An optimal atom matching search method for surface reconstruction path of solid material

Abstract

The application relates to a solid material surface reconstruction path optimal atom matching searching method, which comprises the following steps: S1, initializing population parameters; S2, initializing gene sequences corresponding to population individuals; S3, calculating an adaptive value, and selecting an optimal population individual; S4, performing a cross operation; S5, performing a mutation operation on each population individual; S6, calculating the adaptive value of a new generation population, selecting a result population individual, and simultaneously updating the optimal population individual searched at present; S7, judging whether a convergence standard or a generation upper limit is reached, if yes, stopping generation, and outputting the result population individual of S6 as an optimal atom matching mode of the structure phase, otherwise, taking the new generation population individual generated in S5 as each population individual in S4, and returning to S4. Compared with the prior art, the application has the advantages of improving the accuracy of atom matching modes between two structures and the like.

Description

Technical Field

[0001] This invention relates to the field of surface reconstruction path technology for generating structural phases, and in particular to an optimal atomic matching search method for surface reconstruction paths of solid materials. Background Technology

[0002] With the establishment of density functional theory and the continuous development of computer technology, theoretical simulation plays an increasingly prominent role in materials science research. In the field of solid materials, multiphase solid materials are expected to become important candidates for future memory storage and semiconductor materials. Determining the surface reconstruction paths and transformation mechanisms between different phases of solid materials through theoretical simulation is fundamental to further finely controlling the surface reconstruction process. In computational materials science, the basic method for determining the surface reconstruction path between two structural phases is the Nudged Elastic Band Method. This method initializes the surface reconstruction path between the two phases on the potential energy surface through linear interpolation between the corresponding atomic coordinates of the two structural phases. Then, through energy optimization of the elastic band, the optimal surface reconstruction path between the two structural phases on the potential energy surface is determined. However, this method requires pre-determining the atomic matching mode between the two structures before application, and the atomic matching mode directly affects the optimization result of the surface reconstruction path. Especially when the two crystal phase structures involve a large number of atoms and have complex structures, the atomic matching becomes diverse and cumbersome. Existing methods of matching by manual observation are prone to introducing many subjective factors, leading to errors and low efficiency. Summary of the Invention

[0003] The purpose of this invention is to provide an optimal atomic matching search method for reconstructing paths on the surface of solid materials in order to improve the accuracy and efficiency of atomic matching between two structures.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] An optimal atomic matching search method for reconstructing paths on the surface of a solid material, the method comprising:

[0006] S1. Initialize population parameters. The individuals in each population are arranged in an atomic order, which is a gene sequence composed of atomic numbers.

[0007] S2. Initialize the gene sequences corresponding to individuals in the population;

[0008] S3. Select a structural phase as a reference structural phase, calculate the fitness value of each individual under the corresponding gene sequence, and select the individual with the lowest fitness value as the optimal individual in the population currently searched.

[0009] S4. Each individual in the population performs a crossover operation with the currently searched best individual in the population;

[0010] S5. Individuals in each population undergo mutation operations to generate a new generation of population;

[0011] S6. Calculate the fitness values ​​of the new generation population, and select the N individuals corresponding to the N lowest fitness values ​​as the resulting population individuals;

[0012] S7. Determine whether the convergence criterion or the upper limit of the number of generations has been reached. If so, stop reproduction and output the population individuals resulting from S6 as the optimal atomic matching mode for this structural phase. Otherwise, use the new generation population individuals selected in S6 as the population individuals in S4 and return to S4.

[0013] Furthermore, the specific steps of S2 are as follows:

[0014] S21. Set the sequence of atom numbers in the reference structure phase to (1, 2, ..., n), set the sequence of atom numbers in the matching structure phase to (1*, 2*, ..., n*), and set the gene sequence to (i1, i2, i3, ..., i...). n ), where the x-th element i in the gene sequence x This represents the atom number in the matching structure phase (1*, 2*, ..., n*) that matches the x-th atom among atoms 1 to n in the reference structure phase. x Let {1*, 2*, ..., n*} be the reference structure phase and the matching structure phase, where the atoms of the same chemical element are numbered consecutively. Let the atoms of the same chemical element M in the reference structure phase be numbered y, y+1, ..., z. Then the atoms of the same chemical element M in the matching structure phase corresponding to the reference structure are numbered y*, (y+1)*, ..., z*. In the gene sequence, any atom number in {y*, (y+1)*, ..., z*} must be the value of the element at position y, y+1, ..., z in the gene sequence. The elements at position y, y+1, ..., z are called elements of the same chemical element M, and y, y+1, ..., z are called element positions of the same chemical element M.

