Aluminum foil surface oxide dielectric constant calculation method and system

Abstract

The invention provides an aluminum foil surface oxide dielectric constant calculation method and system, and the method comprises the steps: simulating the surface reaction of aluminum and water through reaction molecular dynamics, calculating the radial distribution function of the surface of a model after the reaction reaches equilibrium, and carrying out the systematic comparison of the radial distribution function with a known oxide structure model in a standard crystallography database. A known crystal model highly matched with the structural characteristics of a simulated product is screened out, complete crystallographic parameters of the model are extracted, and the dielectric constant of a corresponding substance is solved by using a first principle. According to the method, cross-scale connection from a surface reaction process to dielectric property calculation is realized, and the accuracy of dielectric constant calculation is improved; the problems of performance uncertainty and the like of oxidation films generated by the aluminum foil in different traditional formation processes are solved, and a new solution is provided for preparation of high-performance electronic information materials.

Description

A method and system for calculating the dielectric constant of oxides on aluminum foil surfaces Technical Field

[0001] This invention relates to the fields of computer modeling, computer simulation, and electrode materials, and particularly to a method and system for calculating the dielectric constant of oxides on the surface of aluminum foil. Background Technology

[0002] Anode aluminum foil, as a key basic material for aluminum electrolytic capacitors, undergoes a formation process to generate a dense oxide film on the surface of the tunnel holes. This oxide film plays a crucial role in the electrical performance and long-term stability of the capacitor. The dielectric constant, as an important parameter characterizing the dielectric properties of the oxide film, is one of the core factors affecting the performance of aluminum electrolytic capacitors. In actual formation processes, due to differences in aluminum foil crystal orientation, formation voltage, temperature conditions, and formation dielectric, the types and microstructures of oxides formed on the surface of the tunnel holes vary significantly, making it difficult to accurately predict and control the dielectric constant of the oxide film.

[0003] Currently, oxide films typically possess multi-layered structures accompanied by complex surface effects and defect characteristics. The dielectric constant of oxide films is primarily measured experimentally, but this method is easily limited by various factors such as sample preparation conditions, material surface state, preparation process, and testing conditions, resulting in large testing errors, high costs, and difficulty in reflecting the essence of the microstructure. With the development of computational materials science, first-principles calculation methods (density functional theory, molecular dynamics) can analyze the electronic structure and atomic interactions of materials from the atomic scale, providing a new approach for the theoretical calculation of dielectric constants. However, single-scale calculation methods cannot simultaneously account for the relationship between microscopic reaction processes and dielectric properties, leading to limitations in describing interactions at different scales and their impact on the dielectric constant.

[0004] To address the aforementioned issues, there is an urgent need for a cross-scale computational method that can combine computational techniques of different scales to connect the surface reactions, structural evolution, and dielectric property calculations during the oxide film formation process across scales, thereby improving the reliability and applicability of the calculation results while ensuring computational accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a calculation scheme for the dielectric constant of surface oxides on aluminum foil, aiming to solve the problem that in existing traditional formation processes, due to differences in surface structure and process conditions, the dielectric constant of oxides is difficult to predict and control accurately, thus affecting the performance stability and reliability of aluminum electrolytic capacitors. This invention identifies the type of oxide by analyzing the interactions between molecules and calculates its dielectric constant, thereby providing a calculation scheme for the dielectric properties of surface oxides with good universality and low cost. Specifically, this invention provides the following technical solutions:

[0006] On one hand, this invention provides a method for calculating the dielectric constant of oxides on the surface of aluminum foil. The method includes: Step 1, constructing a reaction model of the interaction between the aluminum foil surface and water molecules; Step 2, performing molecular dynamics simulation based on the reaction model to obtain a post-reaction model; the molecular dynamics simulation applies external conditions corresponding to the actual aluminum foil formation process; Step 3, based on the post-reaction model, extracting and analyzing the trajectory of key thermodynamic parameters over time until the reaction process reaches equilibrium to obtain a stable-state trajectory; Step 4, performing structural analysis on the stable-state trajectory to obtain the characteristic peak values ​​of the radial distribution functions of aluminum and oxygen atoms in the reaction products, and determining the corresponding characteristic peak values ​​of the simulated products. Step 5: Compare the obtained characteristic peak positions with the characteristic peak positions of known oxide structure models in the standard crystallography database, select the known oxide models that match closely, and extract the complete crystallographic parameters of the known oxide models; Step 6: Calculate the ionic and electronic contributions of the known oxide models to the dielectric properties based on the complete crystallographic parameters, and then calculate the dielectric constant; Step 7: Based on the calculation results of Step 6, analyze the frequency dependence of the dielectric properties and obtain the relationship spectrum between the frequency of ionic and electronic contributions and the dielectric constant; Step 8: Based on the relationship spectrum, extract the dielectric constant at the specified frequency as the final dielectric constant.

