Simulation and prediction method, device and equipment for surface electric field of ceramic material and medium

Abstract

The invention relates to the technical field of material analysis, and discloses a ceramic material surface electric field simulation and prediction method, device, equipment and medium, and the method comprises the steps: building a crystal model according to the crystallographic information of a ceramic material; calculating the defect formation energy, the defect energy level, the carrier migration potential barrier and / or the migration rate of the crystal model; constructing a finite element simulation multi-physical field based on the defect energy level, the carrier migration potential barrier and / or the migration rate; and simulating and predicting the electric field intensity and distribution on the surface of the ceramic material based on the finite element simulation multi-physical field. Thus, accurate prediction from microscopic physical essence to macroscopic engineering performance is constructed for the first time, the simulation precision is greatly improved, and a physical mechanism of electric field distortion can be deeply disclosed, so that a formula and a structure can be simulated and optimized before material preparation, the research and development period is greatly shortened, and the research and development cost is reduced; and a core theoretical basis is provided for realizing accurate design of the high-voltage insulator.

Description

Technical Field

[0001] This application relates to the field of materials analysis, and in particular to a method, apparatus, equipment and medium for simulating and predicting the electric field on the surface of ceramic materials. Background Technology

[0002] In the field of high-voltage gas-insulated equipment, the reliability of its internal insulation largely depends on the surface insulation performance of ceramic components such as basin insulators. Therefore, the analysis and optimization of the surface electric field distribution of such components is crucial, and current research mainly focuses on two directions: experimental measurement and finite element simulation. At the experimental measurement level, techniques such as electrostatic probes and Kerr electro-optic effects are often used to directly measure the charge distribution or electric field intensity on the insulator surface. At the finite element simulation level, researchers use COMSOL software to construct geometric models of the insulators and simulate the electric field distribution by calculating electrostatic or transient current fields. This method has now become a primary tool in the equipment design phase. In the current field of high-voltage insulation technology, accurately predicting the surface electric field of ceramic materials is also of critical importance for ensuring the reliability of gas-insulated equipment.

[0003] Existing technologies mainly rely on two types of approaches to achieve surface electric field correlation analysis of ceramic materials: one is to conduct experimental measurements through methods such as electrostatic probes. Although this can obtain real data, it suffers from problems such as expensive equipment and complex operation procedures. Moreover, it can usually only obtain the surface electric field integral value or local value of the prepared sample, making it difficult to achieve forward-looking prediction in the equipment design stage, and it cannot reveal the physical root cause behind the electric field distortion. The second is to use macroscopic finite element simulation based on empirical parameters. The key material parameters input, such as conductivity, charge injection barrier, carrier mobility, trap energy level and density, are mostly derived from literature or macroscopic fitting, failing to reflect the microscopic characteristics of specific materials. For example, silicon nitride ceramics prepared by different sintering processes or doping formulations may have huge differences in ionic conductivity. Using general empirical parameters will inevitably lead to a large deviation between the simulation results and the actual situation, thus making it impossible to accurately predict the degree and location distribution of surface electric field distortion. Furthermore, existing methods are essentially mathematical fitting processes, not physical simulations. When simulation results differ from experimental results, a physical mechanism explanation cannot be obtained from the simulation model, and it is difficult to diagnose the process by which charge carrier types and defect mechanisms dominate charge accumulation. This results in a loss of the ability to guide material optimization through simulation. Due to the unreliability of simulation results, the equipment design optimization process still heavily relies on a trial-and-error cycle of "sample preparation - experimental testing - failure - re-preparation," ultimately leading to a significant extension of the development cycle and a substantial increase in development costs for new products and materials. Therefore, there is an urgent need in this field for a simulation and prediction method for the surface electric field of ceramic materials that meets the requirements of high-voltage insulation technology for precise design and material customization.

[0004] Therefore, there is an urgent need in this field for a method to simulate and predict the surface electric field of ceramic materials that meets the requirements of high-voltage insulation technology for precise design and material customization. Summary of the Invention

[0005] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important component particles or to describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0006] This disclosure provides a method, apparatus, device, and medium for simulating and predicting the surface electric field of ceramic materials to accurately quantify the ion migration rate of ceramic materials.

[0007] In some embodiments, the method includes:

[0008] Construct a crystal model based on the crystallographic information of ceramic materials;

[0009] Calculate the defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model;

[0010] Based on the aforementioned defect energy levels, carrier migration barriers, and / or mobility, a finite element simulation of a multiphysics field is constructed.

[0011] Based on the aforementioned finite element simulation multiphysics field, the electric field intensity and distribution on the surface of ceramic materials are simulated and predicted.

