JP2019211209A - Measurement method of diffracted x-ray intensity by one-dimensional or two-dimensional detector - Google Patents

Abstract

To provide a measurement method for reducing a variation in sensitivity between detector elements in a one-dimensional/two-dimensional detector in X-ray diffraction measurement.SOLUTION: A measurement method of diffracted X-ray intensity in the present invention includes: an acquisition step of diffraction data by scanning a detector arm from a start angle to an end angle by a fixed step width by letting W be the central angle of a one-dimensional or two-dimensional detector whose chord is the length in the direction perpendicular to the diffracted X-ray, and N be the number of elements contained in the detector; a step of further acquiring diffraction data, after an increasing step of the start angle by n×W/N ( where n is a natural number satisfying 1≤n≤N ), by scanning the detector arm from the increased start angle to the end angle by the fixed step width; a step of repeating the increasing step and the further acquiring step; a step of performing 2θ angle conversion and correction of the diffraction data and sorting by 2θ: and a step of averaging the diffraction data for each W/N 2θ interval.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a method for measuring the intensity of diffracted X-rays using a one-dimensional or two-dimensional detector, and more particularly, to a diffraction X with reduced variation in sensitivity between detector elements of a one-dimensional or two-dimensional detector. This is a method for measuring the intensity of a line.

  In recent years, in X-ray diffraction and X-ray scattering experiments, in order to realize high-speed and high-sensitivity measurement, a position-sensitive detector (hereinafter simply referred to as a single-dimensional or two-dimensional array of detector elements) One-dimensional or two-dimensional detectors) are widely used.

  In the X-ray diffraction measurement using such a one-dimensional or two-dimensional detector, when the range of the diffraction angle 2θ to be measured is larger than the detector surface, the scanning method is used to move the detector to cover the entire measurement range. Is a step scan in which the one-dimensional or two-dimensional detector is moved by a predetermined step width (for example, the detector width) and stopped to perform counting, scanning from the start angle to the end angle, and acquiring diffraction data. (See, for example, Non-Patent Document 1) and a continuous scan (eg, detector element) that simultaneously counts the detector elements contained in the detector while moving the one-dimensional or two-dimensional detector continuously at a constant speed. There is known a time delay integration (TDI) scan in which outputs of all points are distributed to 2θ angles in synchronization with detector movement (see Patent Document 1).

In radiation measurement, random errors in measurement intensity are thought to follow a Poisson distribution, but in one-dimensional or two-dimensional detectors, the count increases due to systematic errors due to sensitivity variations between detector elements. It is known that deviation from the Poisson distribution cannot be ignored as the influence of random errors becomes relatively small. For example, in order to reduce systematic errors due to variations in sensitivity between detector elements, the count of each detector element is counted after exposure until a sufficient count is obtained using a light source with uniform intensity such as fluorescent X-rays. Uniformity correction (Flat Filled correction) in which correction coefficients are obtained so as to be equal and applied thereto has been used. However, not always sufficient, for example greater than the influence of the systematic error of 10 ⁴ counts if widely MYTHEN detector used in the synchrotron X-ray powder diffraction is known to be significant, also the sensitivity of the detector element Since the variation differs depending on the energy of the X-ray, there is a problem that it is necessary to obtain a correction coefficient for each energy.

  In the case of the step scan described above, no consideration is given to variations in sensitivity between detector elements. Furthermore, by applying a smoothing process such as a moving average method that takes the average of the diffraction intensity data at each measurement point and the diffraction intensity data around it, the diffraction intensity data obtained by the step scan can be obtained at random. It is known that the error can be reduced and the influence of the variation in sensitivity between detector elements can be reduced. However, there is a problem in accuracy because the diffraction peak is flattened excessively.

  In the case of the above-described continuous scanning, all the detector elements are scanned, and as a result, variations in sensitivity among the detector elements are reduced. However, in continuous scanning, in order to increase the diffraction intensity count, it is necessary to increase the 2θ passage time of one detector element, and in particular, an X-ray source such as synchrotron radiation is disconnected. When there was a trouble, there was a restriction that continuous measurement up to the end point could not be performed.

  For this reason, there is a demand for a method for reducing variation in sensitivity between detector elements in a one-dimensional / two-dimensional detector simply and reliably.

