JPH0760139B2 - Grain boundary display method - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method for displaying an image of the difference between adjacent crystal orientations by the line width of each crystal grain boundary, and particularly to a crystal orientation measuring sample in a minute region. The measurement sample is automatically driven according to the digital image obtained by image-processing the scanning electron microscope image or the optical microscope image, and the X-ray Cossel diffraction images at each measurement point are sequentially input to the image memory, and after image processing, the measurement sample is digitized. Automatically analyze the crystal orientation of the micro region
Using the device that creates the crystal orientation color map, the orientation difference between adjacent crystal grains on the map is automatically calculated, and the thickness of the grain boundary of the crystal orientation color map is changed according to the orientation difference. It is about how to display.

(Prior art) As a method for measuring the crystal orientation of a minute region, a Cossel line analysis method using a scanning electron microscope image (hereinafter referred to as SEM image) is being used instead of the conventional micro-laue method or etch pit method. is there. In this method, the inventors combined a scanning electron microscope and a Kossel camera as disclosed in JP-A-55-33660 and JP-B-57-47791, and a micro region to be crystallized was obtained. An electron beam for a scanning electron microscope, which has been narrowed down to a few microns in diameter, is irradiated, and an image of a Kossel beam generated by exciting atoms in a minute region is photographed by a Kossel camera.

However, because of the use of X-ray film, setting the film on the device, developing, fixing the film,
It took time and labor to analyze the film, and it was very difficult to obtain information on a wide range of textures.

In order to solve the above-mentioned drawbacks, the inventors of the present invention have disclosed Japanese Patent Laid-Open No.
Japanese Patent No. 248 discloses an X-ray Cossel diffraction image observation apparatus using an X-ray image intensifier. This device can replace the conventional X-ray film and convert the output of the X-ray image intensifier into digital data for display on a cathode ray tube. However, the Cossel diffraction image obtained in this way cannot be used as the experimental data as it is, and in order to minimize the error in the analysis of the Cossel diffraction image and to save labor, the analysis is performed. Automation was essential.

Computer-aided image analysis methods have been developed since the early 1960s, and automatic measurement of the distance of a diffraction spot by the X-ray Laue method or electron beam diffraction method has been performed. We believe that it is possible to automate the analysis of the orientation and distortion of the Kossel line image by connecting an image analysis device, and in Japanese Patent Application No. 59-21580, it is possible to process a large amount of data with high accuracy and in a short time. By solving the above-mentioned drawbacks and automatically analyzing the azimuth and the amount of distortion of the Cossel diffraction image, an X-ray Cossel diffraction image analysis apparatus which can process a large amount of data with high accuracy and in a short time and has few errors was proposed.

In the 1980s, the image processing / analyzing device became faster than the general-purpose computer as before, but the introduction of a dedicated processor using a personal computer made it possible to speed up data processing and build a software program suitable for the site. Therefore, it has been widely used in fields such as industry, communication, medical care, and commerce, and different types of input data can be processed and analyzed in parallel with the increase in memory capacity (multi-memory channel) and color images. A memory can be provided and the processing and analysis results can be displayed in color.

The inventors of the present invention have introduced the above-mentioned multi-memory channel system into the X-ray Cossel diffraction image observation apparatus disclosed in Japanese Patent Laid-Open No. 56-26248. In Japanese Patent Application No. 60-70186, an automatic X-ray diffraction analysis device for X-ray diffraction, which enables automatic irradiation of electron beams, automatic creation of pole figure and color mapping by connecting a device (CRT, printer, etc.), was proposed. According to this, a binarized image is created by extracting only the crystal grain boundaries from an optical microscope image or SEM image of crystal grains existing in a minute region, and then the crystal orientations of the individual crystal grains in the entire region are automatically and sequentially obtained. The crystal orientation is measured using an image processor dedicated to image processing / analysis, and the result is (hk
l) Print the positive pole diagram and reverse pole (N.
By superimposing the crystal orientation color image of each crystal grain by D. and RD) on the grain boundary binarized image, it becomes possible to create a crystal orientation color map of a minute region. Since this color map displays the orientation of individual crystal grains in a visually easy-to-understand manner, it can be said to be an effective method for describing the state of preferential orientation formation of recrystallized texture.

