Analysis method of crystal structure distribution by X-ray diffraction

Abstract

To provide an analytic method for clarifying crystalline structure distribution.SOLUTION: An analytic method includes: a first step of arranging a measuring object surface 12 of a sample 11 in a prescribed direction D corresponding to a prescribed plane index; a second step of irradiating the measuring object surface with an X-ray to obtain X-ray diffraction intensity from the measuring object surface by a detector 3; a third step of repeating the second step while moving the sample two-dimensionally inside a plane parallel to the measuring object to obtain an in-plane distribution of the diffraction intensity; and a fourth step of using a theoretical value according to a prescribed direction to calculate normalization distribution from the in-plane distribution. The prescribed direction is a plurality of directions respectively corresponding to a plurality of plane indices. For each of the plurality of directions, the first to fourth steps are repeated to calculate a plurality of normalization distributions. By a first calculation, a crystal orientation distribution of the measuring object surface can be obtained from the plurality of normalization distributions.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a method for analyzing crystal structure distribution by X-ray diffraction. [Background technology]

[0002] REPublication No. 2015 / 152166 (Patent Document 1) discloses a method for observing crystal orientation by the EBSD method. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Re-tabled publication No. 2015 / 152166 Summary of the Invention [Problem to be solved by the invention]

[0004] An object of the present disclosure is to provide an analytical method for clarifying the in-plane distribution of a crystal structure by X-ray diffraction. [Means for solving the problem]

[0005] The analysis method of the present disclosure includes a measurement method including a first step of arranging a measurement target surface of a sample in a predetermined direction corresponding to a predetermined plane index, a second step of irradiating the measurement target surface with X-rays to obtain the diffraction intensity of the X-rays from the measurement target surface by a detector, a third step of obtaining an in-plane distribution of the diffraction intensity by repeating the second step while moving the sample two-dimensionally in a plane parallel to the measurement target surface, and a fourth step of calculating a normalized distribution from the in-plane distribution using a theoretical value based on the predetermined direction. The predetermined directions are a plurality of directions corresponding to a plurality of plane indexes, and a plurality of the normalized distributions are calculated by repeating the first to fourth steps for each of the plurality of directions, and a crystal orientation distribution of the measurement target surface can be obtained from the plurality of normalized distributions by a first calculation. Effect of the Invention

[0006] According to the present disclosure, it is possible to provide an analytical method for clarifying the crystal structure distribution by X-ray diffraction. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 shows the positional relationship between a sample, X-rays, a detector, and the like in this embodiment. [Diagram 2] FIG. 2 is a flowchart that outlines the method for analyzing a sample in the first embodiment. [Diagram 3] FIG. 3 is a schematic diagram showing the configuration of a sample in the first embodiment. [Figure 4] FIG. 4 is a schematic diagram showing the measurement position of the sample in the first embodiment. [Diagram 5] FIG. 5 is an example of an in-plane distribution of the diffraction intensity of a sample in the first embodiment. [Figure 6] FIG. 6 is an example of a data exclusion area in the first embodiment. [Figure 7] FIG. 7 is an example of a normalized distribution of a sample in the first embodiment. [Figure 8] FIG. 8 is an example of the crystal orientation distribution of a sample in the first embodiment. [Figure 9] FIG. 9 is an example of the crystal orientation distribution of a sample in the first embodiment. [Figure 10] FIG. 10 shows an example of the distribution of non-uniform strain in a sample in the second embodiment. [Figure 11] FIG. 11 shows an example of the crystallite size distribution of a sample in the second embodiment. [Figure 12] FIG. 12 is a graph summarizing the relationship between a plurality of peak widths and integral values ​​corresponding to each index in the second embodiment, and the non-uniform distortion and crystallite size. [Figure 13] FIG. 13 is a diagram showing the relationship between the measurement position on the sample and time in the conventional measurement method according to the second embodiment. [Figure 14]FIG. 14 is a diagram showing the relationship between the measurement position on the sample and time in the novel measurement method of the present application in the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] [Overview of the embodiment of the present disclosure]

[0009] First, an overview of the embodiments of the present disclosure will be described. In the crystallographic description in this specification, an individual orientation is represented by [], a collective orientation by <>, an individual plane by (), and a collective plane by {}. A negative index in crystallography is usually represented by placing a "-" (bar) above the number, but in this specification, a negative index in crystallography is represented by placing a negative sign before the number.

