Crystal size-mediated solute incorporation and solid-solution stability in RuO₂ during acidic oxygen evolution

Abstract

Understanding the miscibility of foreign cations in pristine oxides is a fundamental step toward synthesizing multicomponent single-phase oxide crystals with unprecedented functionalities. In rutile RuO₂, we find that many solute cations, which typically exhibit limited miscibility below a few percent in the bulk, can substitute Ru at levels exceeding 20 at% when the crystal size is reduced below 10 nm. More importantly, this size-dependent enhancement in solubility is not restricted to a few specific elements but appears as a general trend across 20 distinct foreign cations. These results suggest that the phase equilibria of RuO₂ are remarkably altered under the high Laplacian pressure induced by nanoscale crystal dimensions. The successful synthesis of solid-solution RuO₂ nanocrystals smaller than 10 nm, with 20 different compositions, enables quantitative and systematic evaluation of their stability numbers (S-numbers) under identical electrochemical conditions as anodic electrocatalysts for acidic water oxidation. In addition to identifying significant RuO₂-based solid solutions with Ta, Ir, Nb, Sb, and Mn among many proposed candidates for high-durability nanoscale electrocatalysts, the findings in our study demonstrate that the extent of chemical modification in RuO₂ is strongly dependent on crystal size.

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Broader context

The Hume-Rothery rules, established in 1936, indicate that substantial miscibility between two crystalline oxides typically requires identical crystal structures, minimal differences in cationic radii (less than 15%), and matching valence states. Deviations from these criteria hinder the formation of wide-range solid solutions between dissimilar oxide systems. Since many oxides differ from the rutile structure and have cation valence states that do not match that of RuO₂, most metal oxides are considered to exhibit limited miscibility with RuO₂ according to these rules. This study demonstrates that such immiscibility can be overcome by reducing the crystal size. The solubility of foreign cations (M) in RuO₂ is found to remarkably increase as crystal size decreases, with at least 20 at% M dissolving in crystals smaller than 10 nm. These physically significant findings critically contribute to fair benchmarking and the identification of more electrochemically stable dopants for enhancing RuO₂-based catalyst longevity for acidic water oxidation.

Introduction

Substituting the original cations with foreign cations in crystalline metal oxides is a simple yet effective approach to both enhance existing physicochemical properties and induce novel physical characteristics. To attain a thermodynamically stable substitutional solid-solution oxide, the solubility limit of solute cations in a matrix oxide should first be examined. As suggested by Hume-Rothery in 1936 (widely known as the Hume-Rothery rules),^1,2 a large extent of miscibility between two crystalline oxides is rarely achievable unless (i) the crystal structures of the two end members are identical, (ii) the ionic sizes of the cations differ by no more than 15%, and (iii) their valence states are the same. The NiO–MgO system,³ in which both NiO and MgO adopt the rocksalt structure and the ionic radii of divalent Ni²⁺ and Mg²⁺ are 69 and 72 pm, respectively, serves as a representative example that fully satisfies these criteria and thus exhibits complete solid solubility. In contrast, it is considerably difficult to form solid solutions between two oxide systems with different crystal structures, ionic sizes, and valence states across a wide compositional range.

Rutile-type RuO₂ has been regarded as a notable exception to the Hume-Rothery rules. As illustrated in the phase diagram of the rutile RuO₂–TiO₂ system^4,5 (see the Methods section in SI) in Fig. 1a, a surprisingly large miscibility gap exists between RuO₂ and TiO₂, despite their identical crystal structures and the nearly identical ionic radii of tetravalent Ru⁴⁺ and Ti⁴⁺ (62 and 61 pm, respectively). This observation highlights the complexity of oxide miscibility and suggests that forming RuO₂-based solid solutions with other metal oxides possessing different crystal structures is likely to be even more thermodynamically challenging. Consequently, as summarized in Table S1 and the references therein, many recent studies reporting RuO₂ solid solutions as alternative electrocatalysts for acidic water oxidation appear to conflict with conventional phase equilibria, implying that additional factors may influence solute miscibility in RuO₂.