[0015] S22. Randomly rearrange the elements of the same chemical element in the gene sequence within the range of the element positions of the same chemical element to obtain the initial gene sequence of each individual.

[0016] Furthermore, the fitness value is specifically as follows:

[0017]

[0018] Where, d x Represents the x-th element i of an individual in the population. xThe corresponding number in the matching structure phase is the atom, that is, the atom number in the matching structure phase is i. x The shortest distance between the atom in the reference structure phase and the corresponding atom in the reference structure phase, that is, the atom with atomic number x in the reference structure phase.

[0019] Furthermore, the specific steps of S4 are as follows:

[0020] S41. Retain the portion of the gene sequence of each individual in the initial population that overlaps with the gene sequence of the individual in the optimal population.

[0021] S42. Select the parts of the gene sequence of each individual in the population that are different from the gene sequence of the individual in the optimal population. For the selected parts, randomly select two elements of the same chemical element within the element position range of the same chemical element and swap their positions so that the element value at one of the two positions is the same as the element value at that position of the individual in the optimal population.

[0022] Furthermore, the specific steps of S5 are as follows:

[0023] For each individual in the population obtained from S4 after crossover, randomly swap the positions of two elements of the same chemical element within the same element position range of the individual to obtain a new generation population.

[0024] Furthermore, the specific steps to determine whether the convergence criterion or the upper limit of the proliferative generation has been met are as follows:

[0025] Determine whether any one of the four conditions is met, where the four conditions are as follows:

[0026] In a continuously generated population of generations L, the fitness value of the currently searched best individual in the population changes within a threshold range;

[0027] In the continuously generated L-generation population, each individual in the population is optimized to the currently searched best individual in the population;

[0028] The best individual in the population found so far The value reaches 0, where d x Represents the x-th element i of an individual in the population. x The corresponding atom in the matching structure phase, that is, the atom with atomic number i in the matching structure phase. x The shortest distance between the atom of the reference structure phase and the corresponding atom in the reference structure phase, that is, the atom with atomic number x in the reference structure phase;

[0029] The number of generations of reproduction has reached its limit.

[0030] Furthermore, the specific steps of S3 are as follows:

[0031] Calculate the fitness value of each individual under the corresponding gene sequence, select the individual with the lowest fitness value as the current optimal individual in the population, and use the fitness value of each individual as the initial historical lowest fitness value of each individual.

[0032] Furthermore, the specific steps of S6 are as follows:

[0033] Obtain the current historical minimum fitness value, calculate the fitness value of each individual in the new generation of population S5, update the historical minimum fitness value and corresponding gene sequence of each individual in the new generation of population, take the gene sequence corresponding to the N smallest fitness values ​​of each individual in the new generation of population as the N individuals with the lowest fitness values, which are the result population individuals, and take the individual corresponding to the smallest historical minimum fitness value of each individual in the new generation of population as the new currently searched optimal population individual.

[0034] Furthermore, when S6 is executed for the first time, the initial historical minimum fitness value of S3 is used as the current historical minimum fitness value.

[0035] Furthermore, the specific steps for obtaining the current historical minimum fitness value, calculating the fitness value of each individual in the new generation of S5, and updating the historical minimum fitness value and corresponding gene sequence of each individual in the new generation are as follows:

[0036] Obtain the current historical minimum fitness values ​​{c1, c2, ..., cn}, calculate the fitness values ​​{b1, b2, ..., bn} of each individual in the new generation population of S5, compare bj with cj, update cj to the smaller value between bj and cj, and obtain the new historical minimum fitness values ​​{c1, c2, ..., cn}. The new historical minimum fitness values ​​{c1, c2, ..., cn} are the historical minimum fitness values ​​of each individual in the new generation population, and update the gene sequences corresponding to the historical minimum fitness values ​​of each individual in the new generation population.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) This invention realizes the automation of atomic matching between two structural phases, freeing up manpower and reducing human error. Especially for complex systems with a large number of atoms, it can efficiently and accurately construct the surface reconstruction path.

[0039] (2) By changing the atomic matching method between two structural phases, the paths with the lowest fitness values ​​are selected, thereby realizing the design of multiple possible optimal surface reconstruction paths. This overcomes the limitation of manual enumeration of atomic matching on path search, greatly expands the path search space, and finds the optimal surface reconstruction path from the level with the shortest distance between the atoms that match the two structures, making the found surface reconstruction path closer to the globally optimal surface reconstruction path. Attached Figure Description

[0040] Figure 1 This is a flowchart of the present invention;

[0041] Figure 2 A schematic diagram for calculating the fitness value;

[0042] Figure 3 This is a diagram illustrating crossover and mutation operations;

[0043] Figure 4 To match the structure of the (011) facet of rutile titanium dioxide with itself using the present invention, the variation of the adaptation value after 120 generations of propagation is shown in the figure.

