Method and device for calculating metal replacement atom body diffusion coefficient, and electronic equipment

Abstract

The application discloses a calculation method and device of a metal replacement atom bulk diffusion coefficient and electronic equipment, and the method comprises the following steps: constructing a superlattice model of base metal atoms, replacing one atom near the center of the superlattice model with a replacement atom, and respectively constructing a first initial state model and a first final state model in a ring diffusion process; performing structure optimization and energy optimization on the first initial state model and the first final state model to obtain an optimized second initial state model and a second final state model; correlating the second initial state model and the second final state model, determining a ring diffusion model, searching for a transition state of the ring diffusion model, and obtaining a potential barrier curve with the lowest energy barrier; determining the transition distance of the replacement atom from the initial state to the final state in the superlattice model; and determining the bulk diffusion coefficient of the replacement atom based on the diffusion activation energy, the transition distance and the effective transition frequency of the replacement atom, wherein the diffusion activation energy is determined by the potential barrier curve.

Description

Methods, apparatus, and electronic equipment for calculating the bulk diffusion coefficient of metal substitution atoms Technical Field

[0001] This invention relates to the field of metallic materials technology, and in particular to a method, apparatus, and electronic device for calculating the diffusion coefficient of metal-substituted atoms. Specifically, it relates to a method, apparatus, and electronic device for calculating the diffusion coefficient of metal-substituted atoms based on first principles. Background Technology

[0002] The diffusion of microscopic atoms is a universal phenomenon. For metallic materials, the diffusion of metal atoms involves many aspects of material applications. For example, the inter-atomic diffusion at the interface during diffusion welding affects interfacial bonding, and atomic diffusion on the surface of stainless steel affects its corrosion resistance. To quantitatively characterize the rate of atomic diffusion, it is necessary to obtain the diffusion coefficient of materials under different conditions.

[0003] Diffusion coefficients can be directly measured experimentally, such as using chromatographic pulse response to determine the infinite dilution diffusion coefficient of various solutes in supercritical CO2, and using transient pulse response technology to measure the internal diffusion coefficient of powders. Other methods include permeation, adsorption rate measurement, and transient neutron scattering. These methods are not only relatively complex to operate, but also require the construction of mathematical models based on the relationship between diffusion amount and diffusion time. The measurement and calculation of the diffusion coefficient of metal atoms in a matrix first requires conducting a diffusion process under specific conditions, followed by analysis of the diffusion cross-section composition. The diffusion distance is determined based on the content of relevant components, and a mathematical model is constructed from a set of data to derive the diffusion coefficient.

[0004] Besides experimental testing, numerical simulation is also a feasible method for calculating the diffusion coefficient. Existing methods first consider vacancy diffusion of substitutional atoms, which requires a large number of vacancies in the matrix crystal structure; secondly, interstitial atom diffusion, which requires the diffusing atoms to be interstitial atoms with atomic radii much smaller than those of the matrix atoms. However, for the bulk diffusion process of substitutional atoms, due to the absence of defects such as vacancies in the crystal structure and the relatively large size of the substitutional atoms, existing vacancy diffusion and interstitial diffusion methods are difficult to form. Regarding the diffusion of substitutional atoms in the absence of vacancies, the diffusion path and modeling have always been challenging issues. Existing theoretical models explain relatively little research on diffusion in the absence of vacancies. The main consideration should be the diffusion process following the substitutional metal occupying a lattice site in the matrix metal. Summary of the Invention

[0005] To address the problem that existing methods struggle to obtain accurate bulk diffusion coefficients of metal atoms, this application provides a method, apparatus, and electronic device for calculating the bulk diffusion coefficient of metal substitutional atoms. To solve the existing problem, it offers a ring diffusion approach, enabling the calculation of the diffusion coefficient of substitutional metal atoms in a matrix structure without vacancies.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides a method for calculating the bulk diffusion coefficient of metal substitution atoms, the method comprising the following steps:

[0008] A supercrystal model of the matrix metal atoms is constructed, and an atom near the center of the supercrystal model is replaced with a substitution atom to construct the first initial state model and the first final state model in the ring diffusion process, respectively.

