Alloy doped atom aggregation behavior identification and performance prediction method and system

Abstract

The invention discloses an alloy doped atom aggregation behavior identification and performance prediction method and system, and relates to the field of material calculation, calculation material science and alloy microstructure analysis, and the method comprises the steps: constructing an alloy structure model; performing staged training of a machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function; performing molecular dynamics simulation on the alloy structure model according to the machine learning potential function qualified in training to obtain an alloy doped atom aggregation behavior recognition result; and performing performance prediction by using the alloy doped atom aggregation behavior recognition result to obtain a performance prediction result. According to the method, a machine learning potential function is combined with molecular dynamics simulation, quantitative recognition of the aggregation behavior of the doped atoms is achieved, and macroscopic performance is directly associated. Through staged training, multi-index verification and kinetic analysis, the method has high efficiency and reliability, and micromechanism guidance is provided for alloy design.

Description

Technical Field

[0001] This invention relates to the fields of materials calculation, computational materials science, and alloy microstructure analysis, and particularly to a method and system for identifying the aggregation behavior of doped atoms in alloys and predicting their performance. Background Technology

[0002] Cu-Zn based alloys (brass) are widely used in electronics, information technology, target backplates, and electromagnetic equipment due to their excellent comprehensive properties. To further improve their wear resistance, electrical conductivity stability, and eddy current resistance, Sn doping is often used in industry for performance tuning. However, the microscopic distribution state (dispersion / clustering) of Sn in the alloy after doping directly determines the alloy's electrical conductivity, diamagnetism, eddy current resistance, and mechanical properties. The quantitative identification of its microscopic aggregation state and the correlation prediction of macroscopic properties have become a technical bottleneck in this field.

[0003] Traditional techniques mainly rely on experimental characterization, such as scanning electron microscopy and transmission electron microscopy. However, these methods are costly, time-consuming, and make it difficult to observe atomic migration and cluster dynamics in real time. Current techniques for analyzing and simulating the aggregation behavior of doped atoms in alloys mainly rely on two mainstream approaches: molecular dynamics simulations based on traditional empirical potential functions and direct simulations based on first-principles calculations.

[0004] The core of molecular dynamics simulations based on traditional empirical potential functions is to select pre-parameterized empirical potential functions (such as Modified Embedded Atom Method (MEAM) and EAM) to describe interatomic interactions. Molecular dynamics simulations are then performed using these selected potential functions to obtain atomic trajectories. Qualitative or semi-quantitative analysis of the aggregation behavior of doped atoms is then performed using methods such as visual observation, radial distribution function (RDF) calculation, or statistical average distance. However, the parameters of empirical potential functions are determined based on limited experimental data or quantum mechanical calculations of simple systems, resulting in poor generalization ability. They cannot simultaneously guarantee the quantization accuracy of energy, force, lattice, defect behavior, and diffusion behavior, leading to distorted predictions of Sn atom aggregation behavior. Furthermore, the analytical methods lack uniformity, making it difficult to accurately distinguish subtle aggregation states such as "dispersion," "transition," and "convergence."

[0005] The core of direct simulation based on first-principles calculations is to directly utilize first-principles methods such as density functional theory (DFT) to perform molecular dynamics simulations. It does not rely on empirical parameters and directly calculates interatomic forces based on quantum mechanical principles, resulting in extremely high computational accuracy, considered the "gold standard" for result accuracy. However, DFT calculations are extremely time-consuming, and the number of atoms that can be simulated (typically on the order of hundreds) and the time scale (typically on the order of picoseconds) are strictly limited. This makes it difficult to handle large systems (>200 atoms), long relaxation times, or scenarios involving a large number of random structures. It cannot provide sufficient statistical samples for behaviors such as doped atom aggregation and diffusion, leading to highly random analytical results and difficulty in systematically identifying doped atom aggregation behavior.

[0006] Furthermore, existing technologies lack standardized quantitative indicators for doping aggregation: existing literature mostly uses coordination number, energy difference, critical distance and other methods for qualitative judgment, without clear and reproducible algorithm flow, threshold algorithm applicable to different concentrations and phase structures, and even more so, lacking a causal relationship model between aggregation state and macroscopic performance.

[0007] Therefore, there is an urgent need for a method and system for identifying the aggregation behavior of alloy doped atoms and predicting their performance, in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0008] The purpose of this invention is to propose a method and system for identifying the aggregation behavior of doped atoms in alloys and predicting their performance, so as to solve the technical problem that existing technologies cannot efficiently and accurately quantitatively identify the micro-aggregation state of doped atoms in alloys and cannot reliably predict their macroscopic performance.

[0009] On the one hand, to achieve the above objectives, the present invention provides a method for identifying the aggregation behavior of doped atoms in alloys and predicting their performance, comprising:

[0010] S1. Construct the alloy structure model;

[0011] S2. Perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function;

[0012] S3. Perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function to obtain the identification results of the alloy doped atom aggregation behavior;

[0013] S4. Use the results of the alloy doping atom aggregation behavior identification to perform performance prediction and obtain the performance prediction results.

[0014] Optional, S1, construct the alloy structure model, including:

[0015] Set key phase structure parameters and alloy doping concentration;

[0016] Based on the key phase structure parameters and the alloy doping concentration, a special quasi-random structure is generated;

[0017] Based on the aforementioned special quasi-random structure, an alloy structure model is constructed using a random structure generator.

[0018] Optionally, S2, performing phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function includes:

[0019] Based on the alloy structure model, density functional theory is used to obtain high-precision training data. The high-precision training data includes training data for elemental systems, binary systems, and ternary systems. The training data includes atomic energy, interatomic forces, and stress tensors.

[0020] The high-precision training data is used for phased training to obtain the machine learning potential function.

[0021] The machine learning potential function is compared and verified to obtain a qualified machine learning potential function.

[0022] Optionally, the high-precision training data is used for phased training to obtain the machine learning potential function, including:

[0023] The single-mass potential function is trained using the training data of the single-mass system, and the trained single-mass potential function is obtained.

[0024] The binary potential function is trained based on the trained single-mass potential function and the training data of the binary system to obtain the trained binary potential function.

[0025] Based on the trained binary potential function and the training data of the ternary system, the potential function of the entire target alloy system is obtained.

[0026] Based on the potential function of the entire target alloy system, a machine learning potential function is obtained using a hybrid optimization strategy.

[0027] Optionally, a comparative verification is performed based on the machine learning potential function to obtain a qualified machine learning potential function, including:

[0028] Using the high-precision training data, set up multi-dimensional qualification indicators;

[0029] Based on the comparison between the machine learning potential function and the high-precision training data, the index error value between the machine learning potential function and the high-precision training data is obtained.

[0030] Based on the multi-dimensional qualification indicators combined with the indicator error value between the machine learning potential function and the high-precision training data, a qualified machine learning potential function is obtained.

[0031] Optionally, S3. Perform molecular dynamics simulation on the alloy structure model according to the qualified trained machine learning potential function to obtain the identification result of the aggregation behavior of alloy doped atoms, including:

[0032] Perform molecular dynamics simulation on the alloy structure model by using the qualified trained machine learning potential function to obtain atomic trajectory data;

[0033] Based on the atomic trajectory data, obtain the Euclidean distance of alloy doped atoms;

[0034] According to the Euclidean distance of the alloy doped atoms, extract three distance metrics, and the three distance metrics include the nearest neighbor distance, the next nearest neighbor distance, and the third nearest neighbor distance;

[0035] Based on the three distance metrics and combined with a dynamic critical threshold, obtain the identification result of the aggregation behavior of alloy doped atoms.

