A first-principles-based method for synergistic regulation of grain boundary stability and grain boundary bonding strength

Abstract

This invention discloses a first-principles-based method for synergistic regulation of grain boundary stability and grain boundary bonding strength. The method includes the following steps: 1. Constructing a grain boundary model; 2. Screening for strongly segregating elements to obtain a stable segregation configuration; 3. Introducing a second solute element to obtain a stable multi-solute co-segregation configuration and calculating the multi-solute co-segregation energy; 4. Constructing a free surface model; 5. Calculating the grain boundary separation work and strengthening energy; 6. Establishing a synergistic regulation relationship between grain boundary stability and grain boundary bonding strength, as well as a synergistic criterion system, and screening different solute element combinations to achieve synergistic optimization of grain boundary stability and grain boundary bonding strength. This invention, by introducing multi-solute co-segregation, establishes a synergistic regulation relationship between grain boundary stability and bonding strength, enabling quantitative evaluation and optimized design of grain boundary properties, thereby providing theoretical basis and methodological support for the compositional design of high-stability, high-strength nanocrystalline alloys.

Description

Technical Field

[0001] This invention belongs to the field of computational materials science and metallic materials design technology, specifically relating to a method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations. Background Technology

[0002] As one of the most important interface structures in polycrystalline materials, grain boundaries have a decisive influence on the mechanical properties, thermal stability, and service reliability of these materials due to their structural stability and bonding strength. Especially in nanocrystalline materials, the grain boundary-dominated deformation and failure mechanisms are more prominent due to the significantly increased grain boundary volume fraction. Therefore, optimizing performance by controlling the grain boundary structure and composition has become an important direction in current materials science research.

[0003] Solute segregation is an effective means of regulating grain boundary structure and properties. Existing research shows that different solute elements have different segregation tendencies at grain boundaries, and their segregation behavior is closely related to factors such as element size difference, electronegativity difference, and electronic structure. First-principles calculations can obtain the segregation energy of solutes at different sites on the grain boundary, thus enabling quantitative prediction of the segregation behavior of a single solute. However, current research mainly focuses on the grain boundary segregation behavior of single solute elements, and the understanding of the interactions between solutes and their synergistic segregation mechanisms in multi-component systems remains insufficient. In practical engineering materials, multiple alloying elements often act simultaneously at grain boundaries, and different solutes may produce synergistic or competitive effects, i.e., co-segregation behavior. This co-segregation not only affects the distribution of solutes at grain boundaries but also significantly alters the elemental structure and bonding strength of the grain boundaries. For example, certain element combinations can significantly reduce system energy and stabilize the grain boundary structure, while other combinations may weaken the grain boundary bonding strength, leading to grain boundary embrittlement. Therefore, clarifying the co-segregation behavior and its mechanism among different solutes is crucial for achieving precise control of grain boundary properties. On the other hand, grain boundary strengthening or weakening is typically characterized by grain boundary separation work. Although existing studies have calculated the influence of some solutes on grain boundary separation work using first-principles methods, most are limited to single-solute systems, lacking a systematic analysis of grain boundary strengthening behavior under multi-solute co-segregation conditions. Furthermore, a unified quantitative model has not yet been established for the intrinsic relationship between segregation behavior and grain boundary strengthening, limiting the ability to design efficient alloys based on computational methods. In addition, existing studies typically analyze segregation energy, co-segregation energy, or grain boundary separation work separately, lacking a systematic method for coupling these three aspects, making it difficult to fundamentally reveal the intrinsic correlation mechanism between "solute segregation—solute interaction—grain boundary strengthening." This results in reliance on experience or trial-and-error methods in multi-component alloy design, leading to low efficiency and high costs.

[0004] To address the challenges of synergistic optimization of grain boundary stability and grain boundary bonding strength in existing technologies, and the lack of quantitative control methods based on the synergistic effects of multiple solutes, current research typically focuses on analyzing single solute segregation or single performance indicators. This fails to simultaneously consider both grain boundary thermodynamic stability and mechanical properties, leading to grain boundary instability or deterioration of mechanical properties under high-temperature or service conditions. Therefore, a unified methodological system is needed to characterize both grain boundary stability and bonding strength, and to achieve synergistic optimization of both.

