Atomic interaction information prediction method based on machine learning potential function, storage medium and equipment

Abstract

The invention discloses an atomic interaction information prediction method based on a machine learning potential function, a storage medium and equipment, and relates to the field of artificial intelligence and new energy, in particular to the atomic interaction information prediction method, the storage medium and the equipment. The objective of the invention is to solve the problem that precision and efficiency are difficult to consider when atomic interaction information is obtained by an existing method. The atomic interaction information prediction method based on the machine learning potential function specifically comprises the steps of 1, obtaining an initial data set, and expanding the initial data set to obtain a comprehensive data set which finally covers a bulk phase and a surface structure; 2, training a machine learning potential function MLP based on the comprehensive data set to obtain a trained machine learning potential function MLP; 3, predicting metal lithium, silicon and lithiated silicon atoms to be detected based on the trained machine learning potential function MLP, and outputting atom interaction information of the metal lithium, silicon and lithiated silicon atoms; the interaction information is energy and stress.

Description

Technical Field

[0001] The present invention relates to the fields of artificial intelligence and new energy, and in particular to a method, storage medium and device for predicting atomic interaction information. Background Art

[0002] With the rapid development of renewable energy and electric vehicle industries, lithium-ion batteries, as key energy storage devices, have become a research hotspot for performance optimization. As a high-capacity negative electrode material, lithium-ion silicon has attracted much attention due to its significant theoretical capacity and low cost. However, lithium-ion silicon has problems such as large volume expansion and short cycle life in practical applications, which are mainly attributed to its complex lithiation process and the dynamic evolution of multiphase interfaces. Therefore, accurately describing the potential energy surface (PES) of the lithium-ion silicon system is of great significance for understanding its lithiation mechanism and optimizing material properties.

[0003] In the prior art, the commonly used methods for describing the potential energy surface of lithium silicon mainly include classical force field methods and calculation methods based on first principles. The classical force field method can simulate the dynamic behavior of large-scale systems at a low computational cost through empirical parameter fitting, but its accuracy depends on parameter optimization and it is difficult to accurately capture complex chemical reaction processes. Methods based on first principles, such as density functional theory (DFT), can provide high-precision potential energy descriptions, but their high computational cost limits their application in large-scale systems and long time scale simulations.

[0004] In recent years, with the development of deep learning technology, potential energy function fitting methods based on neural networks have gradually become a research hotspot. This type of method trains the neural network model through a large amount of first-principles data, which can significantly reduce the computational cost while maintaining high accuracy. For example, Neural Network Potential (NNP) has demonstrated superior performance in a variety of material systems. However, existing neural network-based methods still face challenges such as large data requirements, long training time, and insufficient model generalization capabilities when dealing with complex lithium-silicon systems.

[0005] In summary, the current technology for describing the potential energy surface of lithiated silicon has a trade-off between accuracy and computational efficiency, especially when dealing with complex lithiation processes and dynamic evolution of multiphase interfaces, it is difficult to achieve both high accuracy and high efficiency. These shortcomings limit the further optimization and promotion of lithiated silicon materials in practical applications. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that it is difficult to strike a balance between accuracy and efficiency when obtaining atomic interaction information using existing methods, and to propose an atomic interaction information prediction method, storage medium and device based on machine learning potential function.

[0007] The interaction information is energy and force.

[0008] The specific process of the atomic interaction information prediction method based on machine learning potential function is as follows:

[0009] Step 1: Obtain an initial data set, expand the initial data set, and finally obtain a comprehensive data set covering bulk and surface structures;

[0010] Step 2: Train the machine learning potential function MLP based on the comprehensive data set to obtain a trained machine learning potential function MLP;

[0011] Step 3: Based on the trained machine learning potential function MLP, the metal lithium, silicon, and lithiated silicon atoms to be tested are predicted, and the atomic interaction information of the metal lithium, silicon, and lithiated silicon atoms is output; the interaction information is energy and force.

[0012] A storage medium stores at least one instruction, which is loaded and executed by a processor to implement an atomic interaction information prediction method based on a machine learning potential function.

[0013] A device for predicting atomic interaction information based on machine learning potential functions, the device comprising a processor and a memory, the memory storing at least one instruction, the at least one instruction being loaded and executed by the processor to implement a method for predicting atomic interaction information based on machine learning potential functions.

[0014] The beneficial effects of the present invention are:

[0015] The present invention provides a method for predicting atomic interaction information based on machine learning potential functions. First, the system extracts bulk structure data of metallic lithium, silicon and lithiated silicon crystals covering different lithium contents and crystalline and amorphous states from the initial data set as the initial training data of the neural network model. Then, the multi-layer deep neural network model is preliminarily trained using these initial data to obtain a preliminary potential energy function fitting model. Subsequently, based on the preliminary training model, the system performs a series of molecular dynamics simulations, including surface structure simulation, uniaxial stretching simulation and diffusion process simulation, to generate new structure and force data. During the simulation process, the error detection module analyzes the simulation results and identifies key structures with large atomic force errors. These key structures are then used to obtain accurate energy and force data through high-precision first-principles calculations (such as DFT single-point energy calculations). The high-precision calculation results are integrated into the original data set to expand and optimize the training data set, especially to supplement the data of surface and interface structures. The updated data set is used to retrain the neural network model, and the model structure and parameters are optimized using transfer learning and active learning techniques, thereby improving the fitting accuracy and generalization ability of the model. This iterative process is repeated under the management of the iteration control module until the model reaches the predetermined accuracy and data coverage. Ultimately, the system generates a comprehensive data set covering both bulk and surface structures, providing a solid data foundation for efficient simulation and performance optimization of lithiated silicon materials.

[0016] The entire program execution process can be summarized by the following flowchart: first, data extraction and initial model training are performed, then molecular dynamics simulation is performed, followed by error detection and high-precision calculations, followed by updating the data set and optimizing the model, and finally iterating to determine whether to continue the cycle, finally generating a comprehensive data set and ending the program.

[0017] The present invention effectively fits the potential energy surface of the lithiated silicon system by adopting an advanced neural network structure and an efficient data training strategy, overcoming the problems of large data requirements, long training time, and insufficient model generalization in the prior art. Specifically, the present invention uses a multi-layer deep neural network model, combined with transfer learning and active learning technology, to significantly improve the fitting accuracy and calculation efficiency of the potential energy function, providing a powerful tool for efficient simulation and performance optimization of lithiated silicon materials.

[0018] Through the method of the present invention, the potential energy surface of lithiated silicon materials can be efficiently and accurately fitted, solving the deficiencies in data coverage and computational efficiency in the prior art. Specifically, the method uses an active learning strategy to selectively select key structures with high information content for high-precision calculations, significantly improving the fitting accuracy of the neural network potential energy function. At the same time, the optimized data training strategy effectively reduces unnecessary high-precision calculations, saves computing resources and time, and is suitable for the simulation of large-scale material systems. In addition, during the iterative optimization process, the model continuously receives diversified data training, which enhances its adaptability and predictive ability under different lithiation conditions. The comprehensive data set finally generated covers the bulk and surface structures, making up for the deficiencies of the initial data set, and providing comprehensive data support for material performance optimization. These beneficial effects provide a solid theoretical basis for the efficient simulation and performance optimization of lithiated silicon materials in battery technology, and promote their further development and industrialization in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flow chart of the present invention;

[0020] Figure 2 This is a flow chart of the present invention using active learning method to expand the data set of metal lithium and silicon negative electrode materials, MD is molecular dynamics simulation;

[0021] Figure 3 The four typical structures included in the lithium metal training data set are: (a) body-centered cubic; (b) face-centered cubic; (c) close-packed hexagonal; (d) amorphous phase;

[0022] Figure 4 These are the three typical structures included in the silicon training data set: (a) diamond structure; (b) I41amd; (c) amorphous phase;