[0036] Optionally, based on the three distance metrics and combined with a dynamic critical threshold, obtain the identification result of the aggregation behavior of alloy doped atoms, including:

[0037] Obtain a dynamic critical threshold according to the alloy doping concentration of the alloy structure model;

[0038] Use the dynamic critical threshold to obtain the classification criteria for alloy doped atoms;

[0039] Based on the three distance metrics, the dynamic critical threshold, and combined with the classification criteria for alloy doped atoms, obtain the identification result of the aggregation behavior of alloy doped atoms.

[0040] Optionally, the classification criteria for alloy doped atoms include:

[0041] When d1 > R th , and d1 < d2 < d3, the alloy doped atoms are determined to be in a dispersed state;

[0042] When d1 < R th , and d2 - d1 ≤ ΔR, the alloy doped atoms are determined to be in a cluster state;

[0043] When R th is between the dispersed state and the converged state, the alloy doped atoms are determined to be in a transition state;

[0044] Where, d1 is the nearest neighbor distance, d2 is the next nearest neighbor distance, d3 is the third nearest neighbor distance, R th is the dynamic critical threshold, and ΔR is a reasonable threshold based on atomic bonding.

[0045] Optionally, S4. Use the identification result of the aggregation behavior of alloy doped atoms for performance prediction to obtain a performance prediction result, including:

[0046] Based on the identification results of the atom aggregation behavior of the alloy doping, a dataset of micro-aggregation states is obtained;

[0047] Based on the identification results of the atom aggregation behavior of the alloy doping and the alloy micro-aggregation mechanism, a correlation model between the micro-aggregation state and the macro-performance is established.

[0048] The micro-aggregate state dataset is input into the correlation model between the micro-aggregate state and macro-performance to obtain performance prediction results.

[0049] On the other hand, in order to achieve the above objectives, the present invention provides an alloy doping atom aggregation behavior identification and performance prediction system, including: a data generation module, a potential function training module, a simulation analysis module and a performance prediction module;

[0050] The data generation module is used to construct the alloy structure model;

[0051] The potential function training module is used to perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function.

[0052] The simulation analysis module is used to perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function, and obtain the identification results of the aggregation behavior of alloy doped atoms.

[0053] The performance prediction module is used to perform performance prediction based on the identification results of the atom aggregation behavior of the alloy doping and to obtain the performance prediction results.

[0054] Compared with the closest existing technology, the present invention has the following advantages:

[0055] This invention combines machine learning potential functions with molecular dynamics simulations to achieve quantitative identification of the aggregation behavior of doped atoms and directly correlate it with macroscopic properties. Through phased training, multi-index verification, and kinetic analysis, the method combines high efficiency and reliability, providing microscopic mechanism guidance for alloy design. Specifically:

[0056] (1) High accuracy of cluster identification: Through the machine learning potential function trained in stages, the simulation accuracy close to the first principle is achieved. At the same time, it breaks through the computational scale limitation of DFT and can handle simulations of large systems and long time scales. Combining the three distance index and dynamic critical threshold, a unified, scalable and quantifiable cluster identification system is established for the first time. It can accurately distinguish between dispersed state, transitional state and significant convergence state, and solve the limitations of qualitative analysis of traditional methods.

[0057] (2) Strong generalization ability: The three-distance index and dynamic threshold algorithm are applicable to Cu-Zn-Sn alloys with different Sn doping concentrations (and different phase structures), and the algorithm process is reproducible, providing a general framework for the identification of doped atom aggregation in other multi-component alloys.

[0058] (3) Revealing the aggregation mechanism and linking macroscopic performance: Through simulation, it was found that the migration barrier of β phase Sn atoms is significantly lower than that of α phase, revealing the intrinsic mechanism that β phase Sn is more likely to form clusters; at the same time, a causal chain of "micro-aggregate state → macroscopic performance" was established, that is, the higher the proportion of significant clusters, the lower the conductivity of the alloy and the better the eddy current resistance, providing a clear control basis for the optimization of alloy performance.

[0059] (4) Efficiency and reliability are both taken into account: 100 SQS structures are constructed by combining each concentration and phase structure. The randomness of a single structure is reduced by large-scale statistical analysis, ensuring the reliability of the results. Compared with traditional experimental characterization, this method is low in cost and short in cycle, and can observe the atomic migration and cluster dynamic evolution process in real time. Attached Figure Description

[0060] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0061] Figure 1 This is a flowchart of a method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance, according to an embodiment of the present invention.

[0062] Figure 2 This is a schematic diagram of the Sn atom aggregation state analysis proposed in an embodiment of the present invention;

[0063] Figure 3 This is a schematic diagram illustrating the stepwise fitting of the potential function from a single element to a ternary system according to an embodiment of the present invention.

[0064] Figure 4 This is a schematic diagram showing the energy and force prediction results of the Cu single-mass potential function proposed in an embodiment of the present invention;

[0065] Figure 5 This is a schematic diagram showing the property prediction results of the Zn single-mass potential function proposed in an embodiment of the present invention;

[0066] Figure 6 This is a comparative diagram of the DFT, DP, and MEAM methods proposed in the embodiments of the present invention for predicting the properties of Cu-Zn alloys.

[0067] Figure 7This is a schematic diagram of the structure of an alloy doping atom aggregation behavior identification and performance prediction system according to an embodiment of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0069] The terminology used in the embodiments section of this invention is for the purpose of explaining specific embodiments of the invention only, and is not intended to limit the invention.

[0070] like Figure 1 As shown, this embodiment of the invention provides a method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance, including:

[0071] S1. Construct the alloy structure model;

[0072] The mcsqs random structure generator in ATAT software was used to construct an initial structural model for Cu-Zn-Sn alloys. The model design fully covered two core phase structures, α (FCC) and β (BCC), namely face-centered cubic (FCC) and body-centered cubic (BCC). The Sn doping concentration was set to three key gradients: 1%, 2%, and 3%. For each combination of phase structure and concentration, 100 special quasirandom structures (SQS) were constructed, with a uniform supercell size of 3×3×3 (approximately 200 atoms). This design ensured that the model possessed sufficient randomness and diversity, effectively avoiding interference from long-range ordered structures on subsequent simulation results, and providing basic structural data that conformed to the actual microscopic characteristics of the alloy for subsequent potential function training and kinetic simulation.

[0073] S2. Perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function;

[0074] The training was conducted in stages using the DeepMD-kit (an open-source software package based on deep learning). The training data came from high-precision data such as energy, interatomic forces, and stress tensors of elemental, binary, and ternary systems obtained by DFT calculation. The training process proceeded sequentially as follows: elemental potential function training (Cu, Zn, Sn), binary potential function training (Cu-Zn, Cu-Sn, Zn-Sn), and ternary potential function training (Cu-Zn-Sn), gradually introducing many-body effects to reduce errors caused by changes in the coordination environment. The training process employed a multi-objective weighted loss function and a combined Adam and L-BFGS optimizer, accumulating 800,000 iterations. Finally, qualified machine learning potential functions with both quantum-level accuracy and large-scale simulation capabilities were obtained through DFT data verification.