[0009] Structural optimization and energy optimization are performed on the first initial state model and the first final state model to obtain the optimized second initial state model and the second final state model;

[0010] The second initial state model and the second final state model are correlated to determine the ring diffusion model, and the transition state of the ring diffusion model is searched to obtain the barrier curve with the lowest energy barrier.

[0011] Determine the transition distance from the initial state to the final state of the substitutional atom in the supercrystal model;

[0012] The bulk diffusion coefficient of the substitution atom is determined based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, wherein the diffusion activation energy is determined by the potential barrier curve.

[0013] In one possible implementation, the bulk diffusion coefficient of the substituted atom is determined by the following formula:

[0014]

[0015] Where v0 is the effective transition frequency of the substitution atom, E a For diffusion activation energy, N A Let R be Avogadro's constant, R be the ideal gas constant, and T be the temperature.

[0016] In one possible implementation, the supercell of the supercrystal model is at least 2×2×1.

[0017] In one possible implementation, the diffusion activation energy is determined by the potential barrier curve, specifically:

[0018] The maximum barrier interpolation is calculated based on the barrier curve, and the barrier unit is converted from electron volts to joules to calculate the diffusion activation energy.

[0019] In one possible implementation, the bulk diffusion coefficient is determined based on first-principles density functional theory.

[0020] In one possible implementation, the supercrystal model is free of interstitial atoms and vacancy defects.

[0021] In a second aspect, the present invention provides a device for calculating the bulk diffusion coefficient of metal substitution atoms, the device comprising:

[0022] A construction module is used to construct a supercrystal model of the matrix metal atoms, and replace one atom in the middle of the supercrystal model with a substitution atom to construct the first initial state model and the first final state model in the ring diffusion process, respectively.

[0023] The optimization module is used to perform structural optimization and energy optimization on the first initial state model and the first final state model to obtain the optimized second initial state model and the second final state model.

[0024] The correlation module is used to correlate the second initial state model and the second final state model, determine the ring diffusion model, and search for the transition state of the ring diffusion model to obtain the barrier curve with the lowest energy barrier.

[0025] A distance module is used to determine the transition distance of the substitution atom from the initial state to the final state in the supercrystal model.

[0026] The bulk diffusion coefficient module is used to determine the bulk diffusion coefficient of the substitution atom based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, wherein the diffusion activation energy is determined by the barrier curve.

[0027] In one possible implementation, the bulk diffusion coefficient of the substituted atom is determined by the following formula:

[0028]

[0029] Where v0 is the effective transition frequency of the substitution atom, E a For diffusion activation energy, N A Let R be Avogadro's constant, R be the ideal gas constant, and T be the temperature.

[0030] Thirdly, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0031] Memory, used to store computer programs;

[0032] When a processor executes a program stored in memory, it implements the steps of the method for calculating the bulk diffusion coefficient of metal substitution atoms as described in any embodiment of the first aspect.

[0033] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for calculating the bulk diffusion coefficient of metal substitution atoms as described in any embodiment of the first aspect.

[0034] The technical solutions provided in this application have the following advantages compared with the prior art:

[0035] This application provides a method for calculating the bulk diffusion coefficient of metal substitution atoms. The method involves constructing a supercrystal model of the matrix metal atoms, replacing an atom near the center of the supercrystal model with a substitution atom, and constructing a first initial state model and a first final state model for a ring-shaped diffusion process. The first initial state model and the first final state model are then structurally and energy-optimized to obtain optimized second initial state models and second final state models. The second initial state model and the second final state model are correlated to determine the ring-shaped diffusion model, and the transition states of the ring-shaped diffusion model are searched to obtain the barrier curve with the lowest energy barrier. The transition distance from the initial state to the final state of the substitution atom in the supercrystal model is determined. Based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, the bulk diffusion coefficient of the substitution atom is determined. The diffusion activation energy is determined by the barrier curve. This invention calculates the energy barrier curve using first-principles calculations, intuitively demonstrating that the energy reaches its maximum value during ring-shaped diffusion. Overcoming this barrier enables diffusion, and the bulk diffusion coefficient is derived from the energy using relevant physical formulas. Furthermore, this invention can compare the magnitude of the diffusion coefficient between metal atoms from a theoretical perspective, which can save tedious experimental steps or help explain related experimental phenomena. Attached Figure Description

