# Beyond configurational entropy: the role of solubility equilibria in the stability of the system (Co,Cu,Mg,Ni,Zn)O

Martina Fracchia, Mauro Coduri, Simone Bonati, Catherine Dejoie, Paolo Ghigna, Umberto Anselmi-Tamburini

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## To cite this version:

Martina Fracchia, Mauro Coduri, Simone Bonati, Catherine Dejoie, Paolo Ghigna, et al. Beyond configurational entropy: the role of solubility equilibria in the stability of the system (Co,Cu,Mg,Ni,Zn)O. Journal of the European Ceramic Society, 2025, 45 (7), pp.117237. 10.1016/j.jeurceramsoc.2025.117237. hal-05099686

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# Beyond configurational entropy: the role of solubility equilibria in the stability of the system (Co,Cu,Mg,Ni,Zn)O

Martina Fracchia<sup>a,b,*</sup>, Mauro Coduri<sup>a,b</sup>, Simone Bonati<sup>a</sup>, Catherine Dejoie<sup>c</sup>, Paolo Ghigna<sup>a,b</sup>, Umberto Anselmi-Tamburini<sup>a,b,*</sup>

## ARTICLE INFO

### Keywords:

- High entropy oxides

- Phase stability

- Configurational entropy

- Solid solution

- Solubility equilibria

## ABSTRACT

High entropy oxides are a novel class of materials, where multiple cations can be incorporated in a single-phase structure. Since the discovery of the prototypical compound Co<sub>0.2</sub>Cu<sub>0.2</sub>Mg<sub>0.2</sub>Ni<sub>0.2</sub>Zn<sub>0.2</sub>O, the research on these materials has shown an impressive boost. This compound adopts a rock-salt structure, even if CuO and ZnO are usually stable as tenorite and wurtzite. The attainment of a single phase is usually ascribed to the substantial value of configurational entropy that counterbalances unfavourable enthalpy terms. Here, we reconsider the effective role of configurational entropy in the stabilization in view of the solubility and redox equilibria involved. A careful examination of the high-temperature solubility limit of CuO in each native rock salt oxide proves to be useful to predict the phase stability. However, when the number of components is high, the behaviour becomes, at least to some extent, distinct from that of the constituent rock-salt oxides and difficult to predict.

## 1. Introduction

Since the emergence of high entropy alloys in 2004 [1,2], there has been a widespread interest within the materials science community regarding multicomponent materials. In recent times, research in this field has experienced a significant upswing after the discovery of high entropy oxides (HEOs) [3], which successfully demonstrated that the high entropy concept can be extended to ceramics as well. HEOs have shown promising characteristics in a wide variety of applications, including energy production and storage [4–8], catalysis [9–13], magnetism [14–16], thermoelectricity [17–19], etc. In these oxides, multiple cations are incorporated in equimolar or near-equimolar quantity into a single-phase structure that often cannot host them. The first HEO to be discovered had the chemical formula Co<sub>0.2</sub>Cu<sub>0.2</sub>Mg<sub>0.2</sub>.Ni<sub>0.2</sub>Zn<sub>0.2</sub>O and possessed a single-phase rock salt (RS) structure [3]. It should be noted that while CoO, MgO and NiO are stable in the RS structure, this does not happen for CuO and ZnO, which present instead a monoclinic and wurtzite structure, respectively. The possibility to obtain a single-phase compound is generally ascribed to the particularly high value of configurational entropy that, above a critical temperature,

compensates for the unfavourable enthalpy terms. This hypothesis seems to be corroborated by the presence of a reversible multiphase to single phase transition occurring above ~ 850 °C [3,20,21]. Indeed, this compound is metastable and can only be obtained by rapid quenching from the synthesis temperature to room temperature (RT). However, we have recently demonstrated that three- and four-component solid solutions, having the same ratio of native rock salt oxides and the molar fraction of CuO (χ<sub>CuO</sub>) and ZnO (χ<sub>ZnO</sub>) fixed to 0.20, are not markedly different from that of the quinary compound [20]. In particular, we investigated compounds with chemical formula Cu<sub>0.2</sub>Ni<sub>0.8</sub>O, Cu<sub>0.2</sub>Zn<sub>0.2</sub>Ni<sub>0.6</sub>O and Cu<sub>0.2</sub>Zn<sub>0.2</sub>Co<sub>0.2</sub>Ni<sub>0.4</sub>O, demonstrating that they all possess a single-phase RS structure in the temperature range from 850 °C to 1000 °C, just like in the case of Co<sub>0.2</sub>Cu<sub>0.2</sub>Mg<sub>0.2</sub>Ni<sub>0.2</sub>Zn<sub>0.2</sub>O. This study casted some doubts into the leading role of configurational entropy in stabilizing the (Co,Cu,Mg,Ni,Zn)O system, which should be instead reconsidered in view of the solubility equilibria involved. Since the seminal work by Rost *et al.* in 2015, the role of configurational entropy in the phase stability of HEOs has been reconsidered [22,23], as testified by the prompt change in terminology from “entropy stabilized oxides,” as the multicomponent oxides were referred to in the first research

<footnote><sup>a</sup> Department of Chemistry, University of Pavia, V.le Taramelli 12, Pavia I27100, Italy</footnote>

<footnote><sup>b</sup> INSTM, National Inter-University Consortium for Materials Science and Technology, Via G. Giusti 9, Florence 50121, Italy</footnote>

<footnote><sup>c</sup> ESRF – The European Synchrotron, 71, Avenue des Martyrs, Grenoble 38000, France</footnote>

