| The phase-field method has become in recent years the method of choice for modelling the evolution of complex microstructures in materials. In particular, for solidification, quantitative agreement between simulations and experiments has been obtained for the growth of single crystals. The same accuracy has not yet been reached, however, for polycristalline materials. The reason is that one has to face the additional problem of how to represent the crystalline orientation of different grains and the anisotropic properties of interfaces and grain boundaries. Two types of phase-field models have been proposed. The first uses a separate phase-field variable for each grain, whereas the second combines a single phase field with one or more fields representing the local crystalline orientation. We discuss in detail the properties of the second class of models and analyze some simple test cases, such as a tricrystal with planar grain boundaries and a crystallite in equilibrium with its melt, and point out some difficulties arising from the traditional representation of crystalline anisotropy in these models, such as a shift of the equilibrium melting temperature and a spurious grain boundary drift. Several possibilities to remove these (small) spurious effects are discussed. |
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