Local chemical inhomogeneities in TiZrNb-based refractory high-entropy alloys

Abstract

(1) The local chemical order features in the TiZrNb-based alloys are as follows: (i) For the TiZrNb alloy, the Ti-Zr pair is the most favored, while there exists relatively weaker Nb-Nb pair; (ii) For the TiZrHfNb alloy, Ti and Nb prefer to pair with Zr and Hf, respectively; (iii) For TiZrHfNbTa, Ta is prone to form sub-nanoscale segregation, in addition to the existing chemical preference among Ti, Zr, Hf and Nb. (2) Accompanying the LCO, there exists compositional undulation in the TiZrHfNb alloy on nanometer scale, arising from the preferred local enrichment of [(Ti, Zr)] or [(Hf, Nb)] CSROs. (3) The local chemical inhomogeneity evolves strongly with temperature, from the RSS structure at high temperatures to the pronounced tendency of forming chemically favored pairs at low temperatures. The LCO develops beyond the range of CSRO, to a characteristic length scale of at least one nanometer. (4) The predicted yield strengths of the RSS samples are generally lower than the experimental values by ∼ 100 MPa, while those calculated for CSRO-containing samples approach the experimental measurements. This strongly suggests the need to take into account the contribution of CSRO (and/or other local chemical inhomogeneities) to achieve a more accurate prediction of the yield strength of TiZrNb-based bcc HEAs. (5) When the strong CSRO-promoting Ti is replaced by Ta, the resultant TaZrHfNb alloy is found to contain only a weak degree of local chemical order, unlike the three representative TiZrNb-based HEAs in the present study. (6) Our work reveals the trend of the chemical inhomogeneities and compositional undulation that would develop as intrinsic features in these TiZrNb-based bcc HEAs. Meanwhile, the CSRO tendency also sheds light on the fertile emergence of (Ti,Zr,O)- complexes that form upon the addition of oxygen/nitrogen into such HEAs to purposely accentuate (sub)nanometer-scale chemical complexes/heterogeneities. Multi-principal element solid solutions are prone to develop local chemical inhomogeneities, i.e. , chemical order/clustering and/or compositional undulation. However, these structural details from short-range (first couple of nearest-neighbor atomic shells) to nanometer length scale are very challenging to resolve in both experimental characterization and computer simulations. For instance, Monte Carlo modeling based on density-functional-theory calculations is severely limited by the sample size and the simulation steps practical in the simulations. Adopting the cluster expansion approach, here we systematically reveal the local chemical inhomogeneity, including chemical order and compositional fluctuation, in three representative equiatomic TiZrNb-based body-centered cubic refractory high-entropy alloys (HEAs): TiZrNb, TiZrHfNb and TiZrHfNbTa. Ti-Zr pairs are found to exhibit the highest degree of chemical preference among all atomic pairs. Such chemical short-range order (CSRO) induces an accompanying compositional undulation, both extending to characteristic dimensions of the order of one nanometer. The chemical inhomogeneity trend uncovered for this series of TiZrNb-based HEAs is expected to impact their mechanical properties; e.g. , incorporating the CSRO effects in a current model significantly improves its agreement with experimental measured yield strength.