Fig. 1 XRD patterns and EDS maps for large RuO₂ crystals with foreign elements. (a) The phase diagram of the RuO₂–TiO₂ system shows that less than 5% of Ti is soluble below 1100 K in RuO₂, indicating low solubility. (b) The presence of secondary phases, indicated by asterisks in the XRD patterns, shows that the solubility limit of the foreign elements is well below 20 at%. White arrows in the EDS maps denote secondary phases rich in foreign elements. (c) This series of samples exhibits the formation of ruthenate intermediate phases. The asterisks in the XRD patterns and the white arrows in the EDS maps correspond to the presence of CaRuO₃, SrRuO₃, BaRuO₃, La₂RuO₅, Pr₃RuO₇, and Nd₂Ru₂O₇ phases, respectively.

Beyond the primary criteria outlined by the Hume-Rothery rules, another significant parameter is crystal size. As demonstrated in CdSe nanocrystals,⁶ doping semiconductor nanocrystals with foreign elements presents substantial challenges.^7–9 At the nanoscale, the solubility limit of dopants is often significantly lower than in the bulk counterpart, making successful incorporation of foreign atoms much more difficult.⁹ For example, a theoretical study indicated that when the size of Si nanocrystals is less than 2 nm, P atoms, which are typical p-type dopants, are expelled toward the surface, resulting in strongly suppressed P solubility.¹⁰ Contrary to semiconductor nanocrystals, a recent report showed that Au and Rh, which are mutually immiscible in the bulk, become completely miscible when the metallic Au–Rh particles are smaller than 1.8 nm.¹¹ These two divergent size-dependent solubility behaviors observed in semiconductors and metallic alloys underscore the need to systematically investigate solubility variations in other oxide systems of interest.

In this work, we demonstrate that the solubility limit of foreign cations (denoted as M) in the RuO₂ matrix is notably enhanced as the crystal size decreases. Specifically, we observe that at least 20 at% of M is soluble in RuO₂ crystals with sizes of approximately 10 nm or less, whereas far less than a few percent of M are detected in crystals much larger than 50 nm, illustrating a strong size-dependent variation in solubility. This solubility enhancement is not limited to several cations but is found to be universal across a variety of cations, even when the ionic radius and valence state of M differ substantially from those of Ru⁴⁺.

As summarized in Table S1, many foreign elements have been proposed over the past five years to effectively suppress Ru dissolution and thereby enhance the stability of RuO₂.^12–38 However, no direct comparisons among these solid solutions have been conducted to determine which elements are most beneficial in improving the durability of RuO₂ during the acidic oxygen evolution reaction (OER). The controlled synthesis of nanoscale solid-solution Ru_0.8M_0.2O₂ (<10 nm) in this study allows for accurate and systematic comparison of 20 different substitutional cations under identical electrochemical conditions. This provides a fair evaluation of dopants aimed at reinforcing the stability of RuO₂-based anodic catalysts. It is important to note that durability assessments based on membrane–electrode assemblies (MEAs) can be highly sensitive to the quality of MEA preparation and may not accurately reflect intrinsic stability of the catalyst material. To minimize such variability, we systematically measure the stability numbers (known as the S-numbers)³⁹ of the 20 different nanocrystalline RuO₂ solid solutions under consistent testing protocols, allowing for objective comparisons. Through this integrated approach, which combines rigorous chemical characterization with standardized electrochemical evaluation, we objectively identify suitable solid-solution candidates for durable acidic OER catalysis.

Results and discussion

Low solubilities in large crystals

To examine the extent of the solubility of M in RuO₂, we first carried out X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDS) analyses using powder samples with a starting composition of 20 at% M (Ru_0.8M_0.2O₂), prepared with a total of 30 different foreign cations. As samples were annealed at relatively high temperature of 700–850 °C, the average crystal sizes were larger than 50 nm and even above 100 nm. The appearance of additional Bragg reflections, denoted by asterisks in the XRD patterns in Fig. 1b and c, directly indicates the presence of secondary phases and demonstrates that the solubility limit of most M cations in RuO₂ does not exceed 20 at% (see Fig. S1–S3 for details of the Bragg-peak positions for the secondary phases).

