Modeling method for constructing arbitrary chemical short-range ordered multi-principal element alloy structure

Abstract

The invention relates to the technical field of computational simulation, in particular to a modeling method for constructing any chemical short-range ordered multi-principal element alloy structure, which comprises the following steps: setting target values and convergence conditions of chemical short-range ordered parameters; calculating parameter values of chemical short-range order parameters of the initial configuration; calculating an initial difference value; judging whether the initial difference value meets a convergence condition or not; if yes, outputting an atomic configuration; if not, carrying out iterative operation; the iterative operation process comprises the following steps of: randomly exchanging two atomic positions to obtain a new configuration; calculating a difference value between a parameter value number of the chemical short-range order parameter of the new configuration and a target value to obtain an exchanged difference value; judging whether the difference value after exchange is smaller than the difference value before exchange or not; if yes, current exchange is accepted; and after the convergence condition is met, outputting the atomic configuration. According to the method, the function of directly generating a specific structure from structural features is achieved, and atom configuration of any chemical short-range ordered feature can be customized in a wide component space.

Description

Technical Field

[0001] This application relates to the field of computational simulation technology, and in particular to a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures. Background Technology

[0002] Compared to traditional alloys, multi-principal element alloy systems, composed of multiple principal elements, exhibit a superior combination of mechanical properties, such as high strength, high ductility, high fracture toughness, and impact resistance. This greatly expands the service life of these materials, attracting widespread attention. However, limited by existing experimental techniques and research costs, computational simulation has become one of the main research methods for studying the structural properties of multi-principal element alloys.

[0003] In traditional computational simulations, modeling of multi-principal alloys is often based on stochastic solid solution models, assuming that various alloying elements are distributed with equal probability at lattice sites, thus forming a stochastic ideal solid solution model. However, numerous theoretical and experimental studies have shown that due to the different affinities between elements, it is almost impossible for elements to be completely randomly distributed at lattice sites in multi-principal alloys; Chemical Short Range Order (CSRO) is unavoidable in multi-principal alloys.

[0004] However, short-range chemical ordering has not yet been directly observed experimentally. Although numerous experimental reports have documented the observation of short-range ordered structures, the methods used remain controversial. Therefore, determining the short-range chemical ordering structure in a given alloy still relies on computational simulations rather than direct experimental evidence.

[0005] Existing computational simulation methods often construct short-range ordered structures using Monte Carlo (MC) simulations. However, these methods have certain drawbacks. First, Monte Carlo simulations rely on thermodynamic calculations, judging the rationality of structural changes based on energy levels. However, energy calculations often employ first-principles or molecular dynamics methods. First-principles calculations only consider the structural energy state at 0K; different temperatures, lattice distortions, and strain conditions all affect the energy calculations, leading to inaccurate structures. Furthermore, first-principles calculations are too costly and unsuitable for large-scale models, while short-range ordered structures in small models are often affected by periodic boundary conditions, causing the degree of order to deviate excessively from reality. While molecular dynamics simulations are significantly less computationally expensive than first-principles calculations, their accuracy depends heavily on the potential function used. Potential functions often do not accurately describe the interactions between elements. More importantly, both of these methods are directional constructions of short-range ordered structures, making it difficult to change the direction of short-range order construction by adjusting inter-element interactions. This poses a significant challenge for those seeking a comprehensive understanding of the correlation between short-range ordered structures and their properties. Summary of the Invention

[0006] This application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures. It directly takes the short-range ordered structure as the construction target, and by parameterizing the chemically short-range order and considering the changing directions of different parameters, it realizes the function of directly generating specific structures from structural features. It can customize the atomic configuration of arbitrary chemically short-range ordered features in a wide composition space.