[0044] Figure 5 To use this invention to match the (001) surface structure of brookite-type titanium dioxide with itself, the variation of the adaptation value after 120 generations of propagation is shown in the figure.

[0045] Figure 6 This is a diagram showing the change in the adaptation values ​​of the 12 atoms in the outermost layer of the (011) facet structure of rutile titanium dioxide and the (001) facet structure of brookite titanium dioxide after 5 generations of propagation.

[0046] Figure 7 This is a graph showing the adaptation values ​​of the (011) facet structure of rutile titanium dioxide and the (001) facet structure similar to brookite titanium dioxide after 220 generations of propagation according to the present invention. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0048] To efficiently and accurately determine the optimal atomic matching scheme between two structural phases, this invention proposes an optimal atomic matching search method for reconstructing paths on the surface of solid materials. This method calculates the optimal and potential atomic matching modes between the two structural phases. The flowchart of the method is as follows: Figure 1 As shown.

[0049] The method includes the following steps:

[0050] S1. Obtain two structural phases that can be converted into each other. The geometric structures of the two structural phases are determined and different. Select one structural phase as the reference structural phase and the other structural phase as the matching structural phase corresponding to the reference structural phase. Initialize the population parameters.

[0051] S2. Initialize the gene sequence corresponding to the individual in the population. The gene sequence is a sequence composed of the sequence numbers of the atoms in the matching structural phase that correspond one-to-one with the atoms 1 to n in the reference structural phase.

[0052] S3. Calculate the fitness value of each individual under the corresponding gene sequence, and select the individual with the lowest fitness value as the best individual in the population currently searched.

[0053] S4. Each individual in the population performs a crossover operation with the currently searched best individual in the population;

[0054] S5. Individuals in each population undergo mutation operations to generate a new generation of population;

[0055] S6. Calculate the fitness value of the new generation population, select the N population individuals corresponding to the N lowest fitness values ​​as the result population individuals, and update the currently searched best population individual.

[0056] S7. Determine whether the convergence criterion or the upper limit of the number of generations has been reached. If so, stop reproduction and output the population individuals resulting from S6 as the optimal atomic matching mode between the two structural phases. Otherwise, use the new generation of population individuals generated in S5 as the population individuals in S4, and use the updated currently searched optimal population individual as the currently searched optimal population individual in S4, and return to S4.

[0057] In S1, two interconvertible structural phases represent two structural phases with the same number of atoms and the same number of atoms of the same chemical element.

[0058] The specific steps of S2 are as follows:

[0059] S21. Set the sequence of atom numbers in the reference phase to (1, 2, ..., n), and set the sequence of atom numbers in the matching phase to (1*, 2*, ..., n*). Then the initial gene sequence is (i1, i2, i3, ..., i...). n ), where the x-th element i in the gene sequence x This represents the atom number in the matching structure phase (1*, 2*, ..., n*) that matches the x-th atom among atoms 1 to n in the reference structure phase. x ∈{1*, 2*, ..., n*};

[0060] S22. Randomly rearrange the elements corresponding to the atoms of the same chemical element in the gene sequence to obtain the initial gene sequence of each individual.

[0061] In S21, the sequence of atom numbers in the reference phase is set to (1, 2, ..., n), the sequence of atom numbers in the matching phase is set to (1*, 2*, ..., n*), and the gene sequence is (i1, i2, i3, ..., in ), where the x-th element i in the gene sequence x This represents the atom number in the matching structure phase (1*, 2*, ..., n*) that matches the x-th atom among atoms 1 to n in the reference structure phase. x ∈{1*,2*……,n*}, where n is the number of atoms in the structural phase.

[0062] In the reference and matched structural phases, the atoms of the same chemical element are numbered consecutively. It is assumed that the atoms of the same chemical element M in the reference structural phase are numbered consecutively as y, y+1, ..., z, and the atoms of the same chemical element M in the matched structural phase corresponding to the reference structure are numbered as y*, (y+1)*, ..., z*, where y*, (y+1)*, ..., z* are also consecutively arranged values.

[0063] In the reference structure phase, the elements are arranged in the order of all atomic numbers of all elements M1, all atomic numbers of all elements M2, all atomic numbers of all elements M3, and so on. The elemental order of the matching structure phase (M1, M2, M3, ...) is the same as that of the reference structure phase.

[0064] Therefore, elements y to z in a gene sequence are called elements with the same chemical element, and y, y+1, ..., z are called the element positions of the same chemical element. In the gene sequence, y*, (y+1)*, ..., z* must be arranged in a certain order at the positions y, y+1, ..., z. Any value in {y*, (y+1)*, ..., z*} must be the value of an element at one of the positions y, y+1, ..., z in the gene sequence. Elements y, y+1, ..., z are called elements of the same chemical element M, and y, y+1, ..., z are called the element positions of the same chemical element M.

