Development and application of first-principles methods to study the properties of high entropy alloys

 High entropy alloys (HEA) are an important class of materials consisting of many elements in high concentrations. Many HEAs are known to have desirable structural and functional properties, but we do not know a-priori what compositions will be suitable. First-principles density functional theory calculations are an effective tool that can predict these attractive properties, and also capture system behavior in extreme conditions like high temperature or pressure. As a result, these simulations play a major role in alloy design. This thesis details efforts towards the development and application of first-principles methods to describe the thermodynamical, electrical and mechanical properties of high entropy alloys. 

The first three chapters serve as “theory”, introducing the readers to high entropy alloys, first-principles simulations and the KKR Green’s function method. This is important background information that is needed to understand our work. We then describe our Cluster Averaged CPA (CA-CPA) method which can incorporate chemical short range order in the KKR-CPA method. This is achieved by using user defined short range order parameters to create an averaged cluster that is embedded in the CPA medium. We validate this method by studying the effect of short range order on the total energy of binary CuZn and quaternary AlCrTiV. These alloys are interesting as they exhibit order-disorder transitions. We compare the fully self-consistent CA-CPA with the averaged cluster embedded in the single-site CPA medium. 

We also apply the Kubo-Greenwood equation in the framework of the KKR-CPA effective medium technique to calculate electrical resistivity of alloys where the disorder is purely chemical. We use this method to study the resistivity of AlxCoCrFeNi multi-phase high entropy alloy as a function of Aluminum concentration. We then introduce our LSMS resistivity approach to calculate electrical resistivity of large systems with more complex forms of disorder. In this approach, the Kubo-Greenwood equation is combined with the highly efficient locally self-consistent multiple scattering (LSMS) method. We discuss the theoretical underpinnings of the method and validate it by calculating the first-principles resistivity of very large (16,000 atom) structures of high resistivity binary alloys Al-V and Fe-Si. The values obtained compare well with experiment. 

In the third part of the thesis, we pivot to mechanical properties. We apply uniaxial strain to study the ductility of refractory high entropy alloys. We observe various deformation mechanisms like stacking faults, splay, twinning. We also study the finite strain mechanical stability of the alloys using the symmetric Wallace tensor, and compare the different ductility parameters used in literature. Finally, we conclude the thesis by discussing some of the ongoing work in our group.