A method for correcting multiple scattering in X-ray diffraction

Abstract

This invention belongs to the field of materials analysis and discloses an X-ray diffraction multiple scattering correction method, comprising: Step 1, obtaining equivalent diffraction points based on the symmetry characteristics of the crystal, wherein the equivalent diffraction points are the set of points with diffraction intensities I(h, k, l); Step 2, determining whether the criteria for judging outliers are met; if met, deleting; otherwise, retaining; Step 3, determining whether the deletion rate is met; if met, deleting; otherwise, retaining; Step 4, the remaining dataset I without outliers. 校正 (h, k, l) is used for subsequent fine-tuning; the corrected I 校正 (h, k, l) is more conducive to the accuracy of electronic structure refinement.

Description

Technical Field

[0001] This invention relates to the field of materials analysis technology, and in particular to a method for correcting multiple scattering in X-ray diffraction. Background Technology

[0002] Materials science is the foundation and precursor of modern science and technology. The level of understanding of material structure and material composition directly determines the research and development capability of new materials.

[0003] The microstructure of materials includes atomic-level structures such as crystal structure, local structure, and defect structure, as well as electronic structure. Among these, electronic structure fundamentally determines the intrinsic properties of materials. Currently, experimental testing techniques for the atomic-level structure of materials are very mature, but experimental testing of electronic structure remains in the exploratory stage. Although electronic structure can be obtained through first-theory calculations, theoretical calculations often rely on numerous assumptions and approximations, leading to discrepancies between the calculated results and actual conditions, making it difficult to guide the design of high-performance materials.

[0004] Therefore, obtaining the experimental electronic structure of materials is a key scientific problem. Solving this problem will help my country's experimental research on material structure to leap from the atomic level to the electronic level, and accelerate the research and development of a number of key functional materials for national defense and civilian use.

[0005] Figure 1 This is an experimental structure diagram using existing X-ray technology. X-rays are incident on the crystal under test and diffract after passing through the crystal. By obtaining high-precision, high-resolution X-ray single-crystal diffraction data (position and intensity information) and refining the electronic structure, it is feasible to deduce the experimental electronic structure of the material. Finally, the experimental electronic structure of the material under static and service conditions can be obtained. The electronic structure can be described using electron density, density matrix, or electron wave function.

[0006] like Figure 2 As shown: Equivalent diffraction points usually have roughly the same diffraction intensity. However, during X-ray diffraction experiments, the sample will have a certain proportion of multiple scattering. Multiple scattering will significantly enhance or reduce the intensity of some diffraction points, causing the intensity of some diffraction points to deviate significantly from the median intensity of equivalent diffraction points. This will bring errors to the subsequent electronic structure refinement. Summary of the Invention

[0007] This invention proposes a method for correcting multiple scattering in X-ray diffraction.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: an X-ray diffraction multiple scattering correction method, comprising: Step 1, obtaining equivalent diffraction points based on the symmetry characteristics of the crystal, wherein the equivalent diffraction points are the set of points with diffraction intensities I(h, k, l); Step 2, determining whether the criteria for judging outliers are met; if met, deleting; otherwise, retaining; Step 3, determining whether the deletion rate is met; if met, deleting; otherwise, retaining; Step 4, the remaining dataset I without outliers. 校正 (h, k, l) will be further refined.

[0009] The preferred scheme is as follows: A set of equivalent diffraction points is obtained from a symmetrical crystal, such as [(h, k, l); (-h, -k, -l); (-h, k, -l); (h, -k, l)]. The intensities of the equivalent diffraction points belonging to the same set are sorted from low to high to obtain (I1, I...). i The sequence (h, k, l) is given, where i = 1, 2, 3, ..., n, and n is the number of equivalent points in the same set of equivalent diffraction points.

[0010] The preferred scheme is as follows: the criteria for judging outliers include: the slope of the mutation must not exceed W times the normal slope; and the signal-to-noise ratio of the outlier must be greater than V.