[0007] Preferably, in step 2, the external conditions include: the system temperature of the reaction model is determined by the actual formation temperature; an electric field is applied perpendicular to the surface of the aluminum foil, and the magnitude of the electric field is determined by the actual formation voltage; the total simulation time of the reaction model is not less than 800 ps.

[0008] Preferably, in step 3, the key thermodynamic parameters include instantaneous temperature and total energy, and the total energy includes the system's kinetic energy and potential energy; the change trajectory is a curve showing the change of instantaneous temperature and total energy fluctuation data over time; the equilibrium state is determined as follows: when the average values ​​of instantaneous temperature and total energy remain stable within a preset time interval, and the fluctuation amplitude of the average values ​​is less than a preset threshold, and there is no continuous large fluctuation over time, the reaction process is determined to have reached equilibrium.

[0009] Preferably, step 4 further includes: using the atomic coordinate data at each moment in the steady-state trajectory as input data, and under the set radius range and step size conditions, performing frame-by-frame statistical and time-averaged processing on the atomic spacing between aluminum atoms and oxygen atoms to obtain the radial distribution function curve:

[0010] Where ρ is the density; N is the number of particles in the system; T is the total computation time; and r is the radius of the atom from the center. ΔN represents the thickness of the spherical shell taken near radius r; ΔN represents the thickness of the shell within the distance interval [r, r+]. Within [the reference atom], the average number of atoms counted around the reference atom.

[0011] Preferably, in step 5, the comparison method is as follows: the characteristic peak position of the simulated product obtained in step 4 is used as the main comparison parameter; the radial distribution function of the corresponding aluminum-oxygen atom pair is calculated using the known oxide model data in the standard crystallography database as input, and its characteristic peak position is further calculated to form a set of comparison structure characteristic parameters; the characteristic peak position of the simulated product is matched one by one with the characteristic peak position in the set of comparison structure characteristic parameters, and when the two are within the set distance deviation threshold range, the corresponding known oxide model is selected as a candidate matching structure.

[0012] Preferably, the electronic contribution is calculated as follows: Under the condition of fixed lattice structure and no displacement of ion positions, an external electric field perturbation is introduced, and only the response of electronic polarization to the external electric field is considered to obtain the dielectric constant of the corresponding known oxide, which is used as the value of the electronic contribution. The ion contribution is calculated as follows: Based on electronic polarization, the structural response of lattice ions under the action of the external electric field is further considered to obtain the dielectric constant of the corresponding known oxide, which is used as the value of the ion contribution. Preferably, the formula for calculating the electronic contribution is:

[0013] Where Ω represents the volume of the calculated system, P e Where E is the electronic polarization intensity, and E is the applied electric field intensity. Characterizes the first-order response relationship of electronic polarization to an applied electric field.

[0014] Preferably, the formula for calculating the ion contribution is:

[0015] Where Ω represents the volume of the calculated system, This represents the ionic polarization intensity caused by the displacement of lattice ions under the action of an applied electric field, where E represents the applied electric field intensity. Characterize the first-order response relationship of ions in an applied electric field.

[0016] Preferably, in step 6, the dielectric constant is calculated as follows:

[0017] In the formula: The dielectric constant is given at a frequency of ω. This represents the electronic contribution at frequency ω. The contribution of ions at frequency ω.

[0018] Preferably, in step 7, the relationship graph is established as follows: in the calculation results of step 6, data on the change of dielectric function with frequency are obtained, the main diagonal component of the dielectric function tensor corresponding to each frequency point is extracted, and the average is processed to obtain the equivalent dielectric constant at each frequency point. The data on the change of the equivalent dielectric constant with frequency is used as the data sequence of the change of dielectric constant with frequency. Based on the frequency and the corresponding dielectric constant in the data sequence, a relationship graph is drawn.

[0019] Preferably, the reaction model is a reaction surface model formed by the inner surface of the aluminum foil tunnel hole and water molecules, and the aluminum foil is the anode aluminum foil used in aluminum electrolytic capacitors.