Consistent with the XRD results, the EDS maps in color together with bright-field (BF) scanning transmission electron microscopy (STEM) images in Fig. 1b also verify the formation of M-rich secondary phases (colored particles indicated by white arrows in the maps) in the samples. Individual EDS quantification, provided in Fig. S4 and S5, demonstrates that less than 3 at% of foreign M is detected in RuO₂ crystals in most cases. For example, as can be seen in the phase diagram of the RuO₂–TiO₂ system in Fig. 1a, the solubility of TiO₂ in RuO₂ does not exceed ∼5% below 850 °C.⁴ This low miscibility is consistently verified by EDS, indicating the Ti detection of 2.6 at% in RuO₂ (Fig. S4).

It is observed that the three alkaline-earth (Ca, Sr, and Ba) and lanthanide (La, Pr, and Nd) cations in Fig. 1c easily form intermediate ruthenate compounds, such as SrRuO₃, resulting in limited solubility in RuO₂ as well (see Fig. S3 for details of the Bragg peak positions for the intermediate compounds). Among the 30 cases, only four cations, V, Cr, Mo, and Ir are found to be soluble. The absence of additional Bragg peaks in the XRD patterns and the homogeneous distribution of the four cations of 20 at% in the EDS maps consistently support the formations of solid solutions (see Fig. S6 for details).

Enhanced solubilities in nanocrystals

In stark contrast, when we investigated nanoscale crystals with an average size of less than 10 nm, synthesized by annealing at lower temperature of 350–500 °C, we identified the formation of a rutile-type single phase without secondary phases in the samples with 20 individual foreign cations. Fig. 2a shows a series of XRD patterns confirming the single-phase solid-solution Ru_0.8M_0.2O₂ crystals. As the size of most substituted cations differs from that of Ru⁴⁺, the lattice parameters in solid-solution Ru_0.8M_0.2O₂ should change. Consequently, in addition to the absence of extra Bragg reflections for the secondary phases in this set of XRD patterns, the shift of the (110), (101), and/or (211) Bragg peaks, as denoted by vertical lines, for the rutile phase is another important feature that should not be overlooked when verifying the formation of solid solutions.

Fig. 2 XRD patterns of nanoscale Ru_0.8M_0.2O₂ solid solutions along with EXAFS data. (a) The absence of additional Bragg peaks corresponding to secondary phases confirms that a single rutile phase is successfully achieved in each case. Small vertical markers are inserted at the three major reflections to highlight the peak shifts resulting from solid solution formation. (b) EXAFS analysis shows that the M–O and M–M radial distances in the four samples containing Fe, Co, Ni, and Cu agree well with the Ru–O and Ru–Ru distances in RuO₂. This indicates that 20 at% Fe, Co, Ni, and Cu is incorporated as solid solutions, although the major peaks in these samples exhibit minimal shifts. Corner-sharing Ru–Ru peaks are exclusively indicated due to the lower intensities of edge-sharing Ru–Ru peaks.

While the shift of the Bragg reflections is readily identifiable in most samples, no shifts are observed in the XRD patterns in four samples containing Fe, Co, Ni, and Cu. We thus further conducted X-ray absorption spectroscopy (XAS) to acquire the extended X-ray absorption fine structure (EXAFS) that can provide interatomic information, such as the M–O radial distance in the lattice. As shown in Fig. 2b, the M–O (where M is Fe, Co, Ni and Cu) distance obtained from the EXAFS spectra is consistent with the Ru–O distance in rutile RuO₂ rather than the M–O distance in each secondary MO_x phase (see Table S2 for the EXAFS fitting parameters and Fig. S7 and S8 for the EXAFS spectra of Ru and foreign elements). Therefore, the EXAFS results along with the single-phase XRD patterns verify that added Fe, Co, Ni and Cu is substituted in the nanoscale crystals without forming secondary phases. The lattice parameters estimated from the XRD data in Fig. 2a are plotted in Fig. S9.