[0010] (1) The analytical method disclosed herein includes a first step of positioning a measurement surface of a sample in a predetermined direction corresponding to a predetermined surface index; a second step of irradiating the measurement surface with X-rays and obtaining the diffraction intensity of the X-rays from the measurement surface with a detector; a third step of determining an in-plane distribution of the diffraction intensity by repeating the second step while moving the sample two-dimensionally in a plane parallel to the measurement surface; and a fourth step of calculating a normalized distribution from the in-plane distribution using theoretical values ​​based on the predetermined direction. The specified directions are a plurality of directions corresponding to a plurality of plane indices, and the first to fourth steps are repeated for each of the plurality of directions to calculate a plurality of the normalized distributions, and a crystal orientation distribution of the measurement target surface can be obtained from the plurality of normalized distributions by a first calculation.

[0011] According to the above method, the two-dimensional crystal structure distribution of the surface of the sample to be measured can be clarified by X-ray diffraction.

[0012] (2) Furthermore, a second calculation may be performed to obtain either the distribution of non-uniform strain on the measurement surface or the distribution of crystallite sizes, or both, from the X-ray profile data of the multiple normalized distributions. In addition to the crystal orientation distribution, more detailed crystal structure distribution can be measured.

[0013] (3) The number of the multiple plane indices may be 3 or more. When the number of indices is 3 or more, the crystal orientation distribution can be measured more accurately.

[0014] (4) The X-rays may be X-rays obtained by synchrotron radiation, because the use of synchrotron radiation makes it possible to measure the crystal orientation distribution in a short period of time.

[0015] (5) The detector may be a one-dimensional detector or a two-dimensional detector, because the use of a one-dimensional detector or a two-dimensional detector makes it possible to measure the crystal orientation distribution in a short period of time.

[0016] (6) At least two of the plurality of plane indices may include (111), (200), and (220) when the crystal structure of the sample is a face-centered cubic lattice structure, (110), (200), and (222) when the crystal structure of the sample is a body-centered cubic lattice structure, and (1-100), (11-20), and (0002) when the crystal structure of the sample is a hexagonal close-packed structure. This is because the crystal orientation distribution can be measured with high accuracy.

[0017] (7) The maximum width of the measurement target surface can be 5 mm or more. The maximum width of the measurement target surface is the widest point of the measurement target surface. In the case of a circle, it is equivalent to the diameter. In the case of a rectangle, it may be the diagonal. In the case of an irregular shape, it is the longest part of the shape. The maximum width of the measurement target surface that can actually be measured is limited by the movable range of the movable stage 21, but in the case of this method, the movable range of the movable stage can be made sufficiently wide. If the movable range of the movable stage 21 is, for example, 100 mm, it is possible to measure the crystal orientation distribution even if the maximum width of the measurement target surface 12 is 100 mm. In the case of EBSD, measurements require the creation of a smooth surface by electrolytic polishing or ion etching, but it is difficult to process large areas using these methods, with the limit being around 5 mm or 10 mm.

[0018] (8) In the third step, the sample may be moved continuously in a plane parallel to the measurement target surface without stopping, because this allows the crystal orientation distribution to be measured in a short period of time.

[0019] [Details of the embodiment of the present disclosure] Next, the details of the embodiments of the present disclosure will be described. In the following description, the same or corresponding elements are denoted by the same reference numerals, and the same description will not be repeated. In addition to the details of the embodiments, examples will also be described.

[0020] (First embodiment) A method for analyzing a sample in the first embodiment will be described below, along with examples.

[0021] FIG. 1 is a diagram showing the configuration of an apparatus for carrying out the analysis method in this embodiment. The positional relationship between the sample, the X-rays, the detector, and the like will be described with reference to FIG. 1. As shown in FIG. 1, the sample 11 is placed on a movable stage 21. The X-rays 1 are irradiated to the measurement target surface 12 of the sample 11 from a predetermined direction D. The angle between the predetermined direction D and the crystal plane of the sample 11 defined by a predetermined plane index F is θ. The X-rays 2 diffracted from the measurement target surface 12 of the sample 11 is detected using a detector 3. The angle between the predetermined direction D and the diffracted X-rays 2 is 2θ. The angle θ between the crystal plane of the sample 11 defined by a predetermined plane index F and the X-rays 1 is determined by the Bragg formula based on the material and crystal structure of the sample 11, the predetermined plane index F, and the wavelength of the X-rays 1. Similarly, 2θ, which is the angle of the diffracted X-rays 2, is determined. The intensity of the X-rays detected by the detector 3 is sent to a calculation device 4 as X-ray intensity data. The calculation device 4 performs calculations on the X-ray intensity data to calculate the crystal orientation and the like.