[0020] On the other hand, the present invention also provides a system for calculating the dielectric constant of oxides on the surface of aluminum foil. This system includes: a surface reaction model construction module for constructing a reaction model of the interaction between the aluminum foil surface and water molecules; a reaction molecular dynamics simulation module for performing reaction molecular dynamics simulation based on the reaction model to obtain a post-reaction model; a post-reaction surface structure extraction module for extracting and analyzing the trajectory of key thermodynamic parameters over time based on the post-reaction model until the reaction process reaches equilibrium to obtain a stable-state trajectory; the molecular dynamics simulation applies external conditions corresponding to the actual aluminum foil formation process; a radial distribution function analysis module for performing structural analysis on the stable-state trajectory to obtain the characteristic peaks of the radial distribution functions of aluminum and oxygen atoms in the reaction products, and determining the corresponding characteristic peak positions of the simulated products; and a system for calculating known oxides in a standard crystallography database. The module identifies the characteristic peak positions of the radial distribution function of the structural model; the oxide crystal structure determination module compares the obtained characteristic peak positions with those of known oxide structural models in the standard crystallography database, selects highly compatible known oxide models, and extracts the complete crystallographic parameters of the known oxide models; the dielectric constant calculation module calculates the ionic and electronic contributions of the known oxide models to the dielectric properties based on the complete crystallographic parameters, and then calculates the dielectric constant; based on the calculation results of the dielectric constant calculation module, the frequency dependence of the dielectric properties is analyzed, and the relationship spectrum between the frequency of ionic and electronic contributions and the dielectric constant is obtained; the cross-scale dielectric property analysis module extracts the dielectric constant at a specified frequency based on the conditions applied by the reaction molecular dynamics simulation and the relationship spectrum, and uses it as the final dielectric constant.

[0021] The beneficial effects of this invention are as follows: by using a cross-scale calculation method, a cross-scale connection from surface reaction process to dielectric property calculation is realized, which improves the accuracy of dielectric constant calculation; it can identify the specific oxide types generated during the formation process, providing a reliable basis for the analysis of oxide film dielectric properties; it provides theoretical guidance for the optimization of the formation process of anode aluminum foil for aluminum electrolytic capacitors, reduces experimental trial and error costs, and has high engineering application value. Attached Figure Description

[0022] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 is a flowchart of the dielectric constant calculation provided by the present invention.

[0024] Figure 2 is a surface reaction model constructed according to an embodiment of the present invention, and a schematic diagram of temperature and energy changes.

[0025] Figure 3 is a schematic diagram of the radial distribution function of an embodiment of the present invention and a schematic diagram of the radial distribution function of the corresponding material found from the crystallographic structure library.

[0026] Figure 4 is a graph showing the relationship between frequency and dielectric constant of the dielectric properties of ion and electron pairs in an embodiment of the present invention, as well as the dielectric constant of alumina at a specified frequency close to 1 MHz.

[0027] Figure 5 is a schematic diagram of the dielectric constant determination system according to an embodiment of the present invention. Detailed Implementation

[0028] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Those skilled in the art should understand that the following specific embodiments or implementation methods are a series of optimized configurations listed to further explain the specific content of the invention. These configuration methods can be combined or used in conjunction with each other, unless the invention explicitly states that some or a specific embodiment or implementation method cannot be associated with or used in conjunction with other embodiments or implementation methods. Furthermore, the following specific embodiments or implementation methods are merely optimized configurations and are not intended to limit the scope of protection of the invention.

[0030] The present invention will be further explained below with reference to specific embodiments.

[0031] This invention provides a scheme for predicting and simulating the dielectric constant of oxides on the surface of aluminum foil based on computer models and simulation analysis. This scheme mainly includes the following key steps performed sequentially: reaction model construction, reaction process simulation, structural analysis and identification, and dielectric property calculation. In specific implementation, commonly used computational simulation tools in the field can be used to complete each process. For example: using crystal modeling tools to construct initial surface and interface models; using reaction molecular dynamics methods to simulate chemical reaction processes such as bonding and breaking; and performing quantitative analysis of electronic structure and performance parameters based on first-principles calculations.

[0032] It should be noted that the computing tools or programs mentioned above are merely examples for implementing the technical solutions of this invention and are not intended to limit the invention. Those skilled in the art can implement this invention using other computing software or programs with equivalent functions, based on the technical concepts disclosed herein. Such equivalent substitutions or modifications should be included within the scope of protection of this invention.

[0033] As shown in Figure 1, one feasible method of this scheme is as follows: Step 1: Construct a reaction model of the interaction between aluminum surface and water molecules. The aluminum surface model needs to cover the common and representative crystal orientations in industrial aluminum foil, specifically including three crystal plane structures: Al(100), Al(011), and Al(012). This design ensures that the model can accurately reflect the structural diversity of the actual aluminum foil surface.

