Oriented silicon steel oxide layer nondestructive determination method based on XPS and electrochemical impedance

Abstract

The invention belongs to the technical field of electrochemistry, and particularly relates to an oriented silicon steel oxide layer nondestructive determination method based on XPS and electrochemical impedance, and the method comprises the following specific steps: S1, XPS test; s2, testing electrochemical impedance of the oxide layer structure: transferring the sample to a three-electrode electrolytic cell of an electrochemical workstation, automatically injecting electrolyte into the electrolytic cell from a water inlet above after the sample is embedded into the cell position, and initializing parameters; after the three electrodes are covered with the electrolyte, an electrochemical impedance spectroscopy test is started immediately, and test data are fitted through an equivalent circuit model; s3, dynamic data association of XPS and electrochemical impedance: representing electrochemical behaviors of the multi-level structure component characteristics obtained in the step S1 from outside to inside in a corrosion environment through equivalent circuit parameters; and mapping the XPS data to the resistance value of each layer of oxide film by adopting a nonlinear regression model. According to the method, the data of the oriented silicon steel oxide layer can be rapidly and accurately measured under the condition that the sample is not damaged, and the evolution process of the oxide layer under different conditions is monitored in real time.

Description

Technical Field

[0001] The present invention belongs to the field of electrochemistry technology, and particularly relates to a method for non-destructive determination of the oxide layer of grain-oriented silicon steel based on XPS and electrochemical impedance. Background Art

[0002] Grain-oriented silicon steel is a high-performance silicon steel material with specific grain orientations, and its grains are highly ordered along the rolling direction. The uniformity, compactness, and chemical stability of the oxide layer on the surface of grain-oriented silicon steel are the core factors restricting its magnetic properties and service life. Parameters such as the composition, structure, and thickness of the oxide layer will change dynamically with the production process conditions. At present, there are certain limitations in the methods for determining the oxide layer of grain-oriented silicon steel, and it is difficult to achieve comprehensive, accurate, and rapid detection of its dynamic change process. The traditional determination methods mainly include the following: (1) Chemical dissolution method: Specific components in the oxide layer are dissolved by chemical reagents. For example, iron oxides are dissolved in an acidic solution, and then the content of the corresponding component in the solution is measured to estimate the content of this component in the oxide layer. For example, Chinese Patent CN102628848A discloses a method for determining the iron content in the oxide layer on the surface of silicon steel, which can only determine the content of a specific component, iron oxide, in the oxide layer alone, and cannot simultaneously obtain the chemical state, thickness, and dynamic corrosion resistance information of the oxide layer. Moreover, this method will cause irreversible damage to the sample piece, and at the same time requires multiple-step chemical treatment and solution composition calibration, and the time consumption is usually more than 24 hours, which is difficult to meet the requirements of rapid detection on the production line.

[0003] (2) Scanning electron microscope (SEM) and energy dispersive spectrometer (EDS) combined use: SEM is used to observe the microscopic morphology of the oxide layer to obtain the structural information of the oxide layer, such as layered, spherical, etc.; at the same time, EDS is used to analyze the composition of the oxide layer to determine the content and distribution of each element in the oxide layer. For example, Chinese Patent CN117347409A discloses a method for evaluating the quality of the oxide layer after decarburization annealing of grain-oriented silicon steel. SEM point scanning and surface scanning are performed on the surface of the decarburized plate to determine the internal structure of the oxide layer. This method can only obtain the morphology of the oxide layer and a static snapshot of the morphology and element distribution of the oxide layer, and cannot reflect the evolution law of the oxide layer under dynamic corrosion or service conditions; secondly, EDS cannot distinguish the chemical states of elements (such as Fe²⁺ and Fe³⁺), and has low detection sensitivity to light elements (such as oxygen).

[0004] (3) Glow discharge spectroscopy: Use a glow discharge spectrometer to perform sputtering detection on the sample and determine the content and distribution of elements in the sample. By measuring the total oxygen content and silicon content of the sample, the silicon content curve and the oxygen content curve are drawn to determine the total thickness of the oxide layer, the thickness of the inner and outer oxide layers, and the oxygen content of the inner oxide layer. This method can accurately obtain the oxygen content of the inner oxide layer, but the uneven sputtering rate leads to insufficient accuracy in the analysis of the oxide layer thickness and composition gradient (error>5%); and it can only determine the total amount of elements, and cannot analyze the oxide type (distinguish between SiO2 and Fe3O4); at the same time, the sputtering process is irreversible, and the sample cannot be reused for other tests.

