Composition design method for low-layer misfit high-entropy alloys based on machine learning

Abstract

The application provides a component design method for low-layer dislocation energy high-entropy alloys based on machine learning, which comprises the following steps: establishing a high-entropy alloy component-dislocation energy dataset through literature research and establishing physical and thermodynamic characteristic descriptors; performing Pearson correlation analysis and feature importance analysis on the characteristic descriptors, and screening out key features that rank first in the influence on alloy dislocation energy; then screening out the best feature set of the model by using a forward selection strategy, and screening out the top three machine learning models with optimal performance, and then determining the machine learning model used to construct an integrated algorithm framework; determining the component space of candidate alloys according to the component range of the alloy, and finally screening out the candidate alloy components for prediction of the integrated algorithm framework, and predicting the candidate alloy components by using the integrated algorithm framework to screen out high-entropy alloy components with low dislocation energy. The application significantly improves the design accuracy and efficiency of low-layer dislocation energy high-entropy alloys.

Description

Technical Field

[0001] This invention relates to the field of alloy composition design technology, specifically to a composition design method for low-storage-fault-energy high-entropy alloys based on machine learning. Background Technology

[0002] With the rapid development of productivity, modern industries such as aerospace, energy, military defense, and transportation have placed higher demands on metallic materials, especially structural components for extreme low-temperature environments. These components often experience brittle fracture during cryogenic applications, leading to casualties and resource waste. However, traditional alloying strategies limit the number of possible alloying element combinations, and improvements in alloy performance are increasingly reaching a bottleneck. Therefore, finding new alloy design concepts and developing high-performance cryogenic structural components is imperative. As pioneers in high-entropy alloy research, face-centered cubic (FCC) CoCrFeNiMn-based high-entropy alloys have attracted widespread attention. These alloys have a wide adjustable range of stacking fault energy (SFE), and at low temperatures, the stacking fault energy further decreases. This low stacking fault energy introduces abundant deformation mechanisms into the alloy, thereby improving its low-temperature toughness.

[0003] However, this vast compositional space also brings complexity and uncertainty to alloy composition design. Currently, the compositional design of low stacking fault energy CoCrFeNiMn-based high-entropy alloys mainly relies on fine-tuning the content of alloying elements and empirical formulas. This method suffers from the blindness in estimating stacking fault energy and requires a large amount of experimental data, which not only increases the cost of alloy design but also makes it difficult to quickly and accurately explore the composition of low stacking fault energy alloys.

[0004] In recent years, the development of computer science and artificial intelligence has provided new ideas for alloy composition design. Machine learning, as a data-driven science, is now widely used in materials science for composition design, process optimization, and other aspects. Its active learning strategy can quickly push alloy composition from low to high dimensions, significantly reducing the cost of alloy development. However, due to the very limited experimental data on the stacking fault energy of CoCrFeNiMn-based high-entropy alloys, research on machine learning for predicting the stacking fault energy of high-entropy alloys is very limited. Summary of the Invention

[0005] To address the problems existing in the aforementioned background technology, this invention provides a composition design method for low-stack fault energy high-entropy alloys based on machine learning. Based on composition-stack fault energy simulation data from the literature, the accuracy of the machine learning model is improved by utilizing screened physical and thermodynamic parameters. Preliminary phase screening is performed according to the VEC criterion. Finally, a machine learning ensemble algorithm framework is used to screen out high-entropy alloy compositions with low stacking fault energies, thereby improving the accuracy and efficiency of composition design for CoCrFeNiMn-based low-stack fault energy high-entropy alloys.

[0006] Specifically, this invention provides a composition design method for low-stacking-energy high-entropy alloys based on machine learning, comprising the following steps:

[0007] Step 1: Collect stacking fault energy simulation data, establish a simulation dataset of alloy composition-stacking fault energy, calculate the corresponding physical and thermodynamic characteristic parameters based on the alloy composition, and analyze the alloy composition distribution in the simulation dataset;

[0008] Step 2: Analyze the correlation between each pair of the aforementioned feature parameters using the Pearson correlation coefficient, eliminate feature parameters with high correlation coefficients, and then use the random forest feature importance analysis method to screen out the key feature parameters that affect the stacking fault energy.