[0034] Step 2: Based on the initial reaction model constructed in Step 1, perform reaction molecular dynamics simulation. The simulation process requires the application of external conditions corresponding to the actual aluminum foil formation process, specifically including: controlling the system temperature within the range of 90±2℃; applying an electric field direction perpendicular to the aluminum foil surface, the electric field strength of which can be set according to the actual formation voltage; and setting the total simulation time to be no less than 800ps to ensure that the model system fully undergoes chemical reaction under the process conditions and reaches a dynamic equilibrium state.

[0035] Step 3: Based on the model after the reaction in Step 2, extract and analyze the trajectory of key thermodynamic parameters of the system over time to assess the stability of the reaction process. Specifically, this includes: calculating the instantaneous temperature of the system at each time step based on the instantaneous velocity information of each atom during the molecular dynamics simulation in Step 2, and outputting the total energy of the system in real time from the reaction force field model. This total energy includes the system's kinetic energy and the potential energy term described by the reaction force field. Analyze the fluctuation data of the instantaneous temperature and total energy of the system throughout the simulation process, and plot the curves of temperature and total energy changes over time. Quantitatively determine whether the aluminum surface reaction has stabilized and whether the simulated system has reached equilibrium by observing whether the curves enter a stable fluctuation range (i.e., reach a convergence state) in the later stages of the simulation. Figure 2 shows a schematic diagram of the surface reaction model and an example of temperature and energy changes.

[0036] The determination of the equilibrium state is based on the quantitative analysis of key thermodynamic parameters of the system during the simulation process. Specifically, statistical analysis is performed on the instantaneous temperature and total energy changes of the system over time. When the average values ​​of the temperature and total energy remain stable within the time interval, and their fluctuation amplitudes are all less than the preset thresholds, and there are no sustained large fluctuations over time, as shown in Figure 2(b), the temperature is almost maintained at 363K, indicating that the temperature is in a stable state; as shown in Figure 2(c), the energy fluctuation does not show a sharp decrease after 300Ps, indicating that the energy tends to stabilize. It is determined that the simulation system has reached a thermodynamic equilibrium state, and the aluminum molten surface reaction process tends to stabilize.

[0037] Step 4: Based on the equilibrium model obtained in Step 3, perform structural statistical analysis on the stable-state trajectories (i.e., stable-state atomic motion trajectories) obtained from the reaction molecular dynamics simulation to characterize the local coordination structure of aluminum and oxygen atoms in the reaction products. Specifically, this includes: using the atomic coordinate data at each time step in the stable-state trajectory file as input data, and under the conditions of setting the statistical radius range and step size, calculating the radial distribution function, performing frame-by-frame statistical and time-averaged processing on the interatomic distance between aluminum and oxygen atoms, to obtain the radial distribution function curve of the aluminum-oxygen atom pair.

[0038] The formula for calculating the radial distribution function is:

[0039] In the formula: ρ is the density; N is the number of particles in the system; T is the total calculation time; r is the radius of the atom from the center. The thickness of the spherical shell taken near radius r is represented by ΔN; ΔN represents the thickness of the shell at a distance r centered on a reference atom. The average number of atoms counted within the spherical shell, that is, the number of atoms within the distance interval [r, r+]. Within [the reference atom], the average number of atoms counted around the reference atom.

[0040] Using the radial distribution function plot proposed above, the changes in the main interatomic spacing of the product can be observed more intuitively, and the transformation of the product structure can be further analyzed.

[0041] In the transformation analysis of product structure, based on the radial distribution function plot, the vertical axis corresponds to the peak intensity, i.e., the number of atoms. Peaks with low intensity, broad peak shape, or large variations with statistical intervals are considered random distribution characteristics caused by thermal perturbation or unstable coordination and are ignored. Only peaks with high intensity significantly higher than the aforementioned random distribution background and relatively sharp and stable peak shape are retained as characteristic peaks of the radial distribution function. In a preferred embodiment, the main peak in the radial distribution function plot is used as the characteristic peak; typically, the simulation result shows only one significant main peak.

[0042] Step 5: Based on the characteristic peak positions of the aluminum-oxygen radial distribution function obtained in Step 4, systematically compare them with the radial distribution function characteristics of known oxide crystal structure models in the standard crystallography database to identify the possible oxide structure types corresponding to the reaction products; screen out known oxide crystal models that highly match the structural characteristics of the simulated products, and extract the complete crystallographic parameters of the known oxide crystal models, including space group, lattice constant, and atomic occupancy information. Specifically, this includes: using the peak positions of the characteristic peaks in the simulated aluminum-oxygen radial distribution function as the main comparison parameters; using known oxide crystal structure models in the standard crystallography database as input, calculating their corresponding aluminum-oxygen atom pair radial distribution functions, and extracting their characteristic peak position information to construct a set of structural feature parameters for comparison.