[0075] S3. Perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function to obtain the identification results of the alloy doped atom aggregation behavior;

[0076] The trained machine learning potential functions are imported into LAMMPS software, and large-scale molecular dynamics (MD) simulations are performed on all initial structural models using high-precision machine learning potentials (MLP) to obtain reliable atomic trajectory data. Based on the trajectory data, for each Sn-doped atom, its Euclidean distance to all other Sn atoms is calculated and sorted, and three distance indices (nearest neighbor distance d1, second nearest neighbor distance d2, and third nearest neighbor distance d3) are extracted to form a three-dimensional feature space. Subsequently, a dynamic critical threshold related to Sn concentration is introduced, and the automated and quantitative identification of Sn atom aggregation states is achieved according to preset classification criteria. Sn atom aggregation state analysis is as follows: Figure 2 As shown.

[0077] S4. Use the identification results of the aggregation behavior of the alloy doped atoms to perform performance prediction and obtain the performance prediction results;

[0078] Based on the obtained aggregation behavior identification results and combined with the revealed aggregation mechanism, a quantitative causal relationship model between micro-aggregate state and macro-performance is established. This model can accurately predict key properties of Cu-Zn-Sn alloys such as electrical conductivity and eddy current resistance, and clarify the rule that "the higher the cluster ratio, the lower the electrical conductivity and the better the eddy current resistance", providing data support for the structural control of alloy target backing plates and achieving performance optimization goals.

[0079] In summary, steps S1 to S4 first construct an alloy structure model covering α (FCC), β (BCC) phases and 1%-3% Sn doping concentration using ATAT's mcsqs random structure generator. Then, relying on DeepMD-kit, a phased strategy of "elemental → binary → ternary" is used to train the machine learning potential function. Subsequently, large-scale molecular dynamics simulations are performed using LAMMPS. By calculating the three-distance index of Sn atoms and combining it with concentration-dependent dynamic critical thresholds, automated quantitative identification of dispersed, transitional, and significantly aggregated states is achieved. Finally, a correlation model between micro-aggregated states and macroscopic properties is established. This method overcomes the shortcomings of traditional empirical potentials, such as poor generalization ability and limited DFT computation scale, and fills the gap in the lack of unified quantitative identification standards. It can not only distinguish the aggregation state of doped atoms with high precision, but also reveals the mechanism that β-phase Sn is more likely to form clusters due to its lower migration barrier. It achieves quantitative prediction that "the higher the cluster ratio, the lower the conductivity and the better the eddy current resistance," providing a scientific basis for the structural control of Cu-Zn-Sn alloy target backplates.

[0080] As one possible implementation, in the above embodiments, step S1 may specifically include the following steps:

[0081] S1-1, Set the key phase structure parameters and alloy doping concentration;

[0082] Based on the microscopic characteristics and performance control requirements of Cu-Zn-Sn alloys in practical applications such as electronic information and target backplates, the core key phase structure parameters are first defined: α (FCC) and β (BCC) phase structures, which are widely present in the alloy and have a significant impact on performance, are selected, and their lattice constants are determined (α phase a≈3.6Å, β phase a≈2.9Å). This parameter directly determines the basic interatomic spacing and spatial arrangement. Simultaneously, based on the commonly used control range for optimizing alloy wear resistance and eddy current resistance through Sn doping in industry, Sn doping concentration gradients of 1%, 2%, and 3% (atomic percentage) are determined. This not only covers the key performance control range but also allows for a systematic analysis of the impact of concentration on the aggregation behavior of doped atoms, providing a clear core parameter basis for subsequent structure generation.

[0083] S1-2. Generate a special quasi-random structure based on the key phase structure parameters and the alloy doping concentration;

[0084] Using the obtained phase structure parameters and doping concentration combinations as input conditions, the mcsqs tool in ATAT software was used to generate SQS. For each of the two phase structures, α (FCC) and β (BCC), and three Sn concentrations of 1%, 2%, and 3% (a total of 6 groups), 100 SQS structures were generated. Large-scale sample design reduces the random error of single structures. The core advantage of the special quasi-random structure is that it can simulate the random distribution characteristics of atoms in the actual alloy, while avoiding the interference of long-range ordered structures on the identification of dopant atom aggregation behavior, ensuring that the generated structure closely matches the real microscopic state of the alloy and providing high-quality basic structural units for subsequent model construction.

[0085] S1-3. Based on the aforementioned special quasi-random structure, a random structure generator is used to construct an alloy structure model;

[0086] The generated SQS sets were imported into ATAT's mcsqs random structure generator, and the supercell size was uniformly set to 3×3×3, so that the total number of atoms in each structure was controlled to about 200. This size can accurately reflect the atomic arrangement and interaction in the microscopic region, and balance the computational efficiency and result accuracy of subsequent machine learning potential function training and molecular dynamics simulation. During the generation process, the algorithm optimization of the random structure generator further ensured that the atomic distribution in the structure was uniform and there were no long-range order defects. Finally, a Cu-Zn-Sn alloy structure model covering all preset phase structures and doping concentrations with both randomness and reliability was output, providing stable basic data support for subsequent machine learning potential function training and identification of doped atom aggregation behavior.

[0087] In summary, steps S1 to S3 first clarify the key phase structure parameters and Sn doping concentration gradient of the Cu-Zn-Sn alloy. Then, based on the combination of phase structure and concentration, ATAT's mcsqs tool generates 100 SQS per group. Finally, an alloy structure model is constructed at a 3×3×3 supercell scale. This process ensures that the model closely matches the random atomic distribution characteristics of the actual alloy, avoids interference from long-range ordered structures in subsequent analyses, reduces the random errors of single structures through large-scale sample design, and balances the efficiency and accuracy of subsequent calculations. The resulting alloy structure model provides reliable and practically applicable basic data support for the phased training of machine learning potential functions, accurate identification of doped atom aggregation behavior, and prediction of the alloy's macroscopic properties, effectively guaranteeing the scientific rigor of the entire technical process and the accuracy of subsequent analysis results.

[0088] As one possible implementation, in the above embodiments, step S2 may specifically include the following steps:

[0089] S2-1. Based on the alloy structure model, high-precision training data is obtained using density functional theory. The high-precision training data includes training data for elemental systems, binary systems, and ternary systems. The training data includes atomic energy, interatomic forces, and stress tensors.

[0090] Based on the constructed Cu-Zn-Sn alloy structure model, high-precision calculations were performed using density functional theory, a first-principles method. Training data for the system was generated for all-element systems (Cu, Zn, Sn), binary systems (Cu-Zn, Cu-Sn, Zn-Sn), and ternary systems (Cu-Zn-Sn). The training data covered key information such as atomic energy, interatomic forces, and stress tension. The training data for the all-element systems originated from atomic trajectories derived from relaxation paths and surface energy calculations in DFT simulations. The training data for the binary and ternary systems specifically covered random structures, defect structures, and cluster structures under different phases and doping concentrations in the alloy structure model. This ensured that the data accurately reflected the atomic interaction characteristics and microstructural properties of the target alloy, providing high-precision basic data support with both quantum precision and system integrity for the subsequent phased training of the machine learning potential function. This ensured that the potential function accurately characterized the interaction laws between atoms of different components.

