JP5668561B2 - Grain orientation analysis method and crystal orientation analyzer - Google Patents

Description

  The present invention relates to a crystal grain orientation analysis method and a crystal grain orientation analysis apparatus, and, for example, relates to a crystal grain orientation analysis method and a crystal grain orientation analysis apparatus for analyzing a crystalline domain in an electron microscope image.

  Various methods for measuring the crystal orientation of a polycrystalline sample or the like for each crystalline domain have been proposed. For example, a method of discriminating crystal orientation using a diffraction pattern of a Kossel pattern obtained by an X-ray diffraction method is known (for example, Patent Document 1). Also known is a method of discriminating crystal orientation using a diffraction pattern of Kikuchi pattern obtained by electron beam diffraction. For example, an EBSP (Electron Back Scattering Pattern) method for analyzing a Kikuchi pattern formed by backscattered electrons in a scanning electron microscope is known (for example, Non-Patent Document 1). A method using a multivariate curve decomposition method for an acquired Raman spectrum with respect to two-dimensional position information is known (for example, Non-Patent Document 2). By this method, the Raman spectrum can be classified.

Japanese Patent Laid-Open No. 62-119445 Kobelco Research Institute Co., Ltd. Kobel Niks vol. 9, APR (2000) pp.10-11. Analytica Chimica Acta, 500 (2003) 195.

  When the crystalline domain forming a polycrystal is miniaturized to a nano size, a nano size spatial resolution is required. Spatial resolution is insufficient in measurement using a general-purpose X-ray apparatus. A method using an electron microscope is effective for analysis of nano-sized domains. However, in EBSP, in addition to high image noise and a complicated azimuth determination algorithm, the spatial resolution is several tens of nanometers, which is one digit less than the required spatial resolution. Although the transmission electron microscope has sufficient spatial resolution, in order to specify the domain, a dark field image is measured with respect to the appearing diffraction spot. Neither method can automatically analyze the crystalline domain.

  The crystal grain orientation analysis method and the crystal grain orientation analyzer are intended to automatically analyze a crystalline domain.

For example, a Fourier image is generated by performing Fourier transform for each of a plurality of regions included in a polycrystalline electron microscope image having a plurality of crystalline domains, and the intensity with respect to the angle of the Fourier image is calculated, and based on the intensity Then, the grain orientation analysis method is used, wherein the region in the electron microscope image is classified into a crystalline domain having a corresponding crystal grain orientation among the plurality of crystalline domains .

For example, a Fourier image is generated by performing Fourier transform on each of a plurality of regions included in the electron microscope image and an input unit to which a polycrystalline electron microscope image having a plurality of crystalline domains is input, and the Fourier image And an analysis unit that classifies the region in the electron microscope image into a crystalline domain having a corresponding crystal grain orientation out of the plurality of crystalline domains based on the intensity. And a crystal grain orientation analyzer.

  According to the crystal grain orientation analysis method and the crystal grain orientation analyzer, the crystalline domain can be automatically analyzed.

FIG. 1 is a schematic diagram of a transmission electron microscope. FIG. 2 is a block diagram of a computer that functions as the crystal grain orientation analyzer according to the first embodiment. FIG. 3 is a functional block diagram of the crystal grain orientation analyzer according to the first embodiment. FIG. 4 is a flowchart illustrating the crystal grain orientation analysis method according to the first embodiment. FIG. 5A to FIG. 5C are schematic diagrams (part 1) illustrating data processing in the first embodiment. FIG. 6A and FIG. 6B are schematic diagrams (part 2) illustrating data processing in the first embodiment. FIG. 7A to FIG. 7C are diagrams illustrating examples of histogram data generated in the first embodiment. FIG. 8 is a flowchart showing processing performed by the multivariate analysis unit. FIG. 9 is a diagram in which two-dimensional position coordinates are arranged in one dimension in the multidimensional matrix data of FIG. FIG. 10A and FIG. 10B are examples of a two-dimensional image having a density for each main component. FIG. 11 is a diagram in which the region 62 in FIG. 10A and the region 64 in FIG. 10B are superimposed on the electron microscope image. FIG. 12 is an electron microscopic image of Example 2. FIG. 13 is an image showing an example of the second image of the second embodiment. FIG. 14 is a diagram illustrating a two-dimensional image of the concentration distribution of the main component of the second embodiment. FIG. 15 is a diagram showing the classified domains in the electron microscope image of Example 2.

