A Gaussian correction method for the intensity uniformity of the light source in X-ray diffraction experiments

Abstract

This invention belongs to the subfield of materials science and provides a Gaussian correction method for the intensity uniformity of X-ray diffraction experiments. The method includes: Step 1: Defining the intensity along the X-ray source cross-section as a Gaussian distribution function, where a and c are parameters to be determined; and x and y are the coordinates of the diffraction point. Step 2: Based on the crystal's geometry, the index parameters of the diffraction point are K((h, k, l), and the absorbed intensity can be calculated, where μ is a known parameter. Step 3: Based on the crystal's symmetry, multiple sets of equivalent diffraction points are generated. Refinement is performed based on the differences between the equivalent points, and the parameters a and c are obtained through least squares refinement. Step 4: Based on the obtained a and c values, the measured intensity is I. 实测 (h, k, l), calculate I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 (h, k, l) is used for electronic structure refinement.

Description

Technical Field

[0001] This invention relates to the field of materials analysis technology, and in particular to a Gaussian correction method for the uniformity of light source intensity in X-ray diffraction experiments. 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 a diffraction pattern of X-rays in the prior art. X-rays are incident on the crystal under test and diffract after passing through the crystal. The diffraction intensity I(h, k, l) is related to the diffraction direction index parameter K(h, k, l), the path H through the crystal, the absorption coefficient μ of the crystal, the structure factor, etc. Summary of the Invention

[0006] This invention proposes a method for correcting non-Gaussian bias in high-angle diffraction data of X-ray single-crystal diffraction experiments.

[0007] To achieve the above objectives, the present invention employs the following technical solution: a Gaussian correction method for the intensity uniformity of an X-ray diffraction experiment, characterized by comprising: Step 1, defining the intensity along the cross-sectional direction of the X-ray source as a Gaussian distribution function: Where a and c are parameters to be determined; where x and y are the coordinates of the diffraction point; Step 2: Based on the geometric shape of the crystal, the index parameter of the diffraction point is K((h, k, l), and the amount of light absorbed by the sample can be calculated. Where μ is a known parameter; Step 3: Based on the symmetry of the crystal, multiple sets of equivalent diffraction points are generated, and the diffraction is refined by the differences between the equivalent points. The parameters a and c can be obtained by refining using the least squares method; Step 4: Based on the obtained values ​​of a and c, the measured intensity is I. 实测 (h, k, l), calculate I校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 (h, k, l) is used for electronic structure refinement.

[0008] The preferred embodiment is: in step two, the path function P of the X-rays passing through the crystal is... (h,k,l) (x, y) and the absorption coefficients μ and P of the crystal. (h,k,l) (x, y) can be obtained from the geometry of the crystal, and μ is a known parameter.

[0009] The preferred solution is as follows: In step three, the equivalent points of a crystal with point group 2 / m have a set of equivalent points K[(h, k, l); (-h, -k, -l); (-h, k, -l); (h, -k, l)], which can be refined by the least squares method to obtain parameters a and c.

[0010] The preferred scheme is as follows: the equivalent point in step three, the equivalent point set of the point group I-42d 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),(k,h,-l),(-h,k,-l)], and the parameters a and c can be obtained by refining through the least squares method.

[0011] The preferred solution is as follows: Step 3 further includes: defining the objective function of the difference function. P n Let a and c be parameters, representing the I of the equivalent point set K. 校正 The difference from the average, where m is the number of equivalent points.

[0012] The preferred solution is to calculate the difference function R(P) using the least squares method. n The minimum value of ) is used to obtain the optimal model parameters a and c: A: Randomly select two sets of parameter values ​​P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c 2}, Substitute Obtain R(P) respectively 1 ) and R(P 2 ), by P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c2 Substitute them respectively Calculate I 吸收 (P 1 ) and I 吸收 (P 2 ); through I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P 1 ) and I 校正 (P 2 B: According to the formula A is the step size factor, and P is calculated. 3 ={a 3 ,c 3}, that is, n=3, and P 3 Substitution R(P) was calculated using a similar method. 3 C: Calculate P using the same formula as step B. 4 (i.e., n=4), similar to calculating R(P) 4 Repeat n steps until R(P) is reached. n )-R(P n-1 If R(P) is less than the preset precision value, then R(P) n P has reached its minimum. n The optimal value is D:P. n Substitution and I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P n );I 校正 (P n Used for fine-tuning of electronic structures.