JP 2012-88094 A

M.M. Tanaka et al., Journal of the Ceramic Society of Japan, 121 [3], 287-290, 2013.

  In view of the above, an object of the present invention is to provide a measurement method for reducing variation in sensitivity between detector elements in a one-dimensional / two-dimensional detector in X-ray diffraction measurement.

One-dimensional or two-dimensional detection for detecting the intensity of diffracted X-rays from a sample mounted on a detector arm centered on the sample and an X-ray source that irradiates incident X-rays toward the sample according to the present invention A method of measuring the intensity of the diffracted X-ray while changing the angle formed between the incident X-ray and the detector arm, and When scanning by moving the one-dimensional or two-dimensional detector on a circumference in a plane including the diffracted X-ray, the diffracted X-ray included in the plane of the one-dimensional or two-dimensional detector The central angle with the length in the vertical direction as a chord is W, the number of elements contained in the one-dimensional or two-dimensional detector is N, and the detector arm is moved by a predetermined step width to a starting angle (2θ_start). ) To end angle (2θ_end) Scanning and acquiring diffraction data of 2θ and intensity by the one-dimensional or two-dimensional detector, and increasing the starting angle by n × W / N (n is a natural number satisfying 1 ≦ n ≦ N) And scanning the detector arm by the predetermined step width from the increased start angle to the end angle, and further acquiring diffraction data of 2θ and intensity by the one-dimensional or two-dimensional detector. Repeating the step, the increasing step, and the further obtaining step, and performing the 2θ angle conversion / correction on the diffraction data obtained in the obtaining step and the repeating step and sorting each 2θ And the step of averaging the diffraction data obtained in the step of sorting every 2θ in every 2θ section of W / N. The above problems are solved.
The constant step width may be an angle W or W−ΔW (ΔW <W).
The repeating step may be repeated a number of times less than N.
The repeating step may be performed so that the number of repetitions is at least four.
The repeating step may be performed so that the number of repetitions is 15 or more.
The sample may be a powder sample.

  According to the method for measuring the intensity of diffracted X-rays according to the present invention, scanning is performed by moving a one-dimensional or two-dimensional detector around a 2θ axis on a circumference in a plane including incident X-rays and diffracted X-rays. In this case, the number of elements contained in the one-dimensional or two-dimensional detector is W, where W is a central angle that is included in this plane of the one-dimensional or two-dimensional detector surface and has a length perpendicular to the diffracted X-ray. N is increased by n × W / N (n: natural number, N is the upper limit), scanning from the start angle to the end angle, and acquiring diffraction data are repeated a plurality of times. At this time, the end angle is the maximum angle that the detector surface includes the initial end angle. Furthermore, the obtained diffraction data is subjected to angle correction for the deviation from the circle or cylinder and the detector surface inclination for each detector surface being flat, and then the data are combined for each angle. The sorted ones are averaged for every 2θ section of W / N. Thereby, since data of a plurality of detector elements with respect to X-rays having the same diffraction angle are averaged, the flattening of the diffraction peak does not occur unlike the smoothing like the moving average method. By increasing the number of repetitions, the total exposure time increases, so that random errors in counting can be reduced, and the accuracy of diffraction data can be improved. Unlike continuous scanning, even if the X-ray source is interrupted in the middle, it is only necessary to average the diffraction data up to that point, so that data for the entire measurement range can be obtained and there is no measurement failure such as missing data.

  In addition, smooth data can be obtained in detecting weak diffraction peaks and measuring the scattering intensity of a sample having low crystallinity. If the method of the present invention is adopted, it is not necessary to collect uniform correction data for obtaining a correction coefficient for calibrating the sensitivity of each detector element, so that it is not complicated and extremely simple. Moreover, since it can respond | correspond freely with respect to the energy change of incident X-ray | X_line, it is excellent in versatility.