[0023] Figure 5 The training data set for lithium-ion silicon materials contains 6 typical structures, namely (a) c-Li1Si1; (b) c-Li2Si1; (c) c-Li 12 Si7; (d) c-Li 15 Si4; (e) c-Li 22 Si5; (f) a-Li x Si,0 <x<4.5;

[0024] Figure 6 Comparison diagram of MLP prediction value and DFT calculation value in (a) root mean square error, (b) energy, (c) force, and (d) stress; Percrntage is the percentage of samples in the interval;

[0025] Figure 7Volume-energy comparison diagram of MLP predicted value and DFT calculated value in (a) metallic lithium crystal and (b) silicon crystal, where Volume is volume and Energy is energy;

[0026] Figure 8 Anisotropy diagram of the elastic modulus of metallic lithium, (a) three-dimensional view; (b) two-dimensional projection, E X is the elastic modulus in the x direction, E Y is the elastic modulus in the y direction, E Z is the elastic modulus in z direction, GPa is the stress unit;

[0027] Fig. 9 Anisotropy diagram of the maximum shear modulus of metallic lithium, (a) three-dimensional view; (b) two-dimensional projection, G maxX is the maximum shear modulus in the x direction, G maxY is the maximum shear modulus in the y direction, G maxZ is the maximum shear modulus in the z direction;

[0028] Fig.10 Anisotropy diagram of elastic modulus of single crystal silicon, (a) three-dimensional view; (b) two-dimensional projection;

[0029] Fig.11 Anisotropy diagram of the maximum shear modulus of single crystal silicon, (a) three-dimensional view; (b) two-dimensional projection;

[0030] Fig.12 The elastic modulus of amorphous lithium silicon under different lithium contents is shown in Figure 2. Lithium fraction is the lithium content in lithium silicon, and Elastic modulus is the elastic modulus.

[0031] Fig.13 This is a comparison of the unrelaxed surface energy of lithiated silicon calculated by DFT and MLP. Unrelax surface energy is the unrelaxed surface energy.

[0032] Fig.14 Schematic diagram of uniaxial tensile simulation of lithium metal and stress-strain curve. (a) Schematic diagram of the initial crystal structure, green dots are lithium atoms, black arrows indicate crystal directions

[100] ,

[010] and

[001] ; (b) Stress-strain curves of systems with different atomic numbers (864, 2048, 4000, 6912), showing the convergence and reliability of the simulation results; Strain is strain, Stress is stress;

[0033] Fig.15Schematic diagram of uniaxial tensile simulation of lithium metal and stress-strain curve; (a) Schematic diagram of the initial crystal structure, green dots are lithium atoms, black arrows indicate crystal directions

[100] ,

[010] and

[001] ; (b) Stress-strain curves of systems with different atomic numbers (864, 2048, 4000, 6912), showing the convergence and reliability of the simulation results; Strain is strain, and Proportion structure is the content of the structure;

[0034] Fig.16 The structural diagram of the silicon crystal stretched along different crystal directions; (a) Stretching along the

[100] direction, the black arrows indicate the crystal directions

[100] ,

[010] and

[001] ; (b) Stretching along the

[111] direction, the black arrows indicate the crystal directions

[111] , [-110] and [11-2];

[0035] Fig.17 The stress-strain relationship of silicon crystals with different crystal orientations during uniaxial tension and the change of peak stress with the number of atoms; (a) along the

[100] crystal orientation, (b) along the

[111] crystal orientation, (c) along the

[100] crystal orientation, the change of the ultimate stress with the increase of the number of atoms, (d) along the

[111] crystal orientation, the change of the ultimate stress with the increase of the number of atoms; atoms means atoms;

[0036] Fig.18 The stress distribution and failure morphology of silicon crystal under different strains along the

[111] crystal direction;

[0037] Fig.19 The figure shows the effect of point defect concentration on the mechanical properties of crystalline silicon. (a) shows the changes in the atomic structure of cubic diamond under different defect ratios (0%, 0.1%, 1%, 5%), (b) stress-strain curve, (c) the effect of defect ratio on the elastic modulus and strength of cubic diamond in the

[111] direction. Perfect is a perfect crystal, defects are defects, Non-Diamond is a non-diamond structure, Cubic Diamond is cubic diamond, Cubic Diamond (1st neighbor) is the first neighbor of cubic diamond, Cubic Diamond (2nd neighbor) is the second neighbor of cubic diamond, E of

[111] direction is the elastic modulus in the

[111] direction, Strength of

[111] direction is the strength in the

[111] direction, and Defects ratio is the defect ratio. DETAILED DESCRIPTION

[0038] Specific implementation method 1: The specific process of the atomic interaction information prediction method based on machine learning potential function in this implementation method is as follows:

[0039] Step 1: Obtain an initial data set, expand the initial data set, and finally obtain a comprehensive data set covering bulk and surface structures;

[0040] Step 2: Train the machine learning potential function MLP based on the comprehensive data set to obtain a trained machine learning potential function MLP;

[0041] Step 3: Based on the trained machine learning potential function MLP, the metal lithium, silicon, and lithiated silicon atoms to be measured are predicted, and the atomic interaction information of the metal lithium, silicon, and lithiated silicon atoms is output;

[0042] The interaction information includes energy, force, etc.

[0043] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that, in step 1, an initial data set is obtained, and the initial data set is expanded to obtain a comprehensive data set covering both the bulk phase and the surface structure. The specific process is as follows:

[0044] Step 11: Obtain the initial data set; the specific process is:

[0045] The initial data set includes metallic lithium, silicon, and lithiated silicon;

[0046] Step 1 and 2: Expand the initial data set to obtain a comprehensive data set covering both bulk and surface structures.

[0047] The other steps and parameters are the same as those in the first embodiment.

[0048] Specific embodiment 3: This embodiment is different from specific embodiment 1 or 2 in that the metallic lithium in step 1 is body-centered cubic (BCC), face-centered cubic (FCC), hexagonal close-packed (HCP) and amorphous structure, such as Figure 3 As shown;

[0049] Silicon has diamond structure, I41amd structure and amorphous structure, such as Figure 4 As shown;

[0050] Lithium silicon includes crystalline and amorphous lithium silicon.

[0051] The other steps and parameters are the same as those in the first or second embodiment.

[0052] Specific embodiment 4: This embodiment is different from any one of the specific embodiments 1 to 3 in that the crystalline lithium silicon is c-Li1 Si1, c-Li2 Si1, c-Li 12 Si7、c-Li 15 Si4、c-Li22 Si5;

[0053] Amorphous lithium silicon is a-Li x Four.

[0054] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0055] Specific implementation method 5: This implementation method is different from specific implementation methods 1 to 4 in that the initial data set is expanded in step 1 and 2 to obtain a comprehensive data set covering the bulk and surface structures; the specific process is:

[0056] Step 121: Based on the initial data set, four machine learning potential function MLPs are trained respectively to obtain four trained machine learning potential function MLPs respectively;

[0057] Step 122: Based on the first trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed (for example, different stacking modes of lithium metal also result in different structures, and the element ratios of lithium and silicon are different, which can be subdivided into many structures), and simulation results A are obtained (the simulation results are the atomic interaction forces of specific structures); simulation results A are the atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials;

[0058] Based on the second trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation result B (the simulation result is the atomic interaction force of a specific structure); simulation result B is the atomic force of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials;

[0059] Based on the third trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation results C (the simulation results are the atomic interaction forces of specific structures); simulation results C are the atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials;

[0060] Based on the fourth trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation results D (the simulation results are the atomic interactions of specific structures); the simulation results D are the atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials;

[0061] Step 1, 2, 3, calculate the difference in atomic force of the same atomic structure in any two simulation results of A, B, C, D, and the maximum difference is the maximum atomic force error E;

[0062] Step 1, 2, 4,

[0063] If the maximum atomic force error E is less than 0.15, the final comprehensive data set is obtained;

[0064] If the maximum atomic force error is 0.15≤E≤0.45, perform DFT calculation on the atomic structure corresponding to the maximum atomic force error E to obtain the atomic energy, atomic force and lattice stress information of the atomic structure, add the atomic energy, atomic force and lattice stress information of the atomic structure to the initial data set, and repeat steps 121 to 124 until the maximum atomic force error E is less than 0.15, thereby obtaining the final comprehensive data set;

[0065] DFT stands for density functional theory;

[0066] If the maximum atomic force error E is greater than 0.45, the calculation ends (structures greater than 0.45 are considered non-physical and are not considered and do not participate in subsequent calculations).

