Materials Talks

Thesis Defense- Advisor Chelsey Hargather

Ab Initio Calculations of Elastic and Thermodynamic Properties of High Entropy Alloys and Their Alloying Components

Jones Hall 227

Abstract

High-entropy alloys (HEAs) are a class of engineering metals of recent scientific interest. HEAs usually consist of five or more alloying components in roughly equiatomic proportions that can form single-phase or dual-phase solid solutions such as face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close packed (HCP). They take on the name high entropy because they exhibit unusually high entropy of mixing. The reason for the interest in HEAs in the scientific community is that these alloys can display promising combinations of material properties. The properties can include better ductility and strength relationship, lighter and stronger, higher oxidation resistance, superior resistance to corrosion, and better fracture resistance when compared to traditional alloys. Because of these qualities, HEAs are candidate materials to replace traditional alloys as structural engineering materials.

However, before HEAs can replace traditional alloys, their mechanical properties including thermodynamic and elastic properties must be understood. In industrial applications, the understanding of thermodynamic and elastic properties of refractory alloys are crucial because their utility depends on these properties. The application of refractory alloys depends on their resistance to different processes such as high temperature and high oxidation. This means that in their application, they must have low thermal expansion and high strength at elevated temperatures. Thermal expansion and strength at elevated temperatures are part of their thermodynamic and elastic properties in general. So to understand how these alloys will react under these types of conditions, these properties must be well understood. This thesis explores thermodynamic and elastic properties of BCC refractory high-entropy alloys through density functional theory computation and modeling. By using Vienna Ab initio Simulation Package (VASP), thermodynamic and elastic properties such as Debye temperature, Helmholtz free energy, entropy, enthalpy, heat capacity, thermal expansion, elastic constants, bulk modulus,  shear modulus, Young’s modulus, and Poisson’s ratio are calculated as a function of temperature and discussed in this thesis. First, the computational method is compared to well known experimental values of pure systems Ag, Ni, Al, Ta, Ti, and V for procedural validation and then used on BCC refractory HEAs including three quarternary and three quinary systems, NbTaTiZr, NbTaTiV, AlMoNbV, HfNbTaTiZr, MoNbTaVW, and AlNbTaTiV with 40 and 60 atom cells for the quarternary systems, and 50 and 75 atom cells for the quinary systems.

This work has calculated the entropy and enthalpy of the pure metals, Al and Nb to be in close agreement with NIST JANAF reported experimental values. This was done to validate the methodology of the thermodynamic modeling. Elastic properties such as elastic constants, bulk, shear and Young’s moduli for pure metals are also in close agreement with literature values. After method validation on pure metals this work then applies the modeling process to more complicated systems such as RHEAs and is further validated on AlMoNbV. For the first time, the finite temperature thermodynamic properties of all 24 atomic configuration permutations of a quaternary RHEA are calculated. At most, 1.7% difference is found between the resulting properties as a function of atomic configuration, indicating that the atomic configuration of the SQS has little effect on the calculated thermodynamic properties. The behavior of thermodynamic properties among the RHEAs studied is discussed based on valence electron concentration and atomic size. Among the quaternary RHEAs studied, namely AlMoNbV, NbTaTiZr, and NbTaTiV, it is found that the presence of Zr contributes to higher entropy. Additionally, at lower temperatures, Zr contributes to higher heat capacity and thermal expansion compared to the alloys without Zr, possibly due to its valence electron concentration. At higher temperatures, Al contributes to higher heat capacity and thermal expansion, possibly due its ductility. Among the quinary systems, the presence of Mo, W, and/or V causes the RHEA to have a lower thermal expansion than the other systems studied. When comparing the systems with the NbTaTi core, the addition of Al increases thermal expansion, while the removal of Zr lowers the thermal expansion. Enthalpy, entropy and thermal expansion of all six RHEA systems were calculated and results discussed.

The elastic properties of all 24 atomic configurations of AlMoNbV were calculated and it was found that elastic constants had a standard deviation of up to 6.4%, with elastic constant C44 being the highest, while C11 and C12 varied by 1.85% and 2.28% respectively. When comparing 1-, 40, 50, and 64-atom cell sizes, elastic constants varied by at most 1.2% different, showing that cell size, shape, and orthogonality does not vary the results of the elastic properties significantly. MoNbTaVW, out of all six RHEAs studied had the highest bulk, shear and Young’s moduli, and lowest thermal expansion, giving promise to its use and utility in refractory settings. This may be due to its high valence electron concentration. Other results and trends are discussed thoroughly in this thesis. This thesis offers novel insights for cutting down computational time and resources while calculating properties of systems that have not previously been published before.

Keywords: High-Entropy Alloys, Refractory, BCC Body-Centered Cubic, Density Functional Theory, Elastic Properties, Thermodynamic Properties