[0012] As one possible implementation, constructing a crystal model based on the crystallographic information of the ceramic material includes:

[0013] Based on the crystallographic information of ceramic materials, construct crystal unit cell models;

[0014] A crystal supercell model is formed using multiple crystal unit cell models;

[0015] Multiple point defects are introduced into the crystal supercell model to form a defect supercell model.

[0016] As one possible implementation, the calculation of the defect formation energy, defect energy level, carrier migration barrier, and / or mobility of the crystal model includes:

[0017] Based on the first principles of density functional theory, the defect formation energy corresponding to different point defects is calculated;

[0018] The defect energy level is obtained by calculating the density of states curves of the crystal supercell model and the defect supercell model.

[0019] The migration barrier is determined by utilizing the defect formation energy and the carrier migration mode of the ceramic material;

[0020] The migration barrier is substituted into the conductivity formula and Einstein's relation to calculate the carrier mobility.

[0021] As one possible implementation, determining the migration barrier using the defect formation energy and the carrier migration mode of the ceramic material includes:

[0022] In response to the ceramic material being ionicly conductive, the defect formation energy is equivalent to a migration barrier;

[0023] In response to the fact that the ceramic material is electronically conductive and the carrier migration mode of the ceramic material is electron or hole, half of the defect formation energy is equivalent to the migration barrier;

[0024] In response to the fact that the ceramic material is electronically conductive and the carrier migration mode of the ceramic material is charge injection at the electrode-dielectric interface, the defect formation energy is equivalent to a migration barrier.

[0025] As one possible implementation, the construction of a finite element simulation multiphysics field based on the defect energy level, carrier migration barrier, and / or mobility includes:

[0026] A two-dimensional axisymmetric or three-dimensional finite element model is established based on the actual geometric structure of the ceramic material.

[0027] The defect energy level, carrier migration barrier and / or mobility are set as parameters of the two-dimensional axisymmetric or three-dimensional finite element model to obtain the simulated charge physics field.

[0028] A multiphysics field coupling electrostatic field and charge transport field is constructed for the simulated charge physical field to obtain the finite element simulation multiphysics field.

[0029] As one possible implementation, the simulation and prediction of the electric field intensity and distribution on the surface of ceramic materials based on the finite element simulation multiphysics field includes:

[0030] Based on the finite element simulation of the multiphysics field, the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface are obtained.

[0031] Substituting the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface into the electrostatic field control equation, the surface electric field intensity and distribution of the ceramic material are solved.

[0032] In some embodiments, the device includes:

[0033] The crystal construction module is used to construct crystal models based on the crystallographic information of ceramic materials.

[0034] The calculation module is used to calculate the defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model;

[0035] The physics field construction module is used to construct a finite element simulation multiphysics field based on the defect energy level, carrier migration barrier and / or mobility.

[0036] The simulation module is used to simulate and predict the electric field intensity and distribution on the surface of ceramic materials based on the finite element simulation of multiphysics.

[0037] As one possible implementation, the crystal building module includes:

[0038] Unitary building blocks are used to construct crystal unit cell models based on the crystallographic information of ceramic materials;

[0039] A perfect supercell building unit is used to form a crystal supercell model using multiple crystal primitive cell models;

[0040] The defect supercell building unit is used to introduce various point defects into the crystal supercell model to form a defect supercell model.

[0041] In some embodiments, the device includes a processor and a memory storing program instructions, wherein the processor is configured to perform the method as described above when executing the program instructions.

[0042] In some embodiments, the computer-readable storage medium stores a computer program thereon, wherein the computer program, when executed by one or more processors, implements the method as described above.

[0043] This disclosure provides a method, apparatus, device, and medium for simulating and predicting the surface electric field of ceramic materials. The method involves constructing a crystal model based on the crystallographic information of the ceramic material; calculating the defect formation energy, defect energy levels, carrier migration barriers, and / or mobility of the crystal model; constructing a finite element simulation multiphysics field based on the defect energy levels, carrier migration barriers, and / or mobility; and simulating and predicting the surface electric field intensity and distribution of the ceramic material based on the finite element simulation multiphysics field.

[0044] First, first-principles calculations are used to reveal the microscopic intrinsic parameters of the material (defect formation energy, density of states, migration barrier). Then, these calculated intrinsic parameters are used as input parameters for finite element simulation, ultimately achieving high-precision prediction of surface charge and electric field. This significantly shortens the R&D cycle, reduces R&D costs, and provides a core theoretical basis for the precise design of high-voltage insulators.