  Embodiments will be described with reference to the drawings.

  FIG. 1 is a schematic diagram of a transmission electron microscope. As shown in FIG. 1, the transmission electron microscope 20 includes a chamber 21, an electron gun 22, a focusing lens 23, an objective lens 24, a projection lens 26, and a detector 27. The electron beam 28 emitted from the electron gun 22 is focused on the sample 25 via the focusing lens 23 and the objective lens 24. The electron beam 28 transmitted through the sample 25 reaches the detector 27 via the projection lens 26. An electron microscope image is generated by the detector 27. The electron microscope image is output to the computer 10.

  As the transmission electron microscope 20, for example, a high resolution transmission electron microscope (HRTEM) or a high resolution scanning transmission electron microscope (STEM) can be used. The transmission electron microscope is preferably a high-resolution electron microscope capable of obtaining an atomic resolution image.

  FIG. 2 is a block diagram of a computer that functions as the crystal grain orientation analyzer according to the first embodiment. The computer 10 includes a CPU (Central Processing Unit) 11, a display device 12, an input device 13, an output device 14, a main storage device 15, a hard disk drive (HDD) 16, a storage medium drive 17, a communication interface 18, and an internal bus 19. I have. The display device 12 includes a display panel such as a liquid crystal panel, for example, and displays processing results and the like. The input device 13 is, for example, a keyboard, a mouse, and a touch panel, and inputs processing data and the like. The output device 14 is a printer, for example, and outputs a processing result or the like. The main storage device 15 is a volatile memory such as a DRAM (Dynamic Random Access Memory), for example, and stores data being processed. The HDD 16 stores, for example, electron microscope image data and data during or after processing. The storage medium drive 17 is used when a program stored in the storage medium 40 is installed. Alternatively, the processed data is stored in the storage medium 40. The communication interface 18 acquires electron microscope image data from the electron microscope 20. The internal bus 19 connects each device in the computer 10.

  A portable storage medium can be used as the storage medium 40 that can be read by the computer 10 storing the program. As the portable storage medium, for example, a CD-ROM (Compact Disc Read Only Memory) disc, a DVD (Digital Video Disc) disc, a Blu-ray disc, or a USB (Universal Serial Bus) memory can be used. As the storage medium 40, a flash memory or an HDD may be used.

  FIG. 3 is a functional block diagram of the crystal grain orientation analyzer according to the first embodiment. The computer 10 functions as shown in FIG. 3 in cooperation with each member shown in FIG. 2 and software. An electron microscope image is input from the electron microscope 20 to the input unit 30. The calculation unit 32 generates a Fourier image by performing Fourier transform on each of the plurality of regions of the electron microscope image, and calculates the intensity with respect to the angle of the Fourier image. The analysis unit 38 analyzes the crystalline domain in the electron microscope image based on the intensity of the Fourier image. The analysis unit 38 further includes a multivariate analysis unit 36. The multivariate analysis unit 36 classifies the crystalline domains in the electron microscope image using a multivariate curve decomposition method.

  FIG. 4 is a flowchart illustrating the crystal grain orientation analysis method according to the first embodiment. FIG. 5A to FIG. 6B are schematic diagrams illustrating data processing in the first embodiment. As shown in FIG. 4, the input unit 30 acquires two-dimensional data of the electron microscope image 50 from the electron microscope 20 (step S10). FIG. 5A shows a two-dimensional image of the electron microscope image 50. With reference to Fig.5 (a), the size of X and Y of the electron microscope image 50 is 40 nm x 40 nm, for example, and the image corresponding to the arrangement | sequence of an atom is imaged.

