Enhanced Hardness in High‐Entropy Carbides through Atomic Randomness

Abstract

High‐entropy carbides (HECs) are of great interest as they are promising candidates for ultra‐high‐temperature and high‐hardness applications. To discover carbides with enhanced yield strength and hardness, mechanism‐based design approaches are needed. In this study, dislocation core atomic randomness as a mechanism for hardness enhancement is proposed, in which the random interactions between different elements at a dislocation core make it more difficult for the dislocation to slip. The Peierls stress of an a/2false⟨11¯0false⟩false{110false} edge dislocation is calculated based on density functional theory, in which atomic randomness is increased by increasing the number of elements at the dislocation core. The results show that the Peierls stress statistically increases with increasing number of elements, indicating that incorporating more elements is likely to produce higher hardness. Based on this guiding principle, three eight‐cation HECs are fabricated (Ti,Zr,Hf,V,Nb,Ta,X,Y)C (X,Y = Mo,W, Cr,Mo, or Cr,W), the composition of which is guided by ab initio calculations of their formation enthalpy and entropy forming ability. The single‐phase dense ceramics all show high nanoindentation hardness of around 40 GPa. The random interactions between different elements at a dislocation core provide a mechanism for improving the hardness of structural ceramics.

Bulk high-entropy nitrides and carbonitrides

“…Wang et al . 52 found that in eight-metal high-entropy carbides, randomness increases hardness due to the increase in possible configurations of dislocation cores, which impedes the movement of dislocations, and that Peierls stress increases with the number of elements. This effect is calculated using density functional theory, where the effect of randomness on specific slip systems can be analyzed.…”

“…This is similar to the concept of solid solution strengthening, where the strain fields of atoms of different sizes in a solid solution impede dislocation motion. However, simple measures such as atomic size variance or lattice parameter differences, which capture hardening trends for solid solutions, do not apply to HENs and HECNs in this work, nor HECs in the literature 52 . This is likely due to the fact that each metal atom is coordinated to 6 anions, and vice versa, as opposed to each atom position being equivalent in a solid solution.…”

Prediction of Single‐Phase High‐Entropy Nitrides from First‐Principles Calculations

“…[2,8] Recently, first-principles calculations have been used to predict single-phase solid solutions based on the calculated enthalpy of formation. [9,10] Based on the calculated formation enthalpies of different supercells of the same composition, entropy-forming ability (EFA) [11] is proposed to predict singlephase solid solution of five-cation highentropy carbides, and the prediction is verified by the following experiments. [12,13] The EFA and enthalpy formation are combined to predict eight-cation high-entropy carbides.…”

“…[12,13] The EFA and enthalpy formation are combined to predict eight-cation high-entropy carbides. [10] In this work, EFA is used to predict the single-phase composition of HENs.…”

High-entropy ceramics: propelling applications through disorder

“…Finer grains lead to improved toughness, and to Hall-Petch strengthening due to the nanograin microstructure impeding the motion of dislocations. Bulk (HfNbTaTiZr)C, prepared by spark-plasma sintering, shows a hardness 50% higher than what would be expected from the rule-of-mixtures of the binary carbides [10,17,51], while carbo-nitride versions of this composition are slightly harder than the carbides [5,6], and an 8-cation carbide is even harder [52]. High-entropy nitrides show even greater improvements, doubling both hardness and fracture toughness compared to their components (Figure 1a) [19].…”