Method for simulating gap transitions

Abstract

The embodiments of the present application relate to the technical field of diffusion behavior analysis of interstitial pair atoms in metal materials, and in particular to a method for simulating interstitial pair transitions, comprising the following steps: S1: determining the position information of the initial position of the interstitial pair; S2: determining the transition mode of the interstitial pair, and determining the target position after the interstitial pair transition according to the transition mode; S3: simulating the interstitial pair transitioning from the initial position to the target position; S4: updating the position information of the interstitial pair according to the information of the target position; S5: determining the state of the periphery of the updated position of the interstitial pair; S6: determining that the interstitial pair continues to transition according to the state of the periphery, and repeating the S2-S6 steps; S7: determining that the interstitial pair stops transitioning according to the state of the periphery. The method provided in the embodiments of the present application does not need to distinguish the orientation of the interstitial pair, has strong applicability, and can be widely applied to different material systems; and when simulating the interstitial pair transition, there is no need for the interstitial pair to participate in probability sampling, so that the interstitial pair transition is faster than the vacancy transition.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of analysis of the diffusion behavior of interstitial pair atoms in metal materials, and in particular to a method for simulating interstitial pair transitions. Background Art

[0002] The statements herein merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] Lattice dynamics Monte Carlo simulations are commonly used to simulate the behavior of solute atoms rearranged in reactor materials due to the transitions of irradiation-induced point defects. Irradiation-induced point defects typically include vacancies and interstitial pairs. Vacancy transitions are relatively straightforward to handle. For example, in body-centered cubic (BCC) materials, a vacancy can transition to its eight 1NN (first nearest neighbor) neighbors. However, the transitions of interstitial pairs are more complex. This is because interstitial pairs have a specific orientation and two atoms share a lattice site. Ideal methods for handling interstitial pair transitions have yet to be developed. Summary of the Invention

[0004] A brief overview of the present application is provided below to provide a basic understanding of certain aspects of the present application. It should be understood that this overview is not an exhaustive overview of the present application. It is not intended to identify key or important portions of the present application, nor is it intended to limit the scope of the present application. Its purpose is simply to present certain concepts in a simplified form as a prelude to the more detailed description that will be discussed later.

[0005] An embodiment of the present application provides a method for simulating gap pair transitions, the method comprising the following steps:

[0006] S1: Determine the position information of the initial position of the gap pair;

[0007] S2: determining the transition mode of the gap pair, and determining the target position of the gap pair after the transition according to the transition mode;

[0008] S3: simulate the gap pair jumping from the initial position to the target position;

[0009] S4: Update the position information of the gap pair according to the target position information;

[0010] S5: Determine the state of the gap pair's updated position surroundings;

[0011] S6: According to the surrounding state, determine the gap pair to continue the transition and repeat steps S2-S6;

[0012] S7: According to the surrounding state, determine that the gap pair stops transitioning.

[0013] The method provided in the embodiments of the present application does not require the use of first-principles methods to calculate the energy characteristic parameters of different neighboring atomic environments of different gap pairs. By determining the initial position and transition mode of the gap pair, the gap pair can be simulated to transition from the initial position to the target position. Then, based on the state around the updated position, it is determined whether the gap pair continues to transition or stops transitioning. Such a transition method does not require distinguishing the orientation of the gap pair, has strong applicability, and can be widely applied to different material systems; and when simulating the gap pair transition, there is no need for gap pair participation probability sampling, which can make the gap pair transition faster than the vacancy transition.

[0014] These and other advantages of the present application will become more apparent through the following detailed description of the preferred embodiments of the present application in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] To further illustrate the above and other advantages and features of the present application, the following detailed description of specific embodiments of the present application is provided in conjunction with the accompanying drawings. The accompanying drawings, together with the detailed description below, are incorporated into and form a part of this specification. Elements with the same function and structure are denoted by the same reference numerals. It should be understood that these drawings depict only typical examples of the present application and should not be construed as limiting the scope of the present application.

[0016] Figure 1 is a flow chart of a method for simulating gap pair transitions provided according to one embodiment of the present application;

[0017] Figure 2a Schematic diagram of Re atom aggregation caused by interstitial pair transitions in a Mo-Re system at a temperature less than 600K according to one embodiment of the present application;

[0018] Figure 2b Schematic diagram of Re atom aggregation caused by interstitial pair transitions in a Mo-Re system at a temperature of 600K to 800K according to one embodiment of the present application;

[0019] Figure 2c Schematic diagram of Re atom aggregation caused by interstitial pair transitions in a Mo-Re system at temperatures of 800K to 1100K according to one embodiment of the present application;

[0020] Figure 2d This is a schematic diagram of Re atom aggregation caused by interstitial pair transitions in a Mo-Re system at a temperature greater than 1100K according to one embodiment of the present application.