[0065] For example, let the gene sequence be (i1, i2, i3, i4), the reference phase numbering sequence be (1, 2, 3, 4), and the corresponding matching phase numbering sequence be (1*, 2*, 3*, 4*). Assuming atoms numbered 1 and 2 are atoms of the same element M1, and atoms numbered 3 and 4 are atoms of the same element M2, then atoms numbered 1* and 2* are atoms of the same element M1, and atoms numbered 3* and 4* are atoms of the same element M2. In the initialized individual (i1, i2, i3, i4), the values ​​of i1 and i2 are 1*, 2* or 2*, 1*, and the values ​​of i3 and i4 are 3*, 4* or 4*, 3*.

[0066] In S22, the elements of the same chemical element in the gene sequence are randomly rearranged within the range of the element positions of the same chemical element to serve as the initial gene sequence for each individual. Taking the individual (1*, 2*, 3*, 4*) initialized in S1 as an example, the first and second element positions are the element positions of the same chemical element M1, and the third and fourth element positions are the element positions of the same chemical element M2.

[0067] When performing a random rearrangement, elements 1* and 2* are rearranged between the first and second element positions, and elements 3* and 4* are rearranged between the third and fourth element positions.

[0068] In S3, the distance between each atom in the corresponding atomic matching sequence and the corresponding atom in the reference structure is calculated to obtain the fitness value of the individual.

[0069] The principle of calculating distance in fitness values ​​is as follows: Figure 2 As shown. Figure 2 In this example, assume structural phase A is the reference structural phase and B is the corresponding matching structural phase. Structural phases A and B are placed in a supercell. During the transformation from structural A to structural B, assume that atom number 1 in structural phase A and atom number 2* in structural B are the same atom before and after the transformation, and atom number 2 in structural phase A and atom number 1* in structural B are the same atom before and after the transformation. The gene sequence is (2*, 1*). Let d1 be the distance between atom number 1 in structural A and atom number 2* in structural B, and d2 be the distance between atom number 2 in structural A and atom number 1* in structural B. Then d1 and d2 represent the distances between each atom in this individual's gene sequence and its corresponding atom in the reference structure.

[0070] The negative of the sum of the reciprocals of the squares of the distances between the corresponding atoms is chosen as the fitness value, i.e.:

[0071]

[0072] Where fit is the fitness value of an individual in the population, d i It is the shortest distance between atoms i of two structures under periodic boundary conditions. To avoid d i If the value is 0, the threshold is set to 0.01, meaning all distances d less than the threshold of 0.01 are considered. iAll values ​​are truncated to 0.01. Considering the movement of atoms during the reconstruction reaction, which is usually accompanied by bond breaking and requires additional energy for excitation, it is generally necessary to have fewer atoms involved in the movement and to minimize the distance the atoms involved in the movement travel. Choosing this fit value allows the surface reconstruction paths between the two optimized structures to preferentially match atoms in similar positions before and after surface reconstruction, while avoiding multi-atom cooperative motion modes as much as possible.

[0073] Sum of the squares of the distances between each corresponding atom As another fitness metric, it is used to track and observe the optimization progress;

[0074] Square the largest corresponding atomic distance As another fitness metric, it is used to track and observe the optimization progress.

[0075] Figure 2 In this context, the distance between atom number 2 in structure A and atom number 1* in structure B, and the distance between atom number 1 in A and atom number 2* in structure B, represent the distances between each atom in the individual's gene sequence (2*, 1*) and its corresponding atom in the reference structure. Similarly, taking the individual [1*, 2*, 4*, 3*] as an example, assuming the atom numbers of the reference structure phase are [1, 2, 3, 4], the distances between each atom and its corresponding atom in the reference structure represent the distances between atom number 1 in the reference structure phase and atom number 1* in the matching structure phase, atom number 2 in the reference structure phase and atom number 2* in the matching structure phase, atom number 4 in the reference structure phase and atom number 3* in the matching structure phase, and atom number 3 in the reference structure phase and atom number 4* in the matching structure phase. Fitness values ​​are then calculated based on these distances.

[0076] In S3, the specific steps for selecting the individual with the lowest fitness value as the currently searched optimal individual are as follows:

[0077] First, calculate the fitness value of each individual in the population. The fitness value of each individual in the population is used as the current fitness value. The minimum current fitness value is set as the optimal fitness value found in the current search.

[0078] The fitness value of each individual in the population is used as the initial historical minimum fitness value of each individual, and the gene sequence corresponding to the historical minimum fitness value of each individual is updated.

