Method for calculating vacancy formation energy in equimolar-ratio NbTiZr solid solution

Abstract

The invention discloses a method for calculating vacancy formation energy in an equimolar-ratio NbTiZr solid solution, and relates to the technical field of numerical simulation of nuclear material irradiation effect, and the method comprises the following steps: calculating atomic potential in a solid solution system; constructing a vacancy-containing solid solution system; calculating vacancy formation energy in the solid solution system; and calculating the electronic structure of the vacancy-containing solid solution system. Based on a first principle method of a density functional theory, atomic chemical potential is obtained through a method of mutual substitution of elements; based on the chemical potential, atoms on the atomic sites are deleted respectively, and formation energy of all kinds of vacancies is calculated; and calculating the differential charge density of different types of vacancies to obtain the influence mechanism of the local environment on the vacancies. Vacancy formation energy can be obtained without complex experimental results or difficult-to-obtain precise empirical potential, and the method has important scientific significance in research of vacancy defects in solid solutions; the defect that it is difficult to reveal single vacancy formation in the initial stage of irradiation from the atomic scale in experiments is overcome.

Description

Technical Field

[0001] The invention relates to the technical field of numerical simulation of nuclear material irradiation effects, and in particular to a method for calculating vacancy formation energy in an equimolar NbTiZr solid solution. Background Art

[0002] With the increasing requirements for the fourth-generation reactor, the irradiation damage of materials has attracted more and more attention as an important issue restricting its development. High entropy alloy (HEA) is a new type of material containing multiple main elements. It breaks the limitation of traditional alloys with one or two elements as the main element and provides a new way to explore new materials and new properties. Due to its unique composition characteristics, high entropy alloys have many properties superior to traditional alloys, such as high strength and hardness, excellent wear resistance and corrosion resistance, good thermal stability, etc. Therefore, high entropy alloys have become a frontier hotspot in the field of materials science and engineering in recent years. Since high entropy alloys may have many ideal properties, they are quite important in materials science and engineering. The main metal components in traditional alloys may be only one or two, for example, iron is used as the basis, and some trace elements are added to improve its properties to obtain iron-based alloys. However, as the number of metal types in the alloy increases, the embrittlement of the material increases, and high entropy alloys will not have such problems. Refractory high entropy alloys (RHEA) composed of refractory elements have shown very broad prospects in high-temperature mechanical properties and are considered to be new high-temperature structural materials that surpass traditional high-temperature alloys. Compared with traditional refractory alloys, refractory high entropy alloys (RHEA) are attracting more and more attention due to their excellent high-temperature mechanical properties, lower density and oxidation resistance.

[0003] Studies have shown that the most common metal elements in refractory high entropy alloys are Ti, Nb, Mo, Zr, V, Ta, Hf and Al. In addition, the most common three-element combinations are (Nb, Ti, Zr), (Mo, Nb, Ti) and (Nb, Ti, V). In addition, only NbTiZr can maintain a stable BCC single-phase crystal structure in the range of 25 to 1000°C.

[0004] Patent CN201810644794.3 discloses a method for improving the catalytic hydrogen evolution performance of molybdenum disulfide, which discloses a method for calculating the formation energy: for a system where Ni atoms replace Mo atoms, E f =E2-E1-E Ni +E Mo For the Ni on Mo and Ni in vacancy systems, E f =E2-E1-E NiWhere E2 is the energy of the system after Ni doping, E1 is the energy of the system before Ni doping, and E Ni is the energy of a Ni atom in the bulk, E Mo is the energy of a Mo atom in the bulk.

