CoNiFe OXIDE NANOSTRUCTURED CATALYSTS, AND USES THEREOF CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application claims the benefit of priority to U.S. Provisional Application No. 63/353,182, filed June 17, 2022, the contents of which is incorporated herein by reference in its entirety. FIELD [0002] The present disclosure is directed to CoNiFe nanostructured catalysts, and the use of such catalysts in the electrochemical conversion of methane to methanol. In particular, the present disclosure is directed to nanocube catalysts having the formula Co _1-x Ni _x Fe ₂ O ₄ . INTRODUCTION [0003] Methane (CH ₄ ) is not only the second most prominent greenhouse gas ¹ that contributes to global warming, but also a potentially useful feedstock which can be converted to valuable products for the chemical industry. ^2-4 Given ever-worsening environmental issues and the inevitable depletion of fossil fuel for energy, the development of efficient and eco-friendly strategies for improving direct methane conversion (DMC) to value-added chemicals are urgently required. ^5-7 The traditional Fischer-Tropsch method for methanol synthesis depends primarily on the transformation of syngas (a mixture of CO and H ₂ ) to useful chemicals through energy-intensive reactions, which makes it economically and environmentally prohibitive. ⁸ Furthermore, the C-H activation of CH ₄ molecule and over-oxidation of products also largely limits the conversion kinetics and the selectivity of CH ₄ oxidation. ² Thus, it is critical to develop highly active catalysts with tunable selectivity for the efficient conversion of CH ₄ . In recent years, the conversion of CH ₄ to oxygenates has garnered a high level of interest for resource management and carbon capture. Consequently, numerous alternative strategies have been explored toward the development of DMC technologies using liquid- phase reactions that involve catalysis, ⁹ enzyme catalysis, ¹⁰ biocatalysis, ¹¹ photocatalysis, ⁸ and electrocatalysis. ¹² Due to their low cost, controllable reactions, and easy scale-up, electrocatalytic CH ₄ oxidation provides an attractive, environmentally friendly approach for the efficacious generation of valuable chemical products. Efficient electrocatalysts for the conversion of CH ₄ are essential to improve the thermodynamic and kinetics of the process in contrast to the competing oxygen evolution reaction (OER). [0004] Great efforts have been devoted to the exploration of high-performance electrocatalysts, ^{13, 14} electrochemical reaction cell designs, ^{15, 16} the incorporation of microbes ^{11, 17} or solar cells, ^{18, 19} and density functional theory (DFT) calculation techniques ^{20, 21} to promote the conversion of CH ₄ and its utilization under ambient conditions. Despite the significant advance in the field of CH ₄ conversion to date, one of the great challenges that remain towards the optimal oxidation of CH ₄ is the design of highly active electrocatalysts for C-H activation and product selectivity. In this regard, the development of effective electrocatalysts for the DMC to oxygenates is a critical prerequisite. SUMMARY [0005] The present disclosure is directed to CoNiFe nanostructured catalysts, and the use of such catalysts in the electrochemical conversion of methane to methanol. In particular, the present disclosure is directed to nanocube catalysts having the formula Co _1-x Ni _x Fe ₂ O ₄ . [0006] In one embodiment of the disclosure, there is included an electrochemical catalyst, comprising: (a) a trimetallic oxide of the formula wherein the catalyst is in the form of nano-cubes; and (b) carbon. [0007] In one embodiment, the electrochemical catalysts of the present disclosure are used for the electrochemical oxidation of methane [0008] In one embodiment of the disclosure, there is included a method for preparing methanol from methane in an electrochemical process, the process comprising; (a) introducing methane into an anode chamber of an electrochemical reactor, wherein the anode chamber comprises an anode comprising the electrochemical catalyst of the disclosure; (b) introducing a catholyte into a cathode chamber of the electrochemical reactor, wherein the cathode chamber comprises a cathode; (c) introducing a voltage across the anode and the cathode, whereby at least a portion of the methane is oxidized to methanol; and (d) collecting the methanol from the anode chamber. [0009] Other features and advantages of the present application will become apparent from the following detailed description. It should be understood, however, that the detailed description and the specific examples while indicating preferred embodiments of the application are given by way of illustration only, since various changes and modifications within the spirit and scope of the application will become apparent to those skilled in the art from this detailed description. BRIEF DESCRIPTION OF THE DRAWINGS [0010] The present disclosure will now be described in greater detail with reference to the drawings in which: [0011] Figure 1 is an (a) SEM image and (b) corresponding size distributions of NiFe PBA template catalyst; (c) Thermogravimetry curve of the NiFe PBA template under air conditions at heating rate of 2 °C min ^-1 ; (d) Image of the different ratios of CoNiFe-N/C catalyst inks, in one embodiment of the disclosure. [0012] Figure 2. Are SEM images of Co _y Ni _1-y -Fe ₂ O ₄ -N/C catalysts, (a) y=0, (b) y=0.2, (c) y=0.4, (d) y=0.6, (e) y=0.8, and (f) y=1, respectively [0013] Figure 3 are SEM images of Co _y Ni _1-y -Fe ₂ O ₄ -N/C catalysts, (a) y=0, (b) y=0.2, (c) y=0.4, (d) y=0.6, (e) y=0.8, and (f) y=1, respectively, in one embodiment of the disclosure. [0014] Figure 4 are SEM images of Co _y Ni _1-y -Fe ₂ O ₄ catalysts, (a) y=0, (b) y=0.2, (c) y=0.4, (d) y=0.6, (e) y=0.8, and (f) y=1, respectively, in one embodiment of the disclosure. [0015] Figure 5 shows (a) Average size of Co _y Ni _1-y -Fe ₂ PBA derived catalysts under Air- and Ar-conditions, respectively; (b) Scheme of the structure proposed for the PBA particles in CoFeNi, in one embodiment of the disclosure. The scale between the core and the shell is arbitrary. [0016] Figure 6 are (a)-(b) LSV curves of CoNiFe-N/C-0.8 and CoNiFe-8 in Ar- and N ₂ -saturated 0.1 M Na ₂ SO ₄ solution, respectively; (c)-(d) LSV curves of CoNiFe-N/C-0.6 and CoNiFe-0.6 in Ar- and CH ₄ -saturated 0.5 M Na ₂ CO ₃ solution, respectively, in one embodiment of the disclosure. Scan rate: 20 mV s ^-1 . [0017] Figure 7 are (a)-(e) LSV curves of CoNiFe-N/C-x (x= 0, 0.2, 0.4, 0.6, 1) catalysts in Ar- and N ₂ -saturated 0.1 M Na ₂ SO ₄ solution with a scan rate of 20 mV s ^-1 , respectively. (f) the corresponding current density difference of the CoNiFe-N/C catalysts measured at the N ₂ -saturated and the Ar-saturated solution, in one embodiment of the disclosure. [0018] Figure 8 are (a)-(e) LSV curves of CoNiFe-x (x= 0, 0.2, 0.4, 0.6, 1) catalysts in Ar- and N ₂ -saturated 0.1 M Na ₂ SO ₄ solution with a scan rate of 20 mV s ^-1 , respectively. (f) the corresponding current density difference of the CoNiFe-x catalysts measured at the N ₂ -saturated and the Ar-saturated solution, in one embodiment of the disclosure. [0019] Figure 9 are (a)-(e) LSV curves of CoNiFe-N/C-x (x= 0, 0.2, 0.4, 0.8, 1) catalysts in Ar- and CH ₄ -saturated 0.5 M Na ₂ CO ₃ solution with a scan rate of 20 mV s ^-1 , respectively. (f) current density difference of the CoNiFe-N/C-x catalysts measured at the CH ₄ -saturated and the Ar-saturated solution, in one embodiment of the disclosure. [0020] Figure 10 are (a)-(e) LSV curves of CoNiFe-x (x= 0, 0.2, 0.4, 0.8, 1) catalysts in Ar- and CH ₄ -saturated 