Atomic model generation method, program, material design support method and material design method

Abstract

To provide an atomic model generation method capable of easily generating an atomic model with random grain boundary, a program, a material design support method, and a material design method.SOLUTION: The atomic model generation method generates an atomic model with random grain boundary by atomic simulation. The atomic model generation method includes: an initial atomic model preparation process for preparing two initial atomic models including monocrystal atomic model; a first atomic model generation process for rotating the two initial atomic models and then joining the monocrystal atomic models to thereby generate a first atomic model including a junction interface; a second atomic model generation process for retaining the first atomic model at a retention temperature which is equal to or higher than amorphous-processing temperature of the first atomic model and equal to or lower than a prescribed temperature not exceeding the melting point of the first atomic model, thereby shifting the junction interface to random grain boundary and generating a second atomic model including random grain boundary; and a cooling process for cooling the second atomic model to a cooling temperature which is lower than the amorphous-processing temperature of the first atomic model.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present disclosure relates to an atomic model generation method, a program, a materials design support method, and a materials design method. [Background technology]

[0002] When developing practical materials, it is important to clarify the mechanisms of the materials. In practical materials, materials are not designed to intentionally include twin boundaries, which are typical coincidence boundaries, or to easily induce deformation twins. Therefore, coincidence boundaries are rarely observed in practical materials. In other words, the majority of grain boundaries in practical materials can generally be said to be random grain boundaries that do not correspond to coincidence boundaries. Furthermore, even in practical materials that contain twins and deformation twins, random grain boundaries that do not correspond to coincidence boundaries are inevitably included.

[0003] Therefore, understanding the properties of random grain boundaries is important when developing practical materials. However, even when applying cutting-edge physical analysis methods to practical materials, it is extremely difficult to precisely analyze the grain boundary structure, i.e., the atomic coordinates that make up the grain boundaries.

[0004] On the other hand, in the field of computational materials science, there have been remarkable advances in hardware and software in recent years, and the environment for performing atomistic simulations has been improved. Therefore, attempts are being made to understand the properties of grain boundaries by utilizing atomistic simulations.

[0005] Specifically, analysis of grain boundary segregation or grain boundary strength of actual materials has been conducted focusing on high-energy coincidence grain boundaries. This is because high-energy coincidence grain boundaries have similar energies to high-energy random grain boundaries and are likely to show similar trends in grain boundary segregation or grain boundary strength. Furthermore, the use of a coincidence grain boundary model makes it easy to organize the characteristics of the grain boundaries of materials, and its high symmetry allows for a small model size, thereby reducing the computational load. For example, Patent Document 1 discloses a method for generating a coincidence grain boundary model. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Laid-Open No. 2005-11328 Summary of the Invention [Problem to be solved by the invention]

[0007] Here, high-energy random grain boundaries have energy 10 to 20 percent higher than their corresponding high-energy grain boundaries, and there is a difference in energy values. As mentioned above, analysis of random grain boundaries is considered important when analyzing grain boundaries in actual materials. However, analysis of random grain boundaries requires a large computational load and the burden of deriving statistically guaranteed data. For this reason, modeling and analysis of random grain boundaries has rarely been performed in the past.

[0008] In view of the above circumstances, an object of the present disclosure is to provide an atomic model generation method, a program, a materials design support method, and a materials design method that can easily generate an atomic model having random grain boundaries. [Means for solving the problem]

[0009] (1) An atomic model generation method according to an embodiment of the present disclosure includes: 1. An atomic model generation method for generating an atomic model having random grain boundaries in an atomic simulation, comprising: an initial atomic model preparation step of preparing two initial atomic models each having a single crystal atomic model; a first atomic model generating step of rotating the two initial atomic models and then bonding the single crystal atomic models to generate a first atomic model including a bonding interface; a second atomic model generating step of holding the first atomic model at a holding temperature that is equal to or higher than the amorphous temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonding interface to a random grain boundary and generating a second atomic model having a random grain boundary; and a cooling step of cooling the second atomic model to a cooling temperature that is lower than the amorphous temperature of the first atomic model.

[0010] (2) As one embodiment of the present disclosure, in (1), The method further includes a first element arranging step of arranging at least one of substitutional elements and interstitial elements in at least one of the single crystal atomic models contained in the initial atomic model.

[0011] (3) As an embodiment of the present disclosure, in (1) or (2), The method further includes a first lattice defect arranging step of arranging one or more types of lattice defects in at least one of the single-crystal atomic models contained in the initial atomic model.

[0012] (4) As an embodiment of the present disclosure, in any one of (1) to (3), The method further includes a modification step of modifying at least one of the initial atomic model, the first atomic model, and the second atomic model.

[0013] (5) As an embodiment of the present disclosure, in any one of (1) to (4), The method further includes a second element arrangement step of arranging at least one of substitutional elements and interstitial elements in the second atomic model after the second atomic model generation step and before or after the cooling step.

[0014] (6) As an embodiment of the present disclosure, in any one of (1) to (5), The method further includes a second lattice defect arranging step of arranging one or more types of lattice defects in the second atomic model after the second atomic model generating step and before or after the cooling step.

[0015] (7) A program according to an embodiment of the present disclosure includes: In order to generate an atomic model having random grain boundaries in an atomic simulation, a computer that executes the atomic simulation is an initial atomic model preparation step of preparing two initial atomic models each having a single crystal atomic model; a first atomic model generating step of rotating the two initial atomic models and then bonding the single crystal atomic models to generate a first atomic model including a bonding interface; a second atomic model generating step of holding the first atomic model at a holding temperature that is equal to or higher than the amorphous temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonding interface to a random grain boundary and generating a second atomic model having a random grain boundary; A cooling step is performed in which the second atomic model is cooled to a cooling temperature that is lower than the amorphous temperature of the first atomic model.

[0016] (8) A materials design method according to an embodiment of the present disclosure includes: Calculating grain boundary energy of an atomic model generated by any one of the atomic model generation methods (1) to (6); evaluating the relationship between the grain boundary energy and material properties; and outputting design guidelines for the material based on the evaluation.

[0017] (9) A material design method according to an embodiment of the present disclosure includes: (8) Design the material according to the design guidelines for the material output by the material design support method.

[0018] (10) As an embodiment of the present disclosure, in any one of (1) to (6), A force field utilizing machine learning is used in the atomic simulation, and the force field is generated using training data incorporating data on the amorphization temperature. [Effects of the Invention]

[0019] According to the present disclosure, it is possible to provide an atomic model generation method, a program, a materials design support method, and a materials design method that can easily generate an atomic model having random grain boundaries. [Brief explanation of the drawings]

[0020] [Figure 1] FIG. 1 is a diagram for explaining the formation of grain boundaries in this embodiment. [Figure 2] FIG. 2 is a flowchart illustrating the processing steps of an atomic model generation method according to one embodiment of the present disclosure. [Figure 3] FIG. 3 is a diagram illustrating an example of the configuration of an atomic model generating device. [Figure 4] FIG. 4 is a diagram illustrating the grain boundary structure of the atomic model to be evaluated. [Figure 5] FIG. 5 is a diagram illustrating the grain boundary structure of the atomic model to be evaluated. [Figure 6] FIG. 6 is a diagram illustrating the grain boundary structure of the atomic model to be evaluated. [Figure 7] FIG. 7 is a diagram illustrating the grain boundary structure of the atomic model to be evaluated. DETAILED DESCRIPTION OF THE INVENTION

[0021] Hereinafter, an atomic model generation method, a program, a materials design support method, and a materials design method according to embodiments of the present disclosure will be described with reference to the drawings.