[0009] Step 3: Using the alloy composition and the key feature parameters as input to the machine learning model, and the stacking fault energy as output, a forward selection strategy is adopted for the key feature parameters to select the best feature set for different machine learning models, thereby obtaining a variety of high-precision machine learning models.

[0010] Step 4: Select the top-performing models from the various high-precision machine learning models obtained, adopt the parallel prediction approach, and construct an integrated algorithm prediction framework for subsequent predictions.

[0011] Step 5: Based on the distribution of alloy composition obtained in Step 1, determine the preliminary composition space of candidate alloys, form a candidate alloy composition dataset, and then use the integrated algorithm prediction framework to predict the stacking fault energy of the candidate alloy composition dataset. Rank the alloy compositions according to their scores, and finally select candidate alloy compositions with low stacking fault energy.

[0012] As a further explanation of the present invention, the alloy composition-stacking fault energy simulation dataset includes alloying elements Co, Cr, Fe, Ni, Mn, V, and Al, as well as stacking fault energy values.

[0013] As a further explanation of the present invention, the key characteristic parameters include: specific heat, Pauling electronegativity variance, lattice stability calculated by first-order calculation, elastic constant, variance of lattice stability calculated by phase diagram, lattice stability calculated by phase diagram, elastic constant, ionization energy, atomic weight, Allen electronegativity variance, and Pauling electronegativity.

[0014] As a further explanation of the present invention, the machine learning model includes: multilayer perceptron regression, support vector machine regression model, extreme gradient boosting regression model, gradient boosting regression model, and random forest regression model.

[0015] As a further explanation of the present invention, the optimal feature set includes: 6 features for the multilayer perceptron regression model, 8 features for the support vector machine regression model, 9 features for the extreme gradient boosting regression model, 11 features for the gradient boosting regression model, and 4 features for the random forest regression model.

[0016] As a further explanation of the present invention, the top-performing models selected in step 4 are specifically: multilayer perceptron regression model, support vector machine regression model, and extreme gradient boosting regression model.

[0017] As a further explanation of the present invention, the prediction accuracy of the models selected in step 4 is greater than 90%, and the performance evaluation indicators used include goodness of fit and root mean square error. When evaluating the performance of the machine learning models, the validation set adopts a 10-fold cross-validation strategy, while the test set directly evaluates its prediction accuracy.

[0018] As a further explanation of the present invention, in step 5, the composition space is restricted using the VEC criterion to obtain an alloy composition that does not contain the harmful BCC phase.

[0019] As a further explanation of the present invention, in step 5, the integrated algorithm framework calculates the weighted average and standard deviation of the stacking fault energy prediction values ​​of the models with the highest performance ranking selected in step 4, and then uses a strategy of balancing model stability and uncertainty to calculate the score of the candidate alloy composition, and finally selects the high-entropy alloy composition with low stacking fault energy and excellent strength and plasticity.

[0020] As a further explanation of the present invention, when obtaining the score for each candidate alloy composition through the integrated algorithm framework, the specific formula of the scoring function is as follows:

[0021] ;

[0022] Where Mean is the weighted average and Std is the standard deviation.

