Quantifying local lattice distortions in refractory high-entropy alloys

Severe local lattice distortions (LLDs), originating from the size mismatch among atoms, have been proposed as one of the key mechanisms responsible for the excellent mechanical properties of bcc-structured high-entropy alloys (HEAs). They have also been connected to phase stability, as well as physical properties such as electrical conductivity. Experimental measurements of LLDs are, however, difficult and often ambiguous. Analysis of total scattering data in real space has been proposed to provide a uniquely suitable probe of LLDs, but its widespread application and validation are still limited. We conduct a thorough study of LLD measurements in refractory high-entropy alloys (RHEAs) using small-box pair distribution function (PDF) analysis. We start by reexamining existing literature data using a recently proposed coherent theoretical framework to demonstrate that LLDs in RHEAs can indeed be considered as severe and can be reliably measured even in the absence of known thermal components. We perform total scattering experiments of a typical RHEA (HfNbTaTiZr) using both x-rays and neutrons, and show that real-space PDF analysis of data from different types of radiation gives consistent values of LLDs. The results are also in good agreement with the values derived from reciprocal-space data. Finally, through simulation and analysis of theoretical two-phase PDFs, we demonstrate that the effect of the chemical segregation in the investigated RHEA on the measured LLDs is limited when dealing with comparatively large LLDs. The results show that PDF analysis using small-box modeling provides a fast and reliable tool for measuring LLDs in RHEAs, which makes it ideal for analysis of large data sets from time-resolved in situ measurements.