We utilized EDS compositional mapping in STEM^40–57 to directly visualize the presence of M in individual nanocrystals. A complete set of maps, along with BF-STEM images, is provided in Fig. 3a for 20 foreign M cations. The concentration of M at cation sites within a crystal can be quantitatively estimated by summing the counts of the Ru-L_α and M-K_α (or M-L_α) spectra acquired during mapping, as exemplified for the case of Ti in Fig. 3b. Although the solubility of Ti in RuO₂ is far below 5 at%,^4,5 the EDS results in Fig. 3b directly demonstrate a notable increase in solubility beyond 20 at% in RuO₂ nanocrystals. Additional sets of EDS compositional maps and corresponding spectra are also given in Fig. S10 and S11 to further support the presence of M in Ru_0.8M_0.2O₂ nanocrystals. The concentration data numerically presented in each EDS map for M in Fig. S10 indicate detection at ∼20 at% in each case. Together the three distinct analyses based on the XRD, EXAFS, and EDS offer compelling and consistent evidence of enhanced solubility of M in nanoscale RuO₂ crystals. More importantly, this behavior is not limited to a few specific cations but is universally observed across at least 20 elements. We note that Zn, in addition to very large and corrosive alkaline cations (Na, K, Rb, and Cs), was excluded from this set of foreign cation options because its distribution varies significantly from particle to particle, and thus the overall solubility limit of Zn appears to be less than 20%.

Fig. 3 EDS composition maps visualizing the solid solutions of Ru_0.8M_0.2O₂. (a) The EDS maps directly confirm the incorporation of foreign elements into the nanocrystals. All Ru maps are shown in gray. (b) All the substitution concentrations are quantitatively obtained from the corresponding EDS spectra. A representative case (Ti) consistently shows substantial signal intensity, verifying the presence of Ti in the solid solution.

Phase evolution during crystal growth

As the annealing temperature is raised, nanoscale crystals should spontaneously coarsen through Ostwald ripening to reduce the total surface area of the crystals to minimize surface energy. Consequently, the phase evolution from a single-phase solid solution to a multiple-phase mixture in RuO₂ can be traced in detail using this crystal growth process. Fig. 4a presents a series of XRD patterns acquired after annealing the powder sample with 20 at% of Nb at temperature ranging from 400 to 800 °C. Magnified peaks for the (110), (101), and (211) reflections are shown in Fig. 4b to highlight several key features. First, single peaks, shifted to the left from the reference positions, are observed in all three reflections at 400 °C. This directly indicates the successful synthesis of Ru_0.8Nb_0.2O₂ solid-solution nanocrystals. For further verification, a magnified view of the (110) reflection (blue) is provided in Fig. 4c.

Fig. 4 Crystal-size-dependent XRD patterns and composition variation in 20%-Nb-added samples. (a) XRD patterns were collected for samples annealed between 400 and 800 °C. The secondary Nb₂O₅ phase emerges at 800 °C. (b) Three major Bragg reflections are magnified to highlight the peak variations. In particular, peak splitting is observed for the (110) and (211) reflections at 700 °C and above. (c) Magnified views of the (110) reflection at three temperatures illustrate the following evolution: nanoscale solid-solution Ru_0.8Nb_0.2O₂ crystals at 400 °C; a mixture of solid-solution Ru_0.8Nb_0.2O₂ nanocrystals and larger RuO₂ crystals with negligible Nb content at 700 °C; and large RuO₂ crystals alongside a Nb₂O₅ secondary phase after 24 h at 800 °C. (d) The plot shows Nb concentrations derived from the EDS spectra of individual crystals in the sample annealed at 700 °C. The curve in the plot demonstrates a size-dependent Nb concentration. (e) Two representative EDS results for a nanocrystal and a large crystal (87 nm) are provided to verify the size-dependent solubility.