<footnote>* Corresponding authors at: Department of Chemistry, University of Pavia, V.le Taramelli 12, Pavia I27100, Italy.
E-mail addresses: martinailaria.fracchia@unipv.it (M. Fracchia), umberto.anselmitamburini@unipv.it (U. Anselmi-Tamburini).</footnote>
works, into “high entropy oxides” or “compositionally complex c-
amics” [24]. HEOs have now been reported in several different crystal
structures other than the rock salt, such as the spinel [25–27], the
fluorite [28–30], the perovskite [31–33], etc. In these cases, single-phase
compounds can be obtained even with less than five elements, or for
compositions considerably deviating from equimolarity, all character-
ized by lower values of configurational entropy [24,34]. Even for the
(Co,Cu,Mg,Ni,Zn)O system, the stability region extends well beyond the
equimolar composition [35]. In a more general way, the phase stability
of HEOs can be correlated to the type and nature of the cations involved
[22,35], and can often be predicted on the basis of their relative con-
centration, their valence state, and their ionic radii, as expected by the
Hume-Rothery and/or Pauling rules [36,37]. The prototypical rock salt
Cu<sub>0.2</sub>Co<sub>0.2</sub>Mg<sub>0.2</sub>Ni<sub>0.2</sub>Zn<sub>0.2</sub>O represents one of the few exceptions [23,38]
for which the leading role of configurational entropy is still debated,
even after almost two years from its discovery.

In this work, we go beyond our previous study [20] on the phase
stability of binary, ternary, and quaternary compounds belonging to the
system (Co,Cu,Mg,Ni,Zn)O, in the temperature range from 750 to 1000
°C. We choose the compositions in order to have, alternatively, NiO,
CoO or MgO as the predominant rock salt matrix, and fixing χ<sub>CuO</sub> and
χ<sub>ZnO</sub> to 0.20, as to have the same enthalpy cost as in the quinary com-
pound. This allows to experimentally demonstrate that the phase
behaviour of each solid solution is not strictly dependent on the number
of components, but rather on their chemical nature, that is, the stability is
not directly correlated to the amount of configurational entropy. In
particular, we show that their behaviour can be better explained by
considering the solubility equilibria of the components involved. In any
case, we demonstrate that, especially for Co-rich compositions, also the
equilibrium with atmospheric O<sub>2</sub> involving the Co<sup>3+</sup>/Co<sup>2+</sup> redox couple
must be taken into account for a complete understanding of the phase
stability. In this respect, we noticed that this equilibrium is strongly
influenced by the number of components. These results also allow
attempting a more formal definition of the so-called “cocktail-effect” in
high entropy oxides. Finally, we identified copper as the element critical
to the stabilization of this system and we examined the phase stability of
compositions with different copper content. In this respect, in contra-
diction with the original work on high entropy oxides by Rost et al. [3],
we show that a single high entropy RS phase is stabilized when χ<sub>CuO</sub> is
minimum, i.e. far from the condition of maximum configurational
entropy.

## 2. Experimental

All the samples were synthesized using a wet chemistry approach,
specifically a sol-gel method. The syntheses were carried out starting
from the corresponding metal nitrates, mixed in the stoichiometric
amounts and dissolved in water together with a slight excess (1.1:1) of
citric acid. All the starting reagents were purchased from Sigma-Aldrich
(purity > 98 %) and were used without further purification. The as-
prepared solution was heated overnight at 80 °C under stirring, and
the obtained gel was heated in a furnace at 300 °C for 3 h in air. The
resulting powder was then pressed into a pellet using a uniaxial press
and finally calcined in air at 1000 °C for 18 h and then quenched in air at
RT. Part of the powder was then kept for the subsequent characteriza-
tion, while the remaining part was equilibrated at lower temperature.
This procedure was repeated for each heat treatment, specifically at 900
°C, 850 °C, 800 °C and 750 °C, equilibrating each sample for 18 h and
quenching to RT. In the case of the compositions with different copper
content, each sample was equilibrated at lower temperatures (900 °C,
850 °C, 800 °C and 750 °C) for 2 h.

X-ray diffraction (XRD) patterns were collected on a Bruker D2
diffractometer in Bragg-Brentano geometry equipped with Ni-filtered
Cu-Kα radiation. The data collected in the 10-90° 2θ range were inte-
grated with a step of 0.03° and 1.8 seconds exposure per step, for 1 h
25 min total acquisition time. The Co-rich specimens were subjected to a

longer acquisition (5.0 seconds per step, step size 0.02°, total acquisition
time 5 h 40 min) owing to the fluorescence which decreases the signal-
to-noise ratio. High resolution X-ray powder diffraction (HR-XRPD)
patterns were collected at RT at the ID22 beamline of the European
Synchrotron Radiation Facility (ESRF), in Grenoble, at incident wave-
length λ = 0.354107 Å (~35 keV), using the setup equipped with crystal
analyzers [39,40]. The specimens were filled into borosilicate capillaries
with a diameter of 0.5 mm, mounted on the axis of the diffractometer,
and rotated during acquisition. Rietveld refinements were performed
using the GSAS-II software [41] for quantitative phase analysis and the
determination of lattice parameters. The phases involved are rock salt
(RS) (space group: *Fm\bar{3}m*), tenorite (space group: *C2/c*), spinel (Fd\bar{3}m),
wurtzite (*P6\bar{3}mc*) and guggenite (*Pmmn*). Tenorite, spinel, and wurtzite
were considered with nominal composition CuO, Co₃O₄ and ZnO,
respectively. The RS phase composition was adjusted according to the
nominal distribution of the cations of the specimen. Atomic coordinates
were not refined. The line profile broadening was adjusted considering a
microstrain contribution, while no size effect was implemented because
the thermal treatment at 1000°C induced enough crystal growth. The
anisotropic broadening of the rock salt phase was dealt with the Ste-
phenus function, employed in GSAS-II, which accounts for two terms to
describe the broadening of a cubic system [42]. The full width at half
maximum (FWHM) of the 2θ reflection was determined by single peak
fitting using a pseudo-Voigt function by the WinPLOTR software [43].
When the original 2θ cubic reflection is split into two overlapping
contributions, owing to the tetragonal symmetry, the FWHM is deter-
mined by directly measuring, without a fitting procedure, the broad-
ening from the left to the right side of the peak at the intensity
corresponding to half of the peak height.