[0005] Based on this, there is an urgent need to establish a systematic analysis method based on first principles, which takes into account the co-segregation behavior of multiple solute elements at grain boundaries and their influence on grain boundary bonding strength, and constructs a quantitative correlation between co-segregation energy and grain boundary strengthening energy, so as to achieve efficient screening and optimized design of grain boundary strengthening element combinations, and provide theoretical guidance for the development of nanocrystalline materials and high-performance alloys. Summary of the Invention

[0006] The technical problem this invention aims to solve is to address the shortcomings of existing technologies by providing a first-principles-based method for the synergistic regulation of grain boundary stability and grain boundary bonding strength. This method constructs a multi-solute co-segregation structure model, using segregation energy to characterize grain boundary thermodynamic stability and strengthening energy to characterize grain boundary bonding strength. It establishes a synergistic regulatory relationship between grain boundary stability and grain boundary bonding strength, enabling quantitative evaluation and optimized design of the influence of solute element combinations on grain boundary properties. This provides a theoretical basis and methodological support for the compositional design of high-stability, high-strength metallic materials, solving the problems of difficulty in synergistically optimizing grain boundary thermodynamic stability and grain boundary bonding strength, and the lack of quantitative evaluation and regulation methods based on multi-solute co-segregation behavior. To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations, characterized in that the method includes the following steps: Step 1: Construct a grain boundary model of metallic elements and use first-principles calculations to optimize the structure of the constructed grain boundary model to obtain a stable grain boundary structure; Step 2: Identify typical segregation sites in the grain boundary regions of the stable grain boundary structure obtained in Step 1, calculate the segregation energy of candidate solute elements at typical segregation sites using first-principles calculations, screen out strong segregation elements, and obtain stable segregation configurations through structural relaxation calculations. Step 3: Based on the stable segregation configuration obtained in Step 2, a second solute element is introduced, and structural relaxation calculations are performed using first principles to obtain a stable multi-solute co-segregation configuration, and the multi-solute co-segregation energy is calculated. Step 4: Crack the stable multi-solute cosegregation configuration obtained in Step 3 along the grain boundaries, turning the grain boundaries into free surfaces, and construct a free surface model. Step 5: Optimize the structure of the free surface model constructed in Step 4 using first principles to obtain a stable structure, calculate the energy of the free surface model, and calculate the mechanical performance parameters grain boundary separation work and strengthening energy based on this. Step 6: Use the segregation energy obtained in Step 2 to characterize the thermodynamic stability of the grain boundary, and use the strengthening energy obtained in Step 5 to characterize the grain boundary bonding strength. By comparing the changes in segregation energy and strengthening energy corresponding to different solute element combinations, establish the synergistic regulation relationship between grain boundary stability and grain boundary bonding strength, as well as the synergistic criterion system, and screen different solute element combinations to achieve synergistic optimization of grain boundary stability and grain boundary bonding strength.

[0007] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that, in step one, the grain boundary structure is determined by crystallographic orientation relationship to determine the grain interface and grain boundary normal direction, and periodic boundary conditions are adopted; the grain boundary model is a symmetric tilted grain boundary model, an asymmetric grain boundary model, or an equiaxed polycrystalline model.

[0008] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the segregation energy in step two is calculated using the following formula: ; in, E seg (A) represents the segregation energy of solute element A. This represents the total energy of the system when solute element A is located at the grain boundary. For the total energy of a pure grain boundary system, This represents the total energy of the bulk phase containing solute element A. The segregation energy is the energy of the pure metallic bulk phase; when the segregation energy is greater than zero, the solute cannot segregate to the grain boundary, and when the segregation energy is less than zero, the solute tends to segregate to the grain boundary; the threshold for strong segregation elements is defined as the candidate elements with the most negative segregation energy in the top 10%.

[0009] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the multi-solute cosegregation configuration in step three includes adjacent site combination configuration and non-adjacent site combination configuration. The adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the second site adjacent to the first solute element. The non-adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the third site which is not adjacent to the first solute element. The cosegregation energy of the multiple solutes is calculated using the following formula: ; in, E co-seg (A+B) represents the co-segregation energy when the first solute element A and the second solute element B coexist at the grain boundary, expressed in eV / atom. The total energy of the system when the first solute element A and the second solute element B coexist at the grain boundary is expressed in eV. The total energy of a pure grain boundary system is expressed in eV. The total energy of the bulk phase containing the first solute element A is expressed in eV. This represents the total energy of the bulk phase containing the second solute element B, expressed in eV. This represents the energy of the pure metallic bulk phase, expressed in eV.