0.5 M Na ₂ CO ₃ solution with a scan rate of 20 mV s ^-1 , respectively. (f) the current density difference of the CoNiFe-x catalysts measured at the CH ₄ -saturated and the Ar-saturated solution, in one embodiment of the disclosure. [0021] Figure 11 are Co _0.6 Ni _0.4 -Fe ₂ O ₄ -N/C catalyst: (a) TEM image; (b) HRTEM image; (c) TEM mappings. Co _0.8 Ni _0.2 -Fe ₂ O ₄ -N/C catalyst: (d) TEM image; (e) HRTEM image; (f) TEM mappings. [0022] Figure 12 are constructed crystal structures of (a) bulk Co _y Ni _1-y Fe ₂ O ₄ , (b) Co _y Ni _1-y Fe ₂ O ₄ -CH ³ , (c) Co _y Ni _1-y Fe ₂ O ₄ -N ₂ , (d) Co _y Ni _1-y Fe ₂ O ₄ -N/C and (e) Co _y Ni _1-y Fe ₂ O ₄ - N/C-CH ₃ , (e) Co _y Ni _1-y Fe ₂ O ₄ -N/C-N ₂ [0023] Figure 13 are simulated XRD patterns of built crystalline Co _y Ni _1-y Fe ₂ O ₄ (a) and Co _y Ni _1-y Fe ₂ O ₄ -N/C (b) models, in one embodiment of the disclosure. [0024] Figure 14 are (a) XRD patterns and (b) Raman spectra of the as-prepared CoNiFe-N/C-x catalysts. [0025] Figure 15 are XPS survey scans of the as-prepared CoNiFe-N/C-x catalysts, x refers to the content of Co replacement of Ni atoms; High-resolution XPS spectra of CoNiFe-N/C-x catalysts for Co 2p (b), Ni 2p (c), Fe 2p (d), C 1s (e) and N 1s (f). [0026] Figure 16 are high-resolution XPS spectra of CoNiFe-N/C-x catalysts for N 1s, in one embodiment of the disclosure. [0027] Figure 17 are (a) Contents distribution of nitrogen species of CoNiFe-N/C- x catalysts; High-resolution XPS spectra of CoNiFe-N/C-x catalysts for O 1s (b) and the corresponding oxygen species distribution (c); (d) Olatt/Ov ratios of the CoNiFe-N/C-x catalysts. [0028] Figure 18 are high-resolution XPS spectra of CoNiFe-N/C-x catalysts for O 1s, in one embodiment of the disclosure. [0029] Figure 19 are EIS spectra of: (a) Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C catalyst under the Ar- and N ₂ -saturated conditions; (b) various composition ratios of the CoNiFe-N/C catalysts under the N ₂ -saturation condition [Inset: equivalent circuit model (Point: original data; Line: fitting data)]; (c) the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst under the Ar- and CH ₄ -saturated conditions; (d) various composition ratios of the CoNiFe-N/C catalysts under CH ₄ - saturation conditions, in one embodiment of the disclosure [Inset: equivalent circuit model]. [0030] Figure 20 are ECSA comparisons for (a) CoNiFe-N/C-0.4, (b) 0.6, (c) 0.8 composites based on their double-layer capacitances using CV at different scan rates from 10 to 100 mV s ^-1 in N ₂ -saturated 0.1 M Na ₂ SO ₄ . (d) the corresponding plots of the current density at -0.75 V vs. the scan rate, in one embodiment of the disclosure. [0031] Figure 21 are ECSA comparisons for (a) CoNiFe-N/C-0.4, (b) 0.6, (c) 0.8 composites based on their double-layer capacitances using CV at different scan rates from 10 to 100 mV s ^-1 in CH ₄ -saturated 0.5 M Na ₂ CO ₃ . (d) the corresponding plots of the current density at 1.0 V vs. the scan rate, in one embodiment of the disclosure. [0032] Figure 22 are chronoamperometric curves for the NRR recorded at different potentials over the CoNiFe-NC-0.8 catalyst, in one embodiment of the disclosure. [0033] Figure 23 show (a) NH ₃ yields and the corresponding FEs of CoNiFe-N/C- 0.8 after two-hour electrolysis at the different potentials; NH ₃ yields and the corresponding FEs of CoNiFe-N/C-x (b) and CoNiFe-x (c) after two-hour electrolysis at -1.4 V vs Ag/AgCl, respectively; Products analysis under different potentials of the electrochemical CH ₄ oxidation at Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C in the anode chamber: (d) ¹ H-NMR spectrum of the products after two-hour electrolysis; (e) Products yield and FE (f) of methanol and 2- propanol; (g) Illustration of the integrated electrochemical system for the simultaneous CH ₄ oxidation and N ₂ reduction; (h) Anode current density of the CH ₄ oxidation with or without the NRR in the cathode chamber; (i) Chronoamperometric curves of the cathode chamber for the NRR at -0.8 V vs Ag/AgCl, in one embodiment of the disclosure. [0034] Figure 24 are (a) Calibration curve for the detection of N ₂ H ₄ concentration; (b) UV-vis spectra of the cathode chamber solution after two-hour electrolysis under an Ar- and N ₂ -saturated condition, in one embodiment of the disclosure. [0035] Figure 25 are product yield percentage of the DMC over the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst at different applied potentials, in one embodiment of the disclosure. [0036] Figure 26 are EPR spectra of the electrochemical CH ₄ oxidation over the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst (DMPO-·O ₂ - formed in methanol dispersions, 0.3 M; Blue (middle): open voltage condition; Red (top): with potential), in one embodiment of the disclosure. [0037] Figure 27 are adsorption energy comparison of the CH ₄ absorption over the surface of CoNiFe-x and CoNiFe-N/C-x catalysts, in one embodiment of the disclosure. [0038] Figure 28 are PDOS of (a) Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C and (b) Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C surface; (c) & (d) corresponding PDOS of CH ₄ and N ₂ adsorption, respectively, in one embodiment of the disclosure. (Inset shows the electron density difference between these four optimized structures, blue region: electron rich; red region: electron deficit). [0039] Figure 29 are PDOS of carbon layer for (a) Co _0.6 Ni _0.4 Fe ₂ O ₄ -NC and (b) Co _0.6 Ni _0.4 Fe ₂ O ₄ -NC surface, and the corresponding CH ₄ adsorption (c) and N ₂ adsorption (d) in one embodiment of the disclosure. DESCRIPTION OF VARIOUS EMBODIMENTS [0040] (I) DEFINITIONS [0041] Unless otherwise indicated, the definitions and embodiments described in this and other sections are intended to be applicable to all embodiments and aspects of the present application herein described for which they are suitable as would be understood by a person skilled in the art. [0042] The term “comprising” and its derivatives, as used herein, are intended to be open ended terms that specify the presence of the stated features, elements, components, groups, integers, and/or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and/or steps. The foregoing also applies to words having similar meanings such as the terms, “including”, “having” and their derivatives. [0043] The term “consisting” and its derivatives, as used herein, are intended to be closed terms that specify the presence of the stated features, elements, components, groups, integers, and/or steps, but exclude the presence of other unstated features, elements, components, groups, integers and/or steps. [0044] The term “consisting essentially of”, as used herein, is intended to specify the presence of the stated features, elements, components, groups, integers, and/or steps as well as those that do not materially affect the basic and novel characteristic(s) of features, elements, components, groups, integers, and/or steps. [0045] Terms of degree such as “substantially”, “about” and “approximately” as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. These terms of degree should be construed as including a deviation of at least ^5% of the modified term if this deviation would not negate the meaning of the word it modifies. [0046] As used in this application, the singular forms “a”, “an” and “the” include plural references unless the content clearly dictates otherwise. [0047] In embodiments comprising an “additional” or “second” component, the second component as used herein is chemically different from the other components or first component. A “third” component is different from the other, first, and second