3. Results and discussion

The phase diagrams of the CuO-MO (with M = Mg, Co or Ni) and
ZnO-MO systems are described in the literature, reporting the solubility
limits of CuO and ZnO in each rock salt oxide [44–48]. However, these
values are often imprecise and do not allow for a direct and reliable
comparison with our experimental data. Consequently, we carried out a
preliminary investigation on the solubility limits at 1000 °C of CuO and
ZnO in each rock salt oxide, employing the same synthetic procedure
used for all the subsequent investigations. In particular, we chose the
sol-gel synthesis, which generally allows to reach the thermodynamic
equilibrium more quickly than the solid state synthesis [27]. The syn-
thesis was followed by quenching to RT. The HR-XRPD patterns ob-
tained for the CuO-MgO, CuO-CoO, and CuO-NiO systems in proximity
to the solubility limit are displayed in Fig. 1.

In the case of CuO-MgO, the solubility limit lies between 0.18 and
0.20. Interestingly, this value is slightly lower than 0.20, which is the
molar fraction of CuO in the HEO (Co<sub>0.2</sub>Cu<sub>0.2</sub>Mg<sub>0.2</sub>Ni<sub>0.2</sub>Zn<sub>0.2</sub>O). For χ<sub>CuO</sub>
> 0.20, we observe the segregation of guggenite, a copper-rich phase
already reported for the CuO-MgO and CuO-CoO binary systems [21,45,
49], having formula Cu<sub>2</sub>MgO<sub>3</sub> and Cu<sub>2</sub>CoO<sub>3</sub>, respectively.

The solubility limits of CuO in the CoO and NiO systems are, in turn,
much larger than 0.20. It is interesting to note that a broadening and
then a splitting of all peaks different from the *hhh* occurs increasing χ<sub>CuO</sub>,
indicating a transition from a cubic (space group #225, *Fm\bar{3}m*) to a
tetragonal phase. Having no evidence of any further distortion, we
proposed an *I4/mmm* space group, with all ions lying, as in the parent RS
phase, in special positions.

The Rietveld refinements for Cu<sub>0.25</sub>Co<sub>0.75</sub>O, Cu<sub>0.20</sub>Co<sub>0.80</sub>O and Cu<sub>0.30</sub>Ni<sub>0.70</sub>O are shown in Fig. S1, and the computed cell parameters and interatomic distances are displayed in Table S1. For Cu<sub>0.20</sub>Co<sub>0.80</sub>O, only a peak broadening rather than a peak splitting is observed, while the peak positions still correspond to those of the parent RS phase. This can be associated with a local tetragonal distortion while, on average, the RS atomic structure is preserved. The occurrence of local distortions
<figure><img src="image_4.png" /><figcaption>Fig. 1. : HR-XRPD patterns obtained for the CuO-MgO, CuO-CoO and CuO-NiO systems in proximity to the solubility limit. For the CuO-MgO and CuO-CoO systems, the secondary phase can be indexed as guggenite and is marked by a filled triangle. For the CuO-NiO, the secondary phase is tenorite and is marked by an asterisk. The inset on the right shows a magnification of the 200 peak of the cubic phase, evidencing the splitting upon the cubic to tetragonal transition.</figcaption></figure>

with a lower symmetry than that of the matrix is peculiar of many complex functional ceramics and has been already observed in many other systems [50–52]. A successful refinement was then conducted using a single cubic phase, where the peak broadening was accounted for in terms of an anisotropic microstrain. It can be speculated that the tetragonal transition has a key role in increasing the solubility limit of CuO. Indeed, Cu²⁺, being in a [Ar]3d⁹ configuration, exhibits a strong Jahn-Teller effect, preferring a distorted octahedral coordination [53, 54], with the elongation (or compression) of the axial ligands. Contrarily to MgO, both CoO and NiO can accommodate this distortion that propagates in the long-range, leading to a cubic to tetragonal phase transition. The solubility limit of CuO is between 0.25 and 0.30 in CoO; above this value, guggenite is segregated. The solubility is much higher in NiO, between 0.34 and 0.36. Above these values, the segregation of tenorite, rather than guggenite, is observed. Indeed, we note that Cu₂NiO₃ has never been reported in the literature, and all our attempts to synthesize this compound were unsuccessful, prompting us to conclude that this compound is not stable, at least in these experimental conditions.

The solubility of ZnO at 1000 °C in MgO, CoO and NiO was also investigated. All the pertinent XRD patterns are reported in Fig. S2,

while here we report only the final results, summarized in Table 1, together with those found for the CuO-MO systems. In each rock salt oxide, the solubility of ZnO is larger than 0.20, which corresponds to the molar fraction of ZnO in the quinary HEO compound. No distortion of the cubic structure is observed, and the zinc-containing segregated phase above the solubility limit is wurtzite in any case.

