The importance of the vibrational entropy in the mixing stabilization for complex ceramics

Abstract The concept of high‐entropy materials has been introduced based on the idea that multiple principal components can be mixed through the increase in configurational entropy. Implicit in this idea is that the vibrational entropy, the other component of the mixing entropy, is small compared to the configurational entropy. To explore this relationship, we examined the mixing enthalpy, configurational entropy, and vibrational entropy of two binary ceramic systems—the transition metal carbides and transition metal diborides. We computed the vibrational entropy directly using the dynamical matrices obtained from density functional theory and the quasiharmonic approximation. The mixing vibrational entropy of the mixed diborides is at least as large as the configurational entropy while it is smaller for the carbides. Utilizing the phonon density of states, we further demonstrate the origin of the high mixing vibrational entropy arises because of a large number of new low‐frequency modes that appear in the diborides. Similar modes occur in the carbides but occur at larger frequencies. These differences ultimately arise because of the structural differences where metal atoms share nearest neighbors in the diborides, while they do not in the carbides. This increased vibrational mixing entropy dramatically enhances the mixing of the diborides and demonstrates that this type of entropy cannot be neglected when considering what stabilizes mixtures and provides a new perspective on what is considered high entropy.