Is configurational entropy the main stabilizing term in rock-salt Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O high entropy oxide?

We question the conclusions reported in the paper "Entropy-stabilized Oxides, by C. Rost et al., by looking into the role of configurational entropy as the stabilization of the rock-salt cubic structure of the Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O (HEO) solid solution (SS). First, we demonstrate that configurational entropy can be reduced from 1.61R for HEO to 0.5R for a two-member SS, still obtaining a single-phase material if the molar fractions of ZnO and CuO are 0.2. These SSs behave identically as HEO regarding the reversible transformation between a multi- and single-phase states when temperatures are cycled between 800 and 1000 °C. Second, we demonstrate that the different SSs presenting a configurational entropy significantly lower than HEO, are less prone to the cubic to tetragonal structural distortion, suggesting that the configurational entropy has not the central role as stabilizing factor of the rock-salt structure.

with rock-salt structure as a test case for the concept of high entropy in oxides. Their claim is that "entropy predominates the thermodynamic landscape and drives a reversible solid-state transformation between a multiphase and single-phase state." Here we use the same thermodynamic considerations by Rost et al. and replicate their experiments but reducing appropriately the configurational entropy. We demonstrate that configurational entropy does not dominate the thermodynamic stability of E1.
We show that most of the experimental evidence supporting the entropic stabilization of E1 applies even when the configurational term S Config is considerably reduced. We note that the five cations are not equivalent: Mg, Co and Ni form rock-salt oxides, whereas CuO and ZnO exhibit different crystal structures. The first cations are mutually soluble in the whole compositional range. Conversely, CuO and ZnO present limited solubility in rock-salt oxides. Hence, when modifying the stoichiometry to adjust S Config , particular care must be taken to keep constant the stoichiometric ratio of CuO and ZnO, to avoid modification in the phase composition produced by the solubility equilibria.
To demonstrate the relevance of these considerations, we synthesized various solid solutions (SSs) with different numbers of cations, under the constraint that CuO and ZnO molar fractions are equal to 0.2 as in the E1 phase. With reference to figure 2f and 2g by Rost et al. 1 , showing minima in the formation temperatures for the equimolar composition, we note that our approach is different. In fact, to prove the existence of the minima, Rost The configurational entropy is given by  Table 1. At the synthesis temperature, i.e., 1000°C, TS Config nearly doubled the value required to transform these oxides into rock-salt. This implies that, at 1000°C, E1 composition is stable as a single-phase SS, and the three-and four-component compounds with χ CuO and χ ZnO = 0.2 should be stable as well. Even binary Ni 0.8 Cu 0.2 O at 1000°C has TS Config = 5.3 kJmol −1 , which is greater than 0:24G tenorite!HEO CuO = 5.0 kJmol −1 . In fact, all these SSs do form at this temperature.
To test the stability at lower temperatures, the SSs were annealed at 750, 800, 850 and 900°C for 2 h and then quenched to room temperature (Fig. 1a). All compositions showed segregation of tenorite CuO at T < 850°C, while for T ≥ 850°C single phase was retained. The TS Config terms at 800 and 850°C for all compositions are reported in Table 1  the two-and three-component oxides, these terms were lower than 4G phase transition CuO;ZnO , while for the four-and five-component oxides, they were higher than 4G phase transition CuO;ZnO . Thus, based on configurational entropy only, SSs with two or three cations should not exist at 800 and 850°C, while they should exist with four or five cations. The presence of an additional impurity phase with the spinel structure (probably Co 3 O 4 ), found for the 4-component system at 750°C, is irrelevant for the above discussion as it disappears at T = 800°C. It is therefore concluded that the stability of these SSs cannot be discussed only in term of S Config , and that additional terms must contribute.
Let us now consider the role of solubility equilibria, starting from the simplest case, the binary Ni 0.8 Cu 0.2 O. The equilibrium phase diagram for this system shows that, at 1000°C, this composition corresponds to a stable SS. The solubility of CuO in NiO drops rapidly with temperature 4 . However, Fig. 1a, b show that a homogeneous SS in a metastable form was obtained at RT upon quenching. When this SS was annealed at 750°C, CuO segregated. Further heating at 1000°C restored the SS. This reversible behavior, similar to that reported by Rost et al. for E1 composition, can be easily explained as a reversible transition between monophasic and biphasic regions of the phase diagram. The solubility limit for this composition is indeed around 800°C 4 . We suggest that a similar argument can explain the behavior of the other compositions, although the details of the phase equilibria in multicomponent systems are largely unknown. It is known, however, that all binaries within the MgCoNiCuZn/O system exhibit reciprocal solubility above 20% at 1000°C. A stable rocksalt SS for χ CuO and χ NiO < 0.2 at 1000°C in the system CuO-MgO-NiO was also reported 5 .
Further indications on the stability of the rock-salt SSs were obtained by cooling all the compositions from 1000°C to RT at 30°C/min. This rate was fast enough to inhibit CuO segregation, but slow enough to allow structural relaxations. The diffraction patterns at the end of the cooling procedure are shown in Fig. 1c. E1 shows a considerable broadening of all the reflections, except for the 111 family, which is consistent with a tetragonal distortion of the rock-salt structure 6,7 . The broadening decreases significantly by decreasing the number of components (Fig. 1d), and therefore S Config : thus, decreasing S Config decreases the tendency of the rock-salt structure to distort from the perfect cubic symmetry. This is a clear indication that the S Config does not play the simple role of stabilizing the cubic rock-salt structure.
In summary, we have shown that the synthesis of homogeneous rock-salt SSs is possible in the MgCoNiCuZn/O system with two, three or four components, provided that the molar fractions of CuO and ZnO are kept below a limiting value close to 0.2, which is dictated by the high-temperature solubility equilibria. These SSs behave in a quasi-identical way to E1 when quenched at RT and then annealed at intermediate temperatures.
Also, the tendency of the rock-salt structure to distort from the cubic symmetry decreases with S Config . All this evidence points toward the fact that, although the contribution of S Config is undoubtedly present and significant, its role towards the stability of Mg 0.2 Co 0.2 Ni 0.2 Cu 0.2 Zn 0.2 O is limited. S Config is surely a robust and fruitful approach for controlling the stability of complex oxides, but its role must be carefully analyzed in view of the solubility equilibria under consideration.

Data availability
The data that support the findings of this study are available from the corresponding author upon request.