As the annealing temperature exceeds 700 °C, peak splitting is clearly observed in both the (110) and (211) reflections in Fig. 4b. The magnified view of the (110) reflection at 700 °C in Fig. 4c clarifies that a sharp additional peak, corresponding to pristine RuO₂, begins to appear. The relative intensity of the sharp additional peaks in the (110) and (211) reflections is further enhanced with increasing temperature in Fig. 4b. In addition, the intensity of the shifted peaks for the Ru_0.8Nb_0.2O₂ solid solution is simultaneously reduced with temperature. These two observations show that Nb substituted in nanoscale Ru_0.8Nb_0.2O₂ particles are no longer soluble as the crystals grow and become larger particles whose XRD peaks should have a much narrower full width at half maximum. Nb atoms exsolved out from the grown large particles during annealing at 800 °C for a sufficient time eventually form a secondary phase of Nb₂O₅, as denoted by the asterisks in the last panel in Fig. 4c.

To scrutinize the size-dependent solubility behavior, we carried out further quantitative EDS analyses for more than 50 individual crystals of varying sizes in a Nb-added sample annealed at 700 °C. The plot in Fig. 4d clearly shows that the Nb concentration is significantly lower than 20% when the crystal size exceeds approximately 20 nm. In addition, as indicated by the curve in the plot, the Nb concentration in crystals declines exponentially as the crystal size increases, reaching low bulk solubility (far less than 5%) at sizes greater than 70 nm. Representative EDS spectra for the Ru-L_α and Nb-L_α emissions, acquired from crystals with sizes of 5 and 87 nm, respectively, are shown in Fig. 4e to confirm the quantitative estimation of Nb as the ratio of Nb/(Nb + Ru). An additional set of EDS quantifications showing the size-dependent variation of Nb concentration within crystals is provided in Fig. S12. We also observed consistent features in the XRD and EDS results for the Ta-added sample (see Fig. S13 and S14). In particular, the exponential variation of Nb and Ta concentrations among individual crystals of different sizes underscores the importance of precisely controlling crystal growth; otherwise substantial compositional heterogeneity may arise even within a single batch.

The pressure difference (ΔP) across the surface between a spherical nanoparticle and a vacuum (or vapor) can be easily estimated using the Young–Laplace equation, ΔP = 2γ/r, where γ is the surface energy of the nanoparticle and r is its radius. Assuming a surface energy of approximately 80 meV Å⁻² (equivalently, 1.3 J m⁻²) for a RuO₂ spherical nanocrystal with a radius of 5 nm,⁵⁸ ΔP is calculated to be 0.52 GPa. Our observation of size-dependent variations in solubility indicates that the phase equilibria in RuO₂ can shift substantially when the hydrostatic pressure reaches the gigapascal range. To illustrate the influence of this Laplacian pressure on the solubility enhancement of Nb, a schematic phase diagram of the RuO₂–Nb₂O₅ system is presented in the inset of Fig. 4d. Although this schematic is constructed for the case of Nb, the consistent trends observed for 20 distinct foreign cations in Fig. 2 and 3 clearly demonstrate that the increase of the miscibility in RuO₂ upon reducing crystal size is a general phenomenon.

Durability comparison for electrocatalysis

One of the key applications of rutile-type RuO₂ is its use as a cost-effective catalyst material for the oxygen evolution reaction (OER), as an alternative to IrO₂, for acidic water electrolysis.^11–37 Numerous doping strategies have been explored over the past five years, with each study claiming that many doping elements can improve the durability of RuO₂ (see Table S1 for a summary of key features in previous reports on cation doping in RuO₂). The search for the optimum doping chemistry has thus become a critical line of research issue in RuO₂-based catalysts. However, the wide variety of protocols and conditions used in electrochemical durability tests in previous studies makes it very difficult to precisely determine which dopant most effectively suppresses dissolution of RuO₂ during the OER. The vastly different durability test results reported in two recent studies involving the same Cr doping (20–25%) in RuO₂^20,23 highlight this challenge and emphasize the necessity of precise and objective comparison under unified test conditions and protocols.