[0005] (4) Electrochemical testing method: The dissolution amount of each layer of the oriented silicon steel oxide layer is calculated by electrochemically measuring the potential-time curve of the oriented silicon steel sample, thereby realizing the determination of each layer of the oriented silicon steel oxide layer. For example, Chinese patent CN115372441A discloses a device and method for electrochemically evaluating the oriented silicon steel oxide layer, which calculates the dissolution amount of each layer of the oriented silicon steel oxide layer by electrochemical measurement. Electrochemical testing is an indirect test that lacks support for direct data such as component thickness, and cannot synchronously obtain the real-time correlation between the evolution of the oxide layer composition and the electrochemical behavior. At the same time, the dissolution corrosion test of the oxide layer is also an irreversible test.

[0006] (5) X-ray photoelectron spectroscopy (XPS): XPS is used to analyze the surface of the oxide layer to obtain the chemical state and binding energy information of the elements in the oxide layer, and to determine the existence form and substance content of different compounds in the oxide layer. However, this test can only perform a static analysis of the oxide layer and cannot clearly determine the protective effect of the oxide layer.

[0007] Traditional measurement methods can only obtain static information about the oxide layer, and will damage the sample during the detection process. It is impossible to monitor the evolution of the oxide layer under different conditions in real time. It is difficult to use two or more methods in combination, and the test data is difficult to correlate. Summary of the invention

[0008] The purpose of the present invention is to provide a non-destructive determination method for the oxide layer of oriented silicon steel based on XPS and electrochemical impedance spectroscopy, so as to solve the problem that the traditional determination method can only obtain static oxide layer information, damages the sample during the detection process, and cannot monitor the evolution process of the oxide layer under different conditions in real time.

[0009] In order to achieve the above object, the present invention adopts the following technical scheme: A non-destructive determination method of oriented silicon steel oxide layer based on XPS and electrochemical impedance spectroscopy, the specific steps are as follows: S1: X-ray Photoelectron Spectroscopy (XPS) Test The grain-oriented silicon steel sample was cut into a square, ultrasonically cleaned in absolute ethanol for 10 minutes, dried with nitrogen, and then transferred to the XPS sample chamber. After setting the XPS test parameters, data collection was carried out on the sample, and the full spectrum and high-resolution Fe2p, O1s, and Si2p spectra were scanned. At the same time, depth profiling was performed to obtain the multi-level structural composition characteristics of the oxide layer of the grain-oriented silicon steel; S2: Electrochemical impedance spectroscopy (EIS) test of the oxide layer structure After the XPS test of the grain-oriented silicon steel sample was completed, the integrated robotic arm automatically grasped the sample and transferred the sample from the XPS sample chamber to the three-electrode electrolytic cell of the electrochemical workstation through a preset track. The electrolytic cell had a water inlet at the top and a water outlet at the bottom. After the sample was inserted into the slot, the electrolytic cell automatically injected the electrolyte from the upper water inlet and started the parameter initialization of the electrochemical workstation. Immediately after the electrolyte covered the three electrodes, the electrochemical impedance spectroscopy (EIS) test was started. The test data was fitted through an equivalent circuit model. By analyzing the parameters of each component in the equivalent circuit, information such as the resistance and capacitance of each layer of the oxide layer was obtained. The resistance value representing the three-layer oxide film structure was obtained from the fitting result. After the electrochemical test was completed, the used electrolyte was discharged through the lower water outlet, and the robotic arm took out the tested sample and waited for the next test; S3: Dynamic data correlation between X-ray photoelectron spectroscopy (XPS) and electrochemical impedance The multi-level structural composition characteristics of the oxide layer of the grain-oriented silicon steel obtained by depth profiling in the XPS test in step S1, namely the Fe³⁺ content, the thickness of SiO2, and the O / (Fe + Si) atomic ratio, were characterized by the electrochemical behavior in the corrosion environment from the outside to the inside through the equivalent circuit parameters (R P1 , R P2 , R P3 ). To achieve the precise correlation between the dynamic performance and composition of the oxide layer, a non-linear regression model was used to map the XPS data to the resistance values of each layer of the oxide film; Based on the physical mechanism hypothesis, the outer layer resistance R P1 was synergistically affected by the Fe³⁺ content and the thickness of SiO2. The middle layer resistance R P2 had a square root relationship with the thickness of SiO2, and the inner layer resistance R P3 exponentially decayed with the O / (Fe + Si) atomic ratio. By fitting the experimental data using the least squares method, the contribution weights of each component parameter were quantified. The following was the designed non-linear correlation formula: , d SiO2 represents the thickness of the SiO2 layer (nm), and k1 - k5 and λ are all fitting coefficients calibrated by experimental data.