[0013] Compared with the prior art, the beneficial effects of the present invention are: by compensating for the absorption path of the crystal, the measured intensity is supplemented after correction, thereby ensuring the accuracy of X-ray single crystal diffraction experimental data, which is more conducive to ensuring the accuracy of subsequent electronic structure refinement. Attached Figure Description

[0014] Figure 1 A schematic diagram illustrating the acquisition of diffraction spot intensity in existing X-ray single-crystal diffraction experiments;

[0015] Figure 2 This is a flowchart of the method for correcting non-Gaussian bias in high-angle diffraction data of X-ray single-crystal diffraction experiments according to the present invention.

[0016] Figure 3The intensity diagram after diffraction of the equivalent points of AgGaS2;

[0017] Figure 4 Table of intensity differences after diffraction for equivalent points of AgGaS2. Detailed Implementation

[0018] 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.

[0019] like Figure 2 As shown: In order to obtain a more accurate I through calibration 校正 (h, k, l).

[0020] This includes: Step 1, defining the intensity of the X-ray source cross-section as a Gaussian distribution function: Where a and c are parameters to be determined; where x and y are the coordinates of the diffraction point; Step 2: Based on the geometric shape of the crystal, the index parameter of the diffraction point is K((h, k, l), and the amount of light absorbed by the sample can be calculated. Where μ is a known parameter; Step 3: Based on the symmetry of the crystal, generate multiple sets of equivalent diffraction points, refine the diffraction by the difference between the equivalent points, and obtain the parameters a and c by refining the diffraction by the least squares method;

[0021] A: Randomly select two sets of parameter values ​​P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c 2}, Substitute Obtain R(P) respectively 1 ) and R(P 2 ), by P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c 2 Substitute them respectively Calculate I 吸收 (P 1 ) and I 吸收 (p 2 ); through I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P 1 ) and I校正 (P 2 B: According to the formula A is the step size factor, and P is calculated. 3 ={a 3 ,c 3}, that is, n=3, and P 3 Substitution R(P) was calculated using a similar method. 3 C: Calculate P using the same formula as step B. 4 (i.e., n=4), similar to calculating R(P) 4 Repeat n steps until R(P) is reached. n )-R(P n-1 If R(P) is less than the preset precision value, then R(P) n P has reached its minimum. n The optimal value is D:P. n Substitution and I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P n );I 校正 (P n Used for fine-tuning of electronic structures.

[0022] Taking the well-known nonlinear optical crystal AgGaS2 as an example, from Figure 3 , Figure 4 It is not difficult to see that the diffraction intensity of the equivalent points of AgGaS2 differs. The electron density was refined under two conditions: corrected and uncorrected, based on the diffraction points measured as described above.

[0023] Taking a crystal with a size of 0.2*0.2*0.2mm as an example:

[0024] First, the intensity of the X-ray source cross-section is defined to follow a Gaussian function distribution G(x,y); Where a and c are parameters to be determined.

[0025] Furthermore, based on the crystal's external geometry, the path function of X-rays passing through the crystal when the diffraction point has the parameters K(h, k, l) can be obtained as: P(h, k, l) l P(x, y) and P(x, y) are:

[0026] Table 1 shows the P(x, y) values ​​corresponding to x and y for the K(2,1,3) parameter of the 0.2*0.2*0.2mm optical crystal AgGaS2.