[0043] During the comparison process, the characteristic peaks in the simulated aluminum-oxygen radial distribution function are used as the main comparison parameters. Based on the abscissa (i.e., position) corresponding to these characteristic peaks, the core feature of the length of the main chemical bonds between atoms can be characterized. Using known oxide crystal structure models in the standard crystallography database as input, the corresponding aluminum-oxygen atom pair radial distribution functions are calculated, and the length information of the chemical bonds between atoms (i.e., the position of their characteristic peaks) is extracted to construct a set of structural feature parameters for comparison.

[0044] During the screening process, the positions of the characteristic peaks of the simulated product, i.e., the length of the chemical bonds, were matched one by one with the characteristic peaks of each known oxide structure model. When the positions of the peaks were the same or approximately the same (e.g., the positional deviation threshold was less than 0.05 Å), the known oxide crystal structure model was determined to have a high consistency with the simulated product in terms of local coordination structure, and this model was selected as a candidate matching structure. Subsequently, all candidate matching structures were screened to identify the oxide with the closest position to the characteristic peak of the simulated product; this oxide was the oxide generated by the simulation.

[0045] For the selected oxide crystal structure models, their corresponding complete crystallographic parameter information is further extracted for subsequent structural analysis and dielectric property calculation. Figure 3 shows a schematic diagram of the radial distribution function in a practical example and a schematic diagram of the radial distribution function of the corresponding material found from the crystallographic structure library.

[0046] The execution of the above steps in this scheme can effectively identify the specific oxide types generated during the formation process, providing a reliable basis for the analysis of the dielectric properties of the oxide film.

[0047] Step 6: Based on the complete crystallographic parameters obtained in Step 5, the dielectric constant of the material is calculated using first-principles methods. The contributions of ions and electrons to the dielectric properties are calculated separately, as follows: Electron contribution: Under the condition of fixed lattice structure and no displacement of ion positions, a small external electric field perturbation is introduced. Only the response of electronic polarization to the external electric field is considered to obtain the dielectric constant of the corresponding oxide. The dielectric constant is the contribution of electrons to the dielectric properties, i.e., the electron contribution:

[0048] Where Ω represents the volume of the calculated system, P e Where E is the electronic polarization intensity, and E is the applied electric field intensity. This characterizes the first-order response of electronic polarization to an applied electric field. The response is solely due to electronic polarization and represents the contribution of electrons to the dielectric properties.

[0049] Ion contribution: Based on the aforementioned electronic polarization calculations, the structural response of lattice ions under an applied electric field is further considered. According to linear response theory, the contribution of ion displacement polarization to dielectric properties yields the dielectric constant of the corresponding oxide. This dielectric constant is considered as the contribution of ions to the dielectric properties, i.e., the ion contribution:

[0050] Where Ω represents the volume of the calculated system, This represents the ionic polarization intensity caused by the displacement of lattice ions under the action of an applied electric field, where E represents the applied electric field intensity. Characterizes the first-order response of ions to an applied electric field. The contribution of reacting ions to dielectric properties.

[0051] Step 7: Based on the calculation results of Step 6, further extract and analyze the frequency dependence of dielectric properties, and obtain the frequency-to-dielectric constant relationship spectra of electronic and ion contributions. Specifically, the frequency dependence of dielectric properties is obtained by extracting the frequency-resolved dielectric function data from the first-principles calculation output file. Specifically, the data of dielectric function variation with frequency is read from the calculation result file, the main diagonal component of the dielectric function tensor corresponding to each frequency point is extracted, and averaged to obtain the equivalent dielectric constant value under each frequency condition, thereby forming a data sequence of dielectric constant variation with frequency, which is used to characterize the frequency dependence of the material's dielectric properties.

[0052] The components of the dielectric function tensor are defined as follows:

[0053] Where α and β represent the directions of the Cartesian coordinates. For Kroneck's delta function, For the system at frequency The electric susceptibility tensor is used. In the specific data processing, the principal diagonal component of the dielectric function tensor is read from each frequency point in the calculation results file. , , The equivalent dielectric constant at the corresponding frequency is obtained by arithmetically averaging the principal diagonal components.

[0054] This allows for the construction of a continuous data sequence of dielectric constant as a function of frequency, which can be used to characterize the frequency dependence of the dielectric properties of materials.

[0055] The frequency dependence of the dielectric properties of the above materials can be analyzed by comparing and interpreting the trends of the real and imaginary parts of the dielectric function with frequency. The expression for the dielectric function is:

[0056] in, This represents the real part of the dielectric function, used to characterize the dielectric properties of a material at a frequency of 10000°. The polarization energy storage capacity under the action of an applied electric field is a characterization of the dielectric constant. The imaginary part of the dielectric function is used to characterize the energy dissipation caused by electronic transitions and polarization relaxation processes. For frequency.

