Crystal structure analysis method

Abstract

To provide a crystal structure analysis method with improved analysis accuracy.SOLUTION: The method for analyzing a crystal structure causes a computer to perform a process including the steps for acquiring an atomic resolution image of a predetermined crystal structure, calculating the coordinates of all bright spots in the atomic resolution image, arbitrarily selecting any one of the bright spots at the coordinates as a first bright spot, arbitrarily selecting, from eight bright spots closest to the first bright spot, a first adjacent point, centering on the selected first bright spot, sequentially selecting, from the eight bright spots, either to the right or left of the first adjacent point, a second adjacent point and a third adjacent point, setting the length of each line segment between the first bright spot and any one of the first to third nearest points, and the angle between the respective line segments, as parameters indicating the characteristics of the quadrilateral formed by four points, the first bright spot and the first to third nearest points, and on the basis of these parameters, clustering the atomic resolution image using machine learning methods.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a crystal structure analysis method. [Background technology]

[0002] Various methods have been developed to analyze crystal structures.

[0003] Patent Document 1 discloses a method for analyzing crystal structure by electron diffraction. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-142357 Summary of the Invention [Problem to be solved by the invention]

[0005] There is room for improvement in the accuracy of crystal structure analysis.

[0006] An object of the present disclosure is to provide a crystal structure analysis method with improved analysis accuracy. [Means for solving the problem]

[0007] The present inventors have found that the above problems can be solved by the following means. <Aspect 1> A method for crystal structure analysis, which causes a computer to execute a process including the following steps: obtaining an atomic resolution image of a given crystal structure; Calculating the coordinates of all bright points in the acquired atomic resolution image; arbitrarily selecting one of the bright points at the calculated coordinates as a first bright point; arbitrarily selecting a first nearest point from eight bright points that are closest to the selected first bright point, and then selecting a second nearest point and a third nearest point from the eight bright points in order from the first nearest point in either a clockwise or counterclockwise direction around the first bright point; setting the length of each line segment between the selected first bright point and any of the first to third nearest points and the angle between each line segment as parameters indicating characteristics of a quadrangle formed by four points of the first bright point and the first to third nearest points; Clustering the atomic resolution images using a machine learning technique based on the set parameters. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to provide a crystal structure analysis method with improved analysis accuracy. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a flow chart illustrating the disclosed method for solving a crystal structure. [Figure 2] FIG. 2 is a schematic diagram illustrating the disclosed method for analyzing crystal structures. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, embodiments of the present disclosure will be described in detail. Note that the present disclosure is not limited to the following embodiments, and various modifications can be made within the scope of the present disclosure.

[0011] 《Crystal structure analysis method》 The disclosed method for analyzing a crystal structure causes a computer to execute a process including the following steps: acquiring an atomic resolution image of a predetermined crystal structure, calculating the coordinates of all bright spots in the acquired atomic resolution image, arbitrarily selecting one of the bright spots at the calculated coordinates as a first bright spot, arbitrarily selecting a first neighboring point from the eight bright spots closest to the selected first bright spot, and then selecting a second neighboring point and a third neighboring point from the eight bright spots in order, in either direction, around the selected first bright spot; setting the length of each line segment between the selected first bright spot and any of the first to third neighboring points, and the angle between each line segment, as parameters indicating the characteristics of a rectangle formed by the four points between the first bright spot and the first to third neighboring points; and clustering the atomic resolution image using a machine learning technique based on the set parameters.

[0012] The present inventors have found that it is difficult to analyze crystal structures on the sub-nanometer order using electron beam diffraction. The reason for this, without intending to be bound by any theory, is thought to be that when a narrowed electron beam is irradiated to increase resolution and the crystal structure is analyzed from the resulting diffraction pattern, the accuracy of the analysis decreases due to factors such as scattering of the electron beam and difficulty in determining the electron beam irradiation position.

[0013] In this regard, the present inventors have devised the use of coordinates of bright spots in an atomic resolution image of a predetermined crystal structure, and have made the present disclosure. More specifically, by calculating the coordinates of all bright spots in an atomic resolution image of a predetermined crystal structure, and clustering the atomic resolution image based on predetermined parameters that indicate the characteristics of a quadrangle formed by four adjacent bright spots at these coordinates, it is possible to clarify the crystal structure distribution in the atomic resolution image with high accuracy, and therefore to improve the accuracy of analyzing the crystal structure.

[0014] The method of the present disclosure is particularly effective when the crystal contains lattice defects or when a plurality of structures are mixed at the atomic level.

[0015] In the present disclosure, "clustering" refers to a type of so-called "unsupervised learning" in machine learning, which means classifying a data set based on specific rules, and in particular refers to hard clustering, which classifies each piece of data so that it belongs to a single cluster. Examples of such machine learning techniques include the k-means++ method and the k-medoids method.

[0016] The method of the present disclosure for analyzing a crystal structure will be described below with reference to the flowchart shown in Fig. 1 and the schematic diagram shown in Fig. 2. Fig. 1 is a flowchart illustrating the method of the present disclosure for analyzing a crystal structure, and Fig. 2 is a schematic diagram illustrating the method of the present disclosure for analyzing a crystal structure.