Schematic showing an X-ray diffractometer for carrying out the method of the present invention The flowchart which implements the measurement which reduces the dispersion | variation in the sensitivity between detector elements in the one-dimensional / two-dimensional detector of this invention. The schematic diagram which implements the measurement which reduces the dispersion | variation in the sensitivity between the detector elements in the one-dimensional / two-dimensional detector of this invention. The schematic diagram which shows the relationship between the one-dimensional detector and diffraction X-ray at the time of implementing the measurement which reduces the dispersion | variation in the sensitivity between the detector elements in the one-dimensional / two-dimensional detector of this invention. The figure which shows the procedure of the data processing at the time of implementing the measurement which reduces the dispersion | variation in the sensitivity between the detector elements in the one-dimensional / two-dimensional detector of this invention. The figure which shows the XRD pattern by Example 1. The figure which shows a part of XRD pattern by Example 1, Comparative example 1, and Comparative example 3 The figure which shows a part of XRD pattern by Example 1, Comparative example 1, and Comparative example 4 The figure which shows distribution of the relative error by Example 1, the comparative example 1, and the comparative example 2 The figure which shows the relationship between the standard deviation of the relative error by Example 1, the comparative example 1, and the comparative example 2, and intensity | strength. The figure which shows the relationship between the relative error by Example 1, and the repetition frequency.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In addition, the same number is attached | subjected to the same element and the description is abbreviate | omitted.

  FIG. 1 is a schematic diagram showing an X-ray diffractometer for carrying out the method of the present invention.

  An X-ray diffractometer 100 is mounted on an X-ray source 110 that irradiates incident X-rays directed toward a sample and a goniometer detector arm 120 centered on the sample, and detects the intensity of diffracted X-rays from the sample. A one-dimensional or two-dimensional detector 130. The X-ray source 110 is, for example, a rotating anti-cathode X-ray generator, a synchrotron radiation beam line, or the like. In FIG. 1, as the one-dimensional or two-dimensional detector 130, a one-dimensional position sensitive detector in which a plurality of unit detection regions (pixels) are arranged in the longitudinal direction is shown. As such a one-dimensional detector, a MYTHEN detector, a D / teX detector, and the like are known. The one-dimensional or two-dimensional detector 130 is a detector in which a plurality of pixels are arranged in a matrix in a plane. For example, a PILATUS detector, an EIGER detector, or the like is known as a two-dimensional detector. .

  In such an X-ray diffractometer 100, the one-dimensional or two-dimensional detector 130 measures the intensity of the diffracted X-ray while changing the angle formed by the incident X-ray and the detector arm 120. The one-dimensional or two-dimensional detector 130 is moved on the circumference (around the circle shown in FIG. 1) within the plane (in the plane shown in FIG. 1) including the incident X-ray and the diffracted X-ray around the axis. Scan. Hereinafter, the element of the one-dimensional or two-dimensional detector 130 that the central angle of the one-dimensional or two-dimensional detector 130 with the length in the direction perpendicular to the diffracted X-rays included in the plane as a chord is W is included. Let N be the number. For example, when the one-dimensional detector 130 is a MYTHEN detector, N is 1,280, and W when the sample-detector distance is 1 m is 3.66 °. The values of W and N are uniquely determined by the one-dimensional or two-dimensional detector used and its arrangement.

FIG. 2 is a flowchart for performing a measurement for reducing variation in sensitivity between detector elements in the one-dimensional / two-dimensional detector of the present invention.
FIG. 3 is a schematic diagram for carrying out measurement for reducing variation in sensitivity between detector elements in the one-dimensional / two-dimensional detector of the present invention.
FIG. 4 is a schematic diagram showing the relationship between the one-dimensional detector and the diffracted X-ray when the measurement for reducing the sensitivity variation between the detector elements in the one-dimensional / two-dimensional detector of the present invention is performed.

  Step S210: As shown in FIG. 3A, the detector arm 120 is moved by a certain step width and scanned from the start angle (2θ_start) to the end angle (2θ_end), and the one-dimensional or two-dimensional detector 130 obtains diffraction data of 2θ and intensity of diffracted X-rays. Here, the fixed step width for moving the detector arm 120 is preferably a central angle W formed by the one-dimensional or two-dimensional detector 130 or a measurement data area for each step movement by ΔW (ΔW <W). The angle W−ΔW so as to overlap only. This is the same as a normal step scan. For example, in FIG. 4, assume that the one-dimensional detector 130 shown in the lower stage is the first scan.

