Thesis (M.Sc.(Physics)) -- University of Limpopo, 2020 / Sperrylite (PtAs2), platarsite (PtAsS) and palladoarsenide (Pd2As) are platinum group minerals (PGMs) predominantly found in the Platreef Bushveld Complex in South Africa, which is one of the leading countries with highest percentages of platinum group minerals. In this study the density functional theory (DFT), embodied in the Vienna Ab-initio Simulation Package (VASP) code, was employed to investigate the structural, thermodynamically, elastic, mechanical, vibrational, electronic and surface properties of cubic PtAs2 and PtAsS, and monoclinic Pd2As mineral structures. The PtAsS was investigated from both virtual crystal approximations (VCA) solid solution within the Cambridge Serial Total Energy Package (CASTEP) code and the VASP cluster expansion (CE) approach. The cluster expansion phase stability was employed to generate new stable system of PtAsS model and from the cluster expansion binary ground state diagram we found a greater stability at 50/50 percentage (x = 0.5) of PtAsS where As and S atoms were equally distributed with formation of S-As dimer bond at the centre. The calculated lattice parameters were well reproduced and agreed with the available experimental data. The binary ground state diagram also showed that all structures have negative heats of formation (∆Hf), hence they were thermodynamically stable (miscible constituents). The calculated heats of formation predicted that PtAs2 was more stable than the PtAsS and the order of stability for cubic structures decreased as: PtAs2 > PtAsS (VCA) > PtAsS (CE).The elastic constants indicated mechanically stability for all structures and the phonon dispersion curves showed no soft modes for PtAs2, PtAsS (CE) and Pd2As, suggesting stability. Moreover, the elastic instability (negative Cij) was observed in the PtAsS (VCA) structure. We also observed that the Pd2As and PtAsS (CE) were ductile, while PtAs2 and PtAsS (VCA) were brittle. The calculated Young modulus indicated that PtAs2 was much stiffer compared to PtAsS models. This suggested that PtAs2 was mechanically stronger among all the cubic structures. The PtAs2 was a dominant covalently bonded compound whereas PtAsS and Pd2As were predicted as ionic bonded. The computed Bader charges for the bulk and surface PtAs2, PtAsS (CE) and Pd2As and Mulliken atomic charges for PtAsS (VCA) showed different behaviour. The Pt and Pd species showed negative charges, while As species showed a positive charge for PtAs2 and Pd2As. The PtAsS (CE) showed a negative charge for Pt and S species, while the PtAsS (VCA) showed a negative and a positive charges for Pt and As/S species. The calculated total density of states (TDOS) for the bulk PtAsS and Pd2As showed a metallic behaviour since there was no band gap at the Fermi energy (EF). The PtAs2 model was observed as a semiconductor with a band gap of 0.104 eV. From the DOS, PtAs2 was found the most stable since it had less contribution of DOS at the EF, while PtAsS and Pd2As structures showed least stability due to highest DOS at the EF. The understanding of the aspects of surface stability and preferred surface cleavage were investigated starting from surface terminations and then slab thickness for (100), (110) and (111) surfaces of all mineral structures. We found that (100) surface was the most stable, displaying the lowest positive surface energy for all the PtAs2, PtAsS and Pd2As minerals and was considered as the working surface. The order of surface stability decreased as: (100) > (111) > (110) for PtAs2 and PtAsS (VCA and CE) mineral systems and (100) > (110) > (111) for Pd2As system. Interestingly we found that the surface energies of the PtAsS (VCA) were smaller than for PtAsS (CE), which indicated that the VCA was more stable than the CE. The (100) surface was the most dominant on the surface morphology as expressed by the morphologies for all the mineral structures. Analysis of the DOS of the most stable (100) surface for PtAs2, PtAsS and Pd2As, we found that sperrylite and palladoarsenide showed a metallic behaviour since there was no band gap observed at the EF, while PtAsS surface structures showed a semiconductor behaviour due to presence of band gaps of 0.142 eV and 0.551 eV for PtAsS (CE) and PtAsS (VCA), respectively. The PtAsS (VCA) was found the most stable, while Pd2As was found the least stable. In addition, the intermediate stability was found for PtAsS (CE) and PtAs2 surface structures. These findings gave more insights on the stability of these minerals which may be applicable to their recovery / National Research Foundation (NRF) and Centre for High Performance Computing (CHPC)