Correction device, system, method and program

Abstract

To provide a correction device, a system, a method, and a program capable of correcting a structure factor calculated from total scattering data.SOLUTION: A correction device 400 for correcting a structure factor has: a structure factor acquisition part 410 for acquiring the structure factor; a PDF calculation part 420 for calculating a PDF (Pair Distribution Function) from the acquired structure factor; a correction function creation part 430 for creating a first correction function that includes a cut-off function for cutting off PDF data and PDF long-distance-side data and a second correction function that includes a cut-off function and is Fourier-transformed in a predetermined range; a correction amount calculation part 440 for calculating a correction amount including the first correction function, the second correction function, and a scale factor; a structure factor correction part 450 for correcting a structure factor by using a correction amount; and an R value calculation part 460 that includes the first correction function and the second correction function, and calculates an R value showing precision of correction.SELECTED DRAWING: Figure 14

Description

[Technical Field]

[0001] The present invention relates to a correction device, system, method and program for correcting a structure factor. [Background technology]

[0002] Three-dimensional structural information is essential for a deep understanding of material functions. Many conventional materials are crystalline, and the purpose could be achieved by determining the crystal structure. However, in recent years, in order to maximize the desired functions, many materials in fields such as batteries and electronics have been made non-crystalline (amorphous) with controlled interfaces.

[0003] Structural modeling is essential to obtain structural features of amorphous materials, and density is an essential item for modeling. However, for materials with controlled interfaces, it is difficult to estimate density using conventional methods (such as the Archimedes method). Therefore, a density estimation technique on a modeling scale is required.

[0004] Non-Patent Document 1 focuses on the asymptotic behavior of the PDF (Pair Distribution Function) and introduces a criterion for automatically correcting the PDF, and discloses the criterion. Non-Patent Document 2 discloses a method for extending the density estimation method using the PDF to amorphous materials. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Peter F. Peterson, Emil S. Bozin, Thoms Proffen, Simon JL Billinge. J. Appl. Cryst. (2003), 36, p. 53-64 [Non-patent document 2] Georgios SE Antipas, Konstantinos T. Karalis, Method X (2019), 6, p. 601-605 Summary of the Invention [Problem to be solved by the invention]

[0006] However, the methods described in Non-Patent Document 1 and Non-Patent Document 2 do not take into consideration correcting the structure factor by focusing on noise on the short-distance side of the PDF.

[0007] As a result of intensive research, the inventors have discovered that by searching for density using a wider range of PDF data than in conventional methods, it is possible to correct the structure factor and obtain a more accurate density. Furthermore, they have found that by applying this method assuming that the density is known, it is possible to correct only the structure factor, thereby completing the present invention.

[0008] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a correction device, system, method, and program capable of correcting a structure factor calculated from total scattering data. [Means for solving the problem]

[0009] (1) In order to achieve the above object, the correction device of the present invention is a correction device that corrects a structure factor, and is characterized by comprising: a structure factor acquisition unit that acquires the structure factor; a PDF calculation unit that calculates a PDF (Pair Distribution Function) from the acquired structure factor; a correction function creation unit that creates a first correction function that includes a cutoff function that cuts off data on the PDF and the long-distance side of the PDF and is Fourier transformed within a predetermined range; and a second correction function that includes the cutoff function and is Fourier transformed within the predetermined range; a correction amount calculation unit that calculates a correction amount that includes the first correction function, the second correction function, and a scale factor; a structure factor correction unit that corrects the structure factor using the correction amount; and an R value calculation unit that includes the first correction function and the second correction function and calculates an R value that indicates the accuracy of the correction.

[0010] (2) Furthermore, the correction device of the present invention is characterized in that it further includes a density calculation unit that calculates density based on the first correction function and the second correction function, the scale factor is the density calculated by the density calculation unit, and the R value indicates a rate of change of the density calculated by the density calculation unit.

[0011] (3) Furthermore, in the correction device of the present invention, the density calculation unit further includes a ratio calculation unit that calculates a constraint term based on the limited range of values ​​of the first correction function and the second correction function and calculates a ratio that weights the constraint term, and the density includes the product of the constraint term and the ratio, and the ratio increases or decreases according to an increase or decrease in the R value.

[0012] (4) In the correction device of the present invention, the scale factor is a predetermined value.

[0013] (5) The correction device of the present invention also detects the first peak position r of the PDF. 1st a peak position determining unit that determines a peak position, 1st It is characterized by the fact that

[0014] (6) In the correction device of the present invention, the cutoff function is a monotonically decreasing function that takes values ​​from 1 to 0 in the domain of the cutoff function.

[0015] (7) Furthermore, the correction device of the present invention further includes a structure factor calculation unit that acquires total scattering data of a sample and calculates the structure factor based on the type of radiation source, wavelength, shape and arrangement of the sample, type and composition of constituent elements, and absorption coefficient of the total scattering data, and the structure factor acquisition unit acquires the structure factor calculated by the structure factor calculation unit.

[0016] (8) The system of the present invention is characterized by comprising an X-ray diffraction apparatus including an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a goniometer that controls the rotation of the sample, and a correction device described in any one of (1) to (7) above.

[0017] (9) The method of the present invention is a method for correcting a structure factor, comprising: a structure factor acquisition step for acquiring the structure factor; a PDF calculation step for calculating a PDF (Pair Distribution Function) from the acquired structure factor; a correction function creation step for creating a first correction function that includes a cutoff function for cutting off data on the PDF and the long-distance side of the PDF and is Fourier transformed within a predetermined range; and a second correction function that includes the cutoff function and is Fourier transformed within the predetermined range; a correction amount calculation step for calculating a correction amount that includes the first correction function, the second correction function, and a scale factor; a structure factor correction step for correcting the structure factor using the correction amount; and an R value calculation step for calculating an R value that includes the first correction function and the second correction function and indicates the accuracy of the correction.