Our findings on the enhanced solubility of foreign cations in RuO₂ upon reducing crystal size make a notable contribution to resolving these inconsistencies. First, we used our 20 Ru_0.8M_0.2O₂ solid solutions, as shown in Fig. 2 and 3, to compare the OER catalytic durability. As we verified that all the solid-solution samples consist of a single rutile phase and contain nearly the same amount of M (20%), the distinct effect of each cation M can be objectively evaluated. Moreover, we adopted identical test protocols and conditions, along with the same method for specimen preparation. Since the stability number (known as ‘S-number’),³⁹ which essentially represents the equivalent concept to the activity stability factor (ASF),⁵⁹ was introduced as a metric for activity–stability trade-off of catalysts, it has been accepted that this numerical index along with ASF provides an objective standard for quantitatively representing the durability of catalysts.^60–65 We thus measured the S-numbers of all 20 solid solutions for comparison using two independent methodologies: (i) chronoamperometry (CA) at the same overpotential of 1.58 V vs. a reversible hydrogen electrode (RHE) and (ii) accelerated durability tests (ADTs)^65–67 performed with square-wave potential profiles in an identical overpotential range of 1.23–1.63 V_RHE.

It is important to note that the stability of oxide catalysts deteriorates much more rapidly at higher anodic overpotentials. Therefore, chronopotentiometry (CP) tests, wherein considerably different overpotentials are applied to each sample to achieve the same constant current density, cannot provide a reliable comparison of catalyst durability. As shown in Fig. S15, much longer durations are recorded for samples with smaller crystal sizes during the CP tests, owing to the lower overpotentials required for catalysts with larger surface areas.^65,68 This inherently leads to slower degradation. CP-Based tests are thus unsuitable for durability benchmarking unless the crystal sizes are strictly controlled and identical across all samples.

The bar graphs in Fig. 5 present the S-numbers of the 20 Ru_0.8M_0.2O₂ solid solutions obtained from the CA for 24 h at pH = 1 (see Fig. S16 for the CA test results), as well as the amounts of cations dissolved during the tests. As shown in Fig. 5a, the S-numbers of many solid solutions measured via the CA at 1.58 V_RHE improved to the order of 10⁵, up from 9 × 10⁴ for pristine RuO₂. In particular, as indicated by asterisks, the solid solutions with Mn, Nb, Sb, and Ta exhibit significantly enhanced stability, showing values greater than 3 × 10⁵ (see Fig. S17 for catalytic activity comparison). The cation dissolution shown in Fig. 5b also consistently demonstrates that Ta hardly dissolves (much less than 0.02 nmol), whereas the amount of dissolution for the other doping cations is at least one order of magnitude larger. The S-number values measured during the ADTs at pH = 1 further support the finding that adding Ta significantly improves the stability (Fig. S18 and S19), in agreement with a recent report.³²

Fig. 5 Comparison of S-numbers and elemental dissolution among solid-solution Ru_0.8M_0.2O₂ electrocatalysts for the OER. (a) S-Number values are plotted for 20 different samples. Notably enhanced stability is observed for the samples containing Mn, Nb, Sb, and Ta, as indicated by asterisks. The asterisks denote five solid solutions showing a significant enhancement of S-number. (b) The dissolution amounts of Ru (dark gray) and foreign elements (colors) are represented. Among all tested elements, Ta (gray shading) exhibits the lowest dissolution during the stability test. Accordingly, the Ru dissolution is also minimized in the Ta solid-solution sample.

Lattice oxygen stabilization by d⁰ and d¹⁰ cations

As can be easily seen in the E–pH Pourbaix diagram, Ta₂O₅, Nb₂O₅, and Sb₂O₅ are highly corrosion-resistant oxides that do not decompose over a wide range of pH under anodic potentials^65,68 (see Fig. S20 for their Pourbaix diagrams^69,70). The benchmarking analysis in Fig. 5 emphasizes that incorporating corrosion-resistant cations, such as Ta, Nb, and Sb, is a simple yet effective strategy to construct a robust framework in oxide electrocatalysts and enhance durability during the acidic OER. Furthermore, using density functional theory calculations, we identified that the density of states (DOS) of O 2p near the Fermi level (E_F) significantly shifts to a lower energy level and subsequently the lattice oxygen is stabilized when the corrosion-resistant cations are substituted.