[0023] Compared with the prior art, the present invention has the following beneficial technical effects:

[0024] The composition design method provided by this invention, based on collected simulation data of alloy stacking fault energy, solves the problem of scarce experimental data on stacking fault energy. It establishes additional physical and thermodynamic descriptors based on the alloy's chemical composition and filters out key features affecting the alloy's stacking fault energy through Pearson correlation analysis and random forest feature importance analysis. Through a feature forward selection strategy, the optimal feature set for each machine learning model is obtained, successfully establishing a complex nonlinear relationship between alloy composition, feature parameters, and alloy stacking fault energy. This strategy improves the prediction accuracy of the machine learning model. The VEC criterion is used to limit the phase composition of the alloy in the original composition space, narrowing the candidate alloy composition space and avoiding the model from getting trapped in local optima. An integrated algorithm framework is successfully created using multiple high-precision machine learning models. Thanks to its unique scoring strategy, it avoids the instability of individual model predictions, and is expected to obtain high-entropy alloy compositions with low stacking fault energy and excellent strength-plasticity matching, improving the development efficiency of novel high-entropy alloys for low-temperature applications.

[0025] Other features and advantages of this technical solution will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the technical solution. The objectives and other advantages of this technical solution can be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0026] The technical solution of this invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0027] The accompanying drawings are provided to further illustrate the present technical solution and form part of the specification. They are used together with the embodiments of the present technical solution to explain the present technical solution, but do not constitute a limitation thereof. In the accompanying drawings:

[0028] Figure 1 This is a flowchart illustrating the composition design of a low-stacking-fault-energy single-phase FCC high-entropy alloy in Embodiment 1 of the present invention.

[0029] Figure 2 This is a distribution diagram of alloy composition in the original dataset of stacking fault energy in this invention.

[0030] Figure 3 This is a Pearson correlation analysis diagram of all physical and thermodynamic parameters in this invention.

[0031] Figure 4 This is a feature importance ranking graph obtained using the random forest algorithm in this invention.

[0032] Figure 5 This is a performance evaluation graph of the various machine learning models selected in this invention.

[0033] Figure 6The figures are scatter plots of various machine learning models selected in this invention, where Figures (a) to (e) are scatter plots of five different machine learning models.

[0034] Figure 7 The image shows the XRD pattern of the candidate alloy in this invention.

[0035] Figure 8 Figures (a) to (e) show the engineering stress-strain curves of the candidate alloys in this invention, where Figures (a) to (e) are the engineering stress-strain curves of alloys 1 to 5, respectively.

[0036] Figure 9 Figures (a) to (e) show the work hardening rate curves of the candidate alloys in this invention, where Figures (a) to (e) are work hardening rate curves for alloys 1 to 5, respectively.

[0037] Figure 10 The images shown are TEM images of the candidate alloys after tensile fracture in this invention. Figures (a) to (e) are TEM images of alloys 1 to 5, respectively. Detailed Implementation

[0038] The preferred embodiments of this technical solution are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only for illustration and explanation of this technical solution and are not intended to limit this technical solution. Example 1

[0039] like Figure 1 As shown, this embodiment provides a composition design method for low-stack-fault energy high-entropy alloys based on machine learning, including the following steps:

[0040] Step 1: Collect stacking fault energy simulation data, establish a simulation dataset of alloy composition and stacking fault energy, calculate the corresponding physical and thermodynamic characteristic parameters based on the alloy composition, and analyze the alloy composition distribution in the simulation dataset. The results are as follows: Figure 2 As shown.

[0041] Due to the current scarcity of experimental data on stacking fault energy in high-entropy alloys, the stacking fault energy data included in the dataset are all derived from first-principles calculations, molecular dynamics, and other simulation results. Specifically, the stacking fault energy simulation data were obtained by collecting stacking fault energy simulation data from the literature. The alloy composition-stacking fault energy simulation dataset includes alloying elements such as Co, Cr, Fe, Ni, Mn, V, and Al, as well as stacking fault energy values. The dataset contains data on the stacking fault energy of CoCrFeNiMn-based high-entropy alloys, and a total of 498 sets of data were collected.

[0042] Specifically, based on the alloy composition, a total of 34 physical and thermodynamic characteristic parameters are calculated, including VASP-PAW-GGA LSE, SGTE LSE, Allen EN, Pauling EN, Density, Atomic Weight, Valencee, IE, Melting Point, Specific Heat, Metallic Radius, Shear Modulus, Total Electrons, Atomic Planar Density, C_11, C_12, C', and their respective variances.