[0045] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0046] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein:

[0047] Figure 1 This is an exemplary system architecture diagram to which one embodiment of this disclosure can be applied;

[0048] Figure 2 This is a flowchart of an embodiment of the simulation and prediction method for the surface electric field of ceramic materials according to the present disclosure;

[0049] Figure 3 This is a crystal model diagram based on the simulation and prediction method for the surface electric field of ceramic materials disclosed herein;

[0050] Figure 4 This is a diagram showing the density of states calculation results based on the simulation and prediction method for the surface electric field of ceramic materials disclosed herein;

[0051] Figure 5 This is a different method for simulating and predicting the surface electric field of ceramic materials according to the present disclosure.

[0052] Predicted electric field of Si3N4 surface under Y2O3 concentration;

[0053] Figure 6 This is a schematic diagram of an embodiment of the device for simulating and predicting the surface electric field of ceramic materials according to the present disclosure;

[0054] Figure 7 This is a schematic diagram of the structure of a computer system suitable for implementing embodiments of the present disclosure. Detailed Implementation

[0055] Figure 1 An exemplary system architecture 100 is shown, illustrating an embodiment of a method, apparatus, device, and medium for simulating and predicting the surface electric field of a ceramic material that can be applied according to the present disclosure.

[0056] like Figure 1 As shown, system architecture 100 may include terminal devices 101, 102, and 103, a network 104, and a server 105. Network 104 serves as the medium for providing communication links between terminal devices 101, 102, and 103 and server 105. Network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0057] Users can use terminal devices 101, 102, and 103 to interact with server 105 via network 104 to receive or send messages, etc. Various communication client applications can be installed on terminal devices 101, 102, and 103, such as electric field simulation and prediction applications, voice recognition applications, short video social applications, audio and video conferencing applications, live video streaming applications, document editing applications, input method applications, web browser applications, shopping applications, search applications, instant messaging tools, email clients, social platform software, etc.

[0058] Terminal devices 101, 102, and 103 can be either hardware or software. When terminal devices 101, 102, and 103 are hardware, they can be various electronic devices with displays, including but not limited to smartphones, tablets, e-book readers, MP3 players (Moving Picture Experts Group Audio Layer III), MP4 players (Moving Picture Experts Group Audio Layer IV), laptops, and desktop computers, etc. When terminal devices 101, 102, and 103 are software, they can be installed on the terminal devices listed above. They can be implemented as multiple software programs or software modules (e.g., used to provide electric field simulation and prediction services) or as a single software program or software module. No specific limitations are imposed here.

[0059] In some cases, the simulation and prediction method for the surface electric field of ceramic materials provided in this disclosure can be executed by terminal devices 101, 102, and 103, and correspondingly, the simulation and prediction device for the surface electric field of ceramic materials can be set in terminal devices 101, 102, and 103. In this case, the system architecture 100 may not include server 105.

[0060] In some cases, the simulation and prediction method for the surface electric field of ceramic materials provided in this disclosure can be jointly executed by terminal devices 101, 102, and 103 and server 105. For example, the step of "constructing a crystal model based on the crystallographic information of the ceramic material" can be executed by terminal devices 101, 102, and 103, and the steps of "simulating and predicting the surface electric field intensity and distribution of the ceramic material based on the finite element simulation of multiphysics" can be executed by server 105. This disclosure does not limit this. Correspondingly, the simulation and prediction device for the surface electric field of ceramic materials can also be respectively set in terminal devices 101, 102, and 103 and server 105.

[0061] In some cases, the simulation and prediction method of the electric field on the surface of ceramic materials provided in this disclosure can be executed by server 105. Correspondingly, the simulation and prediction device of the electric field on the surface of ceramic materials can also be set in server 105. In this case, the system architecture 100 may not include terminal devices 101, 102, and 103.

[0062] It should be noted that server 105 can be either hardware or software. When server 105 is hardware, it can be implemented as a distributed server cluster consisting of multiple servers, or as a single server. When server 105 is software, it can be implemented as multiple software programs or software modules (e.g., used to provide distributed services), or as a single software program or software module. No specific limitations are made here.

[0063] It should be understood that Figure 1 The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included.

[0064] Continue to refer to Figure 2 The diagram illustrates a flow 200 of an embodiment of a method for simulating and predicting the electric field on the surface of a ceramic material according to the present disclosure, which includes the following steps:

[0065] Step 201: Construct a crystal model based on the crystallographic information of the ceramic material.

[0066] The crystallographic information of ceramic materials is a set of core parameters that describe the essential characteristics of the ceramic crystal structure. It mainly revolves around "how atoms are arranged in an orderly manner in three-dimensional space" and determines the key properties of ceramics such as mechanical strength, high temperature resistance, insulation, and conductivity.