  Step S220: As shown in FIG. 3B, the start angle (2θ_start) is increased by n × W / N (n is a natural number satisfying 1 ≦ n ≦ N). As a result, the start angle is 2θ_start + n × W / N. The smaller n is, the more the number of repeated measurements at a certain 2θ point is, the more detector elements that measure the 2θ point are, and it is advantageous when the variation in sensitivity between detector elements is large. The larger the value, the smaller the number of repeated measurements at a certain 2θ point, so that the entire measurement time can be shortened, which is advantageous when the sensitivity variation between detector elements is small. What is necessary is just to set n suitably according to the objective. For example, in FIG. 4, it can be seen that the one-dimensional detector 130 shown in the middle stage is moved by one element from the one-dimensional detector 130 shown in the lower stage.

  Step S230: As shown in FIG. 3C, the detector arm 120 is moved from the start angle (2θ_start + n × W / N) increased in step S220 by a certain step width, for example, by an angle W, to the end angle (2θ_end). Scanning is performed, and a one-dimensional or two-dimensional detector 130 acquires diffraction data of 2θ and intensity of diffracted X-rays. This is the same as step S210 except that the start angle of step S210 is different. As a result, the same diffracted X-ray is scanned at least twice with different elements.

  Step S240: Steps S220 and S230 are repeated. As a result, scanning has been performed at least three times. For example, referring to FIG. 4, if the scanning is increased by one element and the scanning is performed three times, the element D, the element C, and the element B surrounded by a dotted line are 2θ with respect to the diffracted X-ray in FIG. Diffraction data with intensity is acquired. Preferably, the number of repetitions is less than the number N of pixels of the one-dimensional or two-dimensional detector 130. As the number of repetitions is closer to N, the total exposure time is increased, random errors in counting are reduced, and the accuracy of diffraction data is improved. The number of repetitions is preferably at least 4, but is preferably 15 or more in consideration of the accuracy of diffraction data.

  Step S250: All diffraction data obtained in step S240 are subjected to 2θ angle conversion / correction and sorted every 2θ. That is, the diffraction data is angle-corrected with respect to the deviation from the circle or cylinder and the inclination of the surface of the detector 130 because the one-dimensional or two-dimensional detector surface 130 is a flat surface, and then the data is combined. And sorting by angle (2θ). The angle correction corrects the angle value of the data and not only accurately captures the angle information of the sharp diffraction peak, but also the diffraction data can be obtained from the angle of the one-dimensional or two-dimensional detector 130 itself. Since sampling finer than the resolution is performed, it is preferable because the peak shape of data having a sharp peak can be accurately captured. For the 2θ angle conversion / correction, for example, a general correction such as the method disclosed in Non-Patent Document 1 can be adopted.

  Step S260: The diffraction data sorted in step S250 is averaged for each 2θ section of W / N. Thereby, the data of a plurality of detector elements for the X-rays having the same diffraction angle (for example, corresponding to the elements D, C, and B for the diffracted X-rays in FIG. 4) are averaged. Become.

  FIG. 5 is a diagram showing a data processing procedure when a measurement for reducing variation in sensitivity between detector elements in the one-dimensional / two-dimensional detector of the present invention is performed.

  In the measurement method of the present invention, since the normal step scan measurement with different starting angles is repeated P times, the one-dimensional / two-dimensional detector of each step movement is performed, for example, in one repeated step scan. When an output data file is created, P sets of data sets including a plurality of data files are obtained. For example, if one step scan consists of Q step movements, P sets of data sets each consisting of Q output data files are obtained. Each repeated data set is converted into diffraction data of a normal step scan by connecting and performing 2θ angle conversion / correction for each data set. For this 2θ angle conversion / correction and connection, one data set can be processed by batch processing by software on the control computer during one step scan operation without creating an individual output data file. You can get it.

  P diffraction data obtained from P step scans having different starting angles are integrated into one diffraction data. The file format of the integrated diffraction data may be any format as long as the correspondence between the 2θ value of the diffraction data and the diffraction intensity can be grasped so that the averaging operation can be performed for each 2θ section. For example, in the case of a one-dimensional detector, the diffraction data is sorted in ascending order of 2θ values, so that the file format is the same as that of normal step scan diffraction data. In the case of a two-dimensional detector, it may be two-dimensional diffraction data including position information in a direction parallel to the 2θ rotation axis on the detector or coordinate information in space in diffractive optics, or the same as that of a one-dimensional detector. You may convert so that it may become data for every 2theta. If there is a variation in the intensity of the incident X-ray, the diffraction intensity is corrected according to the intensity of the incident X-ray with respect to the P pieces of diffraction data in order to remove the influence, and the diffraction intensity scale is adjusted.