(Problems to be Solved by the Invention) By the way, when dealing with problems such as movement and disappearance of crystal grain boundaries due to annealing, it is a large-angle grain boundary in which the nature of the crystal grain boundaries, for example, the orientation difference between adjacent crystal grains is large. It may be noted that it is a small-angle grain boundary, which is also called a sub-boundary. Various display methods and grain boundary models have been considered to solve this problem. For example, Σ value display by corresponding grain boundaries (H. Mykura: “Grain
− Boundary Structure and Kinetics ", ASM Seminar
(1979), Shimizu et al .: Iron and Steel, 71 (1985), S.554, Yoichi Ishida: Journal of the Crystallographic Society of Japan, 12 (1970), 142.), Adams-Murra.
y, Rath-Bernstein, Watanabe-Davis and others graphical methods (MA Adams and GT Murray: J.Appl.Phys., 33, respectively).
(1962), 2126, BBRath and JMBernstein: Met.Tran.
s., 2 (1971), 2845, T. Watanabe and PWDavis.Phil, M
Ag., A37 (1978), 649.) exist, but there is still no established method.

The object of the present invention is to solve the above-mentioned inconvenience and to display a crystal grain boundary, for example, in a crystal orientation color mapping created by using an X-ray Cossel diffraction image automatic analyzer, crystal characteristic values, particularly crystals between adjacent crystal grains. An object of the present invention is to provide a crystal grain boundary display method that allows intuitive and easy-to-understand display by additionally displaying crystal grain boundary information such as orientation difference.

(Means for Solving Problems) The crystal grain boundary display method of the present invention is measured based on the data for displaying each crystal grain boundary obtained by image-processing a scanning electron microscope image or an optical microscope image and the Cossel method. It is characterized in that the crystal grain boundaries are image-displayed with the width of the crystal grain boundaries corresponding to the difference between the adjacent crystal orientations of the respective crystal grain boundaries based on the data of the crystal orientation of each crystal grain.

(Operation) In displaying the crystal grain boundary in the above-described structure,
Since the difference in orientation between adjacent grain boundaries is displayed together with the grain boundary with the line width of the grain boundary corresponding to the difference, it is possible to intuitively understand the difference in orientation between adjacent grain boundaries. it can.

(Example) The details will be described below by taking a crystal orientation color map as an example.

FIG. 1 is a block diagram of an X-ray Cossel diffraction pattern automatic analyzer proposed in Japanese Patent Application No. 60-70186, which is suitable for carrying out the grain boundary display method of the present invention. That is, X
The measurement sample 1-4 loaded into the main body 1 of the line-COSSEL diffraction image observation apparatus is detected by the SEM image detection apparatus 4 or the optical microscope image detection apparatus 3, and is relayed through the input interface 5 to the image processor 6 as a digital image. Is entered. For this digital image, CPU6 dedicated for image processing / analysis
-2 is used to perform the necessary binarization process, and then the image is stored in the image memory 6-1 as a binarized image of only the crystal grain boundaries.
A 1/0 signal is sent to the electron gun starting / stopping device 9, and X-ray Cossel diffraction measurement by the reflection or transmission method is sequentially and automatically performed. The X-ray Cossel diffraction image diffracted by the sample 1-4 is detected by the high-sensitivity X-ray sensor 1-5-1 provided on the image receiving surface of the X-ray image intensifier 1-5,
This is also A / D converted and stored in the image memory 6-1 by relaying through the input interface 5 like the image of the tissue. From this X-ray Cossel diffraction image, two or three {hkl} diffraction lines necessary for crystal orientation analysis are extracted, and the coordinates of the point at the shortest distance from the origin of each diffraction line are read out for image processing / analysis only. From the data of these using CPU, {hk
After calculating all the remaining {hkl} poles required for the l} positive pole diagram, the plotter 8-1 of the display group 8 outputs the {hkl} positive pole diagram. On the other hand, the crystal orientation color map reads the coordinates of the {100} pole point from the measured value in the spherical coordinate system and performs coordinate conversion to find that both ND and RD exist in the basic stereo triangle.
A kind of inverse pole figure is created. Here, the three primary colors of light, blue, red, and green, are placed at the three vertices (001), (011), and (111) of the basic stereo triangle, and by mixing the angle differences from the vertices as the stimulus ND of grain,
Color information representing the RD direction is obtained, and the crystal display color map is output from the color display 8-5.