[0057] The frequency-dielectric constant relationship spectrum of electronic and ion contributions is established by organizing the dielectric constant data obtained at different frequencies and plotting it with frequency as the horizontal axis and dielectric constant as the vertical axis.

[0058] Figure 4 shows the relationship between frequency and dielectric constant for the dielectric properties of ion and electron pairs in an example.

[0059] At this step, the scheme has completed cross-scale calculations, which can effectively connect the calculation of surface reaction processes and dielectric properties, and improve the accuracy of dielectric constant calculation.

[0060] Step 8: Based on the dielectric constant versus frequency spectrum obtained in Step 7, extract the dielectric constant contributed by electrons and ions at a specified frequency. In this embodiment, the dielectric constant contributed by electrons and ions at frequencies close to 1MHz is extracted, i.e., the value corresponding to the real part, as shown in Figure 4. In this scheme, the dielectric constant is calculated as follows:

[0061] In the formula: The dielectric constant is given at a frequency of ω. This is the contribution of electrons to the dielectric constant at frequency ω, i.e., the electron contribution; This represents the contribution of ions to the dielectric constant at frequency ω, i.e., the ion contribution.

[0062] The sum of the two This can be identified as the dielectric constant ε of the substance produced by the reaction, thus completing the quantitative characterization of its dielectric properties.

[0063] By implementing the steps outlined above in this scheme, the formation process can be effectively recorded and key parameters can be reverse-analyzed. This provides theoretical guidance for optimizing the formation process of anode aluminum foil for aluminum electrolytic capacitors, reduces experimental trial-and-error costs, and has high engineering application value.

[0064] The following example will be used to illustrate the method flow provided in this embodiment.

[0065] First, surface models of Al(100)-H2O, Al(011)-H2O, and Al(012)-H2O with water were constructed using common software tools (such as Materials Studio), and labeled as Model 1, Model 2, and Model 3, respectively. Each model contains 1000 aluminum atoms and 400 water molecules. The size of Model 1 was set to 28.6 × 28.6 × 49.2 Å. 3 The size of the second model is set to 40.5 × 28.6 × 39.8 Å. 3 The size of the third model is set to 49.6 × 39.6 × 30.3 Å. 3 .

[0066] Subsequently, based on existing software products (such as LAMMPS), reaction molecular dynamics simulations can be performed on the three models. A Berendsen thermostat is used to set the temperature to 363K. All three models use the ReaxFF force field under the NVT ensemble, with a time step of 0.1fs and a reaction time of 800ps. The motion trajectories of all atoms in the system are output every 1000 steps.

[0067] Based on the model after the reaction was completed, we observed that the temperature fluctuated around 363K, and the energy of the reaction system almost stabilized after 300 ps.

[0068] Based on the above model where the energy tends to be stable, the radial distribution function of the model is analyzed. The results of the radial distribution function of the three models show that the peak of Al-O is concentrated at 1.95 Å, as shown in Figure 3.

[0069] Based on the above radial distribution function results of Al-O, a search of crystallographic databases revealed that the peak value of Al-O in α-Al2O3 was closest to 1.95 Å, indicating that the main product of aluminum foil formation is α-Al2O3.

[0070] The dielectric constant of the α-Al₂O₃ model obtained above was calculated. A functional was used to handle electron exchange correlation. The plane wave cutoff energy was set to "PREC=High". The exact diagonalization algorithm was used, and the energy convergence criterion was set to 1×10⁻⁶. - 8 eV.

[0071] Based on the above parameter settings, the contribution of electrons to the dielectric constant is calculated by introducing an external electric field perturbation under the condition of fixed lattice structure and keeping the positions of each ion from shifting, and solving the linear response of the electron density of the system. This allows for the calculation of the dielectric response caused by electronic polarization, thus obtaining the contribution value of electrons to the dielectric constant.

[0072] Based on the electronic polarization calculation, the contribution of ions to the dielectric constant is calculated by further considering the small displacement response of lattice ions under the action of an applied electric field and combining the polarization change caused by ion displacement. The dielectric response including the ion polarization effect is then calculated, and the contribution of ions to the dielectric constant is determined accordingly.

[0073] Based on the contributions of ions and electrons to the dielectric constant mentioned above, the dielectric constant at 1 MHz is shown below: Electron contribution to dielectric properties ε ele =3.19, the contribution of ions to dielectric properties ε ion =7.46, dielectric constant ε=10.65.

[0074] Based on the above cross-scale calculation studies, it is shown that α-Al2O3 is generated during the aluminum foil formation process, and its dielectric constant is 10.65.