[0067] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0068] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the unit of the atomic force error E is force, and the force is expressed as eV stands for electron volt; Stands for angstrom, a unit of length used primarily to describe distances at the atomic and molecular scales.

[0069] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0070] Specific implementation method seven: This implementation method is different from specific implementation methods one to six in that the four machine learning potential functions MLP in step one two one are machine learning potential functions MLP with the same hyperparameters and different random parameters.

[0071] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0072] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the dynamic simulation in step one two two includes simulations of surface structure, tension and diffusion process.

[0073] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0074] Specific implementation method nine: This implementation method is a storage medium, in which at least one instruction is stored. The at least one instruction is loaded and executed by a processor to implement the atomic interaction information prediction method based on machine learning potential function.

[0075] It should be understood that any method described in the present invention may be provided as a computer program product, software or computerized method, which may include a non-transitory machine-readable medium having instructions stored thereon, and the instructions may be used to program a computer system or other electronic device. The storage medium may include, but is not limited to, magnetic storage media, optical storage media; magneto-optical storage media include: read-only memory ROM, random access memory RAM, erasable programmable memory (e.g., EPROM and EEPROM) and flash memory layer; or other types of media suitable for storing electronic instructions.

[0076] Specific embodiment ten: This embodiment is an atomic interaction information prediction device based on machine learning potential function, the device includes a processor and a memory. It should be understood that including any device including a processor and a memory described in the present invention, the device may also include other units and modules that perform display, interaction, processing, control, etc. and other functions through signals or instructions;

[0077] At least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the atomic interaction information prediction method based on machine learning potential function.

[0078] Establishment of training data sets for metal lithium anode and silicon anode: Active learning methods are used to train the metal lithium and silicon anode potential energy models, and the training data sets use various crystalline and amorphous metal lithium and silicon structure data. Specifically, the data set includes metal lithium and silicon structures with different degrees of lithiation (lithium content), different temperatures (300-1500K), different strains (0%-10%), and different crystal sizes (32-128 atoms). These structures cover the solid and liquid phase transitions of metal lithium and silicon materials during stretching, as well as the mutual transitions between amorphous and crystalline states.

[0079] The typical structures of metallic lithium in the training data set include body-centered cubic (BCC), face-centered cubic (FCC), hexagonal close-packed (HCP) and amorphous structures, such as Figure 3As shown. These structural models cover the possible phases of metallic lithium under different temperature and pressure conditions. The BCC structure has high temperature stability, the FCC structure exhibits higher mechanical strength and toughness due to its high atomic packing density, and the HCP structure is formed under specific pressure conditions and has good isotropic mechanical properties. In the amorphous structure, the atomic arrangement has no long-range order, but it is formed under rapid cooling or high strain rate conditions and has unique physical and chemical properties, such as high diffusion coefficient and excellent mechanical properties. The introduction of these structures can improve the generalization of the force field potential function.

[0080] Typical structures of silicon in the training data set include diamond structure, I41amd structure and amorphous structure, such as Figure 4 These models represent the atomic arrangement of silicon in different crystalline and amorphous phases. Diamond structure is the most stable crystalline phase of silicon at room temperature and pressure. It has a highly symmetrical tetrahedral structure and exhibits excellent mechanical and electronic properties, such as Figure 4 As shown in (a). The I41amd structure is a relatively rare crystalline phase with a unique layered arrangement. It can be formed under specific pressure and temperature conditions and exhibits unique physical properties, such as Figure 4 As shown in (b). Amorphous structure describes the atomic arrangement without long-range order formed by silicon under rapid cooling or non-equilibrium conditions, which usually exhibits mechanical and electrical properties different from those of crystalline silicon, such as Figure 4 As shown in (c).

[0081] The silicon negative electrode embeds lithium atoms to form lithium-ion silicon. The training data set covers the typical structures of crystalline and amorphous lithium-ion silicon with different lithium contents, such as Figure 5 As shown. The c-Li1 Si1 structure represents crystalline lithium silicon with a stoichiometric ratio of 1:1, showing a stable tetrahedral lattice structure. This structure has been observed to have high electrical conductivity and good mechanical stability in experiments, such as Figure 5 As shown in (a). As the lithium content increases, lithium atoms in the c-Li2Si1 structure occupy more lattice positions, forming a layered arrangement, such as Figure 5 As shown in (b), this structure exhibits obvious interlayer interactions and enhanced ionic conductivity in Raman spectroscopy and X-ray diffraction experiments.

[0082] c-Li with further increased lithium content 12 Si7 and c-Li 15 The Si4 structure shows a more complex atomic arrangement and highly occupied lithium atomic sites, e.g. Figure 5These structures show highly ordered microstructures in scanning electron microscopy and transmission electron microscopy experiments, indicating the diverse interaction mechanisms between lithium atoms and silicon atoms. In particular, c-Li 15 The Si4 structure, due to its high lithium content, exhibits significant electrochemical activity and low interfacial impedance in cyclic voltammetry and electrochemical impedance spectroscopy tests. 22 The Si5 structure is formed at extremely high lithium content and has an extremely tight and regular lattice arrangement, indicating that it has potential excellent lithium storage capacity and stability, such as Figure 5 As shown in (e).

[0083] Amorphous lithium silicon (a-Li x Si) structure describes the atomic arrangement without long-range order formed under conditions of rapid cooling or high strain rate, such as Figure 5 As shown in (f). During the charge and discharge process of lithium batteries, when lithium atoms are rapidly embedded in or extracted from silicon-based materials, dramatic volume changes and local structural reorganization occur inside the material. During fast charging, lithium ions are rapidly embedded in silicon-based materials, making it impossible for the silicon atomic structure to adjust in time to form an ordered lattice, resulting in an amorphization process. This phenomenon is particularly significant in actual battery cycles, because rapid lithium insertion and extraction can cause stress and strain inside the material, causing the crystalline structure to break and form an amorphous state. This process was verified in differential scanning calorimetry and in situ X-ray diffraction experiments, showing structural changes caused by charge and discharge cycles. Amorphous lithium-ion silicon has different mechanical and electrical properties from the crystalline state, such as higher volume expansion tolerance and better conductivity, and therefore exhibits excellent electrochemical properties in practical applications.

[0084] Establishment and verification of machine learning force field potential function

[0085] Active learning method: The training data set mainly covers bulk structures with different lithium contents and crystalline and amorphous states, providing an important data basis for studying the physical properties and mechanical behaviors of metallic lithium and silicon anode materials under bulk conditions. However, these data sets are still insufficient in terms of surface structure, which limits the in-depth analysis of metallic lithium and silicon anode materials at the interface and surface reactions and fracture. In order to make up for this deficiency, an active learning strategy is introduced to expand and optimize the data set more efficiently.

[0086] Active learning is a machine learning method that improves the accuracy and generalization ability of the model by iteratively selecting the most informative data points for annotation and training. In materials science, active learning strategies can quickly find the most critical structures for the potential energy function and perform high-precision first-principles calculations with limited computing resources. This process not only improves computational efficiency, but also significantly improves the prediction accuracy of the potential energy function. To this end, a deep potential generator was used, combined with an active learning strategy, to iteratively generate new structural data and perform high-precision calculations to gradually expand and improve the training data set. The deep potential generator can automatically identify and screen the structures that are most critical to the optimization of the potential energy function, including structures under high strain of various surface and interface structures, thereby supplementing the lack of surface data in the original data set.