[0007] To address the aforementioned technical problems, this application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures, comprising the following steps: First, setting the target value and convergence condition for the chemically short-range ordered parameters; then, calculating the parameter values ​​of the chemically short-range ordered parameters of the user-given initial configuration; next, calculating the difference between the parameter values ​​and the target value to obtain the initial difference; then, determining whether the initial difference satisfies the convergence condition; if yes, outputting the atomic configuration; if no, proceeding to iterative computation; wherein, the iterative computation process includes: obtaining a new configuration by randomly swapping the positions of two atoms; calculating the difference between the number of parameter values ​​of the chemically short-range ordered parameters of the new configuration and the target value to obtain the difference after the swap; determining whether the difference after the swap is less than the difference before the swap; if yes, accepting the current swap; outputting the atomic configuration after the current new configuration satisfies the convergence condition; if no, rejecting the current swap, using the initial configuration as input, and re-performing the iterative computation until the current new configuration satisfies the convergence condition.

[0008] In some exemplary embodiments, determining whether the initial difference satisfies the convergence condition includes: determining whether the initial difference is less than or equal to a preset minimum tolerance in the convergence condition; if so, the convergence condition is satisfied; otherwise, the convergence condition is not satisfied.

[0009] In some exemplary embodiments, determining whether the initial difference satisfies the convergence condition includes: determining whether the current number of swaps has reached the maximum number of swaps; if so, the convergence condition is satisfied; if not, the convergence condition is not satisfied.

[0010] In some exemplary embodiments, after the current new configuration satisfies the convergence condition, the atomic configuration is output, including: when the difference after the current new configuration exchange is less than or equal to the minimum tolerance preset in the convergence condition, or when the current number of exchanges has reached the maximum number of exchanges, it is determined that the convergence condition is met and the atomic configuration is output.

[0011] In some exemplary embodiments, when the current new configuration satisfies the convergence condition, it indicates that a configuration with a preset chemical short-range ordering feature has been successfully obtained.

[0012] In some exemplary embodiments, the target value is the target value of the chemical short-range ordering parameter corresponding to the target chemical short-range ordered structure.

[0013] In some exemplary embodiments, the Warren-Cowley parameter quantization method is used to calculate the parameter values ​​of the chemical short-range ordering parameters of the user-given initial configuration.

[0014] In some exemplary embodiments, the Warren-Cowley parameter is quantized using the following formula:

[0015]

[0016] Where i and j represent chemical elements, p(i|j) represents the probability of finding atom i within the nearest neighbor range of atom j, and C i This represents the average concentration of element i in the material.

[0017] In some exemplary embodiments, the Warren-Cowley parameter is quantized using the following formula:

[0018]

[0019] Where i and j represent chemical elements, and m represents the m-th nearest neighbor shell of the central i-type atom. C represents the probability of finding a type j atom near the central type i atom in the m-th nearest neighbor shell; j δ represents the average concentration of type j atoms in the system. ij Let Kronecker function be used.

[0020] In some exemplary embodiments, the difference between the parameter value and the target value is calculated to obtain the initial difference; each target parameter is subtracted from the corresponding initial parameter, and the sum is obtained to obtain the initial difference.

[0021] The technical solution provided in this application has at least the following advantages:

[0022] This application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures. The method includes the following steps: First, setting the target value and convergence condition for the chemically short-range ordering parameters; then, calculating the parameter values ​​of the chemically short-range ordering parameters of the user-given initial configuration; next, calculating the difference between the parameter values ​​and the target value to obtain the initial difference; then, determining whether the initial difference satisfies the convergence condition; if yes, outputting the atomic configuration; if no, proceeding to iterative computation; wherein the iterative computation process includes: obtaining a new configuration by randomly swapping the positions of two atoms; calculating the difference between the number of parameter values ​​of the chemically short-range ordering parameters of the new configuration and the target value to obtain the difference after the swap; determining whether the difference after the swap is less than the difference before the swap; if yes, accepting the current swap; outputting the atomic configuration after the current new configuration satisfies the convergence condition; if no, rejecting the current swap, using the initial configuration as input, and re-performing the iterative computation until the current new configuration satisfies the convergence condition.