[0075] The main method flow of this solution has been described above through specific embodiments. In another specific embodiment, this solution can also be implemented in a systematic manner, as shown in Figure 5. The system includes: a surface reaction model construction module for constructing a reaction model of the interaction between the aluminum foil surface and water molecules; a reaction molecular dynamics simulation module for performing reaction molecular dynamics simulation based on the reaction model to obtain the post-reaction model; a post-reaction surface structure extraction module for extracting and analyzing the trajectory of key thermodynamic parameters over time based on the post-reaction model until the reaction process reaches equilibrium to obtain the stable-state trajectory; the molecular dynamics simulation applies external conditions corresponding to the actual aluminum foil formation process; a radial distribution function analysis module for performing structural analysis on the stable-state trajectory to obtain the characteristic peaks of the radial distribution functions of aluminum and oxygen atoms in the reaction products and determine the corresponding characteristic peak positions of the simulated products; and calculation of standard crystallography. The system identifies the characteristic peak positions of the radial distribution function of known oxide structure models in the database; the oxide crystal structure determination module compares these peak positions with those of known oxide structure models in the standard crystallography database, selects highly compatible known oxide models, and extracts the complete crystallographic parameters of these models; the dielectric constant calculation module calculates the ionic and electronic contributions of the known oxide model to the dielectric properties based on the complete crystallographic parameters, and then calculates the dielectric constant; based on the calculation results of the dielectric constant calculation module, it analyzes the frequency dependence of the dielectric properties and obtains a spectrum showing the relationship between the frequency of ionic and electronic contributions and the dielectric constant; the cross-scale dielectric property analysis module extracts the dielectric constant at a specified frequency based on the spectrum, which is then used as the final dielectric constant.

[0076] In addition, the system also includes a storage module and a processor unit; the storage module is used to store raw data and intermediate data, etc., and the processor unit calls each module to execute the system's functions.

[0077] In another embodiment, this solution can also be implemented by means of a device, that is, by executing instruction code through a processor capable of calling instruction code, so as to implement the dielectric constant calculation method provided in the above embodiments.

[0078] Furthermore, any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a specific logical function or process. The scope of the preferred embodiments of this solution includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which the embodiments of this solution pertain. The processor performs the various methods and processes described above. For example, the method embodiments of this solution can be implemented as software programs tangibly contained in a machine-readable medium, such as memory. In some embodiments, part or all of the software program can be loaded and / or installed via memory and / or a communication interface. When the software program is loaded into memory and executed by the processor, one or more steps of the methods described above can be performed. Alternatively, in other embodiments, the processor can be configured to perform one of the methods described above by any other suitable means (e.g., by means of firmware).

[0079] The logic and / or steps represented in the flowchart or otherwise described herein may be specifically implemented in any readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0080] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the dielectric constant of oxides on the surface of aluminum foil, characterized in that, The method includes: Step 1, constructing a reaction model of the interaction between aluminum foil surface and water molecules; Step 2, performing molecular dynamics simulation based on the reaction model to obtain a post-reaction model; the molecular dynamics simulation applies external conditions corresponding to the actual aluminum foil formation process; Step 3, based on the post-reaction model, extracting and analyzing the trajectory of key thermodynamic parameters over time until the reaction process reaches equilibrium to obtain a stable-state trajectory; Step 4, performing structural analysis on the stable-state trajectory to obtain the characteristic peaks of the radial distribution functions of aluminum and oxygen atoms in the reaction products, and determining the corresponding characteristic peak positions of the simulated products; Step 5, processing the obtained characteristic peaks... Step 6: Based on the complete crystallographic parameters, calculate the ionic and electronic contributions of the known oxide model to the dielectric properties, and then calculate the dielectric constant. Step 7: Based on the calculation results of Step 6, analyze the frequency dependence of the dielectric properties and obtain the relationship spectrum between the frequency of ionic and electronic contributions and the dielectric constant. Step 8: Based on the relationship spectrum, extract the dielectric constant at a specified frequency as the final dielectric constant.

2. The method according to claim 1, characterized in that, In step 2, the external conditions include: the system temperature of the reaction model is determined by the actual formation temperature; an electric field is applied perpendicular to the surface of the aluminum foil, and the magnitude of the electric field is determined by the actual formation voltage; the total simulation time of the reaction model is not less than 800 ps.

3. The method according to claim 1, characterized in that, In step 3, the key thermodynamic parameters include instantaneous temperature and total energy, and the total energy includes the system's kinetic energy and potential energy; the change trajectory is a curve showing the change of instantaneous temperature and total energy fluctuation data over time; the equilibrium state is determined as follows: when the average values ​​of instantaneous temperature and total energy remain stable within a preset time interval, and the fluctuation amplitude of the average values ​​is less than a preset threshold, and there is no continuous large fluctuation over time, the reaction process is determined to have reached equilibrium.

