Designing water resistant high entropy oxide materials

Abstract

The ubiquitous presence of moisture usually shows adverse effects on industrial catalysis. Herein, a concept of engineering entropy to design water-resistant oxide catalysts is proposed. The C₃H₆ oxidation by spinel ACr₂O₄ (A=Ni, Mg, Cu, Zn, Co) catalysts is selected as a model. Through DFT calculation, the adsorption energy of C₃H₆, the dissociation energy of molecular H₂O on the oxide surface, and the formation energy of oxygen vacancy all suggest better performance induced by higher configurational entropy. Indeed, (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ experimentally show excellent water resistance (>100 h) in C₃H₆ oxidation, while in sharp contrast binary oxides (e.g., NiCr₂O₄, CoCr₂O₄) are deactivated in 20 h. H₂O-TPD, in-situ Raman, and in-situ FTIR all confirm the low H₂O adsorption energy and strong hydrothermal stability of high entropy oxide, which is attributed to their lower Gibbs free energy. This work may inspire the rational design of water-resistant catalysts.

Introduction

Heterogeneous catalysis plays a vital role in both fundamental and industrial chemistry. The catalytic performance of solid catalysts is significantly close to their reaction environment. As one of the most important factors, environmental water inevitably influences industrial catalysis, especially in real-world processes^1,2. With metal oxides as a typical case, the effect of moisture on related catalysis is different. Interestingly, the positive impact of water was discovered on a few catalytic systems. For example, Saavedraet et al.² have determined water played a promoting role in the catalytic oxidation of CO by Au/TiO₂ catalyst at room temperature, providing a water-mediated reaction mechanism for CO oxidation. Fang et al.³ altered the water-sorption equilibrium on the catalyst surface, resulting in an increased amount of free surface. This modification nearly doubled the syngas conversion rate. During the water-gas shift reaction, Li et al.⁴ observed higher H₂O activation ability in non-oxide-based reactive metal–support interaction (RMSI). However, the inhibitory role of water was more common in metal oxide-mediated catalysis.

In principle, water can cover the active site and form competitive adsorption with reactants. For example, pure Co₃O₄ had naturally high activity in CO oxidation⁵, NH₃ elimination⁶, CO₂ reduction⁷ and volatile organic compounds oxidation⁸ due to its surface structure. However, Co₃O₄-based catalyst could be poisoned by trace water and become inactivated^9,10, which seriously limited its application in wet environments⁵. Meanwhile, moisture in high-temperature catalysis affected the hydrothermal stability of metal oxide catalysts. For example, ZrO₂, CeO₂, and TiO₂-based catalysts in the ketonization reaction of carboxylic acids were unstable under hydrothermal reaction conditions, which would lose activity when exposed to aqueous acetic acid at temperatures above 473 K¹¹. Hence, moisture removal from raw materials was necessary before coming into catalytic reactors, which resulted in complicated operations and enhanced costs.

To design water-resistant catalysts, both reactant adsorption/activation sites and H₂O stabilization sites were required, while single metal oxides mostly cannot satisfy. Since 2015, there has been growing interest in high entropy oxides (HEOs)¹². For water-resistant catalysis, the high entropy structure had two significant advantages¹³. First, the low Gibbs free energy of HEOs was anticipated to enhance their stability compared to single oxides even in environments containing moisture. Second, the integration of various metal components of HEOs would offer reactant adsorption sites and water-resistant sites. Thus, the strategy of adjusting entropy in oxides may be beneficial for catalysis under water-resistant conditions.

In this work, the water resistance performance of HEOs in catalytic oxidation is initially estimated by theoretical studies. First, with spinel ACr₂O₄(A = Ni, Mg, Cu, Zn, Co) as an oxide model and catalytic C₃H₆ oxidation as a typical process, the adsorption behavior of C₃H₆, dissociation energy of molecular H₂O and formation energy of oxygen vacancy are estimated by DFT calculation. Compared with single metal oxides, the competitive adsorption of H₂O with C₃H₆ could be avoided by (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. Meanwhile, the (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ offers higher dissociation energy of H₂O than single metal oxides, suggesting better hydrothermal stability. Moreover, the formation energy of oxygen vacancies in (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ is much lower than ACr₂O₄, which is expected to improve the catalytic oxidation performance¹⁴. Inspired by DFT calculation results, (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and ACr₂O₄ are prepared. The light-off curves of C₃H₆ catalytic oxidation show the T₉₀ (C₃H₆ conversion is 90%) of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄(265 °C) is lower than the T₉₀ of ACr₂O₄ (318–350 °C) in dry conditions. Under long-term C₃H₆ oxidation in the presence of 4.2 vol% water, single metal oxides lose their activity in ~ 20 h, while (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ is stable in 100 h. Compared with single metal oxides, the H₂O adsorption ability of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ is weaker by H₂O-TPD. Furthermore, H₂O vapor reacts with active oxygen species of CoCr₂O₄ or ZnCr₂O₄ to hinder the adsorption of C₃H₆. However, H₂O vapor would not inhibit the adsorption of C₃H₆ on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ by in situ FTIR. Observed by in situ Raman, an increase in reaction temperature would weaken the force constant of the Cr−O bond in CoCr₂O₄ or ZnCr₂O_4, while the force constant of the Cr−O bond in (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ could be maintained with 4.2 vol% H₂O. Both H₂O-TPD, in situ FTIR, and in situ Raman match the DFT results.