[0036] Figure 1 is a schematic flowchart of a method for calculating the bulk diffusion coefficient of metal substitution atoms provided by the present invention;

[0037] Figure 2(a) is a schematic diagram of the γ-Fe unit cell constructed in Example 1 of the present invention;

[0038] Figure 2(b) is a schematic diagram of the γ-Fe 2x2x1 supercell constructed in Example 1 of the present invention;

[0039] Figure 2(c) is a diagram of the Pb doping model before ring diffusion constructed in Example 1 of the present invention;

[0040] Figure 2(d) is a diagram of the state of the Pb-doped model after ring diffusion constructed in Example 1 of the present invention;

[0041] Figure 3 is a schematic diagram of the annular diffusion process constructed in Embodiment 1 of the present invention;

[0042] Figure 4 shows the annular diffusion barrier curve calculated in Embodiment 1 of the present invention;

[0043] Figure 5(a) is a schematic diagram of the WC primitives constructed in Example 2 of the present invention;

[0044] Figure 5(b) is a schematic diagram of the WC 3x3x2 supercell constructed in Embodiment 2 of the present invention;

[0045] Figure 5(c) is a diagram of the Pb doping model before ring diffusion constructed in Example 2 of the present invention;

[0046] Figure 5(d) shows the state diagram of the Pb doping model constructed in Example 2 of the present invention after ring diffusion;

[0047] Figure 6 is a schematic diagram of the annular diffusion process constructed in Embodiment 2 of the present invention;

[0048] Figure 7 shows the annular diffusion barrier curve calculated in Embodiment 2 of the present invention;

[0049] Figure 8 is a schematic diagram of the structure of a metal substitution atomic bulk diffusion coefficient calculation device provided by the present invention;

[0050] Figure 9 is a schematic diagram of an electronic device structure provided by an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0053] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of the stated features, merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0054] In this application, "exemplary" or "in one example" is used to mean "used as an example, illustration, or description." Any embodiment described as "exemplary" or "in one example" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application.

[0055] To address the technical problems mentioned in the background section, this application provides a method for calculating the bulk diffusion coefficient of metal substitution atoms. See Figure 1 for details. Figure 1 is a schematic flowchart of the method for calculating the bulk diffusion coefficient of metal substitution atoms provided by this invention. As shown in Figure 1, the method for calculating the bulk diffusion coefficient includes the following steps:

[0056] Step 110: Construct a supercrystal model of the matrix metal atoms, replace an atom near the center region of the supercrystal model with a substitution atom, and construct the first initial state model and the first final state model in the ring diffusion process, respectively.

[0057] Bulk diffusion is not vacancy diffusion, but diffusion of atoms heating up within a defect-free lattice. Therefore, the constructed supercrystal model is free of interstitial atoms, vacancies, and other defects. The smallest supercell is 2×2×1, and the substitution atoms can be matrix metal atoms or other metal atoms, located near the central region of the supercrystal model.

[0058] Step 120: Perform structural optimization and energy optimization on the first initial state model and the first final state model to obtain the optimized second initial state model and the second final state model.

[0059] Specifically, the first initial state and the first final state models constructed in step 110 are subjected to structural optimization and energy optimization. In the calculation of structural optimization and energy optimization, the electron wave function is expanded using an ultrasoft pseudopotential and a plane wave basis set, and the electron exchange correlation potential is in the form of a PBE functional under the generalized gradient approximation. After completing the structural optimization and energy optimization, the process proceeds to step 130.