[0017] As shown in FIG. 1, in step 101, a computer executes a process to obtain an atomic resolution image of a given crystal structure.

[0018] The method by which a computer acquires an atomic resolution image is, but is not limited to, exemplified by scanning transmission electron microscopy (STEM). Examples of STEM include, but are not limited to, bright-field scanning transmission electron microscopy (BF-STEM) and dark-field scanning transmission electron microscopy (DF-STEM). BF-STEM may be annular bright-field scanning transmission electron microscopy (ABF-STEM). DF-STEM may be annular dark-field scanning transmission electron microscopy (ADF-STEM), particularly high-angle scattering annular dark-field scanning transmission electron microscopy (HAADF-STEM).

[0019] The target crystal structure is not particularly limited, but may be, for example, an electrode active material for a lithium ion battery, and in particular, a positive electrode active material for a lithium ion battery containing an O2 structure.

[0020] As shown in Figure 1, in step 102, the computer executes a process of calculating the coordinates of all bright spots in the acquired atomic resolution image (see Figure 2(a)). At this time, the computer may execute a process of creating a first list that stores information about the calculated coordinates of all bright spots. Furthermore, the computer may execute a process of creating a second list by deleting from the first list information about the coordinates of bright spots adjacent to the contour line of the acquired atomic resolution image.

[0021] As shown in FIG. 1, in step 103, the computer performs a process of arbitrarily selecting one of the bright spots at the calculated coordinates as a first bright spot (see FIG. 2(b)). At this time, the computer may calculate the length L of each line segment between the first bright spot and all other bright spots, and the angle θ between each line segment. The computer may also perform a process of creating a third list by adding information about the length L and the angle θ to the second list. Furthermore, the computer may also perform a process of sorting the information stored in the third list in ascending order of length L.

[0022] The length L of each line segment and the angle θ between each line segment may mean, for example: L1: Length of the line segment between the first bright point and the first nearest point L2: Length of the line segment between the first bright spot and the second closest spot L3: Length of the line segment between the first bright spot and the third closest spot θ 1-2 ...Angle between the first bright spot and the line segments between the first closest point and the second closest point θ 1-3 ...Angle between the first bright spot and the line segments between the first closest spot and the third closest spot θ 2-3 ...the angle between the line segments between the first bright point and the second and third nearest points.

[0023] As shown in Figure 1, in step 104, the computer randomly selects a first neighboring point from the eight bright points closest to the selected first bright point, and then performs a process of selecting a second neighboring point and a third neighboring point from the eight bright points, in order from the first neighboring point in either the left or right direction, with the first bright point as the center (see Figure 2(c)).

[0024] The computer may execute a process of extracting eight bright spots closest to the first bright spot based on information about each bright spot stored in the third list. More specifically, the computer may execute a process of extracting the eight bright spots by selecting information about the bright spots in the third list, in order from the bright spot with the shortest length L to the eighth shortest length L. In this case, the computer may create a fourth list from which information about bright spots other than the extracted eight bright spots is deleted.

[0025] The computer may perform a process of arbitrarily selecting a first-neighbor point from the eight bright spots, for example, a process of selecting the bright spot with the shortest length L as the first-neighbor point. In particular, as illustrated in FIG. 2(c), the computer may perform a process of selecting the bright spot with the angle θ closest to 0° and the shortest length L as the first-neighbor point. In this case, the computer may perform a process of selecting the first-neighbor point based on information about each bright spot stored in the created fourth list.

[0026] The computer executes a process of selecting the second and third neighboring points from the eight bright points in a clockwise direction starting from the first neighboring point, with the first bright point as the center. For example, as illustrated in FIG. 2(c), the computer may execute a process of selecting the second and third neighboring points from the eight bright points in a clockwise direction starting from the first neighboring point, with the first bright point as the center.

[0027] As shown in Fig. 1, in step 105, the computer executes a process of setting the length L of each line segment between the selected first bright point and any of the first to third nearest points, and the angle θ between each line segment, as parameters indicating the characteristics of a quadrangle formed by the four points of the first bright point and the first to third nearest points (see Fig. 2(d)). For example, the computer may set the lengths L1, L2, and L3, and the angle θ, by deleting information other than that of the first bright point and the first to third nearest points from the fourth list. 1-2 , θ 1-3 and θ 2-3 may be executed to set the above parameters.

[0028] As shown in FIG. 1, the computer may repeat steps 103 to 105 for all bright points with the calculated coordinates.

[0029] As shown in Fig. 1, in step 106, the computer performs a process of clustering the atomic resolution image using a machine learning technique based on the set parameters (see Fig. 2(e)). This makes it possible to clarify the crystal structure distribution in the atomic resolution image with high accuracy, thereby improving the accuracy of crystal structure analysis.

[0030] Specifically, the computer may first execute a process of calculating a first average and / or standard deviation of the length L of each line segment and the angle θ between each line segment.

[0031] A threshold may be set in advance for the first average and / or standard deviation of the calculated length L of each line segment and the angle θ between each line segment, and the computer may change subsequent processing based on the magnitude of the first average and / or standard deviation relative to the threshold. The threshold may be set appropriately depending on the type of crystal structure to be targeted, etc.