Results

The adsorption energy of C₃H₆ on the surface of ACr₂O₄ by DFT calculation

Spinel oxides, especially AB₂O₄ (where A and B represent different metallic ions), are a class of common catalysts¹⁵. In this work, C₃H₆ catalytic oxidation by ACr₂O₄ was selected as a model. Notably, the A sites in the ACr₂O₄ structure, specifically when A was Ni, Mg, Cu, Zn, or Co, were systematically varied from individual metal ions to a combination of five distinct metal ions. Not all permutations and combinations of elements can form a single crystal. Therefore, the A-position element was selected according to the atomic radius and the law of atomic coordination. Cr, as a B-site element, was due to its oxidative activity. The adsorption energy of C₃H₆ on the surface of single oxides and (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ in the dry or 4.2 vol% water conditions were calculated respectively(Fig. 1 and Supplementary Figs. S1,  S2). In the presence of 4.2 vol% water, the adsorption energy of C₃H₆ on the surfaces of single oxides all increased sharply. The presence of H₂O molecules formed competitive adsorption and may reduce the adsorption amount of C₃H₆ on the surface of single oxides, which would affect the C₃H₆ oxidation. In contrast, the presence of H₂O molecules on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ had little effect on the adsorption energy of C₃H₆ (Supplementary Table S1). For example, the adsorption energies of C₃H₆ on (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ surface was − 1.051 eV (crystal plane 311) in dry conditions and − 0.96 eV with 4.2 vol% water. It appeared that the high-entropy structure may reduce the competition between H₂O and the C₃H₆ reactant for adsorption. Then, we wish to discuss the effect of a single metal on C₃H₆ adsorption energy in the presence of moisture. Taking CoCr₂O₄ as an example, the D-value (△_Ead = E_ad(dry conditions) - E_ad(4.2 vol% water)) in C₃H₆ adsorption energy with or without water (△_{Ead (311) =} 0.381 eV; △_{Ead (220)} = − 0.397 eV; △_{Ead (111)} = − 0.33 eV) at (311), (220), (111) crystal planes were all the highest among metal oxides ACr₂O₄ (single metals at A sites = Ni, Mg, Cu, Zn, Co). Moreover, taking Co₃O₄ as an example, the D-value(△_Ead) in C₃H₆ adsorption energy with or without water (△_{Ead (111)} = − 0.21 eV) at (111) crystal plane were the highest among single metal oxides (NiO, MgO, CuO, ZnO, Co₃O_4, Cr₂O₃). Based on those calculations, the type of metal element indeed affected the adsorption behavior of C₃H₆ with 4.2 vol% water. Among them, cobalt oxides are the most affected. Molecular H₂O on the Co₃O₄ surface would be decomposed into H⁺ and OH⁻, lattice oxygen in the catalyst will be hydrogenated, or the surface Co³⁺ will be hydroxylated, resulting in the loss of catalyst activity⁹.

Fig. 1: The adsorption energy of C₃H₆ by DFT calculation.

The adsorption energy of C₃H₆ on the surface (311 plane) of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and single metal ACr₂O₄ (A = Ni, Mg, Cu, Zn, Co) in the absence and presence of 4.2 vol% water vapor.

The dissociation energy and adsorption energy of molecular H₂O on the surface of ACr₂O₄ by DFT calculation

The dissociation energy of molecular H₂O on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and single oxides at crystal plane (220), (311) and (111) were calculated by DFT, respectively(Fig. 2, Supplementary Table S2 and Supplementary Fig. S3). The dissociation energy of molecular H₂O on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was 2.83 eV (311), 2.75 eV (220) and 2.97 eV (111). In contrast, the dissociation energy of molecular H₂O on the surface of ACr₂O₄ at (311) 2.15 eV ~ 2.69 eV, at (220) were, 2.38 eV ~ 2.73 eV, and at (111) were 2.62 eV ~ 2.90 eV. The dissociation energy of molecular H₂O on the surface of ternary control samples at crystal plane (220) and (311), respectively, were shown in Supplementary Figs. S4, S5, and Supplementary Table S3. Those results showed that molecular H₂O was easy to dissociate into H⁺ and OH⁻ on the surface of ACr₂O₄ compared with (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, then OH⁻ could react with ACr₂O₄ to form hydroxide. Thus, the structure of ACr₂O₄ was destroyed, and the catalytic activity decreased in the C₃H₆ oxidation. This DFT calculation suggested the better hydrothermal stability of high entropy oxide catalysts, which may be induced by their lower Gibbs free energy (∆G = ∆H-T∆S).

Fig. 2: The dissociation energy by DFT calculation.

The dissociation energy of molecular H₂O on the surface of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, and single metal ACr₂O₄ (A = Ni, Mg, Cu, Zn, Co) at crystal planes (220) and (311) respectively.

