Numerical Models of Crystallization and Its Direction for Metal and Ceramic Materials in Technical Application

Structure of metallic and also majority of ceramic alloys is one of the factors, which significantly influence their physical and mechanical properties. Formation of structure is strongly affected by production technology, casting and solidification of these alloys. Solidification is a critical factor in the materials industry, e.g. (Chvorinov, 1954). Solute segregation either on the macroor micro-scale is sometimes the cause of unacceptable products due to poor mechanical properties of the resulting non-equilibrium phases. In the areas of more important solute segregation there occurs weakening of bonds between atoms and mechanical properties of material degrade. Heterogeneity of distribution of components is a function of solubility in solid and liquid phases. During solidification a solute can concentrate in inter-dendritic areas above the value of its maximum solubility in solid phase. Solute diffusion in solid phase is a limiting factor for this process, since diffusion coefficient in solid phase is lower by three up to five orders than in the melt (Smrha, 1983). When analysing solidification of these alloys so far no unified theoretical model was created, which would describe this complex heterogeneous process as a whole. During the last fifty years many approaches with more or less limiting assumptions were developed. Solidification models and simulations have been carried out for both macroscopic and microscopic scales. The most elaborate numerical models can predict micro-segregation with comparatively high precision. The main limiting factor of all existing mathematical micro-segregation models consists in lack of available thermodynamic and kinetic data, especially for systems of higher orders. There is also little experimental data to check the models (Kraft & Chang, 1997).