Interplay between α(Ti) nucleation and growth during peritectic solidification investigated by phase-field simulations.

The properties of modern TiAl-based alloys with aluminum contents around 45 at.% critically depend on the as solidified α(Ti) grain structure. Commonly, a rather coarse grain structure is obtained if α(Ti) forms via the peritectic reaction '[Formula: see text]'. Phase-field simulations have been applied to perform a case study of grain structure formation during the early peritectic growth under unidirectional growth conditions. In the absence of foreign nucleation sites, the peritectic α(Ti) phase nucleates on the dendritic surface of the properitectic ß(Ti) phase. For typical values of the critical nucleation undercooling, coarse structures with large elongated grains are reproduced. A delicate interplay between nucleation and growth is predicted for reduced values of the critical undercooling. In this case, the alloy composition is found to play an additional role. An effective grain refinement by frequent nucleation is obtained, if potent nucleants can reduce the critical undercooling below the local growth undercooling. Complementary Scheil calculations and Bridgman experiments show that in situ precipitation of TiB(2) particles can be controlled by adequate boron addition. Both, numerical predictions and experiments confirm that these particles can act as effective nucleation agents and significantly reduce the grain size of α(Ti).

Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application.

A multiphase-field model previously proposed by the authors is reformulated in a thermodynamically consistent form and extended to multicomponent systems. The phase-field and diffusion equations, derived from a free energy functional, are compared to those postulated in the previous model in the limit of a binary alloy. The constraint of local quasiequilibrium, which is equivalent to the postulate of equal diffusion potentials for coexisting phases, is deduced from a variational principle. Solute partitioning and evaluation of the thermodynamic driving force for phase transformation are done by numerical minimization of the free energy of the multiphase system using the Calphad approach. A local extrapolation scheme which enhances the computational efficiency for complex numerical simulations of technical alloys is presented. It is shown that this extrapolation scheme, used in a "multibinary" approximation, reproduces the former model without restriction to dilute solutions.