[Paper Review] Fermi Level Engineering and Mechanical Properties of High Entropy Carbides

Mohammad Delower Hossain, Sarah Lowum+2 more|arXiv (Cornell University)|Jan 13, 2021

High Entropy Alloys Studies48 references4 citations

TL;DR

This study demonstrates that valence electron concentration (VEC) engineering enables precise control over the Fermi level and mechanical properties in high entropy carbides. At VEC = 8.4, optimal d-p orbital overlap maximizes shear resistance, yielding a peak hardness of ~30 GPa, while deviations reduce hardness by 50% at VEC = 9.4, validating theoretical predictions with experimental synthesis.

ABSTRACT

Fermi level engineering and mechanical properties evolution in high entropy carbides are investigated by theoretical and experimental means. Massive elemental diversity in high entropy ceramics broadens the compositional space but imposes great challenges in composition selection and property investigation. We have utilized the valence electron concentration (VEC) descriptor to design and predict properties of high entropy carbides. The VEC regulates the Fermi energy and systematically alters the bonding characteristics of materials. As a result, mechanical properties evolve as function of the VEC. At VEC 8.4, the strong σ bonding states stem from filled overlapping metal d and carbon p orbitals, which results in maximum resistance to shear deformation and highest hardness. Beyond or below the optimum VEC point of 8.4, mechanical response degrades due to filling or emptying of energy orbitals that facilitates shear deformation. Furthermore, the optimum VEC point can shift based on the constituent metals that formulate the high entropy carbide. Our analyses demonstrate strong correlation between calculated hardness and shear modulus. As an experimental complement, a set of high entropy carbides are synthesized, and mechanical properties investigated. The measured hardness follows theoretical predictions and the highest hardness of ~30 GPa is achieved at VEC 8.4. In contrast, hardness decreases by 50% when VEC is 9.4. Designing high entropy carbides based on VEC and understanding mechanical properties at an electronic level enables one to manipulate the composition spectrum to procure a desired mechanical response from a chemically disordered crystal.

Motivation & Objective

• To address the challenge of compositional selection in high entropy carbides due to massive elemental diversity.
• To establish a predictive framework linking electronic structure to mechanical properties in high entropy ceramics.
• To identify the optimal VEC for maximizing hardness through Fermi level and bonding character engineering.
• To validate theoretical predictions with experimental synthesis and mechanical testing of high entropy carbides.

Proposed method

• Utilization of valence electron concentration (VEC) as a descriptor to map electronic and mechanical trends across high entropy carbide compositions.
• First-principles calculations to determine Fermi energy and bonding character as functions of VEC.
• Analysis of orbital overlap between metal d-orbitals and carbon p-orbitals to assess covalent bonding strength.
• Correlation of calculated hardness and shear modulus with VEC to identify optimal electronic configuration.
• Synthesis of high entropy carbides at varying VEC values using solid-state reaction methods.
• Experimental measurement of hardness and mechanical response to validate theoretical predictions.

Experimental results

Research questions

• RQ1 How does VEC influence the Fermi level and bonding character in high entropy carbides?
• RQ2 What VEC value maximizes shear resistance and hardness in high entropy carbides?
• RQ3 How does deviation from the optimal VEC affect mechanical degradation mechanisms?
• RQ4 To what extent do theoretical predictions of hardness and shear modulus align with experimental measurements?
• RQ5 Can VEC-based design principles enable targeted engineering of mechanical properties in chemically disordered ceramics?

Key findings

• The highest hardness of ~30 GPa was experimentally achieved at a VEC of 8.4, confirming theoretical predictions.
• Hardness decreased by 50% when VEC increased to 9.4, indicating significant mechanical degradation beyond the optimal point.
• At VEC 8.4, strong σ bonding arises from filled overlapping metal d and carbon p orbitals, enhancing resistance to shear deformation.
• A strong correlation was observed between calculated hardness and shear modulus across the VEC range.
• The optimal VEC point of 8.4 is sensitive to constituent metals, indicating compositional dependence of electronic and mechanical response.
• Theoretical and experimental results confirm that Fermi level engineering via VEC enables systematic tuning of mechanical properties in high entropy carbides.