[0022] FIG. 2 is a flow chart that shows an outline of a method for analyzing a sample in this embodiment. The method for analyzing a sample 11 in this embodiment includes a first step (S001) to a fourth step (S004) and a first calculation step. The first step (S001) is a step of arranging the measurement target surface 12 of the sample 11 in a predetermined direction D corresponding to a predetermined surface index F. The second step (S002) is a step of irradiating the measurement target surface with X-rays and obtaining the diffraction intensity of the X-rays from the measurement target surface by a detector. The third step (S003) is a step of obtaining an in-plane distribution of the diffraction intensity by repeating the second step (S002) while moving the sample two-dimensionally in a plane parallel to the measurement target surface. The fourth step (S004) is a step of calculating a normalized distribution from the in-plane distribution using a theoretical value based on the predetermined direction D.

[0023] Step (S005) is a step of judging whether normalized distributions for a plurality of directions corresponding to a plurality of plane indices have been obtained. If all the required normalized distributions have not been obtained, the judgment in step (S005) is No, and the process is repeated from the first step (S001). That is, a different index is selected as the predetermined plane index F, and the first step is performed in which the measurement target surface 12 of the sample 11 is arranged so as to be in the predetermined direction D corresponding to the different predetermined plane index F, and then the second step, the third step, and the fourth step are performed. If all the required normalized distributions have been obtained, the judgment in step (S005) is Yes, and the process proceeds to the next step (S006). In step (S006), the crystal orientation distribution of the measurement target surface is obtained from the plurality of normalized distributions obtained by the above steps by the first calculation.

[0024] Below, each process will be described along the flow chart of FIG. 2 with reference to FIG. 1 and FIG. 3 to FIG.

[0025] The first step S001 is a step of placing the measurement target surface 12 of the sample 11 in a predetermined direction D corresponding to a predetermined plane index F. Here, the "index" refers to the Miller indices that represent the crystal orientation, and the "predetermined plane index" refers to the crystal plane specified by the Miller indices. The "predetermined direction corresponding to the predetermined plane index" refers to the direction of the X-ray 1 when X-ray diffraction is obtained by irradiating this crystal plane with X-rays.

[0026] The second step (S002) is a step of irradiating the measurement target surface 12 with X-rays 1 and obtaining the diffraction intensity of the X-rays 1 from the measurement target surface 12 by the detector 3.

[0027] The positional relationship between the sample 11, the X-ray 1, the detector 3, etc. in this embodiment will be described with reference to Figures 1 and 3. Figure 3 is a schematic diagram showing the configuration of the sample 11 in the first embodiment. In Figure 3, the sample 11 is depicted as having a disk shape, but is not limited to this.

[0028] First, the configuration of the sample 11 in the first embodiment will be described. As shown in Fig. 3, the sample 11 has a measurement target surface 12. The material of the sample 11 may be a metal such as aluminum, iron, steel, copper, nickel, magnesium, titanium, etc. The shape of the sample 11 is not limited as long as the sample 11 has the measurement target surface 12. The shape of the sample 11 may be, for example, a disk shape as shown in Fig. 3. The shape of the sample 11 may be, for example, a rectangle.

[0029] In the following description of the embodiment, a disk-shaped sample obtained by slicing a cylindrical aluminum wire rod was used as the sample 11, and the in-plane distribution of the crystal structure of a cross section of the aluminum material with a diameter of 10 mmφ was analyzed.

[0030] The measurement target surface 12 of the sample 11 is a plane. The distribution of the crystal structure in the plane of the sample 11 can be obtained by moving the sample 11 two-dimensionally in the plane by the movable stage 21. The surface of the measurement target surface 12 of the sample 11 may be in a state after mechanical polishing. For example, the surface may be in a state after polishing with waterproof paper of No. 2000. The surface roughness Ra may be, for example, about 0.2 μm. This is because the in-plane distribution of the crystal structure can be measured by using X-ray diffraction. In addition, in the case of cross-sectional observation by EBSD, if the sample surface is mechanically polished, it may be difficult to measure due to the influence of an altered layer generated on the surface during processing, so electrolytic polishing or ion etching must be added. This is not necessary in the X-ray diffraction according to the present disclosure, and the sample can be prepared only by mechanical polishing. The maximum width of the measurement target surface 12 of the sample 11 can be 1 mm or more, or 5 mm or more. It can also be 100 mm or more. This is because even if the size is 1 mm or more, the distribution of the crystal structure can be obtained by using X-rays with a width of, for example, 0.05 mm. The crystal structure of the sample 11 is preferably polycrystalline, and the crystal grain size is preferably 0.1 μm to 20 μm.