  Next, as shown in FIG. 4, the computing unit 32 cuts out the first image 52 from the electron microscope image 50 (step S12). As illustrated in FIG. 5A, for example, a 3 nm × 3 nm range of the electron microscope image 50 is cut out as the first image 52. For example, the center position coordinate of the first image 52a in the upper left of the electron microscope image 50 is set to (X1, Y1), and the first image 52a is cut out.

  Next, as shown in FIG. 4, the calculating unit 32 calculates a window function (step S14). As shown in FIG. 5B, the first image 52a is multiplied by a window function. Thereby, the first image 54a multiplied by the window function is generated. The window function is used to increase the signal-noise ratio of the image after Fourier transform. Step S14 may not be performed.

  Next, as illustrated in FIG. 4, the calculation unit 32 generates a second image 56 that is a Fourier image by performing a Fourier transform on the first image 54 (step S <b> 16). As shown in FIG. 5C, the second image 56a is obtained by Fourier-transforming the first image 54a multiplied by the window function. The spot 53 appearing in the second image 56a is caused by a specific plane orientation of the crystalline domain. Therefore, the second images 56 included in the same domain have the same pattern. In addition, the second images 56 included in domains having different angles even on the same crystal plane appear as the positions of the spots 53 rotate.

  Next, as illustrated in FIG. 4, the calculation unit 32 generates a distribution of intensity with respect to the angle from the second image 56 (step S <b> 18). As shown in FIG. 6A, the integration of the intensity of the second image 56 included in the range of the constant angle θi (for example, 6 °) around the center 55 of the second image 56a is from −90 ° to 90 °. It calculates | requires by fixed angle (theta) i space | interval. Here, for example, the −Y direction is −90 °, the Y direction is 90 °, and the X direction is 0 °. The constant angle θi can be arbitrarily determined, for example, 1 °. FIG. 6B is a histogram of the intensity with respect to an angle from −90 ° to 90 °. Note that the histogram in FIG. 6B is an example, and is not a histogram created from the second image 56a in FIG. The intensity is increased at an angle of the spot 53 in the second image 56. As described above, a histogram of the intensity with respect to the angle is generated as the intensity distribution with respect to the angle. For example, when the first image 52 is an amorphous region, the strong spot 53 does not appear in the second image 56, and thus no peak appears in the histogram. When the first image 52 is a crystal region, a spot 53 peculiar to the plane orientation appears in the second image 56. Therefore, a peak appears at a specific angle in the histogram.

  Next, as shown in FIG. 4, the calculation unit 32 stores the position coordinates (X1, Y1), the angle, and the intensity distribution of the first image 52a in the main storage device 15 or the HDD 16 (step S20). Next, the CPU 11 determines whether it is the last first image 52 (step S22). In the case of No, the first image 52 is incremented (step S24). Return to step S12. For example, in FIG. 5A, a first image 52b having a position coordinate (X2, Y1) shifted in the X direction by a predetermined dimension (for example, 1 pixel) is set as the next first image 52. Thus, the histogram 58 corresponding to the first image 52 is generated while shifting in the predetermined dimension X direction. After the histogram of the first image 52 at the right end of the electron microscope image 50 is generated, from the first image 52c whose position coordinates (X1, Y2) are shifted from the first image 52a by a predetermined dimension (for example, 1 pixel) in the Y direction. Generate a histogram. In this manner, a plurality of first images 52 are cut out from the entire electron microscope image 50, and a histogram corresponding to the position coordinates of the first image 52 is generated.

  In FIG. 5A, the first image 52d whose lower right position coordinate of the electron microscope image 50 is (Xn, Ym) is cut out and a histogram is generated, and then the CPU 11 determines Yes in step S22 of FIG. . Next, the analysis unit 38 analyzes the crystalline domain (step S26).

  In the first embodiment, the calculation unit 32 cuts out the first images 52 so that the adjacent first images 52 overlap as shown in FIG. 5A, but the adjacent first images 52 do not overlap. The first image 52 may be cut out. However, in order to classify domains with high accuracy, it is preferable that the adjacent first images 52 overlap. Further, the calculation unit 32 may cut out an arbitrary first image 52 from the electron microscope image 50. For example, a region where the atomic arrangement can be observed in the electron microscope image 50 may be cut out as the first image 52. A region in the electron microscope image 50 where the atomic arrangement cannot be observed does not have to be cut out as the first image 52.