[0021] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding. DETAILED DESCRIPTION

[0022] Exemplary embodiments of the present application will be described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the developer's specific goals, such as meeting those constraints related to the system and business, and these constraints may vary depending on the implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is a routine task for those skilled in the art who benefit from the content of this application.

[0023] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, the accompanying drawings only show the device structure and / or processing steps that are closely related to the solution according to the present application, while other details that are not closely related to the present application are omitted.

[0024] The disclosure below provides a plurality of different embodiments or examples for implementing the present application. In order to simplify the disclosure of the present application, the components and methods of specific examples are described below. Of course, they are merely examples and are not intended to limit the present application. In the description of the embodiments of the present application, the meaning of "plurality" is at least two, for example, two, three, etc., unless otherwise specifically defined.

[0025] In the related art, interstitial pair transition events, like vacancy transition events, must participate in the probability sampling of the dynamic Monte Carlo method. Probability sampling is related to the probability of the transition event. When calculating the probability of interstitial pair transitions, it is necessary to calculate the energy difference between the material system after the interstitial pair transition and before the transition. When calculating the energy of the material system before and after the interstitial pair transition, it is necessary to consider the relative position relationship between the interstitial pair and the surrounding neighboring atoms, and it is necessary to use the first-principles method to calculate and obtain the various neighboring atomic environment energies of different interstitial pairs as a reference. It can be seen from this that the treatment of interstitial pair transition behavior in the lattice dynamics Monte Carlo model is more complicated, and different material systems are treated differently, which is not scalable; at the same time, interstitial pair transitions need to participate in probability sampling, which cannot reflect the characteristic that interstitial pair transitions are faster than vacancy transitions.

[0026] To solve the above problems, the present invention provides a method for simulating gap pair transitions. Figure 1 The method may include the following steps S1 to S7.

[0027] S1: Determine the position information of the initial position of the gap pair.

[0028] S2: Determine the transition mode of the gap pair, and determine the target position of the gap pair after the transition according to the transition mode.

[0029] S3: Simulate the gap pair jumping from the initial position to the target position.

[0030] S4: Update the position information of the gap pair according to the target position information.

[0031] S5: Determine the state of the gap pair's updated position periphery.

[0032] S6: According to the surrounding state, determine whether the gap pair continues to transition and repeat steps S2-S6.

[0033] S7: According to the surrounding state, determine that the gap pair stops transitioning.

[0034] The method provided in the embodiments of the present application does not require the use of first-principles methods to calculate the energy characteristic parameters of different neighboring atomic environments of different gap pairs. By determining the initial position and transition mode of the gap pair, the gap pair can be simulated to transition from the initial position to the target position. Then, based on the state around the updated position, it is determined whether the gap pair continues to transition or stops transitioning. Such a transition method does not require distinguishing the orientation of the gap pair, has strong applicability, and can be widely applied to different material systems; and when simulating the gap pair transition, there is no need for gap pair participation probability sampling, which can make the gap pair transition faster than the vacancy transition.

[0035] In some embodiments, in step S1 , the position information of the initial position of the gap pair can be expressed as [x0, y0, z0].

[0036] In some embodiments, in step S2, the transition mode of the gap pair may include continuing transition and stopping transition. In the case where the gap pair continues to transition, the transition mode of the gap pair continuing to transition may specifically include three-dimensional transition and one-dimensional transition. If the transition mode of the gap pair continuing to transition is three-dimensional transition, a lattice position can be randomly selected in the material system, and the lattice position is determined as the target position after the gap pair transition. If the transition mode of the gap pair continuing to transition is one-dimensional transition, a lattice position can be selected along the transition direction of the gap pair, and the lattice position is determined as the target position after the gap pair transition.

[0037] In some embodiments, the transition behavior of the interstitial pair can be simulated using first principles or molecular dynamics. The interstitial pair's trajectory can then be tracked to determine the transition mode of the interstitial pair as it continues to transition. If the interstitial pair's trajectory is an irregular random walk, it is a three-dimensional transition; if the interstitial pair's trajectory follows a specific direction, it is a one-dimensional transition.

[0038] For example, the target position after the gap pair transition can be expressed as [x1, y1, z1].

[0039] In some embodiments, the next step can be selected based on the surrounding state of the gap pair's position. If the gap pair can continue to transition, steps S2-S6 can be repeated; if the gap pair no longer continues to transition, the transition processing of the gap pair is terminated.