[0087] The calculation process of active learning strategy to expand the data set of lithium metal and silicon negative electrode materials is as follows Figure 2 As shown in the figure. First, the structural data of various metal lithium, silicon and lithiated silicon crystals are extracted from the initial data set, and the neural network model is trained using these data. Then, molecular dynamics simulations are performed, including simulations of surface structure, uniaxial tension and diffusion process. Through the iterative active learning process, the machine learning force field potential energy function of metal lithium and silicon is gradually improved to generate a comprehensive data set covering bulk and surface structure. In this process, four neural network models are trained at the same time in this chapter. The key structures with large atomic force errors are identified through molecular dynamics simulations, and high-precision DFT single-point energy calculations are performed on these structures to update the data set. The core of active learning is to efficiently select the most informative data points for calculation and training, so as to maximize the performance improvement of the model. In order to more comprehensively capture the details of the potential energy surface, the crystal plane structures (100), (110) and (111) of metal lithium, silicon and lithiated silicon crystals are added, which play a key role in accurately simulating the interface properties and reactions of the materials. By simulating these surfaces, various conditions that the materials may encounter in practical applications can be more comprehensively captured, thereby improving the model's ability to predict surface behavior. This chapter also conducts uniaxial tensile simulations to study the stress-strain relationship and mechanical properties of metallic lithium, silicon, and lithiated silicon materials under external forces. These simulation data help understand the strength, ductility, and fracture behavior of the materials. In addition, another key part is to study the simulation of the diffusion of lithium atoms on the (111) surface of silicon, which is of great significance for understanding the movement and distribution of lithium ions during battery charging and discharging. Through continuous iterations of active learning and high-precision DFT calculations, the potential energy functions of metallic lithium and silicon materials have been gradually improved, generating a comprehensive data set covering bulk and surface structures.

[0088] The VASP package was used for DFT single-point energy calculations, and PAW pseudopotential was used. The interaction between lithium and silicon atoms was taken into account during the calculation. The electronic configuration of lithium is 1s, and the electronic configuration of silicon is 1s. 2 2s 2 2p 2 The PBE functional was selected to handle the exchange-correlation energy. To ensure the accuracy of the calculation, a cutoff energy of 560 eV was set, and a Gaussian broadening of 0.1 eV was selected to describe the occupation of the electronic state. The K-point sampling used the Gamma center grid with a density of The energy convergence criterion is set to 10 -6 eV to ensure that the electronic self-consistent cycle achieves the required accuracy. After the DFT calculation is completed, information such as configuration energy, atomic forces, and potential forces on the lattice are extracted and integrated into the data set to further train and optimize the potential energy function.

[0089] Training accuracy verification: Extract the distance and angle information used by the local environment of the atom and set the cutoff range Rc to After testing, this truncation radius balances the accuracy and time consumption of the calculation. The same truncation setting is also used in the existing relevant literature. Through 32 iterations, a total of 1923 frames of DFT single-point energy calculation data including transition structures in the simulation process of surface, stretching and surface diffusion were collected. After the data collection was completed, the final potential function training was carried out. During the training process, four neural network models with the same hyperparameters and different random parameters were constructed and trained. The model embedding and fitting network include formatting the descriptor vector, which is then used as the input of the deep neural network model. The number of neurons in the three-layer structure of the embedded network is (25, 50, 100) and (240, 240, 240), respectively. For the initial data set, the number of data samples used for one training is set to 8, and the number of data samples for the new configurations explored is set to 2. The weight coefficients of energy, force and virial stress in the total loss function increase from 0.02 to 1.0, decrease from 1000 to 1.0, and increase from 0.02 to 1.0, respectively. The initial learning rate is 0.001, and decays to 0.95 every 4000 steps. In each iteration, the model is trained for 300,000 steps, and the final effective model is trained for 2 million steps. After completing a round of training, the dataset is shuffled and the next round of training is entered. The learning rate (lr) of the model decreases exponentially with the increase of the current training batch:

[0090] lr(t)=start_lr×decay_rate t / decay _ steps

[0091] Among them, the initial learning rate (start_lr), decay rate (decay_rate) and decay interval steps (decay_steps) are set to 0.001, 0.95 and 1500 respectively.

[0092] Figure 6 The comparison between the machine learning potential (MLP) predictions and DFT calculations for energy, force, and stress is described in Figure 2. Figure 6 (a) shows the root-mean-square error (RMSE) of energy, force, and stress as the number of training steps increases. As the number of training steps increases, the RMSE of all three physical quantities gradually decreases, especially in the early stages of training, where the RMSE drops rapidly, indicating that the model is rapidly optimized during the initial learning process. Eventually, the RMSE stabilizes, indicating that the model has reached a convergence state. Among them, the RMSE of energy is the lowest, eventually tending to below 0.05 eV / atom, indicating that the MLP model is very accurate in predicting energy; the RMSE of force is slightly higher than that of energy, but still The RMSE of stress is the highest, about 0.2 eV / atom, but it is still within an acceptable range. Figure 6 (b) compares the energy calculated by MLP and DFT. The results show that the data points are closely distributed near the diagonal, and the error histogram shows that most energy errors are concentrated in the range of 0 to 5%, indicating that the MLP model is highly consistent with DFT in energy prediction. Figure 6 (c) shows the force comparison. The force values ​​calculated by MLP and DFT are also closely distributed near the diagonal. The error histogram shows that most force errors are concentrated between 0 and The high accuracy of force prediction by MLP model is further verified. Figure 6 (d) compares the stress calculated by MLP and DFT. The data points are mainly concentrated on the diagonal line. The error histogram shows that most stress errors are concentrated in the range of 0 to 0.2 eV / atom, indicating the accuracy of the MLP model in stress prediction. Overall, these comparison graphs verify the effectiveness and reliability of the MLP model, which can replace DFT for material simulation with high accuracy, providing a solid foundation for large-scale material performance prediction and optimization.

[0093] Volume energy verification: The energy-volume curve describes the energy change relationship of a material at different volumes. It is used to study the stability and mechanical properties of the material. The lowest point of the curve corresponds to the equilibrium volume and lowest energy state of the material, indicating that the material is most stable at this volume. Figure 7The energy-volume curves of metallic lithium and silicon crystals calculated by DFT and MLP are shown in the figure. In the metallic lithium crystal part of the figure, the energy changes with volume in a typical parabolic shape, showing an obvious energy minimum point. The DFT calculation results are represented by gray circles, and the MLP calculation results are represented by blue solid lines. The results of the two calculation methods are highly consistent, and the energy minimum point and the overall curve shape almost coincide, indicating that the MLP model can accurately reproduce the DFT calculation results. In the silicon crystal part, the energy-volume curve also presents a parabolic shape, and the DFT calculation results are represented by gray triangles, and the MLP calculation results are represented by yellow solid lines. Similar to metallic lithium crystals, the two methods also show a high degree of consistency in the energy minimum point and curve shape of silicon crystals. This consistency shows that the MLP model can achieve comparable accuracy to DFT calculations when simulating the energy-volume relationship of materials.

[0094] Basic mechanical properties of metallic lithium and silicon anode materials

[0095] Elastic constants: Calculating the elastic constants of a material is crucial to understanding its mechanical properties. The elastic modulus describes the elastic response of a material under external forces and is usually characterized by a stress-strain relationship. For linear elastic materials, the classic stress-strain relationship is as follows:

[0096] σ ij =C ijkl ε kl

[0097] Among them, σ ij Represents the stress component. It is the reaction force generated inside the material under the action of external force, which describes the mechanical state inside the material. ε kl Represents the strain component. It is the deformation of the material under the action of external force and describes the degree of deformation of the material. ijkl It is a fourth-order elastic tensor that represents the elastic constants of the material. It contains the elastic response information of the material under different stress states and is a tensor with 81 components.

