Design method of machine learning potential function for rare earth magnesium alloy
By designing the machine learning potential function DP potential for rare earth magnesium alloys, the accuracy problem of simulating the dislocation slip process on the conical surface of rare earth magnesium alloys was solved, achieving high-precision plasticity prediction and promoting the application of rare earth magnesium alloys.
Patent Information
- Application Number
- CN202210624101.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-03
- Publication Date
- 2025-11-18
- Estimated Expiration
- 2042-06-03
AI Technical Summary
Existing technology in rare earth magnesium alloy conical surfaces
A machine learning potential function DP potential for rare earth magnesium alloys was designed using high-throughput first-principles calculations combined with the deep learning software DeePMD. A high-precision DP potential function was obtained by fitting the training set to simulate large-scale cone dislocation slip in rare earth magnesium alloys and to calculate the generalized stacking fault energy curve.
Accurate simulation of the dislocation slip process on the conical surface of rare earth magnesium alloys was achieved, solving the problem of inconsistency between theoretical calculation results and experimental results, and improving the accuracy of plasticity prediction.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of rare earth magnesium alloys and proposes a machine learning potential function design method for rare earth magnesium alloys. Background Technology
[0002] Magnesium is one of the most abundant and widely distributed chemical elements in nature, found extensively in dolomite, magnesite, and seawater. my country has vast reserves of magnesium ore with great application potential. On the one hand, magnesium alloys possess characteristics such as high specific strength, good shock absorption, good thermal conductivity, and excellent electromagnetic shielding performance, making them widely used in electronic products. On the other hand, magnesium is a lightweight metal, with a density of 23% that of steel and 66% that of aluminum, making it a preferred material for achieving energy conservation and emission reduction, playing a crucial role in lightweighting processes in aerospace, automotive, and other fields. However, compared with lightweight metal structural materials such as aluminum alloys and titanium alloys, the lower strength and poorer processability of magnesium alloys limit their large-scale application in industrial production.
[0003] The main reason for the poor plasticity of magnesium alloys at room temperature is that their sliding mechanism at room temperature is based on the basal plane. Slip can only provide two independent slip systems, which does not satisfy the five independent slip requirements of the von Mises yield criterion. Therefore, promoting non-basal plane slip systems in magnesium alloys is an important means to enhance their plasticity, especially conical slip systems.<c+a> Dislocations not only provide five independent slip systems for the slip process, but also decompose into immobile c dislocations during recrystallization, hindering the movement of basal plane dislocations and grain boundaries, thereby impeding grain growth. Therefore, promoting pyramidal dislocations...<c+a> Dislocation nucleation and slip are important methods to improve the plasticity of magnesium alloys.
[0004] There are currently many reports on Mg-Y magnesium alloys in both experimental and theoretical calculations, but there are still many reports on conical surfaces.<c+a> The study of dislocation-related nucleation and slip processes remains highly controversial. Revealing the formation and decomposition of pyramidal dislocations at the atomic scale is crucial for further research on their role in plastic deformation. Currently, atomic-scale simulations primarily employ first-principles calculations (DFT) and molecular dynamics (MD) methods. First-principles calculations, due to size limitations, cannot simulate large-scale dislocation and slip behavior, while molecular dynamics simulations, limited by the description of atomic interaction potential functions, often yield results that differ significantly from experimental findings. In recent years, using machine learning to train molecular dynamics potential functions based on first-principles calculation results has become a research hotspot in computational materials science. Potential functions trained through machine learning combine the accuracy of first-principles calculations with the scale advantages of molecular dynamics simulations, and hold promise for more accurately describing the complex interatomic interactions in pyramidal dislocation behavior. Summary of the Invention
[0005] Regarding the current experimental and theoretical calculations on rare earth magnesium alloy conical surfaces<c+a> The study of dislocation-related nucleation and slip processes remains highly controversial. This invention, based on high-throughput first-principles calculations, uses the deep learning software DeePMD to train and test the dataset of first-principles calculation results, obtaining the machine learning potential function for rare-earth magnesium alloys—the DP potential. The DP potential is used to simulate large-scale cone dislocation slip in rare-earth magnesium alloys, and its generalized stacking fault energy curve is calculated. The theoretical calculation results are consistent with experimental results, resolving the previous issue of inconsistency between theoretical and experimental results.