[0005] Patent CN201510571341.9 discloses a method for predicting the performance of SiCO negative electrode materials, which discloses a method for calculating the formation energy of lithium-intercalated SiCO: The formation energy of the compound is defined as: Where E defective represents the energy of a defect compound composed of n x atoms, μx represents the chemical potential of x atoms in the complete compound; the formation energy of the material after lithium insertion is: Δ f E=E total (Li x SiC m O n )-(xE total (Li)+E total (SiC m O n )); where E total (Li x SiC m O n ) value is Li after geometric optimization x SiC m O n The structural energy value is divided by the number of silicon atoms in the structure, E total (Li) is the energy of a single Li atom in a body-centered cubic system, E total (SiC m O n ) value is SiC after geometry optimization m O n The structural energy value is divided by the number of silicon atoms in the structure; m = a / 8, n = (16-a) / 8, and x is the number of lithium atoms corresponding to one silicon atom in the system.

[0006] The calculation method of formation energy disclosed in the above patent cannot be applied to NbTiZr solid solutions with equal molar ratios, and no other literature has disclosed a method for theoretically studying the vacancy properties in NbTiZr solid solutions. Although experimental studies have shown that NbTiZr solid solutions have good high-temperature stability and mechanical properties, its radiation resistance and radiation resistance mechanism cannot be obtained by experimental methods alone. In the early stage of irradiation, a large number of vacancy defects will first be generated in the alloy, so it is very important to study the properties of vacancy defects in NbTiZr solid solutions. Summary of the invention

[0007] Based on the problem that the radiation resistance and radiation resistance mechanism of NbTiZr solid solution cannot be obtained only by experimental methods in the prior art, the purpose of the present invention is to provide a method for calculating the vacancy formation energy in equimolar NbTiZr solid solution, based on the first principles method of density functional theory, the atomic chemical potential is obtained by mutual substitution between elements; based on the chemical potential, the atoms at each atomic site are deleted respectively, and the formation energy of all types of vacancies is calculated; the differential charge density of different types of vacancies is calculated to obtain the influence mechanism of the local environment on the vacancies.

[0008] The present invention is achieved through the following technical solutions:

[0009] In a first aspect, the present application provides a method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution, comprising the following steps:

[0010] Calculate atomic potential in solid solution system;

[0011] Constructing a solid solution system containing vacancies;

[0012] Calculate the vacancy formation energy in solid solution systems;

[0013] Calculate the electronic structure of solid solution systems containing vacancies.

[0014] The method for calculating the vacancy formation energy in the NbTiZr solid solution of equal molar ratio in the present invention is based on the first principle method of density functional theory, obtains the atomic chemical potential by a method of mutual substitution between elements, studies the method of vacancy defects in the NbTiZr solid solution, and reveals the difficulty of vacancy formation in the material from the atomic and molecular scale; based on the chemical potential, the atoms at each atomic site are deleted respectively, and the formation energy of all kinds of vacancies is calculated; the differential charge density of different kinds of vacancies is calculated, and the influence mechanism of the local environment on the vacancy is obtained.

[0015] The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution of the present invention belongs to a numerical simulation research method, and the vacancy formation energy can be obtained without complicated experimental results or difficult-to-obtain accurate empirical potentials, which has important scientific significance for the research of vacancy defects in solid solutions; and the method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution of the present invention overcomes the disadvantages of being difficult to experimentally reveal the formation of single vacancies in the initial stage of irradiation from an atomic scale.

[0016] Furthermore, the method for calculating the atomic potential in the solid solution system includes the following steps:

[0017] Construct alternative structures and calculate the energy of alternative structures;

[0018] Based on the obtained substitution energy, the difference in chemical potential of different atoms is obtained;

[0019] Obtain the potential of each atom in the solid solution system.

[0020] Furthermore, the method for calculating the substitution energy of each element in the solid solution system is:

[0021] Select 32 Nb sites in turn and replace the Nb atoms with X (X = Ti, Zr) atoms to obtain 32 E Nb→X , the substitution energy of Nb atoms being replaced by other atoms is obtained by the following formula (1):

[0022]

[0023] Where μ is the chemical potential of Nb replacing X; E is the system energy;

[0024] The substitution energy of other atoms is Δμ Ti→X (X=Nb,Zr), ΔμN Zr→X (X=Nb, Ti) etc. are obtained by the same method as above.