[0010] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the grain boundary cracking mode in step four includes cracking path 1 where the bonds between different solutes are not broken and cracking path 2 where the bonds between different solutes are broken. In path 1, a strongly segregating element is used as the first solute element and the second solute element on the same surface, and the grain boundary cracking process does not involve the breakage of the bonds between different solutes. Path 2 refers to the bonding breakage between different solutes during the grain boundary cracking process on different surfaces, where a strongly segregating element is used as the first and second solute elements. Select two to three layers of elements in the structure files of path 1 and path 2 that are far from the free surface, fix their element coordinates, and ensure that these elements cannot be moved during the structure optimization process.

[0011] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the grain boundary separation work in step five is calculated by the following formula: WOS = ( E surface - E GB ) / A GB ; in, WOS This is the work done to separate grain boundaries, measured in eV / Ų. E GB This represents the total energy of the grain boundary model, expressed in eV / atom. E surface This represents the total energy of the model when two free surfaces are formed after grain boundary separation, expressed in eV / atom. A GB This represents the grain boundary area, in Ų. The strengthening energy is obtained by taking the negative of the difference in grain boundary separation work between the solute-containing system and the pure grain boundary system, and the calculation formula is as follows: E str =(WOS matrix -WOS A ) A GB ; in, E str To enhance energy, the unit is eV / atom, WOS matrix The grain boundary separation work of the matrix, expressed in eV / Ų, WOS A This represents the grain boundary separation work of a solute-containing system, expressed in eV / Ų. A GB The area is the grain boundary area, in Ų. E str When the value is less than zero, it indicates that the solute element increases the grain boundary separation work and enhances the grain boundary bonding strength; when E str When the value is greater than zero, it indicates that the solute element reduces the grain boundary separation work and weakens the grain boundary bonding strength.

[0012] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that, in steps one, two, three and five, the first principle is based on density functional theory, and the electronic structure is calculated using the plane wave pseudopotential method. A stable configuration is obtained through structural relaxation. During the structural relaxation process, element position optimization is allowed, and the cell parameters are optimized according to the calculation requirements. In step four, during the grain boundary cracking process, the element positions at the cell edges far from the grain boundary are fixed.

[0013] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the synergistic regulation relationship in step six is ​​as follows: segregation energy is used as an evaluation parameter for grain boundary thermodynamic stability, and strengthening energy is used as an evaluation parameter for grain boundary bonding strength; by comparing the segregation energy and strengthening energy corresponding to different solute element combinations, the correlation between segregation behavior and grain boundary strengthening behavior is established, thereby achieving synergistic evaluation of grain boundary stability and grain boundary bonding strength.

[0014] The aforementioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations is characterized in that: the synergistic criterion system in step six is ​​as follows: when the co-segregation energy of the co-segregation system formed by the first solute element and the second solute element is less than zero, and the strengthening energy is less than zero, the solute element combination is determined to have a synergistic effect of grain boundary stabilization and strengthening; wherein, a segregation energy of less than zero indicates that the solute element combination can stably segregate at the grain boundary and improve the thermodynamic stability of the grain boundary; a strengthening energy of less than zero indicates that the solute element combination can improve the grain boundary separation work and enhance the grain boundary bonding strength; a solute element combination that simultaneously satisfies both a segregation energy of less than zero and a strengthening energy of less than zero is determined as a synergistically optimized combination of grain boundary stability and grain boundary bonding strength.

[0015] The above-mentioned method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first principles is characterized in that the method is applicable to the synergistic optimization design of grain boundary stability and grain boundary bonding strength in iron-based, nickel-based, cobalt-based, or titanium-based material systems.

[0016] Compared with the prior art, the present invention has the following advantages: 1. Achieving Synergistic Regulation of Grain Boundary Thermodynamic Stability and Grain Boundary Bonding Strength: This invention provides a first-principles-based method for synergistic regulation of grain boundary stability and grain boundary bonding strength. By constructing a multi-solute co-segregation structure model, the segregation energy characterizes the grain boundary thermodynamic stability, and the strengthening energy characterizes the grain boundary bonding strength. A synergistic regulation relationship between grain boundary stability and grain boundary bonding strength is established, realizing a unified evaluation and synergistic optimization of grain boundary thermodynamic stability and mechanical properties. This method provides a theoretical basis and methodological support for the multi-component synergistic design of high-stability, high-strength metallic materials, overcoming the shortcomings of existing technologies that only focus on a single performance index and are difficult to balance grain boundary stability and bonding strength.