The formation energy of oxygen vacancy of ACr₂O₄ by DFT calculation

Oxygen vacancies were beneficial for the C₃H₆ combustion reaction due to they would provide more active sites that can adsorb and activate oxygen molecules, generating highly active oxygen species. These oxygen species can rapidly undergo oxidation reactions with C₃H₆, promoting the breaking of carbon-hydrogen bonds and the generation of oxidation products^16,17. To assess the impact of the high-entropy structure on oxygen vacancies, the formation energy of oxygen vacancy (E_Ov) of ACr₂O₄ were calculated (Fig. 3). The E_Ov of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was lower than those of single oxides in the crystal plane (220), (311) and (111) respectively(Fig. 3, Supplementary Table S4 and Supplementary Fig. S6), confirming better potential catalytic performance. Generally, due to the different atomic radius, the local configuration of polymetallic species can lead to structural distortions to lower E_Ov of HEOs^18,19,20. Furthermore, the creation of a–A–O–B–bond can decrease the Coulombic interactions of ${A}^{\delta+}-{O}^{\gamma -}$ or ${B}^{\delta+}-{O}^{\gamma -}$, thereby resulting in lower E_Ov^21,22,23.

Fig. 3: The formation energy of oxygen vacancy by DFT calculation.

The formation energy of oxygen vacancy (E_Ov) of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, and single metal ACr₂O₄ (A = Ni, Mg, Cu, Zn, Co) at crystal planes (220) and (311) respectively.

Material manufacturing and structural characterization

Inspired by DFT calculations (Figs. 1–3), practical experiments were carried out to validate the theoretical predictions. The traditional method of preparing HEOs usually requires high phase transition temperatures (e.g., 900 ^oC–1000 ^oC), causing pore collapse in HEOs and low surface areas^{19,21,24,25,26,27}. This issue would reduce the catalytic performance of HEOs. This work used a mechanochemical method to construct (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ (Fig. 4 and Supplementary Table S5). The preparation of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ by ball milling mainly relied on the action of mechanical force. During high-energy ball milling, the milling medium exerted repeated impacts and frictional forces on the mixed material, resulting in uniform mixing of different metal elements at the nanoscale. At the same time, mechanical forces induced accelerated chemical reactions between various metal elements, ultimately forming HEOs with uniform multi-component distributions. This method not only improved the uniformity of metal element mixing but also effectively controlled particle size and distribution²⁸.

Fig. 4: The preparation procedure of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄.

(i) Mixing metal acetates by ball milling in 0.5 h. (ii) Calcination of the intermediate at 550 °C for 2 h in air.

To investigate the crystallization of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, the calcination process was examined using in situ XRD (Fig. 5a). Initially, between 100 °C and 400 °C, amorphous phases were detected, likely attributable to the decomposition of acetates. As the temperature reached 450 °C, an increase in diffraction intensity was observed, and the slope vanished. Subsequently, at 550 °C, the distinct broad peaks corresponding to the cubic phase CoCr₂O₄ (JCPDS 80-1668) emerged, without the presence of any additional peaks. When the temperature was maintained at 550 °C for 6 h, no significant change in the diffraction pattern was noted. Thus, 550 °C was the optimal calcination temperature for synthesizing (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄.

Fig. 5: The synthesis of a cubic phase of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄.

a Patterns of in situ XRD of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalysts during the programmed heating temperature. b X-ray diffraction pattern of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and comparative samples ACr₂O₄ (A = Ni, Mg, Cu, Zn, Co). c XRD pattern of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ with the rietveld refinement result. (Source data are provided as a Source Data file).

Then, the XRD of samples were depicted in Fig. 5b. (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, ZnCr₂O₄, and CoCr₂O₄ exhibited distinct diffraction peaks corresponding to the cubic phase spinel structure (JCPDS 80-1668). In contrast, it was not possible to synthesize pure NiCr₂O₄, MgCr₂O₄, and CuCr₂O₄ under identical conditions, specifically calcination at 550 °C in air. This result can be attributed to the influence of configurational entropy ($\Delta {Sconfig}$)^{19,27,29,30,31,32,33}, which can be determined using the following equation^{34,35,36,37,38,39}:

$$\Delta {Sconfig}=-{R}\ast \left({\sum }_{i=1}^{n}{xiInxi}\right){M}-{site}$$

(1)

By calculation, $\Delta {Sconfig}$ value of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ is − 9.752, while $\Delta {Sconfig}$ value of single metal ACr₂O₄(A = Ni, Mg, Cu, Zn, Co) is − 5.287. This disparity in $\Delta {Sconfig}$ value suggests that (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ will exhibit a lower Gibbs free energy (ΔG = ΔH − TΔS) for crystallization at 550 °C.