[0067] Specifically, first, a crystal unit cell model is constructed based on the crystallographic information of the ceramic material; then, multiple crystal unit cell models are used to form a crystal supercell model; finally, various point defects are introduced into the crystal supercell model to form a defect supercell model.

[0068] Based on crystallographic information such as the space group and lattice parameters of ceramic materials, and using relevant software (such as modeling tools accompanying calculation software like VASP and QuantumESPRESSO, or specialized crystal structure visualization software like VESTA), the smallest repeating unit, i.e., the unit cell model, is constructed according to the periodic repetition law of the crystal. This model is the basis for calculating properties such as intrinsic electronic structure.

[0069] Based on the unit cell model, a supercell model containing tens to hundreds of atoms is constructed by enlarging the unit cell. For example, the unit cell can be enlarged by a certain factor (e.g., 2×2×2) along each of the three crystal axes as needed to simulate low-concentration defects. The size of the supercell needs to be reasonably selected according to the research objectives and computational resources, so as to reflect the influence of defects while remaining within the computational limits.

[0070] Different types of point defects are introduced into the supercell by deleting specific atoms (e.g., forming oxygen vacancies or metal vacancies) or replacing atoms (introducing foreign dopants). Then, a geometric optimization algorithm is used to calculate the supercell after introducing defects, allowing the lattice constant and atomic positions to fully relax and reach the stable configuration with the lowest energy. Methods such as the conjugate gradient method are used to allow atoms to move under the influence of forces until the interatomic forces reach equilibrium; this model can then be used for subsequent accurate calculations.

[0071] For example, see Figure 3 Taking Si3N4 ceramics doped with different concentrations of Y2O3 (2%, 4%, 6%) as examples, the surface electric field was predicted. Y2O3 is a commonly used sintering aid, and its concentration significantly affects the composition, structure, and electrical properties of the grain boundary phase. When constructing the β-Si3N4 unit cell model, to simulate Y2O3 doping, an interface model containing Si3N4 grains and a typical Y-Si-ON glass grain boundary phase can be constructed.

[0072] Step 202: Calculate the defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model.

[0073] When point defects (such as oxygen vacancies or doped atoms) exist in a crystal, the defects disrupt the original periodic potential field, introducing isolated electronic states, or "defect energy levels," into the band gap, localized near the defects. The formula for calculating the defect formation energy comprehensively considers the energy difference between the defect supercell and the perfect supercell, the chemical potential of the removed or added atoms, and the electronic chemical potential.

[0074] Density of states (DOS) describes the probability distribution of electrons in different energy states within a crystal, i.e., "the number of electronic states that can be accommodated per unit energy interval." Calculating the DOS of a crystal (perfect crystal) and a defect supercell to obtain the localized electronic states (defect energy levels) of a material requires following a core process: "model construction → calculation execution → data comparison and analysis → localized state verification." By analyzing the difference in electronic state distribution before and after the introduction of defects, the localized energy levels generated by the defects are located and confirmed. DOS acts as a "microscope" for observing defect energy levels, while defect energy levels serve as a "microscopic bridge" for understanding the impact of material defects on macroscopic electrical properties (such as insulation and charge transport), ultimately providing a theoretical basis for the insulation design of high-voltage ceramic equipment.

[0075] The migration barrier is the energy barrier that a charge carrier (ion / electron) must overcome to transition from a stable position to an adjacent position in a material, and it determines the mobility of the charge carrier (the lower the barrier, the easier it is for the charge carrier to move).

[0076] Carrier mobility is the average drift velocity of carriers under a unit electric field strength, and it is also the ultimate calculation target, directly reflecting the transport efficiency of carriers.

[0077] For example, by calculating the formation energy of Y atoms in the grain boundary phase at different Y concentrations, their preferential occupancy sites and solid solubility can be determined. The formation energy of Y ions or carrier defects in the grain boundary phase can be calculated. The density of electronic states (DOS) of the grain boundary phase under different Y₂O₃ doping conditions can be calculated. See also... Figure 4 The results show that the introduction of Y₂O₃ introduces new trap levels into the band gap. At a concentration of 2%, the shallow trap density is relatively high, corresponding to a greater charge accumulation; at a concentration of 4%, the shallow trap density decreases significantly, and the charge accumulation decreases; at a concentration of 6%, the shallow trap density remains essentially unchanged, but the deep trap energy levels increase, the density increases, and the charge accumulation increases. Based on the defect formation energy and electron trap characteristics, the defect formation energy is equivalent to the carrier migration barrier, and the carrier mobility and conductivity are calculated using formulas.

[0078] As a possible implementation, step 202, calculating the defect formation energy, defect energy level, carrier migration barrier, and / or mobility of the crystal model, includes:

[0079] Step 2021: Based on the first principles of density functional theory, calculate the defect formation energy corresponding to different point defects.

