A METHOD FOR MEASURING STRAIN BY ANALYZING SHARPNESS OF ECP WITH IMAGE ANALYSIS

A method for measuring strain by analyzing sharpness of Electron Channeling Pattern (ECP) with Image 
analysis has been newly developed. The relative value of sharpness of first-order pseudo-Kikuchi line 
in ECP is used as a parameter of strain. Strain change of Fe-3.25%Si alloy single crystal and polycrystal 
during deformation and recrystallization was analyzed by this method. This method was compared with 
the conventional methods; hardness and line broadening of X-ray. This method can be used for 
measuring strain in material with any crystal orientation.


INTRODUCTION
It is very important for studying deformation, recovery, recrystallization, texture, fatigue and fracture to know strain in steel or other crystalline material.The strain in material has been evaluated commonly by measuring hardness or line broadening of diffracted beams of X-ray or by observing lattice defects, for example, dislocations with Transmission Electron Microscope(TEM).However, the measurement of strain by hardness is affected by solutes and precipitates in material.In the case of measurement of strain by line broadening of diffracted beams of X-ray, beams of X-ray are difficult to focus on such a small area as under 100/zm in diameter.In the case of observing lattice defects with TEM, it is time consuming for the specimen preparation.
Accordingly, these methods are not sufficient for measuring strain precisely and efficiently in such a small area as under 100 #m in diameter.
On the other hand, several studies have been done on the measurement of strain in the material by quantifying the contrast of specific pseudo-Kikuchi line in the Electron Channeling Pattern (ECP) (e.g.Joy et al., 1971; Sticker et al., 1971; Schulson, 1971;   Davidson, 1974; Ruff, 1976; Davidson et al., 1976; Davidson, 1977; Davidson, 1981;   Farrow et al., 1981).The strain in such a small area as 3 #m in diameter in the material can be measured by quantifying the contrast of specific pseudo-Kikuchi line in ECP because beam of ECP can focus on 3 /zm in diameter (Nakagawa, 1986).However, this method is inapplicable to the quantification of strain in the material with an arbitrarily chosen crystal orientation because the kind of pseudo-Kikuchi line in ECP depends on the crystal orientation (Davidson, 1984).
Quite recently, some studies have been done on the measurement of strain in the material by using Electron Back-scattering Pattern (EBSP) (e.g.Quested et al., 1988, Dingly et al., 1990).The strain in such a small area as less than 1 gm in diameter in the material can be measured by quantifying the contrast of EBSP.For measuring strain in a small area less than 3 /an in diameter.EBSP should be used.However, since ECP is more sensitive to strain than EBSP, ECP can be more appropriate than EBSP in the case of measuring small strain.
Then for measuring the small strain in the material with any crystal orientation, a method by analyzing sharpness of first-order pseudo-Kikuchi lines in ECP with Image analysis has been developed in the present study.The relative value of sharpness of first-order pseudo-Kikuchi line is used as a parameter of strain.Fe-3.25%Si alloy single crystal and polycrystal were used as test specimens.Strain change during deformation and recrystallization was analyzed by this method.The outline of analysis flow, the def'mition of sharpness of ECP (herein after referred as S) and sharpness of first-order pseudo-Kikuchi line (herein after referred as S1) are shown in Figure 1, Figure 2, respectively.When every first-order pseudo-Kikuchi is sharp, the value of S1 is defined as the ideal sharpness of first-order pseudo-Kikuchi (herein after referred as S10).S1 and S10 which are defined by eq. ( 1) and eq. (2)  Image input