FIG. 2 is an example of the color map obtained in this way, showing the crystal orientation distribution of the primary recrystallized structure after decarburization and primary recrystallization annealing of high-grade grain-oriented silicon steel containing a small amount of Mo. There is. In FIG. 2, since the crystal grain boundaries were input from the SEM image photograph through the image pickup tube, the thickness of the crystal grain boundaries was not uniform due to the shadow accompanied by the unevenness of the photograph. After this crystal grain boundary was once made into a uniform crystal grain boundary having a thickness of one pixel, it became possible to display the crystal grain boundary based on the crystal orientation difference between adjacent grains by the method described below. First, the method of determining the crystal orientation from the Cossel diffraction image is the method by Ferran et al. (G.Ferran & R.A.Wood: J.Appl.Gryst.vol.3 (1970)).
To use. That is, when a sample is vertically irradiated with an electron beam, a pear-shaped characteristic X-ray is generated in the sample, and when the sample passes through the sample, Bragg diffraction is caused by its crystal lattice and a diffraction cone with the X-ray generation source as an apex. Is formed. This image is a horizontal image receiving surface 1-5 of the X-ray image intensifier 1-5 which is vertically away from the X-ray source by l.
On -1, it is approximated as a quadratic curve represented by the equation (1).

Here, “−−” is the orthogonal coordinate on the sample surface (rolling surface) parallel to the image receiving surface 1-5-1 and the axis is the line of intersection between the sample surface and the (hkl) diffraction surface. θhkl is the Bragg angle of the (hkl) diffractive surface,
Further, γ is the angle formed by the (hkl) diffraction surface and the sample surface. (H
kl) The positive point diagram is the crystal coordinate system X- based on the sample coordinate system xyz (x axis = RDy axis = TDz axis = ND)
It is a description of YZ (corresponding to a unit cell vector in the case of cubic crystal), and is expressed as a stereo projection point of all {hkl} plane normals.

That is, the-coordinate system of the equation (1) and the sample coordinate system x-
The (hkl) pole is determined by determining the rotation angle ψ of y (and z are the same) and the value of γ.

To say that = 0 in the equation (1) is _{O in the} equation (2).

This _O corresponds to the shortest distance from the origin to the (hkl) diffraction line. Let this point be p, and point p in the xy coordinate system.
If the coordinates of (x _p , y _p ) and the curvature of the (hkl) diffraction line at point p are ξ _p , γ and ψ can be obtained from equations (3) and (4). (However According to the equation (3), in order to determine γ, the diffractive surface index (hkl) of the arbitrarily selected diffracted line must be discriminated. For example, in the case of α iron Cossel diffraction line, the diffraction planes satisfying the Bragg condition are {200}, {110}, {211}, {2
Limited to 4 types of 20}. Curvature ξ of diffraction line at point p
_p is Therefore, if a lookup table for each θhkl for γ is created, by measuring ξ _p (hk
l) can be determined.

Next, a method of creating a (hkl) pole figure from (γ, ψ) of an arbitrary (hkl) diffraction line determined by image analysis will be described.

According to stereo projection, the (hkl) pole point showing the diffractive surface normal is represented by point A in FIG. That is, the point A is on the axis rotated ψ clockwise from RD. (T is the radius of the pole figure).

The (hkl) pole figure needs to show all the poles of the spatially equivalent combinations of {hkl}, but due to the rotational symmetry of the crystal, two points are {200} poles and three points are {110} poles. Once the points are determined, the positions of all remaining poles can be determined.

An example of creating a (200) pole figure is shown in FIG.

Points A and B are (200) and (002) poles obtained from the Cossel diffraction line, and their measured values are (γ _A , ψ _A ) and (γ _B , ψ _B ), respectively. From these two points, point C (γ _C ,
ψ _C ) is determined.

