High-entropy alloys (HEAs) comprise a novel class of scientifically and technologically interesting materials. Among these, equatomic CrMnFeCoNi with the face-centered cubic (FCC) structure is noteworthy because its ductility and strength increase with decreasing temperature while maintaining outstanding fracture toughness at cryogenic temperatures. Here we report for the first time by single-crystal micropillar compression that its bulk room temperature critical resolved shear stress (CRSS) is ~33–43 MPa, ~10 times higher than that of pure nickel. CRSS depends on pillar size with an inverse power-law scaling exponent of –0.63 independent of orientation. Planar ½ < 110 > {111} dislocations dissociate into Shockley partials whose separations range from ~3.5–4.5 nm near the screw orientation to ~5–8 nm near the edge, yielding a stacking fault energy of 30 ± 5 mJ/m². Dislocations are smoothly curved without any preferred line orientation indicating no significant anisotropy in mobilities of edge and screw segments. The shear-modulus-normalized CRSS of the HEA is not exceptionally high compared to those of certain concentrated binary FCC solid solutions. Its rough magnitude calculated using the Fleischer/Labusch models corresponds to that of a hypothetical binary with the elastic constants of our HEA, solute concentrations of 20–50 at.%, and atomic size misfit of ~4%.

Although metals strengthened by alloying have been used for millennia, models to quantify solid solution strengthening (SSS) were first proposed scarcely seventy years ago. Early models could predict the strengths of only simple alloys such as dilute binaries and not those of compositionally complex alloys because of the difficulty of calculating dislocation-solute interaction energies. Recently, models and theories of SSS have been proposed to tackle complex high-entropy alloys (HEAs). Here we show that the strength at 0 K of a prototypical HEA, CrMnFeCoNi, can be scaled and predicted using the root-mean-square atomic displacement, which can be deduced from X-ray diffraction and first-principles calculations as the isotropic atomic displacement parameter, that is, the average displacements of the constituent atoms from regular lattice positions. We show that our approach can be applied successfully to rationalize SSS in FeCoNi, MnFeCoNi, MnCoNi, MnFeNi, CrCoNi, CrFeCoNi, and CrMnCoNi, which are all medium-entropy subsets of the CrMnFeCoNi HEA.

Since the launch of lithium-ion batteries, elements (such as silicon, tin, or aluminum) that can be alloyed with lithium have been expected as anode materials, owing to larger capacity. However, their successful application has not been accomplished because of drastic structural degradation caused by cyclic large volume change during battery reactions. To prolong lifetime of alloy anodes, we must circumvent the huge volume strain accompanied by insertion/extraction of lithium. Here we report that by using aluminum-foil anodes, the volume expansion during lithiation can be confined to the normal direction to the foil and, consequently, the electrode cyclability can be markedly enhanced. Such a unidirectional volume-strain circumvention requires an appropriate hardness of the matrix and a certain tolerance to off-stoichiometry of the resulting intermetallic compound, which drive interdiffusion of matrix component and lithium along the normal-plane direction. This metallurgical concept would invoke a paradigm shift to future alloy-anode battery technologies.

Coefficients of thermal expansion (CTE) and elastic constants of single crystals of ${\mathrm{ZrB}}_2$ have been determined in the temperature ranges from room temperature to 1073 K and from room temperature to 1373 K, respectively. The elastic constants of ${\mathrm{ZrB}}_2$ are best characterized by the large value of the Young modulus (as high as 500 GPa) and the small values of the Poisson ratio (0.13–0.15), indicating the high stiffness and hardness and the brittleness, respectively. The values of CTE along the a- and c-axis directions are ${\text{6.66×10}}^{\text{−6}}$ and ${\text{6.93×10}}^{\text{−6}}\hspace{0.17em}{\mathrm{K}}^{\text{−1}},$ respectively, when averaged over the temperature range from room temperature to 1073 K. The CTE value along the a-axis direction of ${\mathrm{ZrB}}_2$ is only moderately larger than the corresponding value for GaN. This together with the small lattice mismatch along the a-axis direction between ${\mathrm{ZrB}}_2$ and GaN in the heteroepitaxial orientation relationship of ${\text{(0001)}}_{\mathrm{GaN}}{\text{//(0001)}}_{{\mathrm{ZrB}}_2}$ and ${\text{〈112̄0〉}}_{\mathrm{GaN}}{\text{//〈112̄0〉}}_{{\mathrm{ZrB}}_2}$ indicate that only a small compressive stress develops in the GaN thin-film crystal grown on the (0001) surface of the ${\mathrm{ZrB}}_2$ substrate. The stresses developed in the GaN thin-film crystal are evaluated with the values of CTE and elastic constants of ${\mathrm{ZrB}}_2$ determined in the present study. The evaluation verifies the suitability of ${\mathrm{ZrB}}_2$ as a substrate for heteroepitaxial growth of GaN.