  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 {\sigma} 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.