[0018] (10) Also, the program of the present invention is a program for correcting a structure factor, characterized in that it causes a computer to execute the following processes: a process for acquiring the structure factor; a process for calculating a PDF (Pair Distribution Function) from the acquired structure factor; a process for creating a first correction function that includes a cutoff function for cutting off data on the PDF and the long-distance side of the PDF and is Fourier-transformed within a predetermined range; and a second correction function that includes the cutoff function and is Fourier-transformed within the predetermined range; a process for calculating a correction amount that includes the first correction function, the second correction function, and a scale factor; a process for correcting the structure factor using the correction amount; and a process for calculating an R value that includes the first correction function and the second correction function and indicates the accuracy of the correction. [Brief explanation of the drawings]

[0019] [Figure 1] 1 is a graph showing a conventional method for determining density ρ0 from a PDF graph. [Figure 2] 1 is a graph showing an example of total scattering data. [Figure 3] 1 is a graph showing an example of a structure factor S(Q). [Figure 4] 1 is a graph showing an example of PDF G(r). [Figure 5] This graph shows the first peak position r1st of the PDF in the graph of FIG. [Figure 6] 10 is a graph showing an example of a first correction function a(Q) and a second correction function b(Q). [Figure 7] 10 is a graph showing an example of a correction amount c(Q). [Figure 8] 10 is a graph showing an example of a structure factor S(Q) before correction and a structure factor S(Q) after correction. [Figure 9] 1 is a graph showing an example of a structure factor S(Q). [Figure 10] 10 is a graph showing an example of a first correction function a(Q) and a second correction function b(Q). [Figure 11]10 is a graph showing an example of a structure factor S(Q) before correction and a structure factor S(Q) after correction. [Figure 12] FIG. 1 is a conceptual diagram showing an example of the configuration of an X-ray diffraction measurement system. [Figure 13] FIG. 2 is a block diagram showing an example of the configuration of a control device. [Figure 14] FIG. 1 is a block diagram showing an example of the configuration of a correction device. [Figure 15] FIG. 10 is a block diagram showing a modified example of the configuration of the correction device. [Figure 16] FIG. 10 is a block diagram showing a modified example of the configuration of the correction device. [Figure 17] FIG. 10 is a block diagram showing a modified example of the configuration of the correction device. [Figure 18] 10 is a flowchart illustrating an example of the operation of the correction device. [Figure 19] 10 is a flowchart showing a modified example of the operation of the correction device. [Figure 20] 10 is a flowchart showing a modified example of the operation of the correction device. [Figure 21] 10 is a flowchart showing a modified example of the operation of the correction device. DETAILED DESCRIPTION OF THE INVENTION

[0020] Next, an embodiment of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used to designate the same components in the drawings, and duplicated descriptions will be omitted.

[0021] [principle] PDF (Pair Distribution Function) is an analytical method for describing the atoms adjacent to an arbitrary atomic center. Information that can be directly obtained from PDF includes, for example, peak position, peak area, and peak width. Peak position indicates the distance between adjacent atoms, peak area indicates information related to the coordination number, and peak width indicates the degree of distribution.

[0022] Figure 1 is a graph showing how to obtain density ρ from a PDF graph using a conventional method. As shown in Figure 1, in the conventional technique, the first peak position r of the PDF is calculated. 1st The data below this point was fitted to a straight line, and the density ρ0 was calculated from the slope. This is because, ideally, there would be no structure (structural signal) below the first peak position. PDF G(r) is expressed by the following equation (1).

[0023]

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[0024] Here, ρ(r) denotes the local density (signal due to structure), and ρ denotes the average atomic number density in the system. Assuming that no PDF signal is observed below the first peak, r <r 1st Now, since ρ(r)=0, we can rewrite it as follows:

[0025]

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[0026] Therefore, if it is true that there is no structure below the first peak position, the first peak position r of the PDF 1st The density ρ0 calculated from the slope of a linear approximation of data less than ρ0 is also correct. However, since PDFs usually contain noise, the conventional method of linear approximation, which ignores noise on the short-distance side of the PDF, results in poor accuracy in the calculated density, and this effect is particularly pronounced in amorphous materials.

[0027] The noise on the short-distance side of the PDF comes from errors such as measurement errors in the original total scattering data and errors in calculating the structure factor. Furthermore, while the structure factor is originally calculated from the total scattering data over an infinite range, the structure factor and the PDF calculated from it must be limited to a finite range. Therefore, it contains truncation errors and cannot be an ideal state in an essential sense.

[0028] Therefore, the method of the present invention is as follows: 1st If a Fourier transform is performed within a specified range of less than 1 / 2, and the left side is a(Q) and the right side is b'(Q), a(Q) and b'(Q) can be expressed as follows:

[0029]

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[0030]

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[0031] Then, if b(Q) is expressed as the following equation (5), b'(Q) can be expressed as equation (6) using b(Q).

[0032]

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[0033]

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[0034] Then, find ρ0, which minimizes the residual between a(Q) and b(Q). If the total scattering data is not ideal, the value found in this way is the first peak position r of the PDF. 1st This is closer to the actual density than the density calculated from the slope of a linear approximation of data less than 100. Also, the structure factor can be corrected using a(Q) and b(Q).

[0035] In another embodiment of the present invention, when the actual density or a value close to it is known, ρ0 in equation (6) is fixed to that value α. Then, the structure factor can be corrected by correcting a(Q) so that a(Q) and αb(Q) match with a predetermined accuracy.

[0036] The structure factor corrected as described above has reduced noise on the short-distance side of the PDF calculated based on the structure factor, and therefore the accuracy of the information obtained from the corrected structure factor and PDF is improved. The detailed correction method of the present invention will be described in detail in the embodiment.

[0037] [Embodiment] The correction method of the present invention will be described in detail below. Below, we will explain a method for correcting the structure factor while estimating density using total scattering data measured with an X-ray diffraction device, and a method for correcting the structure factor assuming that the density is known. However, the total scattering data to which the present invention can be applied is not limited to total scattering data measured with an X-ray diffraction device, but can also be applied to total scattering data measured with a probe similar to this. Specifically, the present invention can be applied to, for example, total scattering data due to radiation or total scattering data due to particle beams. Furthermore, the present invention does not necessarily require the acquisition of total scattering data, and a structure factor calculated from total scattering data can be used as the initial data.

[0038] In the description of this specification, ρ0 may be referred to as density, but in reality it represents the average atomic number density. 3 ) to the normal density ρ bulk (g / cm 3 ) can be easily converted using the following formula (7): In formula (7), M is the formula weight (or molecular weight, atomic weight) of the composition formula of the material, and n is the number of atoms contained in the composition formula (M and n are values ​​calculated from the same composition formula).

[0039]

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[0040] (Embodiment 1) In the first embodiment, a method for correcting the structure factor while estimating density using total scattering data measured by an X-ray diffraction instrument is described. First, total scattering data is acquired. When the total scattering data is used as the initial data, it is preferable to also acquire information necessary for calculating the structure factor based on the total scattering data, such as the type of radiation source, wavelength, background, sample shape and arrangement, type of constituent elements, composition, and absorption coefficient. This information may be stored in advance, acquired from the X-ray diffraction instrument, or input by the user. FIG. 2 is a graph showing an example of total scattering data.

[0041] Next, the structure factor S(Q) is calculated based on the total scattering data. The structure factor S(Q) is preferably calculated based on the type of radiation source, wavelength, background, sample shape, arrangement, type of constituent elements, composition, and absorption coefficient of the total scattering data. Figure 3 is a graph showing an example of the structure factor S(Q). Figure 3 shows a graph of the structure factor calculated from the total scattering data of Figure 2.

