Materials synthesis and characterization. Schematical illustration for the preparation of NiFe LDH-POMs is shown in Fig. 1a. The NiFe LDH was firstly grown on nickel foam (NF) via a simple electrodeposition method as reported elsewhere,6, 29 followed by representative POMs etching. Three typical Keggin-structured POMs were chosed, which are phosphotungstic acid (pure PW12), tungstosilicic acid (pure SiW12) and phosphomolybdic acid (pure PMo12). Meanwhile, the control samples etched by common inorganic acids of sulfuric acid (pure H2SO4), hydrochloric acid (pure HCl) and nitric acid (pure HNO3) were also prepared, namely NiFe LDH-H2SO4, NiFe LDH-HCl and NiFe LDH-HNO3, respectively. The detailed preparation procedure is described in the Methods section and Supplementary Information.
The structure and morphology evolution of NiFe LDH-POMs are characterized by scanning electron microscope (SEM)/energy dispersive X-ray spectroscopy (EDX), transmission electron microscope (TEM), atomic force microscope (AFM) and the spherical aberration corrected TEM (ACTEM). The SEM images and EDX mapping analysis results (Supplementary Figs. 1 and 2) shows the cross-linked NiFe LDH nanosheets with layer thickness of < 5 nm are uniformly and vertically grown on NF, but accompanied by a large faction of surface NiFe LDH microspheres, which greatly detrimental for charge transfer capability and OER performance. And can be polished finely to a different extent after the etching treatment (Supplementary Fig. 1b-1g). Especially in NiFe LDH-PMo12, the nanosheet arrays with reduced thickness become sparse and providing plentiful mass transfer spaces (Supplementary Fig. 1d4 and d5). It is noteworthy that serious nanosheet arrays loss is observed in cases of H2SO4 and HNO3 etching (Supplementary Fig. 1e and 1g). Further TEM observations also reveal the effective chemical thinning function of PMo12, which is also evidenced by the atomic force microscope (AFM) (Fig. 1c and e, Supplementary Fig. 3e). The thickness of the NiFe LDH-PMo12 is significantly reduced in the range of 2.0 ~ 3.6 nm (2 ~ 4 atomic layers), with respect to pristine one (3.5 ~ 4.4 nm, 4 ~ 6 atomic layers) (Supplementary Fig. 3a and b). The high-resolution TEM (HRTEM) image in Fig. 1b and d and the corresponding selected-area electron diffraction (SAED) patterns (inset of Fig. 1b and d) show the formation of NiFe LDH phase. A blurred diffraction ring can be found from SAED pattern of NiFe LDH-PMo12, as compared to the NiFe LDH with the bright diffraction spots. This implies that PMo12 etching decreases the crystallinity of NiFe LDH, thus accelerating OER kinetics30. The EDX mapping shows the uniform distribution of Ni, Fe, Mo and P elements in NiFe LDH-PMo12 (Supplementary Fig. 3c), confirming the decoration of PMo12 polyanionic clusters into the nanosheet arrays. The detailed EDX elemental analysis (Supplementary Fig. 3d) shows that the P/Mo ratio of 1:1.4 which is far higher than the nominal ratio of 1:12 in pure PMo12. It may be inferred that the acid-base reaction between PMo12 and NiFe LDH leads to the partial disintegration of PMo12, and a good deal of n(PO4)3− structural building units are anchored. To further resolve the structural variation, we employed the atomic-resolution HAADF-STEM image using ACTEM. Figure 1f and g show the formation of metal (Ni or Fe) vacancies in the NiFe LDH as indicated by yellow dotted circle, which is also solidly proved by the integrated intensity distribution profile of the atoms in the yellow dashed box.