After this preliminary study on binary systems, we investigated the role of solubility equilibria in three- and four-component solid solutions. So, we defined for each RS binary oxide a series represented by a sequence of binary, ternary, and quaternary solid solutions obtained by adding in sequence the three oxides, keeping their molar fraction equal to 0.2. Thus, each series is composed of: i) a binary solid solution, where

<caption>**Table 1**</caption>

Solubility limits at 1000 °C of CuO and ZnO in each rock salt oxide (MgO, NiO or CoO), as determined experimentally as described in the text.

<table><thead><tr><td>Matrix</td><td>CuO solubility limit</td><td>ZnO solubility limit</td></tr></thead><tbody><tr><td>MgO</td><td>0.18 ≤ χ &lt; 0.20</td><td>0.22 ≤ χ &lt; 0.25</td></tr><tr><td>CoO</td><td>0.25 ≤ χ &lt; 0.30</td><td>0.25 ≤ χ &lt; 0.30</td></tr><tr><td>NiO</td><td>0.34 ≤ χ &lt; 0.36</td><td>0.35 ≤ χ &lt; 0.40</td></tr></tbody></table>
the molar fraction of the RS oxide is 0.8 and $\chi_{CuO}$ is 0.2; ii) a ternary solid solution, where the molar fraction of the RS oxide is 0.6 and $\chi_{CuO}$ and $\chi_{ZnO}$ are 0.2 each; iii) a quaternary solid solution, where the molar fraction of the RS oxide is 0.4 and $\chi_{CuO}$ and $\chi_{ZnO}$ are 0.2 each, and an additional RS oxide was added with molar fraction equal to 0.2. For instance, the NiO-based series comprises a binary (Cu$_{0.2}$Ni$_{0.8}$O), a ternary (Cu$_{0.2}$Zn$_{0.2}$Ni$_{0.6}$O), and a quaternary (Cu$_{0.2}$Zn$_{0.2}$Co$_{0.2}$Ni$_{0.4}$O) solid solution. The compositions of all the series are listed in Table 2.

As anticipated, this approach was chosen as a way to evaluate the role of configurational entropy in the stabilization of these systems. The free energy of formation of CuO- and ZnO-containing solid solutions can be written as:

$$ \Delta G_{mix} = \Delta G_{mix}^{E} + \Delta G_{mix}^{I} \quad (1) $$

Where $\Delta G_{mix}^{E}$ is the excess free energy of mixing, accounting for the non-ideality of the solid solutions. Its nature is mainly enthalpic and is due to the fact that the stable crystal structure of CuO and ZnO are different from RS. Taking into account the molar fractions of CuO and ZnO, then:

$$ \Delta G_{mix}^{E} = \chi_{CuO}\Delta G_{CuO}^{\text{tenorite--rocksalt}} + \chi_{ZnO}\Delta G_{ZnO}^{\text{wurtzite--rocksalt}} \quad (2) $$

With $\Delta G_{CuO}^{\text{tenorite--rocksalt}} = 25 \text{ kJ/mol}$, and $\Delta G_{ZnO}^{\text{wurtzite--rocksalt}} = 22 \text{ kJ/mol}$, according to literature [55,56]. $\Delta G_{mix}^{I}$, in turn, is the free energy of formation of the ideal solid solution, which is equal to the negative of the configurational entropy times T:

$$ \Delta G_{mix}^{I} = -T \cdot R \sum_{i} \chi_{i} \ln \chi_{i} \quad (3) $$

Where R is the gas constant. It is then obvious that, for the ternary, quaternary, and quinary solid solutions, $\Delta G_{mix}^{E}$ is fixed to the same value. In other terms, this strategy allows to keep the same enthalpy cost, while progressively increasing the number of components and the amount of configurational entropy.

Each solid solution was synthesized at 1000 °C and then treated overnight at 900, 850 and 800 °C, in order to evaluate the dependence of phase stability from temperature. In all cases, all the samples were quenched to RT after the annealing. The XRD patterns obtained for all the samples are shown in Fig. 2. The phase compositions, as obtained by Rietveld refinements, are reported in Table S2. In principle, if the stability of the (Co,Cu,Mg,Ni,Zn)O system depends exclusively on the amount of configurational entropy, the behaviour of all the binary, ternary, and quaternary solid solutions should be similar, notwithstanding the nature of the rock salt matrix oxide. Moreover, a lower stability should be observed by decreasing the number of components. However, even with a cursory analysis of Fig. 2, it can be concluded that this is not the case. The behaviour is more complex than expected and deserves further attention. To facilitate a direct comparison between all the samples, the results are summarized in Fig. 3a, where the fractions of the rock salt phase found at each temperature and for each series are reported. In this figure, only the results between 1000 and 850 °C are reported, as all compositions are polyphasic at lower temperatures. For comparison, we also reported the phase composition of the five-component HEO.

A single phase with the RS structure is found down to 850 °C for the five-component HEO material. Below 850 °C, however, tenorite is present as a secondary phase. At 1000 °C, all the compositions are also monophasic, with the remarkable exceptions of Cu$_{0.2}$Mg$_{0.8}$O, due to the

<caption>**Table 2**</caption>

List of binary, ternary and quaternary compositions for each rock salt oxide matrix.