[0043] Step 2: Analyze the correlation between pairs of feature parameters using the Pearson correlation coefficient, remove feature parameters with high correlation coefficients, and then use the random forest feature importance analysis method to screen out the key feature parameters that affect the stacking fault energy.

[0044] Specific results are as follows Figure 3 and Figure 4 As shown, the key characteristic parameters selected (sorted by importance) include: specific heat, Pauling electronegativity variance (Pauling EN_var), first-practice calculated lattice stability (VASP-PAW-GGA LSE), elastic constant C_12, variance of lattice stability calculated from phase diagram (SGTE LSE_var), phase diagram calculated lattice stability (SGTE LSE), elastic constant C_11, ionization energy (IE), atomic weight, Allen electronegativity variance (Allen EN_var), and Pauling electronegativity (Pauling EN).

[0045] Specifically, when removing features in Pearson correlation analysis, features that are highly correlated with multiple features (> 0.9) are deleted to avoid multicollinearity. In feature importance analysis, features are summed according to their importance, and all features whose sum of importance is greater than 0.98 are retained.

[0046] Step 3: Using the alloy composition and key feature parameters as input to the machine learning model, and the stacking fault energy as the output of the machine learning model, a forward selection strategy is adopted for the key feature parameters to select the best feature set for different machine learning models, thereby obtaining a variety of high-precision machine learning models.

[0047] Specifically, the machine learning models used include: Multilayer Perceptron Regression (MLPR), Support Vector Regression (SVR), Extreme Gradient Boosting Regression (XGBR), Gradient Boosting Regression (GBR), and Random Forest Regression (RFR).

[0048] Specifically, the forward selection strategy is a method that reduces the number of features sequentially based on their importance. For example, a feature set with 5 features, compared to a set with 6 features, removes the feature ranked sixth in importance. Using this strategy, the feature set with optimal model performance is obtained. Five machine learning models are used to fit the non-linear relationship between input and output. The model's performance on the validation set (10-CV) and test set is as follows: Figure 5 and Figure 6 As shown in Table 1, the specific performance indicators are as follows:

[0049] Table 1. Performance metrics of five machine learning models on the validation set (10-CV) and test set.

[0050]

[0051] In summary, the optimal number of features (sorted by feature importance) is: MLPR (6 features), SVR (8 features), XGBR (9 features), GBR (11 features), and RFR (4 features).

[0052] Step 4: Select the top-performing models from the various high-precision machine learning models obtained, adopt the parallel prediction approach, and construct an integrated algorithm prediction framework for subsequent predictions.

[0053] The top three models with the best performance were selected as follows: MLPR model, SVR model and XGBR model.

[0054] The prediction accuracy of the models selected in step 4 is greater than 90%. The performance evaluation metrics used include goodness of fit and root mean square error. When evaluating the performance of machine learning models, the validation set adopts a 10-fold cross-validation strategy, while the test set directly evaluates its prediction accuracy.

[0055] The parallel prediction approach adopted in this invention avoids the uncertainty of single model prediction and improves the stability of model prediction, thereby helping to screen out candidate alloys that meet performance requirements.

[0056] Step 5: Based on the distribution of alloy composition obtained in Step 1, determine the preliminary composition space of candidate alloys, form a candidate alloy composition dataset, and then use an ensemble algorithm prediction framework to predict the stacking fault energy of the candidate alloy composition dataset. Rank the alloy compositions according to their scores, and finally select candidate alloy compositions with low stacking fault energy.

[0057] Furthermore, in order to obtain alloy compositions free of the harmful BCC phase, the composition space was restricted using the VEC criterion. Specifically, when the VEC of the alloy is greater than 8, the brittle BCC phase will not appear in the alloy. By restricting the composition space using the VEC criterion, the composition space was reduced from 500,000 groups to 295,363 groups.