[0022] The present inventors have thoroughly investigated methods for generating atomic models with random grain boundaries in atomic simulations and have completed an atomic model generation method. In the atomic model generation method according to this embodiment, which will be described below, two initial atomic models each having a single-crystal (perfect crystal) atomic model are first prepared. The two initial atomic models are then rotated and the single-crystal atomic models are bonded together to form a bonded interface. Heat treatment at an appropriate heat treatment temperature can transition the bonded interface to a random grain boundary.

[0023] First Embodiment The atomic model generation method includes an initial atomic model preparation step, a first atomic model generation step, and a second atomic model generation step. The atomic model generation method according to the first embodiment further includes a cooling step. Each step is performed in an atomic simulation. The initial atomic model preparation step prepares two initial atomic models each having a single-crystal atomic model. The first atomic model generation step rotates the two initial atomic models and then bonds the single-crystal atomic models to generate a first atomic model including a bonded interface. The second atomic model generation step holds the first atomic model at a holding temperature that is equal to or higher than the amorphization temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonded interface to a random grain boundary and generating a second atomic model having a random grain boundary. The cooling step cools the second atomic model to a cooling temperature lower than the amorphization temperature of the first atomic model. The atomic simulation in which the atomic model generation method according to this embodiment is performed, an apparatus for performing the atomic simulation, and each step are described below.

[0024] (Atomic Simulation) Atomic simulation is a numerical calculation method that enables direct handling of discrete atoms, as typified by first-principles calculations or molecular dynamics calculations. In the materials field, general-purpose software capable of performing atomic simulations has been developed, allowing various boundary conditions, etc., to be freely selected and set in atomic simulations. Free software capable of performing atomic simulations, such as Quantum Espresso and LAMMPS, has been released. Therefore, the atomic model generation method according to this embodiment can be performed using software capable of performing atomic simulations. In this embodiment, the free software AtomEye was used for the visualizations shown in FIGS. 4 to 7. Furthermore, the device (atomic model generation device) that executes the atomic model generation method according to this embodiment may be a device capable of installing such software, such as a computer. For example, a commercially available general-purpose computer may be used. The computer includes, for example, a storage device such as a memory and a hard disk drive, an arithmetic unit (processor), and an input / output device. The atomic simulation (processing of the atomic model generation method) may be performed by a processor. Furthermore, data (such as information about the initial atomic model, described below) and programs required for processing the atomic model generation method may be stored in a storage device. Furthermore, the execution instructions for the atomic model generation method and the output of the results (for example, design guidelines described below) may be realized by an input / output device. The computer may be a computer with high processing power, such as a supercomputer or a quantum computer. The program may cause the computer that executes the atomic simulation to execute each step in order to generate an atomic model having random grain boundaries by the atomic simulation.

[0025] In atomic simulation, the force field of each atom is calculated under set boundary conditions using an atomic model generated by the atomic model generation method. In atomic simulation, static analysis, which performs structural optimization of the atomic model generated by the atomic model generation method, and dynamic analysis, which solves the equations of motion, are possible. Furthermore, based on information obtained by dynamic analysis, the statically stable structure, dynamically stable structure, and dynamic process of the atomic model generated by the atomic model generation method can be analyzed. Here, unless otherwise specified, the atomic model generated by the atomic model generation method refers to the final atomic model. In this embodiment, the atomic model generated by the atomic model generation method mainly refers to the second atomic model cooled by the cooling process.

[0026] In atomic simulations, important force fields are derived from interatomic interactions. The force field may be calculated from the energy obtained by solving the Kohn-Sham equation, which enables numerical analysis by applying density functional theory to the Schrödinger equation in first-principles calculations. Furthermore, to reduce the computational load, an interatomic potential capable of appropriately expressing the interatomic interactions may be used. Here, the interatomic potential is described, for example, by a polynomial function, with parameters set to reproduce various physical property values. To obtain a solution from the first-principles calculation, a machine learning force field, described below, may be used as the interatomic potential. Furthermore, molecular dynamics calculations may be performed directly using the energy obtained from the first-principles calculation.

[0027] In recent years, the development of force fields utilizing machine learning has been actively pursued. Neural networks, deep learning, and other machine learning techniques can be used. For example, force fields designed to be universally applicable to all elements, or force fields specialized for specific purposes, such as CHGNet (Crystal Hamiltonian Graph Neural Network) or MACE-MP, have been generated using machine learning. The quality of a force field generated by machine learning (machine learning force field) varies depending on, for example, the force field elements being trained. In the method disclosed herein, understanding the amorphization temperature is important when generating an atomic model with random grain boundaries in atomic simulation. The method disclosed herein can also utilize a force field utilizing machine learning in atomic simulation, and the quality of the force field can be improved by incorporating amorphization temperature data into the training data. In other words, while incorporating the amorphization temperature into the training data is not essential, incorporating the amorphization temperature can improve the calculation accuracy of the atomic simulation.

[0028] Furthermore, as a method for generating a force field using machine learning, a method has been considered in which new training data is added to an existing machine learning force field to efficiently generate a machine learning force field with improved functionality. Even in such a method for generating a machine learning force field, the selection of the new training data to be added is important. For example, by adding new data on the amorphization temperature based on an existing publicly available machine learning force field and the training data used to generate it, a machine learning force field that can improve the calculation accuracy of atomic simulations can be efficiently generated. In the method of the present disclosure, atomic simulations may also be performed using a machine learning force field generated in this manner.

[0029] Regardless of whether atomic simulation is performed by first-principles calculation or molecular dynamics calculation, both require an atomic model. The atomic model generation method according to this embodiment is effective for atomic simulation using either calculation method. Furthermore, in atomic simulation, various elements can be handled by selecting an appropriate force field, so the target elements (materials) are not limited to specific ones. Furthermore, in this disclosure, in atomic simulation, an atomic model is generated by the atomic model generation method, and analysis is performed using the generated atomic model. However, it is also possible for the generation of the atomic model and the analysis using the generated atomic model to be performed using different software.

[0030] (Initial atomic model preparation process) As described above, the initial atomic model preparation step is a step of preparing two initial atomic models each having a single-crystal atomic model. The initial atomic models are prepared in order to generate the first atomic model. It is important for the initial atomic models to have a single-crystal atomic model in order to easily generate random grain boundaries.

[0031] Here, the single crystal atomic model is an atomic model in which 70% or more of the atoms contained in the single crystal atomic model are crystalline. In this embodiment, the initial atomic model contains a single crystal atomic model having a periodic structure (an atomic model in which 70% or more atoms are crystalline). Here, when all atoms in the single crystal atomic model are crystalline, the single crystal atomic model is a completely crystalline atomic model. The initial atomic model only needs to have at least one single crystal atomic model. That is, the initial atomic model may be composed of only one single crystal atomic model, or may be composed of two or more single crystal atomic models joined together, or may include and be joined with atomic models other than the single crystal atomic model. However, since an increase in the number of atoms constituting the initial atomic model increases the calculation load, the number of atoms constituting the initial atomic model may be appropriately set depending on, for example, the processing power of the computer.

