Simulation method and device for amorphous alloy surface structure stability and computer equipment

Abstract

The invention discloses a simulation method and device for amorphous alloy surface structure stability and computer equipment, and relates to the technical field of material calculation. The simulation method for the surface structure stability of the amorphous alloy comprises the following steps: establishing a bulk phase structure model; establishing a flat plate model; obtaining a surface energy calculation function of the flat plate model, and calculating the surface energy of the flat plate model according to a density functional theory; constructing a data set composed of surface descriptors of the flat plate model; constructing a machine learning model, and training the machine learning model by using the surface descriptor data of the data set; and inputting the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain a surface stability analysis result of the target amorphous alloy. According to the method, the amorphous alloy surface stability judgment efficiency is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of material design, and in particular to a method, device and computer equipment for simulating the surface structure stability of amorphous alloys. Background Technique

[0002] The non-static nickel-phosphorus alloy (Ni-P) has a unique structure, high conductivity and good chemical stability, and exhibits excellent catalytic activity and reversible redox performance in the electrochemical field; by adjusting the phosphorus content and preparation process, the phase structure, specific surface area and electron conductivity of the Ni-P alloy can be optimized to adapt to different electrochemical application requirements; moreover, nickel and phosphorus resources are relatively abundant, the preparation process is mature, and the cost is lower than that of precious metals and other rare materials, making it suitable for large-scale applications; these characteristics make it have important application potential in energy storage and energy conversion devices (such as supercapacitors, batteries, electrocatalysts).

[0003] However, due to the long-range disorder of the amorphous nickel-phosphorus alloy, the surface microstructure is complex, and it is difficult to directly observe the atomic-level dynamic changes by experimental means, and there is also a large randomness in material modeling; the surface reconstruction mechanism of amorphous materials, the correlation between electronic structure and performance have not been clarified, and there is a lack of an effective theoretical model to correlate the surface structure and performance; moreover, the existing calculation models currently have an overly large calculation amount, and the calculation depends on manual task allocation; these factors restrict the material design and performance optimization of amorphous nickel-phosphorus alloys. Summary of the Invention

[0004] The present invention provides a method, device and computer equipment for simulating the surface structure stability of amorphous alloys, aiming to combine density functional theory and machine learning to efficiently screen and evaluate the stability of the surface of amorphous nickel-phosphorus alloys.

[0005] The method for simulating the surface structure stability of amorphous alloys provided by the present invention includes the following steps:

[0006] S1. Establish a bulk structure model: Obtain the cluster structure crystal configuration of the amorphous alloy and perform structure optimization;

[0007] S2. Establish a slab model: Expand the cell of the cluster structure crystal configuration after structure optimization, intercept the crystal plane with a low Miller index, add a vacuum layer to the surface and introduce dipole correction to obtain the original surface, and perform surface reconstruction on the original surface;

[0008] S3. Obtain the surface energy calculation function of the slab model, and calculate the surface energy of the slab model according to density functional theory;

[0009] S4. Construct a dataset consisting of surface descriptors of the slab model; the surface descriptors include at least one of surface energy, work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction;

[0010] S5. Construct a machine learning model and train the machine learning model using the surface descriptor data of the dataset; the machine learning model includes a random forest model and a neural network model; the random forest model classifies the relationship between the surface descriptors and surface stability and obtains the contribution value of different surface descriptors to surface stability; the neural network model includes an input layer, a hidden layer, and an output layer, the input layer parameters include at least one of work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction, and the output layer parameter is surface energy;

[0011] S6. Input the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

[0012] Optionally, in step S2, the method of surface reconstruction is to delete one or more layers of surface atoms to simulate the absence of surface atomic layers.

[0013] Optionally, step S3 further includes:

[0014] Calculate the work function and electron density of states of the slab model according to density functional theory.

[0015] Optionally, in step S4, the calculation formula for the d-band center is:

[0016]

[0017] In the formula, represents the d-band center, x represents the energy level, represents at the energy level, the number of electrons in this energy level state;

[0018] Alternatively, the d-band center is corrected to the following formula:

[0019]

[0020] In the formula, is the corrected d-band center, is the broadening; the calculation formula for the broadening is:

[0021]

[0022] In the formula, is about the d-band center Second moment.

[0023] Optionally, the amorphous alloy is a nickel-phosphorus alloy, and the crystal configuration of the cluster structure of the nickel-phosphorus alloy includes at least one of Ni2P, Ni3P, Ni5P4, NiP2, and Ni5P2.

[0024] Optionally, in the step S3, the calculation function of the surface energy is:

[0025]

[0026] In the formula, is the surface energy, A is the cross-sectional area of the surface, is the Gibbs free energy of the slab model, and are the nickel-phosphorus stoichiometric ratios of Ni x P y respectively, and are the numbers of nickel atoms and phosphorus atoms in the slab model respectively, is the unit Gibbs free energy of the Ni x P y bulk-phase structure, is the phosphorus chemical potential;

[0027] Among them, the phosphorus chemical potential has a value range of:

[0028]

[0029] In the formula, represents the standard formation energy of the Ni x P y bulk-phase structure.