The zone axis passing through the two points A and B (the stereo projection of the great circle) is determined as RAQBS by the OAB plane and ▲ ▼ perpendicular to the line of intersection ROS of the rolling plane. If the point is Q (γ _O , ψ _O ), then ▲ ▼ and ▲ ▼
The angle ψ _I ′ formed by is represented by the equation (6) by the angle ∠AOQ by stereo projection.

As well However, 0 ≦ γ _A , γ _B , 0 ≦ ψ _A , ψ _B , ψ _O ≦ 2π In stereo projection, the equations (8) and (9) generally hold.

_{tanγ O = tanγ A cos (ψ} O -ψ A) ... (8) tanγ O = tanγ B cos (ψ B -ψ 0) ... (9) (8), (9) Equation (6), (7) Substitute into the formula, ▲
Angle between ▼ and ▲ ▼ Therefore, γ _O can be calculated from equation (10).

Substituting this into Eq. (8) or (9), ψ _O becomes (1
It can be calculated by the formula 1).

▲ ▼ which is vertical to both ▲ ▼ and ▲ ▼ is ▲
Since both ▼ are vertical and ∠QOC = π, the point C is (1
It is determined by equations (2) and (13).

The conversion from this (200) pole figure to the (110) pole figure is point A
And B, points B and C, and points C and A, the crystal zone axes are obtained from equations (6) to (11), and the interplane angle between the {200} plane and the {110} plane is calculated. And the angle between {110} and {110} planes The six {110} poles required for display can be determined from the relationship of.

Next, from this positive point diagram, the crystal orientation Miller index (hkl)
[Uvw] is determined and the orientation difference between adjacent grains is calculated. In order to calculate the Miller index of the crystal orientation, first, a (220) positive pole figure of the measured grain is created, and then converted to a reverse pole figure. The inverse pole figure is represented by ND and RD when the (200) positive pole figure is rotated equiangularly so as to agree with the (200) standard projection, but generally, this equiangular rotation exists many times. Here, as will be described below, a method of converting with a minimum rotation angle with reference to ND is used. That is, the (200) positive pole figure of FIG. 4 is converted into the reverse pole figure of FIG. 6 by following the broken line path of FIG.

Here, FIGS. 4, 5 and 6 are drawings plotted by Wolfnet in stereo projection, which correspond to the pole A, the pole B, and the pole C in FIG. 4 (γ _A , ψ _A ),
(Γ _B , ψ _B ), (γ _C , ψ _C ) are orthogonal (200) pole point parameters, γ _A , γ _B , γ _C are longitude, ψ
_A , ψ _B , and ψ _C are represented by circumferential angles. FIG. 5 illustrates the procedure for moving the pole point C closest to the center of the positive pole figure in FIG. 4 to convert it into the (100) standard projection. FIG. 6 illustrates FIG. 5 after rotation. However, the point A'rotated horizontally and the point B'rotated vertically downward. (Ω _N , ψ _N ), (ω _R ,
ψ _R ) is the pole parameter of the point N and the point R (ω is the longitude and ψ is the circumference angle in the angle display), and FIG. 6 shows the points O (ND) and RD in FIG. 4 as (100) standard. This corresponds to the drawing in which the normal line direction N of the sample and the rolling direction R are plotted again on the projection view. Based on the above definition, the conversion from the (200) positive pole figure to the reverse pole figure will be specifically described.

Of the three {200} poles of points A to C in Fig. 4, the origin O (N.
Rotate the point closest to (D.) (point with the smallest γ value) to the origin as the (001) pole. If γ _C <γ _A <γ _B , the point C is rotationally moved to the origin C'as shown in FIG. According to it, point A, point B and point O (ND), point P
(RD) moves equiangularly around RS as a rotation axis to become point A ', point B'and point N point R, respectively. Here, points A'and B'correspond to any of the poles (200), (020), (00), and (00) on the circumference of the cubic (200) standard projection, but (002) The opposite pole figure is determined such that the 180 ° rotation azimuth around the circle is equivalently taken and either the point A ′ or the point B ′ corresponds to the (200) pole. Now in FIG. 5, ψ ′ ₁
Since <ψ ' ₂ , the point A'is determined to be the (200) pole point, and ND and RD in FIG. 4 are converted to the points N and R on the (200) standard projection in FIG. 6, respectively. If the coordinates of points N and R on the (200) standard projection are (ω _N , ψ _N ) and (ω _R , ψ _R ) (ω is longitude and ψ is a circumferential angle), these are given by It can be calculated by equations (14) to (17). (However, ψ _O is the circumferential angle that gives γ = min) ω _N = tan ^-1 (tan γ _C cos ψ _N ) ... (14) Next, the Miller index (hkl) [uvw] of crystal orientation is point N
Using (ω _N , ψ _N ) and the point R (ω _R , ψ _R ),
It is calculated by the formulas 8) to (21).