[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0007] A machine learning potential function design method for rare earth magnesium alloys includes at least the following steps:
[0008] 1) Based on the periodicity and atomic coordinates of the close-packed hexagonal structure, different structural models of rare-earth magnesium alloys within their solid solubility were constructed using Material Studio software, including bulk structures, strained bulk structures, surface structures, and stacking fault structures. After obtaining the structures of rare-earth magnesium alloys with different contents, the structural information was converted into POSCAR format using VESTA software to obtain the model structure for calculation.
[0009] 2) Calculate the volume and energy of multiple bulk structures using VASP, and fit the volume and energy to the BM equation to obtain the equilibrium volume, bulk modulus and equilibrium energy of the crystal, and convert them into lattice constants.
[0010] 3) Under equilibrium volume, the crystal undergoes structural relaxation, and based on the deformation matrix, multiple strains are applied to the crystal in the corresponding directions. The equilibrium energy in the ground state under different strains is calculated, and based on the relationship between strain and energy, a nonlinear curve is fitted to obtain the crystal elastic constant C. 11 C 12 C 13 C 33 and C 44 and through and To determine the corresponding elastic modulus, shear modulus, and Poisson's ratio.
[0011] 4) Calculate the energy of the supercell in a perfect crystal and the energy of the supercell after adding stacking faults. Subtract the difference and divide by the stacking fault surface area to obtain the stacking fault energy. The formula is: Where E SF E0 represents the energy of a supercell containing stacking faults; E0 is the energy of a perfect crystal supercell, and A is the area of the stacking fault plane. The supercell is rigidly divided into upper and lower parts and rigidly moved relative to each other. By moving different distances, the corresponding stacking fault energies are calculated, ultimately yielding a generalized stacking fault energy curve with the distance moved as the x-axis and the stacking fault energy as the y-axis. Added alloying elements are placed as close as possible to the stacking fault plane to highlight the influence of rare earth elements on the stacking fault energy.
[0012] 5) The method for calculating surface energy is as follows: Calculate the difference between the bulk structure and the surface structure containing the same atoms, then divide by the surface area to obtain the surface energy. The formula is: Among them, China E slab E refers to the energy of a system containing a surface; bulk This refers to the energy of a bulk system without a surface, where the atom type and number are related to E. slab The model is consistent; A refers to the surface area. The added alloying elements are placed as close to the surface as possible to highlight the influence of rare earth elements on surface energy.
[0013] 6) Use the dpdata module in the DeePMD software package to convert the collected DFT structure-energy database into a training set. Then, adjust the parameters in DeePMD, mainly including the cutoff radius r. cut And the loss function. By testing the cutoff radius and assigning different weights to energy, force, and virial tension in the loss function, a high-precision machine learning potential function—DP potential—for accurately describing conical dislocations was obtained.
[0014] 7) Using the molecular dynamics software LAMMPS, the fitted DP potential and the classical potential function MEAM potential were used to calculate the lattice constant, elastic constant, generalized stacking fault energy curve, and surface energy of the rare-earth magnesium alloy. These results were then compared with the DFT results, and the relative error was used to calculate the lattice constant, elastic constant, generalized stacking fault energy curve, and surface energy of the rare-earth magnesium alloy. To describe the degree of closeness, when the relative error between the DP potential or MEAM potential result and the DFT result is less than 5%, it has DFT accuracy.
[0015] 8) Based on the generalized stacking fault energy theory, establish the relationship between the change in unstable stacking fault energy and the plasticity of the rare earth magnesium alloy conical slip system. The smaller the unstable stacking fault energy, the easier the slip system slips, and the better the plasticity of the rare earth magnesium alloy. Use the DP potential to model the conical surface of the rare earth magnesium alloy.<c+a> Large-scale simulation of dislocations was performed, and the cone surface was calculated.<c+a> Generalized stacking fault energy curve of slip system.
[0016] Compared with the prior art, the beneficial effects of the present invention are:
[0017] 1. Based on high-throughput first-principles calculations combined with machine learning, the potential function of rare-earth magnesium alloys—DP potential—is obtained by fitting, which has the high accuracy of first-principles calculations and the high efficiency of molecular dynamics simulations.
[0018] 2. Based on the generalized stacking fault energy theory, the relationship between plastic and stable stacking fault energies and unstable stacking fault energies is established. The fitted machine learning potential function is then used to analyze the rare-earth magnesium alloy conical surface.<c+a> Large-scale simulations of dislocation slip were performed, and the generalized stacking fault energy curves were calculated. The results show that adding Y to Mg can promote the stacking of cones.<c+a> The slip of dislocations is consistent with the phenomena observed in the experiment, which solves the problem of inconsistency between previous theoretical calculations and experimental results. Attached Figure Description
[0019] Figure 1 This is a flowchart of the process of the present invention.