According to the XRD Rietveld refinement of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, all diffraction peaks were attributed to the Fd-3m space group, as depicted in Fig. 5c. The determined lattice parameters were a = b = c = 8.3252 Å. In addition, the R_wp and χ² values were found to be 3.912% and 0.769, respectively, indicating a homogeneous distribution of the five transition metal atoms within the A sites, with no evidence of separate single metal oxides. Moreover, SEM images of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ demonstrated that the material consisted of aggregated nanoparticles with sizes ranging from 10 to 30 nm, which was consistent with the XRD results shown in Supplementary Fig. S7. Furthermore, the average crystallite size of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was calculated to be ~ 7.7 nm using Scherrer’s formula⁴⁰. Subsequently, N₂ sorption measurements were performed at 77 K, as illustrated in Supplementary Figs. S8, S9. The specific surface areas of ACr₂O₄ (where A = Ni, Mg, Cu, Zn, Co) were determined to be in the range of 68–75 m²/g (Supplementary Table S6). This range was notably higher than that obtained by conventional methods. For instance, the specific surface area of ZnCr₂O₄ synthesized through the co-precipitation method was only 18 m²/g⁴¹.

To study the atomic-scale structure of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, a high-resolution STEM-HAADF experiment was conducted. As depicted in Fig. 6a, these images revealed a well-defined lattice structure along the [111] zone axis, with no detectable foreign metal atoms present within the crystal interior. Moreover, to further validate this structure, additional domains exhibiting long-range lattice fringes along the [110] zone axis were examined (Fig. 6b). The high-resolution TEM (HRTEM) images showed lattice spacings of 0.481, 0.251, and 0.295 nm, which corresponded to the (111), (311), and (220) crystal planes of the spinel structure, respectively (Fig. 6c). In addition, EDS elemental mapping confirmed a uniform distribution of Ni, Mg, Cu, Zn, Co, Cr, and O within a nanometer-scale domain, indicating the formation of a high-entropy structure (Fig. 6d). To study the experimental error, the optimized high entropy component was prepared three times, and the samples were labeled as a-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O_4, b-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O_4, c-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ respectively_. Characterizations such as XRD (Supplementary Fig. S10), SEM (Supplementary Fig. S11), ICP-MS (Supplementary Tables S8–S10), and TEM (Supplementary Figs. S12–S20) were conducted, finding good reproducibility of high entropy oxides. Characterizations such as XRD (Supplementary Fig. S21), SEM (Supplementary Figs. S22–S24), and N₂ adsorption (Supplementary Fig. S25) of 10 ternary control samples were conducted. In addition, characterizations such as SEM and TEM (Supplementary Figs. S26–S31) of ACr₂O₄(A = Ni, Mg, Cu, Zn, Co) were conducted.

Fig. 6: The characterization of freshly made (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O_4.

a, b STEM-HAADF images and (c) HRTEM images of the (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. d EDS elemental mapping images of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. Source data are provided as a Source Data file.

To verify DFT calculations (Figs. 1–3), C₃H₆ oxidation by as-made oxide samples was carried out (Fig. 7a). There was no influence of internal and external diffusion for C₃H₆ oxidation (Supplementary Figs. S32, S33). The (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalyst exhibited good catalytic performance for C₃H₆ oxidation with T₉₀ (C₃H₆ conversion was 90%) at 265^oC, better than that of single oxides (318 ^oC–350 ^oC) (Supplementary Table S7). This result became understandable if the lower E_Ov of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was considered (Fig. 3). Real-world applications required catalysts to be stable in ubiquitous moisture. Actually, the DFT calculation already suggested better hydrothermal stability of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. To verify the DFT conclusion_, the stability experiments were carried out at a C₃H₆ conversion of ~ 70% with 4.2 vol% water (Fig. 7b). 4.2% water vapor was the saturated vapor pressure of water vapor in the air at 30 °C^42,43,44. The 4.2% water vapor was closest to the actual working conditions. The C₃H₆ conversion of single oxides continuously decreased in 20 h and almost lost their catalytic activity in 50 h. In sharp contrast, the activity of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was well retained within 100 h. To further demonstrate the water resistance of the catalyst, XRD, BET, and TGA characterization of the spent (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalyst was conducted. The XRD pattern of the spent (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalyst after the reaction was unchanged(Supplementary Fig. S79). Furthermore, the spent (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalyst showed almost no change in its surface area after the reaction (Supplementary Fig. S80). No significant quality decrease was observed in the TGA analysis (Fig. S76), indicating that the catalyst produced little coke (0.73 wt%) during the reaction process. This indicated that the catalyst had strong resistance to carbon deposition, especially considering its high catalytic activity.

Fig. 7: Catalytic performance measurements.

a C₃H₆ light-off curve of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, NiCr₂O₄, MgCr₂O₄, CuCr₂O₄, CoCr₂O₄ and ZnCr₂O₄.(20000 mL h⁻¹g⁻¹; the feed gases contain 1vol % C₃H₆, 99 vol% air). b Stability experiments of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, CoCr₂O₄, ZnCr₂O₄, NiCr₂O₄, CuCr₂O₄ and MgCr₂O₄ at T₇₀ (temperatures that C₃H₆ conversion was 70%) in the presence of 4.2 vol% moisture. (Source data are provided as a Source Data file).