[0032] Here, the information on the initial atomic model is one of the initial parameters required to perform an atomic simulation, and includes, for example, information on the size, atomic species, and atomic coordinates of the initial atomic model. The information on the atomic coordinates is, for example, information on a crystallographically defined structure such as a body-centered cubic structure, a face-centered cubic structure, or a hexagonal close-packed structure. Here, the information that can be provided as the information on the initial atomic model differs depending on the atomic simulation software. The information on the initial atomic model may include, for example, information on the size, atomic species, and atomic coordinates of the initial atomic model, as well as factors that control various boundary conditions.

[0033] Furthermore, the initial atomic model can be calculated for any atomic arrangement by describing the numerical values ​​according to the specific rules defined by each atomic simulation software. Therefore, by using general-purpose atomic simulation software, atomic simulations can be easily performed without the need for complex program coding.

[0034] (First atomic model generation process) The first atomic model generation step is a step of generating a first atomic model including a bonded interface by rotating two initial atomic models and then bonding a single-crystal atomic model, as described above. By performing an appropriate heat treatment on the bonded interface generated when the two single-crystal atomic models of the initial atomic models are rotated in a predetermined direction at a predetermined angle relative to a predetermined axis and bonded, an atomic model (second atomic model) having random grain boundaries can be easily generated.

[0035] Here, the predetermined axis, the predetermined angle, and the predetermined direction may be the conditions disclosed in the above-mentioned Patent Document 1, for example.

[0036] In particular, the predetermined angle may be an angle at which a desired crystal orientation mismatch occurs at the bonding interface when the single crystal atomic models contained in the initial atomic models to be bonded are bonded together.

[0037] The initial atomic models may be rotated or translated during bonding to form grain boundaries. However, 360° rotation and one-cycle translation are excluded because they do not form grain boundaries. As shown in FIG. 1 , in this embodiment, one single-crystal atomic model (grain A) and another single-crystal atomic model (grain B) are rotated by (θ / 2) in opposite directions around a rotation axis parallel to the z-axis direction to form a grain boundary parallel to the xy plane. Here, the rotation and translation in FIG. 1 are merely examples, and the models may be rotated, for example, around the x-axis or y-axis other than the z-axis, or one of the upper and lower parts may be rotated by θ.

[0038] Furthermore, as a result of intensive research by the present inventors, it has been discovered that when joining two initial atomic models, joining them at a plane other than the close-packed plane of the single-crystal atomic model contained in the initial atomic model makes it possible to generate an atomic model having a high-energy random grain boundary with a crystal orientation misorientation of 15° or more.

[0039] Random grain boundaries with a crystal orientation misorientation of 15° or more can be considered prior austenite grain boundaries in steel materials, for example. Prior austenite grain boundaries are the starting point for intergranular fracture, and the strength of prior austenite grain boundaries is an important indicator in developing steel materials. Using this method, it becomes possible to simulate the change in strength when additive elements segregate at random grain boundaries, providing an indicator for suppressing intergranular fracture.

[0040] (First lattice defect placement step) The two initial atomic models used to generate the first atomic model may be the same or different. Furthermore, the single-crystal atomic models contained in the two initial atomic models may be the same or different. As described above, a perfect crystalline atomic model may be used as the single-crystal atomic model. However, actual materials inevitably contain lattice defects. Lattice defects include, for example, atomic vacancies, voids, gaps, cracks, dislocations, or precipitates. Therefore, considering the interaction between lattice defects and random grain boundaries is important in developing materials. The atomic model generation method according to this embodiment may further include a first lattice defect placement step. In the first lattice defect placement step, one or more types of lattice defects are placed in the crystalline portion of at least one of the single-crystal atomic models contained in the initial atomic model. The first lattice defect placement step may be performed before the second atomic model generation step, and may be performed, for example, after the first atomic model generation step. Furthermore, after the second atomic model generation step, a first lattice defect placement step may be performed before the tensile simulation is performed.

[0041] In the first lattice defect arrangement step, arranging one or more types of lattice defects may be performed by removing some atoms corresponding to the type of lattice defect from the crystalline portion of the single crystal atomic model. Here, as an example, a constraint may be set such that the lattice defects occupy less than 30% of the total volume of the single crystal atomic model. However, the constraint may be adjusted as appropriate depending on the processing power of the computer, etc.

[0042] For example, if the lattice defect is an atomic vacancy, the atomic vacancy can be placed in the single crystal atomic model by removing the atomic coordinate data corresponding to the atomic coordinate where the atomic vacancy is to be placed. Here, an atomic vacancy is a point defect where one atom is missing.

[0043] For example, when the lattice defect is an atomic vacancy cluster, the atomic vacancy cluster can be arranged by removing the atomic coordinate data (multiple adjacent atoms) corresponding to the atomic coordinates where the atomic vacancy cluster is to be arranged from the information of the single crystal atomic model. Here, the atomic vacancy cluster is formed by multiple adjacent atomic vacancies.

[0044] For example, when the lattice defect is a dislocation, the general functionality of atomistic simulation can be used to model a single dislocation or a dislocation dipole, where a dislocation is a line defect.

[0045] Furthermore, for example, if the lattice defect is a precipitate, a crystalline atomic model of the target precipitate is created, atoms constituting the single crystalline atomic model of the region corresponding to the volume of the crystalline atomic model of the precipitate are deleted to generate space, and the crystalline atomic model of the precipitate is inserted into the generated space.

[0046] (First element placement process) Furthermore, when the object of analysis is an alloy system, the atomic model generation method according to this embodiment may further include a first element placement step. The first element placement step places at least one of substitutional elements and interstitial elements in a crystalline portion of at least one single-crystal atomic model contained in the initial atomic model. The first element placement step may be performed before the second atomic model generation step, and may be performed, for example, after the first atomic model generation step. Furthermore, the first element placement step may be performed after the second atomic model generation step and before the tensile simulation is performed. When the first lattice defect placement step is performed, the order of the first element placement step and the first lattice defect placement step is not limited.

[0047] Alloys include substitutional solid solutions, interstitial solid solutions, and intermetallic compounds. In this process, a single crystal atomic model of a substitutional solid solution or an interstitial solid solution is generated. A single crystal atomic model of a substitutional solid solution is generated by replacing some atoms of a single crystal atomic model made of a pure metal, i.e., a single metal element, with atoms of one or more elements different from the elements that make up the single crystal atomic model. Also, a single crystal atomic model of an interstitial solid solution is generated by arranging (adding) atoms of one or more elements different from the elements of the single crystal atomic model to the single crystal atomic model. Interstitial solid solutions allow for arbitrary atomic positions, allowing for greater design freedom than substitutional solid solutions.

[0048] Generally, general-purpose software capable of performing atomic simulations has the functions of randomly placing elements and placing elements at energetically stable sites according to a set chemical potential. By utilizing these functions, the first element placement step can be easily realized.

[0049] (Second atomic model generation process) As described above, the second atomic model generating step is a step of holding the first atomic model at a holding temperature that is equal to or higher than the amorphization temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonding interface to a random grain boundary and generating a second atomic model having a random grain boundary. In this embodiment, the predetermined temperature that does not exceed the melting point is 90% of the melting point.

