Temperature Dependence of Hardness of High Entropy Alloys

Correlations have been found for the base value of hardness (as the ratio between the heat of fusion and molar volume) and the softening temperature (as the ratio of heat of fusion and specific heat capacity). The relative change of bulk hardness as a function of temperature, H(T), is studied by three new parametric formulas beside the well-known exponential decay and Arrhenius-type expressions. Mathematically, two formulas can be considered as deriving from the exponential decay; the third one is a new rational fraction expression based on the power of normalized temperature. The normalizing temperature is taken as the softening temperature. In the Arrhenius expression, a temperature-dependent activation energy is introduced, which increases steadily with heating but never surpasses the value of self-diffusion. This rational fracture expression has been shown to be applicable to both pure metals and alloys with arbitrary H(T) curve shapes, from convex (pure metals) to concave (alloys). A detailed description of the fitting of these parametric formulas is given, applying the H(T) data from the literature and from our own measurements. Measuring our refractory high entropy alloy (RHEA) samples, an early softening temperature, smaller than the expected half of the melting point (Ts < Tm/2) was detected, signaling a phase instability in the case of Ti-, Zr- and Hf-containing alloys.