[0042] Next, calculate PDF (Pair Distribution Function) G(r) from the structure factor S(Q). PDF G(r) is calculated by finding the minimum value Q of the structure factor S(Q). min and the maximum value Q max is obtained and calculated using the following equation (8): Q min and Q max is included when calculating the structure factor S(Q), but may be input by the user. Figure 4 is a graph showing an example of PDF G(r).

[0043]

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[0044] Next, the first peak position r of the PDF G(r) 1st Determine the first peak position r of G(r). 1stmay be determined by peak search of G(r), or may be determined by referring to a database based on the type of sample, etc. 1st may be a value input by the user. 1st is unlikely to change significantly due to the correction of the structure factor S(Q), so perform a peak search only in the first loop and 1st In the second and subsequent loops, the peak search is not performed and the 1st It is preferable to make r the same as the initial value. 1st When determining the first correction function a(Q) and the second correction function b(Q), which will be described later, can be created within the range corresponding to the calculated G(r), so the accuracy of the correction is improved. 1st This is a graph showing the above.

[0045] Next, the cutoff function Φ(r) is determined. The cutoff function Φ(r) is a function that cuts off the data on the long-distance side of the PDF G(r). The cutoff function Φ(r) is a monotonically decreasing function that takes values ​​from 1 to 0 in its domain. A simple cutoff function Φ(r) is a step function. However, since the actual PDF G(r) contains noise, the cutoff function Φ(r) is a C function that takes values ​​from 1 to 0 in its domain. ∞ It is preferable that the function Φ(r) be a monotonically decreasing function of the order of magnitude. This allows for a smooth connection of the data in the PDF G(r) with the long-distance data cut off. The cutoff function Φ(r) can also be replaced by a sigmoid function or a function expressed in exponential form.

[0046] The cutoff function Φ(r) can be, for example, a function such as the following equation (9).

[0047]

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[0048] In equation (9), R max , R minis preferably determined based on the structure factor S(Q) and the PDF G(r). For example, the following formulas (10) to (11) are used: (12) It can be defined as follows.

[0049]

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[0050]

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[0051]

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[0052] Next, a first correction function a(Q) is created by Fourier transforming the data of PDF G(r) and the cutoff function Φ(r) within a predetermined range, and a second correction function b(Q) is created by Fourier transforming the data of PDF G(r) and the cutoff function Φ(r) within a predetermined range. At this time, the predetermined range is from 0 to r 1st It is preferable to set the first peak position r of G(r) as 1st is fixed to one value, the second correction function b(Q) is also fixed to one function.

[0053] For example, a(Q) and b(Q) can be functions such as the following equations (13) and (14), respectively. In equations (13) and (14), G(r) represents the PDF G(r) before correction in that loop. FIG. 6 is a graph showing an example of the first correction function a(Q) and the second correction function b(Q). FIG. 6 shows graphs of a(Q) and b(Q) when the first correction function a(Q) and the second correction function b(Q) are defined by equations (13) and (14) for the PDF G(r) in FIG. 4.

[0054]

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[0055]

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[0056] Next, the density ρ0 is calculated based on the first correction function a(Q) and the second correction function b(Q). The calculated ρ0 is used as a scale factor when calculating the correction amount c(Q), which will be described later. For example, the least squares method can be used to calculate ρ0. When the least squares method is used to calculate the density ρ0, it can be calculated as shown in the following equation (15). In equation (15), a(Q i ) and b(Q i ) is the structure factor at each measurement point Q i 10 represents the values ​​of the first and second correction functions at

[0057]

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[0058] Next, a correction amount c(Q) including the first correction function a(Q), the second correction function b(Q), and a scale factor (ρ0 calculated above in this embodiment) is calculated. At this time, the calculated density ρ0 is corrected and refined by setting the scale factor in each loop to the density ρ0 calculated as above. In addition, the structure factor S(Q) can also be corrected accordingly. For example, c(Q) can be defined as an equation such as the following equation (16). FIG. 7 is a graph showing an example of the correction amount c(Q). FIG. 7 shows a graph of c(Q) when the correction amount c(Q) is defined by equation (16).

[0059]

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[0060] Next, the structure factor S(Q) is corrected using the correction amount c(Q). The structure factor S(Q) can be corrected as shown in the following equation (17). In equation (17), S cor(Q) is the corrected structure factor S(Q), and S obs (Q) represents the structure factor S(Q) before correction. In other words, the function obtained by adding c(Q) to S(Q) is the new structure factor S(Q).

[0061]

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[0062] Next, an R value is calculated that includes the first correction function a(Q) and the second correction function b(Q) and indicates the accuracy of the correction. In this embodiment, the R value preferably indicates the rate of change of the calculated density ρ0. When the R value is set to a value indicating the rate of change of the calculated density ρ0, it can be calculated, for example, as shown in the following equation (18). In equation (18), ρ0(j) represents the density ρ0 calculated in the jth loop. Note that the R value may be any value that indicates the accuracy of the correction or the rate of change of the density, and is not limited to equation (18).

[0063]

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[0064] If the R value does not satisfy the set condition, the PDF G(r) is calculated again from the corrected structure factor S(Q), and the process up to calculating the R value is repeated. On the other hand, if the R value satisfies the set condition, the corrected structure factor S(Q) or density ρ0 is output as needed, and the process ends. FIG. 8 is a graph showing an example of the structure factor S(Q) before correction and the structure factor S(Q) after correction. The set condition for the R value can be, for example, a predetermined value of 0.05% or more and 0.1% or less. Also, for example, if priority is given to calculation speed, a predetermined value of 0.1% or more and 1% or less can be set. Also, for example, if priority is given to density accuracy, a predetermined value of 0.005% or more and 0.05% or less can be set. Note that, depending on the definition of the R value, there are cases where it cannot be calculated in the first loop or where no comparison target exists. In such cases, a second loop can be performed without fail. The same applies to the second and third embodiments.

[0065] In this way, the method of this embodiment can start from the total scattering data and correct the structure factor S(Q) and the density ρ0.

[0066] (Embodiment 2) In embodiment 2, a modified method for correcting the structure factor while estimating the density using total scattering data measured by an X-ray diffractometer will be described. Since many of the procedures are the same as those in embodiment 1, only the differences will be described.

[0067] In this embodiment, up to the step of creating the first correction function a(Q) and the second correction function b(Q), the steps can be performed in the same manner as in embodiment 1. The structure factor S(Q) can also be used as the initial data.