[0031] In order to measure the dependence of the intensity of the diffracted X-rays 2 on θ, as in the case of a general X-ray diffraction measurement, the X-rays 1 can be fixed, and the sample 11 can be moved in a direction rotating in the θ direction, while the detector 3 is moved in the 2θ direction. In addition, a one-dimensional detector or a two-dimensional detector can be used as the detector 3. By using a one-dimensional detector or a two-dimensional detector as the detector 3, the angle dependence of the intensity of the diffracted X-rays 2 can also be measured while keeping the positions of θ and the detector 3 fixed. Since the angle dependence of the intensity of the diffracted X-rays 2 can be measured without moving the positions of θ and the detector 3, that is, without moving the sample 11 and the detector 3, the measurement can be performed in a short time. In addition, in the two-dimensional detector, for a certain value of 2θ, a part corresponding to that 2θ is detected in an arc shape on the detection part of the two-dimensional detector. Since a large amount of measurement data can be obtained by using a two-dimensional detector, data with a good S / N ratio can be measured in an even shorter time.

[0032] In the embodiment, a detector with a model number of PILATUS 100K manufactured by Dectris was used as the two-dimensional detector for the detector 3. The distance from the measurement target surface 12 of the sample 11 to the two-dimensional detector was set at a distance of 0.512 m. The 2θ direction of the sample was set to a direction perpendicular to the longitudinal direction of the two-dimensional detector. The time required to measure one point on the measurement target surface 12 of the sample 11 was about 0.2 seconds. The irradiation width of the X-rays can be adjusted according to the required resolution. For example, the irradiation width of the X-rays can be set to 0.05 mm to 1 mm.

[0033] The X-ray 1 used in this analysis method can be X-ray obtained by synchrotron radiation. As a specific example of X-ray obtained by synchrotron radiation, for example, BL16 at the synchrotron radiation facility SAGA-LS can be used. For example, this beamline is monochromatized with a double crystal monochromator using silicon 111 plane, and X-ray diffraction experiments can be performed with a wavelength of λ=0.0413 to 0.155 nm. The irradiation width of the X-ray can be adjusted according to the intensity, resolution, etc. For example, the irradiation width of the X-ray is 0.05 mm to 1 mm. For example, the beam size of the X-ray in the embodiment is 0.5 mm square. Since synchrotron radiation is monochromatic light with high directivity and high brightness, it is possible to perform high-precision measurements in a short time by using synchrotron radiation.

[0034] For the X-ray source, an X-ray tube having a copper target, for example, an X-ray diffraction measurement device manufactured by Rigaku with the model number SmartLab, can be used. Although the measurement time is long, the measurement can be easily performed in a laboratory, etc.

[0035] In the examples, the synchrotron radiation was used as BL16 at the SAGA-LS synchrotron radiation facility. In this beamline, X-rays with a wavelength of λ=0.0919 nm were used. The slit width was 0.5 mm square.

[0036] In the case of the (111) plane of the face-centered cubic lattice structure of aluminum, the specified angles used were θ = 11.3 degrees and 2θ = 22.6 degrees. The values ​​of θ and 2θ for the other plane indices were those shown in Table 1 below.

[0037] [Table 1]

[0038] Next, in a third step (S003), the second step is repeated while moving the sample 11 two-dimensionally in a plane parallel to the measurement target surface 12, thereby obtaining an in-plane distribution of the diffraction intensity. The movable stage 21 has a flat stage surface 22, and the stage can be moved two-dimensionally in a plane parallel to the stage surface 22. The sample 11 is mounted on the stage surface 22 of the movable stage 21. The sample 11 is arranged so that the stage surface 22 of the movable stage 21 and the measurement target surface 12 of the sample 11 are parallel planes. The movable stage 21 is moved two-dimensionally to move the sample 11. When the sample is moved, the X-ray 1 is not moved. The movable stage 21 is moved to move the sample 11, and the X-ray 1 is irradiated onto a part of the measurement target surface 12, and the diffraction intensity of the X-ray 2 diffracted from the measurement target surface 12 is obtained by the detector 3.