[0060] Step 130: Correlate the second initial state model and the second final state model to determine the ring diffusion model, and search for the transition state of the ring diffusion model to obtain the barrier curve with the lowest energy barrier.

[0061] By associating the second initial state model with the second final state model, the determined ring diffusion model is the dynamic model of diffusion.

[0062] Step 140: Determine the transition distance of the substitution atom from the initial state to the final state in the supercrystal model.

[0063] The purpose of step 140 is to obtain the transition distance of the substitution atoms constructed in step 110 in the base metal.

[0064] Step 150: Based on the diffusion activation energy, transition distance, and effective transition frequency of the substitution atom, determine the bulk diffusion coefficient of the substitution atom. The diffusion activation energy is determined by the barrier curve.

[0065] In one example, based on first-principles density functional theory, a ring diffusion model of the substitutional atoms is constructed, and the Schrödinger equation is solved approximately to obtain the theoretically calculated value of the bulk diffusion coefficient, thus determining the bulk diffusion coefficient. The diffusion activation energy is determined by the potential barrier curve: the maximum potential barrier interpolation is calculated based on the potential barrier curve, and the barrier unit is converted from electron volts to joules to calculate the diffusion activation energy. Specifically, the bulk diffusion coefficient of the substitutional atoms is determined by the following formula:

[0066]

[0067] Where v0 is the effective transition frequency of the substitution atom, E a For diffusion activation energy, N A Let R be Avogadro's constant, R be the ideal gas constant, and T be the temperature.

[0068] This application provides a method for calculating the bulk diffusion coefficient of metal substitution atoms. It constructs a supercrystal model of the matrix metal atoms, replaces an atom near the center of the supercrystal model with a substitution atom, and constructs a first initial state model and a first final state model for the ring diffusion process. The first initial state model and the first final state model are then structurally and energy-optimized to obtain optimized second initial state models and second final state models. The second initial state model and the second final state model are correlated to determine the ring diffusion model, and the transition state of the ring diffusion model is searched to obtain the barrier curve with the lowest energy barrier. The transition distance from the initial state to the final state of the substitution atom in the supercrystal model is determined. Based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, the bulk diffusion coefficient of the substitution atom is determined. The diffusion activation energy is determined by the barrier curve. This invention obtains the energy barrier curve through first-principles calculations, intuitively showing that the energy reaches its maximum value during the ring diffusion process. Overcoming this obstacle enables diffusion, and the bulk diffusion coefficient is deduced from the energy using relevant physical formulas. Furthermore, this invention can compare the magnitude of the diffusion coefficient between metal atoms from a theoretical perspective, which can save tedious experimental steps or help explain related experimental phenomena.

[0069] The above are embodiments of the method for calculating the bulk diffusion coefficient of metal substitution atoms provided in this application. Specific embodiments 1 and 2 utilizing the above aspects are described below:

[0070] Example 1

[0071] This embodiment 1 provides a first-principles calculation method for the bulk diffusion coefficient of Pb-substituted atoms in an austenitic Fe matrix, including the following steps:

[0072] S1. The unit cell structure of γ-Fe crystal was established using first-principles calculation software. The γ-Fe unit cell belongs to the tetragonal crystal system, space group FM-3M, with a face-centered cubic structure. The lattice parameters are as follows: α = β = γ = 90°, as shown in Figure 2(a). A 2x2x1 supercell of γ-Fe is constructed, as shown in Figure 2(b). One Fe atom in the center of the supercell is replaced by a Pb atom, and the initial state model is shown in Figure 2(c). To obtain the final state model in Figure 2(d), as shown in Figure 3, the ring diffusion process involves the four atoms in the center forming a ring. After rotating a quarter circle clockwise, the Pb atom at the replacement site moves to another position, realizing the diffusion process.