components, and further enumerated or “additional” components are similarly different. [0048] The term “and/or” as used herein means that the listed items are present, or used, individually or in combination. In effect, this term means that “at least one of” or “one or more” of the listed items is used or present. [0049] The term “nanocube” as used herein refers to the structural atomic arrangement of the trimetallic oxide in cube-like form having dimensions having nanoscale dimensions, for example, about 10 nanometers to 1 micrometer. [0050] The term “carbon” as used herein includes both non-graphitic and graphitic forms of carbon. [0051] The term "adjacent" as used herein, when referring to the carbon layer and the nano-cubes, means that the two are in proximity with one another with little or no intervening open space. [0052] The term “layer” as used herein refers to a layer of carbon atoms or molecules on a substrate which is adjacent or near the trimetallic oxide nano-cubes. [0053] (II) ELECTROCHEMICAL CATALYSTS [0054] The present disclosure is directed to highly active electrochemical catalysts for the efficient conversion of methane to methanol. In addition, the same catalysts are useful for the conversion of nitrogen gas to ammonia. [0055] Accordingly, in one embodiment, the present disclosure is directed to an electrochemical catalyst, comprising: (i) a trimetallic oxide of the formula wherein the catalyst is in the form of nano-cubes; and (ii) carbon. [0056] In one embodiment, the trimetallic oxide is Co _0.8 Ni _0.2 Fe ₂ O ₄ . [0057] In one embodiment, the trimetallic oxide is Co _0.6 Ni _0.4 Fe ₂ O ₄ . [0058] In one embodiment, the catalyst has XRD peaks of 18.28°, 26.15°, 35.69° and 43.36°. [0059] In a further embodiment, x is an integer between 0.01 and 0.99, or 0.1 to 0.9. [0060] In another embodiment, x is about 0.20, about 0.40, about 0.60, or about 0.80. [0061] In one embodiment, the carbon is elemental carbon. In one embodiment, the carbon may contain other atoms such as oxygen or nitrogen which do not affect the catalytic activity of the electrochemical catalysts of the disclosure. [0062] In another embodiment, the elemental carbon is graphite or graphene. [0063] In one embodiment, the carbon is in the form of a layer adjacent to the nano- cube. [0064] In one embodiment, the carbon, optionally in the form of a layer, is a structure of carbon atoms which are held together by covalent, ionic or other strong intramolecular forces. Layers may be planar or contoured. In one embodiment, there are more than one carbon layers which may be held together via intermolecular forces, such as van der Waals interactions. Examples of carbon layers include, but are not limited to, graphite layers, graphene sheets, and carbon films. A carbon layer may also refer to a carbonaceous coating the outer surface of the nanocube. [0065] In one embodiment, the dimensions of the nanocubes with the adjacent carbon layer is between 10 nm and 1000 nm [0066] In one embodiment, the dimensions of the nanocubes with the adjacent carbon layer is between 500 nm and 700 nm. [0067] In one embodiment, the dimensions of the nanocubes with the adjacent carbon layer is between 600 nm and 700 nm. [0068] In one embodiment, the dimensions of the nanocubes with the adjacent carbon layer is between 640 nm. (III) ELECTROCHEMICAL PROCESSES [0069] The present disclosure is directed to electrochemical catalysts for the efficient conversion of methane to methanol, and also of nitrogen gas to ammonia. Accordingly, in one embodiment of the disclosure, there is included a method for preparing methanol from methane in an electrochemical process, the process comprising; (a) introducing methane into an anode chamber of an electrochemical reactor, wherein the anode chamber comprises an anode comprising the electrochemical catalyst of the disclosure; (b) introducing a catholyte into a cathode chamber of the electrochemical reactor, wherein the cathode chamber comprises a cathode; (c) introducing a voltage across the anode and the cathode, whereby at least a portion of the methane is oxidized to methanol; and (d) collecting the methanol from the anode chamber [0070] In another embodiment, the process further produces isopropanol. [0071] In one embodiment, the electrochemical catalyst is Co _0.6 Ni _0.4 Fe ₂ O ₄ . [0072] In one embodiment, the voltage is between 0.5 V and 1.5 V. [0073] In one embodiment, the present disclosure is also directed to a method for preparing ammonia from nitrogen gas (N ₂ ) in an electrochemical process, the process comprising; (a) introducing ammonia into a cathode chamber of an electrochemical reactor, wherein the cathode chamber comprises a cathode comprising the electrochemical catalyst of the disclosure; (b) introducing an anolyte into am anode chamber of the electrochemical reactor, wherein the anode chamber comprises an anode; (c) introducing a voltage across the anode and the cathode, whereby at least a portion of the nitrogen gas is reduced to ammonia; and (d) collecting the ammonia from the cathode chamber [0074] In another embodiment, the electrochemical catalyst is Co _0.8 Ni _0.2 Fe ₂ O ₄ . [0075] In one embodiment, the voltage is between 0.5 V and 1.5 V. [0076] In another embodiment, the catalysts of the present disclosure are dual use and are useful as anodes and cathodes in an electrochemical process for preparing methanol from methane and ammonia from nitrogen gas in an electrochemical process, the process comprising; (a) introducing methane into an anode chamber of an electrochemical reactor, wherein the anode chamber comprises an anode comprising the electrochemical catalyst of the disclosure; (b) introducing ammonia into a cathode chamber of an electrochemical reactor, wherein the cathode chamber comprises a cathode comprising the electrochemical catalyst of the disclosure; (c) introducing a voltage across the anode and the cathode, whereby at least a portion of the methane in the anode chamber is oxidized to methanol and at least a portion of the nitrogen gas is reduced to ammonia in the cathode chamber; and (d) collecting the methanol from the anode chamber and the ammonia from the cathode chamber [0077] In one embodiment, the electrochemical catalyst in the anode chamber is Co _0.6 Ni _0.4 Fe ₂ O ₄ . [0078] In one embodiment, the electrochemical catalyst in the cathode chamber is Co _0.8 Ni _0.2 Fe ₂ O ₄ . [0079] In one embodiment, the voltage is between 0.5 V and 1.5 V [0080] Although the disclosure has been described in conjunction with specific embodiments thereof, if is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present disclosure. EXAMPLES [0081] The operation of the disclosure is illustrated by the following representative examples. As is apparent to those skilled in the art, many of the details of the examples may be changed while still practicing the disclosure described herein. [0082] Experimental Section [0083] Chemicals [0084] Nickel (II) nitrate hexahydrate (99%, Ni(NO ₃ ) ₂ ·6H ₂ O), cobalt (II) nitrate hexahydrate (98%, Co(NO ₃ ) ₂ ·6H ₂ O), sodium citrate (99%, Na ₃ C ₆ H ₅ O ₇ ), potassium hexacyanoferrate (III) (99% ⁺ , K ₄ Fe(CN) ₆ ), sodium sulfate (99%, Na ₂ SO ₄ ), sodium carbonate (99% ⁺ , Na ₂ CO ₃ ), sodium hydroxide (97% ⁺ , NaOH), sodium salicylate (99%, C ₇ H ₅ O ₃ Na), sodium hypochlorite (5%, NaClO), sodium nitroferricyanide (III) (99% ⁺ , C ₅ FeN ₆ Na ₂ O), hydrazine (98% ⁺ , N ₂ H ₄ ), and ammonium chloride (99% ⁺ , NH ₄ Cl) were purchased from Sigma-Aldrich Chemical Reagent Ltd.. Nafion (1 wt.