[0025] Further, the method for obtaining the difference in chemical potential of different atoms based on the obtained substitution energy is:

[0026] Based on the obtained substitution energy, the difference between the chemical potentials of each atom is obtained by the following formula (2):

[0027]

[0028] Among them, μ Nb is the chemical potential of Nb, μ X is the chemical potential of X; Δμ X →Nb is the chemical potential difference when X is replaced by Nb; Δμ Nb→X is the chemical potential difference when Nb is replaced by X;

[0029] The difference between the chemical potentials of other atoms, such as μ Ti -μ X (X=Nb,Zr),μ Zr -μ X (X=Nb, Ti) etc. are obtained by the same method as above.

[0030] Furthermore, a method for constructing a solid solution system containing vacancies is to delete atoms at lattice sites respectively to obtain a system containing vacancy defects.

[0031] Furthermore, the method for calculating the vacancy formation energy in the solid solution system is: the energy of the system is calculated by a first-principles calculation method based on density functional theory, and then substituted into the calculation formula of the vacancy formation energy to finally obtain the formation energy of all vacancies.

[0032] Furthermore, the calculation of vacancy formation energy in the solid solution system specifically includes:

[0033] Based on the free energy of all systems obtained, combined with the chemical potential of each atom, and the energy difference between the vacancy-containing system and the perfect system, the formation energy of each vacancy is calculated, and an overall distribution diagram of the vacancy formation energy is drawn.

[0034] Furthermore, the method for calculating the electronic structure of a solid solution system containing vacancies is:

[0035] Calculate the differential charge density of different types of vacancy systems when the local atomic environment is the same;

[0036] Based on the results of differential charge density, the mechanism of the influence of electronic structure on vacancy formation energy is analyzed.

[0037] Furthermore, the calculation of the electronic structure of the solid solution system containing vacancies includes the differential charge density of different types of vacancies with the same environment to determine the effect of the local environment on different types of vacancies, specifically including:

[0038] Calculate the Vac Nb The differential charge density of the system and plot it;

[0039] Calculate the Vac Ti The differential charge density of the system and plot it;

[0040] Calculate the Vac Zr Calculate the differential charge density of the system and plot it.

[0041] In a second aspect, the present application provides a computer program, which can implement the steps of any one of the methods described above.

[0042] The computer program instructions may be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0043] The computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable device to implement the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0044] In a third aspect, the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of any one of the methods described above.

[0045] The computer device may be a desktop computer, a notebook, a PDA, a cloud server, etc. The computer device may interact with the user through a keyboard, a mouse, a remote control, a touch pad, or a voice control device.

[0046] Among them, the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or D interface display memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. The memory can be an internal storage unit of the computer device, for example, the hard disk or memory of the computer device. The memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. Of course, the memory can also include both the internal storage unit of the computer device and an external storage device. The memory is often used to store the operating system and various application software installed on the computer device, such as running the program code of the calculation method of the vacancy formation energy in the equimolar ratio NbTiZr solid solution, etc. In addition, the memory can also be used to temporarily store various types of data that have been output or are to be output. The processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments. The processor is generally used to control the overall operation of the computer device. The processor is used to run the program code stored in the memory or process data, such as running the program code of the calculation method of the vacancy formation energy in the equimolar ratio NbTiZr solid solution.

[0047] In a fourth aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of any one of the methods described above.

[0048] The computer-readable storage medium stores an interface display program, and the interface display program can be executed by at least one processor so that the at least one processor performs the steps of the method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution.