<table><thead><tr><th></th><th>Binary</th><th>Ternary</th><th>Quaternary</th></tr></thead><tbody><tr><td>NiO matrix</td><td>Cu<sub>0.2</sub>Ni<sub>0.8</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Ni<sub>0.6</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Co<sub>0.2</sub>Ni<sub>0.4</sub>O</td></tr><tr><td>MgO matrix</td><td>Cu<sub>0.2</sub>Mg<sub>0.8</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Mg<sub>0.6</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Ni<sub>0.2</sub>Mg<sub>0.4</sub>O</td></tr><tr><td>CoO matrix</td><td>Cu<sub>0.2</sub>Co<sub>0.8</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Co<sub>0.6</sub>O</td><td>Cu<sub>0.2</sub>Zn<sub>0.2</sub>Mg<sub>0.2</sub>Co<sub>0.4</sub>O</td></tr></tbody></table>

low solubility of CuO in MgO (~ 0.19 molar fraction, as shown before) and Cu$_{0.2}$Co$_{0.8}$O and Cu$_{0.2}$Zn$_{0.2}$Co$_{0.6}$O solid solutions, where some spinel is found as a secondary phase. The formation of the spinel is due in this case to a partial oxidation of cobalt. However, both ZnO and CuO are still incorporated in the RS structure, implying that this solid solution, contrarily to Cu$_{0.2}$Mg$_{0.8}$O, can still be considered “entropy stabilized”. To distinguish between the two situations, we also show another set of histograms evidencing the total amount of tenorite and guggenite which are found as secondary phases (Fig. 3b).

The Co(III)/Co(II) redox equilibrium is influenced by the exchange with atmospheric O$_{2}$, and cannot be easily controlled. For this reason, samples with low spinel content (≤ 3% for the Cu$_{0.2}$Co$_{0.8}$O and Cu$_{0.2}$Zn$_{0.2}$Co$_{0.6}$O compositions) were treated as monophasic.

At 900 °C, all the quaternary compositions are still monophasic. At this temperature, the ternary compositions of the MgO- and CoO-based series still present guggenite and spinel as secondary phases, similarly to what found at 1000 °C. We note that for the Cu$_{0.2}$Zn$_{0.2}$Co$_{0.6}$O composition, copper and zinc are still included in the RS phase. At 850 °C, the quaternary compositions of the NiO- and CoO-based series are monophasic, while for the MgO-based series it shows a secondary phase (tenorite). At this temperature only the ternary composition Cu$_{0.2}$Zn$_{0.2}$Ni$_{0.8}$O is monophasic. Notably, in the composition Cu$_{0.2}$Zn$_{0.2}$Co$_{0.6}$O the RS phase is not even present. Concerning the binary compositions, for Cu$_{0.2}$Mg$_{0.8}$O the fraction of the guggenite secondary phase is increased. Again, for the Cu$_{0.2}$Co$_{0.8}$O composition, no RS is found at this temperature. Even for Cu$_{0.2}$Ni$_{0.8}$O, a small fraction (2%) of tenorite can be detected: in conclusion, no binary composition is found to be monophasic at 850 °C.

It is important to describe the individual behaviour within each series, as they are significantly distinct. In the NiO-based series, all the samples are single phase down to 900 °C. At 850 °C, in the binary Cu$_{0.2}$Ni$_{0.8}$O only a slight fraction of tenorite is segregated, while Cu$_{0.2}$Zn$_{0.2}$Ni$_{0.6}$O and Cu$_{0.2}$Zn$_{0.2}$Co$_{0.2}$Ni$_{0.8}$O are single phase, segregating tenorite at 800 °C. It can be seen that, as we already pointed out in our previous work [20], the behaviour of all the compositions belonging to this series is not markedly different from that of the five-component HEO.

In the MgO-based series, the binary Cu$_{0.2}$Mg$_{0.8}$O is already segregating guggenite at 1000 °C. Guggenite is also found in Cu$_{0.2}$Zn$_{0.2}$Mg$_{0.6}$O below 900 °C, while in Cu$_{0.2}$Zn$_{0.2}$Ni$_{0.2}$Mg$_{0.4}$O the partial substitution of Mg with Ni promotes the segregation of tenorite rather than guggenite.

In the CoO-based series, the partial oxidation of Co(II) to Co(III) favours the formation of a spinel, which in some cases is the majority phase (at least for T < 900 °C). Interestingly, at 900 °C and 1000 °C, segregation of tenorite, guggenite, and wurtzite is never observed. For the binary and the ternary compositions, at T ≤ 850 °C the RS phase is never found: in this case, only the spinel and tenorite phases are present, in a fraction that reflects the stoichiometry ratio between Cu and Co, due to the low miscibility of CuO into Co$_{3}$O$_{4}$. A single RS phase is observed down to 850 °C for the quaternary composition. Interestingly, in this case, cobalt oxidation is completely prevented.

These experimental results can be analysed considering the thermodynamics of these solid solutions. For this purpose, Eqs. 1, 2, and 3 were used to calculate $\Delta G_{mix}$ as a function of temperature for two-, three-, four- and five-component compositions (Fig. 4). $\Delta G_{mix}$ is large and negative between 750 °C and 1000 °C for both five- and four-component solid solutions, implying that these solid solutions should be stable in the whole temperature range. This is contrary to our experimental results.