[0073] S2. Perform structural and energy optimization on the initial and final state models constructed in step S1. In the calculation, the electron wave function is expanded using an ultrasoft pseudopotential and a plane wave basis set, and the electron exchange correlation potential is selected in the PBE functional form under the generalized gradient approximation.

[0074] S3. Correlate the optimized initial state model and final state model from step S2 to obtain the dynamic model of diffusion. Search for the transition state of the toroidal diffusion process and calculate the diffusion coefficient. The final simulation result required is the diffusion barrier curve, as shown in Figure 4. The difference between the highest and lowest energy points in the curve is the diffusion barrier. The highest energy point in the curve is the transition state of diffusion, where the cell energy rises to its highest point and then decreases after reaching its maximum value along the path.

[0075] S4. Based on the lattice parameters and the annular diffusion path, the transition distance L of Pb atoms in the γ-Fe matrix metal is approximately...

[0076] S5. Calculate the maximum barrier difference using the barrier curve obtained in step S3, and obtain the diffusion activation energy E. a Thus, the relationship between the bulk diffusion coefficient D of the replaced atoms and temperature T is obtained:

[0077]

[0078] Where, N A is Avogadro's constant, approximately 6.0221 × 10⁻⁶. 23 mol -1 R is the ideal gas constant, approximately 8.3141 J·mol⁻¹. -1 ·K -1 The effective transition frequency of impurity atoms in a solid is generally 10. 13 In this embodiment, the effective transition frequency v0 of the atom is selected as 10 Hz. 13 Hz; As shown in Figure 5, the Ea of Pb ring diffusion in the γ-Fe unit cell is approximately 15.5 eV. Substituting the above data into the above equation, we can obtain the expression for the bulk diffusion coefficient of Pb atoms in the γ-Fe unit cell as a function of temperature:

[0079]

[0080] Example 2

[0081] This embodiment 2 provides a first-principles calculation method for the bulk diffusion coefficient of Pb-substituted atoms in a WC matrix, including the following steps:

[0082] S1. The unit cell structure of WC crystal is established using first-principles software. The WC unit cell belongs to the P-6M2 space group, and the lattice parameters are as follows: α = β = 90°, γ = 120°, as shown in Figure 5(a). A 3x3x2 supercell of WC is constructed, as shown in Figure 5(b). A W atom in the middle of the supercell is replaced with a Pb atom, and the initial state model is shown in Figure 5(c). To obtain the final state model shown in Figure 5(d), as shown in Figure 6, the ring diffusion process involves the three atoms in the middle forming a ring. After rotating one-third of the circle clockwise, the Pb atom at the replacement site moves to another position, thus realizing the diffusion process.

[0083] S2. Perform structural and energy optimization on the initial and final state models constructed in step S1. In the calculation, the electron wave function is expanded using an ultrasoft pseudopotential and a plane wave basis set, and the electron exchange correlation potential is selected in the PBE functional form under the generalized gradient approximation.

[0084] S3. Correlate the optimized initial state model and final state model from step S2 to obtain the dynamic model of diffusion. Search for the transition state of the toroidal diffusion process and calculate the diffusion coefficient. The final simulation result required is the diffusion barrier curve, as shown in Figure 7. The difference between the highest and lowest energy points in the curve is the diffusion barrier. The highest energy point in the curve is the transition state of diffusion, where the cell energy rises to its highest point and then decreases after reaching its maximum value along the path.

[0085] S4. Based on the lattice parameters and the annular diffusion path, the transition distance L of Pb atoms in the WC matrix metal is approximately...