In agreement with the SAED results, X-ray diffraction (XRD) patterns of the as-synthesized samples (Supplementary Fig. 4a) reveal the reduced nanosheets both in size and crystallinity for NiFe LDH-PMo12, since the diffraction peaks of (01n) planes (JCPDS #51–0463) become lower and border. Moreover, a negative shift of ~ 0.4° for (006) peak is clearly observed in NiFe LDH-PMo12, which are also found in control powder-form samples. The resultant increase of inter-layer distance can be ascribed to the inter-layer anion exchange of PMo12 polyanionic clusters with inherent interlayered anions (e. g. NO3−, SO42−). The Fourier transform infrared spectroscopy (FTIR) spectra (Supplementary Fig. 4b and Supplementary Fig. 5a) and Raman spectra (Supplementary Fig. 4c and Supplementary Fig. 5b) of the as-synthesized samples also confirm the reduction of nanosheets thickness and existence of ion-exchanged PMo12 polyanionic clusters.
To gain insights into the chemical composition and oxidation states of Ni, Fe and O elements, the X-ray photoelectron spectroscopy (XPS) was carried out (Supplementary Fig. 6). Surprisingly, the amount of α-Ni(OH)2 is tremendously increased from only 8.6 % in NiFe LDH to 43.7% in NiFe LDH-PMo12. The same rising trend is also observed in other controlled samples (Supplementary Fig. 6a). Since α-Ni(OH)2 is easier to transform into γ-NiOOH than β-Ni(OH)2, more α-Ni(OH)2 would greatly contribute to prompt OER activity31, 32. The calculated ratios of α-Ni(OH)2 to β-Ni(OH)2 are shown in Fig. 2a, and the highest ratio is obtained in NiFe LDH-PMo12. After the PMo12 etching, a 0.6 eV shift of Fe 2p3/2 peak towards higher binding energy (Supplementary Fig. 6b) suggests the transformation of Fe2+ into Fe3+ accompanied by the formation of Fe vacancies for charge neutrality33, 34. Similarly, the phenomenon is also be observed in other controlled samples (Supplementary Fig. 6b), and the highest ratio of Fe3+ to Fe2+ has been found for NiFe LDH-SiW12 (Fig. 2a). As shown in Supplementary Fig. 7, all these POMs possess oxidation peaks but no reduction peaks, which prove their irreversible oxidation properties. The order of oxidation ability is in a sequence of pure PW12 (0.11 V vs. RHE) < pure PMo12 (0.13 V vs. RHE) < pure SiW12 (0.16 V vs. RHE), which is consistent with the change trend of Fe3+ content in Fig. 2a.
The Mo 3d spectrum of NiFe LDH-PMo12 have slight negative shifts of 0.3 eV as compared to that in pure PMo12 (Supplementary Fig. 4d). It indicates a strong influence of Mo ions on the electronic structure of NiFe LDH, that is, the electron transfer from Fe2+ to Mo6+. The peak located at 133.84 eV in P 2p spectrum (Supplementary Fig. 4e) shows the present of PO43− both in pure PMo12 and NiFe LDH-PMo12. The O 1s XPS peak with broad and asymmetrical shape can be deconvoluted into four peaks (Supplementary Fig. 6c), i.e., OI (529.68 eV) for oxygen-metal bonds (M-O) in the lattice, OII (531.26 eV) for metal-hydroxyl groups (M-OH), OIII (531.70 eV) for oxygen vacancies with low oxygen coordination, and OIV (532.98 eV) for the loosely bound oxygen species such as NO3−, SO42−, CO32− or surface-adsorbed H2O35. We note that, the OIII ratio in NiFe LDH-PMo12 (23.66%) is obviously higher than that in NiFe LDH (22.53%), implying the generation of surface oxygen vacancies (Fig. 2a)35, 36.