[0030] Optionally, in the step S5, the stable surface is defined by the following formula:

[0031]

[0032] In the formula, is the difference between the surface energy and the surface energy of the most stable surface, is the Boltzmann constant, and T is the Kelvin temperature;

[0033] The determination method of the stable surface is: when the difference between the surface energy and the surface energy of the most stable surface is not greater than 25.85 meV, it is determined as a stable surface; when the difference between the surface energy and the surface energy of the most stable surface is greater than 25.85 meV, it is determined as an unstable surface; the most stable surface is the surface with the lowest surface energy among all the crystal configurations of the cluster structure of the amorphous alloy.

[0034] The simulation device for the surface structure stability of amorphous alloys provided by the present invention includes:

[0035] A bulk structure model establishment module, configured to obtain the cluster structure crystal configuration of the amorphous alloy and perform structure optimization;

[0036] A slab model establishment module, configured to expand the cell of the cluster structure crystal configuration after structure optimization, intercept the crystal planes with low Miller indices, add a vacuum layer on the surface and introduce dipole correction to obtain an original surface, and perform surface reconstruction on the original surface;

[0037] A density functional calculation module, configured to calculate the surface energy, work function, and electronic density of states of the slab model based on the density functional theory according to the established slab model and its surface energy calculation function;

[0038] A training data providing module, including a data set composed of surface descriptor data of the slab model; the surface descriptors include at least one of surface energy, work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction;

[0039] A machine learning module, configured to construct a machine learning model, and the machine learning model is trained using the surface descriptor data of the data set; the machine learning model includes a random forest model and a neural network model; the random forest model classifies the relationship between the surface descriptors and surface stability and obtains the contribution values of different surface descriptors to surface stability; the neural network model includes an input layer, a hidden layer, and an output layer, the input layer parameters of the neural network model are at least one of work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction, and the output layer parameter is surface energy;

[0040] A surface stability analysis module, configured to input the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

[0041] Optionally, the simulation device for the surface structure stability of amorphous alloys further includes:

[0042] A cross-validation module, configured to divide the data set into a training set and a validation set, and cyclically cross-train and validate the machine learning model to evaluate the generalization ability of the machine learning model.

[0043] The present invention also proposes a computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, it implements the above-mentioned simulation method for the surface structure stability of amorphous alloys.

[0044] The present invention has the following beneficial effects:

[0045] Starting from the existing crystalline cluster structure of the alloy, based on density functional theory, this invention analyzes the relationships between surface descriptors such as work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction and surface stability, and combines the random forest model and neural network model in machine learning to construct an automated calculation model for analyzing the surface stability of amorphous alloys; for the target amorphous alloy that needs to calculate and judge surface stability, inputting the relevant surface descriptor data can automatically obtain the analysis result of the surface stability of the target amorphous alloy, significantly improving the efficiency of surface stability judgment, which is of great significance for the analysis of complex systems of amorphous alloys and the design of new amorphous alloy materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0047] Figure 1 It is a block diagram of the steps of the simulation method for the surface structure stability of the amorphous alloy of the present invention;

[0048] Figure 2 It is a schematic flow chart of the simulation method for the surface structure stability of the amorphous alloy of the present invention;

[0049] Figure 3 It is a comparison diagram before and after the optimization of the crystal structure (where the left side is before optimization and the right side is after optimization; (a) NiP2, (b) Ni2P, (c) Ni3P, (d) Ni5P2, (e) Ni5P4, silver gray is Ni atoms, and light purple is P atoms);

[0050] Figure 4 It is a schematic diagram of various different surface reconstructions of the optimized Ni5P4(110) (where, (a) Ni5P4(110)-Pris, (b) Ni5P4(110)-L1, (c) Ni5P4(110)-L2, and the schematic diagram is a side view of the bc plane);

[0051] Figure 5 For different Ni x P y Surface free energy phase diagram of the surface structure varying with the phosphorus chemical potential;

[0052] Figure 6Ball stick model diagrams of surface structures with lower surface energy (where (a) Ni5P2(001)-L1, with a phosphorus-nickel ratio of 0.3 on its top surface; (b) NiP2(010)-Pris, with a phosphorus-nickel ratio of 3.0 on its top surface; (c) Ni x P y Scatter plot of surface energy varying with surface phosphorus-nickel ratio);

[0053] Figure 7 Work function distribution diagrams of different Ni-P surfaces of the present invention;

[0054] Figure 8 Schematic diagram of the random forest model algorithm of the present invention;

[0055] Figure 9 Schematic diagram of the multi-layer perceptron of the neural network model of the present invention (the leftmost is the input layer, the middle is the hidden layer, and the rightmost is the output layer);

[0056] Figure 10 Schematic diagram of the importance ratio results of the random forest model in some embodiments of the present invention for solving the contribution of descriptors to surface stability;

[0057] Figure 11 Violin plot of the prediction accuracy of cross-validation results for different numbers of neurons in the hidden layer in some embodiments of the present invention. Detailed implementation manners

[0058] To make the objectives, features, and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described below are only a part of the embodiments of the present invention, rather than all of the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0059] The terms "including" and "having" in the specification of this application and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products, or devices.