i) When ω _R ≠ 0, ± 90 ° ii) When ω _R = 90 ° or −90 ° iii) When ω _R = 0, ψ _R = 90 ° or −90 ° Next, the difference in orientation between adjacent crystal grains is ND (or R.
The misorientation angle is calculated from the following equations (22) and (23) as the angle θ formed by the vectors representing the directions of ND and RD, in order to add it to the inverse pole figure of D.) as information on the grain boundaries.

θ _N = cos ^-1 (h ₁ h ₂ ＋ k ₁ k ₂ ＋ l ₁ l ₂ )… (22) θ _R ＝ cos ^-1 (u ₁ u ₂ ＋ v ₁ v ₂ ＋ w ₁ w ₂ ) ・ ・ ・ (23) Where (H ₁ k ₁ l ₁ ) [u ₁ v ₁ w ₁ ] and (h ₂ k ₂ l ₂ ) [u ₂ v
₂ w ₂ ] is a Miller index indicating the crystal orientation of adjacent crystal grains 1 and 2. θ is 0 ≦ θ ≦ 180 °, but when θ> 90 °, a complementary angle is taken to calculate 180 ° −θ.

The crystal orientation difference angle θ by the image processor 6 in FIG.
_N and θ _R are calculated automatically, and ND and RD are calculated as follows.
The information is output as the information of the crystal grain boundary of the crystal orientation color map indicating the orientation of.

For simplification, a method for displaying the thickness of the grain boundary by the misorientation angle of adjacent crystal grains using the binarized image of the crystal grains 1 and 2 shown in FIG. 7 only will be described.
In general, in a binarized image of a crystal grain by a grain boundary on a CRT, a gray (0) or white (1) gray tone value is input to a memory address of each unit pixel. That is, 2 of the pixels in the crystal grain region
All 1's are entered in the binarization memory and 0's are entered in the grain boundaries. In the binarized image of FIG. 7, the pixel B with diagonal lines is the crystal grain boundary (the grain boundary thickness is all 1 pixel at the beginning).
0 is input to the binary memory. Next, the crystal grain whose crystal orientation is to be measured is extracted from this binarized pixel, and the crystal grain number is input to the memory address (16-bit unit) of each pixel of the grayscale image memory. In FIG. 7, 1 is input to all the pixels occupied by the crystal grain 1, and 2 is input to all the pixels occupied by the crystal grain 2. According to this number, the Cossel X-ray diffraction and the crystal orientation measurement are sequentially and automatically performed, and two or three sets of (γ, ψ) parameters are stored in the disk memory of the external storage unit using the crystal grain number of each crystal grain as an index number. Is entered. These are shown in Fig. 1. The CPU 6-2 dedicated to image processing / analysis calculates the parameters required for the color map, and ND (ω _N , ψ _N ) of each crystal grain shown in equations (14) to (17).
And RD (ω _N , ψ _N ) are calculated, and the former is the RGB of each pixel
Is input to the color memory A and the latter is input to the color memory B. That is, (ω _N1 , ψ _N1 ) and (ω _R1 , ψ _R1 ) in all the pixels G ₁ showing the crystal grain 1 in FIG. 7 are (ω _N2 , ψ _N2 ) and all in the pixel G ₂ showing the crystal grain 2. (Ω _R2 , ψ _R2 )
Is entered. To calculate the crystal orientation difference of all adjacent crystal grains, the binarization memory of the CRT is raster-scanned from left to right, and when the pixel B indicating the crystal grain boundary is reached, the pixel G adjacent to the left of the pixel B is detected. (18) to (21) are calculated from the memory contents of ₁ and the G ₂ adjacent to the right, respectively, and the azimuth difference angles θ _N12 and θ of ND and RD are calculated using equations (22) and (23).
_{Find R12} and enter these into the memory of pixel B. Further, similar processing is performed on the pixel adjacent to the pixel B and the pixel adjacent to the pixel B in the figure. This is performed for all the stages from the upper stage to the lower stage, and all the crystal grain boundary pixels B existing in the raster region are associated with the ND and RD misorientation angles θ _N , θ _R of the crystal grains on both sides sandwiching it. . The thickness of the crystal grain boundary to be displayed is determined by the magnitudes of the misorientation angles θ _N and θ _R. For example, in FIG. 8, the misorientation angle is 0 ≦ θ _N , θ _R ≦ 10 deg. For 1 pixel, and 10 <
2 pixels for θ _N and θ _R ≦ 25 deg. and 3 pixels for θ _N and θ _R > 25 deg.
It is a crystal grain boundary and a crystal orientation color map having a thickness for a pixel. In this way, θ _N and θ _R input to the grain boundary pixel B are divided into several stages according to size, and the pixel on the right side or the left side, the upper side, and the lower side of the pixel B is determined as the grain boundary pixel according to the rank. Of the corresponding pixels of color memory A and color memory B
RGB gray tone is converted to 0.