[0080] Based on density functional theory (DFT, Hohenberg-Kohn Theorems), the defect formation energy is calculated using first-principles calculation software. By changing the Fermi level, the formation energy changes of different types of defects are systematically calculated. By comparing the numerical values, the "dominant defect" type under specific preparation conditions can be determined; this type of defect is the easiest to form and has the highest concentration. By systematically calculating the functional relationship between the formation energy of different types of defects and the Fermi level, and comparing the numerical values, the "dominant defect" type that is easiest to form and has the highest concentration under specific preparation conditions can be determined. The formula for calculating the defect formation energy can use formulas commonly used in this field, and no restrictions are imposed here.

[0081] Step 2022: Obtain the defect energy level by calculating the density of states curves of the crystal supercell model and the defect supercell model.

[0082] Using first-principles calculation software, the density of states (DOS) of both perfect crystal supercells and supercells with dominant defects was calculated. During the calculations, appropriate parameters such as energy cutoff values ​​and k-point grids were set to ensure accuracy and efficiency. The calculation results provide information on the material's band structure and band gap, allowing analysis of the localized electronic states (defect levels) introduced by defects within the band gap. The location and distribution of these defect levels directly determine their effectiveness as electron or hole traps, serving as a direct theoretical source for defining trap parameters in finite element simulations. By calculating the DOS curves of perfect crystals and supercells with dominant defects, the material's band structure and band gap can be clearly obtained. The location and distribution of these defect levels directly determine their effectiveness as electron or hole traps, providing a direct theoretical source for defining trap parameters in subsequent finite element simulations.

[0083] Step 2023: Determine the migration barrier using the defect formation energy and the carrier migration mode of the ceramic material.

[0084] Wherein, in response to the ceramic material being ionicly conductive, the defect formation energy is equivalent to a migration barrier. In response to the ceramic material being electronically conductive and the carrier migration mode of the ceramic material being electrons or holes, half of the defect formation energy is equivalent to a migration barrier. In response to the ceramic material being electronically conductive and the carrier migration mode of the ceramic material being charge injection at the electrode-dielectric interface, the defect formation energy is equivalent to a migration barrier.

[0085] Step 2024: Substitute the migration barrier into the conductivity formula and Einstein's relation to calculate the carrier mobility.

[0086] In summary, steps 2021 to 2024 respectively calculated the defect formation energy, defect energy level, carrier migration barrier, and mobility of the crystal model. Through the joint calculation of first-principles calculations and finite element simulation, the material formulation and insulation structure were screened and optimized in the simulation, which greatly reduced the experimental research and development costs and cycle.

[0087] Step 203: Based on the defect energy level, carrier migration barrier and / or mobility, construct a finite element simulation multiphysics field.

[0088] Specifically, this step may include:

[0089] Step 2031: Establish a two-dimensional axisymmetric or three-dimensional finite element model based on the actual geometric structure of the ceramic material.

[0090] Based on the actual geometric structure of the insulators of high-voltage equipment, two-dimensional axisymmetric or three-dimensional models are established using finite element software (such as COMSOL Multiphysics, ANSYS, etc.).

[0091] Step 2032: Set the defect energy level, carrier migration barrier and / or mobility as parameters of the two-dimensional axisymmetric or three-dimensional finite element model to obtain the simulated charge physical field.

[0092] The mobility calculated using first principles is substituted into the conductivity constitutive relation, the migration barrier is set as the emission condition of the electrode boundary, and the defect energy level and density of states are defined as the source terms of charge trapping and detrapping, thereby simulating the dynamic behavior of charge in ceramic materials.

[0093] Step 2033: Construct a multiphysics field that couples the electrostatic field and the charge transport field for the simulated charge physical field to obtain the finite element simulation multiphysics field.

[0094] Apply voltage to the constructed multiphysics model and perform transient or steady-state solutions.

[0095] Step 204: Based on the finite element simulation multiphysics field, simulate and predict the electric field intensity and distribution on the surface of the ceramic material.

[0096] The model simulates the process of charge being injected from the electrode, migrating within the medium under the action of the electric field, being trapped or recombinizing, etc. by solving the charge transport equation and electric field distribution equation in a self-consistent manner. Finally, it outputs the space charge density distribution inside the medium and the surface charge density distribution accumulated at the medium-gas interface at a specific moment, intuitively showing the charge accumulation situation.