We further conducted the electron paramagnetic resonance (EPR) spectroscopy to verify the oxygen vacancy levels (Fig. 2b). The EPR signal intensities of the as-etched NiFe LDH samples at g = 2.004, corresponding to structural defects induced oxygen vacancies, are obviously higher than that of NiFe LDH. Specially, the peak intensity of oxygen vacancies is nearly twice higher in NiFe LDH-PMo12 while reach the highest value in NiFe LDH-HNO3 (Fig. 2b). This is consistent with the XPS results. The EPR signal at g = 2.16 and g = 4.32 can be ascribed to Fe3+ species (Supplementary Fig. 4f), since Fe2+ species cannot be detected by EPR. The oxidation state of Ni remains unchanged after POMs and common inorganic acids etching. The amount of Fe3+ is increased after PMo12 etching as evidenced by the increased EPR signal peak intensity. The presence of Fe vacancies is also determined by inductively coupled plasma optical emission spectroscopy (ICP-OES), showing that the Fe concentration is relatively lower in all of the as-etched samples than the pristine one (Supplementary Fig. 9a).
Electronic structure analysis. To make more clear the effects of multi-skilled POMs on the local atomic coordination and electronic structure of NiFe LDH-PMo12, the X-ray absorption spectroscopy (XAS) analysis (Fig. 2c-g and Supplementary Fig. 8) was performed to probe the local atomic structures around Mo, Ni and Fe atoms. Figure 2c shows the Mo K-edge X‐ray absorption near‐edge structure (XANES) spectra. The absorption edge for NiFe LDH-PMo12 shift to lower position as compared with that of MoO2 and pure PMo12, suggesting a partial reduction of the electron density of Mo atoms in NiFe LDH-PMo12. This indicates the existence of three species of Mo4+, Mo5+ and Mo6+, consistent with the XPS results. As observed in the Fourier transform (FT) Mo K-edge extended X-ray absorption fine structure (EXAFS) spectra (Fig. 2d) of NiFe LDH-PMo12 as well as commercial Mo foil, MoO3, pure PMo12, FeMoO4 and MoO2 samples, two different peaks located at ~ 1.79 Å and ~ 3.48 Å for NiFe LDH-PMo12 are assigned to the features of Mo-O and Mo-O-Mo bonds, respectively. And this corresponds with the structure of Mo in pure PMo12. In collaboration with above XRD, FTIR and Raman data, a fraction of Keggin structured PMo12 is confined between the LDH layers for NiFe LDH-PMo12, thus increasing the interlayer distance and form the α-Ni(OH)2 species. It is worth noting that the intensity of the Mo-O-Mo bond is significantly weaker than that of pure PMo12. This may be because the atomic weight of Fe is smaller than that of Mo, which is similar to the Mo-O-Fe bond in FeMoO4 (~ 3.27 Å). This also verified that the MoO42− clusters are chemisorbed on the NiFe LDH surface, which was consistent with the XPS results. Moreover, the results of the full-range wavelet transform representation of the EXAFS signal (Fig. 2e-g and Supplementary Fig. 8f-j) show that in the coordinate system composed of k space and R space, the Mo-O-Mo bond in pure PMo12 is located at ~(10.43, 3.71), and the Mo-O-Fe bond in FeMoO4 is located at ~(8.83, 3.39), and the Mo-O-Mo(Fe) bond in LDH-PMo12 is located at ~(9.66, 3.54), which further confirms that there are both Mo-O-Mo and Mo-O-Fe in NiFe LDH-PMo12. The k2‐weighted XAFS χ(k) versus reciprocal wave vector (Supplementary Fig. 8e) indicates good qualities of all the data.