[0049] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0050] (1) The present invention provides a method for studying vacancy defects in NbTiZr solid solution using a first-principles calculation method based on density functional theory, revealing the ease of vacancy formation in the material from the atomic and molecular scale;

[0051] (2) The method for calculating the vacancy formation energy in the equimolar NbTiZr solid solution of the present invention belongs to a numerical simulation research method, which can obtain the vacancy formation energy without complicated experimental results or difficult-to-obtain accurate empirical potentials, and has important scientific significance for the study of vacancy defects in solid solutions;

[0052] (3) The method for calculating the vacancy formation energy in the equimolar NbTiZr solid solution of the present invention overcomes the disadvantage that it is difficult to reveal the formation of single vacancies at the initial stage of irradiation at the atomic scale in experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0054] Figure 1 Schematic diagram of a process for calculating vacancy formation energy of equimolar NbTiZr solid solution in Example 1 of the present invention;

[0055] Figure 2 is a graph of the atomic chemical potential in Example 1 of the present invention;

[0056] Figure 3 This is a diagram showing the vacancy formation energy in Example 1 of the present invention;

[0057] Figure 4 Vac in Example 1 of the present invention Nb The differential charge density display of the system;

[0058] Figure 5 Vac in Example 1 of the present invention Ti The differential charge density display of the system;

[0059] Figure 6 Vac in Example 1 of the present invention Zr Display of the differential charge density of the system. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0061] The following detailed description specifically discloses the implementation method of the method for calculating the vacancy formation energy in the equimolar ratio NbTiZr solid solution of the present application with appropriate reference to the accompanying drawings. However, there may be cases where unnecessary detailed descriptions are omitted. For example, there are cases where detailed descriptions of well-known matters and repeated descriptions of actually the same structure are omitted. This is to avoid the following description from becoming unnecessarily lengthy and to facilitate the understanding of those skilled in the art. In addition, the drawings and the following description are provided for those skilled in the art to fully understand the present application and are not intended to limit the subject matter described in the claims. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0062] Unless otherwise specified, all embodiments and optional embodiments of the present application can be combined with each other to form a new technical solution.

[0063] Unless otherwise specified, all technical features and optional technical features of this application can be combined with each other to form a new technical solution.

[0064] The terms "comprises," "comprising," or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0065] Example 1

[0066] This embodiment provides a method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution, a method for calculating the vacancy formation energy in the NbTiZr solid solution based on the first principle, a substitution method is used to obtain the chemical potential in the NbTiZr solid solution, the formation energy of all vacancies is calculated according to the chemical potential, and the influence of the same chemical environment on the formation energy of different vacancy types is analyzed by differential charge density. The present invention has important scientific significance for the study of vacancies in the NbTiZr solid solution system.

[0067] See also Figure 1 ,like Figure 1 As shown, it is a flow chart of a numerical simulation method for NbTiZr solid solution vacancy formation energy provided in this embodiment. Specifically, the numerical simulation method for studying NbTiZr solid solution vacancy includes the following steps:

[0068] S101. Calculate the atomic potential of the constituent elements in the solid solution.

[0069] First, calculate the substitution energy of each atom in the solid solution system:

[0070] Select 32 Nb sites in the solid solution and replace the Nb atoms with X (X = Ti, Zr) atoms to obtain 32 E Nb→X , the substitution energy of Nb atoms being replaced by other atoms is obtained by the following formula (1):

[0071]

[0072] Where μ is the chemical potential of Nb replacing X; E is the system energy;

[0073] Other alternatives such as Δμ Ti→X (X=Nb,Zr), Δμ Zr→X (X=Nb, Ti) etc. are obtained by the same method as above;

[0074] Based on the obtained substitution energy, the difference in chemical potential of different atoms can be obtained:

[0075] Based on the above substitution energy, the difference between the chemical potentials of each atom is obtained by the following formula (2):

[0076]

[0077] Among them, μ Nb is the chemical potential of Nb, μ X is the chemical potential of X; Δμ X→Nb is the chemical potential difference when X is replaced by Nb; Δμ Nb→X is the chemical potential difference when Nb is replaced by X;

[0078] The difference between the chemical potentials of other atoms, such as μ Ti -μX (X=Nb,Zr),μ Zr -μ X (X=Nb, Ti) etc. are obtained by the same method as above;

[0079] Finally, the chemical potential of each atom is calculated, such as Figure 2 shown.