[0032] For example, if the first average and / or standard deviation of all of the lengths L of each line segment and the angles θ between each line segment are smaller than a threshold value, the computer may determine that there is a single crystal structure and not cluster the atomic resolution images.

[0033] On the other hand, if the first average and / or standard deviation of either the length L of each line segment or the angle θ between each line segment is equal to or greater than a threshold, the computer can cluster the atomic resolution image into n clusters.

[0034] The computer may cluster the atomic resolution image using the k-means++ method, the k-medoids method, or the like.

[0035] The computer may execute a process of calculating the nth average and / or standard deviation of the length L of each line segment and the angle θ between each line segment for each of the n clusters obtained by clustering.

[0036] A threshold may be set in advance for the nth mean and / or standard deviation of the calculated length L of each line segment and the angle θ between each line segment, and the computer may change subsequent processing based on the magnitude of the nth mean and / or standard deviation relative to the threshold.

[0037] For example, if the average and / or standard deviation of all nth lengths L of each line segment and angles θ between each line segment is smaller than a threshold, the computer determines that the crystal structure should be classified into n clusters, and no further clustering of the atomic resolution image is required.

[0038] On the other hand, if the n-th average and / or standard deviation of either the length L of each line segment or the angle θ between the line segments is equal to or greater than a threshold, the computer can further cluster the atomic resolution image into n+1 clusters. In this case, rectangles with approximately the same parameters can be clustered into the same cluster. As shown in Figure 2(e), each cluster may be mapped, which makes it easier to visually understand the crystal structure distribution in the atomic resolution image.

[0039] The computer can execute this process, setting the initial value of n to 2, until the average and / or standard deviation of all n-th lengths L of line segments and angles θ between line segments becomes equal to or less than a threshold. The computer may execute the above process so as to cluster the entire atomic resolution image. [Example]

[0040] Example 1 Mn(NO3)2·6H2O, Ni(NO3)2·6H2O, and Co(NO3)2·6H2O were used as raw materials. Each raw material was dissolved in pure water at a molar ratio of Mn, Ni, and Co of 5:2:3. A 12% Na2CO3 solution was then prepared. Each solution was simultaneously added dropwise to a beaker containing water premixed with 10% surfactant, followed by titration. The titration rate was controlled to maintain a pH between 7.0 and 7.1. After titration, the mixture was stirred at 50°C and 300 rpm for 24 hours. The resulting reaction product was washed with pure water and separated by centrifugation to form a powder. The resulting powder was dried at 120°C for 48 hours and then crushed in an agate mortar.

[0041] The resulting powder was added with a composition ratio of Na 0.75 Mn 0.5 Ni 0.2 Co 0.3 Na2CO3 was added to the mixture to obtain O2, and the mixture was mixed. The mixed powder was pressed using cold isostatic pressing under a load of 2 tons to produce pellets. The resulting pellets were pre-fired in air at 600°C for 6 hours, then fired at 900°C for 1 hour, cooled to 250°C, and then allowed to cool to synthesize the Na-doped precursor.

[0042] The amount of Na-doped precursor was weighed so that the molar ratio of Li contained in the mixed powder obtained by mixing LiNO3 and LiCl at an 88:12 ratio was 10 times that of the Na-doped precursor. The Na-doped precursor was mixed with the LiNO3·LiCl·LiH mixed powder, and ion exchange was carried out in air at 280°C for 1 hour. After the ion exchange, water was added to dissolve the salt, and the target sample was obtained by further washing with water.

[0043] The obtained sample was thinned and 10 atomic resolution images were obtained as HAADF-STEM images. The obtained images were clustered using the method disclosed herein. The K-Means++ method was used for clustering. The number of stacking faults was counted based on the clustering results, and the average number of stacking faults per lattice was found to be 0.21.

[0044] Example 2 The number of stacking faults was counted in the same manner as in Example 1 except that the K-Medoids method was used for clustering, and the average number of stacking faults per lattice was found to be 0.22.

[0045] 《Reference example》 When the number of stacking faults was manually counted for the atomic resolution image obtained in Example 1, the average number of stacking faults per lattice was found to be 0.23.

[0046] The above results demonstrate that the crystal structure can be analyzed with high accuracy by clustering atomic resolution images using machine learning techniques.

Claims

[Claim 1] A crystal structure analysis method, which causes a computer to execute a process including the following steps: obtaining an atomic resolution image of a given crystal structure; Calculating the coordinates of all bright points in the acquired atomic resolution image; arbitrarily selecting one of the bright points at the calculated coordinates as a first bright point; arbitrarily selecting a first nearest point from eight bright points that are closest to the selected first bright point, and then selecting a second nearest point and a third nearest point from the eight bright points in order from the first nearest point in either a clockwise or counterclockwise direction with the first bright point as a center; setting the length of each line segment between the selected first bright point and any of the first to third neighboring points and the angle between each line segment as parameters indicating characteristics of a quadrangle formed by four points of the first bright point and the first to third neighboring points; Clustering the atomic resolution images using a machine learning technique based on the set parameters.

Images