%) solution, hydrogen peroxide (30%, H ₂ O ₂ ), sulfuric acid (99% ⁺ ), methanol and ethanol were purchased from Aladdin Ltd. All reagents were of analytical grade and used without further purification. Additionally, an anion exchange membrane (AEM) was purchased from the DuPont Company (N2050TX, thickness: 0.3 mm). The deionized (DI) water (18.2 MΩ cm) used in all experiments was obtained from a Nanopure Diamond ^TM ultrapure water system. [0085] Synthesis of NiFe PBA NCs template: Uniform Ni-Fe PBA nanocubes (NCs) were synthesized via our previously reported method. ⁴ In a typical procedure, 6 mmol of Ni(NO ₃ ) ₂ ·6H ₂ O and 9 mmol of Na ₃ C ₆ H ₅ O ₇ were dissolved in 200 mL of deionized (DI) water to form solution A. Simultaneously, 4 mmol of K ₄ Fe(CN) ₆ was dissolved in another 200 mL of DI water to form solution B. Subsequently, solution B was added drop- by-drop into solution A under magnetic stirring for 20 min. After that, the mixed solution was aged at room temperature for 24 h. The following collection by centrifugation and washed with water and ethanol, the precipitate was dried at 60°C overnight. [0086] Synthesis of NiFe ₂ O ₄ and NiFe ₂ O ₄ -N/C NCs: Two as-prepared NiFe PBA samples (200 mg each) were further pyrolyzed at 350°C under Air and Ar atmosphere for 2 h at a heating rate of 2 °Cmin ⁻¹ , respectively. After cool down, 110.8 mg and 112.4 mg were obtained, which were ascribed to NiFe ₂ O ₄ and NiFe ₂ O ₄ -N/C NCs, respectively. The catalyst-carbonized yield was calculated as follows: [0087] Yield of catalyst (%) = (mCarbonization / mCatalyst precursor) * 100% [0088] Preparation of CoNiFe-x PBA NCs templates: CoNiFe-x PBA nanocubes (NCs) were synthesized using the same method as the synthesis of NiFe PBA. In a typical route, the content of Co was used to replace the Ni ions in the NiFe PBA, such that the total Co and Ni precursors were 6 mmol, where x refers to the Co contents (x = 0.2, 0.4, 0.6, 0.8). For example, to prepare the sample with x = 0.2, 4.8 mmol of Ni(NO ₃ ) ₂ ·6H ₂ O, 1.2 mmol of Co(NO ₃ ) ₂ ·6H ₂ O and 9 mmol of Na ₃ C ₆ H ₅ O ₇ were dissolved in 200 mL of DI water to form Solution A. Meanwhile, 4 mmol of K ₄ Fe(CN) ₆ was dissolved in another 200 mL of DI water to form Solution B. Subsequently, Solution B was added dropwise into Solution A under magnetic stirring for 20 min. After that, the mixed solution was aged at room temperature for 24 h. The precipitate was separated and purified through centrifugation and washing with DI water and ethanol; it was then dried at 60°C overnight to obtain the CoNiFe-0.2 PBA NCs, CoNiFe-0.4 PBA NCs, CoNiFe-0.6 PBA NCs and CoNiFe-0.8 PBA NCs samples. [0089] Synthesis of Co _y Ni _1-y Fe ₂ O ₄ and Co _y Ni _1-y Fe ₂ O ₄ -N/C NCs: Two of the as- prepared CoNiFe-x PBA NCs (200 mg each) were further pyrolyzed at 350°C under Air and Ar atmosphere for 2 h at a heating rate of 2 °Cmin ⁻¹ , respectively. After cooling, 121.8 mg, 134.2 mg, 130 mg and 122.2 mg were obtained under the air atmosphere, which was ascribed to Co _0.2 Ni _0.8 Fe ₂ O ₄ NCs, Co _0.4 Ni _0.6 Fe ₂ O ₄ NCs, Co _0.6 Ni _0.4 Fe ₂ O ₄ NCs and Co _0.8 Ni _0.2 Fe ₂ O ₄ NCs, respectively. Simultaneously, under the Ar atmosphere, 144.2 mg, 154.2 mg, 134.6 mg and 127.2 mg, corresponded to Co _0.2 Ni _0.8 Fe ₂ O ₄ -N/C NCs, Co _0.4 Ni _0.6 Fe ₂ O ₄ -N/C NCs, Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C NCs and Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C NCs, respectively. [0090] Preparation of CoFe PBA NCs template: CoFe PBA nanocubes (NCs) were prepared using the same method as the synthesis of NiFe PBA. 6 mmol of Co(NO ₃ ) ₂ ·6H ₂ O and 9 mmol of Na ₃ C ₆ H ₅ O ₇ were dissolved in 200 mL of DI water to form Solution A. Meanwhile, 4 mmol of K ₄ Fe(CN) ₆ was dissolved in another 200 mL of DI water to form Solution B. Afterwards, Solution B was added dropwise into Solution A under magnetic stirring for 20 min. After that, the mixed solution was aged at room temperature for 24 h. The following collection was made by centrifugation and washing with water and ethanol; the precipitates were dried at 60°C overnight, and the obtained sample was named as CoFe PBA NCs. [0091] Synthesis of CoFe ₂ O ₄ and CoFe ₂ O ₄ -N/C NCs: Two of the as-prepared CoFe PBA NCs (200 mg) were further pyrolyzed at 350^°C under Air and Ar atmosphere for 2 h at a heating rate of 2 °Cmin ⁻¹ , respectively. After cooling, 107.8 mg and 124.2 mg were obtained, which were ascribed to CoFe ₂ O ₄ and CoFe ₂ O ₄ -N/C NCs, respectively. [0092] Electrochemical measurements: The electrochemical characterization of the as-prepared Co _y Ni _1-y Fe ₂ O ₄ -N/C and Co _y Ni _1-y Fe ₂ O ₄ -N/C catalysts was carried out in a single cell (30 mL) with the required gas inflow systems using an electrochemical workstation (Voltalab Potentiostat PGZ301). Each as-prepared 5 mg sample was dispersed in a mixed 480 µL ethanol, 480 µL water and 40 µL Nafion (0.5 wt.%) solution under continuous sonication for 60 min. The obtained catalyst inks (10 µL) were coated onto a well-polished and cleaned glassy carbon electrode (Ø3 mm, 0.071 cm ² ) as the working electrodes. A saturated Ag/AgCl and graphite rod (Ø3 mm) were used as the reference and counter electrodes, respectively. For the nitrogen reduction reaction (NRR), before the electrochemical experiment, ultra-pure nitrogen gas (99.999%) was purged into the electrolyte solution for at least 20 min to achieve saturation.0.1 M Na ₂ SO ₄ solution was chosen as the electrolyte for all electrochemical nitrogen reduction experiments. To test the CH ₄ oxidation activity, ultra-pure CH ₄ gas (99.999%) was purged into a 0.5 M Na ₂ CO ₃ solution, which was used as the electrolyte for the CH ₄ oxidation reaction. To assess the hydrogen evolution behavior and other interferences, measurements were carried out under the argon-saturated and open potential conditions, respectively. [0093] Linear sweep voltammetry (LSV) was employed to evaluate the catalytic activity under Ar-, N ₂ -and CH ₄ -saturated conditions (sweep rate: 20 mV s ^-1 ). To determine the electrochemical surface area (ECSA) of these catalysts, the cyclic voltammograms (CVs) of these electrocatalysts were recorded in the double-layer region at different scan rates (10, 20, 30, 40, 50, 60, 70, 80, 90, 100 mV s ^-1 ) under different conditions for the NRR (electrolyte: 0.1 M Na ₂ SO ₄ ) and for the CH ₄ oxidation (electrolyte: 0.5 M Na ₂ CO ₃ ), respectively. The charge transfer resistance for the NRR and DMC was investigated using electrochemical impedance spectroscopy (EIS) (10 ^-2 - 10 ⁵ Hz). All experiments were performed at room temperature (20 ± 2°C). [0094] As presented in Fig.1a, a field-emission scanning electron microscopic (FE- SEM) image shows that hollow Ni-Fe NCs were successfully synthesized via a facile Prussian blue analogues (PBA) method, with an average size of 208 nm (Fig.1b). The weight loss of the template was investigated via thermogravimetric analysis. As depicted in Fig.1c, the first stage of weight reduction at nearly 80°C could be explained by the loss of surface water molecules. The weight loss of the second stage (340°C) was attributed to the conversion of the PBA structure to the final metal oxides. As illustrated in Scheme 1, with different Co/Ni ratio regulation and the thermal conversion of Co _y Ni _1-y Fe-PBA at 350°C under Ar conditions, the CN- groups of the PBA were converted into the N-doping carbon layer (N/C), where Co, Ni and Fe species were transformed to CoNiFe oxides. ³² Concurrently, as Co-doping content increased, the color of the CoNiFeO-N/C-x (x refers Co ratio, 0, 0.2, 0.4, 0.6, 0.8 and 1) catalyst inks became dark brown (Fig. 1d). Considering the function of the carbon layer in the electrochemical reaction, the carbon- free catalysts were