[0060] Compared with crystalline materials, amorphous alloys exhibit significant advantages in physical and chemical properties due to their unique disordered structure. They use non-precious metals as the alloy framework, with non-metal doping but still maintaining their metallicity. Coupled with the excellent mechanical properties of the material itself, amorphous alloys have great potential as electrode materials for hybrid capacitors. However, the disorder of amorphous alloys also poses a huge challenge to their structural stability.

[0061] For many years, researchers have been committed to developing more accurate models to describe the structure of amorphous solids. The Reverse Monte Carlo (RMC) model is a method for simulating the three-dimensional atomic configuration of amorphous solids. This method reconstructs an amorphous alloy model containing thousands of atoms through a simulated annealing algorithm, providing a new perspective for the study of amorphous materials. Some studies start from the perspective of mesoscale modeling and calculation, use the concept of quasi-equivalent cluster packing, quantify the structural order during the formation of metallic glasses, reveal the complex interaction between structural defects and the dynamic properties of metallic glasses, and apply the model to the study of Ni-P-based amorphous materials. It can be concluded that the disorder degree of Ni-P-based amorphous materials has a boundary at a size of 10 Å. Outside this boundary, the atoms are disordered, while inside, there is still an ordered arrangement. At the same time, researchers have also found that there are cluster structures with crystal configurations of Ni2P, Ni3P, and Ni5P2 in the ordered structure of amorphous Ni-P materials. Therefore, for the theoretical study of amorphous materials, the crystalline structure properties can be used as a starting point to find the correlation between the two and predict the properties of amorphous materials.

[0062] With the rapid development of supercomputers and the continuous update of artificial intelligence algorithms, material design is no longer limited to the one-way process from experimental preparation to theoretical explanation of performance. Instead, it is more about material research and development that combines theory with experiment and even guides experiments. For example, in the theoretical study of some amorphous materials, a multi-layer perceptron model can be designed to simulate and predict the variation law of the crystallization temperature of Ni-P-based amorphous alloys with alloy composition and heating rate. The input parameters of this model include alloy composition, heating rate during the heating process, and processing parameters of the alloy, while the output parameters are the crystallization temperatures (starting temperature, peak temperature, and ending temperature) of the main crystallization reactions of the amorphous alloy.

[0063] The exploration of various excellent properties of amorphous materials includes the study of the structural stability of these materials. However, current research on the structural stability of amorphous materials, especially the structural stability of the formed surface state, still faces many challenges. First, the complexity and instability of the amorphous structure make it difficult to conduct in-depth experimental research, and there is also a great deal of randomness in material modeling. Second, traditional experimental methods are difficult to directly observe the structural changes at the atomic level on the surface. Even with the use of advanced microscopy techniques, it is very difficult to directly observe the dynamic change process at the atomic scale on the surface of amorphous alloys. Finally, there is a lack of effective theoretical models to describe and predict the surface stability of amorphous alloys.

[0064] In terms of theoretical research, although some studies have involved the structure of amorphous Ni-P and the construction at the micro-nano scale on the surface, most studies still remain at the level of classical molecular dynamics simulations. Although these simulation methods can provide certain structural information, they are limited by experience and assumptions and often difficult to accurately describe the true structure of amorphous alloys. In addition, although reverse Monte Carlo methods such as the RMC algorithm have been used for the structural simulation of amorphous alloys, they tend to be more random and it is difficult to obtain a stable structural model.

[0065] In view of this, the embodiments of the present invention start from the existing cluster structure of amorphous alloys, conduct a structure analysis on the surface problems of crystal structures with lower Miller indices, analyze their surface structural stability, and combine with a machine learning model to predict the structural stability of the surface of amorphous alloys starting from the microstructural information of the materials.

[0066] Refer to Figure 1 、 2 The simulation method for the surface structural stability of amorphous alloys provided by the embodiments of the present invention includes the following steps:

[0067] S1, establish a bulk-phase structure model: Obtain the crystal configuration of the cluster structure of the amorphous alloy and conduct structure optimization.

[0068] Among them, the cluster structure refers to the structure of a relatively stable microscopic or submicroscopic aggregate composed of several to thousands of atoms, molecules or ions through physical or chemical binding forces. In amorphous alloys, the cluster structure usually has high symmetry and order. Clusters are between macroscopic and microscopic substances and are an important bridge for understanding the relationship between the structure and properties of substances. By studying the cluster structure, the evolution law of substances from the atomic and molecular levels to the macroscopic scale can be deeply understood, providing a theoretical basis for the design, synthesis and application of new materials.

[0069] The geometric structure of the crystal configuration mainly includes the positions of atoms, bond lengths, bond angles, and lattice parameters, etc. The objective of optimizing the structure of the crystal configuration is to adjust these parameters to minimize the total energy of the crystal. The electronic structure and total energy can be calculated by solving the Kohn-Sham equation through density functional theory calculations. During the optimization process, the atomic positions and lattice parameters are continuously adjusted to make the total energy converge to the minimum value. The structure of the crystal configuration can also be optimized by molecular mechanics based on classical mechanics principles or the Monte Carlo method based on statistical mechanics.

[0070] S2, Establish a slab model: Expand the unit cell of the crystal configuration of the optimized cluster structure, intercept the crystal plane with low Miller indices, add a vacuum layer on the surface and introduce dipole correction to obtain the original surface, and perform surface reconstruction on this original surface.