On the contrary, ternary compositions should not be formed below 900 °C. However, Cu$_{0.2}$Zn$_{0.2}$Ni$_{0.6}$O is still monophasic at 850 °C. Overall, it can be observed how the actual stability of the solid solutions depends not only on the number of components, but also on the chemical nature of the RS matrix. In other terms, the thermodynamic depiction given by Eq. 1, commonly employed for high entropy oxides, is too simplistic to represent the complex behaviour of multicomponent
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** : XRD patterns obtained at 1000 °C, 900 °C, 850 °C and 800 °C for the five-component HEO and for all the binary, ternary and quaternary compositions. The legend indicates how the secondary phases are marked in the patterns.</figcaption></figure>

Recently, more complex approaches have been employed to predict the temperature-dependent phase stability in high entropy alloys [57] and in high entropy carbides and carbonitrides [58]. In particular, these approaches aim at comparing the Gibbs free energy of the complex oxide in its targeted form with the convex hull built with every possible competitive phase, including simple oxides but also any existing multinary oxide but the one that is considered. However, all these methods require effective calculations of the Gibbs free energy of all the possible phases. This is far from being trivial and, in any case, we are here demonstrating that, at least for the five-component solid solution, the usual approach of considering only configurational entropy as the main stabilizing term, ignoring favourable enthalpy contributions, is not sufficient. Recently, the cluster-plus-glue atom model has been introduced as a new possible strategy to predict the thermodynamic stability of high and medium entropy oxides [59]. According to this approach, any crystallographic structure can be thought as composed by a primary nearest-neighbour cluster unit (assumed to be the most strongly bonded local structure) and multiple glue atoms situated outside the primary clusters, satisfying the octet rule [59,60]. It has been employed to various high entropy oxides in various crystal structures, i.e. rock salt [59–61], fluorite [62] and perovskite [63]. In the case of fluorites and perovskites, this model allowed demonstrating that simple geometric predictors (i.e. the standard deviation of the ionic radii of the constituents or the Goldschmidt tolerance factor, respectively) may be not sufficient to predict a priori the formation of a single phase at a given temperature, and that the chemical nature of the components must be also taken into account [62,63]. In the specific case of the (Co,Cu,Mg,Ni, Zn)O system, non-equimolar compositions selected using the cluster-plus-glue-atom model proved to have a larger thermodynamic stability with respect to the equimolar one (presenting the largest entropy value) [59]. This result is in agreement with what we observed by

a recent chemometrics-assisted investigation [35], and again suggests that the nature of the constituents, and thus the overall enthalpy, is an important criterium that must be taken into account when designing new high entropy compounds. Dong *et al*. identified the ΔG value and the average cation-size difference as the two critical factors in predicting the stability of these medium-entropy oxide compositions [61]. However, our findings demonstrate that the simple thermodynamic description based solely on ΔG calculations may not be sufficient. Geometric parameters based on the ionic radius of the cations also do not provide, in the present case, an adequate explanation for the observed differences in stability among compositions. Indeed, we note that the Ni-rich compositions exhibit the highest stability, despite the fact that the ionic radius of Ni²⁺ (0.69 Å) [64] deviates the most from that of Cu²⁺ and Zn²⁺, equal to 0.73 Å and 0.74 Å, respectively (while the ionic radius of Co²⁺ and Mg²⁺ are equal to 0.745 Å and 0.72 Å) [64].

An effective description allowing to explain the experimental results shown above can be rather obtained by considering the role of conventional solubility limits, and especially by carefully analysing the behaviour of the binary systems CuO-MO and ZnO-MO. Generally, we observed that, notwithstanding the number of components, Ni-rich compositions tend to stabilize the solid solutions, while Mg-rich compositions show the opposite behaviour, having the tendency to segregate copper as guggenite. Finally, Co-rich compositions show a peculiar behaviour, due to the tendency of Co(II) to oxidize to Co(III), via equilibrium with atmospheric O₂, leading to the formation of a spinel phase. This behaviour is indeed mirrored by the binary CuO-NiO, CuO-MgO and CuO-MgO phase diagrams. Moreover, as shown before, the solubility limit of CuO in each rock salt oxide is generally lower than that of ZnO. This is also reflected in the experimental data obtained for each series, where the segregated phases at T ≥ 850 °C are always copper-rich (tenorite or guggenite), while ZnO is still incorporated in the rock
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** : The percentage of a) rock salt oxide and b) the sum of tenorite and guggenite found at each temperature and for each binary, ternary, quaternary and quinary compositions are reported as histograms. The red histograms represent the compositions belonging to the NiO-based series (where NiO is the main matrix), while the yellow and green histograms refer to compositions belonging to the MgO- and CoO-based series, respectively.</figcaption></figure>

salt. The only exception is represented by Cu₀.₂Zn₀.₂Co₀.₆O at 800 °C, where the RS phase has completely disappeared and tenorite, wurtzite and spinel co-exist.

Generally, the dissolution processes are endothermic and entropy-driven. As a consequence, it could be argued that Eq. 1 should be able to represent the behaviour of the investigated multicomponent systems. Since this is not the case, we must conclude that the (Co,Cu,Mg,Ni,Zn)O system deviates from this simple description. Again, a careful evaluation of the solubility equilibria involved proves to be helpful. Bulazirk *et al.* investigated the thermodynamics of solid solution formation in the binary CuO-NiO system, showing that a model based on the thermodynamics of simple solutions is not able to describe the complexity of the system [56]. In particular, the enthalpy associated with the process is far more negative (i.e., favourable) than expected. This can explain why the

NiO-based compositions are generally more stable and points toward the presence of a synergistic effect between NiO and CuO.