[0040] In some embodiments, step S7 may also include: determining that there are vacancies around the position of the gap pair, and then the gap pair stops transitioning, so that it can be determined that the gap pair and the vacancies are recombined and annihilated so that the gap pair disappears from the material system, and then the simulation of the gap pair transition is ended, so that the gap pair transitions faster.

[0041] In some embodiments, whether there are vacancies around the positions of the gap pair may be determined by traversing the perimeter of the positions of the gap pair.

[0042] In some embodiments, step S6 may further include: determining that there are no vacancies around the position of the gap pair; determining the number of other gap pairs around the position of the gap pair; and determining the gap pair to transition based on the number of other gap pairs.

[0043] In an embodiment of the present application, when there are no vacancies around the position of the gap pair, the gap pair can be determined to continue to transition based on the number of other gap pairs around the position of the gap pair, so that the transition of the gap pair is faster.

[0044] In some embodiments, when it is determined that there is no vacancy around the position of the gap pair, the periphery of the position of the gap pair can be traversed to determine whether there are other gap pairs around the position of the gap pair, and then the number of other gap pairs can be determined.

[0045] In some embodiments, the number of other gap pairs around the position of the determined gap pair is less than a first predetermined value, and a first escape probability is determined based on the number of other gap pairs around the position of the gap pair and the first predetermined value; a first random number is generated based on the first escape probability; and the gap pair is determined to transition based on the first escape probability and the first random number.

[0046] Since there is a strong binding effect between gap pairs, when there are other gap pairs in the immediate vicinity of a gap pair, the gap pair and the other gap pairs will combine with each other to form a stable gap pair cluster and no longer continue to transition. The number of other gap pairs with which a gap pair can form a stable gap pair cluster is related to the binding energy between the gap pairs. When the number of other gap pairs around a gap pair is less than a first predetermined value, the gap pair has a certain probability of escaping from the gap pair cluster. The embodiment of the present application generates a first random number based on the first escape probability, and then determines the gap pair to transition based on the first escape probability and the first random number, thereby improving the efficiency of the gap pair transition.

[0047] In some embodiments, the first predetermined value can be calculated based on first principles or molecular dynamics methods. The first predetermined value indicates that when the number of other gap pairs around the position of the gap pair is greater than the first predetermined value, the gap pair will be constrained by other gap pairs and cannot continue to transition.

[0048] According to the first escape probability, a first random number is generated. In some embodiments, the first random number can be randomly generated by a computer.

[0049] In some embodiments, the number of other gap pairs around the position of the gap pair and the first predetermined value determine the first escape probability to be in accordance with the following expression:

[0050]

[0051] in, represents the first escape probability, N SIA Indicates the number of other gap pairs around the position of the gap pair, N inter Indicates the first predetermined value.

[0052] The embodiment of the present application determines the first escape probability through the above expression (1), and then determines the transition of the gap pair according to the first escape probability and the first random number, thereby further improving the transition efficiency of the gap pair.

[0053] In some embodiments, if N SIA <N inter , the first escape probability can be calculated using expression (1) Then generate a random number rand1. According to the first escape probability and the random number rand 1, determine the gap pair to transition.

[0054] In some embodiments, based on the first escape probability being greater than the first random number, it is determined that the gap pair is to be transitioned, so as to ensure the transition efficiency of the gap pair.

[0055] In some embodiments, if Then determine the gap pair to stop transition; if It is determined that the gap pair continues to transition.

[0056] In some embodiments, in step S7, it is determined that there is no vacancy around the position of the gap pair; it is determined that the number of other gap pairs around the position of the gap pair is greater than a first predetermined value; and it is determined that the gap pair stops transitioning.

[0057] The embodiment of the present application does not need to participate in probability sampling when the gap pair transitions. When there are no vacancies around the position of the gap pair, it can quickly determine whether the gap pair needs to stop transitioning based on the number of other gap pairs around it and the first predetermined value.

[0058] In some embodiments, when determining that the perimeter of the position of the gap pair does not have a vacancy, if N SIA >N inter , the number of gap pairs is greater than the first predetermined value N inter The other interstitial pairs will combine with each other to form stable interstitial pair clusters and no longer continue to jump.

[0059] In some embodiments, in step S7, it is determined that there are no vacancies around the position of the gap pair; the number of other gap pairs around the position of the gap pair is determined; the number of other gap pairs around the position of the gap pair is determined to be less than a first predetermined value; based on the number of other gap pairs around the position of the gap pair and the first predetermined value, a first escape probability is determined; based on the first escape probability, a first random number is generated; based on the first escape probability being less than the first random number, it is determined that the gap pair does not make a jump.