[0068] Here, assume that the calculated or acquired structure factor S(Q) contains a large distortion. FIG. 9 is a graph showing an example of the structure factor S(Q). FIG. 9 shows a structure factor S(Q) that is significantly distorted on the large Q value side. There are various possible causes for this distortion, but one example is that it may result from insufficient acquisition of Compton scattering intensity.

[0069] When the structure factor S(Q) contains a large distortion, the accuracy of the corrected density ρ may not be very good when using the method of embodiment 1. The method of embodiment 1 assumes that a(Q) = ρb(Q) ultimately holds. This assumption means that the same density ρ can be calculated at any point Q from the final a(Q) and b(Q). On the other hand, when the structure factor S(Q) contains a large distortion, the density ρ calculated using the method of embodiment 1 is calculated as a value that reflects the distortion, and therefore the accuracy is not very good.

[0070] Therefore, in this embodiment, the density is not only calculated from the values ​​of a(Q) and b(Q) at all measurement points Q of the structure factor S(Q), but also calculated and corrected so as to include constraint terms that emphasize data in a limited range of a(Q) and b(Q). When the structure factor S(Q) is significantly distorted on the large Q value side as shown in Figure 9, the limited range of a(Q) and b(Q) is preferably a range or points on the small Q value side.

[0071] First, a provisional density ρ0' is calculated based on the first correction function a(Q) and the second correction function b(Q). The provisional density ρ0' can be calculated using the same method as the method for calculating the density ρ0 in the first embodiment, for example, the least squares method. When the provisional density ρ0' is calculated using the least squares method, it can be calculated as shown in the following formula (19). In formula (19), a(Q i ) and b(Q i ) is the structure factor at each measurement point Q i 10 represents the values ​​of the first and second correction functions at

[0072]

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[0073] Next, calculate the constraint term d that emphasizes the data in the limited range of a(Q) and b(Q). If the limited range is the range or point on the small value side of Q, for example, the Q that gives the first maximum value of the second correction function b(Q) is calculated. 1st The Q 1st Whereas, a(Q 1st ) and b(Q 1st ), the constraint term d can be calculated as shown in the following equation (20). FIG. 10 is a graph showing an example of the first correction function a(Q) and the second correction function b(Q). 1st ) and b(Q 1st ) position. In equation (20), the constraint term d is a(Q 1st ) and b(Q 1st ) represents the density estimated from the

[0074]

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[0075] The constraint term d is a value for emphasizing the data in the limited range of a(Q) and b(Q), so it can be any value that represents the density estimated from a(Q) and b(Q) in the limited range or point of Q. For example, Q in Equation (19) i Alternatively, the value calculated by limiting the values ​​to those included in a predetermined range may be used as d.

[0076] The density ρ0 is calculated based on the calculated tentative density ρ0' and the constraint term d. The calculated density ρ0 is used as a scale factor when calculating the correction amount c(Q), as in the first embodiment. By using the density ρ0 calculated as described above as the scale factor for each loop, the calculated density ρ0 is corrected and refined while reducing the influence of distortion on the structure factor S(Q). Accordingly, the structure factor S(Q) can also be corrected.

[0077] The density ρ0 can be calculated, for example, as in the following formula (21). In formula (21), the initial value of the ratio w for weighting the constraint term d can be arbitrarily set within a range greater than 0 and less than 1. For example, the initial value of w is preferably 0.5. The initial value of w may also be a value input by the user. Note that the method for calculating the density ρ0 based on the provisional density ρ0’ and the constraint term d is not limited to formula (21).

[0078] [Number]

[0079] The calculation of the correction amount c(Q), the correction of the structure factor S(Q), and the calculation of the R value are the same as in Embodiment 1 and are thus omitted. Also in this embodiment, the R value preferably indicates the change rate of the calculated density ρ0.

[0080] Let the R value in the j-th loop be R(j). When the R value does not satisfy the set conditions, the value of w is updated so that the value of w increases or decreases according to the increase or decrease of the value of R(j) with respect to the value of R(j - 1). For example, when R(j) < R(j - 1) is satisfied, with the original w as w old , the updated w as w new , and w old < w new it is updated as such. Also, when R(j) < R(j - 1) is not satisfied, w old > w new it is updated as such.

[0081] When R(j) < R(j - 1) is satisfied, the update of w can be, for example, as in the following formula (22) using a constant p1 that satisfies 0 < p1 < 1. Also, when R(j) < R(j - 1) is not satisfied, the update of w can be, for example, as in the following formula (23) using a constant p2 that satisfies 1 < p2. p1 and p2 may be given in advance. They may also be values input by the user. Note that the method for updating w is not limited to formulas (22) and (23), and may be, for example, a method of subtracting or adding a predetermined constant from w.

[0082]

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[0083]

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[0084] After updating w, the PDF G(r) is calculated again from the corrected structure factor S(Q), and the process up to calculating the R value is repeated. On the other hand, if the R value satisfies the set condition, the corrected structure factor S(Q) or density ρ0 is output as needed, and the process ends. The condition for setting the R value can be specified in the same way as in embodiment 1.

[0085] 11 is a graph showing an example of the structure factor S(Q) before correction and the structure factor S(Q) after correction. As shown in FIG. 11, the method of this embodiment can appropriately correct a range of the structure factor S(Q) that includes large distortion. Note that when the value of the ratio w is set to 0 and w is not updated, the method of this embodiment produces the same results as the method of embodiment 1, and therefore, this embodiment can be said to include embodiment 1.

[0086] In this way, the method of this embodiment starts from total scattering data and can correct the structure factor S(Q) and the density ρ0 while reducing the influence of distortion of the structure factor S(Q).

[0087] (Embodiment 3) In embodiment 3, a method for correcting the structure factor using total scattering data measured by an X-ray diffractometer, assuming that the density is known, will be described. Since many procedures are similar to embodiment 1, only the differences will be described.

[0088] In this embodiment, the steps up to the step of creating the first correction function a(Q) and the second correction function b(Q) can be performed in the same manner as in embodiment 1. The structure factor S(Q) can also be used as the initial data.

[0089] In this embodiment, the density of the sample is assumed to be known, so there is no need to calculate the density ρ based on the first correction function a(Q) and the second correction function b(Q). Meanwhile, a constant α is used as a scale factor when calculating the correction amount c(Q). This value α is preferably a predetermined value. This value α may be determined by referring to a database or the like based on the type of sample, or may be a value input by the user. In the method of this embodiment, if this value α is given as the known density, the structure factor can be corrected based on the density.

[0090] Next, a correction amount c(Q) including the first correction function a(Q), the second correction function b(Q), and a scale factor (in this embodiment, the constant α given above) is calculated. For example, c(Q) can be defined as the following equation (24).