[0017] 2. Propose a quantitative synergistic criterion based on physical essence: This invention uses segregation energy and strengthening energy as core evaluation parameters to establish a synergistic criterion system of "segregation energy less than zero and strengthening energy less than zero", so as to achieve a unified evaluation of grain boundary stabilization effect and strengthening effect. This criterion has clear physical meaning and calculability, and can realize quantitative comparison and efficient screening of different solute element combinations, thereby improving the pertinence and reliability of material design.

[0018] 3. Introducing a multi-solute co-segregation mechanism to improve the degree of freedom in grain boundary regulation: This invention constructs a multi-solute co-segregation structural model and systematically considers the synergistic effect between different solute elements. Compared with the traditional single-solute segregation analysis method, it can more realistically reflect the co-segregation behavior of solute elements in actual multi-component alloy systems, thereby expanding the design space for synergistic regulation of grain boundary structure and properties.

[0019] 4. Achieving a direct correlation between element-scale structural behavior and grain boundary performance: Based on first-principles calculations, this invention directly obtains the segregation behavior of solute elements at grain boundaries and its influence on grain boundary separation behavior, and establishes the correlation between segregation energy, grain boundary separation work and strengthening energy. This enables quantitative analysis from element-scale structural characteristics to grain boundary performance regulation, improving the theoretical depth and predictive ability of the method.

[0020] 5. Excellent versatility and engineering application value: This invention is applicable to iron-based materials, nickel-based materials, cobalt-based materials, titanium-based materials, and other transition metal material systems, and can be extended to multi-component alloy systems. This method can be used for composition optimization and performance design of high-stability, high-strength nanocrystalline alloys, ultrafine-grained alloys, and multi-component alloy materials. By screening solute element combinations with synergistic effects of grain boundary stabilization and strengthening, the stability of grain boundary structure and mechanical properties can be improved simultaneously. It has important engineering application value for the development of high-performance metal materials and the optimization of service performance.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the grain boundary structure model, segregation site distribution, and grain boundary cracking constructed in Embodiment 1 of the present invention.

[0023] Figure 2 This is a schematic diagram showing the synergistic relationship between grain boundary segregation energy and strengthening energy in Embodiment 1 of the present invention.

[0024] Figure 3 This is a schematic diagram comparing the separation work of path 1 and path 2 in Embodiment 1 of the present invention.

[0025] Figure 4 This is a schematic diagram comparing the enhancement energy of path 1 and the enhancement energy of path 2 in Embodiment 1 of the present invention. Detailed Implementation

[0026] Example 1 This embodiment illustrates the specific implementation process of a first-principles-based method for synergistic regulation of grain boundary stability and grain boundary bonding strength in an iron-based Σ5(310) grain boundary system, including the following steps: Step 1: A body-centered cubic iron Σ5(310) symmetric tilted grain boundary model was constructed using ATOMSK software, with the grain boundary normal in the