[0086] S5. Calculate the maximum barrier difference using the barrier curve obtained in step S3, and obtain the diffusion activation energy E. a Thus, the relationship between the bulk diffusion coefficient D of the replaced atoms and temperature T is obtained:

[0087]

[0088] Where, N A is Avogadro's constant, approximately 6.0221 × 10⁻⁶. 23 mol -1 R is the ideal gas constant, approximately 8.3141 J·mol⁻¹.-1 ·K -1 The effective transition frequency of impurity atoms in a solid is generally 10. 13 In this embodiment, the effective transition frequency v0 of the atom is selected as 10 Hz. 13 Hz; As shown in Figure 6, the Ea of Pb ring diffusion in the WC unit cell is approximately 21.4 eV. Substituting the above data into the above equation, we can obtain the expression for the bulk diffusion coefficient of Pb atoms in the WC unit cell as a function of temperature:

[0089]

[0090] The above are two examples illustrating the calculation method for the metal substitution atomic diffusion coefficient provided in this application. Other embodiments of the metal substitution atomic diffusion coefficient provided in this application are described below.

[0091] Figure 8 illustrates a calculation device for the bulk diffusion coefficient of metal substitution atoms provided by the present invention. This device includes: a construction module 81, an optimization module 82, a correlation module 83, a distance module 84, and a bulk diffusion coefficient model 85.

[0092] The construction module 81 is used to construct a supercrystal model of the matrix metal atoms, and replace one atom in the middle of the supercrystal model with a substitution atom to construct the first initial state model and the first final state model in the ring diffusion process, respectively.

[0093] The optimization module 82 is used to perform structural optimization and energy optimization on the first initial state model and the first final state model to obtain the optimized second initial state model and the second final state model.

[0094] The association module 83 is used to associate the second initial state model and the second final state model, determine the ring diffusion model, and search for the transition state of the ring diffusion model to obtain the barrier curve with the lowest energy barrier.

[0095] Distance module 84 is used to determine the transition distance of the substitution atom from the initial state to the final state in the supercrystal model.

[0096] The bulk diffusion coefficient module 85 is used to determine the bulk diffusion coefficient of the substitution atom based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, wherein the diffusion activation energy is determined by the barrier curve.

[0097] In one example, the bulk diffusion coefficient of the substituted atom is determined by the following formula:

[0098]

[0099] Where v0 is the effective transition frequency of the substitution atom, E a For diffusion activation energy, N A R is Avogadro's constant, R is the ideal gas constant, and T is the temperature.

[0100] In one example, the supercell of the supercrystal model is as small as 2×2×1.

[0101] In one example, the diffusion activation energy is determined by the barrier curve, specifically:

[0102] The maximum barrier interpolation is calculated based on the barrier curve, and the barrier unit is converted from electron volts to joules to calculate the diffusion activation energy.

[0103] In one example, the bulk diffusion coefficient is determined based on first-principles density functional theory.

[0104] In one example, the supercrystal model has no interstitial atoms or vacancy defects.

[0105] The functions performed by each component in the metal substitution atomic diffusion coefficient calculation device provided in this embodiment have been described in detail in any of the above method embodiments, and therefore will not be repeated here.

[0106] This invention provides a method for calculating the bulk diffusion coefficient of metal substitution atoms. The method involves constructing a supercrystal model of the matrix metal atoms, replacing an atom near the center of the supercrystal model with a substitution atom, and constructing a first initial state model and a first final state model for a ring-shaped diffusion process. The first initial state model and the first final state model are then structurally and energy-optimized to obtain optimized second initial state models and second final state models. The second initial state model and the second final state model are correlated to determine the ring-shaped diffusion model, and the transition states of the ring-shaped diffusion model are searched to obtain the barrier curve with the lowest energy barrier. The transition distance from the initial state to the final state of the substitution atom in the supercrystal model is determined. Based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, the bulk diffusion coefficient of the substitution atom is determined. The diffusion activation energy is determined by the barrier curve. This invention obtains the energy barrier curve through first-principles calculations, intuitively showing that the energy reaches its maximum value during ring-shaped diffusion. Overcoming this barrier enables diffusion, and the bulk diffusion coefficient is derived from the energy using relevant physical formulas. Furthermore, this invention can compare the magnitude of the diffusion coefficient between metal atoms from a theoretical perspective, which can save tedious experimental steps or help explain related experimental phenomena.