The Ni K-edge X‐ray absorption near‐edge structure (XANES) spectra of NiFe LDH-PMo12 and NiFe LDH, as well as commercial Ni foil, NiO and Ni(OH)2 as reference are shown in Supplementary Fig. 8a. The overlapped XANES spectra of NiFe LDH-PMo12, NiFe LDH, NiO and Ni(OH)2 samples reveal that Ni2+ remains the dominant valence state of NiFe LDH-PMo12 and NiFe LDH. As observed with Ni K-edge EXAFS (Supplementary Fig. 8b), the first-shell peak at ~ 1.87 Å, representative of the Ni-O bond. The lower intensity in NiFe LDH-PMo12 and NiFe LDH samples than that of Ni(OH)2, suggesting a lower metal-oxygen coordination number and more oxygen vacancies37. Compared with NiFe LDH, the bond distance of second-shell peak at ~ 2.96 Å (Ni-O-Fe (Ni) bond) increases in NiFe LDH-PMo12 by ~ 0.02Å, indicating the formation of α-Ni(OH)2 in NiFe LDH-PMo1238. Supplementary Fig. 8c shows the Fe K‐edge XANES spectra of NiFe LDH-PMo12 and NiFe LDH, as well as commercial Fe foil, Fe2O3, FeO, and Fe(OH)3 samples, indicating the Fe of NiFe LDH-PMo12 and NiFe LDH are in Fe3+ oxidation stat. Two shell peaks at ~ 1.83 and ~ 2.97 Å represents of Fe-O and Fe-O-Ni are observed in Fe K-edge EXAFS (Supplementary Fig. 8d). Similar to Ni-O-Ni (Fe), slight positive shift is also found in Fe-O-Ni, which indicates the formation of more α-Ni(OH)2 species.
Electrocatalytic OER catalysis. Figure 3a shows OER cyclic voltammetry (CV) curves of the as-etched samples. The required overpotentials to deliver current densities of 10, 100 and 500 mA·cm− 2 are given in Fig. 3b. Besides the Ni2+/3+ redox peak at around 1.4 V vs. RHE, we can find that the OER performance of NiFe LDH-PMo12 is greatly enhanced, that is, the lowest overpotentials (η) of only 206 and 249 mV at the current densities of 10 and 100 mA cm− 2, respectively. In contrast, the η10 and η100 are observed at 213 and 258 mV for NiFe LDH, 286 and 353 mV for IrO2, respectively. More remarkably, only a very small overpotential of 305 mV can drive high current density of 500 mA cm− 2 for the NiFe LDH-PMo12, which is significantly superior to 339 mV (η500) for pristine NiFe LDH and most reported data in literature39–41. Similarly in the control samples, the powder-form NiFe LDH-PMo12 shows η10 and η100 decrease by 31 and 62 mV as comparison with the corresponding powder-form NiFe LDH, respectively, unveiling the fast and versatile POMs etching approach to tailor NiFe LDH based materials (Supplementary Fig. 10). Figure 3d and Supplementary Table 4 show that the NiFe LDH-PMo12 yields the lower Tafel slope of 47.5 mV·dec− 1, which is much smaller than the NiFe LDH (57.6 mV·dec− 1) and IrO2 (73.6 mV·dec− 1). The fastest OER kinetics is most favorable for the inherent OER activity of NiFe LDH-PMo12 and the rate-determining step (RDS) is the third electron transfer step9. To further deepen the understanding of the OER performance evolution, detailed comparison with the data recently reported in the literature is given in Fig. 3c and Supplementary Table 3. We can evidently conclude that the POMs etched catalysts affords an extraordinary OER performance, outperforming many state-of-the-art noble metal-free OER catalysts in alkaline. The stability test at a constant current density of 500 mA·cm− 2 confirms the robust electrochemical stability of the NiFe LDH-PMo12 for 24 h (Supplementary Fig. 9b). Interestingly, the OER activity increases from initial 1.666 V vs. RHE to 1.638 V vs. RHE after 24 h. After electrochemical OER tests, the same Raman peaks located at 475 and 552 cm− 1 can be attributed to the OER active phase of γ-NiOOH (Supplementary Fig. 5c) 42, 43. Next, the electrochemical impedance spectroscopy (EIS) is used to measure the OER catalytic charge transfer resistance (Rct) (Fig. 3e and Supplementary Table 4). An equivalent electrical circuit model is developed to fit the Nyquist plots (inset in Fig. 3e), which consists of featuring solution resistance (Rs), OER charge transfer resistance (Rct1) and Ni2+/3+ redox charge transfer resistance (Rct2). The NiFe LDH-PMo12 possesses smaller Rct1 (0.35 Ω) than that of pristine NiFe LDH (1.70 Ω). Such a significant decrease in Rct can infer to the fast electron transfer and favorable reaction kinetics, thus lead to a small Tafel slope.