[310] direction. Periodic boundary conditions were applied in the grain boundary direction. Then, the constructed grain boundary model was optimized using first-principles calculations to obtain a stable grain boundary structure. The plane wave cutoff energy was set to 500 eV. The k-point mesh was sampled using the Monkhorst-Pack method with a value of 7×7×3. Step 2: Identify typical segregation sites in the grain boundary regions of the stable grain boundary structures obtained in Step 1. The Σ5(310) grain boundary has four segregation sites, see... Figure 1 For single solute segregation, the four sites are equivalent. 3d-5d transition metal elements are selected as candidate solute elements. The segregation energy of the candidate solute elements at typical segregation sites is calculated using first principles. Strong segregation elements are screened out. Stable segregation configurations are obtained through structural relaxation calculations. The segregation energy is calculated using the following formula: ; in, E seg (A) represents the segregation energy of solute element A. This represents the total energy of the system when solute element A is located at the grain boundary. For the total energy of a pure grain boundary system, This represents the total energy of the bulk phase containing solute element A. The segregation energy represents the energy of the pure metallic bulk phase. When the segregation energy is greater than zero, the solute cannot segregate to the grain boundaries; when the segregation energy is less than zero, the solute tends to segregate to the grain boundaries. The threshold for strong segregation elements is defined as the candidate elements with the most negative segregation energy in the top 10%. The calculation parameters are as follows: the plane wave cutoff energy is set to 500 eV; the k-point mesh is sampled using the Monkhorst-Pack method with a value of 7×7×3. The results are shown in […]. Figure 2 ,from Figure 2 As can be seen, the criterion for determining the 10% of elements with the most negative segregation energy is approximately -1.3 eV / atom. Metallic yttrium (element symbol Y) has the most negative segregation energy, reaching -1.87 eV / atom, and belongs to the typical strong segregation elements. Step 3: Based on the stable segregation configuration obtained in Step 2, i.e., based on Y occupying grain boundary site 1, a second solute element is introduced. The second solute element is a transition metal element. Considering that the solute-solute interaction between adjacent segregation sites is stronger, the co-segregation behavior of adjacent sites is considered here, and the structural relaxation calculation is performed using first principles to obtain a stable multi-solute co-segregation configuration. In all structural optimization processes, the key parameters energy cutoff, k-point grid, convergence criterion, and cross-correlation function are kept the same. The relaxation of elements, cell shape, and cell volume is allowed during the structural optimization process. For magnetic elements, an initial magnetic moment of 2 is set, and the multi-solute co-segregation energy is calculated. Multi-solute cosegregation configurations include adjacent site combination configurations and non-adjacent site combination configurations; The adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the second site adjacent to the first solute element. The non-adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the third site which is not adjacent to the first solute element. The cosegregation energy of the multiple solutes is calculated using the following formula: ; in, E co-seg (A+B) represents the co-segregation energy when the first solute element A and the second solute element B coexist at the grain boundary, with units of eV / atom. The total energy of the system when the first solute element A and the second solute element B coexist at the grain boundary is expressed in eV. The total energy of a pure grain boundary system is expressed in eV. The total energy of the bulk phase containing the first solute element A is expressed in eV. This represents the total energy of the bulk phase containing the second solute element B, expressed in eV. This represents the energy of a pure metallic bulk phase, expressed in eV. Step 4: Crack the stable multi-solute co-segregation configuration obtained in Step 3 along the grain boundaries, turning the grain boundaries into free surfaces, and construct a free surface model. The specific process is as follows: Step 401: Along the Z-axis, divide the unit cell into two parts along the grain boundary plane: 0-0.5Z and 0.5Z-1.0Z. Fix the element coordinates of the lower half (0-0.5Z) and move the element coordinates of the upper half upwards by 0-10 Å. Step 402: The cracking behavior is divided into path 1 and path 2. Path 1 refers to solute 1 (the first solute element) and solute 2 (the second solute element) being on the same side during the cracking process, and the cracking process does not involve the breaking of bonds between solute 1 and solute 2. Path 2 refers to solute 1 and solute 2 being on different sides during the cracking process, and the bonds between solute 1 and solute 2 breaking during the cracking process; see... Figure 1 ; Step 5: Optimize the free surface model constructed in Step 4 using first-principles calculations to obtain a stable structure. Calculate the energy of the free surface model and, based on this, calculate the mechanical property parameters: grain boundary separation work and strengthening energy. The specific process is as follows: Step 501: Fix the elements in the top and bottom 2-3 layers, fix the cell shape and volume, and only optimize the element coordinates in the middle part; Step 502: Structural optimization process at different stages of the cracking process, with the same energy, convergence criteria, and k-point density settings.

[0027] Step 503: Calculate the complete separation energy-separation distance curve for a small number of elements. It is found that when the grain boundary separation distance is about 4-6 Å, the grain boundary has separated into a surface. The elemental interaction between the upper and lower surfaces is very weak. It can be considered that the grain boundary has cracked. Step 504: For solutes other than the test element, only the energy required to achieve a separation distance of 10 Å needs to be calculated, which is used to calculate the separation work and enhancement energy.

