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High entropy alloys (HEAs) are considered as a novel class of materials with a large number of components available in nearly equatomic proportions. One of the characteristic properties of HEAs was believed to be so-called sluggish diffusion. The faith on this myth instead of rigorous experimental analysis played such a dominant role that the first set of data on interdiffusion, in fact based on an improper analysis, were cited in hundreds of articles to state the presence of sluggishness of diffusion rates in high entropy alloys. In this review, the recent data on atomic diffusion in HEAs are critically discussed. The discussion is focused on tracer diffusion which is already measured dominantly for polycrystalline, but in some cases for single crystalline high-entropy alloys. Alternatively, a rigorous analysis of the interdiffuson experiments, which provide the diffusion rates of chemical species, too, becomes more and more sophisticated for three and more elements in an alloy and it is challenging to derive physically sound quantities from a general multicomponent diffusion experiment. Most promising in this case is the diffusion couple technique, especially the so-called pseudo-binary approach. This approach is analyzed with a focus on the applicability and the possible errors induced if up-hill diffusion appears. It is shown that atomic diffusion in HEAs cannot a priori be considered as sluggish and both atomic interactions as well as correlation effects are responsible for the observed trends. Even if estimated on the same homologous scale, the diffusion retardation induced by a high entropy in FCC crystals is not simply proportional to the number of alloying components and it is shown to be similar to that induced by the L12 ordering in a binary system. Furthermore, the importance of cross-correlations in diffusion of different species in HEAs is highlighted.