[0050] When generating an atomic model with random grain boundaries, it is important to verify the appropriate dynamic structural relaxation temperature to ensure a physically stable structure. If the holding temperature is too low, the effects of artifacts (such as noise) in the atomic model cannot be eliminated. On the other hand, if the holding temperature is too high, the atomic model may melt and not maintain its crystalline structure. For example, the set lattice defects may disappear, and the atomic model may transition to an amorphous structure or a fluid. For example, by holding the atomic model to be analyzed at different temperatures and plotting the relationship between the energy of the atomic model and the holding temperature, it is possible to identify the temperature range in which the energy of the atomic model remains stable and does not change with changes in the holding temperature.

[0051] However, it is difficult to use the above-mentioned identification method of directly calculating energy in an atomic model with random grain boundaries, which inevitably results in a large model size. Therefore, the present inventors conducted extensive research and found that an atomic model with energetically stable random grain boundaries can be generated by holding the model at a holding temperature that is equal to or higher than the amorphization temperature identified in the single-crystal atomic model and equal to or lower than 90% of the melting point. It is generally known that a single-crystal atomic model (an atomic model with 70% or more crystallinity) can evaluate appropriate physical properties even when the model size is small compared to an atomic model with many lattice defects.

[0052] First, when the holding temperature of the first atomic model is set to or above the amorphization temperature of the single-crystal atomic model contained in the initial atomic model, the atomic structure of the single-crystal atomic model is significantly disrupted not only in the grain boundary regions but also in regions of the single-crystal atomic model far from the grain boundaries. Then, by cooling the model from the holding temperature to below the amorphization temperature, the grain boundaries transition to another structure, such as an amorphous structure or a perfect crystal, resulting in a random grain boundary. Details of the amorphization temperature will be described later.

[0053] Furthermore, in order to obtain an atomic model with random grain boundaries that is appropriate from the viewpoint of energy, it is important and efficient to increase the number of atomic diffusions, i.e., to increase the holding temperature. However, if the holding temperature is too high (specifically, above the melting point), the crystalline portion will transition to a random structure. Therefore, it is important that the holding temperature for generating an atomic model with random grain boundaries is a temperature equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model. In this embodiment, as described above, the predetermined temperature that does not exceed the melting point is set to 90% of the melting point. Here, 90% is an example of an appropriate value, and it is possible to further adjust 90% (for example, set to 95%), for example, from the viewpoint of increasing the number of diffusions (efficiency).

[0054] Furthermore, in the second atomic model generation step, there is no lower limit to the time (holding time) held at the holding temperature. However, if the holding time is short, the atomic structure of the obtained atomic model may not be sufficiently relaxed, resulting in an unstable structure. Therefore, the holding time is preferably 5,000 fs or more, and more preferably 10,000 fs or more. Furthermore, there is no upper limit to the holding time in the second atomic model generation step. However, if the holding time is long, the calculation cost for obtaining the atomic model increases. Therefore, the holding time is preferably 300,000 fs or less, and more preferably 150,000 fs or less.

[0055] Furthermore, the random grain boundaries of the atomic model must have a physically stable structure. Therefore, it is preferable to define a standard grain boundary energy and evaluate the stability of the grain boundary energy of the resulting random grain boundaries. The average temperature between the amorphization temperature and the melting point is taken as the standard temperature, and the grain boundary energy obtained by maintaining the sample at the standard temperature is taken as the standard grain boundary energy. The value obtained by subtracting the standard grain boundary energy from the grain boundary energy under each condition and dividing the result by the standard grain boundary energy is taken as the energy deviation, and evaluation is performed using the energy deviation. After extensive research, the present inventors have found that a physically stable structure has an energy deviation of 2.0% or less. It is more preferable that the energy deviation be 1.5% or less.

[0056] (Amorphous temperature) Here, the amorphization temperature of the first atomic model is the temperature at which the single-crystal atomic model contained in the initial atomic model constituting the first atomic model can no longer maintain a crystalline structure at the atomic level. The crystalline structure at the atomic level is, for example, a body-centered cubic structure, a face-centered cubic structure, or a hexagonal close-packed structure. Here, the crystalline structure at the atomic level is information held by each atom in an atomic simulation, and can be calculated from the positional relationship of an atom with a group of neighboring atoms. Methods for specifying the crystalline structure at the atomic level include a method of specifying it by coordination number and common neighbor analysis (CNA).

[0057] If the single-crystal atomic model contained in the first atomic model has a crystalline structure, all atoms constituting the single-crystal atomic model are numerically classified as having a body-centered cubic structure, a face-centered cubic structure, or a hexagonal close-packed structure. Atoms that do not fit into any of these structures can be treated as amorphous atoms. However, even if the single-crystal atomic model has a crystalline structure, increasing the temperature can cause atomic positions to fluctuate due to thermal vibration, resulting in some atoms becoming amorphous. Therefore, in this embodiment, the amorphous temperature is defined as the temperature at which the number of amorphous atoms is 1% or more of the total number of atoms constituting the entire single-crystal atomic model. Here, the amorphous temperature is a temperature that can be derived by analyzing the behavior of each atom in an atomic simulation and is different from the melting point, which is a physical property value from a macroscopic perspective at which a solid changes to a liquid. Furthermore, a perfect crystal without defects is used as the atomic model when calculating the amorphous temperature.

[0058] The amorphization temperature of the first atomic model may be determined by comparing the amorphization temperatures of the two bonded single-crystal atomic models and determining the higher temperature. When lattice defects are disposed in the two bonded single-crystal atomic models, the amorphization temperature of the first atomic model may be determined using the amorphization temperature of the single-crystal atomic model before the lattice defects are disposed.

[0059] Furthermore, when less than 10 at % of substitutional or interstitial elements are arranged between two bonded single-crystal atomic models, the amorphization temperature of the first atomic model may be determined using the amorphization temperature of the single-crystal atomic model before the arrangement of the substitutional or interstitial elements. Furthermore, when 10 at % or more of substitutional or interstitial elements are arranged between two bonded single-crystal atomic models, the amorphization temperature of the first atomic model may be determined using the amorphization temperature of the single-crystal atomic model after the arrangement of the substitutional or interstitial elements.

[0060] (Melting Point) For example, the common neighbor analysis described above can quantitatively calculate the proportion of amorphous atoms in the single-crystal atomic model. Therefore, it is possible to determine the melting point. In the present disclosure, the melting point of the first atomic model is defined as the temperature at which the proportion of amorphous atoms in the single-crystal atomic model constituting the first atomic model is 99% or more.

[0061] The melting point of the first atomic model may be determined by comparing the melting points of the two bonded single-crystal atomic models and determining the lower temperature. When lattice defects are disposed in the two bonded single-crystal atomic models, the melting point of the first atomic model may be determined using the melting point of the single-crystal atomic model before the lattice defects are disposed.

[0062] Furthermore, when substitutional or interstitial elements of less than 10 at % are arranged between two bonded single-crystal atomic models, the melting point of the first atomic model may be determined using the melting point of the single-crystal atomic model before the arrangement of the substitutional or interstitial elements. Furthermore, when substitutional or interstitial elements of 10 at % or more are arranged between two bonded single-crystal atomic models, the melting point of the first atomic model may be determined using the melting point of the single-crystal atomic model after the arrangement of the substitutional or interstitial elements.