Moreover, tests of water resistance at humidity levels of 10 vol% were conducted to further demonstrate the water resistance (Supplementary Fig. S81). In addition, the (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ catalyst was aged at 800 ^oC in the presence of 4.2 vol% moisture for 30 h. Then, the aged catalyst was subjected to XRD, BET, and stability experiments of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ at T₇₀ in 4.2 vol% moisture within 100 h. The crystal structure and specific surface area are almost unchanged (Supplementary Figs. S82, S83). After being aged at 800 ^oC in the presence of 4.2 vol% moisture for 30 hours, the activity of spent (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was still well maintained in stability experiments at T₇₀ in 4.2 vol% moisture within 100 h(Supplementary Fig. S84). TGA test results indicated that no carbon deposition occurred during the aging process of 800 ^oC(Supplementary Fig. S85).

To study the water resistance mechanism of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, H₂O-TPD experiments were conducted (Fig. 8a). The peak of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ appeared at a low temperature (80 ^oC) compared with NiCr₂O₄, MgCr₂O, CuCr₂O₄, CoCr₂O₄ and ZnCr₂O₄. It revealed that the H₂O adsorption ability of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was weaker, matching well with the DFT calculation results (Figs. 1, 2). Furthermore, the H₂O desorption peak of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was smaller. This result indicated that there were fewer adsorption sites for water on (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and the amount of water molecules adsorbed by (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was smaller compared to NiCr₂O₄, MgCr₂O₄, CuCr₂O₄, CoCr₂O₄ and ZnCr₂O₄.

Fig. 8: Study of the water resistance mechanism of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄.

a H₂O -TPD profiles, (b) O₂ -TPD profiles of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, ZnCr₂O₄, CoCr₂O_4, NiCr₂O₄ CuCr₂O₄ and MgCr₂O₄. c H₂-TPR profiles of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, ZnCr₂O₄ and CoCr₂O₄. d O 1s XPS spectra of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. e O 1s XPS spectra of ZnCr₂O₄. f O 1s XPS spectra of CoCr₂O₄. Source data are provided as a Source Data file.

In situ Raman spectroscopy was conducted to study the role of water in the Cr−O bond of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, CoCr₂O_4, and ZnCr₂O₄ catalysts under real reaction conditions. To study the mechanism of water resistance, in situ Raman spectroscopy experiments were carried out with 4.2 vol% water. The peak between 450 cm⁻¹ and 600 cm⁻¹ corresponded to Cr-O bonds in Fig. 9a, d, g. The Cr−O bond of CoCr₂O₄ and ZnCr₂O₄ catalysts exhibited a red shift with increased reaction temperature, which can reflect the change in the Cr−O bond force constant calculated by Hooke’s law⁴⁵. In the presence of 4.2 vol% H₂O, an increase in reaction temperature could decrease the force constant of the Cr−O bond of CoCr₂O₄ and ZnCr₂O₄ catalysts, thus weakening the Cr–O bonds. This indicated that the crystal structure of CoCr₂O₄ and ZnCr₂O₄ catalysts were unstable with 4.2 vol% H₂O. In contrast, an increase in reaction temperature cannot change the force constant of the Cr−O bond in (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ with 4.2 vol% H₂O (Fig. 9c, f, i). This difference may be due to the lower Gibbs free energy of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ structure³³. Associated with the results of H₂O-TPD (Fig. 8a) and DFT calculations (Figs. 1, 2), the chemically adsorbed water on the surface of CoCr₂O₄ and ZnCr₂O₄ catalysts would reduce the adsorption of C₃H₆ at the same time damage their crystal structure, thereby losing the catalytic activity for C₃H₆ oxidation.

Fig. 9: In situ Raman measurements.

a, d, g In situ Raman spectra of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, CoCr₂O₄, ZnCr₂O₄with 4.2 vol% H₂O using the 532 nm radiation for excitation (C₃H₆ flow rate, 30 mL min⁻¹; sampling interval was 10 min). b, e, h The enlarged image of (a, d, g). c, f, i The Cr−O bond force constant of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, CoCr₂O₄, ZnCr₂O₄ at different temperatures. Source data are provided as a Source Data file.

Based on the above DFT theoretical calculations and experiments, the water resistance mechanism by a high entropy structure can be proposed. The surfaces of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and single oxides all showed hydrophilicity (Supplementary Fig. S34), indicating that water molecules can successfully reach the outer surface of the catalysts. However, DFT calculations indicated that the water molecules on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ would not affect the adsorption of C₃H₆, while the water molecules on the surface of single oxides could undergo competitive adsorption with C₃H₆, which was not conducive to C₃H₆ catalytic oxidation(Fig. 1). Furthermore, molecular H₂O was easy to dissociate into H⁺ and OH^- on the surface of single oxides compared with (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, then OH⁻ could react with single oxides to form hydroxide(Fig. 2). In addition, (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ had weak H₂O adsorption ability by H₂O-TPD (Fig. 8a). Interestingly, the Cr-O bond and crystal structure of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ were more stable under humid conditions by in situ Raman (Fig. 9). In situ infrared spectroscopy indicated that water molecules can adsorb on the surface of CoCr₂O₄ and ZnCr₂O₄ and react with surface reactive oxygen species to form hydroxyl groups to hinder the adsorption and reaction of C₃H₆. In contrast, the structure of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was almost unchanged with 4.2 vol% water(Supplementary Figs. S35–S40). In summary, the above results provided theoretical and experimental evidence for the water resistance mechanism of high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄.