[0023] The modeling method for constructing chemically short-range ordered multi-principal alloy structures provided in this application, by setting arbitrary target parameters and evolving based on an iterative algorithm, can obtain directional acquisition of chemically short-range ordered structures, rather than the traditional single-path exploration driven solely by energy. This allows for a comprehensive exploration of all chemically short-range ordered structures. Since the parameter calculations for a single iteration are only in the millisecond range, far exceeding the time required for a single energy calculation in Density Functional Theory (DFT), this invention not only obtains the desired structure quickly and efficiently, but also, due to the time savings, can handle larger-scale configurations. Attached Figure Description

[0024] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations do not constitute a limitation on the embodiments, and unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0025] Figure 1 This is a schematic flowchart illustrating a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures, provided in an embodiment of this application.

[0026] Figure 2This is a schematic diagram illustrating the evolution of the NiNi parameters of the CrCoNi alloy over time using the DFT-MC method, as provided in an embodiment of this application.

[0027] Figure 3 This is a schematic diagram illustrating the evolution of the CrCr parameter of the CrCoNi alloy over time using the DFT-MC method, as provided in an embodiment of this application.

[0028] Figure 4 This is a schematic diagram illustrating the evolution of the CoCo parameter of the CrCoNi alloy over time using the DFT-MC method, as provided in an embodiment of this application.

[0029] Figure 5 This is a schematic diagram illustrating the mutual evolution between a random distribution state provided in an embodiment of this application and a chemically short-range ordered state of a low-energy structure obtained by the DFT-MC method.

[0030] Figure 6 This is a schematic diagram illustrating the mutual evolution between a random distribution state and a high-energy chemically short-range ordered state, provided in an embodiment of this application.

[0031] Figure 7 This is a schematic diagram illustrating the mutual evolution between a high-energy chemical short-range ordered state and a low-energy chemical short-range ordered state obtained by the DFT-MC method, as provided in an embodiment of this application.

[0032] Figure 8 This is a schematic diagram illustrating the mutual evolution between a random distribution state provided in an embodiment of this application and a chemically short-range ordered state of a low-energy structure obtained by the DFT-MC method.

[0033] Figure 9 This is a schematic diagram illustrating the mutual evolution between a random distribution state and a high-energy chemically short-range ordered state, provided in an embodiment of this application.

[0034] Figure 10 This is a schematic diagram illustrating the mutual evolution between a high-energy chemical short-range ordered state and a low-energy chemical short-range ordered state obtained by the DFT-MC method, as provided in an embodiment of this application.

[0035] Figure 11 This is a schematic diagram illustrating the mutual evolution between a random distribution state and a high-energy chemically short-range ordered state, provided in an embodiment of this application. Detailed Implementation

[0036] As is known from the background technology, existing Monte Carlo simulation methods can affect energy calculations under different temperatures, lattice distortions, and strain conditions, resulting in inaccurate structures.

[0037] Chemical short-range order in multi-principal-element alloys can effectively influence the mechanical properties of the materials. For example, the stacking fault energy of single-phase face-centered cubic CrCoNi alloys often exhibits a wide distribution range. This is because the stacking fault energy is strongly correlated with the local atomic environment, and the stacking fault energy can be controlled by adjusting the chemical short-range order. Furthermore, chemical short-range order can also effectively affect the energy barrier of dislocation motion, thus allowing for the regulation of dislocation dynamics.

[0038] Currently, in exploring the construction and characterization of chemically short-range ordered structures in high / medium entropy alloys (HEAs / MEAs), the computational method combining density functional theory (DFT) and mechanical modulometry (MC) simulations holds a dominant position. The advantage and core idea of ​​this method is to utilize the high-precision energy description provided by DFT to drive configuration sampling in MC simulations, enabling the identification of lower-energy chemically short-range ordered states under specific compositions. However, this strategy faces significant bottlenecks:

[0039] (1) High computational cost: DFT calculation itself has extremely high computational complexity, especially for medium-to-high entropy alloy systems containing multiple elements, which require the construction of large supercells. Therefore, energy calculation requires a lot of computation time and resources. Even with the help of MC sampling, its computational and time costs are often extremely high.