A further point worth noting is that the larger the number of components, the smaller the effect of the chemical nature of individual oxides on the stability of the solid solution. This effect is particularly evident in the CoO-based series. At 850 °C, both the binary and ternary compositions are multiphasic at 850 °C, and the rock salt phase is completely absent. However, the quaternary composition, at the same temperature, is monophasic, implying that cobalt oxidation is completely inhibited. This is particularly surprising, considering that CoO is still the main native rock salt oxide, and that the other native RS is MgO, which usually leads to destabilization of the solid solutions. A similar behaviour is also found in the MgO-based series, where the quaternary composition is stable at lower temperatures when compared
<figure><img src="image_7.png" /><figcaption>Fig. 4. $\Delta G_{mix}$ as a function of temperature, for two, three, four and five-component compositions.</figcaption></figure>

to the binary and ternary compositions. Also, at 850 °C, the segregated phase is tenorite, even if Mg-rich compositions tend to present guggenite as the secondary phase.

Overall, it can be stated that i) the association of more elements has a positive effect on the stability and ii) the behaviour of a multicomponent mixture is distinct from that of the constituent RS oxides and difficult to predict. This peculiar effect seems not related to the amount of configurational entropy, but can be rather correlated to the so-called “cocktail effect”, usually vaguely defined as a synergy arising between cations. The cocktail effect actually implies that the behaviour of a complex mixture is distinct and, to some extent, independent from the constituents. This may have important implications. For instance, we have demonstrated how the redox equilibria in Co-rich solid solutions may drastically change, and this may significantly influence the functional properties.

As we observed before, the segregation occurring by decreasing the temperature always involves copper-rich phases, rather than wurtzite, implying that copper has a critical role in the stabilization of this system. We then examined the phase stability of the five-component (Co,Cu,Mg, Ni,Zn)O system when $\chi_{CuO}$ is progressively increasing at the expense of all the other cations, which were kept in equimolar ratio. The compositions are listed in Table 3, while the HR-XRPD patterns of the samples obtained at 1000 °C and quenched to RT are shown in Fig. 5a.

For $\chi_{CuO} \le 0.2$, the structure is cubic. Above this value, all peaks apart from those related to the {hhh} family are considerably broadened, as evidenced by the sudden increase in the FWHM of the 200 reflection, displayed in Fig. 5b for compositions up to $\chi_{CuO} = 0.28$. At the same time, all these peaks show a marked asymmetry. This effect was previously reported [10,35,54] and can be attributed to a tetragonal distortion driven by the strong Jahn-Teller effect correlated to $Cu^{2+}$ forced in an octahedral environment. We here note that this same cubic-to-tetragonal distortion occurs in the CuO-NiO and CuO-CoO binary systems for copper-rich solid solutions, as shown above in the text. In the case of the five-component solid solution, however, a clear splitting of the reflections does not occur, owing to the lower extent of

<table><caption>**Table 3**
List of compositions with increasing copper amount.</caption><thead><tr><th>Label</th><th>Composition</th></tr></thead><tbody><tr><td>CuO</td><td>Zn<sub>0.25</sub>Co<sub>0.25</sub>Mg<sub>0.25</sub>Ni<sub>0.25</sub>O</td></tr><tr><td>CuO.05</td><td>Cu<sub>0.05</sub>Zn<sub>0.2375</sub>Co<sub>0.2375</sub>Mg<sub>0.2375</sub>Ni<sub>0.2375</sub>O</td></tr><tr><td>CuO.10</td><td>Cu<sub>0.10</sub>Zn<sub>0.225</sub>Co<sub>0.225</sub>Mg<sub>0.225</sub>Ni<sub>0.225</sub>O</td></tr><tr><td>CuO.15</td><td>Cu<sub>0.15</sub>Zn<sub>0.2125</sub>Co<sub>0.2125</sub>Mg<sub>0.2125</sub>Ni<sub>0.2125</sub>O</td></tr><tr><td>CuO.20</td><td>Cu<sub>0.20</sub>Zn<sub>0.20</sub>Co<sub>0.20</sub>Mg<sub>0.20</sub>Ni<sub>0.20</sub>O</td></tr><tr><td>CuO.25</td><td>Cu<sub>0.25</sub>Zn<sub>0.1875</sub>Co<sub>0.1875</sub>Mg<sub>0.1875</sub>Ni<sub>0.1875</sub>O</td></tr><tr><td>CuO.26</td><td>Cu<sub>0.26</sub>Zn<sub>0.185</sub>Co<sub>0.185</sub>Mg<sub>0.185</sub>Ni<sub>0.185</sub>O</td></tr><tr><td>CuO.28</td><td>Cu<sub>0.28</sub>Zn<sub>0.18</sub>Co<sub>0.18</sub>Mg<sub>0.18</sub>Ni<sub>0.18</sub>O</td></tr><tr><td>CuO.30</td><td>Cu<sub>0.30</sub>Zn<sub>0.175</sub>Co<sub>0.175</sub>Mg<sub>0.175</sub>Ni<sub>0.175</sub>O</td></tr></tbody></table>

the tetragonal distortion compared to the binary systems, as evidenced in Table S3, where the cell parameters obtained after refinement are reported. In addition, in the XRD patterns, a contribution located in the same position as the original 200 reflection of the cubic phase is still observed, despite the clear tetragonal splitting. This suggests the formation of a complex phase distribution involving the coexistence of both tetragonal and cubic phases, which does not occur in binary compounds. However, considering the complex peak broadening and overlaps, a quantification of the two phases via Rietveld refinement is unreliable. Examples of Rietveld refinements for the samples CuO.25, CuO.26 and CuO.28 are shown in Fig. S3.