[0020] Figure 2 These are the bulk structure (a), surface structure (b), and stacking fault structure (c) of the close-packed hexagonal Mg-Y alloy of the present invention.
[0021] Figure 3 This is a diagram showing the composition of the first-principles calculation dataset of the present invention.
[0022] Figure 4 These are test results of the machine learning potential function DP potential of this invention: (a) energy test results, (b) force test results in the x direction, (c) force test results in the y direction, and (d) virial test results in the x-direction.
[0023] Figure 5 This is a comparison chart of the lattice constants a(a) and c(b) of Mg-Y calculated by DP potential and MEAM potential under different contents, and the DFT calculation results.
[0024] Figure 6 This is a comparison chart of the results of DP potential and MEAM potential calculations of Mg-Y elastic modulus (a), bulk modulus (b), shear modulus (c), and Poisson's ratio (d) under different contents, and the results of DFT calculations.
[0025] Figure 7 This is a comparison chart of the surface results of Mg-Y basal surface (a), cylindrical surface (b), cone I (c) and cone II (d) with different contents calculated by DP potential and MEAM potential according to the present invention, and the DFT calculation results.
[0026] Figure 8 This is a comparison of the results of the generalized stacking fault energy curves of the Mg-Y basal plane slip system calculated by the DP potential and the classical potential function MEAM potential under different contents, and the results calculated by DFT. (a) Mg 120 Generalized stacking fault energy curves of the {0001}<11-20> slip system, (b) Mg 119 The generalized stacking fault energy curve of the {0001}<11-20> slip system of Y, (c)Mg 118 The generalized stacking fault energy curve of the {0001}<11-20> slip system of Y2, (d)Mg 120 Generalized stacking fault energy curves of the {0001}<1-100> slip system, (e)Mg 119 The generalized stacking fault energy curve of the {0001}<1-100> slip system of Y, (f)Mg 118 The generalized stacking fault energy curves of the {0001}<1-100> slip system of Y2. Hollow circles in the figure represent MEAM potential results, solid squares represent DFT results, and other solid lines represent DP potential results.
[0027] Figure 9 This invention uses DP and MEAM potentials to calculate Mg-Y cylindrical surfaces with different contents. and cone surface Comparison of generalized stacking fault energy curves and DFT calculations for slip systems. (a) Mg 120 Generalized stacking fault energy curves of the {10-10}<11-20> slip system, (b) Mg 119 The generalized stacking fault energy curve of the {10-10}<11-20> slip system of Y, (c)Mg 118 The generalized stacking fault energy curve of the {10-10}<11-20> slip system of Y2, (d)Mg 120 Generalized stacking fault energy curves of the {10-11}<11-20> slip system, (e)Mg 119 The generalized stacking fault energy curve of the {10-11}<11-20> slip system of Y, (f)Mg 118 The generalized stacking fault energy curves of the {10-11}<11-20> slip system of Y2. Hollow circles in the figure represent MEAM potential results, solid squares represent DFT results, and other solid lines represent DP potential results.
[0028] Figure 10 This invention uses DP and MEAM potentials to calculate Mg-Y cone surfaces with different contents.<c+a> Comparison of generalized stacking fault energy curves and DFT calculations for slip systems. (a) Mg 120 Generalized stacking fault energy curves of the {10-11}<11-23> slip system, (b) Mg 119 The generalized stacking fault energy curve of the {10-11}<11-23> slip system of Y, (c)Mg 118 The generalized stacking fault energy curve of the {10-11}<11-23> slip system of Y2, (d)Mg 120 The generalized stacking fault energy curves of the {11-22}<11-23> slip system, (e)Mg 119 The generalized stacking fault energy curve of the {11-22}<11-23> slip system of Y, (f)Mg 118 The generalized stacking fault energy curves of the {11-22}<11-23> slip system of Y2. Hollow circles in the figure represent MEAM potential results, solid squares represent DFT results, and other solid lines represent DP potential results.
[0029] Figure 11 This invention relates to a large-scale conical surface for calculating the DP potential.<c+a> Generalized stacking fault energy curves of slip systems and generalized stacking fault energy curves calculated by DFT at small scales, (a) DFT results (b) DP potential results. Detailed Implementation
[0030] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0031] Example
[0032] (1) Using Materials Studio software, the Mg unit cell structure was imported, and through cell expansion and alloy element substitution, a total of 945 Mg-Y alloy bulk structures, surface structures, and stacking fault structures were established, such as... Figure 2 As shown. Next, the structural model is converted into a POSCAR structural file that can be used for calculations in VASP software using VESTA software.
