High-entropy oxides (HEOs) are complex oxides that contain five or more principal metal cations and have a single-phase crystal structure. The first HEO, (MgNiCuCoZn)0.2O in a rock salt structure, was reported in 2015 by Rost et al. HEOs have been successfully synthesized in many structures, including fluorites, perovskites, and spinels. HEOs are currently being investigated for applications as functional materials.
History In the realm of high-entropy materials, HEOs are preceded by high-entropy alloys (HEAs), which were first reported by Yeh et al. in 2004. HEAs are alloys of five or more principal metallic elements. Some HEAs have been shown to possess desirable mechanical properties, such as retaining strength/hardness at high temperatures. HEA research substantially accelerated in the 2010s. The first HEO, (MgNiCuCoZn)0.2O in a rock salt structure, was reported in 2015 by Rost et al. Similar to HEAs, (MgNiCuCoZn)0.2O is a multicomponent single-phase material. The cation site in (MgNiCuCoZn)0.2O material is compositionally disordered, similar to HEAs. However, unlike HEAs, (MgNiCuCoZn)0.2O contains an ordered anion sublattice. Following the discovery of HEOs in 2015, the field rapidly expanded. Since the discovery of HEOs, the field of high-entropy materials has expanded to include high-entropy metal diborides, high-entropy carbides, high-entropy sulfides, and high-entropy alumino-silicides.
Predicting HEO Formation
Principle of Entropy Stabilization The formation of HEOs is based on the principle of entropy stabilization. Thermodynamics predicts that the structure which minimizes Gibbs free energy for a given temperature and pressure will form. The formula for Gibbs free energy is given by:
Δ G = Δ H − T Δ S {\displaystyle \Delta G=\Delta H-T\Delta S}
where G is Gibbs free energy, H is enthalpy, T is absolute temperature, and S is entropy. It can clearly be seen from this formula that a large entropy reduces Gibbs free energy and thus favors phase stability. It can also be seen that entropy becomes increasingly important in determining phase stability at higher temperatures. In a multi-component system, one component of entropy is the entropy of mixing ( Δ S m i x {\displaystyle \Delta S_{mix}} ). For an ideal mixture, Δ S m i x {\displaystyle \Delta S_{mix}} takes the form:
Δ S m i x = − R ∑ i = 1 n c i ln c i {\displaystyle \Delta S_{mix}=-R\sum _{i=1}^{n}c_{i}\ln c_{i}}
where R is the ideal gas constant, n is the number of components, and ci is the atomic fraction of component i. The value of Δ S m i x {\displaystyle \Delta S_{mix}} increases as the number of components increases. For a given number of components, Δ S m i x {\displaystyle \Delta S_{mix}} is maximized when the atomic fractions of the components approach equimolar amounts. Evidence for entropy stabilization is given by the original rock salt HEO (MgNiCuCoZn)0.2O. Single-phase (MgNiCuCoZn)0.2O may be prepared by solid-state reaction of CuO, CoO, NiO, MgO, and ZnO. Rost et al. reported that under solid state reaction conditions that produce single-phase (MgNiCuCoZn)0.2O, the absence of any one of the five oxide precursors will result in a multi-phase sample, suggesting that configurational entropy stabilizes the material.
Other Considerations It can clearly be seen from the formula for Gibbs free energy that enthalpy reduction is another important indicator of phase stability. For an HEO to form, the enthalpy of formation must be sufficiently small to be overcome by configurational entropy. Furthermore, the discussion above assumes that the reaction kinetics allow for the thermodynamically favored phase to form.
Synthesis Methods
Solid-State Reaction Bulk samples of HEOs may be prepared by the solid-state reaction method. In this technique, oxide precursors are ball milled and pressed into a green body, which is sintered at a high temperature. The thermal energy provided accelerates diffusion within the green body, allowing new phases to form within the sample. Solid-state reactions are often carried out in the presence of air to allow oxygen-rich and oxygen-deficient mixtures to release and absorb oxygen from the atmosphere, respectively. Oxide precursors are not required to have the same crystal structure as the desired HEO for the solid-state reaction method to be effective. For example, CuO and ZnO may be used as precursors to synthesize (MgNiCuCoZn)0.2O. At room temperature, CuO has the tenorite structure and ZnO has the wurtzite structure.
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