A plot of the O 2p state near the E_F is shown in Fig. 6a along with an isosurface map of the electronic density difference at each atom. Upon Ru atom dissolution and the formation of a corresponding vacancy, a non-bonding character emerges at the six surrounding O atoms, as indicated by red arrows in the electron–density isosurface map in Fig. 6b. This results in higher O 2p states near the E_F in the DOS plot. The energy band diagrams in Fig. 6c describe the formation of O non-bonding states induced by Ru dissolution. Consequently, the remaining lattice O is more easily activated and can be evolve as O₂ gas under anodic potential, leading to lattice instability and further Ru dissolution (see Fig. S21 for more details).

Fig. 6 Suppression of lattice oxygen activation. (a) and (b) Two DOS plots of O 2p demonstrate that the non-bonding lattice oxygen by Ru dissolution (red arrows) results in the higher O states near E_F. The electron-density isosurface maps are also provided. (c) The energy band diagrams schematically illustrate the formation of O non-bonding states. This contributes to activation of lattice oxygen that can be evolve as O₂ gas under anodic potential. (d) and (e) Two extreme electronic configurations of entirely empty d⁰ Ta⁵⁺ and fully occupied d¹⁰ Sb⁵⁺ allow adjacent O²⁻ anions (purple) to be stabilized by achieving a fully occupied 2p⁶ configuration of O. Consequently, the DOS of O 2p near E_F shifts to a lower energy level, as indicated by arrows. (f) The major O 2p states are separated from the unoccupied Ta 5d⁰ states and Sb 5p⁰ states without overlapping. The stabilized lattice oxygen can thus effectively reduce electrochemical redox activation.

In contrast, it is noted that the empty Ta 5d⁰ states predominantly lie at higher energy levels above E_F (>0.5 eV) (see Fig. S22). As a result, minimal overlap occurs between the O 2p and Ta 5d states, resulting in the highly ionic bonding characteristics of Ta–O. The fully empty d⁰ configuration of ionic Ta⁵⁺ allows adjacent O²⁻ anions (purple) to be stabilized by achieving a fully occupied 2p⁶ configuration of O, without forming covalent bonds with Ta. The DOS plot of the six neighboring O atoms in Ta-doped RuO₂ in Fig. 6d consistently represents a substantial lowering of O 2p energy levels. The electronic density difference isosurface further illustrates increased electron density around O atoms adjacent to Ta (Fig. 6d). As illustrated in the band diagram in Fig. 6f, Ta doping stabilizes O 2p states below E_F, which are separated from the unoccupied Ta 5d states above E_F. This electronic structure effectively suppresses electrochemical redox activation of lattice oxygen and subsequent Ru dissolution (see Fig. S20 for more details). Other d⁰ cations, such as 4d⁰ Nb⁵⁺, can be understood to have the same effect.

The influence of corrosion-resistant d¹⁰ Sb⁵⁺ appears similar to that observed in d⁰ Ta⁵⁺. As demonstrated in the DOS plot of Sb-doped RuO₂ (see Fig. S23), the energy level of the empty Sb⁵⁺ 5p⁰ states lies far above E_F, while that of the fully occupied 4d¹⁰ states is situated much further below E_F. As a result, the ionic nature of Sb⁵⁺, characterized by an electronic configuration of 4d¹⁰ 5s⁰ 5p⁰, stabilizes the adjacent O²⁻ anions (purple) by enabling them to achieve a fully occupied 2p⁶ configuration without forming any covalent bonds with Sb. As indicated by an arrow in Fig. 6e, the DOS plot of the six neighboring O atoms in Sb-doped RuO₂ consistently shows noticeable energy lowering of the O 2p states. Therefore, the stabilized O 2p states below E_F results in efficiently suppressing the electrochemical redox activation of lattice oxygen in the same manner.