[0010] Further, in step S2, the robotic arm adopts a high-precision vision positioning system to ensure accurate alignment of the sample with the working electrode slot of the electrolytic cell, with an error < 0.1 mm.

[0011] Further, the connection relationship of the electrical components in the fitting circuit in step S2: The starting end of the circuit is the solution resistance R C , which is connected in series at the front end of the entire circuit. R C is the solution resistance, representing the conductivity of the electrolyte. The outer layer oxide film double-layer capacitor C P1 is directly connected after R C . The outer layer oxide film structure resistance R P1 is in parallel with C P1 . Among them, R P1 is the outer layer oxide film structure resistance, reflecting the conductivity of the outer layer oxide film (FeO / forsterite). C P1 is the outer layer oxide film double-layer capacitor, representing its charge storage capacity. The middle layer oxide film structure resistance R P2 and the middle layer oxide film double-layer capacitor C P2 are in series and then in parallel with the outer layer oxide film structure resistance R P1 . R P2 is the middle layer oxide film structure resistance, reflecting the ion transport resistance of the middle layer spherical SiO2. C P2 is the middle layer oxide film double-layer capacitor, representing the charge storage characteristics of the middle layer; The inner layer oxide film resistance R P3 in series with C P3 is also in parallel with the previous two layers. R P3 is the inner layer oxide film resistance, reflecting the compactness of the inner layer flaky SiO2. C P3 is the inner layer oxide film double-layer capacitor, representing the charge storage capacity of the inner layer. The charge transfer resistance R CT between the outermost layer oxide film and the electrolyte is in parallel with the actual double-layer capacitor Q CT and is connected in parallel after the outer layer oxide film structure resistance R P1 . Among them, R CT is the charge transfer resistance between the outermost layer oxide film and the electrolyte, representing the charge transfer resistance at the interface between the outermost layer oxide film and the electrolyte. Q CT is the actual double-layer capacitor, describing the non-ideal double-layer capacitor effect; Finally, the Warburg impedance Z w is connected in series, which is used to reflect the diffusion resistance of the reactants in the oxide layer.

[0012] The oxide layer of grain-oriented silicon steel has a special three-layer structure, including FeO and fayalite on the surface layer, spherical SiO2 in the middle layer, and flaky SiO2 on the side close to the substrate. The complex structure makes it particularly important to accurately measure the properties of each layer. Electrochemical impedance testing can reflect the processes of charge transfer and diffusion in the oxide layer by measuring the impedance values at different frequencies, providing a basis for the analysis of the oxide layer structure.

[0013] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: (1) The circuit model accurately matches the actual structure of the oxide layer of grain-oriented silicon steel (surface layer FeO / fayalite, middle spherical SiO2, inner layer flaky SiO2), and analyzes the denseness, ion transport efficiency, and interface stability of each layer through the resistance and capacitance parameters of each layer; R P1 ,R P2 ,R P3 respectively represent the resistance of the three-layer oxide film structure from the outside to the inside. Quantify the data performance of the oxide layer, and at the same time introduce Zw to quantify the influence of the diffusion process on the corrosion rate, break through the limitations of the traditional single-layer or double-layer model, and significantly improve the fitting accuracy; (2) Design a non-linear correlation formula to map the XPS data to the resistance values of each layer of the oxide film, realizing the accurate correlation between the dynamic performance and composition of the oxide layer; (3) Through X-ray photoelectron spectroscopy (XPS) analysis and electrochemical impedance testing, the composition of the oxide layer can be dynamically correlated with the electrochemical data to more comprehensively understand the performance and changes of the oxide layer; this method realizes the rapid and accurate determination of the data of the oxide layer of grain-oriented silicon steel without damaging the sample, and monitors the evolution process of the oxide layer under different conditions in real time; (4) Based on the data correlation of electrochemical impedance testing, it provides guidance for the production of grain-oriented silicon steel, optimizes the production process, and improves product quality. Description of the Drawings