[0040] (2) It cannot account for external field factors such as temperature and stress. DFT calculations can only accurately describe the interatomic interactions in the ground state. However, chemical short-range order is sensitive to applied temperature and stress fields. The energy information obtained by simply exchanging atoms may not be the lowest energy in the current configuration, which may mislead MC simulations.

[0041] (3) Only directional short-range ordered structures can be considered. The driving force for MC simulation is the reduction of the system's free energy. Therefore, traditional short-range ordered construction methods can only proceed in the direction of reducing the system's free energy, which makes it difficult to fully understand the impact of chemical short-range order on material structure and properties.

[0042] To address the aforementioned technical problems, this application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures, comprising the following steps: First, setting the target value and convergence condition for the chemically short-range ordered parameters; then, calculating the parameter values ​​of the chemically short-range ordered parameters of the user-given initial configuration; next, calculating the difference between the parameter values ​​and the target values ​​to obtain the initial difference; then, determining whether the initial difference satisfies the convergence condition; if yes, outputting the atomic configuration; if no, proceeding to iterative computation; wherein, the iterative computation process includes: obtaining a new configuration by randomly swapping the positions of two atoms; calculating the difference between the number of parameter values ​​of the chemically short-range ordered parameters of the new configuration and the target values ​​to obtain the difference after the swap; determining whether the difference after the swap is less than the difference before the swap; if yes, accepting the current swap; outputting the atomic configuration after the current new configuration satisfies the convergence condition; if no, rejecting the current swap, using the initial configuration as input, and re-performing the iterative computation until the current new configuration satisfies the convergence condition.

[0043] This application addresses the urgent need for a more efficient, comprehensive, and convenient method for constructing short-range ordered models. Targeting short-range order, it enables the efficient acquisition of stable structures with specific chemical short-range order characteristics directly from arbitrary initial configurations of multi-component alloys. This process does not require calculating the system's free energy, but only assessing the degree of short-range order, thus significantly improving construction efficiency. Furthermore, it can construct arbitrary short-range ordered structures, which is of great significance for a comprehensive understanding of the impact of short-range order on material properties. In addition, energy calculations under different external field environments (such as using traditional molecular dynamics) can be performed on the constructed structures to evaluate their stability.

[0044] The embodiments of this application will now be described in detail with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the embodiments of this application to facilitate a better understanding of the application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments.

[0045] See Figure 1 This application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures, including the following steps:

[0046] Step 1: Set the target value and convergence condition for the chemical short-range ordering parameter.

[0047] Step 2: Calculate the parameter values ​​of the chemical short-range ordering parameters for the initial configuration given by the user.

[0048] Step 3: Calculate the difference between the parameter value and the target value to obtain the initial difference.

[0049] Step 4: Determine whether the initial difference satisfies the convergence condition; if yes, output the atomic configuration; if no, proceed to iterative calculation.

[0050] The iterative calculation process includes: obtaining a new configuration by randomly swapping the positions of two atoms; calculating the difference between the number of chemical short-range order parameters of the new configuration and the target value to obtain the difference after the swap; determining whether the difference after the swap is less than the difference before the swap; if so, accepting the current swap; outputting the atomic configuration after the current new configuration meets the convergence condition; if not, rejecting the current swap, using the initial configuration as input, and re-performing the iterative calculation until the current new configuration meets the convergence condition.

[0051] In some embodiments, determining whether the initial difference satisfies the convergence condition in step four includes: determining whether the initial difference is less than or equal to the preset minimum tolerance in the convergence condition; if so, the convergence condition is satisfied; otherwise, the convergence condition is not satisfied.

[0052] In some other embodiments, step four, determining whether the initial difference satisfies the convergence condition, includes: determining whether the current number of swaps has reached the maximum number of swaps; if yes, the convergence condition is satisfied; if no, the convergence condition is not satisfied.

[0053] In some embodiments, during the iterative operation, after the current new configuration satisfies the convergence condition, the atomic configuration is output, including: when the difference after the current new configuration is exchanged is less than or equal to the minimum tolerance preset in the convergence condition, or when the current number of exchanges has reached the maximum number of exchanges, it is determined that the convergence condition is met and the atomic configuration is output.

