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(a) Inverse pole figure (IPF) image obtained from the primary recrystallized sample of Fig. 1(b), (b)-(e) separation of representative grains from the IPF image of (a) such as (001), (011), (111) and (113) grains, respectively, and (f)-(k) number fractions as a function of misorientation angle between two different grains, respectively To understand the role of grain boundary character distribution associated with misorientation angle on selective grain growth, we selected (001), (011), (111) and (113) grains developed from the primary recrystallization state prior to AGG in Fig. 1(b).
The inserted numbers on each histogram in Fig. 3(f)-(k) are the number fractions of the middle misorientation angles.
Both (011) and (113) grains are surrounded by boundaries with the middle misorientation angles, with high average number fractions of 69.5% and 66.8%, respectively.
The average number fraction of 69.5% for (011) grains is the highest number.
In contrast, the average number fraction of 39.8% for the (001) grain is much lower than the others, indicating the low mobility of (001) grain boundaries, and the (111) grain is intermediate (52.0%).

Evaluation of abrasive grain form V.S.
Table 2 Groups of grains Correlation l:b:h 1:1:1 1:1:0,33 1:0,33:0,33 Group of forms Isometric forms Disk – shaped forms Needle – shaped forms Among the disadvantages of qualitative methods of evaluation there is subjectivity of classification and evaluation of grain form by one projection only; whereas the grain itself is a three-dimensional object, loose definition of grain overall dimensions and a small number of groups which leave out of account all possible grain forms.
(6) There is a great number of methods to determine the coefficient of form and all of them include processing of the horizontal grain projection.
To prove this statement abrasive grain 13А100 was evaluated (sample number - 100 grains).
Тable 5 Classification results Group of forms Grade of an abrasive 13А125 13А100 13А80 Content of form group, % Isometric 9 3 3 Flattened 27 22 14 Disk-shaped 3 7 10 Lengthened 14 16 17 Intermediate 40 36 36 Broad disk-shaped 4 10 14 Sward-shaped 3 3 2 Narrow disk-shaped 0 2 3 Needle-shaped 0 1 1 Table 5 demonstrates that the graininess of an abrasive influences on the distribution of grain forms, moreover, the percentage of grain forms is subjected to graininess number.

Results show that a large number of fine ZrB2 particles were observed in the Al-5Zr-1.1B grain refiner and the ZrB2 particles could act as the heterogeneous nuclei of α-Mg grains.
It reveals that there are a large number of fine ZrB2 particles in the Al-5Zr-1.1B grain refiner, as shown in Fig.1 (b).
In the present work, when the Al-5Zr-1.1B grain refiner is added into the AZ91D melt, a large number of ZrB2 particles are dispersed into the AZ91D melt.
The more the addition amount of Al-5Zr-1.1B grain refiner is, the more the number of the α-Mg crystal nucleus are, thus the refiner the α-Mg grains of AZ91D magnesium alloy is.
The Al-5Zr-1.1B grain refiner consists of a large number of fine ZrB2 particles and the ZrB2 particles can act as the heterogeneous nucleus to refine the α-Mg grains.

Castings were examined at the grain scale for determination of the grain size as well as the number.
Number of FE nodes in casting is 1635798.
Comparison of the grain number and mean radii of the grains between calculated and measured are shown in Figure 4.
At the surface of the chill, the number of the grain forming randomly is order of 104.
At the helix selector part, the number of the grain is about 100 and the mean radii of grains is about 0.7mm.

The probability to find a growing grain is proportional to the number of grains per unit volume.
The rate of self-annealing depends on a number of deposition and post-deposition parameters including electrolyte composition, current density, film thickness, seed layer texture, substrate morphology and annealing temperature [1-6].
Journal Title and Volume Number (to be inserted by the publisher) 3 Table 1: As-deposited grain size and characteristic annealing times I [mA/cm2] Bath d0 [nm] t50 [h] ∆ρ [%] 10 A 54 20 21 20 B 82 65 21 7 A 106 137 19 5 A 120 no self-annealing observed 3.5 Model Stage I.
It can be speculated that there are a number of contributing factors including a decrease in point defects, i.e. vacancies and impurities, and other structural defects as well as limited normal grain growth.
The probability to have a growing grain is proportional to the number of grains per unit volume in the untransformed region, i.e. 3 0/ dP κ= (7) where κ is a geometrical factor.

The number density of TiB2 particles added by Al-1.54TiB2 for each sample is equivalent to the TiB2 particle number density of 0.2wt% Al-5Ti-1B (106/cm3).
CP-Al had a coarse columnar grain structure (Fig. 1a), while CP-Al inoculated with both Al-5Ti-1B and Al-1.54TiB2 grain refiners (with the same particle number density of 0.2wt% Al-5Ti-1B grain refiner) show a fine and equiaxed grain structure (Fig. 1a-1c).
Fig. 3 shows that, with the same TiB2 particle number density, CP-Al always has fully equiaxed grain structure when there is no extra free Ti added.
All the samples have the same TiB2 particle number density, which is equivalent to addition of 0.2wt% Al-5Ti-1B grain refiner.
St John, An analysis of the relationship between grain size, solute content, and the potency and number density of nucleant particles, Metall.

The total numbers of nucleation sites were 17580 (586x30).
Variation in the distributions of the number of face, Nf, for individual grains of the simulated microstructures at different time step is shown in Fig.4.
Figure 5 shows variation in the average face number with time.
6WD�H� P ���� 6WD�H� P ����The relationship between the average number of faces of grain adjacent to an N-faced grain, m(Nf), and the face number in grains, Nf, is shown in Fig. 6.
(3) The distributions of the number of face, Nf, for individual grains is also time-dependent.

Of course, grains will only have integer numbers of faces.
They found a wider range of the number of faces per grain.
Other grains with r = 3 but fewer than 41 faces will decrease in relative size, as required since the number of grains with r = 3 must fall with the fall in the total number of grains.
Table 1 Mullins analysis for grain coarsening as a function of number of grain faces, µ.
A loss of 20% of the number of grains will cause the equivalent increase in mean grain volume and give a 6% increase in .

Grain Boundary Segregation versus Precipitation in Grains.
Smirnov 1 Keywords: Grain Boundaries, Segregation, Grain Boundary Segregation Phase, Phase in Grain.
Due to Gibbs phase rule the number of degrees of freedom (DF) for binary polycrystals is equal DF = K + 3 - PH (4) Where K and PH is the number of components (K = 2 for binary systems) and phases, and 3 follow from the number of independent intensite parameters: T, P and γ[2].
The solubility attained, the phase in grain appears.
As pointed out above, 0 b X is an available number of sites in GB or a saturation value of b X .

As a result, the number and length fractions of incoherent Σ3s increases more than coherent twins.
Note that the number fraction increase of Σ3 grain boundaries is larger than the length fraction increase because, as shown in Table 1, the Σ3 grain boundaries resulting from the GBE process have, on average, less area than the pre-existing Σ3 grain boundaries. 0 10 20 30 40 50 60 70 80 90 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Ni ref deviation angle,* boundary fraction (of total) Ni GBE Figure 1.
The second is to decrease the concentrations of the other, random boundaries, while simply maintaining roughly the same number of Σ3 boundaries.
In other words, while the grain boundary engineering process does create additional Σ3 boundaries, it is also effective in reducing the numbers of non- Σ3n boundaries.
Acknowledgements The work at Carnegie Mellon University was supported primarily by the MRSEC program of the National Science Foundation under Award Number DMR-0520425.