CALPHAD-type thermodynamic modeling of the Ti-W-B and Ti-W-Si refractory systems

Based on the thermodynamic descriptions of binary sub-systems as well as the experimental phase equilibria data available in the literature, the Ti-W-B and Ti-W-Si ternary systems have been assessed by the CALPHAD (CALculation of PHAse Diagram) method. The solution phases, i.e. liquid and bcc (beta Ti, W), are described by the substitutional solution model. The binary phases TiB2, TiB, W2B, alpha WB, W2B5, W2B9, Ti5Si3 and W5Si3 with the solubilities of the third element are modeled using the sublattice models. Two ternary compounds tau with composition of (Ti1-xWx)B and Ti3W2Si10 are described by two sublattice model (Ti,W)(1)B-1 and (Ti,W)(1)Si-2, respectively. A set of self-consistent thermodynamic parameters is finally obtained for each of the two ternary systems. Some representative isothermal and vertical sections as well as liquidus surface projections are calculated. Comparisons between the calculated and measured phase diagrams show that the most of experimental data are satisfactorily reproduced by the present thermodynamic descriptions.