[0054] In some embodiments, when the current new configuration satisfies the convergence condition, it indicates that a configuration with a preset chemical short-range ordering feature has been successfully obtained.

[0055] In some embodiments, the target value in step one is the target value of the chemical short-range ordering parameter corresponding to the target chemical short-range ordered structure.

[0056] In some embodiments, in step two, the parameter values ​​of the chemical short-range ordering parameters of the user-given initial configuration are calculated using the Warren-Cowley parameter quantization method.

[0057] In some embodiments, the Warren-Cowley parameter is quantized using the following formula:

[0058]

[0059] Where i and j represent chemical elements, p(i|j) represents the probability of finding atom i within the nearest neighbor range of atom j, and C i This represents the average concentration of element i in the material.

[0060] In some embodiments, in step three, the difference between the parameter value and the target value is calculated to obtain the initial difference; each target parameter is subtracted from the corresponding initial parameter, and the sum is obtained to obtain the initial difference.

[0061] This application provides a novel method for constructing arbitrary chemically ordered short-range structures. Compared to traditional methods that rely on energy as a criterion and atomic exchange to achieve structural evolution and find structures with specific chemically ordered characteristics, this application primarily sets the chemically ordered short-range parameter values ​​for the target structure, exchanges atomic positions, calculates the changes in the chemically ordered short-range parameter values, and iteratively optimizes the method based on the difference between the parameter values ​​after each exchange and the target values, thereby achieving or approximating the target parameters and ultimately realizing a configuration design with preset chemically ordered characteristics. This application directly targets short-range ordered structures, parameterizes chemically ordered short-range structures, and considers the changing directions of different parameters to achieve the function of directly generating specific structures from structural features. It can customize atomic configurations with arbitrary chemically ordered characteristics within a wide composition space.

[0062] The technical solution of this application will be described in detail below through specific embodiments.

[0063] First, for chemical short-range order in multi-principal alloys, chemical short-range order parameters are often used for quantification. The Warren-Cowley parameter is currently a widely accepted quantification method, and its formula is as follows:

[0064]

[0065] Where i and j represent chemical elements, p(i|j) represents the probability of finding atom i within the nearest neighbor range of atom j, and C i This represents the average concentration of element i in the material. The number of chemical short-range ordering parameters varies depending on the number of principal elements in a multi-principal alloy. For example, a three-principal alloy has six different chemical short-range ordering parameters, while a four-principal alloy has ten. The number of parameters N can be calculated using the following formula:

[0066]

[0067] Here, n represents the number of principal components in the alloy. Therefore, to obtain the target chemical short-range ordered structure, it is first necessary to set the target values ​​for one or more corresponding chemical short-range ordered parameters. Furthermore, besides evolving with all known target parameter values, when exploring unknown parameter combinations, the set values ​​may not be fully accurate due to factors such as the size of the initial configuration. Therefore, to accelerate iteration, convergence conditions are also provided, namely the minimum acceptable tolerance or the maximum number of exchanges.

[0068] Next, we will discuss the core process of this application, which utilizes an iterative optimization algorithm to generate the final structure. This algorithm, based on chemical short-range order parameters, replaces the time-consuming and energy-intensive calculations in the DFT-MC method with Warren-Cowley parameter calculations implemented in simple code, and significantly overcomes the spatial scale limitations of the traditional DFT-MC method.

[0069] The specific process is explained below.

[0070] First, the short-range chemical ordering parameters of the initial configuration given by the user need to be calculated. In this application, the short-range chemical ordering parameters of the structure are calculated based on the Warren-Cowley parameters mentioned above.

[0071] After the calculation is completed, subtract each target parameter from its corresponding initial parameter, and sum the results to obtain the initial difference Δa0.

[0072] Next, the initial difference Δa0 will be compared with the minimum tolerance Δa in the user-defined convergence criteria. f Compare the initial difference Δa0 with the minimum tolerance Δa. f If the initial configuration is positive, the subsequent iterative calculations will proceed; otherwise, it indicates that the initial configuration given by the user has achieved the desired short-range chemical order.

