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The number of lattice points in the FDM is 256 ×256, and nodes in FEM is 6156.
The number of nuclei decreaces with increase of number of additional elements.
Grain diameters are calculated on the basis of the number of finite element included in each recrystallized grain.
The number of grains whose diameters are less than 0.4 µm is biggest in the case of .
It is obvious that more additional elements keep grains from recrystallizing, and the number of recrystallized grains become smaller.

Accordingly, the predicted texture evolution depends on temperature, strain rate, chemistry (solute level, particle number and size), and grain size.
Thus, the recovery kinetics scale with the number of slip systems, NGLS, as developed by GIA.
For nucleation to occur, however, a critical number of active slip systems must be defined, and grains exceeding this number were assumed to recover fast and to form viable recrystallisation nuclei, whereas other nucleus orientations were deleted from the spectrum.
The numbers nrand, nGB and nTB can be directly extracted from the output of a GIA-3IVM simulation.
For more than 500 particles the number of nuclei per particle and their orientation were measured (Fig. 5) [42].

The grain site can be assumed one of those states, qgrain = [1, 2 …Q] where Q is the total number of all sites in the simulation space, and q represents the state of a grain site.
A random number, Rg, which is between 0 and 1, is generated.
While simulation, generate a random number, R, which between 0 and 1.
A random number, Ra, which is between 0 and 1, is generated at random.
The grain size R is defined as the radius of the equal-volume sphere of one grain, the surface of total pores is the summation of the number of grain neighbors of each pore site, and the surface of total grain boundaries is the summation of the number of grain neighbors of each grain site.

Before the ECAP process, the materials were annealed at 500˚C for 1hr (grain size: 100µm).
The average size of fine grains is about 250 nm.
Once this specific number of cycles had been exceeded, both the number and area of the damaged regions showed a significant rise.
The number and area of damaged regions including SBs slowly increased with further cycling up to a specific number of cycles, depending on the material and stress amplitude.
Once this specific number of cycles had been exceeded, both the number and area of the damaged regions showed a significant rise.

The microstructure was dominated by nearly equiaxed grains with mean grain size of ~0.9 mm and HAB fraction of 78%.
Importantly, the grains in the tensioned specimens had nearly equiaxed morphology and grain-size distribution was relatively narrow (Fig. 6a).
In contrast to stir zone material, the base material exhibited a duplex microstructure with a small number of large grains being surrounded by arrays of fine grains (Fig. 6c).
This perhaps means a small population of grains grew at a significantly faster rate than the other, “matrix” grains and thus the observed process seems to fit the definition of abnormal grain growth.
Acknowlegement The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.578.21.0097 (ID number RFMEFI57814X0097) is gratefully acknowledged.

The samples all exhibit uniform microstructures with equiaxial grains as shown in Table 1 Summary of microstructures, composition, and dielectric properties of the samples Sample Grain size (nm) No. of GB with NP* Ba/Ti Bi/Ti Sr/Ti εeff (x104) tgδ(%) T1 T2 T3 280 ±120 2300±925 290 ±140 - 49/204 35/229 0.071±0.084 0.106±0.010 0.147±0.085 0.012±0.006 0.012±0.005 0.011±0.010 0.940±0.110 0.892±0.044 0.872±0.093 4.2 39 37 23 5 3 * Given as ratio against the total number of observed GB.
However, significant grain growth happened in sample T2 compared to the sample T1 and T3 as indicated by the cumulative distributions of grain size in these samples (Fig. 1b).
The data of average grain sizes are also listed in Table 1.
The number of GB decorated with NP is different in the T2 and T3 samples: the percentage of such GB decreases from about 25% in T2 to 15% in T3, as also listed in Table 1.
McLean: Grain Boundaries in Metals.

The number and length of side crack increased with increasing Ca content.
As can be seen in the figure, the number and length of side crack increased with Ca addition.
On the other hand, the number and length of side crack increased with decreasing the preheating temperature and increasing the reduction ratio per pass.
Conclusion The number and length of side crack increased with increase Ca content.
The hot-rolled AZ31-xCa sheets had the equiaxed grains measured to 4∼8µm in average grain size.

Grain boundary is defined as in different number of grain orientation between two adjacent grid points.
When the grain orientation of two adjacent points at the same time, the number of phase can be thought of as the adjacent lattice as part of the same grain.
The number of conventional grain-oriented is 32 or 64.
If the number is infinite, there will be a very large amount of calculation, the cost of calculation will be very high.
In front of the MC simulation time step, the average grain size increases quickly with the increases of the simulation time step, number of grain declined sharply with the increase of time step.

The grain size was found to be increasing with the rise in temperature.
The bandgap was found to be increasing with decrease in grain size.
The Fourier transform infrared (FTIR) analysis was carried out by using Perkin Elmer Spectrum 100 series FTIR spectrometer in the wave number range of 4000-400 cm-1.
The variation of grain size with temperature is shown in figure 2.
That is, smaller the grain size, larger would be the bandgap.

One is “intragranular” grain, which exits in the alumina grain and the number is less.
The other is “intergranular” grain, which exits among the alumina grains and the number is larger.
One is “intragranular” grain[10,11], which exits in the alumina grain and the number is less.
The other is “intergranular” grain, which exits among the alumina grains and the number is larger.
One is “intragranular” grain, which exits in the alumina grain and the number is less.