Segmentation
Binary image processing Unifying the width of image, erasing the isolated points, selecting the first-order pseudo-Kikuchi line, etc. Measurement Sharpness of first-order pseudo-Kikuchi line Figure 1 Flow of analysis.respectively are measured.Then, relative value of sharpness of first-order pseudo-Kikuchi line (herein after referred as Sl*) is calculated.
where L1 is the length of sharp first-order pseudo-Kikuchi line in ECP, L loi is the length of first-order pseudo-Kikuchi line in ECP, W, the width of sharp first-order pseudo-Kikuchi line in ECP, is constant, A, the area of ECP image, is constant.S1 is measured as the area rate of sharp first-order pseudo-Kikuchi lines in ECP image because the area of crossing points of sharp first-order pseudo-Kikuchi lines in ECP image is so small that it can be neglected.S10 is also measured as the area rate of first-order pseudo-Kikuchi lines in ECP image.Sl* is used as a parameter of strain in the present study.It is true that Sl* has no information on the strain influence of higher order of pseudo-Kikuchi lines.However, Sl* is practically superior to S as a parameter for expressing the degree of strain in the sense that SI* can be defined for any crystal orientation but S needs the reference value, for example, the value of S of fully annealed specimen with the same orientation as the test specimen has.To prepare this reference specimen for any orientation is very difficult.
(2) Procedure The analysis flow is shown in Figure 1.First, a SEM-ECP image is transferred to an image analyzer with frame-store averaging.Then, Gray image processing, Segmentation, Binary image processing and Measurement are performed as follows.
1) Gray image processing Smoothing by median filtering, standardizing the gray level by gray-scale transformation and smoothing by selective local averaging are performed.Then, the gray image is transferred to 2-dimensional differential calculus image with Sobel's method (e.g.Matuyama, 1985).This 2-dimensional differential calculus image is made more distinct by performing GAMMA transformation, LOG transformation, GAMMA transformation and smoothing by median filtering in this order.

2) Segmentation
Segmentation with constant threshold is preformed to obtain the image of area including the first-order pseudo-Kikuchi lines.
3) Binary image processing Erasing isolated points is performed to delete noise with small area.Then, expanding the figure and shrinking the figure are performed.The operation of expanding the figure is the transformation by which the output picture element has "1" in the case that the input picture element or the picture elements with 8-adjacent relation to the input picture element has "1" and the output picture element has "0" in other cases.On the other hand, the operation of shrinking the figure is the transformation by which the output picture element has "0" in the case that the input picture element or the picture elements with 8-adjacent relation to the input picture element has "0" and the output picture element has "1" in other cases.By these processing, the region comprising the first- order pseudo-Kikuchi line, inserted between two area with high value of 2-dimensional differential calculus in original SEM-ECP image, is obtained.Then, holes in the region comprising the first-order pseudo-Kikuchi lines are filled.And, thinning by Tamura's method (Tamura, 1978) and expanding the figure are performed to get the image made up of lines with constant width.The operation of thinning is the transformation by which the width of line in the image becomes 1 picture element.Through these processing, the image of sharp ECP described its definition in Figure 2 is obtained.And, each line in the image of sharp ECP is judged to be a sharp pseudo-Kikuchi line.And also, the thin line image just after thinning is defined as the thin line image of sharp ECP.On the other hand, the image included every first-order pseudo-Kikuchi line in ECP is made with the crystal orientation or by manual operation on the basis of the original ECP image.Then, the operation of making the logical product of the image of sharp ECP and the image included every first-order pseudo-Kikuchi line in ECP is performed to get the image made up of sharp first-order pseudo-Kikuchi lines with constant width.This corresponds to the image of sharp first-order pseudo-Kikuchi line described its definition in Figure 2.

4) Measurement
S1 and S10 which are defined by eq. ( 1) and eq. ( 2 respectively are measured.Then, Sl* defined by eq. ( 3) is calculated.S1 is the area rate of sharp first-order pseudo- Kikuchi lines in ECP image and S10 is the area rate of first-order pseudo-Kikuchi lines in ECP image.
5) Approximate method for measuring SI* If the other method, for example EBSP, for measuring the crystal orientation of the specimen with some amount of strain is used, S10 value can be calculated with the crystal orientation.However, in the case that such a method isn't available, it is possible but not easy to measure the value of S10 of any specimen with any degree of strain.This is because it isn't easy to make the image included every first-order pseudo-Kikuchi line in indistinct ECP by manual operation.Then, the approximate value of S10 and its error range are measured as follows.
The value of S10 depends on the Miller index of normal direction.However, it is thought that the specimens with the similar orientation have the similar value of S10.Then, the mean value of S10 of each Box which is used in the Vector method (Ruer et al., 1977) for analyzing 3-dimensional crystal orientation distribution is used as the approximate value of S10 of each Box.And then, the mean value of S10 of 36 Boxes is used as the approximate value of S10 of any specimen with any crystal orientation and the range between the minimum value and maximum value of S10 of 36 Boxes is used as the error range of S10 of any specimen with any crystal orientation.According to this method, the approximate value of S10 and its error range for any specimen with the same crystal structure and the lattice constant can be given by measuring the values of S10 of 36 Boxes for one fully annealed specimen.
This approximate is a practical way based on the mathematical concept described in eq. ( 3).This approximate is useful in the case of the system, like our system mentioned below, without the method, for example EBSP, for measuring the crystal orientation of the specimen with some amount of strain.
(3) Analyzing System SEM:JSM-840 with an auto-stage and Image analyzer:TOSPIX-II are used in the present study.JSM-840 has a Selected Area Electron Channeling Pattern Unit (Nakagawa, 1986).TOSPIX-II has 16 bit cpu, two 132 MB HD, two 1 MB FD and 512 x 512 x 8 bit picture size.ECP image is transmitted as an electrical signal from SEM to Image analyzer.