[0079] Based on the updated results, obtain the fitness value and corresponding atom number sequence of the currently searched optimal population individual.

[0080] In S3, the fitness value of each individual in the initial population is calculated, and the minimum fitness value x among all individuals is calculated. The individual corresponding to the minimum fitness value x is the initial currently searched optimal individual in the population. At the same time, the fitness value of each individual in the initial population is used as the initial historical minimum fitness value {a1, a2, ..., an} of each individual.

[0081] In S4, the specific steps for the crossover operation between each individual in the population and the currently found best individual in the population are as follows:

[0082] S41. Retain the portion of the gene sequence of each individual in the initial population that overlaps with the gene sequence of the individual in the optimal population.

[0083] S42. Select the parts of the gene sequence of each individual in the population that are different from the gene sequence of the individual in the optimal population. For the selected parts, randomly select two elements of the same chemical element within the element position range of the same chemical element and swap their positions so that the element value at one of the two positions is the same as the element value at that position of the individual in the optimal population.

[0084] In S5, the specific steps for each individual in the population to undergo mutation operations to generate a new generation of population are as follows:

[0085] For each individual in the population obtained from S4 after crossover, randomly swap the positions of two elements of the same chemical element within the same element position range of the individual to obtain a new generation population.

[0086] Example diagrams of crossover and mutation are shown below. Figure 3 As shown. Figure 3 In the crossover operation, assuming the reconstructed unit cell contains 9 atoms numbered 1 to 9, and all elements 1 to 9 are the same chemical element. Let the gene sequence of the currently searched optimal individual be [3 5 7 2 6 4 9 1 8], and the current generation's individual i is [2 53 7 6 4 1 8 9]. Then its 2nd and 5th-6th elements match those of the currently searched optimal individual, such as... Figure 3 The part highlighted in black. Then, randomly select the atom number from individual i in the current generation that is inconsistent with the currently searched best individual within the elemental position range of the same chemical element. For example... Figure 3 The first element 2 of the current generation of population individual i is swapped to make the first atom number of the current generation of population individual i consistent with the currently searched best individual.

[0087] When performing a mutation operation, the swapped element can be either the same as the currently found best individual or an element that is different from the currently found best individual. For example... Figure 3 As shown, the third and sixth elements of an individual in the population are randomly selected, and then their positions are swapped.

[0088] In S6, the fitness values ​​of each individual in the population are recalculated, and the N individuals with the lowest fitness values ​​are determined. The specific steps are as follows:

[0089] S6.1. Obtain the current historical lowest fitness value {c1, c2, ..., cn};

[0090] When S6 is executed for the first time, the initial historical minimum fit value {a1, a2, ..., an} is used as the current historical minimum fit value {c1, c2, ..., cn}. The value of a1 is assigned to c1, the value of a2 is assigned to c2, and so on, until the value of an is assigned to cn.

[0091] S6.2 Recalculate the fitness values ​​of each individual in the new generation population, and update the historical minimum fitness values ​​and corresponding gene sequences of each individual in the new generation population.

[0092] The specific steps for updating are as follows:

[0093] The current historical minimum fitness value of each individual is compared with the fitness values ​​of all individuals in the new generation population. The current historical minimum fitness values ​​are {c1, c2, ..., cn}, and the fitness values ​​of all individuals in the new generation population are {b1, b2, ..., bn}. c1 is compared with b1, c2 with b2, and so on. The c1 value in the current historical minimum fitness values ​​{c1, c2, ..., cn} is updated to the smaller of c1 and b1. This process is repeated to obtain new historical minimum fitness values ​​{c1, c2, c3, ...}. The individual corresponding to the smallest value in the new historical minimum fitness values ​​{c1, c2, c3, ...} is the new optimal individual found in the current population.

[0094] The gene sequences corresponding to the N smallest fitness values ​​among the individuals in each population of the new generation are taken as the N individuals with the lowest fitness values, which are the resulting population individuals.

[0095] In S6, based on the lowest fitness values ​​of each individual in the new generation population, the top N optimal gene sequences, as well as the atomic matching sequence with the lowest fitness value and its corresponding three fitness indices, are updated. Depending on the complexity of the reconstruction reaction, the number of individuals N in the resulting population can be appropriately increased; for common reconstruction reactions, a value of 20 for N is recommended.

[0096] In S7, if any of the following four conditions are met, reproduction stops, and the top N individuals of the population are output. These N individuals may all be the optimal atomic matching patterns.

[0097] ① In the L generations of continuous generation, the fitness value of the currently searched optimal population individual does not change significantly. Depending on the complexity of the reconstruction response, the threshold L can be appropriately increased; for common reconstruction responses, it is recommended that the value of L be 100.