[0039] FIG. 4 is a schematic diagram showing irradiation of X-ray 1 to measurement area A on measurement target surface 12 on sample 11. The center of X-ray 1 is measurement point a1. Furthermore, the movable stage 21 is moved to move the center of X-ray 1 from measurement point a1 to measurement point b1, and the irradiation of X-ray 1 is moved from measurement area A to measurement area B, and the diffraction intensity of X-ray 2 diffracted from measurement area B is obtained by detector 3. The above series of operations is repeated. As shown in FIG. 4, the area to be analyzed within the measurement target surface 12 is comprehensively measured, and the in-plane distribution of the diffraction intensity of the measurement target surface 12 is obtained. It is possible to repeat the process until the entire surface of the measurement target surface 12 can be measured.

[0040] Fig. 5 shows the results of measuring the in-plane distribution of diffraction intensity in the third step (S003) when the predetermined plane index F of the face-centered cubic lattice structure of aluminum is (200). In Fig. 5, the measurement positions on the measurement target surface 12 are indicated by the X and Y positions in the figure. The shading corresponds to the integral value of the fitting curve of the X-ray profile data of each measurement region of the measurement target surface 12 of the sample 11. Here, the fitting function used for fitting can be a general one such as a Gauss function or a Lorentz function. Each cell is shaded according to the count number, as shown by the bar on the right of Figure 5. In actual analysis results, the count number of each cell can be displayed in a continuously changing color from black (0: zero) - blue - green - orange - red - white (100) to make it easier to understand visually. In this application, the following explanation will be given using figures in which the colors have been converted into grayscale shading. Alternatively, in addition to colors and shading, it may be displayed using contour lines that connect areas with the same intensity ratio.

[0041] In addition, in a position where the measurement target surface 12 of the sample does not exist, the intensity of X-ray diffraction becomes close to zero, and inappropriate values ​​may occur in the data processing to be performed later. For example, as shown in FIG. 5, when a measurement is performed in a rectangular region, since the measurement target surface 12 of the sample 11 is circular, the intensity of X-ray diffraction in the measurement region Z located at the edge of the sample 11 or outside thereof becomes close to zero. Therefore, it is possible to perform the exclusion process. FIG. 6 shows an example of a region where the exclusion process is performed. In FIG. 6, the X position and Y position in the figure indicate the position on the measurement target surface 12, and the black part is the region where data is to be deleted. In other words, when the measurement target surface 12 of the sample 11 is circular, it is also possible to set the region excluding the circular region of the measurement target surface 12 as shown in FIG. 6 as a data exclusion region 32, and delete the data of that region.

[0042] Next, in the fourth step (S004), a normalized distribution is calculated from the in-plane distribution using a theoretical value based on a predetermined direction D. The theoretical value based on the predetermined direction D is, for example, when the plane index F is (200), the theoretical value of the diffraction intensity at the plane index of (200) obtained from a completely unoriented random crystal, for example, a crystal in a powder state. This theoretical value can be obtained, for example, from a database such as the PDF (Powder Diffraction File) published by the ICDD (International Centre for Diffraction Data). The normalized distribution is obtained by dividing the diffraction intensity of each measurement region of the in-plane distribution of the diffraction intensity by the theoretical value of the peak intensity of the diffraction intensity of the X-ray diffraction. Note that the peak intensity is not obtained from the peak intensity of the raw data, but rather the maximum value or integral value of the fitting curve obtained by fitting the X-ray profile data of each measurement region can be used. The fitting function used for fitting can be a general one such as a Gauss function or a Lorentz function.

[0043] Fig. 7 shows the measurement results of the normalized distribution when the predetermined plane index F of the face-centered cubic lattice structure of aluminum is (200). The X and Y positions in the figure indicate the measurement positions on the measurement target surface 12, and the shading is the normalized distribution of each measurement region of the measurement target surface 12 of the sample 11. The normalized distribution in Fig. 7 had a value of approximately 60 to 100. By processing this value in step S006, the value of the degree of crystal orientation can be obtained.

[0044] Next, in step (S005), it is determined whether normalized distributions for multiple directions corresponding to multiple plane indices have been obtained. If the answer is Yes, proceed to the next step (S006). If the answer is No, return to the first step (S001) and continue until normalized distributions for multiple directions corresponding to multiple plane indices are obtained. For example, if it is intended to calculate multiple plane indices (200), (111), and (220), but only (200) is obtained, repeat the process until a normalized distribution of (111) and (220) is obtained. When repeating, it is preferable to repeat the measurement while keeping the sample 11 placed on the movable stage 21 in place without removing it from the movable stage 21, etc. This is because calculations will be performed in the subsequent steps.

