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Results and Discussion The percentage results for certain grain orientations and grain size distribution for all grains in the matrix and particularly for the Goss grains are been shown.
Grains having diameter lower than 21μm will be called small grains, grains with diameter between 21 and 42 μm will be called medium grains and finally, grains having diameter higher than 42 μm will be named as large grains.
For the samples annealed without field, the number fraction of small grains decreased as the annealing time increased being 48.4% on sample O3 and 34.6% on sample O30.
For the magnetically annealed samples the number fraction of small Goss-grains increased with increasing in annealing time, principally from 3 and 15 minutes.
Comparing the development of the Goss-oriented grains in the samples annealed with and without field, after 3 minutes of magnetic annealing, the small Goss grains are in less number and their percentage increases with time becoming equivalent after 30 minutes.

Measurements were made on a statistically representative number of microstructural elements.
The deformed regions tend to have a large number of lowangle grain boundaries and there is a greater fraction of these at the higher strain rate (Fig. 3). 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 Strain Mean grain size, µm Non-deformed part Deformed part Fig. 1 left: EBSD maps for the deformed (strain: 0.9) and non-deformed regions of tensile specimen of the Al-4wt.
~3.33 hrs ~1.28 hrs 10-4 s-1 10-3 s-1 Non-deformed regions Deformed regions 225 µm 225 µm ND RD, σ In a number of works [6-10] dynamic grain growth was well-described using an exponential expression )exp(0 ελ⋅= DD , where 0D is the initial grain size and ε is the strain.
A number of works [11-15] have shown a similar effect after plastic strain, however, without particular relation to dynamic grain growth.
There is no doubt that behaviour of the second phase particles during deformation of an abnormally large grain structure cannot be absolutely the same as that in the presence of a large number of high-angle grain boundaries.

Coarse grains broke into fine grains, and grew into medium grains.
During rolling of the alloy, the time and number of slippages occurred are different for the difference of grain orientation, and the distribution of grain orientation as well [9-11].
In Table 2, the grain with the size less than 10 mm was defined as the fine grain, the grain with the size between 10 mm and 35 mm was defined as the medium grain, and the grain with the size more than 35 mm was defined as the coarse grain.
Grain size percentages of rolled 1235 aluminum alloy (%) Grain Grain size /mm 50 % hot rolling 90 % hot rolling Fine grain <10 30.03 92.16 Medium grain 10~35 28.53 7.84 Coarse grain >35 41.44 0 The percentages of fine grains, medium grains, and coarse grains were close in 50 % hot-rolled 1235 aluminum alloy, and the percentage of coarse grains was the largest by 41.44%.
Due to the different orientation of crushed grain blocks, there were a large number of dislocation tangles along the boundaries, which prevented the dislocation from further slipping and resulted in strengthened work hardening.

The average grain diameters as well as well as the ASTM grain size number (G) were analyzed.
The ASTM grain size number (G) of unalloyed samples were 2.4 while the Cr added samples showed an ASTM grain size of 2.6 to 3.7 and the average grain diameter varied from 151µm to 92µm.
(G) (e) Microstructure of 4 wt. % Cr Figure 2 shows the variation in the ASTM grain size number (G) of the various compositional microstructures.
The strain induced in the 4 wt. % specimen corresponds this reduction in the ASTM grain size number (G).
These particles refined the as cast grain structure as well as found to control the grain growth.

Namely, the new grains resulted from a progressive evolution of strain-induced grain boundaries, the number and misorientation of which gradually increased during deformation.
The new grains evolve in place of deformation subgrains, when the misorientations between subgrains attain values, which are typical of ordinary grain boundaries.
The new ultrafine grains appear at the frequently corrugated original grain boundaries and their triple junctions as well as at the deformation microbands.
Then, the rapid reduction in the grain size takes place in the strain range of 0.8 < e < 1.2 followed by a decrease in the grain refinement rate at larger strains.
On the other hand, a progressive increase in the misorientations among the uniform subgrain structure at high temperature results in simultaneous development of a number of the DRX grains at large strains.

However, the second phase particles would break off the grain boundary and the grain nucleus more or less during electrolytic polishing.
Furthermore, due to the 3D distribution of grains and nuclei in the samples, the polishing plane or the plane observed impossibility overpass all the grain nucleus, in this way, the number of the nuclei was finite.
If the C content was higher, the number of the TiC particles was larger and more efficient.
The more complex of nucleation and the nuclei the smaller grain
After the refinement of TiC particles, the number of the stable heterogeneous nucleation is not always increased.

In this paper, the initial state using point of saturated nucleation to produce the Voronoi mesh, let the nucleation rate is 0.1, the mesh size is 400 × 400 matrix, the simulation area is 2mm × 2mm, and the number of generated grain is 400 × 400 × 0.1 = 16000.
Figure 2 shows the simulation of grain structures with different simulation time steps, while Fig. 3 shows the number of grain size by the Linear intercept method count.
From the Fig. 2, it can be found that with the simulation time increases, large grains annexation small and the grains size become large, the number of edges grains tends to be 6, the shapes of grains tend to be hexagonal, in line with the Neumann-Mullins theoretical equation: (4) Where n is the number of edges grains, αn is the grain size, k is the diffusion constant [10].
Grain Growth Kinetics.
The small grain is annexed by large grains, which follows the principle of the decrease of grain boundary energy and the theory of grain growth.

Each site or voxel has its own number, Si that represents the crystallographic orientation at that location, so that if adjacent sites have the same number, they are considered to belong to the same grain.
The lattice site energy is given by the following sum over the sites: , (1) where nn is the number of nearest neighbors (26 for cubic lattice), J(Si, Sj) is the grain boundary energy, Si is the orientation of site i, and δij is the Kronecker delta function.
The number of sub-grain inside the near Goss grain was 1, 3, 5, or 7.
One sub-grain means that the near Goss grain contains no sub-grain boundaries.
Fig. 5 shows that the growth rate of the near Goss grain increases as the number of sub-grains increases.

As usual in the physical models aimed at a quantitative description of material transformations, there are a number of constants to be determined empirically [9].
A considerable portion of the volume is occupied by the largest austenite grains though their relative number is very small.
The distribution of grain numbers over grain size is recalculated into the distribution of the normalized volume over the grain size: ∫ ∞ ⋅ ⋅ = 0 3 3 )( 6 )( 6)( auauNau auNau auV dDDD DD D ρ π ρ π ρ
The integral distribution function Fv(Dau) shows that roughly 24% of the volume is occupied by the large grains with sizes larger than (+3 σD), whereas the number fraction of these large grains is negligible (1.5%).
suggestion that grain volume distribution is more meaningful than the number distribution.

We have developed a coarse-grain model (CG) for PMMA-b-PVP[6].
Using atomistic simulation technique to modeling the PMMA melts at meso-scale is still difficult nowadays because of the huge number degrees of freedom in the system.
A possible solution to this problem is to reduce the number of degrees of freedom through the mapping of an atomistic model onto coarse grained structures.
Fig. 1 Illustration of the coarse graining mapping schemes for PMMA.
Coarse-Grained Simulations The coarse graining mapping schemes for PMMA is shown in Fig.1.The Iterative Boltzmann Inversion (IBI) method is applied in this study to coarse grain the polymers.