[0097] For example, a three-dimensional geometric model of the insulator is established. The calculated results of the carrier migration barrier and mobility are set as simulation parameters, and an actual DC operating voltage is applied to calculate the surface charge density distribution of the ceramic material under different formulations. (See also...) Figure 5 Simulation results show that the 4% Y₂O₃ concentration sample exhibits the lowest surface charge accumulation. This is because its grain boundary phase has the lowest carrier mobility, making it difficult for charge to be transported to the surface and accumulate. Correspondingly, its maximum surface electric field intensity is reduced by approximately 40% compared to the 2% Y₂O₃ doped sample. The Y₂O₃ concentration directly affects the carrier migration barrier by altering the grain boundary phase structure and chemical environment, thus dominating the macroscopic conductivity and charge accumulation behavior. Therefore, a 4% Y₂O₃ doping concentration is the optimal choice for balancing sintering densification and insulation performance.

[0098] As one possible implementation, step 204, based on the finite element simulation multiphysics field, simulates and predicts the electric field intensity and distribution on the surface of the ceramic material, including:

[0099] Step 2041: Based on the finite element simulation multiphysics field, obtain the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface.

[0100] The dynamic evolution of space charge is simulated using a multiphysics model, outputting the space charge density distribution within the medium and the surface charge density distribution accumulated at the gas-solid interface. A voltage is applied to the multiphysics model for transient or steady-state solutions. The model simulates the dynamic evolution of space charge by self-consistently solving for charge transport and electric field distribution, i.e., charge injection from electrodes, migration within the medium under the influence of the electric field, trapping, or recombination. The final output shows the space charge density distribution within the medium and the surface charge density distribution accumulated at the medium-gas interface at a specific moment. These results directly reveal the severe areas and total amount of charge accumulation, which is the root cause of electric field distortion.

[0101] Step 2042: Substitute the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface into the electrostatic field control equation to solve for the electric field intensity and distribution on the surface of the ceramic material.

[0102] The steady-state space charge and surface charge distributions obtained from finite element simulation are substituted as source terms into the electrostatic field control equations for solution. Since charge accumulation distorts the original electric field, the electric field intensity and distribution on the ceramic material surface can be calculated, revealing the region of most severe electric field distortion and the maximum field strength value. This provides a quantitative basis for evaluating insulation reliability and optimizing insulator design.

[0103] Because charge accumulation severely distorts the original electric field determined by the electrode structure, the surface electric field intensity distribution reflects the actual insulation state of the insulator. This result visually displays the region with the most severe electric field distortion and provides the maximum field strength value, offering a quantitative basis for assessing insulation reliability and optimizing insulator design.

[0104] In summary, steps 2041 and 2042, through simulation and prediction, obtain the space charge density distribution inside the medium and the surface charge density distribution at the gas-solid interface. Substituting these values ​​into the electrostatic field control equations allows for accurate acquisition of the electric field strength and distribution on the ceramic material surface. This simulation and prediction method based on finite element method (FEM) multiphysics not only clearly presents the charge accumulation region and total amount, identifying the root cause of electric field distortion, but also visually displays the region with the most severe electric field distortion and the maximum field strength. By mastering this key information, researchers and engineers can more accurately assess insulation reliability, optimize and improve weak points in insulator design, and effectively enhance the overall performance and safety of high-voltage equipment. This method has broad application prospects and significant practical value in many fields, such as power and electronics, that rely on the insulation performance of ceramic materials.

[0105] In summary, this embodiment achieves significant technical effects by constructing a cross-scale, full-chain simulation system spanning "atomic scale to macroscopic performance." At the microscopic level, relying on first-principles calculations, it accurately calculates defect formation energy and migration barriers, reliably predicting intrinsic parameters of ceramic materials such as conductivity and carrier mobility. This provides a theoretically grounded core input for macroscopic simulation, overcoming the limitations of traditional simulations that rely on empirical parameters. At the macroscopic level, it deeply couples microscopic parameters with the finite element model, obtaining steady-state space charge and surface charge distributions through simulation. Using these as source terms, it accurately predicts the surface electric field distribution of ceramic materials, providing quantitative support for insulation reliability assessment and insulator design optimization. In application, this technology establishes a causal chain of "defect-migration barrier-charge accumulation-electric field distortion," providing theoretical guidance for the design of high-voltage ceramic insulation materials. This significantly reduces the R&D costs of traditional trial-and-error methods and has significant promotional value in fields with extremely high insulation reliability requirements, such as ultra-high-voltage transmission equipment and pulsed power devices, strongly supporting the development of high-reliability insulation products.

[0106] Further reference Figure 6 As an implementation of the methods shown in the above figures, this disclosure provides an embodiment of a device for simulating and predicting the electric field on the surface of ceramic materials. This device embodiment is similar to... Figure 2 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0107] like Figure 6 As shown, the simulation and prediction device 600 for the surface electric field of ceramic materials in this embodiment includes: a crystal construction module 601, a calculation module 602, a physical field construction module 603, and a simulation module 604.