[0027]

[0028] The absorption coefficient μ of AgGaS2 crystal is 14.54 mm. -1 Taking point K(2, 1, 3) as an example, the point group of the AgGaS2 crystal is I-42d, and the corresponding equivalent point set is [(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)]. Two sets of parameter values ​​P are randomly selected. 1 ={a 1 ,c 1}={0.5431,0.2178} and P 2 ={a 2 ,c 2}={0.1379,0.6283} (superscripts 1 and 2 represent group 1 and group 2), by P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c 2 Substitute them respectively

[0029] Calculate I 吸收 (P 1 ) and I 吸收 (P 2 ); through I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P 1 ) and I 校正 (P 2 ); I of the equivalent point of K(2,1,3) 实测， I 吸收 (P 1 ), I 吸收 (P 2 ), I 校正 (P 1 ) and I 校正 (P 2 As shown in Table 2, through Obtain R(P) respectively 1 ) and R(P 2 ):

[0030]

[0031] R(P 1 = |223.7165-223.5089|+|229.5669-223.5089|+...+|213.0888-223.5089|=67.6652

[0032]

[0033] R(P 2 = |222.2681-222.0649|+|220.8713-222.0649|+...+|219.2336-222.0649|=52.8158

[0034] Table 2. Equivalent points I of K(2, 1, 3) 实测 I 吸收 (P 1 ), I 吸收 (P 2 ), I 校正 (P1) and I 校正 (P 2 )

[0035]

[0036]

[0037] according to n=3, calculate p 3 .

[0038] A is set to 0.1;

[0039]

[0040]

[0041] Similarly, calculate P 4 ,…,P n ,P n ={a n ,c n}={0.3285,0.4714},R n =14.2118. As shown in Table 3, and using I 校正 (hkl) performs electronic structure refinement.

[0042] Table 3. Equivalent points I of K(2, 1, 3) 实测 I 吸收 (P 3 ), I 吸收 (P n ), I 校正 (P 3) and I 校正 (P n )

[0043]

[0044]

[0045] Taking a crystal with a size of 0.25*0.1*0.05mm as an example: First, the intensity of the X-ray source cross section is defined as having a Gaussian function distribution G(x,y); Where a and c are parameters to be determined.

[0046] Furthermore, based on the crystal's geometric shape, the path function P(x,y) of the X-rays passing through the crystal, which generates the diffraction point parameter k(h,k,l), can be obtained. Taking point K(4,5,7) as an example, P(x,y) is shown in Table 4:

[0047] Table 4 shows the P(x, y) values ​​corresponding to x and y for the 0.25*0.1*0.05mm optical crystal AgGaS2 with parameter K(4,5,7).

[0048]

[0049] The absorption coefficient μ of AgGaS2 crystal is 14.54 mm. -1 ,

[0050] Taking point K(2, 1, 3) as an example, the point group of the AgGaS2 crystal is I-42d, and the corresponding equivalent point set is [(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)]. Two sets of parameter values ​​P are randomly selected. 1 ={a 1 ,c 1}={0.4578,0.3129} and P 2 ={a 2 ,c 2}={0.2183,0.5114} (superscripts 1 and 2 represent group 1 and group 2), by P 1 ={a 1 ,c 1} and P 2 ={a 2 ,c 2 Substitute them respectively Calculate I吸收 (P 1 ) and I 吸收 (P 2 ); through I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P 1 ) and I 校正 (P 2 ); I of the equivalent point of K(2,1,3) 实测 I 吸收 (P 1 ), I 吸收 (P 2 ), I 校正 (P 1 ) and I 校正 (P 2 As shown in Table 5, through Obtain R(P) respectively 1 ) and R(P 2 ):

[0051]

[0052] R(P 1 = |58.0620-58.3476|+|61.1739-58.3476|+...+|54.2368-58.3476|=58.1011

[0053]

[0054] R(P 2 = |58.2473-58.1294|+|60.4942-58.1294|+...+|54.9176-58.1294|=36.3975

[0055] Table 5. Equivalent points I of K(4, 5, 7) 实测 I 吸收 (P 1 ), I 吸收 (P 2 ), I 校正 (P 1 ) and I 校正 (P 2 )

[0056]

[0057]

[0058] according to n=3, calculate p3 .

[0059] A is set to 0.1;

[0060]

[0061]

[0062] Similarly, calculate P 4 ,…,P n ,P n ={a n ,c n}={0.2538,0.4697},R n =8.3227.K(4,5,7) equivalent point I 实测 I 吸收 (P 3 ), I 吸收 (P n ), I 校正 (P 3 ) and I 校正 (P n As shown in Table 6, and using I 校正 (hkl) performs electronic structure refinement.