[0091] S2-2. Use the high-precision training data to perform phased training and obtain the machine learning potential function;

[0092] Using high-precision training data as input, the DeepMD-kit framework is used to perform phased machine learning potential function training, following a progressive logic of "simple → binary → ternary". A multi-objective weighted loss function is employed during training, with an initial learning rate starting from 10. -3 Decrease to 10 -5 The Adam optimizer was initially used, but later switched to the L-BFGS algorithm to improve the smoothness of the potential energy surface. After 800,000 iterations, a preliminary machine learning potential function was obtained.

[0093] S2-3. Compare and verify the machine learning potential function to obtain a qualified machine learning potential function.

[0094] Using the DFT calculation results (i.e., high-precision training data) as a benchmark, the initially obtained machine learning potential function is compared and verified in multiple dimensions. The verification indicators cover the mean absolute error of energy (MAE), root mean square error of force (RMSE), lattice constant error, elastic constant error, and diffusion coefficient deviation. By comparing the potential function prediction results with the high-precision DFT data one by one, the potential function that meets all the requirements is selected. This potential function is the qualified machine learning potential function and can be used for subsequent molecular dynamics simulations.

[0095] In summary, steps S2-1 to S2-3, based on the constructed alloy structure model, use density functional theory (DFT) to calculate high-precision training data such as atomic energy, interatomic forces, and stress tensors for elemental, binary, and ternary systems. Then, relying on the DeepMD-kit framework, machine learning potential functions are trained in a phased process of "elemental → binary → ternary," employing a multi-objective weighted loss function and a phased optimizer. After 800,000 iterations, multi-dimensional verification is conducted based on the DFT data to screen out qualified potential functions that meet multiple accuracy indicators, including energy, force, and lattice constant. This process overcomes the shortcomings of traditional empirical potentials, such as poor generalization ability and inability to accommodate multiple types of quantum precision, while also breaking through the bottleneck of DFT computational scale limitations. It enables qualified potential functions to possess both near-first-principles high precision and high efficiency suitable for large-scale molecular dynamics simulations. This lays a reliable foundation for the subsequent automated quantitative identification of alloy doped atom aggregation behavior and the prediction of macroscopic properties such as conductivity and eddy current resistance, significantly improving the scientific rigor and efficiency of alloy microstructure analysis and performance optimization.

[0096] As one possible implementation, in the above embodiments, step S2-2 may specifically include the following steps:

[0097] S2-2-1. Train the single-mass potential function using the training data of the single-mass system, and obtain the trained single-mass potential function;

[0098] Based on high-precision data such as energy, interatomic forces, and stress tensors of Cu, Zn, and Sn elemental crystals generated by density functional theory (DFT), the training of elemental potential functions (Cu, Zn, Sn) is initiated using the DeepMD-kit framework. The core objective is to ensure the basic accuracy of the benchmark interactions between atoms of the three elements. By fitting the atomic interaction laws of the elemental system, the trained elemental potential function can be obtained to accurately describe the atomic interactions within a single element, laying the foundation for subsequent training of potential functions for multi-component systems.

[0099] S2-2-2. Based on the trained single-mass potential function and the training data of the binary system, the binary potential function is trained to obtain the trained binary potential function.

[0100] Based on the already trained single-element potential function, high-precision training data for three binary systems, Cu-Zn, Cu-Sn, and Zn-Sn, are introduced. The training of binary potential functions (Cu-Zn, Cu-Sn, and Zn-Sn) is then initiated through the DeepMD-kit framework. The core purpose is to introduce the many-body effect between atoms, effectively reduce the interaction description error caused by changes in the coordination environment, and enable the potential function to accurately adapt to the atomic interaction rules in the coexistence scenario of two elements. This lays the intermediate layer accuracy foundation for the subsequent full-coverage training of the ternary system.

[0101] S2-2-3. Based on the trained binary potential function and the training data of the ternary system, obtain the potential function of the entire target alloy system;

[0102] Based on a qualified binary potential function, high-precision training data of the Cu-Zn-Sn ternary system is incorporated. The training of the ternary potential function (Cu-Zn-Sn) is initiated through the DeepMD-kit framework. By expanding the training range of the potential function to the entire target alloy system, comprehensive coverage of the interatomic interactions when Cu, Zn, and Sn coexist is achieved, ensuring that the potential function can reach the quantum precision description level and meet the core requirements of molecular dynamics simulation of the target alloy system.

[0103] S2-2-4. Based on the potential function of the entire target alloy system, a hybrid optimization strategy is used to obtain the machine learning potential function;

[0104] The obtained potential function of the entire target alloy system was further optimized using a hybrid optimization strategy combining the Adam optimizer in the early stage and the L-BFGS algorithm in the later stage to obtain the final machine learning potential function. A multi-objective weighted loss function was set during training, with energy weights p. E =0.5, force weight p F =1.0, stress weight p S =0.01; In the early stage of the Adam optimizer phase, the learning rate was gradually reduced from 10⁻³ to 10⁻⁵ to ensure rapid model convergence. Later, the L-BFGS algorithm was switched to improve the smoothness of the potential energy surface. A total of 800,000 iterations were completed, of which 500,000 were used for convergence analysis. The model uses a network architecture with 210,000 trainable parameters and continuously uses a smooth activation function to avoid energy surface oscillations. Through continuous optimization of parameters, the potential function is made to fully fit the atomic interaction law of the Cu-Zn-Sn alloy system, and finally a machine learning potential function that meets the needs of subsequent simulations is obtained.

[0105] In summary, steps S2-2-1 to S2-2-4 rely on the DeepMD-kit framework. Figure 3 This paper intuitively presents a step-by-step fitting method for the potential function from a single element to a ternary system, following this visualized progressive training logic throughout: first, the single-element potential function is trained with high-precision training data to solidify the accuracy foundation of the benchmark interaction; then, based on this, a binary potential function is trained using binary system data to effectively reduce errors caused by changes in the distribution site environment across multiple sets; subsequently, ternary system data is fused to obtain a potential function covering the entire target alloy system; finally, a hybrid optimization strategy is used to optimize the trainable parameters of the model. Figure 3The stepwise fitting path shown clearly ensures the systematic and coherent training. This process takes into account both the comprehensiveness and accuracy of the potential function in describing atomic interactions, and significantly improves the model's generalization ability through a phased progressive mode.

[0106] As one possible implementation, in the above embodiments, step S2-3 may specifically include the following steps:

[0107] S2-3-1. Using the high-precision training data, set up multi-dimensional qualification indicators;

[0108] By combining high-precision training data of elemental, binary, and ternary systems obtained through density functional theory (DFT), multi-dimensional qualification indicators covering energy, force, structure, mechanical properties, and diffusion behavior are established. These indicators are based on the core requirement that the potential function must accurately characterize the interactions between alloy atoms. Specifically, they include mean absolute error of energy (MAE) <5 meV / atom (as low as 1.8 meV / atom in Cu-rich regions), root mean square error of force (RMSE) <0.1 eV / Å, lattice constant error <0.3%, elastic constant error <5%, and diffusion coefficient deviation <8%, comprehensively ensuring the accuracy and reliability of the potential function after training and providing clear judgment criteria for subsequent verification.

[0109] S2-3-2. Based on the machine learning potential function and the high-precision training data, the index error value between the machine learning potential function and the high-precision training data is obtained.