The turnover frequency (TOFFe, mol) values are estimated, taking into account solely the intrinsic activity of Fe sites (Supplementary Note 1). Remarkably, the NiFe LDH-PMo12 catalyst displays high intrinsic activity with TOFFe, mol values up to 2.03 s− 1 at the overpotential of 350 mV (Fig. 3f), which is nearly 2 times higher than that for NiFe LDH (0.99 s− 1). The content of W elements in NiFe LDH-PW12, NiFe LDH-SiW12 and the content of Mo elements in NiFe LDH-PMo12 are < 0.005 mg·cm− 2, indicating that polyanionic clusters of PW12, SiW12 or PMo12 existed in trace amounts (Supplementary Table 1). The intercalation of PMo12 polyanionic clusters was further confirmed by ICP-OES measurements, showing that the atomic ratio of Ni/Fe and P/Mo are nearly equal to 1:7 and 1:6 in powder-form NiFe LDH-PMo12 (Supplementary Table 2). The P/Mo atomic ratio in TEM observation result (P/Mo ~ 1:1.4) is far higher than that of 1:12 in pure PMo12. It is reasonable that the residual P species are preserved with partial decomposition of PMo12, while a portion of stable PMo12 polyanionic clusters are between the nanosheet layers.
Furthermore, we demonstrated the feasibility of large-scale production of NiFeLDH-PMo12 electrodes for practical applications into scale-up anion exchange membrane (AEM) electrolyzer cells. Figure 5c shows the as-prepared NiFeLDH-PMo12 electrodes with different sizes between Ф50 to Ф180 mm in diameter and 30 × 30 mm in square, to adapt the different electrolyzer cells. By assembling NiFe LDH-PMo12 as anode and Ni@NiFe LDH from our earlier work44 as cathode (NiFe LDH-PMo12(+) ‖ Ni@NiFe LDH(-)), the cell voltages of only 1.57(6), 1.76(9) and 1.85(0) V are needed to achieve current densities of 10, 100 and 200 mA·cm− 2, respectively (Fig. 5d). Figure 5e shows the detailed configuration of our AEM electrolyzer in a sequence from left to right: cathode current collector, seal ring, titanium mesh gas diffusion layer (GDL), anion exchange membrane (AEM), NiFe LDH-PMo12 electrode, titanium mesh GDL and anode current collector.
Theoretical insights on OER activity improvement. Based on the above discussed electronic structure analysis and OER electrochemical analysis, to further understand the effect of PMo12 etching on the outstanding OER catalytic activities of the NiFe LDH-PMo12, density functional theory calculations with Hubbard-U approach (DFT + U) were conducted. Theoretically, the OER in an alkaline medium consists of four proton-transfer steps, and the adsorption energies of intermediates (*OH, *O, and *OOH) on the surface of the electrocatalyst are directly affected the OER activity. As illustrated in Fig. 4a and Supplementary Fig. 13, the first step of the OER process involves the phase transformation during which the detachment of H from the topmost surface of the regular LDH occur, NiFe LDH could be covered to γ-NiFeOOH, which has also been proved by previous works45, 46. All the simulation are carried out on the oxygen bridge between Ni and Fe atom. In order to study the influence of oxygen vacancies and MoO42− clusters on the OER activity, we established four calculation models, denoted as pristine LDH (NiFe LDH), LDH containing only oxygen vacancies (NiFe LDH + Vo), LDH containing only MoO42− clusters (NiFe LDH + Mo) and LDH containing both oxygen vacancies and MoO42− clusters (NiFe LDH-PMo12).
