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However, most of the initial microstructures [10, 11] used for simulation are equiaxed grains, which could not correctly reflect the effects of the shape of the deformed grain on the dynamics of recrystallization and grain growth.
The centers and the radii are derived independently from pseudo-random numbers.
The ordinary Voronoi model can generate equiaxed grains as initial microstructures for MC grain growth simulation.
The grain size distributions are similar and follow lognormal function.
Grest, Computer simulation of grain growth – II . grain size distribution, topology, and local dynamics, Acta Metallurgica. 32 (1984) 793-802

It is shown that dielectric properties of these materials may be modified by a combination of different BTS powders as well as layers number.
Combinations of powders were 0-15, 2.5-15, 7-15, 2-7-10-12 and 2.5-7-10-12-15 (numbers designate mol% of Sn in BTS).
BTS ceramics have been electrically studied as a function of temperature, Sn contents, as well as a function of number of layers.
The grain size is between 20 and 40 µm.
There is an obvious difference in the grain shape between barium titanate sample (polyhedral grains) and BTS ceramics (spread and burst grains).

The number of primary Si increases obviously and the average grain size of primary Si decreases largely, less than 50μm.
Also the number of the primary Si particles increased significantly and the average grain size of primary Si decreased substantially(shown in Table.3）.
This is because that a large number of AlP compound had formed in Al-Fe-P master alloy, which has a lower melting point.
So the average grain size of primary Si maintains 40μm or less in 5 hours.
The number of primary Si increases obviously and the average grain size of primary Si decreases less than 50μm respectively.

Accordingly, a slightly reduced twin volume fraction, but an increased number of smaller twins was observed after compression in the aged samples.
This has enabled a greater number of twin/particle interactions to be studied over a large area than using transmission electron microscopy.
Moreover, particles decorating the grain boundaries are present in in both aged specimens.
The average grain size values are included as insets in the OM micrographs.
The number of twins per unit area of the three samples was also calculated by counting manually the number of twins on several SEM pictures.

The largest grain size is less than 50μm and the smallest grain is about 10μm.
Small grain is the growing recrystalized grain, but the growing is not enough.
It also promotes the grain growth along different orientations because of the larger number of meta-crystal orientations in the shear zone.
Grain growth is due to the grain boundary migration process where the boundary of the growing grain migrate toward outside.
However, only the grain with highest grain boundary migration rate grows fast and the grain with slow grain boundary migration rate will be consumed.

There are only a few dynamic effective grains and a large number of redundant grits, which can not only increase the cost of the tool and a waste of abrasive resources, but also will cause a high grinding temperature and make the inclusive chip space of the grinding wheel decreasing.
According to the theory above, each grain on the surface of the grinding wheel can be seen as a seed, with the method of photolithography and electroplating, and using UV photosensitive dry film as a mask layer, an electroplating grinding wheel with abrasive phyllotactic configurations can be made [5].Then using same method, the grinding wheels with other configuration were also done, and the grain number per unit on the grinding wheel surface keeps the same amount.
CBN abrasive size is 70/80 Mesh and the abrasive grain number per unit is 129.69/cm2.
(a) Photograph (b) Schematic diagram Fig 2 The experimental setup of grinding Experimental results and analysis As is shown in the Fig.3, for electroplating CBN grinding wheel, as the workpiece materials are removed by the grains, the abrasive grains are worn, the number of effective abrasive grains in the contact arc length of the grinding wheel will increase and reach a steady state, which make the grinding force is increasing and tends to be stable.
Fig 6 The influence of the depth of cut on the grinding force For ordering grinding wheel, the grain number of cutting material are increased and the grain number of rubbing and ploughing material are decreased in grinding contact region since the abrasive grains are reasonably arranged on the surface of the grinding wheel.

For the solution of this equations it is necessary to use the two kinds of kinetic parameters: the first one is the triple product hDs ~ of the segregation coefficient, of the grain-boundary diffusion coefficient and grain-boundary thickness and second one is the grain boundary mobility.
The calculation of the entropy production rate due to grain boundary diffusion and atom jumps through grain boundary.
We calculate the grain boundary energy between two grains of the same phase with different compositions according to Pines [26]: ( ) constczczc +−⋅= 2 0 0 ))(()( γγ , (18) where A m ss Nz Vg zn 2 0 =γ , sn is the number of atoms in the interface unit, 3=sz is the coordination number of atoms in the grain boundary, 12=z is the coordination number in the grains, and AN is Avogadro constant.
In this approach sszn is considered to be the number of broken bonds between atoms in the grain boundary in comparison with the bulk structure.
(21) The first term in the square bracket corresponds to differences in the structure between the grain boundary Sn precipitation and grain Sn precipitation.

The microstructure is homogeneous, the average grain size of the matrix was ~1.2 mm, the average size of the second phases or precipitates which homogeneously dispersed within grains was <50 nm, and the size of the precipitates observed at grain boundaries was ~0.25 mm.
（1） where n is the total number of valid fatigue tests, m is the number of stress levels, is the maximum stress at i level, is test number at i stress level.
Effect of fine-grain strengthening.
It is well known that grain boundaries can strengthen the metallic materials, and the yield strength of an alloy with fine grain size is higher than that with coarse-grain structure.
Crack can propagate more easily through the coarse-grained structure, so the fine-grained alloys have higher fatigue limit.

The contribution of each element in the spectral analysis is normalized into a single number in term of the carbon equivalence to indicate the hardenability.
It consists of ferrite and pearlite grains.
A gradation in grain size beginning with large grains at the top to smaller grain sizes at the bottom of the weld zone is observed in all the multiple welded samples.
The grains of the microstructure progressively become finer as the number of runs increases and coarser as the interpass time increases.
It has been shown that the fusion zone and heat affected zone hardness decreases as both the number of weld and interpass time increases.

Some grains contain annealing twins.
The numbered white boxes show the areas for detailed microstructure analysis presented in Fig. 3.
Figure 3 shows SEM images obtained from different areas of the weld (these areas are indicated by numbers in Fig. 2).
In area #1, a fine-grained microstructure with an average grain size 2.0±0.8 μm is formed after friction stir welding.
The contrast suggests that the particles were enriched with elements with high atomic number.