Structural Phase State of High-Entropy NbTiHfVZr Alloy

The results of studying the stability of high-entropy NbTiHfVZr alloy on the basis of analysis of (i) the critical Hume-Rothery parameters, (ii) the enthalpy of binary alloys by the Miedema method, and (iii) the mixing entropy of NbTiHfVZr alloy near the melting point are presented. The temperature stability regions extending from the melting point to 1200 K for NbTiHfVZr alloy have been revealed by the method of inverse hull webs. In the case of NbTiHfZr, the temperature stability region extends up to the room temperature. The obtained results evidence that NbTiHfVZr and NbTiHfZr can be classified as high-entropy alloys, whose lattices belong to the class of single-phase one-element solid solutions. It has been established by the Rietveld method on the basis of an experimental X-ray diffraction pattern that the cubic HfNbTiVZr, Hf₂Nb₂Ti₂V₂Zr₂, NbHfTiZr, and Hf₂Nb₂Ti₂Zr₂ lattices found by the USPEX code with space group P1 make a predominant contribution to the integral intensity. In this study, the full structural information including unit cell lattice parameters, atomic coordinates, space group, population of sites, etc. has been established for the HfNbTiVZr, Hf₂Nb₂Ti₂V₂Zr₂, NbHfTiZr, and Hf₂Nb₂Ti₂Zr₂ cubic lattices. The mentioned alloys are stable and characterized by a high bound energy and, according to the found room-temperature elasticity moduli, belong to high-strength materials. The cubic HfNbTiVZr, Hf₂Nb₂Ti₂V₂Zr₂, NbHfTiZr, and Hf₂Nb₂Ti₂Zr₂ lattices can be incorporated into the crystallographic database used to identify the structural state of high-entropy NbTiHfZr and NbTiHfVZr alloys.