After studying the water resistance mechanism of high entropy structures under humid conditions, the catalytic performance of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was better than that of single metal ACr₂O₄ (A=Ni, Mg, Cu, Zn, Co) under dry conditions(Fig. 7a and Supplementary Table S6), which required further evidence to figure out the reason. Initially, to investigate whether the adsorption behavior of C₃H₆ influences catalytic performance, C₃H₆-TPD was performed on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, CoCr₂O₄ and ZnCr₂O₄ (Supplementary Fig. S41). The peak area of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was larger compared to CoCr₂O₄ and ZnCr₂O₄, and the higher adsorption amount of C₃H₆ by (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ is beneficial to C₃H₆ catalytic oxidation. The oxygen species of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, ZnCr₂O_4, and CoCr₂O₄ were closely related to their C₃H₆ oxidation performance, so O₂-TPD experiments were conducted (Fig. 8b). Two desorption peaks of oxygen species appeared at around 350 and 720 °C for ZnCr₂O₄^46,47,48. The O₂ peak desorbed at below 400 °C was usually considered as the reactive oxygen species (ROS) of oxide catalysts^{17,44,49,50,51}. Notably, (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ desorbed surface lattice oxygen at a lower temperature (220^oC) than ZnCr₂O₄ (320^oC) and CoCr₂O₄ (315 ^oC). This feature suggested the lower E_Ov of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, matching well with the DFT calculation(Fig. 3). The weak binding between ROS and adjacent atoms made it easier to escape from the catalyst surface, which was crucial for enhancing the catalytic performance of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ in C₃H₆ oxidation (Fig. 7a)^17,43. In addition, Oxygen adsorption energy and charge transfer are shown in Supplementary Figs. S90–S92. For three different crystal planes (220), (311), and (111), the charge transfer of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was higher than those of single oxides respectively, facilitating the activation of oxygen molecules. Compared to single metal oxides (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ had higher oxygen adsorption energy, and oxygen molecules can stably adsorb on the active sites on the catalyst surface. These active sites would activate oxygen by interacting with oxygen molecules, being expected to promote subsequent catalytic reactions. To further assess the redox properties of the metal species in the oxides, H₂-TPR analyses were performed on (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, ZnCr₂O₄, and CoCr₂O₄ (Fig. 8c). Notably, (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ began to consume H₂ at 150 °C, likely due to the removal of surface-adsorbed oxygen. The corresponding metal ions in (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ were easier to reduce to the low oxidation state compared with the bimetallic oxide ZnCr₂O₄ and CoCr₂O₄.

In fact, the content of oxygen vacancies can be determined through the analysis of O 1s XPS spectra(Fig. 8d–f)⁴⁴. Generally, the peak at 529.9 eV was attributed to lattice oxygen (O^α), while the peak at 531.5 eV corresponded to oxygen vacancies (O^β). Therefore, the ratio of O^β to O^α served as an indicator of the concentration of oxygen vacancies⁵². O^β/O^α of ZnCr₂O₄ (0.55) and CoCr₂O₄(0.31) were much lower than (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ (0.96). The result matched well with the regularity of E_ov calculated by DFT (Fig. 3). This suggested that a high-entropy structure could create more oxygen vacancies^53,54. This further provided explanatory evidence for the differences in the catalytic performance of oxides under dry conditions in Fig. 7a.

To further investigate the effect of the high-entropy structure on redox characteristics, in situ XPS analyses were performed before and after reduction at 300 °C in an atmosphere consisting of 5% H₂ and 95% N₂. The surface chemical states of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ before reduction were first investigated (Fig. 10). The Cu 2p XPS spectra revealed a distinctive peak for Cu²⁺ at 934.6 eV. Simultaneously, the Co 2p1/2 and Co 2p3/2 had peaks at 794.5 eV and 779.7 eV, respectively. Subsequent fine-scanning of the Co spectra indicated the coexistence of Co³⁺ and Co²⁺ species. Only divalent Ni²⁺, Mg²⁺_, and Zn²⁺ ions were detected by Ni 2p3/2, Mg 2p, and Zn 2p3/2 or 2p1/2, respectively. The main component was Cr³⁺(576.2 and 586 eV) and contained a small amount of Cr⁶⁺(578.3 eV). The surface chemical states of pristine CoCr₂O₄ and ZnCr₂O₄ samples were also investigated(Supplementary Figs. S42, S43). To study the redox ability at a low temperature (the first peak of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ appeared in H₂-TPR at 100 °C, Fig. 8c), (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was reduced at 300 °C by 5%H₂/95%N₂ and conducted in situ XPS(Fig. 9). A part of Ni (13%) and Cu (30%) ions were reduced to the metallic phase. The ratio of Co³⁺/Co²⁺ was 72%/28% before reduction and 61%/39% after reduction. The ratio of Cr³⁺/Cr⁶⁺ was 88%/12% before reduction and 93%/7% after reduction. Interestingly, the reduction temperature of metals other than Cu decreased significantly. Hydrogen spillage from active Cu species may cause this phenomenon^55,56. As the reduction temperature of Mg and Zn ions with valence 0 was very high, no metallic Mg and Zn species with valence 0 were observed (Fig. 10). The in situ XPS results matched with H₂-TPR (Fig. 8c), both confirming HEOs were easier to be reduced by H₂ than single metal oxides under the same conditions. This suggested that the high-entropy structure can enhance the elimination of surface-adsorbed oxygen more effectively than single metal oxides, consequently leading to improved catalytic efficiency. In summary, the above results provide theoretical and experimental evidence as to why the catalytic activity of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was superior to that of single oxides under dry conditions.