[0014] Figure 1 It is the Fe2p orbital spectrum of the XPS of the oxide layer of grain-oriented silicon steel in the embodiment of the present invention; Figure 2 It is the O1s orbital spectrum of the XPS of the oxide layer of grain-oriented silicon steel in the embodiment of the present invention; Figure 3 It is the Si2P orbital spectrum of the XPS of the oxide layer of grain-oriented silicon steel in the embodiment of the present invention; Figure 4 It is the fitting circuit diagram in the embodiment of the present invention; Figure 5 It is the EIS fitting result of the oxide layer of grain-oriented silicon steel in the embodiment of the present invention; Figure 6 It is the SEM diagram of the oxide layer structure of grain-oriented silicon steel in the comparative example of the present invention. Detailed implementation manners

[0015] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments. Embodiment 1

[0016] A non-destructive determination method for the oxide layer of grain-oriented electrical steel based on XPS and electrochemical impedance is as follows: S1: X-ray photoelectron spectroscopy (XPS) test: Take a grain-oriented electrical steel sample with a thickness of 0.23 mm, cut it into a size of 30×30 mm, ultrasonically clean it in absolute ethanol for 10 minutes, dry it with nitrogen, and then transfer it to the XPS sample chamber. Set the XPS test parameters as AlKα (1486.6 eV), beam spot 400 μm, Ar⁺ energy 500 eV, beam current 2 μA, and sputtering rate 0.5 nm / min, and then collect data on the sample, and scan to obtain the full spectrum and high-resolution Fe2p, O1s, and Si2p spectra (step size 0.1 eV); at the same time, perform depth profiling: pause every 5 minutes of sputtering (corresponding to a depth of 2.5 nm), and collect the Si2p spectrum until the intensity ratio of the substrate Si peak (99.3 eV) is >90%.

[0017] The depth profiling results are as Figure 1-3 shown in the figure. In the figure, A is the surface, B is the intermediate layer, and C is the substrate. Data: The area ratio of Fe³⁺ is 72%, the thickness of SiO2 = 40 min × 0.5 nm / min = 88 nm, the surface O atom concentration = 65.3%, Fe = 21.5%, Si = 13.2%, and O / (Fe + Si) is calculated to be 0.57.

[0018] S2: Electrochemical impedance (EIS) test of the oxide layer structure After the XPS test is completed, use the robotic arm to grab the sample stage to take out the sample, and transfer it to the electrolytic cell through the preset trajectory of the computer in 2 minutes and insert the sample into the working electrode hole; the robotic arm uses a high-precision vision positioning system to ensure accurate alignment of the sample with the working electrode slot of the electrolytic cell, with an error <0.1 mm; after the sample is inserted into the slot, set the Pt mesh as the counter electrode and Ag / AgCl as the reference electrode, set the distance between the three electrodes to 2 cm, inject 1.5% sodium chloride solution as the electrolyte from the upper water inlet of the electrolytic cell until the sample is submerged and stop injecting, and start the electrochemical workstation for parameter initialization; the whole process does not require complex environmental control, the transfer time of the robotic arm is ≤2 minutes, and immediately start the electrochemical impedance spectroscopy (EIS) test after the electrolyte covers the three electrodes. Fit the test data through the equivalent circuit model, and obtain information such as the resistance and capacitance of each layer of the oxide layer by analyzing the parameters of each component in the equivalent circuit. The fitting result obtains the resistance value representing the three-layer oxide film structure. The electrical component connection relationship of the fitting circuit is as Figure 4 shown: The starting end of the circuit is the solution resistance R C, connected in series at the front end of the entire circuit, R C is the solution resistance, characterizing the conductivity of the electrolyte, and the outer oxide film double-layer capacitance C P1 is directly connected to R C After that, the outer oxide film structure resistance R P1 is in parallel with C P1 , where R P1 is the outer oxide film structure resistance, reflecting the conductivity of the outer oxide film (FeO / forsterite), and C P1 is the outer oxide film double-layer capacitance, characterizing its charge storage capacity. The middle oxide film structure resistance R P2 is in series with the middle oxide film double-layer capacitance C P2 and then in parallel with the outer oxide film structure resistance R P1 , R P2 is the middle oxide film structure resistance, reflecting the ionic transport resistance of the middle spherical SiO2, and C P2 is the middle oxide film double-layer capacitance, characterizing the charge storage characteristics of the middle layer; the inner oxide film resistance R P3 in series with C P3 is also in parallel with the previous two layers, R P3 is the inner oxide film resistance, reflecting the compactness of the inner flaky SiO2, and C P3 is the inner oxide film double-layer capacitance, characterizing the charge storage capacity of the inner layer. The charge transfer resistance R CT between the outermost oxide film and the electrolyte is in parallel with the actual double-layer capacitance Q CT and is connected in parallel after the outer oxide film structure resistance R P1 , where R CT is the charge transfer resistance between the outermost oxide film and the electrolyte, characterizing the charge transfer resistance at the interface between the outermost oxide film and the electrolyte, and Q CT is the actual double-layer capacitance, describing the non-ideal double-layer capacitance effect; finally, the Warburg impedance Z w is connected in series, which is used to reflect the diffusion resistance of the reactants in the oxide layer.