[0091]

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[0092] Since the scale factor in each loop is fixed as a constant α, if a(Q) is corrected to approach αb(Q), the structure factor S(Q) can also be corrected based on α. ​​Note that the first peak position r of G(r) 1st When the second correction function b(Q) is fixed to a single function by fixing it to a single value, the correction amount c(Q) can be said to be a function that changes in accordance with changes in the first correction function a(Q).

[0093] The correction of the structure factor S(Q) can be performed in the same manner as in the first embodiment. Next, an R value is calculated that includes the first correction function a(Q) and the second correction function b(Q), and indicates the accuracy of the correction. In the case of this embodiment, the R value is preferably a value that indicates the degree of agreement between a(Q) and αb(Q). When the R value is a value that indicates the degree of agreement between a(Q) and αb(Q), it can be calculated, for example, as shown in the following formula (25). In formula (25), b'(Q i ) is αb(Qi ) and a(Q i ) and b(Q i ) is the structure factor at each measurement point Q i The R value is not limited to equation (25), and may be any value that indicates the accuracy of correction or the degree of agreement between a(Q) and αb(Q).

[0094]

number

[0095] If the R value does not satisfy the set condition, the PDF G(r) is calculated again from the corrected structure factor S(Q), and the process of calculating the R value is repeated. On the other hand, if the R value satisfies the set condition, the structure factor S(Q) corrected as necessary is output and the process ends. Note that in this embodiment, the set condition for the R value can also be, for example, a predetermined value of 0.05% or more and 0.1% or less. Furthermore, for example, if priority is given to calculation speed, the predetermined value can be 0.1% or more and 1% or less. Furthermore, for example, if priority is given to correction accuracy, the predetermined value can be 0.005% or more and 0.05% or less.

[0096] In this way, the method of the present embodiment allows correcting the structure factor S(Q) based on the scale factor, starting from the total scattering data.

[0097] [Overall system] Fig. 12 is a conceptual diagram showing an example of the configuration of an X-ray diffraction measurement system 100. The system 100 includes an X-ray diffraction device 200, a control device 300, and a correction device 400. The X-ray diffraction device 200 forms an optical system that irradiates X-rays onto a sample and detects diffracted X-rays generated from the sample, and the optical system includes a goniometer. Note that the configuration shown in Fig. 12 is just one example, and various other configurations can be adopted.

[0098] The control device 300 is connected to the X-ray diffraction device 200 and controls the X-ray diffraction device 200 and processes and stores acquired data. The correction device 400 corrects the structure factor. The control device 300 and the correction device 400 are devices equipped with a CPU and memory, and may be PC terminals or servers on the cloud. Furthermore, not only the entire device, but also some of the devices or some of the functions within the devices may be provided on the cloud. The input device 510 is, for example, a keyboard or mouse, and performs input to the control device 300 and the correction device 400. The display device 520 is, for example, a display, and displays structure factors, PDFs, etc.

[0099] Using such a system 100, total scattering data can be measured and the structure factor calculated from the total scattering data can be corrected, and the density can be calculated and corrected.

[0100] 12, the control device 300 and the correction device 400 are shown as the same PC. However, as explained above, the method of the present invention can acquire total scattering data or structure factors and perform correction independently of the X-ray diffraction device 200 and the control device 300, and therefore the correction device 400 may be configured as a device different from the control device 300. The following describes a case where the control device 300 and the correction device 400 are configured as different devices.

[0101] [X-ray diffractometer] The X-ray diffraction apparatus 200 includes an X-ray generation unit 210 that generates X-rays from an X-ray focus, i.e., an X-ray source, an incident-side optical unit 220, a goniometer 230, a sample stage 240 on which a sample is placed, an exit-side optical unit 250, and a detector 260 that detects X-rays. The X-ray generation unit 210, incident-side optical unit 220, goniometer 230, sample stage 240, exit-side optical unit 250, and detector 260 that configure the X-ray diffraction apparatus 200 may be general components, and therefore description thereof will be omitted.

[0102] [Control device] 13 is a block diagram showing an example of the configuration of the control device 300. The control device 300 is configured by a computer having a CPU (Central Processing Unit), ROM (Read Only Memory), RAM (Random Access Memory), and memory connected to a bus. The control device 300 is connected to the X-ray diffraction device 200 and receives information from it.

[0103] The control device 300 comprises a control unit 310, a device information storage unit 320, a measurement data storage unit 330, and a display unit 340. Each unit can send and receive information via a control bus L. The input device 510 and the display device 520 are connected to the CPU via an appropriate interface.

[0104] The control unit 310 controls the operation of the X-ray diffraction instrument 200. The instrument information storage unit 320 stores instrument information acquired from the X-ray diffraction instrument 200. The instrument information includes information about the X-ray diffraction instrument 200, such as the instrument name, type of radiation source, wavelength, background, etc. Other information required for calculating the structure factor based on the total scattering data may also be included, such as the shape and arrangement of the sample, the type of constituent elements, composition, and absorption coefficient.

[0105] The measurement data storage unit 330 stores the measurement data acquired from the X-ray diffraction instrument 200. The measurement data includes total scattering data. The total scattering data may also include information necessary for calculating the structure factor based on the total scattering data, such as the type of radiation source, wavelength, background, sample shape, placement, type of constituent elements, composition, and absorption coefficient. Note that if the background is low, the background need not be included in the information necessary for calculating the structure factor. The display unit 340 displays the measurement data on the display device 520, allowing the user to confirm the measurement data. The user can also issue instructions and specifications to the control device 300, correction device 400, etc. based on the measurement data.

[0106] [Correction device] 14 is a block diagram showing an example of the configuration of the correction device 400. The correction device 400 is configured by a computer having a CPU, a ROM, a RAM, and a memory connected via a bus. The correction device 400 may be connected to the X-ray diffraction device 200 via the control device 300.

[0107] The correction device 400 includes a structure factor acquisition unit 410, a PDF calculation unit 420, a correction function creation unit 430, a correction amount calculation unit 440, a structure factor correction unit 450, and an R value calculation unit 460. Each unit can send and receive information via a control bus L. When the correction device 400 and the control device 300 have separate configurations, the input device 510 and the display device 520 are also connected to the CPU of the correction device 400 via an appropriate interface. In this case, the input device 510 and the display device 520 may be different from those connected to the control device 300.

[0108] The structure factor acquisition unit 410 acquires a structure factor calculated from the total scattering data. The structure factor acquisition unit 410 may acquire a structure factor based on the total scattering data acquired directly from the X-ray diffraction instrument 200 or via the control device 300, or may acquire a structure factor stored in advance in a database or the like.

[0109] The PDF calculation unit 420 calculates a PDF (Pair Distribution Function) from the structure factors acquired by the structure factor acquisition unit 410.