[0028] Step 505: Based on the optimized stable structure, calculate the grain boundary separation work, which characterizes the energy required for grain boundary separation into a free surface. Calculate the strengthening energy, defined by the difference in grain boundary separation work between the solute-containing system and the pure grain boundary system, which characterizes the effect of the solute on the grain boundary bonding strength. The grain boundary separation work is calculated using the following formula: WOS = ( E surface - E GB ) / A GB ; in, WOS This is the work done to separate grain boundaries, measured in eV / Ų. E GB This represents the total energy of the grain boundary model, expressed in eV. E surface This represents the total energy of the model when two free surfaces are formed after grain boundary separation, expressed in eV. A GB This represents the grain boundary area, in Ų. The strengthening energy is obtained by taking the negative of the difference in grain boundary separation work between the solute-containing system and the pure grain boundary system, and the calculation formula is as follows: E str =(WOS matrix -WOS A ) A GB ; in, E str To enhance energy, the unit is eV / atom, WOS matrix The grain boundary separation work of the matrix, expressed in eV / Ų, WOS A This represents the grain boundary separation work of a solute-containing system, expressed in eV / Ų. A GB The area is the grain boundary area, in Ų. E str When the value is less than zero, it indicates that the solute element increases the grain boundary separation work and enhances the grain boundary bonding strength; when E strWhen the value is greater than zero, it indicates that the solute element reduces the grain boundary separation work and weakens the grain boundary bonding strength; Step Six: Using the segregation energy obtained in Step Two to characterize the thermodynamic stability of grain boundaries, and the strengthening energy obtained in Step Five to characterize the grain boundary bonding strength, by comparing the changes in segregation energy and strengthening energy corresponding to different solute element combinations, a synergistic regulatory relationship between grain boundary stability and grain boundary bonding strength, as well as a synergistic criterion system, is established. Different solute element combinations are then screened to achieve synergistic optimization of grain boundary stability and grain boundary bonding strength. Specifically: Rare earth element Y exhibits a significant negative segregation energy at grain boundary site 1, indicating that it can effectively stabilize the grain boundary structure; however, rare earth element Y also exhibits a corrected grain boundary strengthening energy at grain boundary site 1, indicating that it produces a grain boundary embrittlement effect. When a transition metal element is introduced, the strengthening energy of the two-solute system is significantly reduced, the grain boundary separation work is increased, and the grain boundary bonding strength is enhanced. The addition of the second solute element significantly improves the grain boundary bonding performance. When some transition metal elements are introduced, the co-segregation energy of the two solute system is significantly reduced, for example... Figure 2 The hollow symbol to the left of the vertical dashed line is typically a Y-Hf system, indicating that Y and these elements promote segregation and improve grain boundary stability. When other transition metal elements are introduced, the co-segregation energy of the two solute system actually increases, such as... Figure 2 The hollow symbol to the right of the vertical dashed line indicates that Y and these elements mutually inhibit segregation and reduce grain boundary stability; When both the segregation energy and the strengthening energy are less than zero, it indicates that the combination of solute elements can achieve a synergistic improvement in grain boundary stability and bonding strength. The fitting curves of segregation energy and strengthening energy for the two-solute co-segregation system are as follows: Strengthening energy = 0.23 × cosegregation energy - 0.08 Based on the above criteria, different combinations of solute elements were screened, and it was determined that the combinations of Y-Hf, Y-Mo, YW, and Y-Os solute elements simultaneously possess significantly low segregation energy and strengthening energy in ferrograin boundaries, providing an optimal solution for achieving highly stable and high-strength grain boundaries.

[0029] This embodiment is also applicable to the synergistic optimization design of grain boundary stability and grain boundary bonding strength in iron-based, nickel-based, cobalt-based, or titanium-based material systems.

[0030] Figure 1 This embodiment shows the grain boundary segregation model and grain boundary cracking model. The left side represents the grain boundary segregation model, the middle side represents grain boundary cracking along path 1, and the right side represents grain boundary cracking along path 2. The gray elements represent the matrix iron element, and the black elements represent the solute elements. Solute 1 represents the first solute element, and solute 2 represents the second solute element. Figure 1 As can be seen, solute 1 and solute 2 co-segregate at grain boundary sites 1 and 2. When the grain boundary cracks along path 1, solute 1 and solute 2 are on the same surface, and the interaction between solute 1 and solute 2 does not significantly affect the grain boundary cracking behavior. When the grain boundary cracks along path 2, solute 1 and solute 2 are on different surfaces, and the interaction between solute 1 and solute 2 will significantly affect the grain boundary cracking behavior.