[0098] Strain ε ij is the deformation gradient The symmetric part of can be expressed as:

[0099]

[0100] Here, u i represents the displacement component, represents the partial derivative of displacement with respect to the coordinate. The strain tensor describes the degree of deformation of the material under the action of external force. For small deformations, the above linear strain definition is usually used. When the deformation is large, nonlinear strain needs to be considered. Since both the stress tensor and the strain tensor are symmetric tensors, they can be simplified to vector form using the Voigt representation, making the stress-strain relationship more concise:

[0101] [σ]=[C][ε]

[0102] In this notation, [σ] is the vector containing all stress components, and [ε] is the vector containing all strain components:

[0103]

[0104] Among them, the elastic constant matrix [C] is a symmetric 6×6 matrix that contains the elastic modulus information of the material. For materials with orthogonal symmetry, the elastic constant matrix can be expressed as:

[0105]

[0106] Among them, C ij represents the independent elastic constants of the material. For materials with higher symmetry, the elastic constant matrix will have more zero elements and equal elements, which will further simplify it. In practical materials and engineering literature, elastic properties are usually not expressed in C. ij Instead of expressing the elastic properties of the corresponding anisotropic material, the elastic properties of the equivalent isotropic material are substituted. These averaging methods are particularly important for dealing with polycrystalline materials composed of randomly oriented grains. There are three main averaging methods: Voigt averaging, Reuss averaging, and Hill averaging.

[0107] Voigt averaging method is based on the stiffness matrix C ij This method assumes that the strain of the material in all directions is uniform and is suitable for describing isotropic elastic behavior. Voigt average method calculates bulk modulus (B V ) and shear modulus (G V ) is as follows:

[0108]

[0109] Among them, the bulk modulus B V It reflects the material's ability to resist compression under volume deformation, while the shear modulus G V It describes the material's ability to resist shear deformation.

[0110] Reuss average rule is based on the flexibility matrix S ij, this method assumes that the stress of the material is uniform in all directions. The Reuss average method is suitable for describing isotropic elastic behavior under uniform stress distribution. Its calculation of bulk modulus (B R ) and shear modulus (G R ) is:

[0111]

[0112] In this method, the inverse of the flexibility matrix is ​​the stiffness matrix. Its calculation process is opposite to that of the Voigt method. The corresponding elastic modulus is calculated by averaging the flexibility matrix.

[0113] The Hill average method is the arithmetic average of the Voigt and Reuss methods. It combines the advantages of both methods and provides an elastic modulus estimation method that is closer to the actual material behavior. The Hill average method believes that the elastic behavior of the actual material is neither completely uniform in strain nor completely uniform in stress, but a combination of the two. Therefore, the Hill average method gives a more reliable elastic modulus estimate by averaging the Voigt and Reuss values. This method is widely used in practice because it can more accurately reflect the actual elastic behavior of crystalline materials. The calculation formula is as follows:

[0114]

[0115] Once the bulk modulus (B) and shear modulus (G) of the material are calculated, the Young's modulus (E), Poisson's ratio (v), etc. of the material can be further estimated. The calculation process is as follows:

[0116]

[0117] In MD or DFT calculations, the elastic constant matrix of the material is calculated by applying strains in six directions (including tensile strains along the xx, yy, and zz directions and shear strains along the xy, xz, and yz directions). First, the initial crystal structure of the material is geometrically optimized to ensure that a stable state is achieved under stress-free conditions. Then, small strains in different directions are applied to the optimized structure, and the stress response under each strain is calculated. Based on the stress-strain relationship, the elastic constant matrix C is fitted by linear regression. ij In this chapter, the elastic matrix is ​​calculated by applying strains of -0.01, -0.005, 0.005, and 0.01 in each strain direction of the structure, and the Hill average method is used to calculate the equivalent elastic properties. Tables 1 and 2 summarize the comparison of the elastic constants of metallic lithium and silicon crystals calculated by MLP and DFT.

[0118] Comparing the elastic parameters in the table, the error analysis of MLP relative to DFT calculation shows that for metallic lithium crystals, the maximum relative error in elastic parameters occurs at Poisson's ratio of 4.23%, the minimum relative error occurs at elastic modulus of 2.4%, and the average relative error is about 3.25%. For silicon crystals, the maximum relative error in elastic parameters occurs at C 11 The minimum relative error is 8.50% and occurs at C 12 The average relative error is 2.06% and about 2.40%. These data show that the MLP model shows high accuracy in predicting most elastic parameters. Although there are large errors in specific parameters, the overall average error is still within a reasonable range, which verifies the reliability of the MLP model in predicting material elastic properties.

[0119] Table 1 Calculation results of elastic constants of metallic lithium crystal

[0120]

[0121] Table 2 Calculation results of elastic constants of silicon crystal

[0122]

[0123] In addition to analyzing the elastic constants of lithium metal and silicon crystals, this chapter further explores their anisotropic characteristics, including parameters such as bulk modulus, shear modulus and Young's modulus. These analyses will help reveal the potential performance differences between lithium metal and silicon crystals in practical applications and provide a key scientific basis for material design and optimization.

[0124] Figure 8 The anisotropic analysis results of the elastic modulus of metallic lithium are presented, indicating that its elastic modulus has significant directional dependence in space. Figure 8 The 3D view in (a) shows six protruding regions, indicating that the elastic modulus is higher in a specific direction, which is the diagonal direction of the BCC crystal structure, with an elastic modulus close to 25 GPa, and lower in other directions. Figure 8 The 2D contour map in (b) further refines this feature, with bright areas corresponding to high moduli concentrated at specific angles, confirming the anisotropy of metallic lithium. This anisotropy stems from the characteristics of the crystal structure and atomic arrangement, and is of great significance for optimizing the mechanical properties of lithium-based materials in practical applications.

[0125] Fig. 9 The maximum shear modulus of metallic lithium (G max ) reveals its mechanical properties characteristics in different crystal directions. Fig. 9(a) shows the distribution of shear modulus in various directions through a three-dimensional view, showing a shape that is nearly spherical but slightly concave, and the colors range from 2 GPa to 10 GPa. Fig. 9 (b) is a two-dimensional contour map, which further refines the anisotropic characteristics. Both show that the mechanical properties in different crystal directions are significantly different. Along the

[100] direction, the shear modulus is close to the maximum value of about 10GPa, showing a high resistance to shear deformation; along the

[110] direction, the shear modulus is slightly lower but still maintains a high value; and along the

[111] direction, the shear modulus is lower, about 2GPa to 4GPa.

[0126] Fig.10 The elastic modulus distribution of silicon crystals is shown. The elastic modulus of silicon crystals ranges from 100 GPa to 180 GPa. The yellow area indicates the highest elastic modulus, and the blue area indicates the lowest elastic modulus. Fig.10 As shown in (a). Fig.10 The 2D contour map in (b) further refines this feature, confirming that the elastic modulus is higher in a specific direction. In contrast, the elastic modulus of lithium metal has a smaller range (2GPa to 25GPa), and its shear modulus anisotropy shows significant direction dependence, with a significant increase in the modulus in a specific direction, while the anisotropy of silicon crystals is weaker and not as strong as that of metallic lithium. Silicon crystals have high overall stiffness, and their anisotropic characteristics mainly come from different crystal structures and atomic arrangements.

[0127] Fig.11 The maximum shear modulus of silicon crystal (G max ) distribution, revealing its mechanical properties in different crystal directions. Fig.11 The three-dimensional view in (a) shows that the maximum shear modulus of silicon crystals ranges from 45 GPa to 75 GPa. Fig.11 The 2D contour plot in (b) further refines this feature, confirming that the shear modulus is higher in specific directions.