EXAMPLES OF APPLICATION
(1) Measurement of the Approximate Value and Its Error Range of $1 o For measuring the value of S10 of each 36 Box, Fe-3.25%Si alloy polycrystal annealed sheet with a grain size range from 10 to 50 #m was used as a test specimen.The orientation distribution of the polycrystal annealed sheet measured by X-ray and ECP for 100 grains is shown in Figure 3.The polycrystal annealed sheet had nearly random orientation except slightly high intensity of crystal orientation near {100|.The mean value of S10 of each Box in 36 Boxes measured for 100 images of ECP is shown in Figure 4.In the measurement of SI* mentioned below, these values of S10 in Figure 4 were used to calculate the approximate value and its error range of S10.The maximum value and minimum value of S10 for 36 Boxes were 1.2 and 0.8 times as high as the average value of S10 for 36 Boxes respectively.Slo/S1 in each Box.S10 ideal sharpness of first-order pseudo-Kikuchi line.$1 the mean value of $10 of 36 Boxes.
(2) Test Specimens For analyzing the strain by deformation, Fe-3.25%Si alloy polycrystal annealed sheet mentioned above and Fe-3.25%Si alloy single crystal annealed sheet were used as the test specimens.The 100} pole-figure of the single crystal annealed sheets measured by X-ray are shown in Figure 5.The single crystals of (110)[001] and (100) [011] orientations were used as the test specimens.The single crystal and polycrystal specimens with various degree of strain were made by cold rolling by 1 pass with reduction from 0 to 17% or by tensile deformation with elongation from 0 to 15%.The thickness of specimens before deformation was 0.36 mm.In the case of cold rolling, the lubrication oil was applied to the roll surface and the diameter of the roll was 120 mm.In the case of tensile deformation, the tensile direction was chosen to the same direction with the cold rolling direction.Then, for analyzing the strain decrease during recrystallization, the polycrystal specimens were prepared as follows. 2.3 mm thick Fe-3.25%Si-0.01%Chot rolled sheet was annealed at 1273 K for 300 s and was cold rolled to 0.285 mm thickness and was heated at a rate of 20 K/s to 1173 K and cooled in air at various temperature during the heating stage.
(3) Measuring Method The specimens were chemically polished to the midplane for measuring S, S1 and S10.ECP at 10 points (2 points parallel to the direction deviating from R.D. by zr/12 rad.x 5 points parallel to the direction deviating from that direction by n:/2 rad., at 10 gm intervals) and at 50 points (5 points parallel to the direction deviated from R.D. by zr/12 rad.x 10 points parallel to the direction deviating from that direction by n:/2 rad., at 100 pm intervals) was measured for the single crystal specimens and the polycrystal specimens, respectively.And also, the local inhomogeneity of SI* was investigated for the single crystals deformed by 1.5% cold rolling and the partially recrystallized polycrystal specimen.Then, the relationship between S and S1 was investigated for ECP of polycrystaly annealed sheet and cold rolled sheet.And the grain boundary influence on S was investigated for polycrystal annealed sheet.As measuring condition of SEM-ECP of backscattered electron image, the accelerating voltage of 35 kV. the absorbed specimen current of 9 x 10 -9 A, the working distance of 8 mm and rocking angle of + 8 x (n:/180) rad.were used.The approximate value of S10 and its error range measured for polycrystal annealed sheet as mentioned above were used in this study.As the threshold for segmentation judging whether pseudo- Kikuchi line is sharp or not, the value of 30 was used.
