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IMPACT STATEMENT Experiments and theory are highlighting chemical ordering in high-entropy alloys (HEAs) as important for mechanical properties but the high strength in CoCrFeNiPd is predicted here to be achievable in the random alloy due to the large misfit volume of Pd, in spite of observed ordering. Ordering is thus not essential for attaining high-strength HEAs. Recent experiments show that the CoCrFeNiPd high-entropy alloy (HEA) is significantly stronger than CoCrFeNi and with nanoscale composition fluctuations beyond those expected for random alloys. These fluctuations were suggested to be responsible for strengthening. Here, a recent parameter-free theory for initial yield strength in fcc random alloys is shown to predict the strength of CoCrFeNiPd in good agreement with experiments. The strengthening is due mainly to the large misfit volume of Pd in CoCrFeNi, indicating that effects of the non-random composition fluctuations are secondary. Analyses of strength variations and strengthening-associated length scales helps rationalize why dislocation motion is insensitive to such fluctuations. These findings point to the value of theory for understanding mechanical behavior of HEAs.