[0011] The preferred scheme is as follows: the mutation slope should not exceed W times the normal slope, where W is 2-10; and the signal-to-noise ratio of the outlier should be greater than V, where V is 2-10.

[0012] The preferred solution is to calculate the slope Si = I based on the difference between two adjacent points. i -I i-1 And compare S1, S2, S3, ..., S in sequence. n-1 In the low-strength section, if S1 > WS2, then I1 should be deleted; in the high-strength section, if S... n-1 >WS n-2 Then I should be deleted. n .

[0013] The preferred option is that the deletion rate does not exceed 1 / 5 of the total equivalent diffraction points.

[0014] Compared with the prior art, the beneficial effects of the present invention are: deleting some diffraction points with abnormal intensity caused by multiple scattering, thereby obtaining an accurate diffraction point intensity dataset for subsequent electronic structure refinement. The diffraction dataset with abnormal points removed is more conducive to the accuracy of electronic structure refinement and material design. Attached Figure Description

[0015] Figure 1 A schematic diagram of an experimental structure utilizing X-rays in the context of existing technologies;

[0016] Figure 2This is a schematic diagram illustrating the principle of multiple scattering in X-ray diffraction experiments.

[0017] Figure 3 The flowchart of the X-ray diffraction multiple scattering correction method of the present invention is as follows;

[0018] Figure 4 A schematic diagram of a set of equivalent diffraction points to be corrected is shown, taking the nonlinear optical crystal AgGaS2 as an example.

[0019] Figure 5 A schematic diagram of the slope determination method using the nonlinear optical crystal AgGaS2 as an example. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0021] like Figure 3 As shown: To remove abnormal diffraction points, including step one, based on the crystal's symmetry, many sets of equivalent diffraction points can be generated. Equivalent diffraction points should have almost identical diffraction intensities I(h, k, l). For example, a crystal with a point group of 2 / m has an equivalent diffraction point set [(h, k, l); (-h, -k, -l); (-h, k, -l); (h, -k, l)]. The intensities belonging to the same set of equivalent diffraction points are sorted from low to high to obtain (I, I... i (h, k, l) sequence, where i = 1, 2, 3, ..., n, n is the number of equivalent points in the same set of equivalent diffraction points; Step 2: Based on the criteria for judging outliers, delete some diffraction points with abnormal intensity (too low or too high intensity) to obtain a set of I without outliers. 校正 (h, k, l), outlier identification criteria: 1. The slope of the abrupt change must not exceed 5 times the normal slope; 2. The number of outliers must not exceed 1 / 5 of the total number of equivalent points; 3. The signal-to-noise ratio of outliers must be greater than 3; the slope Si = I is calculated based on the difference between two adjacent points. i -I i-1 And compare S1, S2, S3, ..., S in sequence. n-1 In the low-strength section, if S1 > 5S2, then I1 should be deleted; in the high-strength section, if S... n-1 >5S n-2 Then I should be deleted. n Similarly, if S2 > 5S3, then I1 and I2 should be deleted; if S... n-2 >5S n-3 Then I should be deleted. nBefore performing deletion operations, it's necessary to determine whether the signal-to-noise ratio (SNR) of the points to be deleted is greater than 3. If not, deletion is not performed (because data points with an SNR less than 3 have almost no impact on electronic structure refinement). Otherwise, deletion is performed. Simultaneously, it's calculated whether the number of points to be deleted is greater than n / 5. If not, deletion is performed; otherwise, deletion is not performed (to prevent deleting too much data and making electronic structure refinement impossible). Finally, the dataset I without outliers is used. 校正 (h, k, l) are refined.

[0022] Taking the well-known nonlinear optical crystal AgGaS2 as an example, the diffraction points were measured, and the electron density was refined under two conditions: corrected and uncorrected using the method described above.