[0033] (2) The system energy under different structures was calculated using VASP software, resulting in a series of structure-energy correspondences, which formed a DFT dataset (e.g., Figure 3 Based on this structural energy information, the lattice constant, elastic constant, generalized stacking fault energy curve, and surface energy of the system are calculated.
[0034] (3) The DFT dataset was converted into a training set using the deep learning software DeePMD. After adjusting the parameters, the final setting was: cutoff radius r. cut =20, with the loss function set as follows: initial energy weight start_pref_e = 0.02, final energy weight limit_pref_e = 2; initial force weight start_pref_f = 1000, final force weight limit_pref_f = 1; initial virial weight start_pref_v = 0.01, final virial weight limit_pref_v = 1; at this point, the root mean square error of the energy is 1.31 × 10⁻⁶. -2 The root mean square error of the force is less than 1.13 × 10⁻⁶ eV. -3 The root mean square error of the virial is less than 7.52 × 10⁻⁶ eV / A. -1 eV, yielding our desired machine learning potential function—the DP potential. The energy, forces in the x and y directions, and the virial test results in the x-direction are as follows: Figure 4 As shown in the figure, the closer a point is to y = x, the more accurate the fitted potential function is.
[0035] (4) The DFT dataset was calculated using the fitted DP potential and the classical potential function MEAM potential in the molecular dynamics software LAMMPS. The calculation results were compared with the DFT calculation results. Comparison of lattice constants was also performed. Figure 5 As shown, the relative error between the DP potential and the DFT result is less than 0.2%, while the relative error of the MEAM potential is greater than that of the DP potential; the comparison of elastic properties is as follows. Figure 6As shown, the relative error of the DP potential is generally less than 5%, while the relative error of the MEAM potential reaches a maximum of 12%; the comparison of surface energy is as follows: Figure 7 As shown, the relative error of the DP potential calculation for the basal plane and cone I is less than 5%, while the relative error for the cylindrical plane is larger, reaching 20%. However, the relative error of the MEAM potential is greater than that of the DP potential, reaching up to 40%. A comparison of the generalized stacking fault energy curves is also provided. Figure 8-10 As shown, the curve obtained by the DP potential is closer to the DFT curve, with a smaller error than that of the MEAM potential. The relative error of DP is generally less than 5%, while the error of the MEAM potential is greater than 15%. These results demonstrate that the DP potential can reproduce small-scale DFT calculation results more accurately than the classical potential function MEAM potential, exhibiting higher computational precision.
[0036] (5) Using DP potential to target Mg-Y alloy cone dislocations<c+a> Large-scale simulations of slip were performed, and its generalized stacking fault energy curve was calculated, such as... Figure 11 As shown, the addition of Y element reduced the unstable stacking fault energy of Mg pyramidal dislocations, indicating that adding Y element to Mg can promote the stacking fault energy of pyramidal dislocations.<c+a> The dislocation slip is consistent with the experimental observations. However, the DFT calculation results are contrary to the DP potential results; the addition of Y increases the unstable stacking fault energy of Mg pyramidal dislocations, indicating that adding Y to Mg inhibits the pyramidal dislocations.<c+a> The slip of dislocations does not match the experimental results, so the DP potential resolves the discrepancy between previous theoretical calculation methods (density functional theory and molecular dynamics) and experimental results regarding the cone surface.<c+a> The problem of inconsistent results from dislocation slip.
[0037] This invention is not limited thereto. The above description is merely an embodiment of this invention and does not limit the patent scope of this invention. Any equivalent structural or procedural transformations made based on the description and drawings of this invention, or any direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this invention.
Claims
1. A machine learning potential function design method for rare earth magnesium alloys, characterized in that, Specifically, the following steps are included: 1) Based on the periodicity and atomic coordinates of the close-packed hexagonal structure, different structural models of rare earth magnesium alloys within solid solubility were constructed using Material Studio software, including bulk structure, strained bulk structure, surface structure and stacking fault structure. 2) The relationship between structure and energy was calculated using VASP software, and the lattice constant, elastic constant, generalized stacking fault energy and surface energy of rare earth magnesium alloy were determined using the relationship between structure and energy. 3) The DFT structure-energy dataset was trained and tested using the deep learning software DeePMD to obtain the molecular dynamics potential function—DP potential; 4) The lattice constant, elastic constant, generalized stacking fault energy and surface energy of rare earth magnesium alloys were calculated using the DP potential, and the results were compared with the DFT results using the classical potential function MEAM potential. 5) Based on the generalized stacking fault energy theory, establish the relationship between the changes in stable and unstable stacking fault energy of the rare earth magnesium alloy conical slip system and its plasticity. The smaller the unstable and stable stacking fault energies, the better the plasticity of the magnesium alloy. Use the DP potential to perform large-scale simulation of conical dislocations of pure magnesium and rare earth magnesium alloys, calculate the generalized stacking fault energy curves of their conical slip systems, compare them, find their variation law, and compare them with experimental results.