[0098] ② In the L generations of continuous generation, all individuals in the population are optimized to the currently searched best individuals in the population;

[0099] ③The currently found optimal individual in the population The value reaches 0;

[0100] ④ The number of generations of reproduction has reached its limit;

[0101] If none of the above four conditions are met, the individual corresponding to the smallest value among the new historical minimum fitness values ​​{c1, c2, c3...} will be the new currently searched optimal population individual, and the new historical minimum fitness value {c1, c2, c3...} will be used as the current historical minimum fitness value. The new generation of population individuals generated in S5 will be used as the population individuals in S4 and returned to S4 for crossover and mutation operations.

[0102] If any condition is met, the resulting population of S6 is output as the optimal atomic matching mode between the two structural phases.

[0103] Compared to manually matching atomic sequences between two structural phases when constructing the initial path using existing NEB calculations, this invention has the following advantages:

[0104] (1) It realizes the automation of atomic matching between two structural phases, freeing up manpower and reducing human error. Especially for complex systems with a large number of atoms, it can efficiently and accurately construct the surface reconstruction path.

[0105] (2) By changing the atomic matching method between two structural phases, the paths with the lowest fitness values ​​are selected, thereby realizing the design of multiple possible optimal surface reconstruction paths. This overcomes the limitation of manual enumeration of atomic matching on path search, greatly expands the path search space, and makes the found surface reconstruction path closer to the globally optimal surface reconstruction path;

[0106] (3) Find the optimal surface reconstruction path from the level where the distance between the atoms of two matched structures is the shortest.

[0107] The following is an actual experiment:

[0108] Experiment 1: Taking structure 1 of the (011) face of rutile titanium dioxide and its 2×1 reconstructed structure 2, which is similar to the (001) face of brookite titanium dioxide, as examples, both structures contain 48 atoms (including 32 O atoms and 16 Ti atoms). Therefore, the theoretical atomic matching number between the two structures is as high as 10. 48 (32! × 16!) kinds. To test the accuracy and efficiency of our algorithm, we performed atomic matching between structure 1 and itself, and between structure 2 and itself. Clearly, for these two matching tasks, the optimal matching result is that the gene sequences of the two matched objects are the same in each task; that is, the gene sequence corresponding to the optimal matching pattern is (1*, 2*, 3*, 4*, 5*, ..., 47*, 48*). After 116 and 123 generations of reproduction respectively, the gene sequences of structure 1 and structure 2 are:

[0109]

[0110] as well as The value has reached its lowest point, such as... Figure 4 and Figure 5 As shown, all of them have been matched with their own matching patterns, and the gene sequences of the patterns are (1*, 2*, 3*, 4*, 5*, ..., 47*, 48*).

[0111] The method of the present invention includes the following steps:

[0112] Step 1: Set the number of individuals in the population to 100 and the maximum number of generations to 50,000;

[0113] Step 2: Randomly initialize the gene sequences of individuals in the population. The specific steps are as follows:

[0114] 2.1 Each Ti atom and O atom in the unit cell is labeled with a number, and the numbers of all atoms form a sequence [i1, i2, i3…, i…]. n ], where n is the number of atoms, and the Ti atoms are numbered consecutively, and the O atoms are numbered consecutively;

[0115] 2.2 The atomic numbers of Ti element in each individual population are randomly rearranged, and the atomic numbers of O element in each individual population are randomly rearranged to serve as the initial gene sequence for each individual population.

[0116] Step 3: Select one of the (011) plane structures of the two rutile titanium dioxide phases as the reference structure phase, and calculate the distance d between each atom and the corresponding atom in the reference structure for each individual in the population under the corresponding atomic matching sequence. i The fitness value of each individual in the population is calculated using the following formula.

[0117]

[0118] Based on the fitness values ​​of each individual in the population, the individual with the lowest fitness value is selected as the currently searched optimal individual. The specific steps for selecting the individual with the lowest fitness value as the currently searched optimal individual are as follows:

[0119] 3.1 Update the historical minimum fitness value of each individual in each population and its corresponding gene sequence, and set the minimum historical minimum fitness value of each individual in each population as the currently searched optimal fitness value;

[0120] 3.2 Based on the updated results, obtain the fitness value and corresponding gene sequence of the currently searched optimal population individual.

[0121] Step 4: Perform cross-operation between each individual in the population and the currently found best individual in the population:

[0122] 4.1 Retain the portion of the gene sequence corresponding to each individual in the population that overlaps with the sequence of the currently searched best individual;

[0123] 4.2 Randomly select two atomic numbers from different parts of each individual in the population and swap their positions so that one of them matches the currently searched best individual.