[0110] The correction function creation unit 430 creates a first correction function and a second correction function. The first correction function is a function obtained by Fourier transform within a predetermined range, including a cutoff function that cuts off the PDF data calculated by the PDF calculation unit and the data on the long-distance side of the PDF. The second correction function is a function obtained by Fourier transform within the same predetermined range as the first correction function, including the same cutoff function as the first correction function. The cutoff functions are stored in advance. Alternatively, the cutoff functions may be configured so that they can be arbitrarily set by the user by selecting the function form, the predetermined range, etc.

[0111] The cutoff function is a monotonically decreasing function that takes values ​​from 1 to 0 in the domain of the cutoff function. The cutoff function is a C ∞ It is preferable that the cutoff function be a monotonically decreasing function of the same order. This allows the PDF data to be smoothly connected. The cutoff function can also be a sigmoid function or a function expressed in exponential form.

[0112] The correction amount calculation unit 440 calculates a correction amount including the first correction function, the second correction function, and the scale factor created by the correction function creation unit 430.

[0113] The structure factor correction unit 450 corrects the structure factor using the correction amount calculated by the correction amount calculation unit 440.

[0114] The R-value calculation unit 460 includes a first correction function and a second correction function and calculates an R-value indicating the accuracy of correction. The R-value may be a value indicating the degree of agreement between the first correction function and the second correction function. Depending on its definition, the R-value may not be calculated in the first loop or there may be no comparison target. In such cases, a second loop may be performed without fail. Furthermore, if the correction device 400 is configured to include a density calculation unit 435 (described later) and the R-value indicates the rate of change in density, a density estimated for the sample may be used as data for calculating the R-value in the first loop or as a comparison target. Furthermore, a density calculated by the density calculation unit 435 may be used as data for calculating the R-value in the second or subsequent loops or as a comparison target. The estimated density may be input by the user.

[0115] 15, 16, and 17 are block diagrams showing modified examples of the configuration of correction device 400. As shown in FIGS. 15 to 17, correction device 400 preferably includes a density calculation unit 435 (density calculation unit 435-1 or density calculation unit 435-2). Density calculation unit 435-1 calculates density based on a first correction function and a second correction function. This allows correction device 400 to correct the density calculated based on the structure factor based on the first correction function and the second correction function.

[0116] The density calculation unit 435-2 calculates the constraint term based on the limited range of values ​​of the first and second correction functions. The density calculation unit 435-2 calculates the density based on the first and second correction functions and the constraint term. This allows the correction device 400 to correct the density calculated from the structure factor based on the first and second correction functions and the constraint term. In this case, the calculated density preferably includes the product of the constraint term and a ratio that weights the constraint term.

[0117] When the correction device 400 is configured to include a density calculation unit 435-2, the correction device 400 preferably includes a ratio calculation unit 437, as shown in FIGS. 16 and 17. The ratio calculation unit 437 calculates or updates a ratio w that weights a constraint term. The R value in the jth loop is defined as R(j). The ratio calculation unit 437 preferably updates the value of w so that the value of w increases or decreases depending on the increase or decrease in the value of R(j) relative to the value of R(j-1). This allows the degree of involvement of the constraint term in the density calculation to be changed. The ratio value is preferably updated when the R value does not satisfy a set condition. In FIG. 17, when the density calculation unit 435 is a density calculation unit 435-1 that does not use a constraint term, the correction device 400 does not need to include the ratio calculation unit 437.

[0118] When the correction device 400 is configured to include a density calculation unit 435 (density calculation unit 435-1 or density calculation unit 435-2), the R value calculated by the R value calculation unit 460 preferably indicates the rate of change of the density calculated by the density calculation unit 435. This makes it possible to improve the accuracy of the density calculated by the density calculation unit 435.

[0119] As shown in FIG. 17, the correction device 400 preferably includes a structure factor calculation unit 405. The structure factor calculation unit 405 acquires total scattering data of the sample and calculates a structure factor based on the type of radiation source, wavelength, background, shape and arrangement of the sample, type and composition of constituent elements, and absorption coefficient of the total scattering data. Note that if the background is low, the structure factor may be calculated without using it. In this case, the structure factor acquisition unit 410 acquires the structure factor calculated by the structure factor calculation unit 405. This allows the correction device 400 to calculate a structure factor based on the total scattering data of the sample and correct the structure factor.

[0120] 17, the correction device 400 preferably includes a peak position determiner 425. The peak position determiner 425 determines the first peak position r of the PDF. 1st At this time, the predetermined range is from 0 to r 1st This makes it possible to determine the predetermined range according to the PDF calculated by the PDF calculation unit 420, and to improve the accuracy of the first correction function and the second correction function created by the correction function creation unit 430.

[0121] [Measurement method] A sample S is placed in the X-ray diffraction instrument 200, and the rotation axis is moved and X-rays are projected repeatedly under predetermined conditions under the control of the control device 300. In this way, the sample is irradiated with X-rays and diffraction data is acquired. The X-ray diffraction instrument 200 transmits instrument information and the acquired diffraction data to the control device 300 as measurement data.

[0122] [Correction method] (Explanation of the flow when correcting only the structure factors) Fig. 18 is a flowchart showing an example of the operation of correction device 400. Fig. 18 shows an example of the operation when correcting only the structure factor. First, correction device 400 acquires the structure factor (step S1). Next, it calculates a PDF (Pair Distribution Function) from the acquired structure factor (step S2). Next, it creates a first correction function that includes a cutoff function that cuts off the PDF data and the long-distance data of the PDF and is Fourier transformed within a predetermined range, and a second correction function that includes the cutoff function and is Fourier transformed within a predetermined range (step S3).

[0123] Next, a correction amount including a first correction function, a second correction function, and a scale factor is calculated (step S4). Next, the structure factor is corrected using the correction amount (step S5). Next, an R value including the first correction function and the second correction function, which indicates the accuracy of the correction, is calculated (step S6).

[0124] If the R value does not satisfy the set condition (step S7-NO), the process returns to step S2, calculates the PDF from the corrected structure factor, and repeats the process up to step S6. On the other hand, if the R value satisfies the set condition (step S7-YES), the process outputs the corrected structure factor as needed and ends. Note that, depending on the definition of the R value, there are cases where it cannot be calculated in the first loop or where no comparison target exists. In such cases, the process may be configured to always perform a second loop. In this way, the structure factor can be corrected based on the scale factor.

[0125] (Explanation of the flow for calculating density) Fig. 19 is a flowchart showing a modified example of the operation of correction device 400. Fig. 19 shows an example of the operation when correcting the structure factor and calculating the density at the same time. First, correction device 400 acquires the structure factor (step T1). Next, it calculates the PDF from the acquired structure factor (step T2).