[0071] The crystal planes with low Miller indices usually have a relatively regular atomic arrangement. The distribution of atoms on the crystal plane has high symmetry and periodicity. These crystal planes are representative and can reflect the main characteristics of the material surface.

[0072] Use the crystal plane with low Miller indices to intercept the supercell after expanding the unit cell, and select a slab thick enough in the direction perpendicular to the crystal plane. To avoid the influence of periodicity in the z-axis on crystal calculations, a vacuum layer thick enough needs to be added, and dipole correction is introduced. The basic principle of dipole correction is to introduce a dipole in the center of the vacuum layer with the same magnitude but opposite sign to the surface dipole to cancel the potential energy gradient caused by the surface dipole and eliminate the dipole influence brought by introducing the vacuum layer.

[0073] Since the cut surface has dangling bonds and will show activity, it is necessary to optimize the local movement and rearrangement of surface atoms, that is, surface reconstruction. In addition to constructing the original (pristine, Pris) surface, possible reconstruction phenomena also need to be considered. The method of surface reconstruction is to delete one or more layers of surface atoms (for example, delete 1 - 2 layers of surface atoms) to simulate the absence of surface atomic layers.

[0074] S3, Obtain the surface energy calculation function of the slab model, and calculate the surface energy of the slab model according to density functional theory (DFT).

[0075] Based on the slab model established in step S2, the corresponding work function and density of electronic states can also be calculated according to density functional theory. The work function and density of electronic states can be used to construct surface descriptor data in subsequent steps.

[0076] S4, Construct a dataset composed of surface descriptors of the slab model; surface descriptors include surface energy (which can be expressed as ), work function ( ), d-band center ( ), alloy element stoichiometric ratio ( ), atomic number ( ), average valence electron number ( )、Surface Orientation( ), surface reconstruction ( )

[0077] Among them, the formula Calculate the work function of each surface of each flat plate model; where, represents the vacuum energy level, represents the Fermi level.

[0078] The d-band center represents the expected value of the electronic state and provides important information about the electronic structure. The calculation formula is:

[0079]

[0080] In the formula, represents the d-band center, x represents the energy level, Indicated in The number of electrons in the energy level.

[0081] In some approaches that more fully characterize the d-band, the d-band center can be modified to:

[0082]

[0083] In the formula, is the corrected d-band center, is the widening; the calculation formula of the widening is:

[0084]

[0085] In the formula, About the d-band center The second order moment of .

[0086] In addition, the alloying element stoichiometry is used as a surface descriptor to reflect the elemental composition of the alloy.

[0087] The atomic number as a surface descriptor reflects the overall composition scale of the alloy.

[0088] Among the many factors affecting chemical reactions, the reaction of electrons plays a vital role, especially those active valence electrons, which directly participate in the reaction and determine the progress and results of the reaction. For amorphous alloys, the exploration of the stability of their surface structure is also inseparable from the study of valence electrons. In the embodiments of the present invention, the average number of valence electrons is used as a surface descriptor to reflect the distribution and characteristics of valence electrons in amorphous alloys.

[0089] The surface orientation describes the direction of the crystal plane. For the convenience of using the machine learning model in subsequent steps, values (such as 1, 2, 3, ……, n) can be assigned to the crystal plane directions.

[0090] When constructing the slab model, the embodiments of the present invention also consider surface reconstruction, and values can be assigned to the original crystal plane and the surface of the missing atomic layer; for example, the surfaces in the cases of the original crystal plane (Pris), missing top-layer atoms (L1), and missing second-top-layer atoms (L2) can be assigned 0, 1, and 2 respectively.

[0091] S5. Construct a machine learning model and use the surface descriptor data in the data set in step S4 to train the machine learning model.

[0092] The machine learning model includes a random forest model and a neural network model.

[0093] Refer to Figure 8 , the random forest model is based on decision trees. By randomly sampling with replacement from the original training data set, multiple different sub-data sets are constructed, and then the decision tree models are trained separately. Finally, the prediction results of these decision trees are integrated to make the final decision; the trained multiple decision tree models are integrated to form a random forest model.

[0094] For classification problems, usually the way of voting by multiple decision tree classifiers is adopted to determine the final classification result, that is, each decision tree makes a classification prediction for the test sample, and then the votes obtained for each category are counted, and the category with the most votes is used as the prediction result of the random forest.

[0095] For regression problems, the mean value of the predicted values of multiple trees determines the final prediction result, that is, each decision tree makes a regression prediction for the test sample, and then the average value of the prediction results of all decision trees is used as the prediction result of the random forest. This method can make full use of the advantages of multiple decision trees to improve the accuracy and stability of prediction; at the same time, because randomness is introduced in the random forest, the model is not easy to overfit, the generalization ability of the model is improved, and the importance scores of each feature can also be given, clearly showing the influence degree of each feature in the classification decision or regression calculation.

[0096] Specifically, in the embodiments of the present invention, the surface descriptor data in the data set is divided into a training set and a validation set, and the training set data is used to train the random forest model; the random forest model classifies the relationship between the surface descriptor and the surface stability, and obtains the contribution value of different surface descriptors to the surface stability; by setting parameters such as the number of decision trees, the maximum depth, the minimum sample split number, the minimum number of samples in the leaf node, and the size of the feature subset in the random forest model, the best parameter combination is obtained on the validation set, so as to obtain the trained random forest model.

