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Using this type of grain boundaries with different misorientation angles, we can estimate the number of excess charges given by one grain boundary dislocation.
The number of trapped electrons can be roughly estimated using a simple DSB model from the maximum value, αmax, of the non-linear coefficient using the following equation, drkTN QS kT S εε φ α 0 22 0 2 max 162 == 10 -2 10 -1 10 0 10 1 10 -5 10 -4 10 -3 10 -2 10 -1 VOLTAGE / V CURRENT / A (a) (b) (c) 1 1.5 2 2.5 3 2 2.5 3 3.5 4 NUMBER OF DISLOCATIONS / 106 cm -1 NUMBER OF TRAPPED ELECTRONS / 1013 Fig. 4 Current-voltage relations taken from (a) 2°, (b) 4°, and (c) 6° boundaries.
Figure 5 shows a plot of the number of electrons as a function of dislocation density estimated from the three low angle boundaries.
In the figure, the number of electrons increases with misorientation angles.
By calculating a ratio of the increment of respective values, i.e., the number of electrons and dislocation density, we can estimate the number of electrons related to one grain boundary dislocation having a unit length.

Analyzed the grain size and grain boundary length of low carbon steel by EBSD technique.
The results showed that: the grain refinement increased the number of initial solute carbon atoms and the effect of movable dislocations pinning by carbon.
The grain size and total length of grain boundary were detected by EBSD.
Grain Size and the total length of the grain boundary are shown in Table2.Obviously, the grain size of B is bigger than A.
With increasing the grain size, the total length of the grain boundary decreases.

While these alloys alone are coarse grained, a dispersion of Ti(N,O) particles achieved a fine-grained microstructure.
The number in each image represents the volume fraction of particles obtained by image analysis.
It should be noted that a small number of equiaxed grains were found in Fe-2at%Ti.
The numbers at the lower right of the images in Fig. 1 indicate the volume fractions of the dark particles obtained from image analysis.
As a result, these oxides are not efficient for grain refinement of the ferrite grains.

When compression percentage is 2%, slip system A3 is active in grain 2, and dislocation patterning starts due to accumulation of dislocation (a) Grain 1 (b) Grain 3 Figure 8 Distributions of crystal orientation Initial loading direction [001] [100] Initial loading direction [001] [100] Figure 7 Distribution of induced grain boundary whose misorientation angle is larger than 10° (a) U/L=1% (b) U/L=10% (c) U/L=40% (d) U/L=65% Figure 6 Distributions of total dislocation density (0µm-2 30000µm-2) 0 10 20 30 40 50 60 0.000 0.010 0.020 0.030 0.040 0.050 Compression percentage [%] Number of grains Slip rate 1 2 3 4 5 6 0 Number of grains Slip rate [s ]-1 0 10 20 30 40 50 60 0.000 0.005 0.010 0.015 0.020 0.025 Compression percentage [%] Slip rate [s ] Number of grains Slip rate 1 2 3 4 5 6 0 Number of grains -1 (a) Ultrafine-grained area A (b) Normal area B Figure 9 Evolution of slip rate and number of grains on the conjugate
When compression percentage reaches 65%, a part of the subgrain wall grows into DDWs remarkably in grain 1 in which a larger number of slip system is active than the other grains.
Figure 9 shows the slip rate of active slip systems and the number of grains induced by deformation for the areas A and B represented by two circles in Fig 1.
In Fig. 9, black lines and gray line show the average of slip rate on each slip system and the number of induced grains, respectively.
While, number of active slip systems is small in grain 3 whose normal directions are almost in the initial triangle.

Based on the experimental number, the corresponding austenite grain growth kinetic model was formed.
Since the total grain size is constant, an increase in the average grain size means that some grains in the matrix will disappear.
With the free energy of the grain boundary interface as the driving force, the grain boundary migrates and the grain grows up [9].
The number of fine grains is small, the large grains swallow the small grains, and the austenite grain size increases obviously.
Acknowledgments This work was financially supported by Key R&D plan of Shandong Province in 2019 (item number: 2019JZZY020238).

This is evidenced in the growth of the number of papers published containing results obtained by OIM (see Fig. 1.)
Thus, the recent increase in papers over the last few years may be even greater than shown in Fig. 1. 0 50 100 150 200 250 300 350 400 1980 1985 1990 1995 2000 2005 Year Number of Papers EBSD Papers ICOTOM EBSD Papers Figure 1 - Number of EBSD related papers published over the past 20 years.
In later scans, the two grains coalesce and appear as the same contiguous grain.
Figure 8 shows a grain map where the grains are shaded to show morphology.
While the studies performed provide some insight it should be noted that the number of grains and grain boundaries characterized do not constitute a statistically significant sampling.

Material For this study we used a 2 dimensional, columnar structured Al foil (Fig.1); a material that has been used for a number of grain growth studies as the geometry of grains is much simpler than that of 3 dimensional polycrystalline aggregates.
Grain reconstruction and grain size determination We used the standard procedure of grain reconstruction available in the Channel 5 software (HKL Technologies, Denmark).
(2) detection of grains; to detect grains the user defines a critical misorientation angle α'.
It should be noted that the number of grains detected using the EBSD analysis technique is in most cases below 2000 grains.
Here the slope is generally smaller. 250 Table 1 Grain size measurements according to optical and EBSD analysis; N signifies number of grains.

Stress amplitutes were 45, 56, 68 MPa, and all tests were terminated when the number of cycles reached 10000.
Precise observation by SEM revealed that a number of fine cracks initiated transgranularly in the vicinity of the 5.3º(Σ 1) grain boundary.
The number of passing dislocations across the grain boundary could affect the susceptibility to intergranular SCC.
Yamashita et al. [1] pointed out that the number of the passing dislocations increases when the misorientation becomes lower than 15 to 20 degrees.
In addition, dominant mode of transgranular fracture in the small angle boundaries could be attributed to the large number of passing dislocations.

Recrystallized Grain Size Distributions.
Fig. 3 clearly shows that recrystallized median grain size generally decreases with increasing flow stress and 0 5 10 15 200.0 0.1 0.2 0.3 natural strain (εεεε) flow stress [MPa] p40t109 dry all: strain rate ~5x10 -7 s -1, T=125°C calculated: p40t109 + solution-precipitation p40t114 wet p40t111 wet p40t112 wet p40t115 wet bb a Journal Title and Volume Number (to be inserted by the publisher) 5 2.0 2.1 2.2 2.3 2.4 2.5 2.60.8 0.9 1.0 1.1 1.2 1.3 1.4 log stress [MPa] log median grain size [µµµµm] 100°C 125°C 150°C 175°C 200°C 240°C -0.98 -1.71 -1.24 -1.64 -1.22 -1.99 temperature.
Typical slopes of adjacent points are indicated (numbers).
Strain rate contours for -7 < ε&log < -4 are indicated by thin solid lines (numbers).
Journal Title and Volume Number (to be inserted by the publisher) 7 [12] R.C.M.W.

The PGA may be categorized into three different basic approaches: master-slave, fine grained and coarse grained.
As a multi-population approach, the coarse-grained PGA divides the initial population into several subpopulations (demes) according to the number of processors.
In other words, if the total number of individuals and processors are defined as pop_size and, so the coarse grained model consists of subpopulations that own pop_size/ individuals, and the individuals of each subpopulation evolve independently through generation process.
It can be an integer or a percent commonly describing the number or rate of migrated individuals each time.
This situation may result from the fact that the communication cost will increase with increasing number of demes.