Several parameters might affect SI* value.For example, the surface contamination by long-time measurement tends to decrease the SI* values.However, in this study, ECP is measured only once for the specimen.In addition, this contamination influence on SI* value can be much weaken by standardizing the gray level of original ECP with gray-scale transformation.The measuring parameters, such as primary beam aperture, size of scan area, gradation (gamma settings) and primary beam voltage, which might affect SI* value are carefully fixed in measuring ECP.The influence of dislocation cell-wall distribution on SI* value isn't taken into account in this study.
For comparing this method with the conventional methods, the full width of half-value (FWHV) of (200) diffracted X-ray, the Vickers hardness and the fraction recrystallized were measured.As measuring condition of FWHV, the characteristic X-ray of Mo Kl, the accelerating voltage of 40 kV and the filament current of 20 mA were used.The Vickers hardness of the test specimen was measured with the load of kgf.Then, the fraction recrystallized was measured by point-count method of 100 points with the naked eye for Electron Channeling Contrast (ECC) pictures measured by SEM.For considering the physical meaning of SI*, the relationship between the tensile stress and SI* was investigated.
(4) Results   1) Crystal orientation dependence on accumulated strain The influence of strain on ECP, the image of sharp ECP and the image of sharp first-order pseudo-Kikuchi line of (110)[001] single crystals are shown in Figure 6.ECP became indistinct and the number of sharp pseudo-Kikuchi line decreased with increasing strain.The total length of the sharp pseudo-Kikuchi lines shown in Figure 6, for example, is proportional to S (c, d) and S1 (e, f) respectively.The influence of strain by cold rolling on SI* of single crystals was shown in Figure 7.In Figure 7., the error range of SI* was caused by that of S10.According to eq. ( 3), the error range of SI* was asymmetric to the approximate value of SI*.SI* was decreased with increasing strain in the cold reduction range less than 17%.The degree of this influence was affected by the crystal orientation before deformation.In the case of (110)[001] single crystal, SI* was decreased remarkably by 1.5% cold-rolling reduction and, then, was decreased gradually as the strain was increased in the cold-rolling reduction range from 1.5% to 17%.On the other hand, in the case of (100)[011], SI* was decreased gradually with increasing the strain in the every cold-rolling reduction range less than 17%.
Si* is thought to express the mean contrast of all first-order pseudo-Kikuchi lines in the ECP of the specimen.The contract of specific pseudo-Kikuchi line in ECP was decreased as the dislocation density of the specimen was increased (Stickler et al., 1971).
Figure Ii Influence of strain on ECP, sharp ECP and sharp first-order pseudo-Kikuchi line.Specimen Fe-3.25%Si alloy (110)[001] single crystals at the midplane, a, b ECP.c, d sharp ECP made by Image analysis with our study, e, f sharp first-order pseudo-Kikuchi line made by Image analysis with our study, a, c, e without cold rolling, b, d, f 15% cold rolling.