[0019] The electrochemical test frequency range is set to 10 5 Hz to 10 -2 Hz, the amplitude is 10 mV, the test voltage is -0.3V, the test time is 20 min, and the results shown in Figure 5 are obtained through the fitting of Zsimpwin: R P1 = 130 Ω⋅cm 2 , R P2 = 85 Ω⋅cm 2 , R P3 = 195 Ω⋅cm 2 ; the goodness of fit χ² = 1.2×10 -3, indicating high model reliability; the used electrolyte after the electrochemical test is discharged through the lower water outlet, and the manipulator takes out the tested samples and waits for the next test. The whole test time does not exceed 30 minutes.

[0020] S3: Dynamic data correlation between X-ray photoelectron spectroscopy (XPS) and electrochemical impedance The multi-level structural composition characteristics of the oriented silicon steel oxide layer obtained by XPS depth profiling in S1, namely the Fe³⁺ content, SiO2 thickness, and O / (Fe + Si) atomic ratio, and their electrochemical behaviors in the corrosion environment from the outside to the inside are characterized by equivalent circuit parameters (R P1 , R P2 , R P3 ). To achieve the precise correlation between the dynamic performance and composition of the oxide layer, a non-linear regression model is used to map the XPS data to the resistance values of each layer of the oxide film.

[0021] Based on the physical mechanism hypothesis, the outer layer resistance R P1 is jointly affected by the Fe³⁺ content and the SiO2 thickness. The middle layer resistance R P2 has a square root relationship with the SiO2 thickness, and the inner layer resistance R P3 exponentially decays with the O / (Fe + Si) atomic ratio. By fitting the experimental data with the least squares method, the contribution weights of each component parameter are quantified. The following is the designed non-linear correlation formula.

[0022] According to the substitution of multiple data to obtain the formula constants, and then substituting the data obtained from the XPS test in step S1 into the algorithm model formula, we get: The calculation result is obtained: R P1 = 132.5 Ω·cm 2 , R P2 = 83.8 Ω·cm 2 , R P3 = 197.4 Ω·cm 2 , and the error from the actual measurement is less than 3%.

[0023] By using this method to monitor the evolution process of the oriented silicon steel oxide layer under different conditions, the production process of the oriented silicon steel is adjusted. The annealing oxygen partial pressure is increased to 20 ppm, and the Fe³⁺ content is increased to 75%. Substituting into the model, we get R P1 = 140.2 Ω·cm 2 , and the corrosion resistance is improved by 5.8%.

[0024] Comparative Example 1 A 0.23-mm-thick grain-oriented silicon steel sample was cut into a size of 10×10 mm, ultrasonically cleaned with acetone and absolute ethanol for 10 minutes in sequence, and dried with nitrogen. To avoid damage to the morphology of the oxide layer by the electron beam and enhance the conductivity, a 5-nm-thick gold film was sputtered on the sample surface; a field emission scanning electron microscope with the model of JEOL JSM-7800F was used for testing, and the magnification of the electron microscope was adjusted to 18,000+, as Figure 6 shown is the SEM image of the oxide layer structure of the grain-oriented silicon steel, the oxide layer structure and the results of surface scanning.

[0025] It was observed that the black area in the oxide layer is the region where silicon-rich elements are concentrated. The outermost layer is Fe2SiO4 or FeO, the middle layer is spherical SiO2, and the layer close to the substrate is flaky SiO2. Except for the oxides, it is all iron matrix.

[0026] This scheme for observing the oxide layer structure only provides a morphological snapshot of the oxide layer at a certain time point, cannot reflect the crack propagation or structural evolution during the corrosion process, and cannot distinguish Fe 2+ from Fe 3+ .