(Effect of the Invention) As is clear from the above description, according to the crystal grain boundary display method of the present invention, the difference in the orientation of the adjacent crystal grain boundaries is determined according to the difference in displaying the crystal grain boundaries. Since the image is displayed together with the crystal grain boundary with the line width of the crystal grain boundary, it is possible to intuitively and easily display the difference in the orientation of the adjacent crystal grain boundaries.

[Brief description of drawings]

Fig. 1 is a block diagram of an X-ray Cossel diffraction image automatic diffraction device that automatically creates grain boundaries and crystal orientation color maps, and Fig. 2 is a crystal with crystal orientation color maps using a grain boundary binary image. Fig. 3 is a photograph showing the structure of Fig. 3, Fig. 3 is a diagram showing the relationship between the measured values and the positive electrode dot diagram, Fig. 4 is an explanatory diagram of an example of creating the (200) positive electrode dot diagram, and Fig. 5 is the reverse of the (200) positive electrode dot diagram Diagram of conversion path to pole figure, Fig. 6 is an explanatory diagram of an example of creating an inverse pole figure, Fig. 7 is a schematic diagram of binarized image of grain boundary on CRT, Fig. 8 is misorientation in Fig. 2. 3 is a photograph showing a crystal grain boundary to which a crystal grain boundary display is added and a crystal structure based on a crystal orientation color map. 1 ... X-ray Cossel diffraction image observation device 1-1 ... Electron gun 1-2 ... Converging lens 1-3 ... Objective lens 1-4 ... Sample 1-5 ... X-ray image intensifier 1-5-1 ... High-sensitivity X-ray sensor 3 ... Optical microscope image detection device 3-1 ... Optical microscope 3-2 ... TV camera 4 ... SEM image detection device, 4-1 ... Detector 4-2 Scanning converter 5 Input interface 6 Image processor 6-1 Image memory 6-2 Image processing / diffraction CPU 6-3 Control / editing CPU 7 Output interface 8 ... Display 9 ... Stage drive / electron gun drive stop device 9-1 ... Autofocus / stage controller 9-2 ... XYZ pulse motor

 ─────────────────────────────────────────────────── ─── Continued Front Page (72) Inventor Yo Ito 1 Kawasaki-cho, Chiba-shi, Chiba Kawasaki Steel Co., Ltd. Technical Research Headquarters (72) Inventor Mitsu Yanagisawa 2-3 2-3 Uchisaiwaicho, Chiyoda-ku, Tokyo Kawatetsu System Development Co., Ltd. (56) Reference JP-A-61-228336 (JP, A)

Claims (1)

[Claims] 1. Based on data for displaying each crystal grain boundary obtained by image-processing a scanning electron microscope image or an optical microscope image and data on a crystal orientation for each crystal grain measured by the Cossel method, A method for displaying a grain boundary, wherein the grain boundary is image-displayed with a width of the grain boundary according to a difference between adjacent crystal orientations of the grain boundary.