Chemical and topological parameters have been widely used for predicting the phase selection in high-entropy alloys (HEAs). Nevertheless, previous studies could be faulted due to the small number of available data points, the negligence of kinetic effects, and the insensitivity to small compositional changes. Here in this work, 92 TiZrHfM, TiZrHfMM, TiZrHfMMM (M = Fe, Cr, V, Nb, Al, Ag, Cu, Ni) HEAs were prepared by melt spinning, to build a reliable and sufficiently large material database to inspect the robustness of previously established parameters. Modification of atomic radii by considering the change of local electronic environment in alloys, was critically found out to be superior in distinguishing the formation of amorphous and crystalline alloys, when compared to using atomic radii of pure elements in topological parameters. Moreover, crystal structures of alloying element were found to play an important role in the amorphous phase formation, which was then attributed to how alloying hexagonal-close-packed elements and face-centered-cubic or body-centered-cubic elements can affect the mixing enthalpy. Findings from this work not only provide parametric studies for HEAs with new and important perspectives, but also reveal possibly a hidden connection among some important concepts in various fields.

In this study, we investigate the scandium-containing Sc-Hf-Nb-Ta-Ti-Zr system of refractory high-entropy alloys (HEAs). Using the arc-melting method, we synthesized nine equimolar alloys (five 4-, three 5- and one 6-component), with all of them containing Sc. The alloys were characterized by XRD, electron microscopy and EDS, while superconductivity was investigated via electrical resistivity, specific heat and the Meissner effect. The results were compared to the parent Hf-Nb-Ta-Ti-Zr refractory HEAs, forming a single-phase body-centered cubic (bcc) structure and quite homogeneous microstructure. The addition of Sc produces a two-phase structure in the Sc-Hf-Nb-Ta-Ti-Zr alloys, with one phase being bcc and the other hexagonal close-packed (hcp). The hcp phase absorbs practically all Sc, whereas the Sc-poor bcc phase is identical to the bcc phase in the Hf-Nb-Ta-Ti-Zr parent system. Upon the Sc addition, the microstructure becomes very inhomogeneous. Large bcc dendrites (10–100 µm) are homogeneous in the central parts, but become a fine dispersion of sub-micron precipitates of the bcc and hcp phases close to the edges. The interdendritic regions are also a fine dispersion of the two phases. Superconductivity of the Sc-Hf-Nb-Ta-Ti-Zr alloys originates from the bcc phase fraction, which demonstrates identical superconducting parameters as the bcc Hf-Nb-Ta-Ti-Zr parent alloys, while the Sc-containing hcp phase fraction is non-superconducting.

A convenient method is proposed for the measurement of the characteristic free volumes, viz., the amount of excess free volume annihilation in structural relaxation V_f-sr and the amount of new free volume production in glass transition V_f-gt of bulk metallic glasses (BMGs) by thermal dilation (DIL) test. Through the DIL tests, the characteristic free volumes are found to be sensitive to the change of glass forming ability (GFA). The Pd₄₀Cu₃₀Ni₁₀P₂₀ BMG has a quite small V_f-sr. For a series of Fe–Cr–Mo–C–B–(Er) BMGs, Fe₄₈Cr₁₅Mo₁₄C₁₅B₆Er₂ with the largest GFA is identified to have the largest V_f-gt and smallest V_f-sr. The correlation between V_f-sr and the squares of critical diameters of these iron-based BMGs can be fitted as a negative exponential function with high accuracy.