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Analytical Grain Size Distribution Grain microstructures obtained by curvature-driven normal grain growth can be characterised a mean grain size of the ensemble of grains changing with time according to a parabolic growth law.
The temporal development of the grain size for 17 different randomly picked grains is shown in Figure 2.
Figure 2: Temporal development of the grain size for simulation data and Eq. (7): a – randomly selected grains very well represented by Eqs. (7); b – grains showing only weak agreement with Eqs. (7).
Stochastic Motion of Individual Grains While the grain microstructure shows coarsening and the number of grains is reduced, stochastic changes in the lengths of the triple lines and, hence, a fluctuating quadruple point distance can be observed.
For reasons of a better illustration the 3D coordinates are plotted in projection in the y-z-plane and the associated x-coordinates are marked by numbers.

An original method is used for the construction of initial structures with GBs containing different numbers of EGBDs.
Taking the orientation of grain 1 as a reference, grains 3 and 4 are rotated to angles ±20° to form a symmetric high-angle tilt GB between them.
As an example, consider a deformation of grains 3 and 4.
The grain size of nanocrystals was set equal to 15 nm.
This stress induces oscillating shear stresses on the slip planes of grains 3 and 4 and zero stresses on the slip planes of grains 1 and 2.

As a measure of austenite grain size the mean chord length of austenite grains was assumed.
In this test the value of c2 was calculated using equation: (3) where ni and nei are the experimental and expected numbers of grains in the i-th category of chord lengths.
The variable c2 has a distribution with a degree of freedom equal s=k-r-1, where k is the number of categories and r is number of parameters describing distributions.
For freedom degrees number s=12 the critical value is equal c20,05=21,026 [13].
At temperature 1100oC there is below 10 % of grains with austenite grain chord lengths over 100 mm in B-V2 melt and 40 % in melt B-V1.

av.randle@swansea.ac.uk, bm.p.coleman@swansea.ac.uk Keywords: Grain boundary engineering, annealing twinning, grain growth control.
Grain Size Distributions in Grain Boundary Engineered Microstructures Table 1 is a collation of average grain sizes which have been included in a selection of recent reported GBE investigations.
Average grain size taken from recent GBE investigations Material Average Grain size Source (nm) Copper 12 Randle V. and Coleman M.
The crystallite size is hence smaller than the grain size.
The crystallite size was related to the number of Σ3 boundaries present.

The uniformity of the β grain size is determined by a grain ratio η = A1/A, where A1 is the number of the grains of which sizes are in the range of 0.6 ~ 1.4 D (D is the average β grain size) and A is the total number of the measured β grains.
Thus, the average grain size increases with the holding times, and at any particular instant there will exist a range of grain sizes.
The high value means the more high uniformity of the β grain size and the low value means the non-uniform β grain size.
That means that, the driving force for grain growth is a reduction in the energy which is stored in the material in the form of grain boundaries.
Generally it is said that the kinetics of grain growth are not influenced by the prior grain size (D0) and at longer time D0 term is negligible.

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.

Table 1 Chemical composition of the steel Chemical composition [mass.%] C Mn P S Si Al Nb V N 0.082 1.54 0.01 0.006 0.36 0.033 0.055 0.078 0.005 Journal Title and Volume Number (to be inserted by the publisher) 3 Results and discussion Three different possibilities for grain growth were explored in order to explain the preferential growth of the large grains: (i) transformation induced recrystallization; (ii) selective growth of specific orientations and (iii) growth advantage based on the fact that first nuclei grow first.
The grains larger than 10 µm and smaller than 3 µm were selected as representatives for the large and the small grains (cf.
The local misorientation between the large grains (grain 1) and the neighboring grains (2, 3 etc.) is measured between the marked points.
Journal Title and Volume Number (to be inserted by the publisher) 5 misorientation data between large and small ferrite grains.
The black line in Fig. 8 shows the grain size distribution of the ferritic grains at temperatures close to Ar3 and it is easy to be seen that the area fraction of the large grains is relatively low in comparison to the one corresponding to the small grains.

The Flow Behavior of Ultrafine-Grained Materials Terence G.
The processing of metals by SPD Ultrafine-grained materials are defined formally as polycrystalline metals having average grain sizes less than ~1 mm [10].
This means that UFG metals incorporate both submicrometer grain sizes of 100 to 1000 nm and true nanostructured materials where the grain size is <100 nm.
It is also apparent that the yield stresses increase with increasing numbers of ECAP passes.
Thus, the yield stress is lower after 1p than for the as-received material and it continues to decrease with increasing numbers of passes.

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.