[0045] Next, in step (S006), a crystal orientation distribution of the measurement target surface 12 is obtained from the multiple normalized distributions by a first calculation. For the multiple normalized distributions, the first calculation is as follows. The first calculation is a calculation for adjusting the absolute value of the crystal orientation distribution at the plane index F, and the normalized distribution at the plane index F is the sum of multiple normalized distributions corresponding to each plane index F. For example, when (200), (111), and (220) are used as the multiple plane indexes F, the crystal orientation distribution of (200) can be obtained for each measurement region by calculating the following formula 1. Crystal orientation distribution of (200) = normalized distribution of (200) / {normalized distribution of (200) + normalized distribution of (111) + normalized distribution of (220)} (Formula 1) In addition, if the multiple plane indices include substantially the same plane indices, they must be removed. For example, if (200), (111), (220), and (440) are used as the multiple plane indices F, the crystal orientation distribution of (200) can be calculated for each measurement area by the following formula 2. Crystal orientation distribution of (200) = normalized distribution of (200) / {normalized distribution of (200) + normalized distribution of (111) + normalized distribution of (220)} (Equation 2) Here, the crystal orientation distribution of each index should be between 0 and 100, and it is desirable to exclude points that give values ​​outside these ranges.

[0046] Figure 8 shows the measurement results of the crystal orientation distribution within (111), (200), and (220) when the specified plane index F of the face-centered cubic lattice structure of aluminum is (200). In Figure 8, the X and Y positions in the figure indicate the measurement positions on the measurement target surface 12, and the shading indicates the degree of crystal orientation in each measurement region of the measurement target surface 12 of the sample 11. In this sample 11, the crystal orientation with respect to (200) was low at about 30% near the center, rose to nearly 50% toward the outside of the sample, and tended to decrease again at the outermost periphery, with the in-plane distribution decreasing to approximately 30% at the outer periphery.

[0047] Figure 9 shows the measurement results of the crystal orientation distribution in (111), (200), and (220) when the face index F of the face-centered cubic lattice structure of aluminum is (111). Figure 9 shows contour lines connecting parts with the same crystal orientation distribution value. The crystal orientation for (200) shown in Figure 9 is high at about 70% near the center, and is an in-plane distribution that decreases toward the outside of the sample.

[0048] Second embodiment As the second embodiment, another method for analyzing the sample 11 will be described.

[0049] As a second embodiment, another analysis method of sample 11 performs the same steps as in the first embodiment from the first step (S001) to step (S005). Normalized distributions for multiple directions corresponding to multiple plane indices are prepared. The normalized distribution includes X-ray profile data of each measurement region of the measurement target surface 12 of sample 11 in addition to the maximum diffraction intensity of each measurement region. By performing the second calculation shown below on multiple normalized distributions, it is possible to obtain a distribution of non-uniform strain and a distribution of crystallite sizes.

[0050] The second calculation is a calculation that performs the following steps (1) to (3). (1) First, peak fitting is performed on the X-ray profile data of each measurement region for each normalized distribution corresponding to each index. General fitting functions such as Gaussian and Lorentz functions can be used. For each fitting, the peak width and peak position are obtained. (2) From the multiple peak widths and integral values ​​corresponding to each index, the non-uniform distortion and crystallite size of each measurement area of ​​the measurement target surface 12 of the sample 11 are determined by the Williamson-Hall method. (3) Specifically, the non-uniform distortion and crystallite size of each measurement region are calculated from the half-width or integral width for each measurement region of the measurement target surface 12 on the sample 11 according to the following formula 3. (β×cosθ) / λ=C×ε×(sinθ) / λ+K / D (Formula 3) Here, β is the peak width, and the half-width or integral width (radian) is used. θ is the diffraction angle (peak position) / 2 (degrees). ε is the non-uniform distortion. C is a conversion coefficient. However, in the above formula 3, C is set to 4. K is the Scherrer coefficient. However, in the above formula 3, K is set to 1. D is the crystallite size (nm). Note that the conversion coefficient C may be set to 1, and the Scherrer coefficient K may be set to 0.9, etc.