  The integrated diffraction data obtained from step scans with different P starting angles are averaged for each 2θ interval corresponding to the unit element (pixel) size of the detector of the one-dimensional / two-dimensional detector. In the case of the diffraction data of the one-dimensional detector, or the diffraction data of the two-dimensional detector that has been linearized, the one-dimensional diffraction data is the same as in a normal step scan. In the case of two-dimensional diffraction data, two-dimensional diffraction data is obtained by averaging each position in a direction parallel to the 2θ rotation axis on the detector in a 2θ section in a direction orthogonal thereto.

  In the method of the present invention, the sample is not particularly limited, but even if the sample is a powder sample, a weak diffraction peak can be measured accurately without being flattened, which is preferable.

Here, the difference between the method of the present invention and the conventional method will be described.
(1) Step scan The present invention and step scan differ in that scanning is repeated. Specifically, it is not simply repeating step scanning without changing the starting angle, but by scanning while changing the starting angle, different detector elements are intentionally irradiated to the same diffracted X-ray. Is different.

(2) Step scan using the moving average method When the moving average method is applied to the step scan, a plurality of diffraction angles 2θ average intensity data from different observation points, that is, detector elements. The difference is that the data of different detector elements for the same diffracted X-ray is averaged. In the moving average method, data in a region larger than the size of the detector element is combined into one, and the angular resolution of the diffraction data becomes larger than the detector element size. However, in the present invention, the angular resolution of the diffraction data is the detector element. It is the same as the size.

(3) TDI scan The present invention and TDI scan differ in that scanning is repeated. In the TDI scan, data is continuously acquired as the detector moves, so that the number of scans is one, and the same diffracted X-ray is measured by a plurality of elements in the detector in the one scan. In the present invention, since one scan during repetition is performed by step movement, the correspondence between the diffracted X-rays and the detector elements is one-to-one in one measurement. In the TDI scan, a plurality of detector elements measure one diffracted X-ray in one scan, whereas in the present invention, a plurality of detector elements measure one diffracted X-ray by repeating the scan. Is different.

  The present invention will now be described in detail using specific examples, but it should be noted that the present invention is not limited to these examples.

[Example 1]
In Example 1, the X-ray diffraction measurement of CeO ₂ powder was performed by carrying out the method of FIG. 2 using the beam line BL15XU constructed in SPring-8. CeO ₂ powder was sealed in a Lindeman glass capillary having a diameter of 0.1 mm to obtain a measurement sample. The incident energy used for the measurement is 18.987 keV. As a one-dimensional detector, a silicon semiconductor detector MYTHEN (manufactured by Decris, resolution 50 μm, N = 1280 channel) was used, and the distance between the sample and the detector was 955 mm. At this time, the angular resolution of the detector is 0.003 °, and the 2θ width is 3.84 °. However, the phenomenon that the number of counts increases at both ends of the detector and the shadow of the light receiving window of the housing that houses the detector elements. In order to avoid such an extra effect, W was set to 3.5 ° by discarding data near both ends. In the first scan, the start angle is 5 °, and the start angle is n × W / N (n = 1) with an exposure time of 5 seconds and a step width of 3.5 ° until the end angle (60 °). Approximately increased by 0.003 ° and scanned repeatedly. The total number of repetitions was 51 (steps S210 to S240 in FIG. 2). As shown in FIG. 5, the obtained diffraction data was subjected to 2θ angle conversion / correction for each repeated scan to obtain 51 diffraction data. 4 times, 9 times, 16 times, 25 times, 36 times, 51 times, 4 times, 9 times, 16 times, 25 times, 36 times, 51 times so that the number of repetitions is 51 times from the 51 diffraction data. After connecting the diffraction data, they were sorted by 2θ (step S250 in FIG. 2). The sorted diffraction data was averaged over a section of 0.003 ° (step S260 in FIG. 2). The diffraction data obtained in this way are shown in FIGS.