[0110] Using high-precision DFT training data as a benchmark, the prediction results of the trained machine learning potential function for simple, binary, and ternary systems are compared one by one with the corresponding DFT data. By calculating the differences between the two in each core dimension, error values ​​for indicators such as energy MAE, force RMSE, and percentage errors in structural and performance parameters are obtained. Figures 4-6 As shown, Figure 4 The energy and force prediction results of the Cu single-mass potential function are presented intuitively. The data points are closely distributed near the diagonal of the DFT data, which confirms that the prediction error of energy and force is extremely small. Figure 5 This demonstrates the property prediction results of the Zn single-mass potential function, comparing the predicted force values ​​with the R values ​​of the DFT data. 2 A value close to 1 reflects the high precision of the force index; Figure 6 Further comparison of the prediction results of DFT, deep learning potential (DP) and MEAM methods on Cu-Zn alloy formation energy, equilibrium volume and elastic constants clearly shows that the results of DP and DFT are highly consistent, while the results of MEAM and DFT have a large deviation. Through these graphical data, the error values ​​of key indicators such as energy MAE, force RMSE and structure-performance parameter error can be directly obtained.

[0111] S2-3-3. Based on the multi-dimensional qualification indicators and the indicator error value between the machine learning potential function and the high-precision training data, obtain the qualified machine learning potential function.

[0112] The calculated error values ​​of each indicator are comprehensively verified against the preset multi-dimensional qualification indicators, combined with... Figures 4-6 The visualization verification results show that if all error values ​​meet the preset standards, i.e., energy MAE < 5 meV / atom, force RMSE < 0.1 eV / Å, etc., the machine learning potential function training is deemed qualified. Figures 4-5 This confirms that the energy and force indices of the potential function in a simple system meet the requirements, thus verifying the reliability of the potential function in a simple system. Figure 6 This verifies the high accuracy of the function in assessing the structure and mechanical properties of binary alloy systems. These figures collectively demonstrate that the prediction results of the qualified potential function are highly consistent with the high-precision DFT data, exhibiting quantum precision close to first-principles calculations. This qualified potential function successfully avoids the poor generalization ability of traditional empirical potentials and can be directly used for subsequent large-scale molecular dynamics simulations, providing a reliable computational foundation for the accurate identification of the aggregation behavior of alloy doped atoms.

[0113] In summary, steps S2-3-1 to S2-3-3 first combine the high-precision training data of elemental, binary, and ternary systems obtained by DFT to set multi-dimensional qualification indicators covering energy, force, lattice constant, elastic constant, and diffusion coefficient. Then, the prediction results of the trained machine learning potential function for each system are compared one by one with the high-precision DFT data to obtain the error values ​​of each indicator. Finally, by verifying whether all error values ​​meet the preset standards, the potential function training is deemed qualified. This process, through comprehensive and quantitative verification logic, ensures that the qualified potential function possesses quantum precision close to first-principles calculations. This effectively avoids the shortcomings of poor generalization ability of traditional empirical potentials while also ensuring the efficiency of subsequent molecular dynamics simulations. It provides core assurance for the reliability of large-scale MD simulations and the accurate identification of the aggregation behavior of alloy doped atoms, laying a solid computational foundation for subsequent correlation analysis between microscopic aggregate states and macroscopic properties.

[0114] As one possible implementation, in the above embodiments, step S3 may specifically include the following steps:

[0115] S3-1. Use the trained machine learning potential function to perform molecular dynamics simulation on the alloy structure model to obtain atomic trajectory data;

[0116] First, the trained machine learning potential function is imported into the LAMMPS molecular dynamics simulation software, along with the pre-built Cu-Zn-Sn alloy structure model. Then, simulation parameters that conform to the actual thermodynamic environment of the alloy are set, such as appropriate ensemble, temperature, pressure, relaxation time, and time step. Based on the trained machine learning potential function, the interatomic interactions are accurately calculated, the molecular dynamics simulation is started and continuously run, and finally, complete atomic trajectory data containing the dynamic changes in the positions of all atoms (including Cu, Zn matrix atoms and Sn doped atoms) are output, providing basic data support for subsequent analysis of doped atom behavior.

[0117] S3-2. Based on the atomic trajectory data, obtain the Euclidean distance between the alloy doped atoms;

[0118] From the atomic trajectory data output by molecular dynamics simulations, the real-time coordinate information of all Sn-doped atoms is precisely screened and extracted, effectively eliminating interference from Cu and Zn matrix atoms and focusing on the spatial distribution characteristics of the target doped atoms. For each Sn-doped atom, using its coordinates as the center, the spatial straight-line distance between the Sn atom and all other Sn-doped atoms in the system is calculated one by one using the Euclidean distance calculation formula, obtaining a set of Sn-Sn Euclidean distance data corresponding to each Sn atom, comprehensively characterizing the spatial positional relationship between a single doped atom and other doped atoms.

[0119] S3-3. Based on the Euclidean distance of the alloy doped atoms, extract three distance indices, including the nearest neighbor distance, the second nearest neighbor distance, and the third nearest neighbor distance;

[0120] For each Sn-doped atom, all Sn-Sn Euclidean distance data are sorted in ascending order. The three smallest distances are then extracted and defined as the nearest neighbor distance d1, the second nearest neighbor distance d2, and the third nearest neighbor distance d3, respectively, thus constructing a unique three-dimensional feature vector for each Sn-doped atom. This three-distance index can quantitatively characterize the local microenvironment of a single doped atom, providing a standardized feature basis for the accurate classification of subsequent aggregation states and overcoming the limitations of traditional methods that rely on only a single distance index.

[0121] S3-4. Based on the three distance indicators combined with the dynamic critical threshold, obtain the identification results of the aggregation behavior of alloy doped atoms;

[0122] Introducing a dynamic critical threshold R that is strongly correlated with Sn doping concentration th The three-dimensional feature vector of each Sn-doped atom is compared with the corresponding concentration R. thA comparative analysis was conducted. Based on clear classification criteria, the aggregation states of all Sn-doped atoms were automatically determined. The proportion and distribution patterns of each aggregation state under different phase structures and Sn concentrations were statistically analyzed, ultimately obtaining comprehensive and quantitative identification results of the aggregation behavior of alloy doped atoms.

[0123] In summary, steps S3-1 to S3-4 first import the qualified machine learning potential function that meets the high-precision index into the LAMMPS software, load the Cu-Zn-Sn alloy structure model, set simulation parameters adapted to the thermodynamic environment, and then perform molecular dynamics simulation to output atomic trajectory data containing the dynamic changes of all atomic positions. Next, Sn-doped atom coordinates are selected from the trajectory data, the Euclidean distance of each Sn atom to other Sn atoms is calculated, and after sorting, the nearest neighbor distance d1, the second nearest neighbor distance d2, and the third nearest neighbor distance d3 are extracted to construct a three-dimensional feature vector. Finally, the concentration-dependent dynamic critical threshold R is combined with... th Based on classification criteria, the automated determination of the aggregation states of all Sn atoms was completed. This process overcomes the shortcomings of traditional methods that rely on a single indicator and are highly subjective. By synergistically applying three-distance indicators and dynamic thresholds, the quantitative and accurate identification of the aggregation states of doped atoms was achieved. This not only clarified the aggregation distribution laws under different phase structures and different doping concentrations, but also revealed the core mechanism that β-phase Sn is more likely to form clusters due to its lower migration barrier. This provides high-quality basic data support for the subsequent establishment of a correlation model between micro-aggregate states and macro-alloy properties.