[0058] The stacking fault energy of these 295,363 candidate alloys was predicted using the integrated algorithm framework established above. Based on the framework's unique scoring strategy (calculating the weighted average and standard deviation), the score of each candidate alloy was obtained, and then sorted and screened. Finally, five candidate alloy compositions with low stacking fault energy and excellent strength and plasticity were obtained. The specific alloy compositions, weighted average stacking fault energy, and scores are shown in Table 2.

[0059] Table 2. Nominal composition (at.%) of five candidate alloys with low stacking fault energy

[0060]

[0061] The specific formula for the scoring function when calculating the score for each candidate alloy composition is as follows:

[0062] ;

[0063] Where Mean is the weighted average and Std is the standard deviation. Example 2

[0064] The deformation mechanism of the candidate alloy composition obtained by the design method provided in Example 1 was verified:

[0065] Step 6: Based on the candidate alloy composition in Step 5, prepare candidate alloy ingots using a vacuum arc melting method.

[0066] Specifically, Fe, Mn, Ni, Co, Cr, V, and Al pure metals with a purity of 99.99% wt.% or higher are selected for ingot preparation. All alloys are prepared by arc melting under Ti-absorbed and high-purity argon atmospheres. Based on the alloy composition recommended by the model, 50g ingots are produced according to their atomic ratios. To ensure the uniformity of the casting alloy composition, the raw materials must be repeatedly turned 5 times during melting.

[0067] Step 7: Perform phase identification and mechanical property testing on the candidate high-entropy alloy ingots obtained in Step 6.

[0068] Specifically, phase analysis was performed using a Bruker D8 X-ray diffractometer with Cu-Kα radiation, a scan rate of 4° / min, and a scan range of 20°–100°. The results are as follows: Figure 7 As shown, none of the five candidate alloys contained the brittle BCC phase. Alloy 1 showed a small amount of the HCP phase, while the other four candidate alloys were single-phase FCC. The phase composition of the candidate alloys met the design expectations. Samples used for tensile testing were cut from the ingot and machined into rectangular dog-bone shaped specimens with a geometric dimension of (26.0 mm × 6 mm × 1.5 mm). At least three room-temperature tensile tests were performed using a universal testing machine (Shimadzu AG-X Plus) at a strain rate of 0.001 / s. The experimental results are as follows: Figure 8 and Figure 9 As shown, the yield strength of the as-cast alloy is between 200-400 MPa, and the tensile strength is between 500-650 MPa. The alloy also exhibits excellent plasticity. Alloy 1, due to the presence of martensite, experiences premature stress concentration at the phase interface, leading to premature fracture. The work hardening rate curves of the five candidate alloys show that all five have excellent work hardening capabilities. Furthermore, the single-phase FCC alloy exhibits a secondary increase in work hardening rate, indicating the presence of other deformation mechanisms during the tensile process.

[0069] Step 8: Perform TEM analysis on the five candidate alloy tensile specimens after tensile fracture to determine the deformation mechanism during the tensile process.

[0070] Specifically, a Talos F200X transmission electron microscope (TEM) was used for microstructure analysis. The TEM sample preparation process was as follows: the sample was polished to a thickness of less than 100 μm, and then thinned using a Struers Tenupol-5 electrolytic double-jet system (the double-jet solution was a 1:9 volume ratio of perchloric acid and ethanol, the operating voltage was 30 V, and the operating temperature was -30 ℃). The experimental results are as follows. Figure 10 As shown, low stacking fault energy alloys exhibit deformation twins, HCP phases, and stacking faults during tensile deformation. TEM results show that alloy 1 exhibits HCP phases during tensile deformation, indicating that its deformation mechanism is transformation-induced plasticity (TRIP). For the other four single-phase FCC candidate alloys, as the predicted stacking fault energy increases, the deformation mechanism changes from intersecting deformation twins (alloy 3) to deformation twins and stacking faults (alloys 2 and 4) and then to high-density stacking faults (alloy 5). This demonstrates that the deformation mechanism of the alloys corresponds to the predicted stacking fault energy values ​​of the model, indicating that the constructed machine learning ensemble algorithm framework has excellent generalization and stability.