also discussed, where these of Co _y Ni _1-y Fe-PBA were ripened at 350°C by air-condition to form the CoNiFeO-x catalysts. [0095] The morphology of the as-prepared CoNiFe catalysts was examined by FE- SEM. As shown in Fig.2, with increasing Co content, they showed similar morphologies of nanocubes (NCs) when subjected to treatment under Ar conditions; however, the dimensions (Fig.3) and microstructures of the CoNiFe-N/C-x catalysts obviously changed due to the growth of the carbon layer. Meanwhile, when treated under air conditions, as shown in Fig.4, they maintained a similar framework and the surfaces of the CoNiFe-x catalysts became much cleaner without the generation of the carbon layer, suggesting that the carbon layer could be removed through the air condition treatment. All the CoNiFe PBA samples showed higher yields when treated under Ar conditions than under air conditions (Table 1), further confirming that a carbon layer was generated on the CoNiFe catalyst surface under the Ar pyrolysis. Interestingly, as the Co content increased, both of the yields exhibited similar distribution trends, which might be ascribed to the metal- support interactions. ³³ In addition, the average size of CoNiFe catalysts was calculated and analyzed in Fig.5a, which displayed a positive relationship with the Co atom content. As shown in Fig.5b, with the addition of Co, the dimensions of these NCs with carbon layers were increased from 207 to 640 nm. Without the carbon layer, it was enlarged from 162 to 475 nm, indicating that the size fluctuation could be mainly ascribed to the formation of the carbon layer. The elemental composition of the CoNiFe-N/C catalysts was investigated using an energy-dispersive X-ray spectrometer (EDS) (Table 2), which explained that the N-doped carbon was generated from the CoNiFe PBA. [0096] To explore Co/Ni ratio catalysts for the electrochemical redox performance, linear sweep voltammetry (LSV) was employed to evaluate the electrochemical activity toward the NRR and the DMC. As shown in Figs.6a & 6b and Figs.7 & 8, the cathodic scans of the LSV of a series of Co/Ni composition ratio catalysts were recorded in an Ar- and N ₂ -saturated 0.1 M Na ₂ SO ₄ solution for comparison, revealing that the composition of CoNiFe and the carbon layer support strongly affected the NRR activity. Figs.7f & 8f present the current density differences of the LSVs measured in the N ₂ -saturated electrolyte and the Ar-saturated electrolyte, revealing that the Co _0.8 Ni _0.2 Fe-N/C catalyst exhibited the highest catalytic activity for the NRR. Meanwhile, for the performance of the CH ₄ oxidation operating in an Ar- and CH ₄ -saturated 0.5 M Na ₂ CO ₃ electrolyte, in Figs. 6c & 6d, both CoNiFe-N/C-0.6 and CoNiFe-0.6 exhibited high CH ₄ electrochemical oxidation behavior. As displayed in Figs.9 & 10, the LSV curves also demonstrated that the anodic current densities of the CoNiFe-N/C catalysts exhibited a significant improvement over the CoNiFe catalysts. Compared with the carbon-layer-free samples, the calibrated curves further indicated that the onset CH ₄ oxidation potentials at the CoNiFe-N/C were lower, with the lowest being 0.49 V vs Ag/AgCl at CoNiFe-0.4. Although the onset potential of CoNiFe-N/C was 0.54 V, it exhibited a remarkable anodic current density for CH ₄ oxidation. Overall, the CoNiFe-N/C-0.6 catalyst was employed as the optimized electrode for the CH ₄ oxidation reaction. Based on the above data and analysis, the carbon layer support with CoNiFe oxides would be beneficial for improving electrochemical performance, especially for the NRR and DMC. [0097] To further explore the crystal structure of these catalysts, transmission electron microscopy (TEM), crystal model construction and X-ray diffraction patterns (XRD) were employed. In the TEM images (Fig.11), the optimized CoNiFe-N/C-0.8 and CoNiFe-N/C-0.6 catalysts presented cubical structures comprised of nanoparticles, and the carbon film could also be easily seen. High-resolution TEM (HRTEM) images (Figs. 11b & 11e) depicted the lattice fringes of 0.209 nm, 0.252 nm and 0.482 nm, which could be ascribed to the facet (002) of NiFe ₂ O ₄ , (311) of Co _y Ni _1-y Fe ₂ O ₄ , and (111) of CoFe ₂ O ₄ , respectively. Further, the lattice constant of amorphous carbon was found to be 0.342 nm on the edge of the cube, corresponding to the (002) facet, indicating that the crystal structure of the synthesized catalysts was Co _y Ni _1-y Fe ₂ O ₄ -N/C. The lattice fringes of Co _y Ni _1-y Fe ₂ O ₄ and CoFe ₂ O ₄ were interlaced, indicating that heterojunctions were created. Further, TEM-mapping images demonstrated the uniform metal mixing of Co, Ni, Fe composites (Figs.11c & 11f). These results confirmed that Co _y Ni _1-y Fe ₂ O ₄ -N/C catalysts were successfully synthesized in our study. In addition, certain lattice fringes were broken, which suggested that some defects were generated. Following these data, the Co _y Ni _{1- y} Fe ₂ O ₄ , Co _y Ni _1-y Fe ₂ O ₄ -N/C and the corresponding adsorption models were built as illustrated in Fig.12. In these models, the molecular connecting groups were considered as the main catalytic active sites. Further, the corresponding simulated XRD patterns were calculated and displayed in Figs.13a & 13b. As seen in Fig.14a, the XRD patterns of the as-prepared CoNiFe-N/C-x samples had characteristic peaks located at 18.28°, 26.15°, 35.69° and 43.36°, which belonged to the facet (111) of CoFe ₂ O ₄ (PDF # 22- 1086), (002) of N-doping carbon (PDF # 50-1249), (311) and (400) of NiFe ₂ O ₄ (PDF # 10- 0325), respectively, which agreed with the earlier HRTEM results. The Co _y Ni _1-y Fe ₂ O ₄ -N/C catalysts were further investigated by Raman spectroscopy (Fig.14b). Two peaks located at 2198 cm ^-1 and 2225 cm ^-1 for CoNiFe-x (except x ≠ 1) were assigned to the vibrations of CN(Fe ²⁺ )-Ni ^3+/2+ and CN(Fe ³⁺ )-Ni ²⁺ , respectively; CoNiFe samples (except x ≠ 0) showed two similar signal peaks at 2111 cm ^-1 and 2143 cm ^-1 , which were attributed to CN(Fe ²⁺ )-Co ^3+/2+ and CN(Fe ³⁺ )-Co ²⁺ , respectively. Moreover, it exhibited two weak signals at 1346 cm ^-1 and 1585 cm ^-1 , corresponding to the D-band and G-band of the carbon material, respectively. [0098] The surface chemical states and bonding environments of the Co _y Ni _{1- y} Fe ₂ O ₄ -N/C samples were investigated using the X-ray photoelectron spectroscopy (XPS) technique. In Fig.15a, the full XPS survey of these catalysts determined the presence of Co, Ni, Fe, C, N, and O elements. The intensity of the Ni signal decreased with the increase of the Co ratio, which was consistent with the EDX analysis. The high-resolution XPS spectra of Co 2p, Ni 2p, Fe 2p, C 1s and N 1s are shown in Figs.15b-f. The binding energy of three metals had obvious shifts with the change of the Co/Ni ratio, the peaks of Co and Ni shifted to higher binding energies, while Fe signals moved to lower binding energies, indicating strong trimetallic interaction effects. For the carbon layer, the C 1s peaks of the CoNiFe-x samples were affected by the content of Co atoms. In the corresponding N 1s analysis (Fig.15f), the N 1s signal had a weak fluctuation. As shown in Fig.16, four fitted peaks located at 398.4, 399.5400.4 and 403.2 eV from the Co _y Ni _{1- y} Fe ₂ O ₄ -N/C samples were ascribed to pyridinic-N, metal-N, Pyrrolic-N and oxidized-N, respectively, which confirmed the formation of the N-doped carbon layer. After quantitatively calculating each content of the N-groups (Fig.17a), it was found that the higher metal-N percentage might be beneficial for the DMC and NRR, and that more pyridinic-N species facilitated the performance of