[0128] Although the shear modulus of silicon crystals varies in various directions, the overall change is relatively smooth and does not show extreme anisotropy. In contrast, the maximum shear modulus range of metallic lithium is smaller (2GPa to 10GPa), and its anisotropic distribution is more significant. The shear modulus of metallic lithium increases significantly in specific directions, while it decreases significantly in other directions, showing stronger anisotropy. This difference stems from the different crystal structures and atomic bonding characteristics of the two materials. Due to its covalent bond structure, silicon crystals have little difference in mechanical properties in various directions; while metallic lithium has large differences in mechanical properties in different directions due to its metallic bond characteristics and lower crystal symmetry.

[0129] Due to its disordered atomic arrangement and complex structural properties, the calculation and prediction of the elastic modulus of amorphous lithium silicon poses a huge challenge to the MLP model. Traditional crystalline materials have regular atomic arrangements, so their mechanical properties can be predicted and calculated by standard methods. However, the structure of amorphous materials lacks long-range order, and this disorder leads to the complexity of their mechanical properties. In order to gain a deeper understanding of the mechanical properties of amorphous lithium silicon, this chapter further calculates its elastic modulus using the MLP model, and compares the results with existing literature in detail. This comparison not only verifies the accuracy and robustness of the MLP model when dealing with amorphous materials, but also provides a more comprehensive understanding of the mechanical behavior of amorphous lithium silicon.

[0130] Fig.12 The trends of elastic modulus changes of amorphous lithiated silicon at different lithium contents predicted by different calculation methods (DFT, MLP, MEAM, ReaxFF) are summarized. Both DFT and MLP results show non-monotonic changes, while MEAM and ReaxFF results show a monotonic decreasing trend. This non-monotonic change is more consistent with the experimental results, reflecting the complex structure and mechanical behavior of amorphous lithiated silicon. The reasons for the non-monotonic change may include: the atomic structure of amorphous materials undergoes significant relaxation and rearrangement at different lithium contents, resulting in complex changes in local stress and atomic interactions; with the increase of lithium content, the chemical bond characteristics in amorphous lithiated silicon will change, directly affecting the mechanical properties. The MLP results are very close to the DFT results, especially in the medium and low lithium content range, showing similar non-monotonic trends, which verifies the effectiveness of the MLP model in dealing with amorphous materials. MEAM and ReaxFF show a monotonic decreasing trend, which is significantly different from the DFT and MLP results. The MLP model can reproduce the DFT calculation results well, especially at medium and low lithium contents, which shows that the MLP model has high accuracy and robustness in dealing with complex amorphous materials.

[0131] Surface energy

[0132] Surface energy is important in fracture simulation because it is a key parameter that describes the surface characteristics of materials and fracture mechanics behavior. Surface energy affects the energy release rate, which describes the energy released by the material during the fracture process. The higher the energy release rate, the easier it is for the material to propagate cracks when it fractures. In addition, surface energy determines the difficulty of crack propagation. High surface energy materials require higher energy input to propagate cracks, thus showing higher fracture toughness. In this chapter, the surface energy (γ) can be calculated by the following formula:

[0133]

[0134] Among them, E surface is the total energy of the system including the surface, E bulkis the total energy of the same volume of bulk material, A is the surface area, and the 2 in the denominator means that the double-sided surface energy (i.e. the surfaces on both sides) is taken into account.

[0135] Fig.13 The unrelaxed surface energy results calculated by DFT and MLP are compared. The data points are mainly distributed along the diagonal line, indicating that the results of the two are generally consistent. The surface energy data points of lithium silicon are concentrated between silicon and lithium, indicating that its surface energy is between elemental silicon and elemental lithium. This phenomenon may be due to the mixed structural characteristics of lithium silicon: the strong covalent bonds between silicon atoms and the weaker metallic bonds between lithium atoms work together to make the surface energy of lithium silicon lower than that of pure silicon but higher than that of pure lithium. The strong covalent bonds of silicon atoms provide higher surface energy, while the metallic bonds of lithium atoms reduce the overall surface energy, forming an intermediate value between the two. The comparative analysis in the figure verifies the high accuracy of the MLP model in predicting the surface energy of complex mixed materials, especially in materials with significant heterogeneous structures such as lithium silicon, the MLP model can effectively capture the changing trend of its surface energy.

[0136] Analysis of tensile properties of lithium metal and silicon anode

[0137] Lithium metal stretching simulation

[0138] Molecular dynamics simulation method was used to study the uniaxial tensile behavior of metallic lithium in the

[100] crystal direction. Fig.14 (a) shows a schematic diagram of the initial crystal structure, with green dots representing lithium atoms and black arrows pointing to the three crystal directions

[100] ,

[010] and

[001] respectively. The simulation adopted periodic boundary conditions (ppp) and set the time step to 0.001ps. The initial conditions were determined by setting the initial velocity corresponding to 300K. Before the formal uniaxial tensile simulation, the sample was pre-equilibrated for 200ps in a Nose-Hoover hot bath isothermal and isobaric (NPT) system at 300K to ensure thermodynamic stability. In the tensile simulation, uniaxial tensile strain was applied along the

[100] crystal direction. The strain was applied by gradually changing the size of the simulation box in the

[100] direction. This method ensures the uniform distribution of strain and its precise control. The applied strain rate was 10 10 s -1 The selection of this strain rate balances the computational efficiency and the accuracy of the results, ensuring that a stable and accurate stress-strain curve can be obtained within a reasonable computational time.

[0139] By recording and analyzing the stress and strain data at each time step during the strain application process, the stress-strain relationship curve was obtained, and the convergence of the system size was verified. Fig.14(b) shows the stress-strain curves under different atomic numbers (864, 2048, 4000, 6912 atoms). As can be seen from the figure, although there are certain fluctuations in the high strain region, the overall trend shows that with the increase of the system scale, the stress-strain curve gradually converges, especially below 0.5 strain, the responses of different systems are basically the same, indicating that the simulation results have good convergence and reliability.

[0140] During the uniaxial stretching of metallic lithium, it can be observed that the mechanical response of the material is significantly different at different strain stages. Fig.14 As shown in (b), the elastic modulus of metallic lithium along the

[100] direction in the low strain region of 0-0.05 is 11.4 GPa, while the elastic modulus in the high strain region of 0.2 to 0.4 is 2.9 GPa, a decrease of 74%. This phenomenon suggests the possibility of phase transition behavior. In order to deeply analyze this process, this chapter uses the polyhedron template matching algorithm in the OVITO software to identify and analyze changes in the crystal structure. This method can effectively identify atoms with different structures by matching the local environment of each atom with a predefined template structure. This analysis method provides a technique for accurately identifying different crystal phases, which is particularly suitable for dealing with structural changes of materials under dynamic conditions. In this chapter, the RMSD cutoff radius for identification is set to 0.15. Fig.15 The phase transition of metallic lithium during uniaxial stretching is shown in detail, from a body-centered cubic (BCC) structure to a face-centered cubic (FCC) structure. By analyzing the crystal structure at different strain stages, we can gain a deeper understanding of the material's microscopic mechanism and its impact on macroscopic properties.

[0141] Fig.15 (a) shows the change in the proportion of BCC and FCC structures during the stretching process. In the initial state, the material is completely in the BCC structure. As the strain gradually increases, the atomic arrangement begins to adjust, the BCC structure proportion gradually decreases, and the FCC structure proportion increases accordingly. When the strain reaches about 0.2, the proportions of the two structures are roughly equal. Subsequently, when the strain increases to 0.4, the FCC structure gradually becomes dominant, indicating that the material structure has undergone significant reorganization. Fig.15(b) shows the structural comparison before and after stretching through a specific crystal structure diagram. The initial BCC structure of metallic lithium has a relatively tight atomic arrangement and high symmetry, while the FCC structure formed under higher strain has an atomic arrangement that shows different symmetry and greater spatial stacking efficiency. The occurrence of this phase transition is closely related to the change in modulus. The BCC structure exhibits a higher modulus at low strain due to its higher symmetry and simpler slip system. When the structure is transformed into FCC, although the FCC structure theoretically has more slip systems, making it potentially harder and tougher under ideal conditions, under high-speed stretching conditions, frequent slip activities and structural reorganization may cause local softening of the material, resulting in a decrease in the overall modulus.