[0063] Table 6. Equivalent points I of K(4, 5, 7) 实测 I 吸收 (P 3 ), I 吸收 (P n ), I 校正 (P 3 ) and I 校正 (P n )

[0064]

[0065]

[0066] This invention can supplement the absorbed portion of the crystal into the corrected diffraction intensity, making the data more accurate and facilitating the refinement of the electronic structure.

[0067] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0068] Based on theoretical calculations, as shown in Table 7: for 0.2*0.2*0.2mm 3 and 0.25*0.1*0.05mm3 The results of the sample tests were compared. The results corrected using the patented solution were closer to the theoretical values, while the results without correction were far from the theoretical values, indicating that the patented solution is feasible.

[0069] Table 7 shows the dimensions of AgGaS2 crystals in 0.2*0.2*0.2mm diameters. 3 and 0.25*0.1*0.05mm 3 Comparison table before and after correction

[0070]

Claims

1. A Gaussian correction method for the intensity uniformity of a light source in an X-ray diffraction experiment, characterized in that, include: Step 1: Define the intensity of the X-ray source cross-section as a Gaussian distribution function: Where a and c are parameters to be determined; where x and y are the coordinates of the diffraction point; Step 2: Based on the geometric shape of the crystal, the index parameters of the diffraction point are K(h, k, l), and the absorbed by the sample are calculated. Wherein, the path function P of X-rays passing through the crystal (h,k,l) (x, y), P (h,k,l) (x, y) is obtained based on the crystal's geometry, and the crystal's absorption coefficient μ is a known parameter; Step 3: Based on the crystal's symmetry, multiple sets of equivalent diffraction points are generated, and the differences between the equivalent points are used for refinement. The parameters a and c are obtained through least squares refinement; Step 4: Based on the obtained a and c values, the measured intensity is I. 实测 (h, k, l), calculate I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 (h, k, l), used for electronic structure refinement, the difference function R(P) is calculated using the least squares method. n The steps to obtain the optimal model parameters a and c by finding the minimum value of ) include: A: Randomly select two sets of parameter values ​​P 1 ={a 1 ,c 1 } and P 2 ={a 2 ,c 2 }, Substitute Obtain R(P) respectively 1 ) and R(P 2 ), by P 1 ={a 1 ,c 1 } and P 2 ={a 2 ,c 2 Substitute them respectively Calculate I 吸收 (P 1 ) and I 吸收 (P 2 ); through I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P 1 ) and I 校正 (P 2 ); B: According to the formula A is the step size factor, and P is calculated. 3 ={a 3 ,c 3 }, that is, n=3, and P 3 Substitution R(P) is calculated using this method. 3 )value; C: Calculate P using the same formula as in step B. 4 Similar to calculating R(P) 4 Repeat n steps until R(P) is reached. n )-R(P n-1 If R(P) is less than the preset precision value, then R(P) n P has reached its minimum. n This is the optimal value; D:P n Substitution and I 校正 (h, k, l) = I 实测 (h, k, l) + I 吸收 Calculate I from (h, k, l) 校正 (P n );I 校正 (P n Used for fine-tuning of electronic structures.

2. The Gaussian correction method for the intensity uniformity of the X-ray diffraction experiment according to claim 1, characterized in that, In step three, the equivalent points are the set of equivalent points K[(h, k, l); (-h, -k, -l); (-h, k, -l); (h, -k, l)] of the crystal with point group 2 / m. The parameters a and c are obtained by refining them using the least squares method.

3. The Gaussian correction method for the intensity uniformity of the X-ray diffraction experiment according to claim 1, characterized in that, The equivalent points in step three, the equivalent point set of the point group I-42d 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),(k,h,-l),(-h,k,-l)], and the parameters a and c are obtained by refining using the least squares method.

4. The Gaussian correction method for the uniformity of light source intensity in X-ray diffraction experiments according to claim 2 or 3, characterized in that, In step three, the objective function of the difference function is defined as follows: P n Let a and c be the parameters, representing the equivalent point I. 校正 The difference from the average, where m is the number of equivalent points.

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