Date Available

4-22-2025

Year of Publication

2025

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Engineering

Department/School/Program

Materials Science and Engineering

Faculty

Dr. Matthew J. Beck

Faculty

Dr. Fuqian Yang

Abstract

High entropy alloys (HEAs) are an exciting new class of materials. HEAs combine multiple elements in concentrations ranging from 5% to 35%. The large variation in concentrations increases the alloy’s entropy, stabilizing it. The stabilization is due to both an increased configurational entropy and increases the vibrational entropy when the alloy is at higher temperatures. This was seen for both MoNbTaW and FeNiMoW by combining the atomistic techniques: density functional theory (DFT) and density functional perturbation theory (DFPT). For MoNbTaW, the composition plays a large role in stabilizing the alloy over the configuration of elements. For the three-phase alloy, FeNiMoW, the configurational and vibrational entropy plays a large role in stabilizing the FCC matrix Fe43Ni43Mo17W5. A solid solution FCC matrix was compared with a “semi-ordered” phase based on the mineral, tetrataenite. It is layers of Fe and Ni with the Mo and W interspersed. While comparing the enthalpy of formations for both unit cells, the semi-ordered samples on average are more stable ΔHf = 6.10 ± 0.19 kJ/mol than the solid solution ΔHf = 4.36 ± 2.78 kJ/mol, but past 340 K, solid solution unit cells has a larger Gibb’s Free Energy. By using DFT and DFPT, a second phase in FeNiMoW, the $\mu$ phase Fe13Ni8Mo13W5, was also characterize. It is an A7B6 structure. It is a combination solid solution of Fe and Ni on the A sites and Mo and W on the B sites, with the concentration on the B sites shifting slightly without altering the thermodynamic stability. FeNiMoW demonstrates self-sharpening behavior. In penetration tests, it ends up chipping away instead of curling over. This was in part due to adiabatic shear bands developing in the FCC matrix. This has led to the use of DFT to characterize the elastic properties of the FCC matrix. By straining representative unit cells, nine elastic constants were calculated illustrating that on average the unit cell behaves as an isotropic cube. The elastic properties were calculated from the average elastic constants using the Voigt-Reuss-Hill average. These include a Young’s modulus of 176.42 GPa ±18.47 GPa, and a shear modulus of 65.70 GPa ± 2.30 GPa. The stacking fault energies for the FCC matrix were calculated to understand how easy it would be to create and more dislocation in the alloy. Due to the alloy having no symmetry and varying sizes of elements, there was a large range of stacking fault energies, even some negative which are indications of a preference for a different type of stacking. The average intrinsic stacking fault energy was 26.69 ± 23.54 mJ/m2, and the unstable stacking fault energy is 959.56 ± 143.83 mJ/m2. The large difference in the stacking fault energy curve indicates that it can take a large amount of energy to create stacking faults, but in some cases, it is not unfavorable to have stacking faults. Lastly, a phenomenon known in the HEA space is called sluggish diffusion. It would take a long time to diffuse an alloy. There is a difference in the concentration of refractory elements in the FCC matrix near the µ phase which prompted the study. The first step in studying the diffusion was understanding the point defects. The vacancy energies for the four elements are 1.70 ± 0.04 eV, 1.88 ± 0.05, 1.56 ±0.10 eV, and 1.60 ±0.17 eV for Fe, Ni, Mo, and W respectively. When comparing the values using DFPT, the energies end up being similar. At higher temperatures, HEAs are a combination of many point defects. Overall, there is more to study with these HEAs. There are many combinations of different elements and concentrations that have yet to be fully actualized, but the use of atomistic calculations opens the possibilities to study these alloys alongside physical experiments.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2025.12

Funding Information

This study was supported by the Enabling Advanced Materials Science Engineering from the Department of Education (no.: P200A210059) from 2020-2025.

This study has also been supported by the Next Generation Materials and Processing Technologies from the Army Research Lab (no: 1000100194) from 2021-2025.

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