[0080] S102. Construct a solid solution system containing vacancies.

[0081] Use Materials Studio software to construct a solid solution system containing vacancies and export the structure file in .cif format;

[0082] The constructed crystal structure was opened with VESTA.

[0083] S103. Calculate the vacancy formation energy in the solid solution system.

[0084] The atomic position information and system free energy of all supercell systems containing vacancies are obtained through first-principles calculations, and the system free energy is read out from the OUTCAR file;

[0085] Based on the obtained free energy of all systems, combined with the chemical potential of each atom obtained by S101, the formation energy of each vacancy is calculated by the energy difference between the vacancy-containing and perfect unit cell systems:

[0086] The overall distribution of vacancy formation energy and the distribution of different types of vacancy formation energy are as follows: Figure 3 shown.

[0087] S104. Calculate the electronic structure of a solid solution system containing vacancies.

[0088] In this embodiment, the electronic structure of the solid solution of different types of vacancies under the same local environment, that is, the differential charge density, is calculated to determine the effect of the local environment on the different types of vacancies. Figures 4 to 6 The figure shows the differential charge density diagram of different types of vacancy structures under the same local atomic environment. The yellow area is the charge dissipation area, and the blue-green area is the charge accumulation area. Nb ,Vac Ti ,Vac Zr The charge change of Nb atoms in the local environment is the most obvious, indicating that Nb atoms have a greater impact on the formation of all types of vacancies. In addition, the size of the charge change area around Nb atoms is determined by Vac. Nb ,Vac Ti ,Vac ZrThe order of increasing continuously indicates that in the process of Zr vacancy formation, the charge transfer amount of Nb atoms in the local environment is the largest, that is, the influence of Nb atoms in the local environment on Zr vacancy is the most significant. This can be confirmed by the size of the vacancy formation energy of these three vacancy systems: Vac Nb =0.327, Vac Ti =0.920, Vac Zr =1.230, the formation energy of Zr vacancy is the largest, indicating that more energy is needed to complete more charge transfer.

[0089] The embodiment provides a method for studying vacancy defects in NbTiZr solid solution using a first-principles calculation method based on density functional theory, which reveals the difficulty of vacancy formation in materials from the atomic and molecular scale. Moreover, the method for calculating the vacancy formation energy in the equimolar NbTiZr solid solution of the embodiment belongs to a numerical simulation research method, which can obtain the vacancy formation energy without complicated experimental results or difficult-to-obtain precise empirical potentials, and has important scientific significance for the study of vacancy defects in solid solutions. At the same time, the method for calculating the vacancy formation energy in the equimolar NbTiZr solid solution of the embodiment overcomes the disadvantages that it is difficult to reveal the formation of single vacancies in the initial stage of irradiation from the atomic scale in experiments.

[0090] Example 2

[0091] This embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method for calculating the vacancy formation energy in the equimolar ratio NbTiZr solid solution in the above-mentioned embodiment 1.

[0092] The computer device may be a desktop computer, a notebook, a PDA, a cloud server, etc. The computer device may interact with the user through a keyboard, a mouse, a remote control, a touch pad, or a voice control device.

[0093] The storage device includes at least one type of readable storage medium, and the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or D interface display memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory can be an internal storage unit of the computer device, for example, a hard disk or memory of the computer device. In other embodiments, the memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. Of course, the memory can also include both an internal storage unit of the computer device and an external storage device. In this embodiment, the memory is often used to store an operating system and various application software installed on the computer device, such as a program code for running the method for calculating the vacancy formation energy in the equimolar ratio NbTiZr solid solution, etc. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.

[0094] The processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor or other data processing chip in some embodiments. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code or process data stored in the memory, such as running the program code of the calculation method of the vacancy formation energy in the equimolar ratio NbTiZr solid solution.

[0095] Example 3

[0096] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the above-mentioned method for calculating the vacancy formation energy in the equimolar ratio NbTiZr solid solution.