[0063] (random grain boundaries) In the present disclosure, a random grain boundary is defined as a grain boundary other than a coincidence grain boundary. Therefore, a random grain boundary includes a low-angle grain boundary. A coincidence grain boundary is generally defined by an index called the Σ value. The Σ value is defined as the reciprocal of the ratio of the volume of the unit cell of the coincidence lattice to the volume of the unit cell of the crystal lattice. The smaller the Σ value, the higher the periodicity. Therefore, if the Σ value is equal to or less than a predetermined value, it is treated as a coincidence grain boundary.

[0064] For example, a grain boundary with a Σ value of 11 or less is a coincidence grain boundary. When the Σ value is calculated, a grain boundary with a Σ value of more than 11 can be treated as a random grain boundary.

[0065] (cooling process) As described above, the cooling step is a step of cooling the second atomic model to a cooling temperature lower than the amorphous temperature of the first atomic model.

[0066] If the cooling temperature is set to a temperature equal to or higher than the amorphization temperature, the grain boundary energy may change as the holding time at the cooling temperature increases. In other words, the structure may no longer be physically stable. Therefore, the cooling temperature is set to a temperature lower than the amorphization temperature of the first atomic model. The cooling step may be performed by temperature control. In other words, the cooling rate is not limited. Here, in order to reduce calculation costs, static structural relaxation may be performed after the cooling step to minimize the energy.

[0067] FIG. 2 is a flowchart showing processing steps of an atomic model generation method according to this embodiment. The atomic model generation device may execute each step in the processing order shown in FIG. 2. That is, the initial atomic model preparation step, first atomic model generation step, first lattice defect placement step, first element placement step, second atomic model generation step, and cooling step may be executed in this order. Here, the first lattice defect placement step or the first element placement step may be omitted. FIG. 3 is a diagram showing an example configuration of an atomic model generation device. In the example of FIG. 3, the atomic model generation device is configured by a computer including an arithmetic unit, a storage device, and an input / output device. By executing a program, the arithmetic unit functions as an initial atomic model preparation unit, a first atomic model generation unit, a first lattice defect placement unit, a first element placement unit, a second atomic model generation unit, and a cooling unit. Here, the initial atomic model preparation unit executes the initial atomic model preparation step. The first atomic model generation unit executes the first atomic model generation step. The first lattice defect placement unit executes the first lattice defect placement step. The first element placement unit executes the first element placement step. The second atomic model generating unit performs the second atomic model generating step. The cooling unit performs the cooling step. Here, the first lattice defect arranging unit or the first element arranging unit may be omitted.

[0068] Second Embodiment The atomic model generation method according to the second embodiment includes a second element disposing step in addition to the steps of the first embodiment. The second element disposing step is performed after the second atomic model generation step and before or after the cooling step, and disposes at least one of substitutional elements and interstitial elements in the second atomic model.

[0069] (Second element placement process) When it is desired to simulate a state in which random grain boundaries of the second atomic model and some of the elements of the single crystal atomic model are replaced with different elements, the second element placement step is performed. At this time, the second element placement step replaces some atoms of the single crystal atomic model with atoms of one or more elements different from the elements constituting the single crystal atomic model. Also, when it is desired to simulate a state in which different elements are segregated to the random grain boundaries of the second atomic model and the elements of the single crystal atomic model, the second element placement step places (adds) atoms of one or more elements different from the elements of the single crystal atomic model.

[0070] In the atomic model generation method according to this embodiment, a second element disposing step is included after the second atomic model generation step and before or after the cooling step in the flowchart of Fig. 2. In addition, the arithmetic unit of the atomic model generation device in Fig. 3 executes a program to function as a second element disposing unit that performs the second element disposing step.

[0071] Third Embodiment The atomic model generation method according to the third embodiment includes a second lattice defect arranging step in addition to the steps of the first or second embodiment. The second lattice defect arranging step is performed after the second atomic model generation step and before or after the cooling step, and involves arranging one or more types of lattice defects in the second atomic model.

[0072] (Second lattice defect placement process) In the second lattice defect arranging step, one or more types of lattice defects are arranged in the second atomic model by the same method as in the first lattice defect arranging step.

[0073] In the atomic model generation method according to this embodiment, a second lattice defect placement step is included after the second atomic model generation step and before or after the cooling step in the flowchart of Fig. 2. In addition, the arithmetic unit of the atomic model generation device of Fig. 3 executes a program to function as a second lattice defect placement unit that performs the second lattice defect placement step. When the second element placement step and the second lattice defect placement step are performed, the order of the second element placement step and the second lattice defect placement step is not limited.

[0074] <Fourth embodiment> The atomic model generation method according to the fourth embodiment includes a transformation step in addition to the steps of the first, second, or third embodiment. The transformation step transforms at least one of the initial atomic model, the first atomic model, and the second atomic model.

[0075] (Deformation process) The deformation process is a process of performing a deformation simulation on at least one of the initial atomic model, the first atomic model, and the second atomic model. The deformation process applies stress or strain to the bonding interface (grain boundary), making it possible to express damage at random grain boundaries.

[0076] Here, damage to the random grain boundary refers to a change in the atomic density of the random grain boundary, resulting in a transition of the energy of the random grain boundary to an energetically unstable state. In other words, by performing the deformation process, the grain boundary energy can be transitioned to a higher state compared to the grain boundary energy of the random grain boundary of the second atomic model when the deformation process is not performed.

[0077] The first method for damaging random grain boundaries is to deform the bonded interface (grain boundary). When stress or strain is applied to the bonded interface, dislocations are generated at the bonded interface, which changes the atomic structure of the random grain boundary in the atomic model. This results in a damaged random grain boundary in the atomic model.

[0078] Furthermore, when the initial atomic model contains an atomic model other than the single crystal atomic model, there exists a bonded interface (referred to as a second bonded interface) other than the bonded interface that generates the random grain boundary. When stress or strain is applied to the second bonded interface, dislocations are generated, and in the process of the generated dislocations being absorbed by the bonded interface that generates the random grain boundary, a random grain boundary of the damaged atomic model is obtained.

[0079] A second method for damaging random grain boundaries is to apply stress or strain to lattice defects, which act as dislocation sources. The generated dislocations are absorbed at the interface where the random grain boundaries are formed, resulting in damaged atomic-model random grain boundaries. Examples of dislocation sources include atomic vacancy clusters (e.g., voids, gaps, cracks, or immobile dislocations).

[0080] As a third method for damaging the random grain boundary, lattice defects may be placed directly in the second atomic model in the second lattice defect placement step. By performing dynamic structural relaxation on the second atomic model after the second lattice defect placement step, it is possible to obtain an energetically stable random grain boundary in a state containing lattice defects.

[0081] In the atomic model generation method according to this embodiment, a deformation step is included in the flowchart of Fig. 2. In addition, the arithmetic unit of the atomic model generation device in Fig. 3 executes a program to function as a deformation unit that performs the deformation step.

[0082] Here, in the atomic model generation method, at least one of a static structural relaxation step and a dynamic structural relaxation step may be further performed after any of the above steps.

[0083] (Static structure relaxation process) The static structural relaxation process is a process of minimizing energy by repeatedly adjusting atomic coordinates. By performing the static structural relaxation process, the energy minimum can be obtained, and the energy in the crystal model can be uniquely identified.