Despite this massive tetragonal distortion with increasing copper content, no segregation of secondary phases is observed until $\chi_{CuO} = 0.30$, where the peaks characteristic of guggenite start to appear. This is accompanied by a decrease in the FWHM, as a consequence of copper diffusing out of the high entropy phase. Consequently, $\chi_{CuO} \sim 0.28$ can be regarded as the solubility limit of CuO at 1000 °C in the quinary (Co, Cu,Mg,Ni,Zn)O system.

In order to investigate the phase stability as a function of temperature, each composition with $\chi_{CuO} \le 0.25$ was treated at 900, 850, 800, 750, and 700 °C and then quenched to RT. The pertinent HR-XRPD patterns are reported in the SI (Fig. S4) together with the phase quantification obtained by Rietveld refinement (Table S4). Fig. 5c reports the minimum temperature at which each composition is found as single phase, i.e. where a cubic, tetragonal, or a mix cubic/tetragonal structure is present and no segregation of other secondary phases (tenorite, wurtzite, spinel, etc.) occurs. Practically, this is equivalent to draw a partial phase diagram of the system CuO - (Co-Mg-Ni-Zn)O. The single-phase to multi-phase transition temperature increases with $\chi_{CuO}$. This is the behaviour expected when crossing the phase boundary between a single-phase region and a biphasic region. By increasing $\chi_{CuO}$, the solvus temperature increases after reaching a threshold value.

In the original work by Rost et al. [3], the lowest transition temperature was observed for the equimolar composition, where the configurational entropy is at its maximum. Here we demonstrate that this is not the case: the lowest transition temperature occurs for the compositions with the lowest copper content and the lowest configurational entropy. This is an additional proof that configurational entropy is not the main factor governing the stabilization of this system, which is rather dictated by the copper content. We also stress that, as observed before, this behaviour is directly correlated to the low solubility displayed by CuO in the rock salt oxides. ZnO, in turn, has a highest solubility value, and wurtzite is never observed in a fraction larger than 0.3 % even at low temperatures and for zinc-rich compositions.

## 4. Conclusions

In this study, we employed a rigorous approach to evaluate the role of configurational entropy in the stabilization of the (Co,Cu,Mg,Ni,Zn)O system. In particular, we studied the phase stability over temperature of two-, three- and four-component oxides, where the main rock salt matrix was either NiO, CoO or MgO, with respect to the prototypical compound Co<sub>0.2</sub>Cu<sub>0.2</sub>Mg<sub>0.2</sub>Ni<sub>0.2</sub>Zn<sub>0.2</sub>O. The behaviour of all the investigated compositions was markedly different, depending on the nature of the matrix. A simple thermodynamic description, where configurational entropy is assumed to be the main responsible for the stabilization, compensating for unfavourable enthalpy terms, proved to be too simplistic and inadequate to fully represent the complexity of the system: this conclusion is in line with the recent use of more complex descriptors for the stability of high entropy materials [57,58]. However, we found that precious information can be derived by considering the high-temperature solubility equilibria involved. The larger stability of Ni-rich compositions can be correlated to the high solubility limit of CuO in the NiO rock salt. Conversely, Mg-rich and Co-rich display a lower stability, with the tendency to segregate guggenite and spinel, respectively. This is true for solid solutions with two or three components, while increasing the
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** a) HR-XRPD patterns obtained for the compositions listed in Table 3, synthesized at 1000 °C and quenched to RT. The inset on the right shows a magnification of the 200 peak of the cubic phase, evidencing the splitting upon the cubic to tetragonal transition b) FWHM of the 200 reflection as a function of the copper molar fraction c) Temperature of transition from single phase to multiphase as a function of the copper content.</figcaption></figure>

number of components, the phase stability tends to be independent from the prevailing rock salt matrix. This effect can be rationalized by considering second neighbour (metal-metal) interactions. Indeed, the first neighbour interactions are in any case metal-oxygen bonds. In case of two/three components, the metal-metal interaction is of a specific type, as dictated by the main component of the matrix. Increasing the number of components, the metal-metal interaction becomes non-specific, as each cation lies in a potential well determined by the others. This may be at the basis of the so-called “cocktail effect”, according to which the association of many elements may lead to positive and peculiar effects, difficult to predict and independent of the prevailing rock salt matrix. In the present case, for instance, cobalt oxidation is completely suppressed, allowing to obtain a single-phase solid solution.

In all cases, copper, rather than zinc, proved to be the most critical element of the (Co,Cu,Mg,Ni,Zn)O system, leading to destabilization. Compositions with low copper content ($\chi_{CuO} \le 0.10$) are stable in a large temperature range, i.e. from 750 to 1000 °C. At higher content, the structure undergoes a tetragonal distortion, displaying phase stability only in a restricted temperature range. The same cubic to tetragonal distortion is found in the binary systems CuO-CoO and CuO-NiO for copper-rich compositions.

### CRediT authorship contribution statement

**Anselmi-Tamburini Umberto:** Writing – original draft, Supervision, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. **Ghigna Paolo:** Writing – original draft, Investigation, Funding acquisition, Conceptualization. **Dejoie Catherine:** Methodology, Investigation, Data curation. **Bonati Simone:** Methodology, Investigation, Data curation. **Coduri Mauro:** Writing – original draft, Methodology, Investigation, Data curation, Conceptualization. **Fracchia Martina:** Writing – original draft, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

### Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors acknowledge support from the Ministero dell'Università e della Ricerca (MUR) and the University of Pavia through the program "Dipartimenti di Eccellenza 2023-2027". They acknowledge the ESRF
for provision of beam time (experiment CH-5899). M. F. acknowledges funding from the program "L'Oréal Italia per le Donne e la Scienza 2023".

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jeurceramsoc.2025.117237.

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