Finally, the S-number comparison in Fig. 5a indicates that Mn is also an effective foreign element for improving the durability of RuO₂, consistent with previous studies. However, Mn dissolution is not negligible compared to that of Ta and Sb (Fig. 5b). In this regard, further in-depth surface analyses are suggested to precisely determine whether this distinct behavior is associated with surface reconstruction induced by substantial Mn dissolution.

Implication for the other application

Since a new form of collinear magnetism was identified in 2020,⁷¹ later named ‘altermagnetism’ in 2022,⁷² this peculiar magnetic behavior has garnered substantial attention. It reveals a breaking of time-reversal symmetry and strong spin polarization in the band structure, similar to ferromagnetism, but simultaneously shows no net magnetization, as observed in antiferromagnetism. Although more than 200 materials are predicted to exhibit altermagnetism, researchers have significantly focused on rutile RuO₂,^73–75 despite several recent studies casting doubt on its altermagnetic nature.⁷⁶ Therefore, further experiments with chemically modified single crystals by doping could offer a more precise understanding of the magnetic characteristics of RuO₂. The results of this work show that the range of viable dopants for fabricating large-scale bulk samples is quite limited, especially in studies investigating the influence of foreign cations on magnetic behavior.

Conclusions

Our study uncovers a pronounced size-dependent variation in the solubility of foreign cations in rutile-type RuO₂. Through a systematic investigation of 30 different cations, we show that most elements exhibit limited solubility, typically restricted to just a few atomic percent, in bulk RuO₂ crystals larger than 50 nm. In stark contrast, nanoscale RuO₂ crystals smaller than 10 nm show a substantial increase in solubility, with at least 20 atomic percent incorporation achieved for 20 different elements, except Zn, highlighting a universal trend. A direct composition analysis of a sample containing a broad distribution of crystal sizes provides compelling evidence for this size-dependent cation miscibility. This behavior is likely driven by the substantial Laplacian pressure present at the nanoscale, which can shift the phase equilibria of RuO₂ when the pressure approaches the gigapascal range.

The successful synthesis of solid-solution nanocrystals enables objective and precise benchmarking of 20 Ru_0.8M_0.2O₂ samples using the same test protocols under identical electrochemical conditions. Although many doping elements were found to be influential, Ta, Ir, Nb, Sb, and Mn were particularly effective in enhancing the S-number of their solid solutions during the acidic OER. This consistent approach allows for a fair evaluation of doping cations and helps identify better elements for substantially improving the stability of RuO₂-based anodic catalysts in water electrolysis. The present work emphasizes that a precise understanding of miscibility variation and the ability to synthesize single-phase crystals in multi-component oxides should be the very first step before evaluating any material's performance.

Author contributions

S.-Y. C. conceived and designed the project, performed the DFT calculations, and wrote the paper. J. S. K. and S. L. conducted all syntheses, electrochemical measurements, XRD/XAS analyses, and data processing. D. K. carried out the STEM/TEM and EDS analyses, including image acquisition. All authors discussed the results and prepared, reviewed, and revised the manuscript.

Conflicts of interest

The authors declare personal financial interests in a commercial entity to which patent filings based on the certain subject matter in this publication will be licensed by the Korea Advanced Institute of Science and Technology.

Data availability

Original data are available from the corresponding author upon reasonable request.

The data supporting this article have been included as part of the supplementary information (SI), which includes methods, figures (Fig. S1–S24), tables (Tables S1 and S2), and additional references. Supplementary information is available. See DOI: https://doi.org/10.1039/d5ee03097h.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) under grant numbers 2022M3H4A1A01008918, RS-2024-00347287, RS-2024-00435493, and RS-2023-00222411. S.-Y. C. was also supported by Samsung Research Funding & Incubation Center of Samsung Electronics (project number SRFC-MA2401-04). All authors gratefully acknowledge the valuble support of Dr Sun Hee Choi, the manager of the 7D beamline at PLS-II, Pohang Accelerator Laboratory.

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Footnote

† These authors contributed equally to this work.

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