Hardening in high entropy equiatomic metal alloys

Abstract

A phenomenological approach has been developed for the mathematical description of the hardening of high-entropy alloys (HEAs) and a quantitative assessment of their hardness. It is shown that in HEAs with a bcc lattice, the degree of hardening is always greater than in HEAs with a fcc lattice (with the same number of elements in alloys). To calculate the relative hardening of the alloy, the type of crystal lattice and its parameter value are required. The calculation results are consistent with experimental data. Basic parameters of HEAs are calculated from first principles. The proposed method can be considered acceptable for assessing the hardness and degree of hardening of multi-element alloys (HEAS). For hardening, the number of elements included in the composition of the alloy, the type of crystal lattice and the density of distortion are of key importance. The last parameter depends on both the mismatch parameter and the interatomic interaction potential. It is generally accepted that a model adequately describes a physical process if it obeys two conditions ― physically justified, the calculation results have experimental confirmation. The proposed model satisfies these two conditions. In all used methods (approaches), it is believed that the mechanical characteristics are directly proportional to distortions (mismatch of atomic radii of the elements). However, not all alloys obey this ratio. In our proposed model, in fact, physical characteristics are proportional to distortion to the degree of ½. This approach allows to comprehensively take into account the features of the distorted crystal lattice of HEAs when assessing their physical and mechanical characteristics. The role of the phenomenological approach is the mathematical description of the inhibition of plastic deformation. As a braking force in HEAs, the concept of “grain size” is used, which is defined using a set of unit cells, which is a carrier of information ― the properties and structure of a multi-element alloy. The proposed method, using experimental information on the hardness of metals, can be considered acceptable for assessing the hardness of multi-element alloys (HEAs). The resulting analytical formula is of practical importance, because makes it possible to evaluate the degree of hardening for any single-phase equiatomic HEA, if the experimental data of the alloy are known — the type of crystal lattice and its parameter.