Superconductivity in thermally annealed Ta-Nb-Hf-Zr-Ti high-entropy alloys

Abstract We present a study of superconductivity in Ta-Nb-Hf-Zr-Ti high-entropy alloys (HEAs) by investigating four samples of different atomic concentrations (equimolar and off-equimolar) and number of components (4 and 5), subjected to different thermal treatments. The structure of the samples varied between a homogeneous random solid solution and a partially ordered nanostructure in the form of a three-dimensional grid of short-range ordered atomic clusters enriched in Zr and Hf that has developed during long-time annealing. Superconductivity was found to be a robust phenomenon, being quite insensitive to the actual structure of the material. All investigated samples were superconducting in the entirety of their volumes. The superconducting transition temperatures T C of the samples are scattered in the range between 5.0 and 7.3 K and this scatter could be related to the degree of structural and chemical inhomogeneity of the samples. In the samples with partially ordered nanostructure, short-range atomic clusters possess a slightly different T C than the Ta- and Nb-rich matrix. Our results also demonstrate the important fact that the formation, stability and structure of a regular (non-ideal) HEA mixture are determined by both, the minimization of the mixing enthalpy that favors local atomic ordering and the maximization of the mixing entropy that favors a random solid solution. The actual equilibrium state achieved during long-time thermal annealing via the atomic diffusion is generally partially ordered, and the resulting nanostructure is a sensitive function of the number of components constituting the HEA, their concentrations, the differences in the atomic radii and the annealing temperature and time. This nanostructure essentially determines the electronic properties of HEA materials.