Superconductivity, Hardness, and Materials Design of Body-Centered Cubic High-Entropy Alloys

This chapter discusses the superconductivity and hardnessHardness of Hf–Nb–Ti–V–Zr, Al–Nb–Ti–V–Zr, and HfMoNbTiZr body-centered cubic (bcc) high-entropy alloys (HEAs). In particular, owing to the discovery in superconductivity of equiatomic quinary HfMoNbTiZr, superconducting properties are compared under a fixed maximum configurational entropy. This comparison reveals a negative correlation between the Debye temperatureDebye temperature, \(\theta _\textrm{D}\) , and the superconducting critical temperature, \(T_\textrm{c}\) , which is in contrast with the positive correlation expected for Bardeen–Cooper–Schrieffer superconductors. A negative correlation is a new feature of superconductivity in a high-entropy state, and can be explained by the uncertainty principleUncertainty principle. The hardnessHardness of bcc HEA superconductors depends on their valence electron countValence electron count. Furthermore, \(T_\textrm{c}\) decreases with increasing hardnessHardness, which is also related to the negative correlation between \(\theta _\textrm{D}\) and \(T_\textrm{c}\) . Finally, in this chapter, a simple materials designMaterials design for bcc and hexagonal close-packed HEA superconductors is presented.