Fig. 10: In situ XPS measurements.

a Ni 2p, (b) Co 2p, (c) Cu 2p, (d) Cr 2p, (e) Zn 2p and (f) Mg 2p XPS spectra of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ before reduction and after reduction at 300 °C in 5%H₂/95%N₂ (The spectra directly below is before reduction, while the spectra directly above is after reduction). Source data are provided as a Source Data file.

Discussion

To sum up, inspired by the principle of high entropy-stabilized structure, a concept of engineering entropy to design water-resistant oxide catalysts is proposed. The water resistance performance of HEOs in catalytic oxidation was initially estimated by theoretical studies. First, with spinel ACr₂O₄(A = Ni, Mg, Cu, Zn, Co) as an oxide model and catalytic C₃H₆ oxidation as a typical process, the adsorption behavior of C₃H₆, dissociation energy of molecular H₂O and the formation energy of oxygen vacancies were estimated by DFT calculation. Then, oxide catalysts were prepared to verify DFT calculation results. The T₉₀ (C₃H₆ conversion was 90%) of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄(265 °C) was lower than the T₉₀ of ACr₂O₄ (318–350 °C) in catalytic C₃H₆ oxidation in dry conditions. Interestingly, in the presence of 4.2 vol% water, single metal ACr₂O₄ lost its activity in ~ 20 h under long-term C₃H₆ oxidation. While the high entropy (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was stable at 100 h. Moreover, the H₂O-TPD, in situ FTIR, and in situ Raman results were consistent with the DFT results, providing scientific evidence for the water resistance mechanism of HEOs. Meanwhile, O₂-TPD, H₂-TPR, O 1s XPS, and in situ XPS also matched with the DFT results, offering robust scientific support that HEOs had better catalytic activity than single metal ACr₂O₄ in dry conditions_. In 2015, high-entropy oxide was invented, and its catalytic applications emerged around 2018, revealing unexpected prowess in heterogeneous catalysis¹². This relatively recent exploration of their capabilities is both young and promising. The concept of utilizing entropy engineering for the creation of water-resistant catalysts marks just the initial phase, with the anticipation of inspiring more materials for water-resistant catalysis in the near future.

Methods

DFT calculation method

Prior to obtaining our experimental results, DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP), which employed the projector-augmented wave method^57,58. The total energy of a structure is evaluated by the GGA proposed by the PBE functional⁵⁹. The long-range van der Waals interaction is described by the DFT-D3 approach⁶⁰. All the calculation parameters are carefully tested to meet the convergence criteria, and the structures are relaxed until all the forces on the atoms are less than 0.01 eV/Å. To construct the (Ni_0.2Mg_0.2Zn_0.2Cu_0.2Co_0.2)Cr₂O₄ structure, random atoms (Ni, Mg, Zn, Cu, Co) need to occupy the Mg atomic positions of MgCr₂O₄ structure according to their ratios, achieving SQS^61,62, then we can construct different crystal plane structures to determine the adsorption ability. We generated 20 SQS to calculate the energy as shown in Supplementary Fig. S89, and the relative energy was almost less than 0.2 eV, indicating that the energy was converged. For the molecule adsorption on these high-entropy oxide substrates, we employ the adsorption energy as the criteria to justify the adsorption ability (see the supplementary materials for the details). The dissociation energy of molecular H₂O on the surface of NiO, MgO, CuO, ZnO, Co₃O_4, and Cr₂O₃ at crystal plane (111), respectively, was shown in Supplementary Fig. S44 and Supplementary Table S11. The formation energy of oxygen vacancy (E_Ov) of NiO, MgO, CuO, ZnO, Co₃O_4, and Cr₂O₃ at crystal plane (111), respectively, was shown in Supplementary Fig. S45 and Supplementary Table S12. The adsorption energy of C₃H₆ on the surface (111 planes) of NiO, MgO, CuO, ZnO, Co₃O₄, and Cr₂O₃ in the absence and presence of 4.2 vol% water vapor was shown in Supplementary Fig. S46 and Supplementary Table S13. The linear relationship of E_ads and ε_d is shown in Figure S47.

In addition, the adsorption energy of H₂O on the surface of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and single metal oxides at crystal plane (220), (311), and (111) were calculated by DFT, respectively (Supplementary Figs. S86–S88). The results showed that the water adsorption energy of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ was the lowest of them. In addition, oxygen adsorption energy and charge transfer were shown in Supplementary Figs. S90–S92.