  FIG. 7A to FIG. 7C are diagrams illustrating examples of histogram data generated in the first embodiment. As shown in FIG. 7A, a histogram 58 of the intensity with respect to the angle corresponding to the position coordinates of the first image 52 is generated as four-dimensional matrix data. For example, FIG. 7B is a histogram 58 at the position coordinates (X1, Y1) in FIG. FIG. 7C is a histogram 58 at the position coordinates (X2, Y1) of FIG. As described above, the number of histograms 58 corresponding to the number of the first images 52 is stored in the main storage device 15 or the HDD 16 as four-dimensional matrix data.

  In Example 1, a method of classifying domains using a multivariate curve decomposition method will be described. Non-Patent Document 2 describes a method of analyzing a Raman spectrum using a multivariate curve decomposition method for two-dimensional position coordinates.

  FIG. 8 is a flowchart showing processing performed by the multivariate analysis unit. As shown in FIG. 8, the multivariate analysis unit 36 included in the analysis unit 38 extracts one or a plurality of principal components (step S30). Next, the multivariate analysis unit 36 calculates the density distribution of each position coordinate (step S32). The multivariate analysis unit 36 performs domain classification from the density distribution of each position coordinate (step S34). In Example 1, the distribution (for example, histogram) of the data shown in FIG. 7A with respect to the position coordinates of the first image 52 is distributed using the same multivariate curve decomposition method as in Non-Patent Document 2. Perform domain classification.

FIG. 9 is a diagram in which two-dimensional position coordinates are arranged in one dimension in the multidimensional matrix data of FIG. As shown in FIG. 9, the two-dimensional coordinates (X1, Y1),..., (X1, Y2),... (Xn, Ym) are converted into the one-dimensional coordinates 1,. The matrix data D corresponds to the one-dimensional position coordinates and is associated with each histogram data. Here, using the principal component matrix S and the density distribution matrix C, and data D = CS ^T. The principal component is the principal component of the extracted histogram. A density | concentration is a ratio of the main component in each position data. For example, consider a case where a principal component PA corresponding to the domain DA and a principal component PB corresponding to the domain DB are extracted. For example, if the histogram at coordinate 1 is 80% of the principal component PA and 20% of the principal component PB, the histogram at coordinate 1 is represented by the histogram of the principal component PA × 0.8 + the histogram of the principal component PB × 0.2. The

In step S30 of FIG. 8, the multivariate analysis unit 36 extracts one or more principal components from the matrix data D. Next, in step S32, the multivariate analysis unit 36 calculates a density distribution matrix C of each position coordinate. The one-dimensional coordinates in FIG. 9 are returned to the original two-dimensional position coordinates, and a two-dimensional image of the density for each position coordinate is obtained for each principal component.

  FIG. 10A and FIG. 10B are examples of a two-dimensional image having a density for each main component. FIG. 10A is a two-dimensional image 60a of the main component PA. The position coordinates (X, Y) correspond to the position coordinates of the electron microscope image 50 in FIG. A region 62 in FIG. 10A is a region where the concentration of the main component PA is higher than a predetermined value. This area 62 is an area where a histogram of the main component PA can be obtained mainly. Similarly, FIG. 10B is a two-dimensional image 60b of the main component PB. A region 64 in FIG. 10B is a region where the concentration of the main component PB is higher than a predetermined value. This region 64 is a region where a histogram of the main component PB can be obtained mainly.

  FIG. 11 is a diagram in which the region 62 of FIG. 10A and the region 64 of FIG. In step S34 of FIG. 8, as shown in FIG. 11, a region 62 in the electron microscope image 50 is a domain DA from which a histogram of the principal component PA is obtained. A region 64 in the electron microscope image 50 is a domain DB from which a histogram of the main component PB is obtained. In this way, the domains DA and DB in the electron microscope image 50 can be classified.