Claims

1. A non-destructive determination method for the oxide layer of grain-oriented silicon steel based on XPS and electrochemical impedance, characterized in that, The specific steps are as follows: S1: X-ray photoelectron spectroscopy (XPS) test Cut the grain-oriented silicon steel sample into a square, ultrasonically clean it in absolute ethanol for 10 minutes, transfer it to the XPS sample chamber after drying with nitrogen, set the XPS test parameters, and then collect data on the sample. Scan to obtain the full spectrum and high-resolution Fe2p, O1s, and Si2p spectra, and at the same time perform depth profiling to obtain the multi-level structural composition characteristics of the oxide layer of the grain-oriented silicon steel; S2: Electrochemical impedance spectroscopy (EIS) test of the oxide layer structure After the XPS test of the grain-oriented silicon steel sample is completed, the integrated robotic arm automatically grabs the sample and transfers the sample from the XPS sample chamber to the three-electrode electrolytic cell of the electrochemical workstation through a preset track. The top of the electrolytic cell is provided with a water inlet, and the bottom is provided with a water outlet; After the sample is inserted into the slot, the electrolytic cell automatically injects the electrolyte from the upper water inlet and starts the parameter initialization of the electrochemical workstation; immediately start the electrochemical impedance spectroscopy (EIS) test after the electrolyte covers the three electrodes. Fit the test data through an equivalent circuit model. By analyzing the parameters of each component in the equivalent circuit, obtain information such as the resistance and capacitance of each layer of the oxide layer. The fitting result gives the resistance value representing the three-layer oxide film structure. After the electrochemical test, the used electrolyte is discharged through the lower water outlet, and the robotic arm takes out the tested sample and waits for the next test; S3: Dynamic data correlation between X-ray photoelectron spectroscopy (XPS) and electrochemical impedance The multi-level structural composition characteristics of the oxidized layer of grain-oriented silicon steel obtained by XPS test depth profiling in step S1, namely the Fe³⁺ content, SiO2 thickness, and O / (Fe + Si) atomic ratio, are characterized by the electrochemical behavior in the corrosion environment from the outside to the inside through equivalent circuit parameters (R P1 , R P2 , R P3 ); To achieve the precise correlation between the dynamic performance and composition of the oxidized layer, a non-linear regression model is used to map the XPS data to the resistance values of each layer of the oxide film; Based on the physical mechanism hypothesis, the outer layer resistance R P1 is synergistically affected by the Fe³⁺ content and the SiO2 thickness. The middle layer resistance R P2 has a square root relationship with the SiO2 thickness, and the inner layer resistance R P3 exponentially decays with the O / (Fe+Si) atomic ratio. By fitting the experimental data using the least squares method to quantify the contribution weights of each component parameter, the following non-linear correlation formula is designed: , d SiO2 represents the thickness of the SiO2 layer (nm), and k1−k5 and λ are all fitting coefficients, which are calibrated through experimental data.

2. The non-destructive determination method of the oxide layer of grain-oriented silicon steel based on XPS and electrochemical impedance according to claim 1, characterized in that, In step S2, the robotic arm uses a high-precision vision positioning system to ensure that the sample is accurately aligned with the working electrode slot of the electrolytic cell, with an error <0.1 mm.

3. A non-destructive determination method for the oxide layer of grain-oriented silicon steel based on XPS and electrochemical impedance according to any one of claims 1 or 2, characterized in that, The connection relationship of electrical components in the fitting circuit in step S2: The starting end of the circuit is the solution resistance R C , which is connected in series at the front end of the entire circuit. R C is the solution resistance. The outer oxide film double-layer capacitor C P1 is directly connected after R C . The outer oxide film structure resistance R P1 is in parallel with C P1 , where R P1 is the outer oxide film structure resistance and C P1 is the outer oxide film double-layer capacitor. The middle oxide film structure resistance R P2 and the middle oxide film double-layer capacitor C P2 are connected in series and then in parallel with the outer oxide film structure resistance R P1 , where R P2 is the middle oxide film structure resistance and C P2 is the middle oxide film double-layer capacitor. The inner oxide film resistance R P3 in series with C P3 is also in parallel with the previous two layers, where R P3 is the inner oxide film resistance and C P3 is the inner oxide film double-layer capacitor. The charge transfer resistance R CT of the outermost oxide film in contact with the electrolyte and the actual double-layer capacitor Q CT are in parallel and are connected in parallel after the outer oxide film structure resistance R P1 , where R CT is the charge transfer resistance of the outermost oxide film in contact with the electrolyte and Q CT is the actual double-layer capacitor, describing the non-ideal double-layer capacitor effect; finally, the Warburg impedance Z w is connected in series to reflect the diffusion resistance of the reactants in the oxide layer.

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