Based on the free energy diagram the calculated ΔGn on the four NiFe LDH (001) models is shown in Fig. 4a. The potential determining step (PDS) of NiFe LDH-PMo12 is the formation of OOH* from O* with an overpotential of 0.34 V, which consist with the RDS result from Tafel slope. In contrast, for the NiFe LDH, the overpotential increases up to 0.79 V and the PDS is OH* to O*. The decrease of overpotential after Vo and MoO42− creation on NiFe LDH implies that both Vo and MoO42− play a vital role in improving OER activity. To verify this assumption, we have performed separate calculations on the two models of NiFe LDH + Vo and NiFe LDH + MoO42−. The results show that the PDS of NiFe LDH + Vo is O* to OOH* with an overpotential of 0.68 V, and the PDS of NiFe LDH + MoO42− is the formation of O* from OH* with an overpotential of 0.51 V. In addition, a linear scaling relation between the free energies of OOH and OH on the (001) facet of NiFe LDH, NiFe LDH + Vo, NiFe LDH + MoO42− and NiFe LDH-PMo12, ΔGOOH = ΔGOH + 3.2 ± 0.2 (Fig. 4b) was found, which in good agreement with previous works47–49. Due to the competition between the free energies of the four elementary steps involved (Supplementary Table 4), the calculated overpotential η can be represented by a 2D volcano-type surface with respect to the free energy of the O and OH intermediates (Fig. 4c). As expected, too weak binding of adsorbate over the active site (higher ΔGOH and ΔGO - ΔGOH) impedes the adsorption of OH and increases the subsequent dehydrogenation barrier. On the other hand, too strong interaction (lower ΔGOH and ΔGO - ΔGOH) is detrimental for formation of the OOH intermediate and subsequent generation of O2. The best OER activity (η = 0.34 V) close to the peak of the 2D volcano plot was found on the NiFe LDH-PMo12 (001) surface (Fig. 4a). In contrast, (001) surface of NiFe LDH (Supplementary Fig. 13a), NiFe LDH + Vo (Supplementary Fig. 13b), NiFe LDH + MoO42− (Supplementary Fig. 13c) exhibit overpotentials of 0.79, 0.68 and 0.51 V, respectively, which are less active. Although the trend of the overpotentials (NiFe LDH > NiFe LDH + Vo > NiFe LDH + MoO42− > NiFe LDH-PMo12) reproduces the experimental results well, the difference between the calculated (0.34 V) and experimental (0.206 V at 10 mA·cm− 2) overpotentials for NiFe LDH-PMo12 remains, which might arise because of the simplified model used in the calculations. When comparing NiFe LDH with NiFe LDH + Vo, all of ΔGOH, ΔGO, and ΔGOOH have significant decrease, indicating stronger adsorption, which is brought by the electronic structure change arise from the Vo are introduced to the NiFe LDH (Supplementary Table 5). Moreover, compared with NiFe LDH, the ΔGO of NiFe LDH + MoO42− decreased significantly, and ΔGOH and ΔGOOH remained basically unchanged, indicating that the MoO42− group played a role in stabilizing the surface, and the electronic effect was the dominant effect and Hydrogen bond/Van der Waals weak interaction plays a role in assisting in enhancing OER activity. In addition, comparing NiFe LDH + Vo and NiFe LDH-PMo12, after adding MoO42− groups near the Vo, the changes of ΔGO and ΔGOH are limited, while GOOH are sharply decreased. This dramatic change is mainly caused by the Hydrogen bond/Van der Waals weak interaction between OOH adsorbent and MoO42− groups, with optimized ΔGOH and ΔGO - ΔGOH (Fig. 4c). At last, like the NiFe LDH and NiFe LDH + Vo case, NiFe LDH + MoO42− and NiFe LDH-PMo12, ΔGOH, ΔGO and ΔGOOH of NiFe LDH-PMo12 all have a significant decrease, mainly caused by the electronic structure change. Therefore, the theoretical results agree very well with the experiment that the OER kinetics on the electrode could be facilitated by Vo creation and MoO42− adsorption to improve the electronic conductivity along with the significantly enhanced electrocatalytic activity.