  According to the first embodiment, a Fourier image (for example, the second image 56) is generated by performing Fourier transform on each of the plurality of regions of the electron microscope image 50 as in steps S12 and S16 of FIG. As in step S18, the intensity with respect to the angle of the second image 56 is calculated. As in step S26, the crystalline domain in the electron microscope image 50 is analyzed based on the intensity. The intensity with respect to the angle of the second image 56 is the same if the first image 52 is in the same domain. Therefore, by analyzing the domain using the angle of the second image 56 that has undergone Fourier transform, it is possible to automatically analyze a crystalline domain such as a polycrystalline sample.

  As a method for analyzing a crystalline domain, for example, a multivariate curve decomposition method can be used as in Example 1. A multivariate analysis method other than the multivariate curve decomposition method may be used.

  Further, as shown in FIGS. 6A and 6B, the intensities of the second image 56 included in the predetermined angle range θi of the second image 56 are integrated to generate a distribution of intensity with respect to the angle. In step S26 of FIG. 4, the crystalline domain in the electron microscope image 50 is analyzed based on this distribution. Thus, the domain can be easily analyzed by using the intensity distribution with respect to the angle.

  Furthermore, when the multivariate curve decomposition method is used, principal components are extracted from distributions corresponding to the positions of a plurality of regions in the electron microscope image 50 as in step S30 of FIG. As in step S32, the density of each position with respect to the extracted principal component is calculated. As shown in FIG. 11, a position where the density with respect to a specific main component is higher than a predetermined value is classified as the same domain. In this way, the crystalline domains can be classified.

  As in the example of FIG. 6B, the intensity distribution with respect to the angle may be a distribution having an angle range of 180 degrees. This is because the second image 56 is a point-symmetric image. Furthermore, the angle range may be narrow for crystals with high symmetry.

  Further, in the first embodiment, the histogram is described as an example of the intensity distribution with respect to the angle. However, other than the histogram, any distribution may be used.

  The second embodiment is a specific example of the first embodiment. FIG. 12 is an electron microscopic image of Example 2. The electron microscope image 50 in FIG. 12 is an image obtained by observing a polycrystalline sample using the STEM method. FIG. 13 is an image showing an example of the second image of the second embodiment. The second images A to H in FIG. 13 are second images A to H generated by Fourier transforming the first images A to H cut out from the electron microscope image 50 in FIG. As shown in FIG. 13, the second images A to H show different patterns.

  FIG. 14 is a diagram illustrating a two-dimensional image of the concentration distribution of the main component of the second embodiment. For the electron microscope image 50 of FIG. 12, 16 main components were extracted using the method of Example 1. Each image of FIG. 14 is a two-dimensional image 60 of each principal component P1 to P16. In FIG. 14, since the output color image is illustrated as a black and white image, the density and density of the image do not necessarily correspond. For example, areas P1 to P4 and P6 in FIG. 14 indicate areas where the density is higher than a predetermined value. Further, among the main components P1 to P16, the main components P7, P10, and P14 did not have strong peaks in the histogram as shown in FIG. Therefore, it can be seen that the main components P7, P10 and P14 are the main components of the amorphous region.

  FIG. 15 is a diagram showing the classified domains in the electron microscope image of Example 2. The high-concentration region 70 in the main components P1 to P4 and P6 in FIG. Each of the regions 70 corresponding to the main components P1 to P4 and P6 forms one crystalline domain. It can be seen that these crystalline domains have the same lattice fringes but have different lattice fringe angles.

  As in Example 2, the crystalline domain can be automatically classified using an actual electron microscope image.

  Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications and changes can be made within the scope of the gist of the present invention described in the claims. It can be changed.