[0124] As one possible implementation, in the above embodiments, step S3-4 may specifically include the following steps:

[0125] S3-4-1. Obtain the dynamic critical threshold based on the alloy doping concentration of the alloy structure model;

[0126] Based on the defined Sn doping concentration in the current Cu-Zn-Sn alloy structural model, specifically 1%, 2%, or 3%, the corresponding dynamic critical threshold R is obtained. th This dynamic critical threshold is not a fixed value, but is derived from a statistical formula based on the alloy lattice constant and concentration dependence. Its core logic is to adapt to the differences in interatomic interactions under different concentrations by quantifying the critical range of spatial distribution of doped atoms.

[0127] This example sets a Sn concentration-related critical threshold based on the aggregation state of a dynamic critical threshold. The aggregation state of the doped atoms is quantitatively determined based on comparison results. This aggregation state includes dispersed state, significantly aggregated state, and transitional state. The dynamic critical threshold R corresponding to a 1% Sn doping concentration is... th (1% Sn) = 10.48 Å, the dynamic critical threshold R corresponding to a 2% Sn doping concentration. th(2% Sn) = 8.32 Å, the dynamic critical threshold R corresponding to the 3% Sn doping concentration th (3% Sn) = 7.20 Å, providing a quantitative benchmark that strongly matches the concentration for the determination of subsequent aggregation states, avoiding the defect that traditional fixed thresholds are difficult to adapt to multi-concentration systems.

[0128] R th is a dynamic threshold, depending on the Sn doping concentration and lattice constant. The specific calculation is based on statistical rules:

[0129] First, a large number of random structures are generated by ATAT, and the average nearest-neighbor distance of Sn atoms in these structures when they are completely randomly distributed is calculated as the benchmark.

[0130] Then, the threshold is adjusted according to the Sn concentration (1%, 2%, 3%): the higher the concentration, the smaller the average distance between Sn atoms, so R th decreases with the increase of concentration. These values are derived from a statistical formula dependent on the lattice constant and concentration, and the formula is:

[0131]

[0132] where, R th is the dynamic critical threshold, k is the correction factor determined by fitting DFT data, a is the lattice constant, and c is the Sn atomic concentration.

[0133] S3-4-2. Using the dynamic critical threshold, obtain the classification standard for alloy doped atoms;

[0134] Taking the obtained dynamic critical threshold R th as the core benchmark, combined with the correlation characteristics of the three-distance index, construct the classification standard for alloy doped atoms. This classification standard fully considers the local microenvironment of the doped atoms:

[0135] If d1 > R th and d1 < d2 < d3 shows a significant increasing trend, indicating that the spatial distance between Sn atoms is far and there is no obvious aggregation tendency, it is determined as the dispersed state;

[0136] If d1 < R th and d2 - d1 ≤ ΔR, indicating that Sn atoms are closely adjacent and form a local dense region, it is determined as the significantly convergent state (cluster state), where ΔR is a reasonable threshold based on atomic bonding, and ΔR is defaulted to 0.5;

[0137] If R th is between the dispersed state and the significantly convergent state, indicating that Sn atoms are in a transitional state between dispersion and significant convergence, it is determined as the transitional state.

[0138] This classification standard achieves accurate quantitative division of aggregation states through the collaborative determination of multiple indicators.

[0139] S3-4-3. Based on the three distance indicators and the dynamic critical threshold combined with the alloy doping atom classification standard, obtain the identification result of alloy doping atom aggregation behavior;

[0140] First, the specific values ​​of the three-distance index for each Sn-doped atom are extracted to form standardized feature data; then, based on the current Sn doping concentration of the alloy, the corresponding dynamic critical threshold R is matched. th Next, the three-distance index of each Sn atom is compared with R. th The classification criteria were compared one by one, and the aggregation state of individual atoms was classified according to the judgment rules of "dispersed state, significant aggregation state, and transition state". Finally, the judgment results of all Sn doped atoms were statistically analyzed. The number, proportion and distribution characteristics of each aggregation state were summarized according to the phase structure of the alloy and the Sn doping concentration. The aggregation law of Sn doped atoms under different phase structures and different concentrations was summarized, and finally, a comprehensive, quantitative and physically meaningful identification result of the aggregation behavior of alloy doped atoms was obtained.

[0141] The statistical measures of the d1, d2, and d3 distributions of Sn, which accurately identify the aggregation behavior of doped atoms, can precisely distinguish between dispersed, transitional, and clustered states. Furthermore, the high precision of the machine learning potential ensures that the simulation results are close to the DFT. Table 1 shows the statistical table of significant cluster proportions corresponding to different phase structures and different Sn doping concentrations in Cu-Zn-Sn alloys. It reveals the mechanism by which β-phase Sn is more prone to clustering, i.e., the migration barrier of β-phase Sn is 0.8 eV (easy to diffuse), while that of α-phase is 1.2 eV (not easy to agglomerate). Finally, the results of identifying the aggregation behavior of alloy doped atoms, which combines quantitative data with mechanistic explanation, are obtained.

[0142] Table 1

[0143] Phase structure Sn concentration Significant cluster proportion α(FCC) 1% 15% α(FCC) 3% 35% α(BCC) 1% 40% α(BCC) 3% 65%

[0144] In summary, steps S3-4-1 to S3-4-3 first obtain a dynamic critical threshold derived from the lattice constant and concentration-dependent statistical formula based on the Sn doping concentration of the Cu-Zn-Sn alloy structure model, achieving precise adaptation of the threshold to systems with different concentrations. Then, using this dynamic critical threshold as the core benchmark, and combining the correlation characteristics of the three-distance index, a classification standard is constructed. Finally, by extracting the three-distance index of each Sn doped atom and comparing it one by one with the corresponding dynamic critical threshold and classification standard, the aggregation state of individual atoms is classified. The number and proportion of each aggregation state are statistically analyzed according to the alloy phase structure and doping concentration, ultimately obtaining comprehensive identification results of alloy doped atom aggregation behavior. This process overcomes the shortcomings of traditional fixed thresholds, which suffer from poor adaptability and strong subjectivity. Through dynamic thresholds and multi-index collaborative classification, it achieves precise quantitative identification of aggregation states. It not only clarifies the aggregation distribution law under different phase structures and concentrations but also reveals the core mechanism that β-phase Sn atoms are more likely to form clusters due to their lower migration barrier. This provides a reliable quantitative basis for subsequently establishing a correlation model between micro-aggregate states and macro-alloy properties and optimizing alloy doping processes.

[0145] As one possible implementation, in the above embodiments, step S4 may specifically include the following steps:

[0146] S4-1. Based on the identification results of the aggregation behavior of the alloy doped atoms, obtain the micro-aggregation state dataset;

[0147] Based on the identification results of alloy doping atom aggregation behavior, core parameters reflecting micro-aggregation characteristics are extracted to construct a standardized micro-aggregation state dataset. This dataset needs to comprehensively cover the key structural scenarios of the target Cu-Zn-Sn alloy, including aggregation characteristic parameters under different phases and different Sn doping concentrations. Specifically, it covers dimensions such as aggregation size (e.g., number of cluster atoms, equivalent radius), distribution density (e.g., number of clusters per unit volume, proportion of aggregation region), aggregation phase state (e.g., disordered aggregation, formation of ordered second phase), defect correlation degree (e.g., the combination state of clusters with dislocations and vacancies), and spatial distribution characteristics (e.g., uniform distribution, local enrichment). At the same time, the data is cleaned and normalized, outliers are removed, and feature interpolation for missing scenarios is added to ensure the completeness, consistency, and representativeness of the dataset, providing high-quality input data support for subsequent correlation model construction.