[0097] Refer to Figure 9 , the neural network model adopted in the embodiments of the present invention is based on a multi-layer perceptron, which consists of an input layer, a hidden layer, and an output layer. Neurons in each layer are fully connected to neurons in the next layer, and there is no connection between neurons within the layer; the multi-layer perceptron introduces non-linear characteristics through non-linear activation functions, enabling it to learn and approximate complex functions, a feedforward neural network model of multi-layer perception.

[0098] Specifically, the input layer parameters include one or more of work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction, and the output layer parameter is surface energy.

[0099] Input data enters the network from the input layer. Through a series of linear transformations in the hidden layer and the action of non-linear activation functions, the features of the data are gradually extracted, and finally the prediction result is obtained in the output layer; in each layer, the output of the neuron is obtained by performing a weighted sum of the input and the weights of the neuron, adding a bias term, and then passing through the activation function; during the training process, by calculating the loss function (such as mean square error, cross entropy, etc.) between the prediction result and the true label, and then using the backpropagation algorithm to calculate the gradients of the loss function with respect to each weight and bias, and updating the weights and biases according to the gradient descent method to gradually reduce the loss function; specifically, first calculate the error of the output layer, then backpropagate the error to the hidden layer, calculate the error and gradient of each layer in turn, and finally update the weights and biases according to the gradient. This process is repeated continuously until a preset stop condition is reached. The stop condition can be set to a certain prediction accuracy or error value.

[0100] In some embodiments, the machine learning model can be trained and verified in a cyclic cross-validation manner to evaluate the generalization ability of the machine learning model; for example, the data set can be divided into k parts, and each time one part is taken as the validation set, and the remaining k - 1 parts are used as the training set. The model is trained and the performance is evaluated on the validation set. This is repeated k times to obtain k validation results, and statistical quantities such as their average value and standard deviation are calculated to evaluate the generalization ability of the machine learning.

[0101] In the embodiments of the present invention, a stable surface is defined by the following formula:

[0102]

[0103] In the formula, is the difference between the surface energy and the surface energy of the most stable surface, is the Boltzmann constant, and T is the Kelvin temperature.

[0104] In some embodiments, other surfaces with the difference between the surface energy and the energy of the most stable surface not greater than 25.85 meV can also be classified as stable surfaces to avoid excessive data imbalance; therefore, in the embodiments of the present invention, the method for judging stable surfaces is as follows: when the difference between the surface energy and the surface energy of the most stable surface is not greater than 25.85 meV, it is judged as a stable surface; when the difference between the surface energy and the surface energy of the most stable surface is greater than 25.85 meV, it is judged as an unstable surface; the most stable surface is the surface with the lowest surface energy among all the crystal configurations of the amorphous alloy clusters.

[0105] S6. Input the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

[0106] For example, one or more of the work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction of the target amorphous alloy to be analyzed can be used as input parameters and input into the trained machine learning model to output the surface energy, surface stability judgment result, and contributions of different surface descriptors of the target amorphous alloy; combining the surface energy information and surface descriptor information of the amorphous alloy, the growth habit of the amorphous alloy and surface properties such as wettability, adsorption, and catalytic activity can be further studied;

[0107] Among them, the surface descriptors of the target amorphous alloy can be obtained through experimental means or density functional theory calculations.

[0108] The embodiments of the present invention start from the existing crystalline cluster structure of the alloy, analyze the relationship between surface descriptors such as work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction and surface stability based on density functional theory, and combine the random forest model and neural network model in machine learning to construct an automated calculation model for surface stability analysis of amorphous alloys; for the target amorphous alloy that needs to calculate and judge surface stability, inputting the relevant surface descriptor data can automatically obtain the surface stability analysis result of the target amorphous alloy, significantly improving the efficiency of surface stability judgment, which is of great significance for the analysis of complex systems of amorphous alloys and the design of new amorphous alloy materials.

[0109] Based on the above embodiments, the present invention takes amorphous nickel-phosphorus alloy as the research object and proposes the following specific embodiments. It should be noted that the following specific embodiments are only for illustrative purposes and do not limit the protection scope of the present application in any form.

[0110] Embodiment

[0111] Due to the long-range disorder of the amorphous nickel-phosphorus alloy, the surface microstructure is relatively complex, making it difficult to directly correlate with its excellent physical and chemical properties (such as hardness, corrosion resistance, catalytic activity, etc.), which brings great difficulties to the development of nickel-phosphorus materials as potential hybrid capacitor electrode materials.

[0112] Using the simulation method for the surface structure stability of the amorphous alloy provided by the present invention, starting from the existing crystalline cluster structures of nickel-phosphorus alloys, an automated calculation model for the surface stability analysis of amorphous nickel-phosphorus alloys is constructed, specifically including the following steps:

[0113] (1) Establishment and calculation of the bulk phase structure model

[0114] Select three kinds of Ni in the ICSD inorganic crystal structure database, namely Ni2P (ICSD code 199251), Ni3P (ICSD code 132839) and Ni5P4 (ICSD code 781), x P y and two kinds of Ni in the Materials Project database, namely NiP2 (mp-486) and Ni5P2 (mp-1200923), x P y A total of five unit cells are used to establish a bulk phase model as the experimental basis of the bulk phase model.

