Thesis (M.Sc (Physics)) --University of Limpopo, Turfloop Campus, 2009 / The structural and energetic properties of the Ti-Al and Pt-Ti alloys have been carried out using first-principles total energy calculation of the density functional theory. We found a good correlation between VASP and CASTEP calculations with the experimental data. The equilibrium lattice constants for both systems are in good agreement with the experimental values (within 3% agreement). Furthermore, the heats of formation were calculated in order to determine the relative structural stabilities of the Ti-Al and Pt-Ti alloys. We predict that the L10 TiAl is the most stable structure with the lowest heats of formation (more negative Hf) consistent with the experimental observations. The 50% composition of the PtTi SMA’s in particular B19/B19′ phases predict values to be closer to each other, with B19′ being the most stable phase. A comparison of the energy differences between different PtTi phases, yields the relative energies in the order B2>L10>B19>B19'. The elastic constants for B19/B19′ and L10 show the positive shear modulus while a negative shear modulus was observed for B2 phase (mechanical instability). Similarly, the phonon dispersions and the density of states for the B2, L10, B19 and B19′ PtTi shape memory alloys were calculated and are consistent with the heats of formation. The phonon dispersion curves revealed a softening of modes along high symmetry directions (M and R). This confirms that the B2 structure is less stable as compared to the other structures. The density of states for the 50% PtTi composition structures were also calculated and are consistent with the stability trend. Furthermore the transformation from B2-L10 was investigated using Bain’s path and the B2 and L10 phases were depicted at c/a=1 and c/a=√2 respectively. / NRF & CSIR