5 angular ranges (14.5 ° -17.0 °, 24.7 ° -27.3 °, 37.3 ° -39.5 °, 47.7 ° -48.9 °, 55.8 °- 57.4 °), the relative error distribution was examined. Each of these angular ranges is a region that appears flat at first glance without a crystalline diffraction peak of CeO ₂ , but is gentle due to the scattering from the air around the sample that forms the background and the scattering from the capillary that encloses the sample. In order to draw a simple curve, a quadratic curve is set as a smooth ideal curve instead of a straight line. The distribution of relative error in the interval was obtained. The results are shown in FIG. Furthermore, the standard deviation of the relative error was calculated for each interval. The results are shown in Table 2, FIG. 10 and FIG.

[Comparative Example 1]
In Comparative Example 1, a normal step scan was performed once under the same conditions as in Example 1. That is, it was the same as the first scan in Example 1. The results are shown in FIG. 7 and FIG. Further, as in Example 1, the relative error distribution was examined for the five angle ranges, and the standard deviation was calculated. The results are shown in Table 2, FIG. 9 and FIG.

[Comparative Example 2]
In Comparative Example 2, a normal step scan was performed under the same conditions as in Example 1, except that the exposure time was 250 seconds. Similarly to Example 1, the relative error distribution was examined for five angle ranges, and the standard deviation was calculated. The results are shown in Table 2, FIG. 9 and FIG.

[Comparative Example 3]
In Comparative Example 3, the moving average method with 51 points as the averaging interval was applied to the data obtained by the normal step scan of Comparative Example 1. Since the influence of flattening by the moving average method is negligible for the flat interval, the simple moving average method in which the weight of each point in the averaging interval is equal is used instead of the weighted average. The results are shown in FIG.

[Comparative Example 4]
Comparative Example 4 was the same except that the moving average method was performed 11 times in Comparative Example 3. The results are shown in FIG.

  The measurement conditions of the above Examples / Comparative Examples are summarized in Table 1 for simplicity.

FIG. 6 is a diagram illustrating an XRD pattern according to the first embodiment.
FIG. 7 is a diagram illustrating a part of XRD patterns according to Example 1, Comparative Example 1, and Comparative Example 3.
FIG. 8 is a diagram showing a part of the XRD pattern according to Example 1, Comparative Example 1, and Comparative Example 4.

FIG. 6 shows an XRD pattern when the repetition was performed 51 times in Example 1. It was confirmed that the obtained powder XRD pattern matched well with the standard powder diffraction pattern of CeO ₂ . FIG. 7 shows an enlarged angle range (55.8 ° to 57.4 °) that appears flat in the XRD pattern of FIG. In FIG. 7, the result of Example 1 is indicated by white circles, and the result of polynomial approximation (secondary function) is indicated by a thin solid line. According to the result of comparison with the polynomial approximation according to Example 1, it can be seen that the variation is extremely small. On the other hand, only the step scan according to Comparative Example 1 has a large variation. On the other hand, according to Comparative Example 3 in which the moving average method was performed 51 times, the variation was reduced. From this, it was shown that the method of the present invention can reduce the variation to the same extent as the moving average method with respect to the angle range that seems flat.

  FIG. 8 shows an enlarged angle range (11.94 ° to 12.06 °) showing a clear peak in the XRD pattern of FIG. In FIG. 8, the diffraction peaks of Example 1 and Comparative Example 1 all showed the same diffraction intensity. On the other hand, the intensity of the diffraction peak of Comparative Example 4 subjected to the 11-time moving average method was significantly reduced as compared with that of Example 1 and Comparative Example 1. From this, it was shown that the method of the present invention does not excessively flatten the diffraction peak even if the diffraction data scanned a plurality of times are averaged. Although not shown, the intensity of the diffraction peak of Comparative Example 3 in which the moving average method was performed 51 times was further reduced than that of Comparative Example 4.

  FIG. 9 is a diagram illustrating a distribution of relative errors according to Example 1, Comparative Example 1, and Comparative Example 2.

  9A and 9B show the relative error distribution in the range of 14.5 ° to 17.0 ° and in the range of 55.8 ° to 57.4 °, respectively. According to FIGS. 9A and 9B, it was found that the relative error distribution according to Example 1 (however, 51 repetitions) was extremely small. On the other hand, the relative error distribution of Comparative Example 1 is large, and the exposure time of 50 times the exposure time of Comparative Example 1 is set. In Comparative Example 3 in which the statistical error of the intensity is reduced, the relative error distribution decreases, but the detection is performed. It was larger than the relative error distribution of Example 1 due to the influence of variations in sensitivity between the detector elements.

