Density Functional Theory Study of Bulk Properties of Metallic Alloys and Compounds

Abstract: First-principles methods based on Density functional theory (DFT) are now adopted routinely to calculate the properties of materials. However, one of the biggest challenges of DFT is to describe the electronic behaviors of random alloys. One of the aims of this thesis is to study binary alloys, e.g. Ti-Al, Cu-Au, and multi-component alloys by using two models for chemically random structures: the special quasi-random structure (SQS) and coherent potential approximation (CPA).I investigate these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. Within the SQS approach, the LLD effect can be modeled in a straightforward manner by relaxing the positions of atoms in the supercell. However, within this approach, it is difficult to model the random multi-components alloys due to the large size of the supercells. On the other hand, the CPA approach uses single-site approximation and thus it is not limited by the number of alloy components. But CPA suffers from the neglect of the local lattice relaxation effect, which in some systems and for some properties could be of significant importance.In my studies, the SQS and CPA approaches are combined with the pseudopotential method as implemented in the Vienna Ab-initio Simulation Package (VASP) and the Exact Muffin-Tin Orbitals (EMTO) methods, respectively. The mixing energies or formation enthalpies and elastic parameters of fcc Ti1-xAlx and Cu1-xAux (0 =< x =< 1) random solid solutions and high-entropy multicomponent TiZrVNb, TiZrNbMo and TiZrVNbMo alloys are calculated as a function of concentration. By comparing the results with and without local lattice relaxations, we find that the LLD effect is negligible for the elastic constants C11, C12, and C44. In general, the uncertainties in the elastic parameters associated with the symmetry lowering in supercell studies turn out to be superior to the differences between the two alloy techniques including the effect of LLD. However, the LLD effect on the mixing energies or formation enthalpies is significant and depends on the degree of size mismatch between alloy constituents. In the cases of random Cu-Au and high-entropy alloys, the formation enthalpies and mixing energies are significantly decreased when the LLD effect is considered. This finding sets the limitations of CPA for the mixing energies or formation enthalpies of alloys with large atomic size differences.The other goal of the thesis is to study the effect of exchange-correlation functionals on the formation energies of ordered alloys. For this investigation, we select the Cu-Au binary system which has for many years been in the focus of DFT and beyond DFT schemes. The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in DFT is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most cases, PBE provides theoretical results in good agreement with experiments. However, the ordered Cu-Au system turned out to be a special case where large deviations between the PBE predictions and observations occur. In this work, we make use of a recently developed exchange-correlation functional, the so-called quasi-nonuniform exchange-correlation approximation (QNA), to calculate the lattice constants and formation energies for ordered Cu-Au alloys as a function of composition. The calculations are performed using the EMTO method and verified by a full-potential method. We find that the QNA functional leads to an excellent agreement between theory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which are nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3 relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA. This excellent result demonstrates that one can reach superior accuracy within DFT for the formation energies and there is no need to go beyond DFT. Furthermore, it shows that error cancellation can be very effective for the formation energies as well and that the main DFT errors obtained at PBE or LDA levels originate from the core-valence overlap region, which is correctly captured by QNA due to its particular construction. Our findings are now extended to disordered alloys, which is briefly discussed already in one of my published papers.