[0148] S4-2. Based on the identification results of the atom aggregation behavior of the alloy doping and the alloy micro-aggregation mechanism, establish a correlation model between the micro-aggregation state and the macro-performance.

[0149] Based on the identification results of alloy doped atom aggregation behavior, and combined with the micro-aggregation mechanism of Cu-Zn-Sn alloys, such as the enhanced electron scattering caused by Sn atom aggregation, the dispersion strengthening effect of second-phase particles, and the evolution law of aggregation-induced defects, this study integrates fundamental alloy theories such as electron transport theory, defect strengthening theory, and thermodynamic equilibrium theory to construct a quantitative correlation model between micro-aggregate state and macroscopic properties. First, statistical analysis clarifies the correlation direction and strength between micro-aggregate characteristic parameters (such as aggregation size and distribution density) and macroscopic properties (such as electrical conductivity, eddy current resistance, and mechanical strength). Then, combining experimental data (such as alloy performance test results under different aggregation states) with machine learning algorithms (such as random forests and neural networks) or theoretical derivation methods, the aggregation mechanism is embedded into the model structure to quantify the influence weight of aggregation characteristics on macroscopic properties. Finally, a correlation model with both mechanistic explanatory power and predictive accuracy is formed, ensuring that the model accurately reflects the regulatory law of micro-aggregate state on macroscopic properties.

[0150] S4-3. Input the micro-aggregate state dataset into the correlation model between the micro-aggregate state and the macro-performance to obtain the performance prediction results;

[0151] The acquired standardized micro-aggregate state dataset is preprocessed according to the model's requirements, including feature dimension matching and data format conversion. The preprocessed dataset is then substituted into the established correlation model. Through the model's numerical calculation, logical reasoning, or simulation functions, predicted macroscopic properties of the alloy under corresponding scenarios are output, covering key properties such as electrical conductivity and eddy current resistance. To ensure the reliability of the prediction results, the model output is checked against actual alloy preparation experimental data or performance benchmarks reported in the literature. This includes calculating the average relative error between the predicted and measured values. If the error exceeds a preset threshold, model parameters (such as feature weights and algorithm hyperparameters) can be adjusted retrospectively, or more sample data can be added to retrain the model. Finally, the validated prediction data is integrated to form a complete performance prediction result containing performance values ​​and performance influence laws under different micro-aggregate states, such as the sensitivity curve of Sn aggregation size to electrical conductivity, as well as performance optimization directions. This provides a direct decision-making basis for the microstructure control and macroscopic performance optimization of Cu-Zn-Sn alloy target backplates.

[0152] In summary, steps S4-1 to S4-3 first extract key quantitative features such as phase structure, Sn doping concentration, three-distance index, aggregation state classification, and cluster ratio from the alloy doping atom aggregation behavior identification results, and integrate them to form a standardized micro-aggregate state dataset. Then, combined with the alloy micro-aggregate mechanism, a correlation model between micro-aggregate state and macroscopic performance is established, which has both statistical reliability and physical interpretability, clarifying the core causal relationship that "the higher the cluster ratio, the lower the electrical conductivity and the better the eddy current resistance". Finally, the dataset is input into the model, and the output is a quantitative prediction result containing the electrical conductivity range, eddy current resistance level, and mechanical performance reference values. This process overcomes the shortcomings of existing technologies, such as poor generalization ability, limited computational scale, and lack of unified quantitative standards. It relies on high-precision machine learning potential functions trained in stages to ensure the accuracy of aggregation identification and performance prediction, realizes the automated and quantitative identification of the aggregation state of doped atoms, and establishes a clear correlation between microstructure and macroscopic performance. It provides a reproducible and scalable scientific basis for the structural control of Cu-Zn-Sn alloy target backplates, and effectively optimizes the electrical conductivity stability, eddy current resistance, and mechanical properties of the alloy.

[0153] Further reference Figure 7 As an implementation of the methods shown in the above figures, this disclosure provides an embodiment of a system for identifying the aggregation behavior of doped atoms in alloys and predicting their performance. This system embodiment is similar to... Figure 1 The method embodiments shown correspond to those described.

[0154] like Figure 7 As shown, the alloy doped atom aggregation behavior identification and performance prediction system of this embodiment includes: a data generation module, a potential function training module, a simulation analysis module and a performance prediction module;

[0155] The data generation module is used to construct the alloy structure model;

[0156] The core function of this module is to generate the initial atomic structure model of the alloy. Specifically, it uses the mcsqs random structure generator in ATAT software to generate diverse models covering α (FCC) and β (BCC) phase structures and Sn doping concentrations of 1%, 2%, and 3% for the Cu-Zn-Sn alloy system. Each phase-concentration combination corresponds to 100 SQS, and the supercell size is set to 3×3×3 (approximately 200 atoms). By ensuring the randomness and diversity of the structure, the interference of long-range ordered structures on subsequent analysis is avoided. This provides basic data support that conforms to the actual microscopic characteristics of the alloy for subsequent potential function training and simulation analysis, ensuring the reliability of the starting point of the entire technical process.

[0157] The potential function training module is used to perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function.

[0158] This module is responsible for performing phased training and accuracy verification of the machine learning potential function based on the alloy structure model output by the data generation module. It uses DeepMD-kit as the core training framework, and the training process is divided into three stages: elemental potential (Cu, Zn, Sn), binary potential (Cu-Zn, Cu-Sn, Zn-Sn), and ternary potential (Cu-Zn-Sn). The training data comes from high-precision data such as energy, force, and stress of elemental, binary, and ternary systems calculated using DFT. The training process employs a multi-objective weighted loss function, initially using the Adam optimizer (learning rate from 10). -3 Decrease to 10 -5 Later, the algorithm was switched to L-BFGS to improve the smoothness of the potential energy surface. After 800,000 iterations of training, the core indicators such as average energy error (MAE) < 5 meV / atom and root mean square force error (RMSE) < 0.1 eV / Å were verified by comparing with DFT data. Finally, a qualified machine learning potential function with high accuracy and generalization ability was output, which made up for the shortcomings of poor generalization ability of traditional empirical potential and limited computational scale of DFT. It not only ensures quantum-level computational accuracy, but also breaks through the scale limitation of traditional DFT computation, providing a key tool for large-scale molecular dynamics simulation.

[0159] The simulation analysis module is used to perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function, and obtain the identification results of the aggregation behavior of alloy doped atoms.

[0160] The core task of this module is to utilize the qualified machine learning potential function output by the potential function training module to perform molecular dynamics simulations and calculate distance indices to determine the aggregation state, thereby completing the identification of doped atom aggregation behavior. First, the LAMMPS software is called to perform molecular dynamics simulations on all structural models constructed by the data generation module based on the qualified potential function output by the potential function training module, obtaining atomic trajectory data. Based on the trajectory data, for each Sn doped atom, its Euclidean distance to other Sn atoms is calculated and sorted, and the nearest neighbor distance d1, the second nearest neighbor distance d2, and the third nearest neighbor distance d3 are extracted to form a three-dimensional feature space. Then, a dynamic critical threshold R is combined... th With clear classification criteria, the module automatically completes the quantitative identification of Sn atomic dispersed states, transition states, and significant aggregation states; this module solves the problem of the lack of unified quantitative identification standards in existing technologies, and achieves high efficiency and accuracy in aggregation behavior analysis.