[0051] 12 is a graph summarizing the relationship between multiple peak widths and peak positions corresponding to each index (i.e., each θ) and the inhomogeneous distortion and crystallite size. The X-axis of FIG. 12 is Formula 4, and the Y-axis is Formula 5. (sinθ) / λ (Equation 4) β × (cosθ) / λ (Formula 5)

[0052] The positions of the x marks in Fig. 12 are determined from the multiple peak widths and peak positions corresponding to each index (i.e., each θ). These x marks are converted into a linear line by the least squares method. The crystallite size is determined from the Y-intercept of Fig. 12. The non-uniform strain is determined from the slope of Fig. 12. In this way, by using Fig. 12 and calculating the above formula, the non-uniform strain and crystallite size of each measurement area of ​​the measurement target surface 12 on each sample 11 can be determined. By performing this for each measurement area of ​​multiple normalized distributions, it is possible to obtain the distribution of non-uniform strain or the distribution of crystallite size, or both.

[0053] Figure 10 shows the measurement results of the distribution of non-uniform strain. In Figure 10, the X and Y positions indicate the measurement positions on the measurement target surface 12, and the shading indicates the value of non-uniform strain in each measurement region of the measurement target surface 12 of the sample 11. The unit is percent.

[0054] Figure 11 shows the results of measuring the distribution of crystallite sizes. In Figure 11, the X and Y positions indicate the measurement positions on the measurement surface, and the shading indicates the crystallite size values ​​of each measurement region on the measurement surface 12 of the sample 11. The unit is nm.

[0055] The number of the plane indices can be three or more. In order to obtain the crystal orientation distribution, it is necessary to perform the first calculation on a normalized distribution consisting of at least three plane indices. Furthermore, in order to obtain the distribution of non-uniform strain or the distribution of crystallite size, in addition to the three plane indices, one more index of plane orientation equivalent to any one of them is required. If only non-uniform strain and crystallite size are required, it can be obtained with two. The more the number of plane indices, the more accurately the Y-intercept and the slope in FIG. 12 can be obtained, and as a result, the non-uniform strain and the crystallite size can be obtained accurately.

[0056] In the case of face-centered cubic lattice structures such as copper and aluminum, examples of the three indices include (111), (200), and (220), and the additional index can be selected, for example, as (222). In the case of body-centered cubic lattice structures such as iron and steel, examples of the three indices include (110), (200), and (222), and the additional index can be selected, for example, as (220). In the case of hexagonal close-packed structures such as titanium and magnesium, examples of the three indices include (1-100), (11-20), and (0002), and the additional index can be selected, for example, as (2-200) or (0004). By selecting in this way, it is possible to obtain the crystal orientation distribution of the orientation distribution of three independent directions in space, and it is also possible to calculate the inhomogeneous strain and crystallite size from two indices having the same direction.

[0057] When measuring the crystal orientation distribution of the cross section of a 10 mmφ aluminum wire by this analysis method, the sample 11 used in this analysis method was prepared as follows. First, the 10 mmφ aluminum wire was cut to a length of about 8 mm using a precision cutting machine, and the surface was finished using, for example, waterproof paper of No. 2000. It is preferable that the polished surface of the sample 11, i.e., the measurement target surface 12, and the bottom surface of the sample 11 are parallel. Using such a sample, the crystal orientation distribution can be obtained using X-rays. On the other hand, the EBSD method cannot measure a sample having such a mechanically polished surface.

[0058] In a third step, the sample 11 can be moved continuously without stopping in a plane parallel to the surface 12 to be measured. FIG. 13 is a diagram showing the relationship between the measurement position of the sample and time in the conventional measurement method. The horizontal axis represents time. The vertical axis represents the measurement position in the case where the measurement position where the X-ray 1 is irradiated on the measurement target surface 12 of the sample 11 moves linearly from the measurement area A to the measurement area C in FIG. 4. The sample 11 performs a series of operations of acceleration, movement, deceleration, and stopping toward the measurement point a1, and then the X-ray profile data of the measurement area A centered on the measurement point a1, that is, the angular dependence of the X-ray intensity of the diffracted X-ray 2, is measured. After the measurement of the measurement area A is completed, the sample 11 performs a series of operations of acceleration, movement, deceleration, and stopping toward the measurement point b1, and stops at the measurement point b1. Then, the angular dependence of the diffracted X-ray 2 is measured in the measurement area B centered on the measurement point b1. By repeating this, the entire surface of the sample is measured.