[0073] After entering the iterative operation, a new configuration is obtained by randomly swapping the positions of two atoms.

[0074] Similar to the initial difference calculation method, recalculate the difference Δa between the current configuration parameters and the target parameters. i .

[0075] If the difference after the exchange is Δa i Less than the difference Δa before the exchange i-1 If the initial configuration is correct, the current exchange is accepted; otherwise, the current exchange is rejected, and the exchange is performed again using the initial configuration as input.

[0076] After successfully accepting a certain exchange, it is necessary to check whether the convergence condition has been met. If it is less than or equal to the preset minimum tolerance, or the maximum number of exchanges has been reached, it means that the configuration with the preset chemical short-range order characteristics has been successfully obtained. If the convergence condition is not met, the exchange is repeated based on the current configuration, and the calculation is iterated until the convergence condition is met, and the final configuration is successfully obtained.

[0077] Therefore, by setting arbitrary target parameters and iterative optimization algorithms, this application can obtain arbitrary chemical short-range ordered structures. Furthermore, since the calculation parameters for a single iteration are only at the millisecond level, which is millions of times longer than the time required for a single energy calculation in DFT, it can simultaneously handle structures of larger sizes, completely breaking through the bottleneck of existing methods.

[0078] Compared with existing technologies, the advantages of this application are:

[0079] (1) By setting arbitrary target parameters and evolving based on iterative algorithms, this application can obtain arbitrary chemical short-range ordered structures in a targeted manner, rather than the traditional single-path exploration driven only by energy, and can comprehensively explore all chemical short-range ordered structures.

[0080] (2) Since the calculation parameters for a single iteration are only at the millisecond level, which is millions of times longer than the time required for a single energy calculation of DFT, this application can not only obtain the required structure quickly and efficiently, but also handle larger-sized configurations due to the time cost reduction.

[0081] First, the efficiency of this application was verified. Experiments were conducted on a typical medium-entropy alloy, CrCoNi, using both the traditional DFT-MC method and the method described in this application. Due to the directional nature of the traditional method, this application uses the initial configuration of the DFT-MC method as input and the chemical short-range order parameters of the final configuration obtained after 1000 iterations of the DFT-MC method as target parameters. The method is then used to reproduce the final configuration with the same chemical short-range order parameters. The three-principal CrCoNi alloy has six chemical short-range order parameters, but based on the derivation of the Warren Cowley formula, only three parameters need to be confirmed to determine the other three. Therefore, this application locks in the parameters of each pair of principal components, and their evolution process is as follows: Figure 2 , Figure 3 , Figure 4 As shown in the figure, the blue curve represents the evolution of the chemical short-range ordering parameter over time during the iteration process when using the DFT-MC method, while the red curve represents the evolution of the chemical short-range ordering parameter over time when using the method described in this application. Figures 2 to 4The smaller figures are magnified views of the red curve. As can be seen, this application only takes 1.31 seconds to evolve from the initial state to the target parameter, while the DFT-MC method takes 102 hours to evolve to the same parameter, demonstrating the efficiency of this application.

[0082] On the other hand, to demonstrate that this application can obtain chemically ordered structures of any degree and can handle configurations of different sizes, this application still takes the CrCoNi medium-entropy alloy as an example and selects three different chemically ordered states for cross-validation:

[0083] The first type is the chemical short-range order parameter of the final configuration obtained by iterating 5000 steps using the DFT-MC method in the literature. It shows that NiNi (0.08) and CoCo (0.05) are almost randomly distributed, while CrCr (0.33) tends to be discrete.

[0084] The second type is a high-energy configuration that completely deviates from the literature DFT-MC results. Here, we assume that all element pairs are in a segregated state (Cr-Cr, Co-Co, and Ni-Ni are all set to -0.3).

[0085] The third type is set as a configuration with completely random and disordered element distribution, representing a completely disordered solid solution state.