True st rain
Figure 7 Influence of strain on sharpness of first-order pseudo-Kikuchi line of Fe-3.25%Si alloy single crystals at the midplane.SI* relative value of sharpness of first-order pseudo-Kikuchi line.
And also, the influence of elastic strain on the contrast (line width) of specific pseudo-Kikuchi lines in ECP was negligible (Davidson, 1982).Accordingly, SI* is thought to be the value which is decreased with increasing the dislocation density of the test specimen.
The accumulated strain or the dislocation density is influenced by the crystal orientation before deformation (e.g.Dillamore et al., 1967; Takechi et al., 1968).Figure 7 is thought to show the accumulated strain in (110)[001 single crystal is larger than that in (100)[011 single crystal.The relationship between Sl* and the dislocation density of the test specimen is discussed further in the section of Relationship between tensile stress and Sl*.

2) Local inhomogeneity of strain
The local inhomogeneity of SI* (110)[001] and (100)[011] single crystals deformed by 1.5% cold rolling is shown in Figure 8, Figure 9, respectively.In the case of (110)[001] single crystal, the deformation band parallel to T.D. was observed.At that deformation band, the rotating angle from (110)[001] orientation around [011] axis parallel to T.D. was larger than that elsewhere.In addition, SI* at the deformation band was smaller than that elsewhere.On the other hand, in the case of (100)[011] --0.128 _+ 0.026 S1-0.025 + 0.005 Sl-X--0.080+_ 0.016 0 Figure 8 Local inhomogeneity of sharpness of first-order pseudo-Kikuchi line.Specimen Fe-3.25%Si alloy (110)[001] single crystal at the midplane deformed by 1.5% cold rolling, a, b, c ECP at A, B, C respectively, d ECC.SI* relative value of sharpness of first-order pseudo-Kikuchi line.single crystal, the deformation band parallel to the direction deviated from R.D. by r/4 rad.was observed.There was almost no orientation difference between at that deformation band and elsewhere.In addition, S l* at the deformation band was slightly smaller than that elsewhere.Figure 8 and Figure 9 are thought to show the local inhomogeneity of accumulated strain or dislocation density in (110)[001 single crystal is larger than that in (100)[011 single crystal because SI* is thought to be the value which is decreased with increasing the dislocation density of the test specimen.
Next, the local inhomogeneity of the specimens extracted at 923 K and cooled in air during heating stage after 88% cold rolling is shown in Figure 10.In this case, the fraction recrystallized was 20%.SI* at recrystallization grain (A, B) was remarkably larger than that at recovery grain (C, D).This difference of SI* is thought to express that the dislocation density at recrystallization grain is much smaller than that at recovery grain.S1 = 0.283 5= 0.057 S 1 + O. 248 +/-O. 050S1 0.271 :t: 0.055 Figure 9 Local inhomogeneity of sharpness of first-order pseudo-Kikuchi line.Specimen Fe-3.25%Si alloy (100)[011] single crystal at the midplane deformed by 1.5% cold rolling, a, b, c ECP at A, B, C respectively, d ECC.SI* relative value of sharpness of first-order pseudo-Kikuchi line.
3) Approximation method for measuring $1" In order to measure the value of S l* the measurement of crystal orientation or the manual operation for tracing the first-order pseudo-Kikuchi line is necessary.For avoiding these time-consuming operations, the approximate relationship between S and S1 expressed in eq. ( 4) could be used.

SI-O N 10tzm
Figure 10 Local inhomogeneity of sharpness of first-order pseudo-Kikuchi line.Specimen Fe-3.25%Si alloy polycrystal at the midplane at 923 K during heating at a rate of 20 K/s after 88% cold rolling, a, b, c, d ECP at A, B, C, D respectively, e ECC. S l* relative value of sharpness of first-order pseudo-Kikuchi line.
which was obtained by the method of least squares, where S10, the mean value of S10 of randomly oriented specimen, is constant.The relationship between S and S1 of polycrystal annealed sheet and cold rolled sheet is shown in Figure 11.The number of measuring points was 50 and the coefficient of correlation was 0.9972 and the standard deviation was 0.01578.Eq. ( 4) shows SI* (= S1/Slo) can be calculated from S measured without measuring the crystal orientation nor tracing the first-order pseudo- Kikuchi line.However, the error range of SI* with eq. ( 4) is increased by its standard deviation.
4) Grain boundary influence on S In the" case of measuring S of polycrystal with auto-stage of SEM, the value of S is influenced inevitably by grain boundary.The example of grain boundary influence on ECP of polycrystal annealed sheet is shown in Figure 12.In ECP at grain boundary or triple point, two or three images of ECP of the grains bordering each other were mixed.The grain boundary influence on S of polycrystal annealed sheet is shown in Figure 13.The decrease of S value by mixed ECP at grain boundary or triple point could be estimated about 20% to the average value of S of the grains bordering each other.The relative value of 20% can be considered as the error of S value by grain boundary influence.Figure 11 Relation between sharpness of ECP (S) and sharpness of first-order pseudo-Kikuchi line (S1).Specimen Fe-3.25%Si alloy polycrystal annealed sheet and cold rolled sheet at the midplane.
S1-'the mean value of ideal sharpness of first-order pseudo-Kikuchi line of randomly oriented specimen.

5) Strain of polycrystal by deformation
The influence of strain by cold rolling on SI* and FWHV of polycrystal is shown in Figure 14.In this case, SI* was calculated by e.q.(4) with S value.The SI* value was decreased remarkably by 1.5% cold-rolling reduction and, then, it was decreased gradually with increasing the strain in the cold-rolling reduction range from 1,5% to 15%.On the other hand, FWHV was increased gradually in the cold-rolling reduction range less than 15%.

