Thermodynamics of high entropy oxides

Abstract With the hype of “high entropy” alloys and more recently, “high entropy” ceramics and “high entropy” oxides (HEOs), there has been a great push to investigate and characterize systems with 5 or more components. This push has been extremely beneficial for the materials community as it has led to the development of many new systems with targeted applications. However, with our desire to find “new” and “exotic” materials, we have not spent enough time to step back and think deeply about the fundamental thermodynamic constraints that will guide design of future HEOs. Here, we present data-driven discussions with examples that have been collected from the fields of geology and materials science over the past 50 years to highlight critical thermodynamic parameters and principles that can be used for the design of HEOs. The goal of HEOs is to push the limit of the number of components in a single-phase solid solution to achieve unique and tunable properties. True single-phase HEOs are stabilized if the positive entropy of formation more than compensates an unfavorable enthalpy of formation above some critical temperature, making the overall Δ G f negative i.e. the HEO phase is “entropy stabilized”. Under ideal mixing, the number of components in a solid solution does not affect the solubility of an additional component. In real systems, the types of additional components, their structural transformations, and their associated non-ideal interactions influence the solubility limit. Non-ideal interactions can lead to short- or long-range ordering that decreases the overall configurational entropy. Due to the ionic-covalent nature of oxides, this ordering is the norm, not the exception. In the limited cases where mixing is ideal, charge coupled substitutions can work to influence overall configurational entropy contributions due to unique crystallographic sites. Long-range ordering can be minimized by mixing oxide components that have similar charge or are isostructural. Most excitingly, is the realization that surface energies will drastically affect the stability of oxide polymorphs and solubility limits. Thus, nano-materials are an interesting and novel approach that will vastly extend the HEO engineering space. As one can see, there are many avenues for the design and development of “HEOs” that thermodynamics will allow, even though they all may not be driven explicitly by entropy.