Structure-activity relationship and mechanism elucidation Fig. 5a illustrates the radar chart of the structure-activity relationship between a variety of OER dominant active species comprising Fe3+, α-Ni(OH)2 and Vo specials with OER activities. The increase in Fe3+ content is beneficial to OER, but the NiFe LDH-SiW12 with the most Fe3+ is not perform the best. NiFe LDH-PMo12 with proper Vo content and more α-Ni(OH)2 has the best OER activity. In addition, the samples etched by pure PW12, pure SiW12 and pure HNO3 have similar α-Ni(OH)2 content, Fe3+ and Vo content are different but η500 is similar. Similarly, the samples etched by pure HCl and pure H2SO4 have similar α-Ni(OH)2 content, Fe3+ and Vo content are different but η500 is similar. This may be affected by the synergistic effect of α-Ni(OH)2, Vo and Fe3+. Obviously, when the content of α-Ni(OH)2 is fixed, η decreases with the increase of Fe3+ content. If Fe3+ content is fixed, η will decrease with the increase of α-Ni(OH)2 content, but its influence is smaller than that of Fe3+. It seems that when Fe content is low (about < 30%), η and Fe content are close to linear relationship41, 50. Interestingly, however, η does not reflect a linear relationship with the total content of Fe3+ and α-Ni(OH)2 (Supplementary Fig. 11), and it is necessary to take Vo content into consideration. As listed in Supplementary Table 6 with the Vo content increasing, the η500 values first decrease and then increase. This is also validated by experimental results, showing that the NiFe LDH-HNO3 has the highest Vo content while its OER activity does not reach the maxima. It is probably due to the detrimental effect of excessive oxygen vacancies51. The Cdl values of all the as-etched samples are smaller than the pristine ones (Supplementary Fig. 12), showing the increased electrochemical active surface area (ECSA) which implies that the number of active sites reflected by has a weaker effect on OER activity than the intrinsic activity of active sites.
Toward understanding of these findings in a semi-quantitative approach, we fit η500 values with the Fe3+ (xFe) and α-Ni(OH)2 (xNi) content with a linear relationship, and the Vo content with a Gauss-like distribution relationship by using chemical descriptors and mathematical models. The comparison of η500 values obtained from the simulation and experimental are shown in the Fig. 5b. Trial-and-error verifications with other reported NiFe LDH based masterials (Supplementary Fig. 14 and Supplementary Table 8), proved that the Fe content in Fe-doped Ni(OH)2 is well-matched with the formula when the Fe content located between 0% ~ 25%52–56, except for few cases solely investigated on oxygen vacancy-dependent OER activity51. The developed formula denoted as “SICCAS equation” is as follows:
![](https://myfiles.space/user_files/58854_b38fc7f3db2c487f/58854_custom_files/img1627665231.png)
(where xFe, xNi and Vo are referred to percentage content, k, a, b, and c are defined as constants, in which c is the constant based on overpotential, Δη stands for the overpotential difference between the samples. Vo1 and Vo2 is equal to the optimum oxygen vacancy concentration multiplied by 100. Here, we take k =-0.6, a = 2, b = 1, c = 410, Δη = 50, Vo1 = 24.1 and Vo2 = 23.9. When Fe3+ is considered to be active sites, it can be equivalent to the variation of the total Fe content from 0% ~ 25%. It means that, the independent variable range of xFe range is 0% ~ 25%, xNi can vary from 0% ~ 75%, and Vo can vary from 22% ~ 26%. More mathematical details for the formula derivations are given in Supplementary Note 2 and Supplementary Table 7)
To our knowledge, this is the first time to formulate the inherent relationship between the respective content of dominant active sites (i.e., Fe3+, α-Ni(OH)2 and Vo) with η values. Accordingly, the nonlinear integral SICCAS equation will be helpful to design electrocatalysts better, pointing to an attractive computational and optimization route to NiFe LDH as well as other materials.