the DMC. In Fig.17b, the O 1s plots displayed significant changes in intensity and curve shapes (Fig.18). The signal of O 1s could be divided into four peaks positioned at 530.7, 531.9, 532.8 and 534.9 eV, corresponding to lattice oxygen with metals (O _Latt , O-I), oxygen vacancy (O _V , O-II), surface-adsorbed oxygen (O _ad , O-III) and C-O-H (O-IV), respectively. Furthermore, the percentage of each oxygen species was calculated in Fig.17c, as the surface-absorbed oxygen group might play an important role in electrochemical performance. Vacancy engineering indicated that the oxygen vacancy was a promising strategy for enhancing the activity of the oxygen evolution reaction (OER). Impressively, in this work, higher oxygen vacancies did not appear to promote the performance of the DMC. As shown in Fig.17d, the ratio of the O _Latt /O _V curve displayed a volcano-like trend, which revealed that the highest value of O _Latt /O _V was favorable for improving the NRR and the DCM. This might be ascribed to the triple-metal inner regulation effect for hindering the OER performance. [0099] To evaluate the rate-determining step of the NRR and the DCM over the surface of CoNiFe-N/C-x catalysts, electrochemical impedance spectroscopy (EIS) was performed to analyze the charge transfer of the redox conditions. As shown in Figs.19a - 19c, the CoNiFe-N/C-0.8 catalyst exhibited the smallest semicircle, which suggested that it possessed excellent charge transfer at the electrode surface in the electrochemical NRR. An equivalent circuit model (Fig.19c inset) was employed to fit the EIS curves with the corresponding values listed in Table 3. during the various ratio of Co/Ni, the Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C catalyst displayed the lowest charge transfer resistance (R _ct ), R _ct(CE) and R _ct(AE) , demonstrating that the optimized Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C catalyst had an excellent electron transfer capacity in the electrochemical NRR. Meanwhile, the EIS measurements made in a 0.5 M Na ₂ CO ₃ electrolyte (Figs.19d - 19f) revealed that the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C had a lower Rct compared to the other Co/Ni ratio catalysts. The smallest Rct values (Table 4) with the CoNiFe-N/C-0.6 catalyst were consistent with the LSV measurements, where the highest anodic current density was achieved. The electrochemically active surface areas (ECSAs) of the Co _y Ni _1-y Fe ₂ O ₄ -N/C catalysts were estimated based on their double-layer capacitances. Figs.20 & 21 showed the orders of Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C > Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C > Co _0.4 Ni _0.6 Fe ₂ O ₄ -N/C and Co _0.6 Ni _0.4 Fe ₂ O ₄ - N/C > Co _0.4 Ni _0.6 Fe ₂ O ₄ -N/C > Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C in the N ₂ -saturated Na ₂ SO ₄ and CH ₄ - saturated Na ₂ CO ₃ solution, respectively. The Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C for the NRR and the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C for the DMC exhibited the highest ECSA, suggesting that they possessed the most abundant electrochemically active sites for the NRR and the DMC, respectively. These electrochemical results indicated that the optimized catalysts for N ₂ reduction and CH ₄ oxidation were Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C and Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C, respectively. [00100] To evaluate the electrochemical activity of the as-prepared CoNiFe-based catalysts for N ₂ reduction and CH ₄ oxidation, they were performed in a homemade double chamber with a graphite rod as the counter electrode at room temperature. Fig. 22 presents the chronoamperometric curves of CoNiFe-NC-0.8 for the NRR, showing that the current density increased with the increasing cathodic potential from -1.2 to -1.6 V, which is consistent with the LSV results displayed in Fig. 3a. As shown in Fig. 23a, Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C exhibited the highest NH ₃ yield rate of 52.35 μg h ^-1 mgcat. ^-1 at -1.4 V vs Ag/AgCl and the maximum FE of 15.35% at -1.3 V vs Ag/AgCl. Compared with the CoNiFe-N/C-x samples at the potential of -1.4 V vs Ag/AgCl (Fig.23b), only the catalysts with x = 0.4, 0.6 and 0.8 exhibited catalytic activity for the NRR, where the Co _0.8 Ni _0.2 Fe ₂ O ₄ - N/C showed the best NRR performance. To investigate the effect of the carbon layer, the CoNiFe-x catalysts were also tested at the same potential of -1.4 V vs Ag/AgCl. As shown in Fig.23c, the highest NH ₃ yield rate of 23.22 μg h ^-1 mgcat. ^-1 was achieved at CoNiFe- 0.2, while the highest FE of 10.14% was obtained at CoNiFe-0.6. The aforementioned results suggested that the interactions between Co _y Ni _1-y Fe ₂ O ₄ (y = 0.4, 0.6 and 0.8) and the carbon layer were beneficial for improving the NRR activity. The possible formation of the by-product (N ₂ H ₄ ) was further investigated using the Watt and Chrisp method. Fig. 24a presents a plot with a series of standard N ₂ H ₄ , showing that the absorbance of N ₂ H ₄ was linearly increased with the increase of its concentration. However, as shown in Fig. 24b, the UV-vis spectra of the solution after two-hour electrolysis under the Ar- and N ₂ - saturated conditions were almost identical; there was no absorbance change, confirming that no N ₂ H ₄ was generated during the NRR at the Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C and that N ₂ was reduced to NH ₃ . On the other hand, the by-product H ₂ was detected by gas chromtograph (GC), showing that the hydrogen evolution reaction occurred at the cathode during the NRR. Some promising Co/Ni/Fe-based catalysts recently reported for the NRR, such as CoO QDs/rGO, ⁴³ CoFe ₂ O ₄ /rGO, ⁴⁴ single atoms Co-N/C, ⁴⁵ NiCo2O ₄ -N/C, ⁴⁶ single-atom Fe/N-O/C, ⁴⁷ and Fe-N/C-carbon nanotubes, ⁴⁸ etc., were compared in Table 5, showing that the Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C developed in the present study exhibited superb N ₂ reduction activity. [00101] For CH ₄ oxidation in the anode chamber, Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst was tested in the anode chamber. The DMC products were collected after two hours of the electrolysis of the CH ₄ -saturated Na ₂ CO ₃ solution at the potential of 0.8 V vs Ag/AgCl and analyzed by ¹ H nuclear magnetic resonance spectroscopy ( ¹ H NMR), methanol and 2- propanol were detected with yields of 722.6 mmol gcat. ^-1 h ^-1 and 306.4 mmol gcat. ^-1 h ^-1 , respectively, as listed in Table 6. To fully utilize both the anodic and cathodic reactions, an integrated electrochemical system was assembled and tested for the simultaneous NRR at Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C in the cathode chamber and the DMC at Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C in the anode chamber as illustrated in Fig.23g. As displayed in Fig.23d, the ¹ H-NMR spectra of the products collected after two-hour electrolysis at the different potentials exhibited a strong peak, which was attributed to methanol. The intensity of this peak was increased with the increase of the potential from 0.8 to 1.1 V; however, its intensity was decreased when the potential was further increased to 1.2 V. A by-product 2-propanol was also observed in Fig.23d. To further confirm the results, a control experiment was carried out at the open-circuit potential under the same conditions for 2 h; no methanol and 2-propanol were detected in the resultant ¹ H-NMR spectrum. The rates of the methanol and 2-propanol formation were determined after the two-hour electrolysis at different applied electrode potentials. As shown in Fig.23e