2. The method as described in claim 1, characterized in that, The methods for obtaining different structural models from Material Studio software are as follows: A close-packed hexagonal Mg crystal structure was established using Materials Studio software. By expanding the cell and replacing alloying elements, rare earth magnesium alloy structures with different contents were obtained. The structures were then converted into POSCAR format using VESTA software to obtain the model structure for calculation using VASP software.
3. The method as described in claim 1, characterized in that, The method for obtaining the lattice constant is as follows: In the Origin software's Fitting Manager, create a new fitting function, namely the BM equation of state, and perform nonlinear curve fitting on the VASP calculations of multiple volumes and energies to obtain the equilibrium volume and equilibrium energy of the crystal, which are then converted into lattice constants.
4. The method as described in claim 1, characterized in that, The method for calculating the elastic constants of a crystal is as follows: Under equilibrium volume conditions, the crystal undergoes structural relaxation, and based on the deformation matrix, multiple strains are applied to the crystal in corresponding directions. The equilibrium energy in the ground state under different strains is calculated, and a nonlinear curve is fitted based on the relationship between strain and energy to obtain the crystal's elastic constant C. 11 C 12 C 13 C 33 and C 44 .
5. The method as described in claim 1, characterized in that, The method for calculating the generalized stacking fault energy curve is as follows: The stacking fault energy is obtained by calculating the energy of the supercell in a perfect crystal and the energy of the supercell after adding stacking faults, then subtracting the difference and dividing by the stacking fault surface area. The formula is as follows: Where E SF E0 represents the energy of a supercell containing stacking faults; E0 represents the energy of a perfect crystal supercell; and A represents the area of the stacking fault surface. The supercell is divided into upper and lower parts and rigidly moved relative to each other. By moving different distances, the corresponding stacking fault energies are calculated, and a generalized stacking fault energy curve is finally obtained with the distance moved as the x-axis and the stacking fault energy as the y-axis. The added alloying elements are placed as close as possible to the stacking fault surface to highlight the influence of rare earth elements on the stacking fault energy.
6. The method as described in claim 1, characterized in that, The method for calculating surface energy is as follows: Calculate the surface energy by subtracting the difference between a bulk structure and a surface structure containing the same number and types of atoms, and then dividing by the surface area. The formula is as follows: Where E slab E refers to the energy of a system containing a surface; bulk This refers to the energy of a bulk system without a surface, where the atom type and number are related to E. slab The model is consistent; A refers to the surface area; the added alloying elements are placed as close to the surface as possible to highlight the influence of rare earth elements on surface energy.
7. The method as described in claim 1, characterized in that, The method for training machine learning potential functions using DeePMD is as follows: Use the dpdata module in the DeePMD package to convert the DFT structure-energy dataset into a training set; debug the parameters in DeePMD, including the cutoff radius r. cut The loss function is used to obtain different DP potentials by testing the cutoff radius and assigning different weights to energy, force, and virial in the loss function. These DP potentials are then tested on a test set. When the root mean square error of the energy between the fitted DP potential and the DFT result is less than 5 × 10⁻⁶, the result is considered successful. -2 eV, the root mean square error of force is less than 1×10e -3 eV / A, the root mean square error of the virial is less than 8 × 10⁻⁶. -1 When the value reaches eV, it is considered that a high-precision machine learning potential function—DP potential—that can accurately describe conical dislocations has been obtained.
8. The method as described in claim 1, characterized in that, The method for calculating the properties of rare earth magnesium alloys using DP potential and MEAM potential, and comparing them with DFT calculation results, is as follows: In the molecular dynamics software LAMMPS, the lattice constants, elastic constants, generalized stacking fault energy curves, and surface energies of rare-earth magnesium alloys were calculated using the DP potential and the classical potential function MEAM. The relative error was then used to calculate these parameters. The formula describes the degree of closeness between the calculated DP potential and MEAM potential and the DFT result, where y refers to the calculated DP potential or MEAM potential. DFT This refers to the corresponding DFT result; when the relative error between the DP potential or MEAM potential result and the DFT result is less than 5%, it has DFT accuracy.