Partitioning of solutes in multiphaseTi–Alalloys

Abstract

First-principles calculations based on a plane-wave pseudopotential method, as implemented in the VASP code, are presented for the formation energies of several transition-metal and non-transition-metal dopants in $\mathrm{Ti}--\mathrm{Al}$ alloys. Substitution for either Ti or Al in $\ensuremath{\gamma}\text{\penalty1000-\hskip0pt}\mathrm{Ti}\mathrm{Al}$, ${\ensuremath{\alpha}}_{2}\text{\penalty1000-\hskip0pt}{\mathrm{Ti}}_{3}\mathrm{Al}$, ${\mathrm{Ti}}_{2}\mathrm{Al}\mathrm{C}$, and ${\mathrm{Ti}}_{3}\mathrm{Al}\mathrm{C}$ are considered. Calculated (zero-temperature) defect formation energies exhibit clear trends as a function of the periodic-table column of transition metal solutes. Early transition metals in TiAl prefer the Ti sublattice, but this preference gradually shifts to the Al sublattice for late transition metals; the Ti sublattice is preferred by all transition metal solutes in ${\mathrm{Ti}}_{3}\mathrm{Al}$. Partitioning of solutes to ${\mathrm{Ti}}_{3}\mathrm{Al}$ is predicted for mid-period transition elements, and to TiAl for early and late transition elements. A simple Ising model treatment demonstrates the plausibility of these trends, which are in excellent overall agreement with experiment. The influence of temperature on formation energies is examined with a cluster expansion for the binary TiAl alloys and a low temperature expansion for dilute ternary alloys. Results for Nb-doped alloys provide insight into the relative sensitivity of solute partitioning to individual contributions to the free energy. Whereas the calculated formation energy of Nb (substitution) at zero temperature favors partitioning to ${\ensuremath{\alpha}}_{2}\text{\penalty1000-\hskip0pt}{\mathrm{Ti}}_{3}\mathrm{Al}$, temperature-dependent contributions to the formation free energy, evaluated at $1075\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, favor partitioning to $\ensuremath{\gamma}\text{\penalty1000-\hskip0pt}\mathrm{Ti}\mathrm{Al}$, in agreement with experiment.