New aspects of the energetics of ordered Ti2C and Ti2N

Experimentally, two ordered phases of tetragonal symmetry, namely metastable δ'-Ti2N and stable ε-Ti2N, are found for titanium nitrides of composition Ti2N, whereas for titanium carbides TiCx with x near 0.5 two ordered phases with cubic and trigonal symmetry, respectively, can be traced. By experiment, either cubic Fd3m-Ti2C is found to be a metastable phase which transforms at lower temperatures to trigonal R3-barm-Ti2C, or it is detected to be stable for C contents of 0.52≤x≤0.55 and metastable for higher C concentrations of 0.56≤x≤0.58. FP-LMTO calculations confirm the latter and previous FLAPW investigations the former findings. In the present work, new FLAPW calculations based on the generalized gradient approximation (GGA) for the exchange-correlation potential and using the FLAIR code with force optimization are undertaken for Fd3m- and R3-barm-Ti2C, for δ'- and ε-Ti2N and, for comparison, also for the fictitious phases δ'-Ti2C, ε-Ti2C, Fd3m-Ti2N and R3-barm-Ti2N. These calculations result in cubic Fd3m-Ti2C being the most stable phase and more stable than trigonal R3-barm-Ti2C by 5.0 kJ mol-1 at 0 K, provided that the Ti atoms are allowed to relax. For the nitrides, ε-Ti2N is found to be the most stable phase and more stable than δ'-Ti2N by 3.3 kJ mol-1