. In each case, a steady-state regime is reached after a finite amount of grain growth, where the number and length weighted misorientation distribution functions (MDF) are constant in time, and the mean grain area A as a function of time t follows a power growth law A À A 0 ¼ kt n with n close to 1 and A 0 the initial mean grain area. The final shape of the MDF and value of the prefactor k in the power growth law clearly correlate with the misorienta-tion dependence of the grain boundary energy. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with non-uniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results. In previous studies on grain growth in anisotropic fibre textured systems, this steady-state regime was often not reached, which resulted in wrong conclusions on the growth exponent n and evolution of the MDF. 1. Introduction Many thin films have a columnar grain structure in which all crystals have nearly identical orientation in the axial direction (the direction perpendicular to the film), but random radial orientation (in the plane of the film) [1]. The symmetry is, for example, introduced by a preferential nucleation or growth of certain grain orientations due to anisotropy in the surface energy or film–substrate interfacial energy. Many technically important characteristics of the films, such as their strength, conductivity, corrosion …