[0108] Among them, the crystal construction module 601 is used to construct a crystal model based on the crystallographic information of the ceramic material;

[0109] Calculation module 602 is used to calculate the defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model;

[0110] The physics field construction module 603 is used to construct a finite element simulation multiphysics field based on the defect energy level, carrier migration barrier and / or mobility.

[0111] The simulation module 604 is used to simulate and predict the electric field intensity and distribution on the surface of ceramic materials based on the finite element simulation of multiphysics.

[0112] As one possible implementation, the crystal construction module 601 includes:

[0113] Unitary building blocks are used to construct crystal unit cell models based on the crystallographic information of ceramic materials;

[0114] A perfect supercell building unit is used to form a crystal supercell model using multiple crystal primitive cell models;

[0115] The defect supercell building unit is used to introduce various point defects into the crystal supercell model to form a defect supercell model.

[0116] As one possible implementation, the computing module 602 includes:

[0117] The defect formation energy calculation unit is used to calculate the defect formation energy corresponding to different point defects based on the first principles of density functional theory.

[0118] The defect energy level calculation unit is used to obtain the defect energy level by calculating the density of states curves of the crystal supercell model and the defect supercell model;

[0119] The migration barrier calculation unit is used to determine the migration barrier using the defect formation energy and the carrier migration mode of the ceramic material;

[0120] The carrier mobility calculation unit is used to substitute the migration barrier into the conductivity formula and Einstein's relation to calculate the carrier mobility.

[0121] As one possible implementation, the migration barrier calculation unit includes:

[0122] An ion conductivity component is used to convert the defect formation energy into a migration barrier in response to the ceramic material being ion conductive.

[0123] The first electronic conductivity component is used to, in response to the ceramic material being electronically conductive and the carrier migration mode of the ceramic material being electrons or holes, convert 1 / 2 of the defect formation energy into a migration barrier.

[0124] The second electronic conductivity component is used to convert the defect formation energy into a migration barrier in response to the fact that the ceramic material is electronically conductive and the carrier migration mode of the ceramic material is charge injection at the electrode-dielectric interface.

[0125] As one possible implementation, the physics field construction module 603 includes:

[0126] The initial model building unit is used to establish a two-dimensional axisymmetric or three-dimensional finite element model based on the actual geometric structure of the ceramic material.

[0127] The parameter setting unit is used to set the defect energy level, carrier migration barrier and / or mobility as parameters of the two-dimensional axisymmetric or three-dimensional finite element model to obtain the simulated charge physical field.

[0128] The multiphysics field setting unit is used to construct a multiphysics field that couples the electrostatic field and the charge transport field for the simulated charge physical field, so as to obtain the finite element simulation multiphysics field.

[0129] As one possible implementation, the simulation module 604 includes:

[0130] The density distribution acquisition unit is used to obtain the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface based on the finite element simulation multiphysics field.

[0131] The electric field strength element is used to substitute the space charge density distribution inside the medium and the surface charge density distribution accumulated at the gas-solid interface into the electrostatic field control equation to solve for the electric field strength and distribution on the surface of the ceramic material.

[0132] It should be noted that the implementation details and technical effects of each module and unit in the simulation and prediction device for the surface electric field of ceramic materials provided in the embodiments of this disclosure can be referred to the descriptions of other embodiments in this disclosure, and will not be repeated here.

[0133] The following is for reference. Figure 7 It shows a schematic diagram of the structure of a computer system 700 suitable for implementing the electronic device of the present disclosure. Figure 7 The computer system 700 shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments of this disclosure.

[0134] like Figure 7 As shown, the computer system 700 may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 701, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 702 or a program loaded from a storage device 708 into a random access memory (RAM) 703. The RAM 703 also stores various programs and data required for the operation of the computer system 700. The processing device 701, ROM 702, and RAM 703 are interconnected via a bus 704. An input / output (I / O) interface 705 is also connected to the bus 704.

[0135] Typically, the following devices can be connected to I / O interface 705: input devices 706 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, etc.; output devices 707 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 708 including, for example, magnetic tapes, hard disks, etc.; and communication devices 709. Communication device 709 allows computer system 700 to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 7A computer system 700 with various electronic devices is shown; however, it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed alternatively.

[0136] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication device 709, or installed from storage device 708, or installed from ROM 702. When the computer program is executed by processing device 701, it performs the functions defined above in the methods of embodiments of this disclosure.

[0137] It should be noted that the computer-readable medium described in this disclosure can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this disclosure, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this disclosure, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0138] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device.