[0084] (Dynamic structure relaxation process) The dynamic structural relaxation process is a process in which a state in which the energy at a finite temperature is stabilized is obtained by maintaining the temperature at that finite temperature. By performing the dynamic structural relaxation process, it is possible to obtain energy stabilization that takes into account atomic diffusion. By searching for multiple locally stable states through the dynamic structural relaxation process, it is possible to identify the state with the lowest energy.

[0085] [Material design method] In recent years, materials development has been promoted through digital transformation utilizing data science. For example, principal component analysis is performed on information obtained from physical analysis such as elemental mapping, and each element is described by a polynomial function. However, a problem generally exists in that the physical interpretation of the coefficients of such functions is difficult. To address this problem, atomic simulation using an atomic model generated by the above-mentioned atomic model generation method makes it possible to evaluate the grain boundary energy of random grain boundaries and the trap energy at random grain boundaries. In other words, a materials design support method that obtains material design guidelines by atomic simulation using an atomic model generated by the above-mentioned atomic model generation method can be realized. Furthermore, a materials design method that designs materials according to the material design guidelines output by the materials design support method can be realized.

[0086] (grain boundary energy) The grain boundary energy of a random grain boundary can be calculated by dividing the difference between the energy of a single-crystal atomic model contained in the initial atomic model of an atomic model generated by the atomic model generation method and the energy of a system into which a random grain boundary has been introduced by the grain boundary area.

[0087] (trap energy) The trap energy at the random grain boundary can be calculated by calculating the difference in grain boundary energy between the presence and absence of an added element (interstitial element or substitutional element).

[0088] As a materials design support method, the grain boundary energy of the atomic model generated by the atomic model generation method as described above is calculated, the relationship between the grain boundary energy and the material properties is evaluated, and a material design guideline can be obtained based on the evaluation. Here, the calculation of the grain boundary energy may be the calculation of at least one of the grain boundary energy and the trap energy.

[0089] For example, by comparing the energy of random grain boundaries while varying the concentration of added elements, it is possible to predict the threshold value of element concentration that is effective for stabilizing random grain boundaries, thereby obtaining a material design guideline that prevents excessive addition of elements.

[0090] Furthermore, by comparing the trapping energies of different elements, it is possible to predict which elements are preferentially trapped at random grain boundaries, thereby providing a material design guideline for eliminating elements that are harmful to grain boundaries.

[0091] Furthermore, by combining the coefficients of the principal component analysis with at least one of the grain boundary energy and the trap energy of the random grain boundary, it is possible to obtain a material design guideline as a physical interpretation. For example, the atomic model generation device may also function as a material design support device, in which the computing device executes an atomic simulation and the result of the atomic simulation corresponding to the material design guideline is output by the input / output device.

[0092] The effects of the present disclosure will be specifically described below based on examples, but the present disclosure is not limited to these examples.

[0093] Example 1 The atomic simulation was performed using the molecular dynamics calculation software LAMMPS, and a neural network-type interatomic potential capable of handling the Fe-H binary system was also used.

[0094] The first atomic model generation step in this example is as conceptually shown in Fig. 1. First, two initial atomic models were prepared by dividing a perfect crystal atomic model into two (initial atomic model preparation step). Specifically, an atomic model of pure iron having a body-centered cubic crystal structure was divided into two.

[0095] Two atomic models of pure iron (grains A and B in Figure 1) were rotated in opposite directions by the same angle (θ / 2) and then bonded to generate a first atomic model with a crystal misorientation of θ at the bonded interface (first atomic model generation process). The generated bonded interface was a symmetric twisted grain boundary of a bicrystal. The rotation axis was set to the z-axis, and the size of the first atomic model was adjusted to satisfy periodic boundary conditions in the x- and y-axis directions. To reduce the computational load, the number of atoms in the first atomic model was set to tens of thousands. The conditions for generating the first atomic model (rotation axis, rotation angle, number of atoms, crystal misorientation θ, etc.) are shown in Table 1.

[0096] [Table 1]

[0097] Next, the Nose-Huber method was applied to the resulting first-atom model, and the model was isothermally held at 300 K to achieve zero pressure under the NPT ensemble conditions (dynamic structural relaxation step). Using the LAMMPS "velocity" command, an initial velocity equivalent to 300 K was assigned, followed by the "run" command, which held the temperature at 300 K for 10,000 fs. The time step width was set to 1 fs. Dynamic structural relaxation was performed to obtain an energetically stable structure for the first-atom model. A stable structure for the first-atom model here refers to a structure in which the lattice constants of the pure iron model (initial atomic model) are changed from the arbitrarily set lattice constants to those that are energetically stable under the applied interatomic potential.

[0098] Next, the first atomic model after dynamic structural relaxation was held at the holding temperature to generate the second atomic model (second atomic model generation step). The holding temperatures are shown in Table 1. Several thousand steps were required for the temperature of the first atomic model to stabilize and reach the holding temperature. Therefore, the holding time was set to 30,000 fs.

[0099] The second atomic model was then cooled to room temperature (300 K), which is the evaluation temperature for common materials (cooling process), and static structural relaxation was performed.

[0100] The amorphization temperature and melting point of the first atomic model were calculated using the neural network interatomic potential described above. Here, the first atomic model was generated by preparing a perfect crystal (single crystal) model of pure iron (pure iron model, body-centered cubic structure) as one atomic model, dividing it, and joining it to form two atomic models. Therefore, the amorphization temperature and melting point of the pure iron model before division were used as the amorphization temperature and melting point of the first atomic model.

[0101] First, to calculate the amorphization temperature and melting point of the pure iron model, the pure iron model was held at each evaluation temperature listed in Table 2. The amorphization rate, average volume, and proportion of atoms locally having a body-centered cubic structure of the obtained pure iron model were evaluated.

[0102] [Table 2]

[0103] Here, the "compute cna" command of LAMMPS was used to calculate the proportion of atoms with a local body-centered cubic structure. The cutoff distance in the above command was the threshold value recommended by LAMMPS. That is, since the interatomic potential of pure iron has a body-centered cubic structure, the threshold value was set to 1.207 times the lattice constant of the pure iron model, 2.86 Å.

[0104] The non-crystallization rate was calculated by dividing the number of non-crystallized atoms in the pure iron model by the total number of atoms.

[0105] As shown in Table 2, the average volume gradually increased with increasing evaluation temperature of the pure iron model, and changed discontinuously between 2000K and 2100K. Furthermore, the sum of the body-centered cubic structure ratio and the non-crystallization ratio did not reach 100% at all temperatures. This shows that atoms that do not locally form a body-centered cubic lattice are not necessarily non-crystallized atoms.

[0106] As a result of the evaluation, the amorphization temperature of the pure iron model was found to be between 1000K and 1100K. A more accurate amorphization temperature could be obtained by calculating the holding temperature in increments of 1K or 0.1K, but this would increase the computational cost. Therefore, the amorphization temperature was determined by linear interpolation of the gradient of the amorphization rate between 1000K and 1100K. The obtained amorphization temperature was 1026K. The melting point was found to be between 2000K and 2100K. Similarly, using linear interpolation, the melting point was calculated to be 2093K.