[0086] Based on the above three short-range chemical ordering states, the typical size model of 108 atoms suitable for DFT calculations was first verified. For example... Figures 5 to 7 As shown, the three chemical short-range ordering parameters NiNi, CoCo, and CrCr all achieve reversibility between different states. Figure 5 The diagram shows the evolution from a random state to the final state of the documented DFT-MC result, taking only 1.94 seconds. The evolution from the DFT-MC final state to a random distribution state takes only 0.75 seconds. Figure 6 The diagram shows the evolution from a random state to a high-energy, chemically short-range ordered state, which contradicts the reported DFT-MC results, taking 1.36 seconds. The evolution from the high-energy state to a randomly distributed state takes only 0.28 seconds. Figure 7 A more complex evolution was demonstrated, showing that the transition from a low-energy chemically short-range ordered state obtained from DFT-MC to a high-energy chemically short-range ordered state took 1.57 seconds, while the reverse evolution process took 1.3 seconds. This proves that this application can achieve the customization of arbitrary chemically short-range ordered structures and further verifies the efficiency of this application.

[0087] Furthermore, this application also validated large-size models that are difficult to handle using the DFT-MC method. Based on the aforementioned three chemical short-range ordered states, a model of 2048 atoms was used for experiments, and the results are as follows: Figures 8 to 10As shown, large-scale models require a longer time to transition from a random distribution to a specific distribution, such as... Figure 8 As shown, the evolution from a random state to the final state of the documented DFT-MC result took the longest time, a total of 1938.35 seconds, but this is still far less than the time required for a single energy calculation of the 108-atom model in the DFT-MC method. This proves that this application breaks through the spatiotemporal scale limitations of traditional methods and can quickly and accurately construct models of arbitrary short-range ordered chemical structures.

[0088] It should be noted that this application primarily aims to protect the iterative process for constructing arbitrary short-range ordered structures. It only provides a feasible solution for the Warren-Cowley short-range ordered formulation; other variations of the Warren-Cowley formula can also achieve the same effect. For example, the following formula:

[0089]

[0090] Where m represents the m-th nearest neighbor shell of the central i-type atom. C represents the probability of finding a type j atom near the central type i atom in the m-th nearest neighbor shell; j δ represents the average concentration of type j atoms in the system, while δ ij The Kronecker function takes two integers as inputs. If the two integers are equal, the output is 1; otherwise, it is 0. In this formula, if the elements are the same, a positive value represents clustering, and a negative value represents dispersion; when the elements are different, a negative value represents clustering, and a positive value represents dispersion.

[0091] This application uses this formula as an example, employing a 108-atom model of CrCoNi alloys to transform the randomly distributed state and the chemically short-range ordered state corresponding to the high-energy structure of each principal component segregation, such as... Figure 11 As shown, this application demonstrates its applicability to various formulas describing short-range chemical ordering parameters, which can be replaced as needed for research.

[0092] The modeling method for constructing chemically short-range ordered multi-principal alloy structures provided in this application has two advantages. First, this application obtains structures with arbitrary chemically short-range ordered characteristics through directional acquisition, including single or multiple chemically ordered structures. Second, this application breaks through the spatiotemporal scale limitations of traditional methods, and can quickly obtain chemically ordered structures of arbitrary sizes.

[0093] Based on the above technical solutions, this application provides a modeling method for constructing arbitrary chemically short-range ordered multi-principal alloy structures. The method includes the following steps: First, setting the target value and convergence condition for the chemically short-range ordered parameters; then, calculating the parameter values ​​of the chemically short-range ordered parameters of the user-given initial configuration; next, calculating the difference between the parameter values ​​and the target value to obtain the initial difference; then, determining whether the initial difference satisfies the convergence condition; if yes, outputting the atomic configuration; if no, proceeding to iterative computation; wherein the iterative computation process includes: obtaining a new configuration by randomly swapping the positions of two atoms; calculating the difference between the number of parameter values ​​of the chemically short-range ordered parameters of the new configuration and the target value to obtain the difference after the swap; determining whether the difference after the swap is less than the difference before the swap; if yes, accepting the current swap; outputting the atomic configuration after the current new configuration satisfies the convergence condition; if no, rejecting the current swap, using the initial configuration as input, and re-performing the iterative computation until the current new configuration satisfies the convergence condition.