[0115] Refer to Figure 3 and perform structure optimization on the five nickel-phosphorus alloys. Through this geometric optimization, the nickel-phosphorus unit cell is incorporated into the theoretical calculation system.

[0116] (2) Establishment and calculation of the slab model

[0117] In any suitable visualization tool, perform a 2×2×2 supercell expansion operation on the optimized bulk phase structure.

[0118] Select different low Miller index crystal planes, a total of seven crystal planes, namely (001), (010), (011), (100), (101), (110) and (111). These crystal planes are representative and can reflect the main characteristics of the material surface; use these crystal planes to intercept the expanded supercell and select a slab with a sufficient thickness in the direction perpendicular to the crystal plane; in order to avoid the influence of periodicity on the z-axis on the crystal calculation, a sufficiently thick vacuum layer needs to be added on the surface, and the thickness of the vacuum layer can be set to 16 Å; and dipole correction is introduced. The basic principle of dipole correction is to introduce a dipole in the center of the vacuum layer that has the same magnitude but opposite sign as the surface dipole to cancel the potential energy gradient caused by the surface dipole.

[0119] In addition to constructing the original surface, possible reconstruction phenomena also need to be considered; here, deleting the atoms in the 1st to 2nd surface layers is considered to simulate the possible surface reconstruction caused by the absence of surface atomic layers; the original surface model is named Pris, and the surface models with the topmost and the second topmost atoms deleted are named L1 and L2 respectively, as Figure 4 shown.

[0120] (3)Derivation of surface Gibbs free energy and stability analysis

[0121] For any Ni x P y surface, the definition of surface energy can be written as:

[0122]

[0123] where is the surface energy, is the cross-sectional area of the surface, is the Gibbs free energy of the Ni x P y bulk, and are the numbers of nickel atoms and phosphorus atoms in the slab model respectively, and are the chemical potentials of nickel atoms and phosphorus atoms respectively, then represents the free energy of nickel atoms in the surface phase, represents the free energy of phosphorus atoms in the surface phase; in the formula, the free energies are all physical quantities that vary with temperature T and pressure p; for the Ni x P y surface slab model, its surface energy can also be specifically defined as:

[0124]

[0125] Here, represents the Gibbs free energy of the slab model, which can be approximately obtained by calculating the internal energy of the system. This is because the solid material system itself is relatively stable, and the influence of the entropy change of the system on the Gibbs free energy can be ignored. Therefore, the internal energy of the system obtained by DFT calculation can be directly used as the Gibbs free energy of the system; it should be noted that the chemical potentials and in the above formula should satisfy the following relationship:

[0126]

[0127] where and are Ni x P yThe nickel-phosphorus stoichiometry, is Ni x P y The unit Gibbs free energy of the bulk structure; the surface energy can be obtained from the above formula Regarding the phosphorus chemical potential In the form of a linear function:

[0128]

[0129] This formula reveals the linear relationship between the surface energy and the phosphorus chemical potential, which can help to judge the thermodynamic stability of the surfaces formed between different nickel-phosphorus compounds; the chemical potentials of Ni atoms and P atoms also need to be considered during the calculation and The value ranges; according to the physical meaning, the maximum values of their solid-phase chemical potentials are equal to the atomic free energies of the corresponding elemental states; thus, the phosphorus chemical potential The maximum boundary of the value can be determined:

[0130]

[0131]

[0132] It should be noted that the most stable phosphorus element P8 at room temperature is used as the extreme value here; furthermore, the lower limit of the phosphorus chemical potential can be obtained:

[0133]

[0134] In fact, the threshold of the phosphorus chemical potential for forming a surface in a certain direction is also related to the different stoichiometric Ni x P y solids; in this way, the formation energy of each substance can be used as an interval scale to divide the region of the surface energy, and its definition is:

[0135]

[0136] Combined with the above formula, the complete value range of the phosphorus chemical potential can be determined as:

[0137]

[0138] For the convenience of subsequent calculations and graphical representations, the change in the phosphorus chemical potential is defined as:

[0139]

[0140] In this way, the change in the phosphorus chemical potential The range of values simplifies to:

[0141]

[0142] Through the above derivation, by judging the positive value with the lowest surface energy within the range of the relative chemical potential of phosphorus, the crystal plane direction of the stable surface and the surface atom arrangement can be obtained; according to the range of values, the phase diagrams of the surface structures of each Ni x P y can be plotted (as shown in Figure 5 ), as well as the relationship between the surface nickel-phosphorus ratio and the surface energy (as shown in Figure 6 ). At the same time, the surface energy can also be used as a descriptor ( ) for subsequent machine learning.

[0143] As can be seen from the foregoing embodiments, the stable surface is defined as:

[0144]

[0145] In this embodiment, other surfaces with the difference between the surface energy and the surface energy of the most stable surface not greater than 25.85 meV are also classified into the stable surface to avoid excessive data imbalance. At this time, the stable surface accounts for about 36% of the total number of surfaces, which is more uniform than the 18% proportion of the completely stable surface.