and Fig.25, methanol was the main product with the highest yield rate of 5070.7 mmol gcat. ^-1 h ^-1 obtained at 1.1 V vs Ag/AgCl and a maximum selectivity of 82.8% at 0.8 V vs Ag/AgCl with the yield of 1925.47 mmol gcat. ^-1 h ^-1 , respectively. The FEs of the production of methanol and 2-propanol are presented in Fig.23f; the highest FE (9.02%) for methanol production was achieved at 0.8 V, while the highest FE (6.94%) for 2-propanol formation was obtained at 0.9 V. As shown in Table 6, the yield and FE of methanol were increased by 2.7 and 2.4 times compared to those measured without NRR, respectively, while there was a weak improvement for 2-propanol. Fig.23h showed that the anodic current density measured from the LSVs conveyed some improvement. The impact of the integrated electrochemical system on the NRR was also examined (Table 7), showing that the NH ₃ yield rate was enhanced by 1.6 times. The stability of the integrated two electrochemical processes was further tested (Fig. 23i), showing high stability during the 12-hour electrolysis. The aforementioned results showed that the integrated electrochemical system was efficient for the simultaneous NRR in the cathode chamber and DMC in the anode chamber. In comparison with the published work on the DMC at various anode materials (Table 8), such as TiO ₂ , ¹⁸ Ni-based catalysts, ^{15, 23} ZrO ₂ -based catalysts, ^{13, 14, 24} and CuO/CeO ₂ catalyst, ¹⁹ Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst exhibited the best conversion of CH ₄ to CH ₃ OH. [00102] To explore the electronic structures and suitable Co/Ni molar ratios of the as-prepared Co _y Ni _1-y Fe ₂ O ₄ -N/C NCs catalyst, density functional theory (DFT) calculations were performed to reveal the adsorption energies for the DMC and the NRR at Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C and Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C, respectively. Combining the obtained electron paramagnetic resonance (EPR) spectra (Fig. 26) with the previous work, ⁹ the super oxygen radical (·O ₂ -) was determined to be the active species, demonstrating that Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C could selectively activate CH ₄ to form ·CH ₃ . Further, the adsorption energy of CH ₄ over the surface of CoNiFe-x and CoNiFe-N/C-x was calculated by Eq. S11 in the Supporting Information. As shown in Fig.27, the Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst displayed the lowest CH ₄ adsorption energy, which confirmed that it could serve as a viable catalyst for the effective activation of CH ₄ . As Ma et al. ²⁴ and Park et al. ¹³ demonstrated in their studies, if the methanol product happened to be over-oxidized to 1- propanol or 2-propanol, the formaldehyde or acetaldehyde intermediates could be easily detected in the ¹ H-NMR spectra; however, there were no signals related to the generation of these two by-products. Based on the ¹ H-NMR results and the information reported in the literature, ²² the simultaneous reaction routes for the DMC and the NRR could be summarized as follows: [00103] Integrated electrochemical system: [00104] Anode: [00105] CH ₄ + 2OH- → CH ₃ OH + H ₂ O + 2e- (1) [00106] 3CH ₄ + 6OH- → CH ₃ CHOHCH ₃ + 5H ₂ O + 6e- (2) [00107] 4OH- → 2H ₂ O+ O ₂ + 4e- (3) [00108] Cathode: [00109] N ₂ + 6H ₂ O + 6e- → 2NH ₃ + 6OH- (4) [00110] 2H ₂ O + 2e- → H ₂ + 2OH- (5) [00111] In this integrated system, CH ₄ was selectively oxidized to methanol and 2- propanol by the active radical (·O ₂ -) over a Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalyst in the anode chamber, which was ascribed to the tri-metal-carbon layer interactions. The electrons generated from the anodic oxidation reactions (1)–(3) were transferred to the cathode Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C, which facilitated the cathodic reductions (4) & (5). Subsequently, the possible mechanism of the combined electrochemical system could be presented in Scheme 2. The electron transfer pathways during the CH ₄ and NRR over the optimized catalysts were also explored in Fig. 28. For the CH ₄ oxidation on the surface of Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C, the partial density of states (PDOS) exhibited highly concentrated electrons, and the shape of the electron orbital distribution was also significantly altered after adsorbing the CH ₄ molecule. The overlapping of Co _0.6 Ni _0.4 -3d bands, Fe 3d bands and O 2p bands suggested a strong coupling between the tri-metals and oxygen. Additionally, following the activation of CH ₄ , electron density difference (EDD) mapping indicated that the generated electrons would quickly transfer to the Co _0.6 Ni _0.4 atoms, as shown in the inset of Fig.28c. Besides, the PDOS of the carbon layer (Figs.29a & 29b) revealed that N-doping carbon played a critical role in the electron transfer, as it provided efficient electron transfer channels. Co _0.6 Ni _0.4 and Fe were thus considered as the main catalytic centers for the DMC. and In the NRR condition, compared with the bulk catalyst, the intensity of the dominant peak of Co _0.8 Ni _0.2 in Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C was decreased due to the electron transfer with N ₂ (Fig. 28d). Meanwhile, the wave and overlay of the Co _0.8 Ni _0.2 -3d bands and O-2p bands on the catalyst suggested that the N ₂ molecules could be easily activated by Co _0.8 Ni _0.2 active sites and active oxygen groups, which was agreed with the EDS mapping, where the electrons released from Co _0.8 Ni _0.2 were transferred to N ₂ . In Figs. 29c & 29d, the PDOS of the carbon layer from the Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C catalyst revealed that the intensity of the N-2p bands was improved with the adsorption of N ₂ , indicating that it accelerated the electron transfer. The DFT results demonstrated that the interactions between the trimetallic CoNiFe and carbon layers greatly improved the performance of the CH ₄ oxidation and the N ₂ reduction. [00112] Electrochemical activity evaluation [00113] A two-chamber cell separated by a pre-treated cation exchange membrane (CEM) was used to investigate the products of each chamber. When a single reduction or oxidation reaction was investigated in one chamber, the other chamber was examined without gas bubbling. For the NRR experiments, a graphite rod was used as the counter electrode. In the cathode chamber with N ₂ gas, the generation of ammonia (NH ₃ ) was measured and quantitatively analyzed by the modified indophenol blue method. ^1,2 As follows, 2 mL of the cathode effluent was taken, then 2 mL of solution A (10.0 g salicylic acid and 10.0 g sodium citrate dissolved in 0.32 M NaOH solution), 1 mL 0.05 M NaClO and 0.2 mL of 0.01 g mL ^-1 C5FeN6Na ₂ O was dropped into the testing solution in turn. After 2-hours, the concentration was measured at 655 nm by UV-vis spectrophotometer (Varian Cary 50). A calibration curve was generated using 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 µg mL ^-1 of standard NH ₄ Cl vs. the corresponding UV-vis absorbance, giving a clear linear relationship (y = 0.113 x + 0.013, R ² = 0.999) in triplicate parallel experiments. Each time, the open circuit and Ar-saturated conditions for the NRR experiment were taken as the baseline for the NH ₃ yield calculation to avoid any exogenous sources of nitrogen compounds. ³ The optimized generation in the NRR was calculated as follow: N ₂ -saturated, Ar-saturated and open- circuit conditions for the NRR experiments, respectively. [00115] The NH ₃ yield was calculated by the following equation: [00116] is the obtained NH ₃ concentration; V is the reaction electrolyte solution (20 