[0107] The grain boundary structure and grain boundary energy of the atomic model were then evaluated. The evaluation was carried out at 300 K, which is generally considered room temperature. The atomic model after the cooling process was subjected to a dynamic structural relaxation process, in which the temperature was held at 300 K for 20,000 fs. Furthermore, the atomic model after the dynamic structural relaxation process was subjected to a static structural relaxation process for both the cell size and atomic positions of the atomic model. In the static structural relaxation process, the "minimize" command in LAMMPS was used. Here, to distinguish between the atomic model after the static structural relaxation process and the atomic model after the cooling process, the atomic model after the static structural relaxation process, which is the subject of this evaluation, is referred to as the "atomic model to be evaluated."

[0108] First, the relationship between the holding temperature in the second atomic model generation step and the grain boundary structure of the atomic model to be evaluated was evaluated. In this example, in order to analyze the grain boundary structure in detail, the crystal structure was visualized using the center symmetry parameter (CSP). CSP is a method for quantifying local symmetry based on the positional relationship between the atom of interest and its surrounding atoms. When a crystal structure is present, the value is zero, and a larger value indicates greater local disorder.

[0109] First, a structural analysis of the grain boundary was performed using an atomic model with a rotation axis of 112 and a rotation angle (θ) of 44 degrees. The first atomic model with a rotation axis of 112 and a rotation angle of 44 degrees was held at 1200 K (number 3), a holding temperature higher than the amorphization temperature of the first atomic model (pure iron model), and the atomic model to be evaluated, with the grain boundary structure shown in Figure 4, was obtained. It can be seen that random grain boundaries with a disordered atomic structure have been generated at positions 0% (bottom) and 50% (center) in the Z-axis direction.

[0110] Furthermore, as shown in Figure 5, the grain boundary structure of the atomic model to be evaluated, obtained by holding at temperatures of 300 K (number 1), 900 K (number 2), 1200 K (number 3), and 2200 K (number 7), was analyzed using an atomic model with a rotation axis of 112 and a rotation angle of 44 degrees. Here, the initial structure in Figure 5 is the grain boundary structure of the first atomic model after dynamic structural relaxation at 300 K.

[0111] In the initial structure, periodicity was observed within the grain boundaries. On the other hand, in the atomic models evaluated at holding temperatures of 300 K (number 1), 900 K (number 2), and 1200 K (number 3), no periodicity was observed within the grain boundaries. In other words, random grain boundaries were generated. Similarly, in the atomic models evaluated at holding temperatures of 1500 K (number 4), 1560 K (number 5), and 1800 K (number 6), random grain boundaries were confirmed to be generated.

[0112] Furthermore, analysis of the grain boundary structure of the atomic model evaluated at a holding temperature of 2200 K (No. 7) revealed that no grain boundaries remained on planes parallel to the xy plane, and random grain boundaries were generated irregularly. Therefore, the grain boundary structure of the atomic model at a holding temperature of 2200 K is shown in Figure 5 without separation into the yz and xy planes. Examination of the atomic structure revealed that the entire atomic model was in an amorphous state with no periodicity. It is believed that nucleation of a body-centered cubic structure occurred from the amorphous state when the holding temperature was lowered to room temperature, resulting in irregular fine grains. Therefore, although the grain boundaries were random, it was difficult to identify the grain boundary surfaces and evaluate the grain boundary energy. Therefore, No. 7 was excluded from evaluation.

[0113] As described above, it was confirmed that random grain boundaries are generated for an atomic model with a rotation axis of 112 and a rotation angle of 44 degrees by setting the holding temperature below the melting point of the first atomic model.

[0114] Next, a structural analysis of the grain boundary was performed using an atomic model with a rotation axis of 110 and a rotation angle of 30 degrees (numbers 11 to 13). As a result, the same tendency as in the atomic model with a rotation axis of 112 and a rotation angle of 44 degrees was confirmed.

[0115] Furthermore, a structural analysis of the grain boundary was carried out using an atomic model with a rotation axis of 110 and a rotation angle of 70 degrees.

[0116] An atomic model with a 110-axis rotation axis and a 70° rotation angle was held at 900 K (No. 8) and 1200 K (No. 9), resulting in the atomic model with the grain boundary structure shown in Figure 6. In the atomic model held at 900 K (No. 8), grain boundaries parallel to the xy plane were generated. The generated grain boundary structure was confirmed to have mirror symmetry with respect to the grain boundary, indicating that it could be classified as a coincidence grain boundary. Furthermore, the grain boundary of the atomic model held at 1200 K (No. 9) was wavy. In this case, the locally flat areas were coincidence grain boundaries, but the regions where the plane orientation changed had an irregular structure, partially losing periodicity. Therefore, the generated grain boundary was classified as a random grain boundary. It is believed that the holding temperature, above the amorphization temperature, provided sufficient driving force for iron atoms to overcome the energy barrier, resulting in relatively free diffusion and the formation of random grain boundaries. Analysis of the grain boundary structure of the atomic model evaluated when the holding temperature was 1560 K (number 10) revealed that it showed a similar tendency to the atomic model evaluated when the holding temperature was 1200 K (number 9).

[0117] As described above, it was confirmed that random grain boundaries can be generated for an atomic model with a rotation axis of 112 and a rotation angle of 70 degrees by setting the holding temperature to a temperature equal to or higher than the amorphization temperature of the first atomic model.

[0118] In addition, to evaluate the stability of the atomic model, the grain boundary energy of the atomic model was evaluated as follows.

[0119] The grain boundary energy (F GB ) was calculated. The grain boundary energy is defined by the following equation (1).

[0120]

number

[0121] Here, axis is the rotation axis of the initial atomic model. θ is the rotation angle of the initial atomic model (crystal orientation misorientation at the bonded interface of the first atomic model). E is the potential energy of the atomic model to be evaluated. E GB is the potential energy of the grain boundary model. E BULK is the potential energy of the perfect crystal model. N is the number of atoms in the grain boundary of the grain boundary atomic model being evaluated. M is the number of atoms in the pure iron model. A is the area of ​​the xy plane.

[0122] Here, because the periodic boundary condition is applied, the grain boundary is included at the 0% position as well as the 50% position on the z axis. Therefore, it is divided by 2A. Here, due to the characteristics of the periodic boundary condition, the 0% and 100% positions are synonymous. The grain boundary energy F of the grain boundary, which is a lattice defect, is GB In principle, takes a positive value. The larger the positive value, the more unstable the energy.

[0123] Furthermore, random grain boundaries must have a physically stable structure in order to perform valuable calculations. Therefore, to evaluate the stability of the grain boundary energy of random grain boundaries, a standard grain boundary energy was defined as described above. Specifically, the average temperature of the amorphization temperature and melting point was defined as the standard temperature, and the grain boundary energy obtained by maintaining the sample at the standard temperature was defined as the standard grain boundary energy. The energy deviation was determined by subtracting the standard grain boundary energy from the grain boundary energy under each condition and dividing the result by the standard grain boundary energy. A physically stable structure for performing valuable calculations has an energy deviation of 2.0% or less.

[0124] Here, the rotation axis and rotation angle (θ) in the first atomic model generation process, and the grain boundary energy, standard grain boundary energy, energy deviation, periodicity of the atomic structure, and grain boundary classification of the atomic model to be evaluated with different holding temperatures in the second atomic model generation process are as shown in Table 1.

[0125] In the cases of numbers 1, 2, 8, and 11, where the holding temperature is lower than the amorphization temperature of the first atomic model, it was found that diffusion across the energy barrier was difficult to occur, the energy deviation value was high, and these were unsuitable for analysis.