[0071] Obviously, those skilled in the art can make various modifications and variations to this technical solution without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this technical solution and their equivalents, this technical solution also intends to include these modifications and variations.

Claims

1. A method for designing a composition of a low-layer-error high-entropy alloy based on machine learning, characterized in that, Comprise the following steps: Step 1: Collecting stacking fault energy simulation data, establishing alloy composition-stacking fault energy simulation data set, calculating corresponding physical and thermodynamic characteristic parameters according to the alloy composition, and analyzing the alloy composition distribution in the simulation data set; Step 2: Analyzing the correlation between each two characteristic parameters by Pearson correlation coefficient, eliminating the characteristic parameters with large correlation coefficient, and then screening out the key characteristic parameters affecting stacking fault energy by random forest feature importance analysis method; The Key characteristic parameters include: specific heat, Pauling electronegativity variance, first-principles calculated lattice stability, elastic constant, variance of lattice stability calculated by phase diagram, lattice stability calculated by phase diagram, elastic constant, ionization energy, atomic weight, Allen electronegativity variance, and Pauling electronegativity; Step 3: Taking the alloy composition and the key characteristic parameters as the input of the machine learning model, taking the stacking fault energy as the output of the machine learning model, adopting forward selection strategy for the key characteristic parameters, screening out the best feature set of different machine learning models, and thus obtaining multiple high-precision machine learning models; wherein the machine learning model includes: multilayer perceptron regression, support vector machine regression model, extreme gradient boosting regression model, gradient boosting regression model and random forest regression model; the best feature set includes: 6 features of multilayer perceptron regression model, 8 features of support vector machine regression model, 9 features of extreme gradient boosting regression model, 11 features of gradient boosting regression model, and 4 features of random forest regression model; Step 4: Screening out the models with high performance ranking from the obtained multiple high-precision machine learning models, adopting parallel prediction idea, and constructing an integrated algorithm prediction framework for subsequent prediction; wherein the models with high performance ranking screened out are: multilayer perceptron regression model, support vector machine regression model and extreme gradient boosting regression model; Step 5: According to the distribution of alloy composition obtained in step 1, determining the preliminary composition space of candidate alloy, forming a candidate alloy composition data set, then predicting the stacking fault energy of the candidate alloy composition data set by using the integrated algorithm prediction framework, ranking according to the score of alloy composition, and finally screening out the candidate alloy composition with low stacking fault energy; wherein the integrated algorithm framework calculates the weighted average value and standard deviation of the stacking fault energy prediction values of the models with high performance ranking screened out in step 4, and then calculates the score of the candidate alloy composition by using the strategy of balancing model stability and uncertainty, and finally screens out the high-entropy alloy composition with low stacking fault energy and excellent strength and plasticity. 2.The method for composition design of low-layer-error high-entropy alloy based on machine learning according to claim 1, wherein, The alloy composition-stacking fault energy simulation data set includes Co, Cr, Fe, Ni, Mn, V, Al alloy elements and stacking fault energy values. 3.The method of claim 1, wherein the method comprises: The prediction accuracy of the models screened out in step 4 is greater than 90%, the performance evaluation indicators selected include goodness of fit and root mean square error, and when evaluating the performance of the machine learning model, the validation set adopts 10-fold cross-validation strategy, and the test set directly evaluates the prediction accuracy. 4.The method of claim 1, wherein the method is based on machine learning. In Step 5, the composition space is restricted using the VEC criterion to obtain alloy compositions that do not contain the BCC deleterious phase.

5. The composition design method for low-stack fault energy high-entropy alloys based on machine learning as described in claim 1, characterized in that, The specific formula of the score function when deriving the score of each candidate alloy composition through the integrated algorithm framework is: ； where Mean is the weighted average value, and Std is the standard deviation.

Images