[0142] Silicon crystal stretching simulation

[0143] The machine learning force field potential function is used to simulate the uniaxial tension of silicon crystal models with two different crystal orientations

[100] and

[111] . These two crystal orientations of silicon crystal structures are most widely used in lithium batteries, and their performance and properties are particularly worthy of attention. Fig.16 (a) shows the initial structure of a silicon crystal along the

[100] crystal direction, where the arrangement of silicon atoms along the

[100] ,

[010] , and

[001] directions forms a typical cubic lattice structure. Fig.16 (b) shows the initial structure of a silicon crystal along the

[111] crystal direction, where silicon atoms are located along the

[111] , [-110], and The detailed settings of the tensile simulation are consistent with those of metallic lithium.

[0144] Fig.17 The stress-strain relationship of silicon crystal along the

[100] and

[111] directions during uniaxial tension is shown, as well as the influence of different atomic numbers on the maximum tensile stress. These data not only reveal the mechanical behavior of silicon crystal along two different directions, but also provide important evidence for the convergence and reliability of simulation results. Fig.17 (a) shows that the silicon crystal in the

[100] direction reaches a maximum tensile stress of about 20 GPa when the strain is close to 0.25. The silicon crystal along the

[100] direction has a higher elastic modulus, indicating that the deformation of the material is relatively small under the initial stress. The high elastic modulus of this crystal direction can be attributed to the symmetry of its lattice structure and the strong bonds between atoms. In the cubic crystal structure, the atoms in the

[100] direction are arranged directly and uniformly, and the bond lengths and bond angles between atoms are ideal, which effectively resists deformation in the early stages of stretching. In contrast, silicon crystals along the

[111] direction exhibit slightly different stress response patterns when stretched, such as Fig.17As shown in (b), the stress increases with the strain, and the maximum stress occurs when the strain is about 0.2, with a peak value of 18.5 GPa. Although the

[111] direction is the most densely packed direction of silicon, its elastic modulus is relatively low, which may be related to the dense arrangement between atoms, resulting in easier slip and other deformation mechanisms under strain, reducing the initial resistance to deformation. Fig.17 (c)-(d) show that the maximum tensile stress increases first and then converges gradually with the increase of the number of atoms. This trend may be related to the size effect of the material's microstructure, especially in small-scale systems, where boundary effects and imperfect atomic arrangement may lead to stress concentration, thereby reaching a stress peak at a certain point. For the

[100] crystal orientation, when the number of atoms is 5488, the peak stress reaches a maximum value of 20.07 GPa. For the

[111] crystal orientation, the maximum tensile stress reaches a maximum value of 18.91 GPa at 5040 atoms. Even if the number of atoms continues to increase, the maximum tensile stress does not change much. This trend shows that the simulation is close to the macroscopic behavior of the real material, so it can be considered that the simulation results are close to convergence at this system size.

[0145] In the study of silicon crystals, experimental measurements and literature reports have shown that the

[111] crystal orientation has the lowest surface energy. This phenomenon is mainly attributed to the atomic arrangement in the

[111] direction, which is the most densely packed crystal plane in silicon crystals. In this arrangement, each surface atom is surrounded by more atoms, thereby minimizing the surface free energy. Specifically, a higher atomic occupancy density means that there are more chemical bonds between surface atoms, which can effectively reduce the energy of the entire crystal plane. However, despite the high atomic density in the

[111] crystal orientation, this densely arranged structure also leads to lower surface energy when the crystal is pulled in this direction, which affects the mechanical stability of the crystal. During the stretching process, the reduction in surface energy means that lower energy is required to form a new surface, that is, cracks are more likely to propagate in the material. Therefore, when stress acts on a silicon crystal in the

[111] crystal orientation, the lower surface energy causes it to begin to break at lower stresses, which explains its relatively low tensile strength. In this chapter, the machine learning force field potential function successfully simulated the behavior of a silicon crystal in the

[111] direction when stretched, and accurately reflected how lower surface energy leads to a decrease in tensile strength. The precise capture of this phenomenon demonstrates the potential for the application of machine learning force field potential functions in materials science research, especially when the effects of complex microstructures need to be considered.

[0146] Fig.18The stress distribution and failure morphology of silicon crystals along the

[111] crystal direction at different strain stages are shown, providing a detailed observation of the entire process from stress concentration to brittle fracture. In the initial state, the crystal structure remains intact, the stress level is low and evenly distributed, and is displayed in blue. As the strain increases to 0.05 and 0.1, it is observed that the stress begins to concentrate in local areas, and the color of the stress cloud map gradually changes to green, indicating the increase in stress level. When the strain further increases to 0.15, the internal stress concentration intensifies, and the cloud map appears yellow, although the crystal structure has not yet been significantly damaged. When the strain reaches 0.18, the stress reaches the fracture strength and tiny cracks appear for the first time. At this time, orange appears in the cloud map to indicate the initial formation of cracks. As the strain increases to 0.19 and 0.196, the crack rapidly expands and passes through the entire sample. With the gradual release of stress, the color of the cloud map turns back to green and blue. Finally, when the strain reaches 0.26, the crystal structure breaks significantly, and the crack completely penetrates the sample along the

[111] crystal direction, forming a clear cleavage plane, showing typical brittle fracture characteristics.

[0147] In the study of silicon crystals, vacancy defects are widely considered to be important microstructural factors that affect the mechanical properties of materials. Vacancy defects, that is, the absence of atoms in the crystal lattice, can not only change the electronic properties of the material, but also significantly affect its mechanical behavior. Specifically, vacancy defects will form stress concentration points in the microstructure of the material, which may accelerate the formation and propagation of cracks when subjected to external forces. For example, Ren et al. (2005) showed in their study that the presence of vacancy defects significantly increased the risk of brittle fracture of silicon crystals when subjected to stress.

[0148] In addition, vacancy defects also have a direct impact on the macroscopic mechanical properties of silicon crystals. Studies have shown that as the vacancy density increases, the tensile strength and elastic modulus of the material tend to decrease (Bracht et al., 2008). This is because vacancy defects reduce the number of atoms in the lattice that can effectively carry the load, making the material more susceptible to deformation or fracture under lower stress. In their study, Goel et al. (2015) used molecular dynamics simulation to demonstrate the relationship between vacancy density and the mechanical strength of silicon crystals, further confirming the view that increased vacancy density leads to reduced mechanical properties of silicon materials. In response to the effect of vacancy defects on the mechanical properties of silicon crystals, researchers are also exploring ways to control or reduce these defects through material processing and treatment techniques. For example, high-temperature annealing can effectively reduce the vacancy density in silicon crystals, thereby improving their mechanical properties (Lee et al., 2012). These treatment methods play a key role in improving the reliability and durability of silicon crystals as electrode materials. In order to further explore the effect of vacancy defects on the mechanical properties of silicon crystals, this chapter constructs a crystal model with an initial number of 8640 silicon atoms. In order to simulate vacancy defects of different densities, a certain proportion of atoms were randomly deleted from the complete crystal model, with specific proportions of 0.1%, 0.5%, 1%, 3% and 5%, respectively. Fig.19 These specific scales were chosen to systematically study the effects of very low to high vacancy densities on the mechanical response of silicon crystals in the

[111] direction. This approach enabled the creation of a series of silicon crystal models with different vacancy densities, allowing for detailed analysis of how vacancy defects affect the mechanical strength, stress distribution, and fracture behavior of the material under stress.

