Modelling and simulation of competitive crystal growth : theory, implementation and simulation of the Van der Drift model

Abstract

Residual stresses determine the mechanical properties of metal films. To model these, numerous models based on continuum mechanics have been created which are applicable only for simplified situations. To investigate more sophisticated situations, crystal microstructure morphology simulations can be used as basis. However for this approach the results need to be in a format usable for the subsequent stress simulations. This is possible for the algorithm described in the course of this work, which is based on the Van der Drift model. The approach taken in the creation of the algorithm is flexible and allows for more general cases than previous algorithmic formulations of the model. The program implemented on basis of this algorithm is capable of exporting a mesh usable for the simulation of stress by the finite element method.<br />In addition to the algorithm and its implementations the scaling of the average in-plane crystal size and the a possible extension of the model are investigated. These theoretical results are then used for the simulations and for the analyse of their results.