[0031] Figure 2 To compare the evolution of segregation energy and strengthening energy in single-solute and two-solute systems, from... Figure 2 As can be seen, the segregation energy and strengthening energy of the single-solute system and the two-solute system are mutually exclusive. The main difference is that the slope of the strengthening energy-segregation energy of the two-solute system is flatter. Compared with Y, most solutes have more negative segregation energy and strengthening energy after co-segregation with Y, indicating that co-segregation of two solutes significantly enhances the grain boundary bonding performance while maintaining the strong stabilization effect of Y.

[0032] Figure 3 To compare the separation work of grain boundaries in a two-solute system along path 1 and along path 2, from... Figure 3 It can be seen that the separation work is greater when the grain boundary cracks along path 2, indicating that more energy is required for the grain boundary to crack along path 2, and the grain boundary is less likely to crack along path 2.

[0033] Figure 4 To compare the strengthening energy of grain boundaries cracking along path 1 and grain boundaries cracking along path 2 in a two-solute system, from... Figure 4 It can be seen that the strengthening energy when the grain boundary cracks along path 2 is more negative, and there is a negative value, indicating that the grain boundary is less likely to crack along path 2. Y in the grain boundary causes the grain boundary to become brittle, but the co-segregation of other solutes with Y significantly improves the grain boundary brittleness.

[0034] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Any simple modifications, alterations, and equivalent changes made to the above embodiments based on the inventive essence shall still fall within the protection scope of the present invention.

Claims

1. A method for synergistically regulating grain boundary stability and grain boundary cohesive strength based on first principles, characterized in that, The method includes the following steps: Step 1: Construct a grain boundary model of metallic elements and use first-principles calculations to optimize the structure of the constructed grain boundary model to obtain a stable grain boundary structure; Step 2: Identify typical segregation sites in the grain boundary regions of the stable grain boundary structure obtained in Step 1, calculate the segregation energy of candidate solute elements at typical segregation sites using first-principles calculations, screen out strong segregation elements, and obtain stable segregation configurations through structural relaxation calculations. Step 3: Based on the stable segregation configuration obtained in Step 2, a second solute element is introduced, and structural relaxation calculations are performed using first principles to obtain a stable multi-solute co-segregation configuration, and the multi-solute co-segregation energy is calculated. Step 4: Crack the stable multi-solute cosegregation configuration obtained in Step 3 along the grain boundaries, turning the grain boundaries into free surfaces, and construct a free surface model. Step 5: Optimize the structure of the free surface model constructed in Step 4 using first principles to obtain a stable structure, calculate the energy of the free surface model, and calculate the mechanical performance parameters grain boundary separation work and strengthening energy based on this. Step 6: Use the segregation energy obtained in Step 2 to characterize the thermodynamic stability of the grain boundary, and use the strengthening energy obtained in Step 5 to characterize the grain boundary bonding strength. By comparing the changes in segregation energy and strengthening energy corresponding to different solute element combinations, establish the synergistic regulation relationship between grain boundary stability and grain boundary bonding strength, as well as the synergistic criterion system, and screen different solute element combinations to achieve synergistic optimization of grain boundary stability and grain boundary bonding strength.

2. The method of claim 1, wherein the method is characterized by, In step one, the grain boundary structure is determined by crystallographic orientation relationships to determine the grain interface and grain boundary normal direction, and periodic boundary conditions are adopted; the grain boundary model is a symmetric tilted grain boundary model, an asymmetric grain boundary model, or an equiaxed polycrystalline model.

3. The method of claim 1, wherein the method is characterized by, The segregation energy mentioned in step two is calculated using the following formula: ； wherein, E seg (A) is the segregation energy of solute element A, is the total energy of the system when solute element A is located at the grain boundary, is the total energy of the pure grain boundary system, is the total energy of the body phase containing solute element A, is the energy of the pure metal body phase; when the segregation energy is greater than zero, the solute cannot segregate to the grain boundary, and when the segregation energy is less than zero, the solute tends to segregate to the grain boundary; the threshold positioning of the strong segregation element is the 10% candidate element with the most negative segregation energy.