[0094] The modeling method for constructing chemically short-range ordered multi-principal alloy structures provided in this application, by setting arbitrary target parameters and evolving based on an iterative algorithm, can obtain directional acquisition of chemically short-range ordered structures, rather than the traditional single-path exploration driven solely by energy. This allows for a comprehensive exploration of all chemically short-range ordered structures. Since the calculation parameters for a single iteration are only in the millisecond range, far exceeding the time required for a single energy calculation in DFT by millions of times, this invention not only obtains the desired structure quickly and efficiently, but also, due to the time savings, can handle larger-scale configurations.

[0095] Those skilled in the art will understand that the above-described embodiments are specific examples of implementing this application, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of this application. Any person skilled in the art can make their own modifications and alterations without departing from the spirit and scope of this application; therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. A modeling method for constructing a structure of a multi-principal element alloy with arbitrary chemical short-range order, characterized by, The method comprises the following steps: setting a target value and a convergence condition of a chemical short-range order parameter; calculating a parameter value of the chemical short-range order parameter of an initial configuration given by a user; calculating a difference between the parameter value and the target value to obtain an initial difference value; judging whether the initial difference value meets the convergence condition; if yes, outputting the atomic configuration; if no, entering an iterative operation; the iterative operation comprises: obtaining a new configuration by randomly exchanging two atomic positions; calculating a difference between a parameter value of the chemical short-range order parameter of the new configuration and the target value to obtain an exchanged difference value; judging whether the exchanged difference value is less than the unexchanged difference value; if yes, accepting the current exchange; if the current new configuration meets the convergence condition, outputting the atomic configuration; if no, rejecting the current exchange, taking the initial configuration as input, and re-performing the iterative operation until the current new configuration meets the convergence condition.

2. The modeling method of constructing a multi-principal element alloy structure of arbitrary chemical short-range order according to claim 1, characterized in that, judging whether the initial difference value meets the convergence condition comprises: judging whether the initial difference value is less than or equal to a preset minimum tolerance in the convergence condition; if yes, the convergence condition is met; if no, the convergence condition is not met.

3. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, characterized in that, judging whether the initial difference value meets the convergence condition comprises: judging whether a current exchange number reaches a maximum exchange number; if yes, the convergence condition is met; if no, the convergence condition is not met.

4. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, characterized in that, outputting the atomic configuration when the current new configuration meets the convergence condition comprises: judging that the convergence condition is met and outputting the atomic configuration when the exchanged difference value of the current new configuration is less than or equal to the preset minimum tolerance in the convergence condition or the current exchange number reaches the maximum exchange number.

5. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, wherein, when the current new configuration meets the convergence condition, it indicates that a configuration with a preset chemical short-range order characteristic has been successfully obtained.

6. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, wherein, the target value is a target value of the chemical short-range order parameter corresponding to a target chemical short-range order structure.

7. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, wherein, the parameter value of the chemical short-range order parameter of the initial configuration given by the user is calculated in a Warren-Cowley parameter quantification mode.

8. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 7, characterized in that, the Warren-Cowley parameter quantification mode has the following formula: where i and j represent chemical elements, p(i|j) represents the probability of finding an atom of i within the near-neighbor distance of an atom of j, C i represents the average concentration of element i in the material.

9. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 7, wherein, the Warren-Cowley parameter quantification mode has the following formula: where i and j represent chemical elements, m represents the mth nearest-neighbor shell of the central i-type atom, represents the probability of finding a j-type atom in the vicinity of the central i-type atom in the mth nearest-neighbor shell; C j represents the average concentration of j-type atoms in the system, δ ij is the Kronecker function.

10. The modeling method of constructing a multi-principal element alloy structure with arbitrary chemical short-range order according to claim 1, wherein, calculating a difference between the parameter value and the target value to obtain an initial difference value; subtracting each target parameter from a corresponding initial parameter, summing up to obtain the initial difference value.

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