[0146] (4)Extract surface descriptors:

[0147] Referring to the foregoing method embodiments, the surface descriptors of the slab model can be extracted, including surface energy ( ), work function ( ), d-band center ( ), modified d-band center ( ), alloy element stoichiometry ( ), number of atoms ( ), average number of valence electrons ( ), surface orientation ( ), surface reconstruction ( ), to form a data set.

[0148] Among them, the work functions of each surface calculated are as shown in Figure 7 .

[0149] When considering the stoichiometry descriptor, the phosphorus-nickel stoichiometry of the slab model surface is selected as the value of .

[0150] Surface orientation ( )Describe the direction of the crystal plane. For the convenience of model use, the crystal plane orientations (001), (010), (011), (100), (101), (110), and (111) are respectively assigned values from 1 to 7.

[0151] When constructing the surface model, surface reconstruction is also considered ( ), and at this time, the surfaces of the original crystal plane Pris, the case of missing top-layer atoms L1, and the case of missing second-top-layer atoms L2 are respectively assigned values of 0, 1, and 2 as values.

[0152] Develop a script to automatically submit DFT tasks and extract and calculate core data such as surface energy, electronic density of states, and work function.

[0153] (5)Construction and training of the machine learning model

[0154] The machine learning model includes a random forest model and a neural network model based on a multi-layer perceptron. A data set is constructed through steps (1)-(4). Referring to the foregoing method embodiments, the machine learning model is trained using the surface descriptor data of the data set.

[0155] The surface descriptor data of the data set is divided into a training set and a validation set. The machine learning model is trained using the data of the training set, and the machine learning model is verified using the data of the validation set. The machine learning model is cyclically cross-trained and verified to achieve the expected prediction accuracy.

[0156] Refer to Figure 10 , and use the data of the data set to train the machine learning model to obtain the contribution of different surface descriptors to surface stability.

[0157] Refer to Figure 11 , increasing the number of neurons in the hidden layer or increasing the number of hidden layers can improve the fitting ability of the model; under the training of the data set adopted in this embodiment, the prediction accuracy of the multi-layer perceptron model can reach 92.31%, and it can efficiently predict the surface energy and surface stability of nickel-phosphorus alloys.

[0158] After training the machine learning model, input the surface descriptor data of the target amorphous alloy to be analyzed into the machine learning model, and the surface stability analysis result of the target amorphous alloy can be automatically obtained.

[0159] The embodiment of the present invention also provides a simulation device for the surface structure stability of amorphous alloys.

[0160] The device includes a bulk structure model establishment module, a slab model establishment module, a density functional calculation module, a training data providing module, a machine learning module, and a surface stability analysis module.

[0161] Among them, the bulk structure model establishment module is used to obtain the cluster structure crystal configuration of the amorphous alloy and perform structure optimization.

[0162] The slab model establishment module is used to expand the cell of the cluster structure crystal configuration after structure optimization, intercept the crystal planes with low Miller indices, add a vacuum layer on the surface and introduce dipole correction to obtain the original surface, and perform surface reconstruction on the original surface.

[0163] The density functional calculation module is used to calculate the surface energy of the slab model based on the density functional theory according to the established slab model and its surface energy calculation function.

[0164] The density functional calculation module is also used to calculate the work function and electron density of states of the slab model. The work function can be used as a surface descriptor, and the electron density of states can be used for the calculation of the d-band center.

[0165] The training data providing module includes a data set composed of surface descriptor data of the slab model; the surface descriptors include at least one of surface energy, work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction.

[0166] The machine learning module is used to construct a machine learning model, and the machine learning model is trained using the surface descriptor data of the data set.

[0167] The machine learning model includes a random forest model and a neural network model; the random forest model classifies the relationship between the surface descriptor and surface stability and obtains the contribution value of different surface descriptors to surface stability; the neural network model includes an input layer, a hidden layer, and an output layer. The input layer parameters of the neural network model are at least one of work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction, and the output layer parameter is surface energy.

[0168] The surface stability analysis module is used to input the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

[0169] In some embodiments, the simulation device for the surface structure stability of the amorphous alloy further includes:

[0170] The cross-validation module is used to divide the data set into a training set and a validation set, and cyclically cross-train and validate the machine learning model to evaluate the generalization ability of the machine learning model.

[0171] The device provided by the embodiments of the present invention is used to implement the simulation method for the surface structure stability of the amorphous alloy provided by the above embodiments. The parameter settings of each module can refer to the method embodiments described above; the beneficial effects possessed by the above method embodiments can all be achieved by this device, and will not be elaborated here.

[0172] An embodiment of the present invention further provides a computer device.

[0173] The computer device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the simulation method for the surface structure stability of the amorphous alloy described above is implemented.

[0174] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, the processes of the above method embodiments can be implemented. Among them, any reference to the memory, storage, database or other media used in the various embodiments provided by the present invention can include at least one of non-volatile and volatile memories.

[0175] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. And these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present application.