' 50urn
Figure 12 Influence of grain boundary on ECP.Specimen Fe-3.25%Si alloy polycrystal, a, b, c, d, e ECP at A, B, C, D, E respectively, f ECC. Figure 13 Influence of grain boundary on sharpness of ECP.Specimen Fe-3.25%Si alloy polycrystal annealed sheet.S sharpness of ECP.SGa the mean value of S of two or three grains bordering each other.S10 the mean value of ideal sharpness of first-order pseudo-Kikuchi line of randomly oriented specimen.Figure 14 Influence of strain by cold rolling on sharpness of first-order pseudo-Kikuchi line and FWHV (200) by X-ray at the midplane.Specimen Fe-3.25%Si alloy polycrystal.SI* relative value of sharpness of first-order pseudo-Kikuchi line.
The influence of strain by tensile deformation on SI* of polycrystal is shown in Figure 15.The SI* value was decreased remarkably by small strain and, then, it was decreased gradually with increasing strain to 15% elongation.6) Relationship between tensile stress and $1" The example of the relationship between tensile stress and SI* value of polycrystal is shown in Figure 16.The square root of SI* value was decreased linearly as the tensile stress was increased.The square root of the dislocation density of the specimen is proportional to the tensile stress (e.g.Basinski, 1964).Accordingly, SI* value is thought to be decreased as the dislocation density is increased.
Strictly speaking, the blurring of pseudo-Kikuchi lines in ECP by dislocation depends on the lattice plane and crystallographic direction in relation to dislocation lines.In addition to the dislocation density, the sharpness of pseudo-Kikuchi lines in ECP depends on the type and distribution of dislocation (Kaczorowski et al., 1991).Therefore, SI* value might be influenced not only by the dislocation density, but also by their type and distribution.However, based on the relationship between the dislocation density and the tensile stress (e.g.Basinski, 1964), Figure 16 is thought to suggest that SI* value can be decreased as the dislocation density is increased.Tensile stress., t/rMPa Figure 16 Relation between tensile stress and sharpness of first-order pseudo-Kikuchi line at the midplane.Specimen Fe-3.25%Si alloy polycrystal.SI* relative value of sharpness of first-order pseudo-Kikuchi line.Changes in sharpness of first-order pseudo-Kikuchi line, fraction recrystallized, Vickers hardness and FWHV (200) by X-ray at the midplane during heating at a rate of 20 K/s after 88% cold rolling.Specimen Fe-3.25%Si alloy polycrystal.$1" relative value of sharpness of first-order pseudo-Kikuchi line.

7) Decrease of strain during recrystallization
The changes in SI*, Vickers hardness and FWHV of polycrystal during heating stage after 88% cold rolling are shown in Figure 17.The SI* value was increased remarkably during recrystallization.On the other hand, Vickers hardness and FWHV were decreased gradually during recrystallization.The increase of Sl* value during recrystallization is thought to be caused by the decrease of dislocation density.

CONCLUSIONS
A method for measuring strain by analyzing sharpness of ECP with Image analysis has been developed.The SI* value in ECP is used as a parameter of strain.Fe-3.25%Si alloy single crystal and polycrystal were used as test specimens.Strain change during deformation and recrystallization was analyzed by this method.This method was compared with the conventional methods; hardness and line broadening of X-ray.The main results obtained are as follows.
1.The SI* value decreased with increasing strain in the specimen.This method can be used for measuring strain in material with any crystal orientation.This method could be useful for measuring strain less than 15% cold-rolling reduction or 15% elongation.Its sensitivity for small strain was larger than that of line broadening of X-ray.The SI* value was influenced by crystal orientation before deformation, especially, in the case of smaller strain.This phenome.noncan be considered to be caused by the accumulate strain dependence of the crystal orientation before deformation.The SI* value was increased during recrystallization.In addition, the change of SI* value during recrystallization was more distinguished than both that of hardness and that of line broadening of X-ray.The SI* value can be considered to decrease with increasing the dislocation density in the specimen.2. It is thought that this method can be useful for analyzing crystal orientation dependence on accumulated strain, decrease of strain during recrystallization and inhomogeneity of strain in the the grain or near the grain boundary.

Figure 4
Figure 4 Distribution of ideal sharpness of first-order pseudo-Kikuchi line of Fe-3.25%Si allo specimen.(a) The mean values of Slo/S1 in each Box. (b) The distribution of the mean values of

Figure 15
Figure15Influence of strain by tensile deformation on sharpness of first-order pseudo-Kikuchi line at the midplane.Specimen Fe-3.25%Si alloy polycrystal.SI* relative value of sharpness of first- order pseudo-Kikuchi line.
Figure17Changes in sharpness of first-order pseudo-Kikuchi line, fraction recrystallized, Vickers