[0107] As shown in Figure 9, this application embodiment provides an electronic device, including a processor 111, a communication interface 112, a memory 113, and a communication bus 114, wherein the processor 111, the communication interface 112, and the memory 113 communicate with each other through the communication bus 114.

[0108] Memory 113 is used to store computer programs;

[0109] In one embodiment of this application, the processor 111, when executing the program stored in the memory 113, implements the method for calculating the bulk diffusion coefficient of metal substitution atoms provided in any of the foregoing method embodiments.

[0110] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method for calculating the bulk diffusion coefficient of metal substitution atoms as provided in any of the foregoing method embodiments.

[0111] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0112] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0113] The above are merely specific embodiments of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for calculating the bulk diffusion coefficient of metal substitution atoms, characterized in that, include: A supercrystal model of the matrix metal atoms is constructed. An atom near the center of the supercrystal model is replaced with a substitution atom. First initial state models and first final state models are constructed for the ring diffusion process. Structural and energy optimizations are performed on the first initial state and first final state models to obtain optimized second initial state and second final state models. The second initial state and second final state models are correlated to determine the ring diffusion model. The transition states of the ring diffusion model are searched to obtain the barrier curve with the lowest energy barrier. The transition distance from the initial state to the final state of the substitution atom in the supercrystal model is determined. Based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, the bulk diffusion coefficient of the substitution atom is determined. The diffusion activation energy is determined by the barrier curve. The bulk diffusion coefficient of the substitution atom is determined using the following formula: in, The effective transition frequency of the replacement atom, For diffusion activation energy, Let Avogadro's constant be 1. Let be the ideal gas constant. The temperature is used; the diffusion activation energy is determined by the potential barrier curve, specifically by: calculating the maximum potential barrier interpolation based on the potential barrier curve, converting the potential barrier unit from electron volts to joules, and calculating the diffusion activation energy; and determining the bulk diffusion coefficient based on first-principles density functional theory.

2. The method according to claim 1, characterized in that, The smallest supercell of the supercrystal model is 2×2×1.

3. The method according to claim 1, characterized in that, The supercrystal model has no interstitial atoms or vacancy defects.

4. A device for calculating the bulk diffusion coefficient of metal substitution atoms, characterized in that, include: A construction module is used to construct a supercrystal model of the matrix metal atoms, replacing one atom in the middle of the supercrystal model with a substitution atom, and constructing a first initial state model and a first final state model in the ring diffusion process, respectively; an optimization module is used to perform structural optimization and energy optimization on the first initial state model and the first final state model to obtain an optimized second initial state model and a second final state model; a correlation module is used to correlate the second initial state model and the second final state model to determine the ring diffusion model, and search for the transition state of the ring diffusion model to obtain the barrier curve with the lowest energy barrier; a distance module is used to determine the transition distance of the substitution atom from the initial state to the final state in the supercrystal model; a bulk diffusion coefficient module is used to determine the bulk diffusion coefficient of the substitution atom based on the diffusion activation energy, the transition distance, and the effective transition frequency of the substitution atom, wherein the diffusion activation energy is determined by the barrier curve; the bulk diffusion coefficient of the substitution atom is determined by the following formula: in, The effective transition frequency of the replacement atom, For diffusion activation energy, Let Avogadro's constant be 1. Let be the ideal gas constant. The temperature is used; the diffusion activation energy is determined by the potential barrier curve, specifically by: calculating the maximum potential barrier interpolation based on the potential barrier curve, converting the potential barrier unit from electron volts to joules, and calculating the diffusion activation energy; and determining the bulk diffusion coefficient based on first-principles density functional theory.

5. An electronic device, characterized in that, The device includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other via the communication bus. The memory is used to store computer programs. When the processor executes the program stored in the memory, it implements the steps of the method for calculating the diffusion coefficient of metal substitution atoms as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for calculating the bulk diffusion coefficient of metal substitution atoms as described in any one of claims 1-3.

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