[0161] The performance prediction module is used to perform performance prediction based on the identification results of the atom aggregation behavior of the alloy doping and to obtain the performance prediction results.

[0162] The core function of this module is to predict the electrical conductivity and eddy current resistance of alloys based on their aggregation states. It establishes a correlation between micro-aggregate states and macroscopic properties and performs predictions. Based on the aggregation behavior identification results obtained from the simulation analysis module, and combined with the alloy's micro-aggregate mechanisms such as the difference in Sn atom migration barriers, a correlation model between micro-aggregate states and macroscopic properties is constructed. This model can accurately output the predicted results of key properties of Cu-Zn-Sn alloys, such as electrical conductivity and eddy current resistance, clarifying the influence of aggregation states on performance. This provides a scientific basis for the structural control of alloy target backing plates, ultimately achieving the goal of alloy performance optimization.

[0163] In summary, this alloy doped atom aggregation behavior identification and performance prediction system works collaboratively through four modules: the data generation module generates an initial alloy structure model with sufficient randomness and diversity, laying the foundation for subsequent analysis; the potential function training module outputs a machine learning potential function with both quantum precision and generalization ability through phased training, overcoming the contradiction between accuracy and efficiency in traditional methods; the simulation analysis module completes molecular dynamics simulations in conjunction with qualified potential functions, and achieves accurate identification of doped atom aggregation states by using three-distance indices and dynamic thresholds; and the performance prediction module constructs a micro-macro performance correlation model based on the aggregation identification results. The entire system effectively solves the problems of existing technologies' inability to efficiently and quantitatively identify aggregation states and the lack of a performance prediction framework. It can not only accurately distinguish three aggregation states and reveal the aggregation mechanism, but also reliably predict key properties such as alloy conductivity and eddy current resistance, significantly improving the credibility and application value of multi-component alloy microstructure analysis, and providing efficient technical support for alloy performance optimization.

[0164] In this embodiment, the specific processing of an alloy doping atom aggregation behavior identification and performance prediction system and its resulting technical effects can be referred to separately. Figure 1 The relevant descriptions of steps S1, S2, S3 and S4 in the corresponding embodiments will not be repeated here.

[0165] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0166] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0167] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0168] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance, characterized in that, include: S1. Construct the alloy structure model; S2. Perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function; S3. Perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function to obtain the identification results of the alloy doped atom aggregation behavior; S4. Use the results of the alloy doping atom aggregation behavior identification to perform performance prediction and obtain the performance prediction results.

2. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 1, characterized in that, S1. Construct the alloy structure model, including: Set key phase structure parameters and alloy doping concentration; Based on the key phase structure parameters and the alloy doping concentration, a special quasi-random structure is generated; Based on the aforementioned special quasi-random structure, an alloy structure model is constructed using a random structure generator.

3. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 1, characterized in that, S2. Based on the alloy structure model, perform phased training of the machine learning potential function to obtain a qualified machine learning potential function, including: Based on the alloy structure model, density functional theory is used to obtain high-precision training data. The high-precision training data includes training data for elemental systems, binary systems, and ternary systems. The training data includes atomic energy, interatomic forces, and stress tensors. The high-precision training data is used for phased training to obtain the machine learning potential function. The machine learning potential function is compared and verified to obtain a qualified machine learning potential function.

4. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 3, characterized in that, Using the high-precision training data, staged training is performed to obtain the machine learning potential function, including: The single-mass potential function is trained using the training data of the single-mass system, and the trained single-mass potential function is obtained. The binary potential function is trained based on the trained single-mass potential function and the training data of the binary system to obtain the trained binary potential function. Based on the trained binary potential function and the training data of the ternary system, the potential function of the entire target alloy system is obtained. Based on the potential function of the entire target alloy system, a machine learning potential function is obtained using a hybrid optimization strategy.

5. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 3, characterized in that, Based on the machine learning potential function, a comparative verification is performed to obtain a qualified machine learning potential function, including: Using the high-precision training data, set up multi-dimensional qualification indicators; Based on the comparison between the machine learning potential function and the high-precision training data, the index error value between the machine learning potential function and the high-precision training data is obtained. Based on the multi-dimensional qualification indicators combined with the indicator error value between the machine learning potential function and the high-precision training data, a qualified machine learning potential function is obtained.

6. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 2, characterized in that, S3. Perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function to obtain the identification results of the alloy doped atom aggregation behavior, including: Molecular dynamics simulations were performed on the alloy structure model using the trained machine learning potential function to obtain atomic trajectory data; Based on the atomic trajectory data, the Euclidean distances of the alloy doped atoms are obtained; Based on the Euclidean distance of the alloy doped atoms, three distance indices are extracted, including the nearest neighbor distance, the second nearest neighbor distance, and the third nearest neighbor distance. Based on the three distance indicators combined with the dynamic critical threshold, the identification results of the aggregation behavior of alloy doped atoms are obtained.

7. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 6, characterized in that, Based on the aforementioned three-distance index combined with a dynamic critical threshold, the identification results of alloy doped atom aggregation behavior are obtained, including: The dynamic critical threshold is obtained based on the alloy doping concentration of the alloy structure model; The dynamic critical threshold is used to obtain the alloy doping atom classification criteria; Based on the three-distance index and the dynamic critical threshold combined with the alloy doping atom classification standard, the identification result of the alloy doping atom aggregation behavior is obtained.

8. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 7, characterized in that, The classification criteria for alloy doping atoms include: When d1 > R th , and when d1 < d2 < d3, the alloy doped atoms are determined to be in a dispersed state; When d1 <R th When d2-d1≤ΔR, the alloy doped atoms are determined to be in a cluster state; When R th When the alloy dopant atoms are in a state between the dispersed state and the aggregated state, they are determined to be in a transition state. Where d1 is the nearest neighbor distance, d2 is the second nearest neighbor distance, d3 is the third nearest neighbor distance, and R is the distance between the nearest and second nearest neighbors. th ΔR is the dynamic critical threshold, and ΔR is the reasonable threshold based on atomic bonding.

9. The method for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance according to claim 1, characterized in that, S4. Utilize the alloy doping atom aggregation behavior identification results to perform performance prediction and obtain performance prediction results, including: Based on the identification results of the atom aggregation behavior of the alloy doping, a dataset of micro-aggregation states is obtained; Based on the identification results of the atom aggregation behavior of the alloy doping and the alloy micro-aggregation mechanism, a correlation model between the micro-aggregation state and the macro-performance is established. The micro-aggregate state dataset is input into the correlation model between the micro-aggregate state and macro-performance to obtain performance prediction results.

10. A system for identifying the aggregation behavior of doped atoms in an alloy and predicting its performance, comprising the method described in any one of claims 1-9, characterized in that, include: The module includes a data generation module, a potential function training module, a simulation analysis module, and a performance prediction module. The data generation module is used to construct the alloy structure model; The potential function training module is used to perform phased training of the machine learning potential function based on the alloy structure model to obtain a qualified machine learning potential function. The simulation analysis module is used to perform molecular dynamics simulation on the alloy structure model based on the trained and qualified machine learning potential function, and obtain the identification results of the aggregation behavior of alloy doped atoms. The performance prediction module is used to perform performance prediction based on the identification results of the atom aggregation behavior of the alloy doping and to obtain the performance prediction results.

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