[0139] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the following functions: Figure 2 The embodiments shown and their alternative implementations illustrate a method for simulating and predicting the electric field on the surface of ceramic materials.

[0140] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0141] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0142] The units or modules described in the embodiments of this disclosure can be implemented in software or hardware. The names of the units or modules do not necessarily limit the unit itself; for example, a crystal building module can also be described as "for forming a crystal supercell model using multiple crystal unit cell models".

[0143] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features disclosed in this disclosure that have similar functions.

Claims

1. A method of simulating and predicting the electric field at the surface of a ceramic material, characterized in that, The method comprises the following steps: constructing a crystal model according to crystallographic information of the ceramic material; calculating defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model; constructing a finite element simulation multi-physical field based on the defect energy level, carrier migration barrier and / or mobility; simulating and predicting surface electric field intensity and distribution of the ceramic material based on the finite element simulation multi-physical field.

2. The method of claim 1, wherein, The step of constructing a crystal model according to crystallographic information of the ceramic material comprises the following steps: constructing a crystal unit cell model according to crystallographic information of the ceramic material; forming a crystal supercell model by using a plurality of the crystal unit cell models; forming a defect supercell model by introducing a plurality of point defects into the crystal supercell model.

3. The method of claim 2, wherein, The step of calculating defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model comprises the following steps: calculating defect formation energy corresponding to different point defects based on the first principle of density functional theory; obtaining defect energy level by calculating the density of states curve of the crystal supercell model and the defect supercell model; determining a migration barrier by using the defect formation energy and the carrier migration mode of the ceramic material; calculating carrier mobility by bringing the migration barrier into a conductivity formula and Einstein relationship.

4. The method of claim 3, wherein, The step of determining a migration barrier by using the defect formation energy and the carrier migration mode of the ceramic material comprises the following steps: equivalent the defect formation energy to the migration barrier in response to the ceramic material being ion conduction; equivalent 1 / 2 of the defect formation energy to the migration barrier in response to the ceramic material being electronic conduction and the carrier migration mode of the ceramic material being electron or hole; equivalent the defect formation energy to the migration barrier in response to the ceramic material being electronic conduction and the carrier migration mode of the ceramic material being charge injection of electrode-dielectric interface.

5. The method of claim 1, wherein, The step of constructing a finite element simulation multi-physical field based on the defect energy level, carrier migration barrier and / or mobility comprises the following steps: establishing a two-dimensional axisymmetric or three-dimensional finite element model according to the real geometric structure of the ceramic material; setting the defect energy level, carrier migration barrier and / or mobility as parameters of the two-dimensional axisymmetric or three-dimensional finite element model to obtain a simulated charge physical field; constructing a multi-physical field coupled with electrostatic field and charge transport field for the simulated charge physical field to obtain a finite element simulation multi-physical field.

6. The method of claim 1, wherein, The step of simulating and predicting surface electric field intensity and distribution of the ceramic material based on the finite element simulation multi-physical field comprises the following steps: obtaining spatial charge density distribution in the medium and surface charge density distribution accumulated at the gas-solid interface based on the finite element simulation multi-physical field; substituting the spatial charge density distribution in the medium and the surface charge density distribution accumulated at the gas-solid interface into the electrostatic field control equation to solve the surface electric field intensity and distribution of the ceramic material.

7. An apparatus for simulating and predicting the electric field of a ceramic material surface, characterized by, The method comprises the following steps: a crystal construction module, configured to construct a crystal model according to crystallographic information of the ceramic material; a calculation module, configured to calculate defect formation energy, defect energy level, carrier migration barrier and / or mobility of the crystal model; a physical field construction module, configured to construct a finite element simulation multi-physical field based on the defect energy level, carrier migration barrier and / or mobility. An analog module is configured to simulate the surface electric field intensity and distribution of the ceramic material based on the finite element simulation of the multi-physical field.

8. The apparatus of claim 7, wherein, The crystal construction module comprises: A unit cell construction unit is configured to construct a crystal unit cell model according to crystallographic information of the ceramic material; A perfect supercell construction unit is configured to form a crystal supercell model by using a plurality of the crystal unit cell models; A defect supercell construction unit is configured to introduce a plurality of point defects into the crystal supercell model to form a defect supercell model.

9. An apparatus for simulating and predicting an electric field on a surface of a ceramic material, characterized by, A computer program product comprising a processor and a memory storing program instructions, wherein the processor is configured to execute the method of any one of claims 1 to 6 when running the program instructions.

10. A computer-readable storage medium, characterized in that, A computer program product comprising a processor and a memory storing program instructions, wherein the processor is configured to execute the method of any one of claims 1 to 6 when running the program instructions.

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