[0023] like Figure 4 As shown: The point group of AgGaS2 crystal is I-42d, and the corresponding equivalent point set is K[(h,k,l),(-k,h,l),(-h,-k,l),(k,-h,l),(-h,-k,-l),(k,-h,-l),(h,k,-l),(-k,h,-l),(k,h,l),(-h,k,l),(-k,-h,l),(h,-k,l),(-k,-h,l),(h,-k,-l),(h,-k,-l),(k,h,-l)].

[0024] Taking a set of equivalent diffraction points K(h,k,l)=(4,2,16) as an example, there are a total of 16 diffraction points, which are sorted from low to high intensity as shown in Table 1:

[0025] Table 1. Ranking of the intensity of a set of equivalent diffraction points for AgGaS2 crystal.

[0026]

[0027]

[0028] In this embodiment, as Figure 4 As shown: W=5, V=3, and the deletion rate is 1 / 5; from Si, we can see that S2>5*S3, so the first diffraction point (4,2,16) should be deleted; S15>5*S14, so the 15th diffraction point (2,4,-16) and the 16th diffraction point (-4,2,-16) should be deleted. Figure 5 It can be seen that the data within circle A are the diffraction points that should be deleted:

[0029] Since the signal-to-noise ratio (I / σ) of all three diffraction points to be deleted is greater than 3, and the number of points to be deleted (3) is less than 1 / 5 of the total number of points (16), the deletion operation must be performed.

[0030] The same operation was performed on other (h, k, l) equivalent diffraction points to obtain a dataset without intensity anomalous diffraction points, which was used for electronic structure refinement.

[0031] By comparing the results of theoretical calculations and sample tests in Table 2, the results corrected using the patented solution are closer to the theoretical values, while those without correction are far from the theoretical values, indicating that the patented solution is feasible.

[0032] Table 2 compares the results of theoretical calculations and sample testing for AgGaS2.

[0033] Atomic valence state First-principles computation theory Correction Uncorrected Ag1 0.51 0.49 0.43 Ga2 2.63 2.61 2.50 S3 -1.22 -1.25 -1.10

Claims

1. A method for correcting multiple scattering in X-ray diffraction, characterized in that: include: Step 1: Based on the symmetry of the crystal, many sets of equivalent diffraction points can be generated. The equivalent diffraction points should have almost the same diffraction intensity I(h, k, l). A crystal with a point group of 2 / m has an equivalent diffraction point set [(h, k, l); (-h, -k, -l); (-h, k, -l); ]. [h,-k,l)], sorting the intensities of equivalent diffraction points belonging to the same set from low to high, to obtain (I,I i (h, k, l) sequence, where i = 1, 2, 3, ..., n, n is the number of equivalent points in the same set of equivalent diffraction points; Step 2: Based on the criteria for judging outliers, delete some diffraction points with abnormal intensity to obtain a set of I without outliers. 校正 (h, k, l), outlier identification criteria: the slope of the abrupt change must not exceed 5 times the normal slope; the number of outliers must not exceed 1 / 5 of the total number of equivalent points; the signal-to-noise ratio of the outlier must be greater than 3; the slope Si = I is calculated based on the difference between two adjacent points. i -I i-1 And compare S1, S2, S3, ..., S in sequence. n-1 In the low-strength section, if S1 > 5S2, then I1 should be deleted; in the high-strength section, if S... n-1 >5S n-2 Then I should be deleted. n If S2 > 5S3, then I1 and I2 should be deleted; if S n-2 >5S n-3 Then I should be deleted. n Before performing a deletion operation, it's also necessary to check if the signal-to-noise ratio (SNR) of the points to be deleted is greater than 3. If not, the deletion operation is not performed; otherwise, the deletion operation is executed. Simultaneously, it's calculated whether the number of points to be deleted is greater than n / 5. If not, the deletion operation is performed; otherwise, it is not. Finally, the dataset I without outliers is used. 校正 (h, k, l) are refined.

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