Characterization

Catalysts were characterized by ex-situ/in situ XRD, in situ FT-IR, ex-situ/in situ XPS, ex-situ/in situ Raman, nitrogen adsorption isotherms, SEM, HRTEM, H₂-TPR, O₂-TPD, H₂O-TPD, C₃H₆-TPD. Comprehensive experimental procedures can be found in the Supporting Information. The equipment used for propylene combustion and hydrothermal stability tests is illustrated in Supplementary Fig. S48.

Synthesis of (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ by ball milling

In a typical preparation, 1 mmol of Cu(OAc)₂(181.6 mg), 1 mmol of Zn(OAc)₂ (183.5 mg), 1 mmol of Ni(OAc)₂•4H₂O(248.8 mg), 1 mmol of Co(OAc)₂•4H₂O(249.1 mg), 1 mmol of Mg(OAc)₂•4H₂O(142.4 mg), and 10 mmol of Cr(OAc)₃ (2291 mg) were combined in an 80 ml Nylon reactor. In addition, 10 zirconia balls (four with a diameter of 1.2 cm and six with a diameter of 0.5 cm) were added to the reactor. The mixture was then ground using a high-speed vibrating ball miller for 30 min. Subsequently, the resulting intermediate was calcined in air at 550 °C for 2 h with 2 °C/min. The final product was labeled as (Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄. The synthesis method of single oxides was similar to the above method. The obtained sample was named NiCr₂O_4, MgCr₂O₄, CuCr₂O₄, ZnCr₂O₄, and CoCr₂O₄ respectively.

C₃H₆ oxidation reaction experiment and calculation of carbon balance values

Generally, a mixture of 30 mg of catalyst and 100 mg of quartz sand was employed under 10 mL/min, resulting in GHSV of 20,000 mL/h·g. The feed gases consisted of 1 vol% C₃H₆ and 99 vol% air. The original GC spectrum (The raw gas contains 10ppm CO and the remaining is air) was shown in Supplementary Fig. S49. Original GC spectra with no catalysts at 50 °C (10 mL/min, feed gas ratio: 1vol % C₃H₆ and 99 vol% air) were shown in Supplementary Fig. S50. C₃H₆ light-off curve of control samples NiCr₂O₄, MgCr₂O₄, CuCr₂O₄, CoCr₂O₄ and ZnCr₂O₄ (20000 mL h⁻¹g⁻¹; the feed gases contain 1vol % C₃H₆ and 99 vol% air) was shown in Supplementary Fig. S52. C₃H₆ light-off curves of 10 control ternary oxide samples (20000 mL h ^-1g ^-1; the feed gases contain 1vol % C₃H₆ and 99 vol% air) were shown in Supplementary Fig. S53. Using mass spectrometry to detect signals of CO and CO₂ during the combustion of propylene (Supplementary Fig. S54). Mass spectrometry data in the light-off process of Zn_0.5Mg_0.5Cr₂O₄ and Cu_0.5Co_0.5Cr₂O₄ sample(20000 mL h⁻¹g⁻¹; the feed gases contain 1vol % C₃H₆ and 99 vol% air; 5 °C/min) were shown in Supplementary Figs. S57, S58. C₃H₆ light-off curves and variance (VAR) of a-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄, b-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄ and c-(Ni_0.2Mg_0.2Cu_0.2Zn_0.2Co_0.2)Cr₂O₄(20000 mL h⁻¹g⁻¹; the feed gases contain 1vol % C₃H₆ and 99 vol% air) were shown in Supplementary Figs. S55, S56. The stability experiments were carried out at a conversion of 70% in C₃H₆ oxidation combustion under humid conditions (4.2 vol% H₂O) for 100 h. The images of the original data by (Shimadzu GC-2014C) (Supplementary Figs. S51, S59) were shown in Supplementary Figs. S61–S75. According to the CO₂ internal standard curve (Supplementary Fig. S60), values of carbon balance were obtained (SupplementaryTables S16, S17).

$${{\rm{Remaining}}}\, {{{\rm{C}}}}_{3}{{{\rm{H}}}}_{6}\, {{\rm{concentration}}}\, (\%) \,=({{\rm{Remaining}}}\, {{{\rm{C}}}}_{3}{{{\rm{H}}}}_{6}\, {{\rm{area}}}/ \\ {{\rm{initial}}}\, {{{\rm{C}}}}_{3}{{{\rm{H}}}}_{6}\, {{\rm{area}}})\times 100\%$$

$${{\rm{Value}}}\; {{\rm{of}}}\; {{\rm{carbon}}}\; {{\rm{balance}}}=[({{\rm{generated}}}\, {{{\rm{CO}}}}_{2}\, {{\rm{concentration}}}/3) \\+({{\rm{Remaining}}}\, {{{\rm{C}}}}_{3}{{{\rm{H}}}}_{6}\, {{\rm{concentration}}})]/1\%$$

$$({{\rm{The}}}\; {{\rm{initial}}}\; {{\rm{concentration}}}\; {{\rm{of}}}\,{{{\rm{C}}}}_{3}{{{\rm{H}}}}_{6}\, {{\rm{is}}}\; 1\%)$$

Detailed procedures are in the Supplementary Methods section.