[0060] In some embodiments, the number of solute atoms around the gap pair is determined; the number of solute atoms around the gap pair is determined to be greater than a second predetermined value; and the gap pair is determined to stop transitioning. This can determine that the gap pair will be trapped by the surrounding solute atoms and cannot continue to transition, thereby terminating the simulation of the gap pair transition and making the gap pair transition faster.

[0061] In some embodiments, if Then the gap pair can continue to jump, and then the surroundings of the gap pair can be traversed to determine whether there are solute atoms around the gap pair. If there are solute atoms, the number of the surrounding solute atoms is recorded.

[0062] In some embodiments, the second predetermined value can be calculated based on first principles or molecular dynamics methods. The second predetermined value indicates that when the number of solute atoms around the position of the interstitial pair is greater than the second predetermined value, the interstitial pair will be bound by the solute atoms and cannot continue to transition.

[0063] In some embodiments, the number of solute atoms around the gap pair is determined; the number of solute atoms around the gap pair is determined to be less than a second predetermined value; a second escape probability is determined based on the number of solute atoms around the gap pair and the second predetermined value; a second random number is generated based on the second escape probability; and the gap pair is determined to undergo a transition based on the second escape probability and the second random number.

[0064] When the number of solute atoms around the gap pair is less than a second predetermined value, the gap pair may not be bound by the surrounding solute atoms and can continue to transition. The embodiment of the present application generates a second random number based on the second escape probability, and then determines the gap pair to transition based on the second escape probability and the second random number, which can improve the transition efficiency of the gap pair.

[0065] In some embodiments, those skilled in the art can understand the implementation method of generating the second random number according to the second escape probability by generating the first random number according to the first escape probability, which will not be described here for the sake of brevity.

[0066] In some embodiments, the second escape probability is determined according to the number of solute atoms around the gap pair and the second predetermined value, so as to conform to the following expression:

[0067]

[0068] in, represents the second escape probability, N solute represents the number of solute atoms around the interstitial pair, N trapped Indicates the second predetermined value.

[0069] The embodiment of the present application determines the second escape probability through the above expression (2), and then determines that the gap pair continues to transition based on the second escape probability and the second random number, further improving the transition efficiency of the gap pair.

[0070] In some embodiments, if N solute <N trapped , the second escape probability can be calculated using expression (2) Then generate a random number rand 2. According to the second escape probability and the random number rand 2, to determine whether the gap pair continues to transition.

[0071] In some embodiments, based on the second escape probability being greater than the second random number, it is determined that the gap pair is to be transitioned, so as to ensure the transition efficiency of the gap pair.

[0072] The following is a specific example to further illustrate the process of simulating gap pair transitions using the method of the present application.

[0073] Example 1

[0074] Before simulating the gap pair transition, the first predetermined value N is first determined based on the calculation results of the first principle or molecular dynamics method. inter and the second predetermined value N trapped , and then determine the transition path and mode of the gap pair based on the first principles or molecular dynamics method.

[0075] The process of interstitial pair transition mainly includes:

[0076] Step 1: Get the initial position information of the gap pair [x0][y0][z0].

[0077] Step 2: According to the transition mode of the interstitial pair, find the target position [x1][y1][z1] after the interstitial pair transitions in the material system.

[0078] Step 3: The gap pair completes the transition, and the position information of the gap pair is updated to [x1][y1][z1].

[0079] Step 4: Determine the surrounding environment of the gap pair's location and decide whether the gap pair has been processed or can continue to transition:

[0080] The position of the interstitial pair is traversed to see if there is a vacancy around it. If there is a vacancy, the interstitial pair and the vacancy are recombined and annihilated. The interstitial pair and the vacancy disappear from the material system, and the interstitial pair transition process is terminated.

[0081] If there is no vacancy around the position of the gap pair, then traverse the gap pair to see if there are other gap pairs around it. If there are other gap pairs, record the number N of other gap pairs around it. SIA .

[0082] If N SIA >N inter , then it is determined that the gap pair cannot continue to transition.

[0083] If N SIA <N inter , then use the above expression (1) to calculate the first escape probability And according to the first escape probability Generate a first random number rand 1.

[0084] if It is determined that the gap pair cannot continue to transition.

[0085] if Then determine whether the gap pair can continue to transition, then traverse the gap pair to see if there are solute atoms around it, and record the number of solute atoms around it N solute .