[0097] The computer-readable storage medium stores an interface display program, and the interface display program can be executed by at least one processor so that the at least one processor performs the steps of the method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution.

[0098] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0099] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0100] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0102] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, computer, server or network device, etc.) to execute the methods described in each embodiment of the present application.

[0103] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment," "an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. In addition, it will be appreciated by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0104] The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only the specific embodiments of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention. For those skilled in the art, it is obvious that the present application is not limited to the details of the above exemplary embodiments, and the present application can be implemented in other specific forms without departing from the spirit or basic features of the present application. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present application is limited by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present application.

Claims

1. A method for calculating the vacancy formation energy in an equimolar NbTiZr solid solution, characterized in that: The following steps are involved: Calculate atomic potential in solid solution system; Constructing a solid solution system containing vacancies; Calculate the vacancy formation energy in solid solution systems; Calculate the electronic structure of solid solution systems containing vacancies.

2. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 1, characterized in that: The method for calculating the atomic potential in a solid solution system includes the following steps: Construct alternative structures and calculate the energy of alternative structures; Based on the obtained substitution energy, the difference in chemical potential of different atoms is obtained; Obtain the potential of each atom in the solid solution system.

3. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 2, characterized in that: The method for calculating the substitution energy of each element in the solid solution system is: Select 32 Nb sites in turn and replace the Nb atoms with X (X = Ti, Zr) atoms to obtain 32 E Nb→X , the substitution energy of Nb atoms being replaced by other atoms is obtained by the following formula (1): Where μ is the chemical potential of Nb replacing X; E is the system energy; The substitution of other atoms can be achieved using the same method as above.

4. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 2, characterized in that: The method to obtain the difference in chemical potential of different atoms based on the obtained substitution energy is: Based on the obtained substitution energy, the difference between the chemical potentials of each atom is obtained by the following formula (2): Among them, μ Nb is the chemical potential of Nb, μ X is the chemical potential of X; Δμ X→Nb is the chemical potential difference when X is replaced by Nb; Δμ Nb→X is the chemical potential difference when Nb is replaced by X; The differences between the chemical potentials of other atoms are obtained using the same method as above.

5. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 1, characterized in that: The method for constructing a solid solution system containing vacancies is to delete atoms at lattice sites respectively to obtain a system containing vacancy defects.

6. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 1, characterized in that: The method for calculating the vacancy formation energy in the solid solution system is: calculate the energy of the system through the first principle calculation method based on density functional theory, substitute it into the calculation formula of the vacancy formation energy, and finally obtain the formation energy of all vacancies.

7. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 6, characterized in that: The calculation of vacancy formation energy in a solid solution system specifically includes: Based on the free energy of all systems obtained, combined with the chemical potential of each atom, and the energy difference between the vacancy-containing system and the perfect system, the formation energy of each vacancy is calculated, and an overall distribution diagram of the vacancy formation energy is drawn.

8. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 1, characterized in that: The method for calculating the electronic structure of a solid solution system containing vacancies is: Calculate the differential charge density of different types of vacancy systems when the local atomic environment is the same; Based on the results of differential charge density, the mechanism of the influence of electronic structure on vacancy formation energy is analyzed.

9. The method for calculating the vacancy formation energy in an equimolar ratio NbTiZr solid solution according to claim 8, characterized in that: The electronic structure of solid solution systems containing vacancies is calculated by differential charge density of different types of vacancies with the same environment to determine the effect of the local environment on the different types of vacancies. Specifically, it also includes: Calculate the Vac Nb The differential charge density of the system and plot it; Calculate the Vac Ti The differential charge density of the system and plot it; Calculate the Vac Zr Calculate the differential charge density of the system and plot it.

10. A computer program, characterized in that The computer program can implement the steps of the method according to any one of claims 1 to 9.

11. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes the steps of the method according to any one of claims 1 to 9.

12. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 9.

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