  Table 2 shows a list of standard deviations of relative errors in each angle range. As is apparent from Table 2, the first embodiment in which the method of the present invention was performed was the detector element having the smallest standard deviation and maintaining the diffraction intensity in any angular range compared to the conventional method. It was shown to be effective in reducing the sensitivity variation between the two.

  FIG. 10 is a diagram showing the relationship between the standard deviation of relative error and the intensity according to Example 1, Comparative Example 1, and Comparative Example 2.

  FIG. 10 shows the relationship between the standard deviation of each angle range shown in Table 2 and the strength. Example 1 is indicated by ■, and Comparative Example 1 is indicated by ● on the lower strength side 5 points. Example 2 is indicated by ● on the five points on the strong side. The theoretical curve in FIG. 10 is a Poisson distribution, and the third-order approximation is a curve based on the results of Comparative Example 1 and Comparative Example 2. According to FIG. 10, Example 1 which implemented the method of this invention turned out to agree | coincide well with Poisson distribution. On the other hand, Comparative Example 1 and Comparative Example 2, which are conventional methods, deviated significantly from the Poisson distribution. This also shows that the method of the present invention is advantageous in reducing the variation in sensitivity between detector elements.

  FIG. 11 is a diagram illustrating the relationship between the relative error and the number of repetitions according to the first embodiment.

  In FIG. 11, the result of the number of repetitions of 1 is the result of Comparative Example 1. FIG. 11 shows that the relative error decreases as the number of repetitions increases. However, even if the number of repetitions is only four, the sensitivity variation between detector elements is sufficiently reduced as compared with the conventional step scan. Further, when the number of repetitions was 16 times or more, the degree of reduction of the relative error was reduced. From this, the number of repetitions may be set according to the required accuracy, but it is better to perform at least three times, and it is preferable to perform the number of repetitions 15 times or more. In FIG. 11, although the angle range showed the result of 55.8 degrees-57.4 degrees, the same tendency was shown also in other angle ranges.

  The method of the present invention can reduce the influence of variations in sensitivity between detector elements when a one-dimensional or two-dimensional detector is used in an X-ray diffraction or X-ray scattering experiment. Excellent in properties.

100 X-ray diffractometer 110 X-ray source 120 Detector arm 130 One-dimensional or two-dimensional detector

Claims (6)

An X-ray source that irradiates incident X-rays directed toward a sample, and a one-dimensional or two-dimensional detector that is mounted on a detector arm centered on the sample and detects the intensity of diffracted X-rays from the sample In the X-ray diffractometer, the intensity of the diffracted X-ray is measured while changing the angle formed by the incident X-ray and the detector arm,
When scanning by moving the one-dimensional or two-dimensional detector on a circumference within a plane including the incident X-ray and the diffracted X-ray around the 2θ axis, the one-dimensional or two-dimensional detector A center angle having a chord as a length in a direction perpendicular to the diffracted X-ray included in the plane is W, and N is the number of elements contained in the one-dimensional or two-dimensional detector,
Scanning the detector arm by a predetermined step width from a start angle (2θ_start) to an end angle (2θ_end), and acquiring diffraction data of 2θ and intensity by the one-dimensional or two-dimensional detector;
Increasing the starting angle by n × W / N (where n is a natural number satisfying 1 ≦ n ≦ N);
Scanning the detector arm by the constant step width from the increased start angle to the end angle, and further acquiring 2θ and intensity diffraction data by the one-dimensional or two-dimensional detector;
Repeating the increasing step and the further obtaining step;
Performing the 2θ angle conversion / correction on the diffraction data obtained in the obtaining step and the repeating step, and sorting each 2θ;
And averaging the diffraction data obtained in the step of sorting every 2θ for every 2θ section of W / N.   The method according to claim 1, wherein the constant step width is an angle W or W−ΔW (ΔW <W).   The method according to claim 1 or 2, wherein the repeating step is repeated less than N times.   The method according to claim 1, wherein the repeating step is performed so that the number of repetitions is at least four.   The method according to claim 4, wherein the repeating step is performed so that the number of repetitions is 15 or more.   The method according to claim 1, wherein the sample is a powder sample.