[0126] In addition, although the holding temperature for No. 7 was above the melting point of the first atomic model, it became amorphous as described above, and the energy deviation value was high, making it unsuitable for analysis.

[0127] Here, we checked the thickness of the random grain boundaries on the non-close-packed planes and found that the random grain boundaries on the non-close-packed planes had a thickness of more than three stacked layers, and the grain boundary energy was relatively higher than that of the random grain boundaries on the close-packed planes.

[0128] Example 2 In order to obtain design guidelines for steel materials when hydrogen penetrates them, the following evaluation was carried out. In the atomic model used to obtain the design guidelines for the materials, the two-piece pure iron model was rotated and joined in the above-mentioned atomic model generation method, and then hydrogen, an interstitial element, was placed (first element placement step).

[0129] The pure iron model was divided into two (initial atomic model preparation step), and the first atomic model was generated with a rotation axis of 112 and a rotation angle of 44 degrees (first atomic model generation step). Hydrogen atoms were added to the obtained first atomic model using the grand canonical Monte Carlo method (first element placement step). Subsequently, a dynamic structural relaxation step was performed at 300 K, followed by holding at the holding temperature (second atomic generation step), and then cooling to 300 K (cooling step). Subsequently, a dynamic structural relaxation step and a static structural relaxation step were performed at 300 K. The atomic model thus obtained was further analyzed using the LAMMPS "gcmc" command, with a chemical potential of -2.25 eV at 300 K, to obtain an atomic model with equilibrium hydrogen concentration. Here, 420,000 Monte Carlo steps were required to reach equilibrium hydrogen concentration.

[0130] The grain boundary energy of this atomic model was evaluated by the same method as in Example 1. However, because an interstitial element was added, the grain boundary energy (F GB-int ) is defined by the following equation (2).

[0131]

number

[0132] where C X is the hydrogen concentration in the first atomic model. n is the number of hydrogen atoms in the first atomic model. N is the number of iron atoms in the first atomic model. E BULK (M,H1) is the potential energy of a model in which one hydrogen atom is inserted into a perfect crystal of iron with M atoms.

[0133] Figure 7 shows the grain boundary structure of the hydrogen-doped atomic model of the evaluation target. Hydrogen is trapped in random grain boundaries with no periodicity. The grain boundary energy is 1.38 J / m 2 The energy difference between the hydrogen-loaded grain boundary and the pure iron grain boundary was 0.53 J / m 2 This value corresponds to the grain boundary segregation energy of hydrogen. By evaluating the energy difference before and after the addition of an element, it is possible to quantitatively evaluate the ease with which the added element segregates to the grain boundaries. In other words, the larger the energy difference before and after the addition of an element, the stronger the segregation can be evaluated to be.

[0134] By correlating this evaluation of segregation susceptibility, it is possible to predict the change in the amount of hydrogen trapped when, for example, the amount of carbon segregation at the grain boundaries of steel materials increases, and to obtain material design guidelines such as how to control the amount of carbon segregation at grain boundaries to suppress hydrogen embrittlement and what level of carbon segregation is necessary to suppress hydrogen trapping.

[0135] Furthermore, it is possible to calculate grain boundary strength by performing a simulation in which tensile deformation is applied to an atomic model in which elements are segregated. Based on such simulations, it is possible to search for elements that improve or decrease grain boundary strength. Furthermore, it becomes possible to predict grain boundary strength depending on the amount of segregation, and this can provide guidelines for material design.

[0136] As described above, the atomic model generation method, program, materials design support method, and materials design method according to the present embodiment can easily generate an atomic model having random grain boundaries through the above steps.

[0137] Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art would easily be able to make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included within the scope of the present disclosure. For example, the functions included in each component or step can be rearranged so as not to cause logical inconsistencies, and multiple components or steps can be combined or divided into one. The embodiments of the present disclosure can also be realized as a storage medium on which a program executed by a processor included in an apparatus is recorded. It should be understood that these are also included within the scope of the present disclosure.

[0138] Here, the device (e.g., a computer) that executes the above-described method or program may not be a single device, but may be composed of multiple devices located in multiple locations and capable of transmitting and receiving data to and from each other via a network. In other words, multiple devices connected via a network may function as a whole as a device that executes the above-described method or program. Therefore, for example, the device that executes the above-described method or program may be composed of a single computer as a hardware configuration, or may be composed of multiple computers connected via a network. When composed of multiple computers, a shared memory accessible by each computer may be used to share data or programs.

Claims

1. 1. An atomic model generation method for generating an atomic model having random grain boundaries in an atomic simulation, comprising: an initial atomic model preparation step of preparing two initial atomic models each having a single crystal atomic model; a first atomic model generating step of rotating the two initial atomic models and then bonding the single crystal atomic models to generate a first atomic model including a bonding interface; a second atomic model generating step of holding the first atomic model at a holding temperature that is equal to or higher than the amorphous temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonding interface to a random grain boundary and generating a second atomic model having a random grain boundary; a cooling step of cooling the second atomic model to a cooling temperature that is lower than the amorphous temperature of the first atomic model.

2. 2. The atomic model generating method according to claim 1, further comprising a first element arranging step of arranging at least one of substitutional elements and interstitial elements in at least one of the single-crystal atomic models contained in the initial atomic model.

3. 3. The atomic model generating method according to claim 1, further comprising a first lattice defect arranging step of arranging one or more types of lattice defects in at least one of the single-crystal atomic models contained in the initial atomic model.

4. 3. The atomic model generating method according to claim 1, further comprising a modifying step of modifying at least one of the initial atomic model, the first atomic model, and the second atomic model.

5. 3. The atomic model generation method according to claim 1, further comprising a second element arranging step of arranging at least one of substitutional elements and interstitial elements in the second atomic model after the second atomic model generation step and before the cooling step or after the cooling step.

6. 3. The atomic model generation method according to claim 1, further comprising a second lattice defect placement step of placing one or more types of lattice defects in the second atomic model after the second atomic model generation step and before the cooling step or after the cooling step.

7. In order to generate an atomic model having random grain boundaries in an atomic simulation, a computer that executes the atomic simulation is an initial atomic model preparation step of preparing two initial atomic models each having a single crystal atomic model; a first atomic model generating step of rotating the two initial atomic models and then bonding the single crystal atomic models to generate a first atomic model including a bonding interface; a second atomic model generating step of holding the first atomic model at a holding temperature that is equal to or higher than the amorphous temperature of the first atomic model and equal to or lower than a predetermined temperature that does not exceed the melting point of the first atomic model, thereby transitioning the bonding interface to a random grain boundary and generating a second atomic model having a random grain boundary; a cooling step of cooling the second atomic model to a cooling temperature that is lower than the amorphous temperature of the first atomic model.

8. a step of calculating grain boundary energy of the atomic model generated by the atomic model generation method according to claim 1 or 2; evaluating the relationship between the grain boundary energy and material properties; and outputting design guidelines for the material based on the evaluation.

9. A material design method, comprising the step of designing the material in accordance with the design guidelines for the material output by the material design support method according to claim 8.

10. 3. The atomic model generation method according to claim 1, wherein a force field utilizing machine learning is used in the atomic simulation, and the force field is generated using training data incorporating data on amorphization temperature.

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