4. The method according to claim 1, characterized in that, Step 4 further includes: using the atomic coordinate data at each moment in the steady-state trajectory as input data, and under the set radius range and step size conditions, performing frame-by-frame statistical and time-averaged processing on the interatomic spacing between aluminum and oxygen atoms to obtain the radial distribution function curve: Where ρ is the density; N is the number of particles in the system; T is the total computation time; and r is the radius of the atom from the center. ΔN represents the thickness of the spherical shell taken near radius r; ΔN represents the thickness of the shell within the distance interval [r, r+]. Within [the reference atom], the average number of atoms counted around the reference atom.

5. The method according to claim 1, characterized in that, In step 5, the comparison method is as follows: the characteristic peak position of the simulated product obtained in step 4 is used as the main comparison parameter; the radial distribution function of the corresponding aluminum-oxygen atoms is calculated using the known oxide model data in the standard crystallography database as input, and its characteristic peak position is further calculated to form a set of comparison structure characteristic parameters; the characteristic peak position of the simulated product is matched one by one with the characteristic peak position in the set of comparison structure characteristic parameters, and when the two are within the set distance deviation threshold range, the corresponding known oxide model is selected as a candidate matching structure; among the candidate matching structures, the known oxide model whose characteristic peak position is closest to the characteristic peak position of the simulated product is taken as the highly consistent known oxide model.

6. The method according to claim 1, characterized in that, The electronic contribution is calculated as follows: under the condition of fixed lattice structure and no displacement of ion positions, an external electric field perturbation is introduced, and only the response of electronic polarization to the external electric field is considered to obtain the dielectric constant of the corresponding known oxide, which is used as the value of the electronic contribution; the ion contribution is calculated as follows: based on electronic polarization, the structural response of lattice ions under the action of an external electric field is further considered to obtain the dielectric constant of the corresponding known oxide, which is used as the value of the ion contribution.

7. The method according to claim 1, characterized in that, In step 6, the dielectric constant is calculated as follows: In the formula: The dielectric constant is given at a frequency of ω. This represents the electronic contribution at frequency ω. The contribution of ions at frequency ω.

8. The method according to claim 1, characterized in that, In step 7, the relationship graph is established as follows: In the calculation results of step 6, data on the change of dielectric function with frequency are obtained. For each frequency point, the main diagonal component of the dielectric function tensor is extracted and averaged to obtain the equivalent dielectric constant at each frequency point. The data on the change of the equivalent dielectric constant with frequency is used as the data sequence of the change of dielectric constant with frequency. Based on the frequency and the corresponding dielectric constant in the data sequence, a relationship graph is drawn.

9. The method according to claim 1, characterized in that, The reaction model is a reaction surface model formed by the inner surface of the aluminum foil tunnel hole and water molecules, and the aluminum foil is the anode aluminum foil used in aluminum electrolytic capacitors.

10. A system for calculating the dielectric constant of oxides on the surface of aluminum foil, characterized in that, The system includes: a surface reaction model construction module for constructing a reaction model of the interaction between aluminum foil surface and water molecules; a reaction molecular dynamics simulation module for performing reaction molecular dynamics simulation based on the reaction model to obtain the post-reaction model; a post-reaction surface structure extraction module for extracting and analyzing the changes in key thermodynamic parameters over time based on the post-reaction model until the reaction process reaches equilibrium to obtain the steady-state trajectory; the molecular dynamics simulation applies external conditions corresponding to the actual aluminum foil formation process; and a radial distribution function analysis module for performing structural analysis on the steady-state trajectory to obtain the characteristic peaks of the radial distribution functions of aluminum and oxygen atoms in the reaction products and determine the corresponding characteristic peak positions of the simulated products; and calculating the characteristic peaks of the radial distribution functions of known oxide structure models in the standard crystallography database. The system comprises the following modules: a peak position determination module, an oxide crystal structure determination module, and a dielectric constant calculation module. The latter calculates the ionic and electronic contributions of the known oxide model to the dielectric properties based on the complete crystallographic parameters, and then calculates the dielectric constant. The former analyzes the frequency dependence of the dielectric properties based on the calculation results, obtaining a spectrum showing the relationship between the frequencies of ionic and electronic contributions and the dielectric constant. The latter, based on the conditions applied by the reaction molecular dynamics simulation and the spectrum, extracts the dielectric constant at a specified frequency as the final dielectric constant.

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