[0126] Next, a first correction function is created which includes a cutoff function that cuts off the PDF data and the long-distance side data of the PDF and is Fourier transformed within a predetermined range, and a second correction function is created which includes the cutoff function and is Fourier transformed within a predetermined range (step T3).

[0127] Next, the density is calculated using the first correction function and the second correction function (step T4). Next, a correction amount including the first correction function, the second correction function, and a scale factor is calculated (step T5). At this time, the scale factor is preferably the density calculated by the density calculation unit 435-1. Next, the structure factor is corrected using the correction amount (step T6). Next, an R value indicating the accuracy of the correction is calculated using the first correction function and the second correction function (step T7). At this time, the R value preferably indicates the rate of change of the calculated density.

[0128] If the R value does not satisfy the set conditions (step T8-NO), the process returns to step T2, calculates the PDF from the corrected structure factor, and repeats the process up to step T7. On the other hand, if the R value satisfies the set conditions (step T8-YES), the process outputs the corrected structure factor or density as needed and ends. Note that when the R value indicates the rate of change of the calculated density, there are cases where it cannot be calculated in the first loop or there is no comparison target. In such cases, the process may be configured to always perform a second loop. Alternatively, a density estimated depending on the sample or a value entered by the user may be used as data for calculating the R value or as a comparison target. In this way, the structure factor and density can be corrected at the same time.

[0129] (Explanation of modified flow when calculating density) Fig. 20 is a flowchart showing a modified example of the operation of the correction device 400. Fig. 20 shows an example of the operation when the structure factor includes a large distortion, and the structure factor is corrected and the density is calculated. First, the correction device 400 acquires the structure factor (step U1). Next, the PDF is calculated from the acquired structure factor (step U2).

[0130] Next, a first correction function is created which includes a cutoff function that cuts off the PDF data and the long-distance side data of the PDF and is Fourier transformed within a predetermined range, and a second correction function is created which includes the cutoff function and is Fourier transformed within a predetermined range (step U3).

[0131] Next, the constraint term is calculated using the limited range or point values ​​of the first and second correction functions. Next, a density is calculated based on the first and second correction functions and the constraint term (step U4). The calculated density preferably includes the product of the constraint term and a ratio w that weights the constraint term.

[0132] Next, a correction amount including a first correction function, a second correction function, and a scale factor is calculated (step U5). At this time, the scale factor is preferably the density calculated by the density calculation unit 435-2. Next, the structure factor is corrected using the correction amount (step U6). Next, an R value indicating the accuracy of the correction is calculated (step U7), including the first correction function and the second correction function. At this time, the R value preferably indicates the rate of change of the calculated density.

[0133] Next, if the R value does not satisfy the set condition (step U8-NO), the w value is updated (step U9). It is preferable to update the w value by increasing or decreasing the w value according to the increase or decrease in the R value. Then, the process returns to step U2, the PDF is calculated from the corrected structure factor, and the process up to step U7 is repeated.

[0134] On the other hand, if the R value satisfies the set condition (step U8-YES), the structure factor or density, corrected as necessary, is output and the process ends. Note that when the R value indicates the rate of change of the calculated density, there are cases where it cannot be calculated in the first loop or there is no comparison target. In such cases, a second loop may be performed without fail. Alternatively, a density estimated according to the sample or a value entered by the user may be used as data for calculating the R value or as a comparison target. In this way, the structure factor and density can be corrected while reducing the influence of distortion on the structure factor.

[0135] (Explanation of modified flow when calculating density) Fig. 21 is a flowchart showing a modified example of the operation of the correction device 400. Fig. 21 shows a modified example of the operation when correcting the structure factor and calculating the density at the same time. First, the correction device 400 acquires total scattering data (step V1). Next, the correction device 400 calculates a structure factor from the acquired total scattering data (step V2). At this time, it is preferable to calculate the structure factor based on the type of radiation source, wavelength, background, shape and arrangement of the sample, type and composition of constituent elements, and absorption coefficient of the total scattering data.

[0136] Next, the calculated structure factor is acquired (Step V3). Next, the PDF is calculated from the acquired structure factor (Step V4). Next, the first peak position r of the PDF is calculated. 1st (Step V5) Determine the first peak position r of the PDF. 1st may be determined by a peak search of the PDF or by referring to a database, etc. 1st may be input by the user.

[0137] Next, a first correction function is created by Fourier transforming the PDF data and the long-distance data of the PDF, and includes a cutoff function for cutting off the data, and a second correction function is created by Fourier transforming the PDF data and the long-distance data of the PDF (step V6). 1st It is preferable to set the following.

[0138] Next, the density is calculated using the first correction function and the second correction function (step V7). Next, a correction amount including the first correction function, the second correction function, and a scale factor is calculated (step V8). At this time, the scale factor is preferably the density calculated by the density calculation unit 435-1 or the density calculation unit 435-2. Next, the structure factor is corrected using the correction amount (step V9). Next, an R value indicating the accuracy of the correction is calculated using the first correction function and the second correction function (step V10). At this time, the R value preferably indicates the rate of change of the calculated density.

[0139] If the R value does not satisfy the set condition (step V11-NO), the value of the weighting ratio w for the constraint term is updated (step V12). It is preferable to increase or decrease the value of w according to the increase or decrease in the R value. Then, return to step V4, calculate the PDF from the corrected structure factor, and repeat the process up to step V10. If the scale factor is a density that does not include a constraint term, the value of w can be set to 0, eliminating the need to update the value of w. On the other hand, if the R value satisfies the set condition (step V11-YES), output the corrected structure factor or density as needed, and then terminate. When the R value indicates the rate of change of the calculated density, there are cases where it cannot be calculated in the first loop or where there is no comparison target. In such cases, a second loop can be performed without fail. Alternatively, a density estimated for the sample or a value entered by the user can be used as data for calculating the R value or as a comparison target. In this way, starting from total scattering data, the structure factor and density can be corrected while reducing the influence of distortion in the structure factor.

[0140] Steps for acquiring total scattering data, calculating the structure factor from the total scattering data, and the first peak position r of the PDF 1st The step of determining {overscore (x)} can also be applied to a method of correcting structure factors only or a method of correcting structure factors and densities without using constraint terms.

[0141] [Example 1] Using the system 100 configured as described above, total scattering data of SiO2 glass was measured. Using this, the structure factor and PDF were calculated. Then, using the method of embodiment 1 of the present invention, the average atom number density was calculated. The value was 0.06376 atoms / Å. 3 The R value at this point was 0.01% or less. The loop was repeated 11 times.

[0142] For the same PDF, the average atom number density was calculated from the slope of a linear approximation of the data below the first peak position r1st of the PDF using the conventional method. The value was 0.05995 atoms / Å 3 On the other hand, the average atomic density of the bulk material was calculated to be 0.06613 atoms / Å. 3 It was.