[0086] If Nsolute >N trapped , then it is determined that the gap pair cannot continue to transition.

[0087] Such as N solute <N trapped , calculate the second escape probability using the above expression (2) And according to the second escape probability Generate a second random number rand 2.

[0088] if It is determined that the gap pair cannot continue to transition.

[0089] if It is determined that the gap pair can continue to transition.

[0090] Step 5: Based on the judgment result of the gap pair, if the gap pair can continue to transition, the operations of steps 1 to 4 are executed in a loop; if the gap pair cannot continue to transition, the transition processing of the gap pair is terminated.

[0091] In some embodiments, as Figures 2a to 2d As shown, the interstitial pair transition in the Mo-Re system at different temperatures (T) can lead to the aggregation of Re atoms. By using the method for simulating interstitial pair transitions provided in the embodiments of the present application, the behavior of Re atom aggregation and precipitation induced by interstitial pair transitions in the Mo-Re system can be simulated and studied.

[0092] Regarding the embodiments of the present application, it should also be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other to obtain new embodiments.

[0093] The above are only specific implementation methods of the present application, but the protection scope of the present application is not limited thereto. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for simulating gap pair transitions, characterized in that: The method comprises the following steps: S1: determining position information of the initial position of the interstitial pair in the Mo-Re system; S2: Determine a transition mode of the gap pair, and determine a target position of the gap pair after the transition according to the transition mode; S3: simulating the gap pair jumping from the initial position to the target position; S4: updating the position information of the gap pair according to the target position information; S5: Determine the state of the updated position surrounding the gap pair; S6: Determine that the gap pair continues to transition according to the state of the periphery, and repeat steps S2-S6; S7: Determine that the gap pair stops transitioning according to the state of the periphery.

2. The method according to claim 1, characterized in that In step S7, it also includes: It is determined that there are vacancies around the position of the gap pair, and the gap pair stops transitioning.

3. The method according to claim 1, characterized in that In step S6, it also includes: Determining that the perimeter of the position of the gap pair has no vacancies; Determine the number of other gap pairs surrounding the position of the gap pair; The gap pairs are determined to transition according to the number of the other gap pairs.

4. The method according to claim 3, characterized in that Determine that the number of other gap pairs around the position of the gap pair is less than a first predetermined value, Determine a first escape probability based on the number of other gap pairs around the position of the gap pair and the first predetermined value, Generate a first random number according to the first escape probability, Determine the gap pair to transition according to the first escape probability and the first random number.

5. The method according to claim 1, wherein In step S7, Determining that the perimeter of the position of the gap pair has no vacancies; Determining that the number of other gap pairs around the position of the gap pair is greater than a first predetermined value; It is determined that the gap pair stops transitioning.

6. The method according to claim 4, characterized in that The number of other gap pairs around the position of the gap pair and the first predetermined value determine the first escape probability to meet the following expression: in, represents the first escape probability, N SIA Indicates the number of other gap pairs around the position of the gap pair, N inter Indicates the first predetermined value.

7. The method according to claim 4, characterized in that According to the first escape probability being greater than the first random number, it is determined that the gap pair is to be transitioned.

8. The method according to claim 1, characterized in that In step S7, Determining that the perimeter of the position of the gap pair has no vacancies; Determine the number of other gap pairs surrounding the position of the gap pair; Determine that the number of other gap pairs around the position of the gap pair is less than a first predetermined value, Determine a first escape probability based on the number of other gap pairs around the position of the gap pair and the first predetermined value, Generate a first random number according to the first escape probability, According to the first escape probability being less than the first random number, it is determined that the gap pair does not transition.

9. The method according to claim 7, characterized in that determining the number of solute atoms surrounding the interstitial pair; determining that the number of solute atoms surrounding the interstitial pair is greater than a second predetermined value; It is determined that the gap pair stops transitioning.

10. The method according to claim 7, characterized in that determining the number of solute atoms surrounding the interstitial pair; determining that the number of solute atoms surrounding the interstitial pair is less than a second predetermined value; determining a second escape probability according to the number of solute atoms around the gap pair and the second predetermined value; According to the second escape probability, a second random number is generated, Determine the gap pair to transition according to the second escape probability and the second random number.

11. The method according to claim 10, characterized in that According to the number of solute atoms around the gap pair and the second predetermined value, it is determined that the second escape probability conforms to the following expression: in, represents the second escape probability, N solute represents the number of solute atoms around the interstitial pair, N trapped Indicates the second predetermined value.

12. The method according to claim 10, characterized in that According to the second escape probability being greater than the second random number, it is determined that the gap pair is to be transitioned.

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