Claims

1. A simulation method for the surface structure stability of amorphous alloys, characterized in that, Including the following steps: S1. Establish a bulk structure model: Obtain the cluster structure crystal configuration of the amorphous alloy and perform structure optimization; S2. Establish a slab model: Expand the unit cell of the cluster structure crystal configuration after structure optimization, intercept the crystal plane with low Miller indices, add a vacuum layer on the surface and introduce dipole correction to obtain the original surface, and perform surface reconstruction on the original surface; S3. Obtain the surface energy calculation function of the slab model, and calculate the surface energy of the slab model according to the density functional theory; S4. Construct a data set composed of surface descriptors of the slab model; the surface descriptors include at least one of surface energy, work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction; S5. Construct a machine learning model, and train the machine learning model with the surface descriptor data of the data set; the machine learning model includes a random forest model and a neural network model; the random forest model classifies the relationship between the surface descriptors and surface stability, and obtains the contribution value of different surface descriptors to surface stability; the neural network model includes an input layer, a hidden layer and an output layer, the input layer parameters include at least one of work function, d-band center, alloy element stoichiometry, number of atoms, average valence electron number, surface orientation, and surface reconstruction, and the output layer parameter is surface energy; S6. Input the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

2. The simulation method for the surface structure stability of amorphous alloys according to claim 1, wherein In the step S2, the method of surface reconstruction is to delete one or more layers of surface atoms to simulate the absence of the surface atomic layer.

3. The simulation method for the surface structure stability of amorphous alloys according to claim 1, wherein, The step S3 further includes: Calculating the work function and electron density of states of the slab model according to the density functional theory.

4. The simulation method for the surface structure stability of the amorphous alloy according to claim 3, wherein In the step S4, the calculation formula of the d-band center is: In the formula, represents the d-band center, x represents the energy level, represents at the number of electrons in the energy level state at the energy level; Or, the d-band center is corrected to the following formula: In the formula, is the corrected d-band center, is the broadening; the calculation formula for the broadening is as follows: In the formula, is the second moment about the d-band center.

5. The simulation method for the surface structure stability of an amorphous alloy according to any one of claims 1-4, characterized in that The amorphous alloy is a nickel-phosphorus alloy, and the cluster structure crystal configuration of the nickel-phosphorus alloy includes at least one of Ni2P, Ni3P, Ni5P4, NiP2 and Ni5P2.

6. The simulation method for the surface structure stability of an amorphous alloy according to claim 5, characterized in that, In the step S3, the calculation function of the surface energy is: Wherein, is the surface energy, A is the cross-sectional area of the surface, is the Gibbs free energy of the flat plate model, and are the nickel-phosphorus stoichiometric ratios of Ni x P y respectively, and are the numbers of nickel atoms and phosphorus atoms in the flat plate model respectively, is the unit Gibbs free energy of the bulk structure of Ni x P y respectively, is the phosphorus chemical potential; Among them, the phosphorus chemical potential has a value range of: In the formula, represents Ni x P y is the standard formation energy of the bulk phase structure.

7. The simulation method for the surface structure stability of amorphous alloys according to claim 1, wherein In the step S5, the stable surface is defined by the following formula: where is the difference between the surface energy and the surface energy of the most stable surface, is the Boltzmann constant, and T is the temperature in Kelvin; The method for judging the stable surface is: when the difference between the surface energy and the surface energy of the most stable surface is not greater than 25.85 meV, it is judged as a stable surface; when the difference between the surface energy and the surface energy of the most stable surface is greater than 25.85 meV, it is judged as an unstable surface; the most stable surface is the surface with the lowest surface energy among all the cluster structure crystal configurations of the amorphous alloy.

8. A simulation device for the surface structure stability of amorphous alloys, characterized in that, Including: A bulk structure model establishment module, which is used to obtain the cluster structure crystal configuration of the amorphous alloy and perform structure optimization; A slab model establishment module, which is used to expand the unit cell of the cluster structure crystal configuration after structure optimization, intercept the crystal plane with low Miller indices, add a vacuum layer on the surface and introduce dipole correction to obtain the original surface, and perform surface reconstruction on the original surface; A density functional calculation module for calculating the surface energy, work function, and electron density of states of a slab model based on density functional theory according to the established slab model and its surface energy calculation function; A training data providing module including a data set composed of surface descriptor data of the slab model; the surface descriptors include at least one of surface energy, work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction; A machine learning module for constructing a machine learning model, which is trained using the surface descriptor data of the data set; the machine learning model includes a random forest model and a neural network model; the random forest model classifies the relationship between the surface descriptors and surface stability and obtains the contribution values of different surface descriptors to surface stability; the neural network model includes an input layer, a hidden layer, and an output layer, the input layer parameters of the neural network model are at least one of work function, d-band center, alloy element stoichiometry, number of atoms, average number of valence electrons, surface orientation, and surface reconstruction, and the output layer parameter is surface energy; A surface stability analysis module for inputting the surface descriptor data of the target amorphous alloy into the trained machine learning model to obtain the surface stability analysis result of the target amorphous alloy.

9. The simulation device for the surface structure stability of the amorphous alloy according to claim 8, characterized in that It also includes: A cross-validation module for dividing the data set into a training set and a validation set for cyclic cross-validation to evaluate the generalization ability of the machine learning model.

10. A computer device, characterized in that, It includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it implements the simulation method for the surface structure stability of the amorphous alloy according to any one of claims 1-7.

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