High entropy alloys and thermodynamically derived high stability alloys; a compositional comparative study of all 3–7 element systems composed of ten 3d metals at 1273 K

Abstract

Studies of high entropy or multi-principal element alloys are focused mainly on equimolar or near-equimolar compositions for which configurational entropy is maximized. Negligence of interactions between elements forming such alloys, namely enthalpy of mixing, may detract these studies from a desirable target, which is a stabilization of single-phases instead of intermetallic compounds. In this work, both entropy and enthalpy terms are taken into account for the determination of the high stability compositions, for which the Gibbs free energy of mixing is minimized. For the ten 3d metals (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Al) all possible combinations forming 3- (120 compositions), 4- (210), 5- (252), 6- (210) and 7-component systems (120) are analyzed. Two numerical methods: a genetic algorithm (GA) and a hybrid one (a combination of GA with the gradient method) give convergent results regarding the high stability compositions at 1273 K (a typical temperature used on HEAs synthesis). It is found surprisingly that such compositions are dominated by the Ti and Al or Ni contents with minor ones of the seven remaining elements, especially for 6 and 7-component systems. These numbers can be related to average parameters of interaction (of a given element with the remaining ones) giving almost monotonic dependence; the lower the average value of the interaction parameter of a given element − the higher its content in the alloys of the high stability. Such selective preferences in compositions are reflected by high deviations between the high stability compositions and equimolar ones, with an average reaching 48% for ternary systems to 105% for 7-component alloys (expressed as normalized root mean square errors).