4. The method of claim 1, wherein the method is characterized by, The multi-solute cosegregation configurations mentioned in step three include adjacent site combination configurations and non-adjacent site combination configurations; The adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the second site adjacent to the first solute element. The non-adjacent site combination configuration is a co-segregation configuration formed by a strong segregating element occupying the first solute element as the first solute element and the second solute element occupying the third site which is not adjacent to the first solute element. The cosegregation energy of the multiple solutes is calculated using the following formula: ； wherein, E co-seg (A+B) is the energy of the co-segregation of the first solute element A and the second solute element B in the grain boundary, in eV / atom, is the total energy of the system when the first solute element A and the second solute element B coexist in the grain boundary, in eV, is the total energy of the pure grain boundary system, in eV, is the total energy of the body phase containing the first solute element A, in eV, is the total energy of the body phase containing the second solute element B, in eV, is the energy of the pure metal body phase, in eV.

5. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that, The grain boundary cracking modes described in step four include cracking path 1, where the bonds between different solutes are not broken, and cracking path 2, where the bonds between different solutes are broken. In path 1, a strongly segregating element is used as the first solute element and the second solute element on the same surface, and the grain boundary cracking process does not involve the breakage of the bonds between different solutes. Path 2 refers to the bonding breakage between different solutes during the grain boundary cracking process on different surfaces, where a strongly segregating element is used as the first and second solute elements. Select two to three layers of elements in the structure files of path 1 and path 2 that are far from the free surface, fix their element coordinates, and ensure that these elements cannot be moved during the structure optimization process.

6. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that, The grain boundary separation work mentioned in step five is calculated using the following formula: WOS =（ E surface - E GB ） / A GB ； in, WOS This is the work done to separate grain boundaries, measured in eV / Ų. E GB This represents the total energy of the grain boundary model, expressed in eV. E surface This represents the total energy of the model when two free surfaces are formed after grain boundary separation, expressed in eV. A GB This represents the grain boundary area, in Ų. The strengthening energy is obtained by taking the negative of the difference in grain boundary separation work between the solute-containing system and the pure grain boundary system, and the calculation formula is as follows: E str =(WOS matrix -WOS A ) A GB ; in, E str To enhance energy, the unit is eV / atom, WOS matrix The grain boundary separation work of the matrix, expressed in eV / Ų, WOS A This represents the grain boundary separation work of a solute-containing system, expressed in eV / Ų. A GB The area is the grain boundary area, in Ų. E str When the value is less than zero, it indicates that the solute element increases the grain boundary separation work and enhances the grain boundary bonding strength; when E str When the value is greater than zero, it indicates that the solute element reduces the grain boundary separation work and weakens the grain boundary bonding strength.

7. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that, In steps one, two, three, and five, the first principle is based on density functional theory, using the plane wave pseudopotential method to calculate the electronic structure, and obtaining a stable configuration through structural relaxation. During the structural relaxation process, element position optimization is allowed, and cell parameters are optimized according to calculation needs. In step four, during the grain boundary cracking process, the element positions at the cell edges far from the grain boundary are fixed.

8. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that, The synergistic regulation relationship described in step six is ​​as follows: segregation energy is used as the evaluation parameter for the thermodynamic stability of grain boundaries, and strengthening energy is used as the evaluation parameter for the grain boundary bonding strength; by comparing the segregation energy and strengthening energy corresponding to different solute element combinations, the correlation between segregation behavior and grain boundary strengthening behavior is established, thereby achieving a synergistic evaluation of grain boundary stability and grain boundary bonding strength.

9. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that: The synergistic criterion system described in step six is ​​as follows: when the cosegregation energy of the cosegregation system formed by the first solute element and the second solute element is less than zero, and the strengthening energy is less than zero, the solute element combination is determined to have a synergistic effect of grain boundary stabilization and strengthening; wherein, a segregation energy of less than zero indicates that the solute element combination can stably segregate at the grain boundary and improve the thermodynamic stability of the grain boundary; a strengthening energy of less than zero indicates that the solute element combination can improve the grain boundary separation work and enhance the grain boundary bonding strength; a solute element combination that simultaneously satisfies both a segregation energy of less than zero and a strengthening energy of less than zero is determined as a synergistic optimization combination of grain boundary stability and grain boundary bonding strength.

10. The method for synergistic regulation of grain boundary stability and grain boundary bonding strength based on first-principles calculations according to claim 1, characterized in that, The method is applicable to the synergistic optimization design of grain boundary stability and grain boundary bonding strength in iron-based, nickel-based, cobalt-based, or titanium-based material systems.

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