[0059] On the other hand, FIG. 14 is a diagram showing the relationship between the measurement position of the sample and time in the novel measurement method of the present application. The vertical axis represents the measurement position on the measurement target surface 12 of the sample 11 where the X-ray 1 is irradiated. The sample 11 is moved without stopping at the measurement points a1, b1, and c1. The sample 11 is constantly irradiated with X-rays. Diffracted X-rays 2 can be obtained even while the sample 11 passes through the measurement area A. By measuring the angular dependence of the diffracted X-rays 2, the analysis can be carried out without stopping the sample. The X-ray diffraction from the measurement area A can be used as the data of the measurement point a1, and similarly, the X-ray diffraction from the measurement area B can be used as the data of the measurement point b1. By adopting this method, a series of operations such as acceleration, movement, deceleration, and stopping for each measurement point is not required, so the measurement time can be shortened. It is more preferable that the detector is a one-dimensional detector or a two-dimensional detector, since the measurement of the angular dependence can be performed in a short time. For example, when using conventional measurement methods, it takes one second for acceleration, movement, deceleration, and stopping for each measurement point, and 0.2 seconds for X-ray diffraction measurement, totaling 49 minutes. However, by using this method, this time can be reduced by about half, to about 26 minutes.

[0060] The embodiments and examples disclosed herein are illustrative in all respects and should not be considered as limiting. The scope of the present invention is defined by the claims rather than the above-described embodiments, and is intended to include all modifications within the scope of the claims and the meaning equivalent thereto. [Explanation of symbols]

[0061] 1 X-ray 2 Diffracted X-rays 3. Detector 11 Sample 12 Measurement surface 21 Movable stage 22 Stage Surface A measurement area B Measurement area C measurement area Z measurement area a1 Measurement point b1 Measurement point c1 measurement point L Length θ incident angle 2θ diffraction angle Ra surface roughness D Prescribed direction F given surface index

Claims

1. a first step of positioning a surface to be measured of a sample in a predetermined orientation corresponding to a predetermined surface index; a second step of irradiating the surface to be measured with X-rays and obtaining the diffraction intensity of the X-rays from the surface to be measured with a detector; a third step of repeating the second step for each of a plurality of measurement regions on the measurement target surface while moving the sample two-dimensionally in a plane parallel to the measurement target surface, thereby obtaining an in-plane distribution of the diffraction intensity; and a fourth step of calculating a normalized distribution from the in-plane distribution by using a theoretical value based on the predetermined direction, the normalized distribution includes X-ray profile data of each of the plurality of measurement regions; the predetermined direction is a plurality of directions corresponding to a plurality of plane indices, and a plurality of the normalized distributions are calculated by repeating the first step to the fourth step for each of the plurality of directions; A first calculation is performed to obtain a crystal orientation distribution of the measurement target surface from the plurality of normalized distributions; Furthermore, by repeating the third calculation for each of the plurality of measurement regions by the second calculation, at least one of a distribution of non-uniform strain and a distribution of crystallite sizes on the measurement target surface is obtained; The third calculation includes performing peak fitting on the X-ray profile data in each of the multiple directions to obtain a peak width, and obtaining at least one of the non-uniform strain and the crystallite size from the peak width in each of the multiple directions. Analysis method.

2. The third calculation obtains at least one of the inhomogeneous strain and the crystallite size from the peak widths in each of the multiple directions by the Williamson-Hall method. The method of analysis according to claim 1.

3. The number of the plurality of plane indices is 3 or more. The analytical method according to claim 1 or 2.

4. The X-rays are X-rays obtained by synchrotron radiation. The analysis method according to any one of claims 1 to 3.

5. The detector is a one-dimensional detector or a two-dimensional detector. The method of analysis according to any one of claims 1 to 4.

6. The analysis method according to claim 1 , wherein the plurality of plane indices include at least two of the three indices shown in the following (a), (b), and (c): (a) When the crystal structure of the sample is a face-centered cubic lattice structure, (111), (200), or (220) (b) When the crystal structure of the sample is a body-centered cubic lattice structure, (110), (200), or (222) (c) When the crystal structure of the sample is a hexagonal close-packed structure, (1-100), (11-20), (0002)

7. The maximum width of the measurement surface is 5 mm or more. The method of analysis according to any one of claims 1 to 6.

8. The third step is a step of moving the sample two-dimensionally and continuously without stopping within a plane parallel to the measurement target surface. The method of analysis according to any one of claims 1 to 7.

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