Ab initio study of low-temperature phase transformations in ternary solid solution TiCcN1−c

Complete set of totally ordered structures in TiCcN1−c that are stable with respect to formation of anti-phase domains is considered. The calculations of the formation energies are carried out in the framework of the linearized augmented plane wave (LAPW) method as implemented in Wien2k code. The energetically preferable phases are determined for the stoichiometric compositions, cst = 1/8, 7/8, 1/4, 3/4, and 1/2. Using the concentration wave approach the Fourier transforms of the mixing potential are extracted for these phases from ab initio calculations. The obtained data is applied to analyze temperature dependencies of long range order parameters for the phases where the ordering is described by one or two order parameters. Low-temperatures for the order–disorder phase transformations are obtained. This explains the difficulties in experimental study of the low-temperature phase diagram due to frozen kinetics: the time scales on which equilibration to the thermodynamically stable phase takes place exceed the time available for the experiment.