Designing the mechanical behavior of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ high-entropy carbide ceramics

Groups IVB and VB transition-metal carbides (TMCs) have the same lattice structure but different preferred slip systems, of which group IVB TMCs favor ⟨110⟩{110} while group VB TMCs favor ⟨110⟩{111}. This distinction suggests that the mechanical properties of high-entropy carbide ceramics ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ can be designed by adjusting the concentration of different group metal elements to activate specific slip systems. In this work, we investigated the influence of the proportion and distribution of various metal atoms on mechanical behavior and slip systems using first-principles calculations. The results show that the mechanical properties of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ near the equilibrium point follow the rule of mixture. However, their yield shear strength is influenced by the strength of the metal-C bond located on the slip plane, while the position of the slip plane is primarily determined by the unstable stacking fault energy. Moreover, dissociation on {111} slip plane occurs when $x\ge 0.5$ (i.e., valence electron concentration $\ge 8.5$ electrons per formula unit), suggesting the potential to shift the dominant ⟨110⟩{110} slip system of group IVB TMCs to the ⟨110⟩{111} slip system. By adjusting the proportion and distribution of different group metal atoms in ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$, it is possible to customize the slip behavior and yield shear strength and plasticity.

Figure 1

GSFE curves of (a) (NbTa)C and (b) (HfTiZr)C along different slip systems.

Figure 2

(a) Average lattice constants (${\overline{a}}_0$) and (b) $B, G_H$, and $E_H$ of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ and those predicted by ROM. (c) Map of brittleness and ductility trends of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ with increasing VEC and $x$. (d) τ-γ curves of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ under shear along $\left[\overline{1}\overline{1}2\right]$(111). (e) Average YSSs of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ and those predicted by ROM. (f) Atom distribution and deformation mode of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$, taking ${\left(\mathrm{HfTiZr}\right)}_{0.50}{\left(\mathrm{NbTa}\right)}_{0.50}\mathrm{C}$ as an example. Error bars in (a) and (e) donate standard deviation caused by different atomic distributions at the same $x$, and Burger's vector $\mathbf{b}=1/6\left[\overline{1}\overline{1}2\right]a$.

Figure 3

(a) For each $x$/VEC value, partial slip occurs or not in five supercells with different atom distributions under shear along $\left[1\overline{1}0\right]\left(111\right)$. (b), (c) Comparison of deformation modes: partial slip in ${\left(\mathrm{HfTiZr}\right)}_{0.50}{\left(\mathrm{NbTa}\right)}_{0.50}\mathrm{C}$ and full slip in ${\left(\mathrm{HfTiZr}\right)}_{0.60}{\left(\mathrm{NbTa}\right)}_{0.40}\mathrm{C}$ through front and lateral views of atom distributions, with Burger's vector $\mathbf{b}=1/6\left[\overline{1}\overline{1}2\right]a$.

Figure 4

(a)–(d) GSFE curves of ${\left(\mathrm{HfTiZr}\right)}_{1-x}{\left(\mathrm{NbTa}\right)}_x\mathrm{C}$ on different {111} slip planes in supercells with $x=0.75$, 0.50, 0.40, and 0.25, respectively. (e) Schematic diagram of different slip planes in ${\left(\mathrm{HfTiZr}\right)}_{0.75}{\left(\mathrm{NbTa}\right)}_{0.25}\mathrm{C}$ supercell. Slip_1 and Slip_2 denote two slip planes with different atomic distributions under shear along $\left[\overline{1}\overline{1}2\right]$(111).