[0149] Fig.19 (a) shows the atomic-level changes in the structure of crystalline silicon at different defect concentrations, including four defect ratios: 0%, 0.1%, 1% and 5%. In the absence of defects, crystalline silicon exhibits a perfect crystal structure and no structural defects are observed. However, when the defect ratio is increased to 0.1%, very few non-diamond structures (indicated in pink) can be observed, as well as the first neighboring atoms (light blue) and second neighboring atoms (green) of the cubic diamond connected to them. As the defect ratio increases to 1%, the number of non-diamond structures and their associated first and second neighboring atoms increases significantly. When the defect ratio reaches 5%, a large number of non-diamond structure components and their neighboring atoms in the cubic diamond structure become very obvious. Fig.19 (b) shows the stress-strain relationship of crystalline silicon at different defect concentrations. The data show that as the defect ratio increases, the mechanical strength of the material shows a gradual downward trend. This decline reflects the negative impact of structural defects on the overall mechanical properties of the material. Fig.19(c) further describes in detail the specific effect of the defect ratio on the

[111] crystal direction elastic modulus and material strength. The results show that as the defect ratio increases, the elastic modulus and strength of crystalline silicon both decrease significantly. This downward trend reveals the mechanism by which defects affect the macroscopic mechanical properties of materials at the microscopic scale.

[0150] The following examples are used to verify the beneficial effects of the present invention:

[0151] Embodiment 1:

[0152] The present invention provides a method for calculating the potential energy surface of lithiated silicon materials based on neural network potential function fitting, which is specifically implemented by computer software. First, the system extracts bulk structure data of metallic lithium, silicon and lithiated silicon crystals covering different lithium contents and crystalline and amorphous states from the initial data set as the initial training data of the neural network model. Then, the multi-layer deep neural network model is preliminarily trained using these data to generate a preliminary potential energy function fitting model. Subsequently, molecular dynamics simulations are performed based on the model, including surface structure simulations, uniaxial stretching simulations and diffusion process simulations, to generate new structure and force data. During the simulation process, the error detection module identifies key structures with large atomic force errors, which are then obtained through high-precision first-principles calculations (such as DFT calculations in VASP) to obtain accurate energy and force data, and integrate them into the original data set, especially supplementing the surface and interface structure data. The updated data set is used to retrain the neural network model, and the model structure and parameters are optimized using transfer learning and active learning techniques, thereby improving the fitting accuracy and generalization ability of the model. This process is executed cyclically under the management of the iterative control module until the model reaches the predetermined accuracy and data coverage, and finally generates a comprehensive data set covering the bulk and surface structure. In order to improve the flexibility and applicability of the method, the key parts of the present invention such as the neural network model structure can be replaced by a convolutional neural network (CNN) or a graph neural network (GNN), and the active learning strategy can adopt uncertainty sampling, entropy-based sampling or reinforcement learning methods. In addition to VASP, high-precision calculation methods can also use Quantum ESPRESSO or Gaussian software. In addition, in the data preprocessing stage, dimensionality reduction techniques (such as PCA) or data enhancement techniques can be combined to improve model training efficiency and generalization ability. This method is suitable for the research and development of negative electrode materials for lithium-ion batteries. By accurately fitting the potential energy surface of lithiated silicon materials, the mechanical behavior and physical properties of the materials in the lithiation process are deeply understood, thereby guiding the optimization design and performance improvement of the materials, significantly improving the fitting accuracy and calculation efficiency of the potential energy function, shortening the material development cycle, reducing R&D costs, and providing solid data support for the advancement and industrialization of high-performance lithium-ion battery technology.

[0153] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for predicting atomic interaction information based on machine learning potential function, characterized by: The specific process of the method is: Step 1: Obtain an initial data set, expand the initial data set, and finally obtain a comprehensive data set covering bulk and surface structures; Step 2: Train the machine learning potential function MLP based on the comprehensive data set to obtain a trained machine learning potential function MLP; Step 3: Based on the trained machine learning potential function MLP, the metal lithium, silicon, and lithiated silicon atoms to be measured are predicted, and the atomic interaction information of the metal lithium, silicon, and lithiated silicon atoms is output; The interaction information is energy and force.

2. The atomic interaction information prediction method based on machine learning potential function according to claim 1 is characterized by: In the step 1, an initial data set is obtained, and the initial data set is expanded to obtain a comprehensive data set covering the bulk phase and surface structure. The specific process is as follows: Step 11: Obtain the initial data set; The specific process is: The initial data set includes metallic lithium, silicon, and lithiated silicon; Step 1 and 2: Expand the initial data set to obtain a comprehensive data set covering both bulk and surface structures.

3. The atomic interaction information prediction method based on machine learning potential function according to claim 2 is characterized in that: In the step 1, the metallic lithium has a body-centered cubic, face-centered cubic, hexagonal close-packed and amorphous structure; Silicon has diamond structure, I41amd structure and amorphous structure; Lithium silicon includes crystalline and amorphous lithium silicon.

4. The atomic interaction information prediction method based on machine learning potential function according to claim 3 is characterized by: The crystalline lithium silicon is c-Li1 Si1, c-Li2 Si1, c-Li 12 Si7、c-Li 15 Si4、c-Li 22 Si5; Amorphous lithium silicon is a-Li x Four.

5. The atomic interaction information prediction method based on machine learning potential function according to claim 4 is characterized in that: In the step 1 and 2, the initial data set is expanded to obtain a comprehensive data set covering the bulk and surface structures; The specific process is: Step 121: Based on the initial data set, four machine learning potential functions MLP are trained respectively to obtain four trained machine learning potential functions; Step 122: Based on the first trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation results A; the simulation results A are atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials; Based on the second trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation result B; simulation result B is the atomic force of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials; Based on the third trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation results C; simulation results C are atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials; Based on the fourth trained machine learning potential function MLP and LAMMPS software, dynamic simulations of different crystal structures of metallic lithium, silicon and lithiated silicon materials are performed to obtain simulation results D; simulation results D are atomic forces of different atomic structures corresponding to metallic lithium, silicon and lithiated silicon materials; Step 1, 2, 3, calculate the difference in atomic force of the same atomic structure in any two simulation results of A, B, C, D, and the maximum difference is the maximum atomic force error E; Step 1, 2, 4, If the maximum atomic force error E is less than 0.15, the final comprehensive data set is obtained; If the maximum atomic force error is 0.15≤E≤0.45, perform DFT calculation on the atomic structure corresponding to the maximum atomic force error E to obtain the atomic energy, atomic force and lattice stress information of the atomic structure, add the atomic energy, atomic force and lattice stress information of the atomic structure to the initial data set, and repeat steps 121 to 124 until the maximum atomic force error E is less than 0.15, thereby obtaining the final comprehensive data set; DFT stands for density functional theory; If the maximum atomic force error E is greater than 0.45, end.

6. The atomic interaction information prediction method based on machine learning potential function according to claim 5, characterized in that: The unit of the atomic force error E is force, which is expressed as eV stands for electron volt; Indicates Angstrom.

7. The atomic interaction information prediction method based on machine learning potential function according to claim 6, characterized in that: The four machine learning potential functions MLP in step 121 are machine learning potential functions MLP with the same hyperparameters and different random parameters.

8. The atomic interaction information prediction method based on machine learning potential function according to claim 7, characterized in that: The dynamic simulation in step 122 includes simulation of surface structure, stretching and diffusion process.

9. A storage medium, characterized in that: The storage medium stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the atomic interaction information prediction method based on machine learning potential function as described in any one of claims 1 to 8.

10. A device for predicting atomic interaction information based on machine learning potential function, characterized in that: The device includes a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the atomic interaction information prediction method based on machine learning potential function as described in any one of claims 1 to 8.

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