[0124] Step 5: Perform mutation operations on individuals in each population to generate a new generation of population.

[0125] 5.1 Randomly swap the numbering order of the two Ti atoms in each individual of the population;

[0126] 5.2 Randomly swap the numbering order of the two atoms of element O in each individual of the population.

[0127] Step 6: Recalculate the fitness values ​​of individuals in each population and determine the 20 individuals with the lowest fitness values.

[0128] Step 7: Determine whether the convergence criterion or the upper limit of the number of generations has been reached. Specifically, step (7) includes:

[0129] If any of the following four conditions are met, then reproduction will stop, and the 20 best individuals in the population will be output. These 20 individuals may all be the best atomic matching patterns.

[0130] ① In 100 consecutive generations, the fitness value of the currently searched best individual in the population does not change significantly;

[0131] ② In 100 consecutive generations, all individuals in the population are optimized to the best population individual found in the current search;

[0132] ③The currently found optimal individual in the population The value reaches 0;

[0133] ④ The number of generations of reproduction has reached the upper limit.

[0134] If none of the above four conditions are met, return to step (4).

[0135] In Experiment 1, both structures contained 48 atoms (32 O atoms and 16 Ti atoms). The structural transformation pathways of the 12 atoms in the outermost layer of both structures (8 O atoms and 4 Ti atoms) were analyzed. The theoretical number of matches was as high as 10. 6 (8! × 4!) types, using the method of this invention, only 5 generations are needed, such as... Figure 6 As shown,

[0136]

[0137] The value has reached its lowest point.

[0138] Experiment 2: Using structures 1 (011) of rutile titanium dioxide and 2 (001) of titanium dioxide (similar to brookite titanium dioxide) as examples. Both structures contain 48 atoms (32 O atoms and 16 Ti atoms). Therefore, their theoretical matching number is as high as 10. 48 (32! × 16!) types, matching all atoms in structure 1 and structure 2. After 220 generations of propagation, such as Figure 7 As shown,

[0139]

[0140] and The value has reached its lowest point, the former reaching... The latter reached The optimal atomic matching between the two structural phases has been found.

[0141] This invention proposes an optimal atomic matching search method for surface reconstruction paths of solid materials. The method includes the following steps: (1) setting the number of individuals in the population and the maximum number of generations; (2) randomly initializing the gene sequences of each individual in the population; (3) calculating the fitness value of the gene sequences of each individual in the population, and selecting the individual with the lowest fitness value as the currently searched optimal individual in the population; (4) performing crossover between each individual in the population and the optimal individual in the population; (5) randomly performing mutation operations on each individual in the population to generate a new generation of population; (6) recalculating the fitness value of each individual in the population, and selecting the optimal individual in the population so far; (7) determining whether the convergence criterion or the upper limit of the number of generations has been reached. If so, output the top N individuals in the population that are the best and second best; if not, return to step (4). Compared with the existing manual matching method, this invention can realize the automatic search for the optimal atomic matching mode between two structural phases, freeing up manpower, and overcoming the limitations brought by the inaccuracy / singleness of manual enumeration of atomic matching to the surface reconstruction path search.

[0142] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for searching for optimal atomic matching of reconstructed paths on the surface of a solid material, characterized in that, The methods include: S1. Obtain two structural phases that can be converted into each other. The geometric structures of the two structural phases are determined and different. Select one structural phase as the reference structural phase and the other structural phase as the matching structural phase corresponding to the reference structural phase. Initialize the population parameters. S2. Initialize the gene sequence corresponding to the individual in the population. The gene sequence is a sequence composed of the sequence numbers of the atoms in the matching structural phase that correspond one-to-one with the atoms 1 to n in the reference structural phase. S3. Calculate the fitness value of each individual under the corresponding gene sequence, and select the individual with the lowest fitness value as the best individual in the population currently searched. S4. Each individual in the population performs a crossover operation with the currently searched best individual in the population; S5. Individuals in each population undergo mutation operations to generate a new generation of population; S6. Calculate the fitness value of the new generation population, select the N population individuals corresponding to the N lowest fitness values ​​as the result population individuals, and update the currently searched best population individual. S7. Determine whether the convergence criterion or the upper limit of the number of generations has been reached. If so, stop reproduction and output the population individuals resulting from S6 as the optimal atomic matching mode between the two structural phases. Otherwise, use the new generation of population individuals generated in S5 as the population individuals in S4, and use the updated currently searched optimal population individual as the currently searched optimal population individual in S4, and return to S4.

2. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 1, characterized in that, The specific steps of S2 are as follows: S21. Set the sequence of atom numbers in the reference structure phase to (1, 2, ..., n), set the sequence of atom numbers in the matching structure phase to (1*, 2*, ..., n*), and set the gene sequence to (i1, i2, i3, ..., i...). n ), where the x-th element i in the gene sequence x This represents the atom number in the matching structure phase (1*, 2*, ..., n*) that matches the x-th atom among atoms 1 to n in the reference structure phase. x Let {1*, 2*, ..., n*} be the reference structure phase and the matching structure phase, where the atoms of the same chemical element are numbered consecutively. Let the atoms of the same chemical element M in the reference structure phase be numbered y, y+1, ..., z. Then the atoms of the same chemical element M in the matching structure phase corresponding to the reference structure are numbered y*, (y+1)*, ..., z*. In the gene sequence, any atom number in {y*, (y+1)*, ..., z*} must be the value of the element at position y, y+1, ..., z in the gene sequence. The elements at position y, y+1, ..., z are called elements of the same chemical element M, and y, y+1, ..., z are called element positions of the same chemical element M. S22. Randomly rearrange the elements of the same chemical element in the gene sequence within the range of the element positions of the same chemical element to obtain the initial gene sequence of each individual.

3. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 2, characterized in that, The fitness value is specifically: Where, d x Represents the x-th element i of an individual in the population. x The corresponding number in the matching structure phase is the atom, that is, the atom number in the matching structure phase is i. x The shortest distance between the atom in the reference structure phase and the corresponding atom in the reference structure phase, that is, the atom with atomic number x in the reference structure phase.

4. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 3, characterized in that, The specific steps of S4 are as follows: S41. Retain the portion of the gene sequence of each individual in the initial population that overlaps with the gene sequence of the individual in the optimal population. S42. Select the parts of the gene sequence of each individual in the population that are different from the gene sequence of the individual in the optimal population. For the selected parts, randomly select two elements of the same chemical element within the element position range of the same chemical element and swap their positions so that the element value at one of the two positions is the same as the element value at that position of the individual in the optimal population.

5. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 4, characterized in that, The specific steps of S5 are as follows: For each individual in the population obtained from S4 after crossover, randomly swap the positions of two elements of the same chemical element within the same element position range of the individual to obtain a new generation population.

6. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 1, characterized in that, The specific steps to determine whether the convergence criterion or the upper limit of the proliferative algebra has been met are as follows: Determine whether any one of the four conditions is met, where the four conditions are as follows: In a continuously generated population of generations L, the fitness value of the currently searched best individual in the population changes within a threshold range; In the continuously generated L-generation population, each individual in the population is optimized to the currently searched best individual in the population; The best individual in the population found so far The value reaches 0, where d x Represents the x-th element i of an individual in the population. x The corresponding atom in the matching structure phase, that is, the atom with atomic number i in the matching structure phase. x The shortest distance between the atom of the reference structure phase and the corresponding atom in the reference structure phase, that is, the atom with atomic number x in the reference structure phase; The number of generations of reproduction has reached its limit.

7. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 3, characterized in that, The specific steps for S3 are as follows: Calculate the fitness value of each individual under the corresponding gene sequence, select the individual with the lowest fitness value as the current optimal individual in the population, and use the fitness value of each individual as the initial historical lowest fitness value of each individual.

8. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 7, characterized in that, The specific steps of S6 are as follows: Obtain the current historical minimum fitness value, calculate the fitness value of each individual in the new generation of population S5, update the historical minimum fitness value and corresponding gene sequence of each individual in the new generation of population, take the gene sequence corresponding to the N smallest fitness values ​​of each individual in the new generation of population as the N individuals with the lowest fitness values, which are the result population individuals, and take the individual corresponding to the smallest historical minimum fitness value of each individual in the new generation of population as the new currently searched optimal population individual.

9. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 8, characterized in that, When S6 is executed for the first time, the initial historical minimum fitness value of S3 is used as the current historical minimum fitness value.

10. The optimal atomic matching search method for reconstructing paths on the surface of a solid material according to claim 9, characterized in that, The specific steps for obtaining the current historical minimum fitness value, calculating the fitness value of each individual in the new generation of the S5 population, and updating the historical minimum fitness value and corresponding gene sequence of each individual in the new generation population are as follows: Obtain the current historical minimum fitness values ​​{c1, c2, ..., cn}, calculate the fitness values ​​{b1, b2, ..., bn} of each individual in the new generation population of S5, compare bj with cj, update cj to the smaller value between bj and cj, and obtain the new historical minimum fitness values ​​{c1, c2, ..., cn}. The new historical minimum fitness values ​​{c1, c2, ..., cn} are the historical minimum fitness values ​​of each individual in the new generation population, and update the gene sequences corresponding to the historical minimum fitness values ​​of each individual in the new generation population.

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