[0143] Therefore, it was confirmed that the average atomic number density calculated by the method of the present invention is closer to the actual average atomic number density than the average atomic number density calculated by the conventional method. 3 ) to normal density (g / cm 3 ) are converted to 2.12g / cm 3 , 1.99g / cm 3 , 2.20g / cm 3 This becomes:

[0144] [Example 2] Next, the system 100 was used to measure total scattering data for glassy carbon, graphite, silicon, diamond, LiMn2O4, and LiCoO2. Using these data, the structure factor and PDF of each sample were calculated. The average atomic number density of each sample was then calculated using the method of embodiment 1 of the present invention. The average atomic number density of the bulk of each sample was also calculated. The average atomic number density calculated by the method of the present invention was within a ±10% range of the average atomic number density of the bulk for all samples. This confirms that the method of the present invention can calculate values ​​sufficiently close to the actual density.

[0145] [Example 3] Next, using the system 100, the PDF was calculated using the structure factor S(Q) of SiO2 glass containing large strain at large Q values ​​as the initial data. Then, the average atomic number density was calculated using the methods of embodiment 1 and embodiment 2 of the present invention. In the method of embodiment 2, the initial value of w was set to 0.5, p1 to 0.8, and p2 to 1.05.

[0146] The average atomic number density calculated by the method of embodiment 1 is 0.0574 atoms / Å 3 In contrast, the average atom number density calculated by the method of embodiment 2 was 0.0701 atoms / Å. 3 The average atomic density of the bulk was 0.06613 atoms / Å. 3 This confirmed that when the structure factor S(Q) is significantly distorted, the density estimation results are better when the method of the second embodiment is used. 3 ) to normal density (g / cm 3 ) are converted to 1.91g / cm 3 , 2.33g / cm 3 , 2.20g / cm 3 This becomes:

[0147] From the above results, it was confirmed that the correction device, system, method and program of the present invention can correct the structure factor and also the density. [Explanation of symbols]

[0148] 100 systems 200 X-ray Diffractometer 210 X-ray generator 220 Incident optical unit 230 Goniometer 240 Sample stage 250 Output optical unit 260 detector 300 control device 310 Control Unit 320 Device information storage unit 330 Measurement data storage unit 340 Display section 400 Corrector 405 Structure factor calculation part 410 Structure factor acquisition part 420 PDF calculation section 425 Peak Position Determination Unit 430 Correction function creation unit 435, 435-1, 435-2 Density calculation section 437 Ratio Calculation Section 440 Correction amount calculation unit 450 Structure factor correction section 460 R-value calculation section 510 Input Device 520 Display device

Claims

1. A correction device for correcting a structure factor, comprising: a structure factor acquisition unit for acquiring the structure factor; a PDF calculation unit that calculates a PDF (Pair Distribution Function) from the acquired structure factors; a correction function creating unit that creates a first correction function obtained by Fourier transforming the PDF data and a function including a cutoff function within a predetermined range, and a second correction function obtained by Fourier transforming the PDF data and a function including the cutoff function within the predetermined range; a correction amount calculation unit that calculates a correction amount including the first correction function, the second correction function, and a scale factor; a structure factor correction unit that corrects the structure factor using the correction amount; an R value calculation unit that includes the first correction function and the second correction function and calculates an R value that indicates correction accuracy, A correction device characterized in that the cutoff function is a function that cuts off the data on the long-distance side of the PDF data, with the range above a constant determined based on the first peak position r 1st of the PDF being the long-distance side.

2. a density calculation unit that calculates a density based on the first correction function and the second correction function, the scale factor is the density calculated by the density calculation unit, 2. The correction device according to claim 1, wherein the R value indicates a rate of change of the density calculated by the density calculation unit.

3. the density calculation unit calculates a constraint term based on the limited ranges of values ​​of the first correction function and the second correction function; a ratio calculation unit that calculates a ratio for weighting the constraint term, the density includes the product of the constraint term and the ratio; 3. The correction device according to claim 2, wherein the ratio increases or decreases in accordance with an increase or decrease in the R value.

4. 2. The correction device according to claim 1, wherein the scale factor is a predetermined value.

5. The first peak position r of the PDF １ｓｔ a peak position determining unit for determining a peak position of The predetermined range is from 0 to r １ｓｔ 5. The correction device according to claim 1, wherein:

6. 5. The correction device according to claim 1, wherein the cutoff function is a monotonically decreasing function that takes values ​​from 1 to 0 in a domain of the cutoff function.

7. a structure factor calculation unit that acquires total scattering data of the sample and calculates the structure factor based on the type of radiation source of the total scattering data, wavelength, shape and arrangement of the sample, type and composition of constituent elements, and absorption coefficient; 5. The correction device according to claim 1, wherein the structure factor acquisition unit acquires the structure factors calculated by the structure factor calculation unit.

8. an X-ray diffraction apparatus including an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a goniometer that controls the rotation of a sample; A system comprising: a correction device according to any one of claims 1 to 4.

9. 1. A method for correcting a structure factor, comprising: a structure factor acquisition step of acquiring the structure factor; a PDF calculation step of calculating a PDF (Pair Distribution Function) from the acquired structure factors; a correction function creating step of creating a first correction function obtained by Fourier transforming the PDF data and a function including a cutoff function within a predetermined range, and a second correction function obtained by Fourier transforming the PDF data and a function including a cutoff function within the predetermined range; a correction amount calculation step of calculating a correction amount including the first correction function, the second correction function, and a scale factor; a structure factor correction step of correcting the structure factor using the correction amount; an R value calculation step of calculating an R value indicating the accuracy of correction, the R value including the first correction function and the second correction function; The method is characterized in that the cutoff function is a function that cuts off the data on the long-distance side of the PDF data, with the range equal to or greater than a constant determined based on the first peak position r 1st of the PDF being the long-distance side.

10. A program for correcting structure factors, A process of obtaining the structure factor; A process of calculating a PDF (Pair Distribution Function) from the acquired structure factors; a process of creating a first correction function obtained by Fourier transforming the PDF data and a function including a cutoff function within a predetermined range, and a second correction function obtained by Fourier transforming the PDF data and a function including a cutoff function within the predetermined range; calculating a correction amount including the first correction function, the second correction function, and a scale factor; a process of correcting the structure factor using the correction amount; a process of calculating an R value that includes the first correction function and the second correction function and indicates the accuracy of the correction; The program is characterized in that the cutoff function is a function that cuts off data on the long-distance side of the PDF data, with the range equal to or greater than a constant determined based on the first peak position r 1st of the PDF being the long-distance side.

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