mL); mcat. is the mass of the catalyst, and t is the time of electrolysis reaction (t = 2 h). [00117] Faradaic efficiency was obtained as follows: where F is the Faraday constant (96485.3 C mol ^-1 ); Q is the quantity of electric charge by the applied potential. Besides, the potential by-product (N ₂ H ₄ ) was also investigated by our formerly reported method. ⁴ There was no change for the initial and 2 h for the NRR in the UV-vis spectrum at 455 nm, suggesting that there is no any N ₂ H ₄ generation in this system. [00119] In the anode chamber, the CH ₄ oxidation reaction was investigated. The pure CH ₄ gas was continuously purged into 0.5 M Na ₂ CO ₃ electrolyte at a flow rate of 5 mL min ^-1 . All the gas products were detected by gas chromatography. Liquid products of the CH ₄ electrochemical oxidation were analyzed by ¹ H nuclear magnetic resonance spectroscopy ( ¹ H NMR) measured on a 600 MHz NMR spectrometer (Bruker). Before the measurement, a 0.35 mL sample from the anode chamber was mixed with 0.05 wt% tetramethylsilane (TMS) in 0.35 mL D2O. The yield of products, FEs, the corresponding selectivity, and the CH ₄ conversion rate were calculated as follows: [00120] Yields (mmol gcat. ^-1 h ^-1 ) = mmol of products / g of catalysts / h of the reaction time (S4) [00121] FE (CH ₃ OH, %) = 0.1929 * n (CH ₃ OH, µmol) * 100% / Q (S5) [00122] FE (CH ₃ CHOHCH ₃ , %) = 0.1929 * n (CH ₃ CHOHCH ₃ , µmol) * 100% / Q (S6) [00123] Selectivity of CH ₃ OH = 100% * n (CH ₃ OH) / ( n (CH ₃ OH) + n (CH ₃ CHOHCH ₃ ) (S7) [00124] Selectivity of CH ₃ CHOHCH ₃ = 100% * n (CH ₃ CHOHCH ₃ ) / (n (CH ₃ OH) + n (CH ₃ CHOHCH ₃ ) (S8) where Q is the total quantity of the electric charge. [00125] The integrated reaction system was comprised of two working electrodes and one reference electrode. Where the Co _0.8 Ni _0.2 Fe ₂ O ₄ -N/C and Co _0.6 Ni _0.4 Fe ₂ O ₄ -N/C catalysts were employed as the working electrodes in the cathode and anode chambers, respectively. N ₂ gas and CH ₄ gas were simultaneously purged into the corresponding electrolytes. Considering the measurement of the current density, the reference electrode would be employed in the same chamber with the targeted reaction. After two-hour electrolysis, the corresponding anode- and cathode-electrolyte would be collected and further analyzed. A blank experiment was carried out to get rid of possible interferences, including blank GCE and NiCoFe catalysts under the open potential condition. [00126] Characterization of nanomaterials [00127] The morphologies of CoNiFe-N/C and CoNiFe catalysts were characterized using a field-emission scanning electron microscope (FE-SEM) (FEI Quanta 250) and the high-resolution transmission electron microscopy (HRTEM) (FEI Tecnai F30 electron microscope, using a 200 kV accelerating voltage). An X-ray diffractometer with Cu Kα radiation (D/max-2400, Japan, source light at the wavelength (λ) of 0.1541 nm) was employed to investigate the crystallinity structure of the as-prepared catalysts. X-ray Photoelectron Spectroscopy (XPS) (Scienta Omicron) with a monochromatic Al Kα x-ray source was used to analyze their chemical composition and oxidation states. Raman spectra were recorded at 532 nm by utilizing a Raman spectrophotometer (Renishaw Canada Ltd.). Thermogravimetric (TG) analysis was performed with a QMA200M thermal analyzer (METTLER TOLEDO) at a heating rate of 2 °C min ^-1 under air conditions. The radicals were detected via electron paramagnetic resonance (EPR) spectroscopy, which was conducted with a Bruker ECS106 X-band spectrometer (Bruker A200, Germany). The gas products were transferred using a gas-tight syringe (Hamilton) and examined using a gas chromatograph (GC, Shimadzu, GC-2014, Column:silica gel) that was equipped with a thermal conductive detector (TCD). [00128] Theoretical calculations [00129] To explore the electronic structures and electron transfer in the NRR and CH ₄ oxidation systems, the Co _y Ni _1-y Fe ₂ O ₄ and Co _y Ni _1-y Fe ₂ O ₄ -N/C with one layer of carbon structure models were built based on the NiFe ₂ O ₄ template. The optimization of the constructed structures was enabled by the CASTEP module with the Perdew-Burke- Ernzerhof (PBE) functional of the generalized gradient approximation (GGA). Additionally, the position of the Co doping was thought to be the replacement of Ni atoms with Co atoms. A 2 × 2 × 13D triclinic NiFe ₂ O ₄ cell (a = 8.480 Å, b = 8.480 Å, c = 8.480 Å, α = β = γ = 90°) was used for the doping and the addition of carbon layer cells. A k-point set of 2 × 1 × 1 and an energy cut-off of 320 eV were performed to optimize the geometry of the constructed models with medium k-point set. The convergence criterion was 1.0 × 10 ^-5 eV for energy and 0.05 eV Å ⁻¹ for force. The adsorption energy (E) was calculated as follow: are the electronic energies of the Co _y Ni _1-y Fe ₂ O ₄ -N/C, Co _y Ni _1-y Fe ₂ O ₄ , carbon, CH ₄ and H unit cell, respectively. For the first principle calculation of the activation of CH ₄ to·CH ₃ , an energy cut-off of 350 eV was performed. A force tolerance, SCF tolerance, and electronic field were 0.05 eV Å ⁻¹ , 1.0 × 10 ^-5 eV per atom and -5 eV vs. Vacuum, respectively. The experimental optimal potential on the electrode reaction was performed by adding the value of -n eU (n: the number of electrons in the DMC; U: the electric potential). [00131] While the present disclosure has been described with reference to what are presently considered to be the preferred examples, it is to be understood that the application is not limited to the examples described herein. To the contrary, the present disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. [00132] All publications, patents and patent applications are herein incorporated by reference in their entirety to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated by reference in its entirety. Where a term in the present disclosure is found to be defined differently in a document incorporated herein by reference, the definition provided herein is to serve as the definition for the term.

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Table 1. Yields of Co _y Ni _1-y -Fe PBA catalysts after the high-temperature treatment under the Air- or Ar-condition.

Table 2. EDX analysis of different Co _y Ni _1-y Fe ₂ O ₄ -N/C catalysts

Table 3. Parameter analysis of the equivalent circuit model corresponding to the Nyquist plots of the as-prepared Co _y Ni _1-y Fe ₂ O ₄ -C/N under N ₂ -saturated conditions. R _ohm = Resistance of solution, R _ct(CE) = Charge transfer resistance, R _ct(AE) = Charge transfer and recombination resistance, C = Capacitance of double layer, W = Warburg impedance (mass transfer).

Table 4. Parameter analysis of the equivalent circuit model corresponding to the Nyquist plots of the as-prepared Co _y Ni _1-y Fe ₂ O ₄ -C/N under the CH ₄ -saturated conditions. R _ohm = Resistance of solution, R _ct(CE) = Charge transfer resistance, R _ct(AE) = Charge transfer and recombination resistance, C = Capacitance of double layer, W = Warburg impedance (mass transfer).

^. _s ^t _{s l} ^{y a} _t ^a _{c d} ^e _s ^a _b - _e ^F / _i N ^/ _o C _e ^h t ^t _{a n} ^o _i ^t _{a i} ^{x f} ₂ N _y ^{b s} _i ^s _e ^h _t ⁿ _y ^{s a} _i ⁿ _o m m ^al _a ^c _i ^m _e ^h _c ^o _r ^t _c ^e _l ^ef _o ⁿ _o ^s i _r ^a _p ^m _o ^C. _{5 e} ^l 8 _b ⁰ ₇ 4 ₂ able 6. Comparison of CH ₄ oxidation performance at 0.8 V vs Ag/AgCl for 2 h with or ithout N ₂ gas flow in the cathode chamber.

able 7. Comparison of the NRR performance at -0.8 V vs Ag/AgCl for 2 h with or without H ₄ gas in the anode.

Table 8. Summaries of electrocatalytic CH ₄ oxidation systems at room temperature.