The following appendices are further disclosed with respect to the embodiments including Examples 1-2.
Supplementary Note 1: A Fourier image is generated by performing Fourier transform on each of a plurality of regions of an electron microscope image, an intensity with respect to an angle of the Fourier image is calculated, and based on the intensity, a crystalline domain in the electron microscope image And analyzing the crystal grain orientation.
Supplementary Note 2: The analysis method according to Supplementary Note 1, wherein the crystalline domain is analyzed using a multivariate curve decomposition method.
Supplementary Note 3: The intensity of the Fourier image included in a predetermined angle range of the Fourier image is integrated to generate a distribution of the intensity with respect to the angle, and based on the distribution, a crystalline domain in the electron microscope image is obtained. 3. The crystal grain orientation analysis method according to appendix 1 or 2, wherein the analysis is performed.
Supplementary Note 4: The analysis of the crystalline domain uses a multivariate curve decomposition method to extract principal components from the distributions corresponding to the positions of the plurality of regions in the electron microscope image, respectively, The density of the position of the plurality of regions with respect to a component is calculated, and the position where the density of a specific principal component is higher than a predetermined value among the positions of the plurality of regions is classified as the same domain. Analysis method of crystal grain orientation.
Appendix 5: The crystal grain orientation analysis method according to Appendix 3 or 4, wherein the angle is an angle centered on a center of the Fourier image.
Supplementary Note 6: The grain orientation analysis method according to Supplementary Note 5, wherein the range of the angle is 180 degrees.
Supplementary Note 7: The grain orientation analysis method according to any one of Supplementary notes 3 to 6, wherein the distribution is a histogram of the intensity with respect to the angle.
Appendix 8: An input unit to which an electron microscope image is input, a calculation unit that generates a Fourier image by performing Fourier transform on each of the plurality of regions of the electron microscope image, and calculates an intensity with respect to an angle of the Fourier image; An analyzer for analyzing a crystalline domain in the electron microscope image based on the intensity;
Supplementary Note 9: The grain orientation analysis according to supplementary note 8, wherein the analysis unit includes a multivariate analysis unit that classifies the crystalline domains in the electron microscope image using a multivariate curve decomposition method. apparatus.

DESCRIPTION OF SYMBOLS 10 Computer 20 Electron microscope 32 Operation part 36 Multivariate analysis part 38 Analysis part 50 Electron microscope image 52 1st image 56 2nd image 58 Histogram

Claims (6)

A Fourier image is generated by performing a Fourier transform for each of a plurality of regions included in an electron microscope image of a polycrystal having a plurality of crystalline domains ,
Calculating the intensity with respect to the angle of the Fourier image;
A method for analyzing grain orientation, wherein the region in the electron microscopic image is classified into crystalline domains having a corresponding crystal grain orientation among the plurality of crystalline domains based on the intensity. The analysis method according to claim 1, wherein a multivariate curve decomposition method is used to classify the region into a crystalline domain. Integrating the intensity of the Fourier image contained within a predetermined angular range of the Fourier image to generate a distribution of the intensity with respect to the angle;
3. The grain orientation analysis method according to claim 1, wherein the region in the electron microscope image is classified into a corresponding crystalline domain among the plurality of crystalline domains based on the distribution. . Classification of the region into a crystalline domain uses a multivariate curve decomposition method, and extracts principal components from the distribution corresponding to the positions of the plurality of regions in the electron microscope image,
Calculating the density at the position of the plurality of regions with respect to the extracted principal component;
4. The crystal grain orientation analysis method according to claim 3, wherein, among the positions of the plurality of regions, a position having a concentration with respect to a specific main component higher than a predetermined value is classified as the same crystalline domain. An input unit for inputting a polycrystalline electron microscope image having a plurality of crystalline domains ;
A Fourier image is generated by performing a Fourier transform for each of a plurality of regions included in the electron microscope image , and an arithmetic unit that calculates the intensity with respect to the angle of the Fourier image;
An analysis unit that classifies the region in the electron microscope image into a crystalline domain having a corresponding crystal grain orientation out of the plurality of crystalline domains based on the intensity. Crystal grain orientation analyzer. The analyzing unit, the region in the electron microscope image using multivariate curve decomposition method, a multivariate analysis unit which classifies the crystalline domains having a direction corresponding grain of the plurality of crystalline domains 6. The crystal grain orientation analyzer according to claim 5, further comprising:

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