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�umerical Models and Results Observation of Grain Boundary.
In order to investigate the transition of the number of lattice defects during the deformation, the number of atoms with centro-symmetry parameter greater than 0.25 for each entire model region is plotted in Fig. 5.
Although large variation of the number of defects is observed, we can detect the several regions showing the almost constant number of defects after 100000step (after the plastic deformation).
While the number of defects in the model 2 - 4 increases more smoothly than model 1.
Change of the Number of Defects

Such a computing mode of grain growth is in good agreement with practical situations of ceramic grain growth.
Moreover, each process gets an exclusive ID (rank), numbered from 0 at the beginning of running an MPI program.
After growth times exceed 400, the total number of atoms is nearly kept at a stable level.
Sp = Ts/Tp (1) fp = Sp/p (2) where p is the number of nodes, Tp is the time in a PC cluster and Ts is the time in a single PC.
Thus, with an increasing number of PCs, the evolution of grain growth is greatly accelerated and the time for the parallel simulation is significantly reduced.

The fact that grain boundary diffusion (GBD) decreases under the action of grain boundary segregation (GBS) is now generally recognized.
Note here, that NGB is unknown number, and the data are obtained for all atoms in the model, including the grains.
Hence, due to the complexes formation the number of mobile atoms decreases.
Rodin, Grain Boundary Diffusion and Grain Boundary Segregation in Metals and Alloys.
Rodin, New model of grain boundary segregation with formation atomic complexes in grain boundary, Phys.

Based on Cellular Automata method, combining the laboratory triaxial tests of coarse-grained soil developed the HHC-CA model which generated the coarse-grained soil samples of different initial fabric of grain to characterize the heterogeneous and random distribution of coarse-grained soil grain group.
When the cellular state was zero, the total neighbor cellular numbers with similar state will be calculated.
Num_1 is representative of the total number of neighbor cellular whose state is 1, Num_2 is representative of the total number of neighbor cellular whose state is 2.
To compare Num_1 with Num_2, the central center has the evolution trend to the cellular of big number, its probability of evolution is Max (Num_1, Num_2) × 0.125.
For obtaining the gravel contents of shear band, the article generated the total cell N (the HHC-CA model unit numbers) and displayed the ID number of grid to use the FLAC3D in the triaxial simulation test, and then inducing the producing grid image into Autocad and setting the shear band.

The grain size is enlarged with increasing Bi addition; while the number and size of the pores are decrease.
Further increase in Bi addition up to 1 mol % (S3) leads to the following; slight increase in the grain size, the average size of the white batches decreases, while the number of these batches increases.
In case of higher Bi content S2, S3 the probability of reaction (1) decreases to avoid large number of the negatively charged V"zn and instability of the grain, while the probability of the following reaction (2) increases.
The decrease of Eo is attributed to the decrease in the number of grain boundaries as a result of increasing the grain size Fig. 2.
Consequently the decrease in the number and size of the pores with Bi addition means decrease in the amount of the liberated oxygen, so probability of reaction (1) and the number of V"Zn.

However, for the case of the thin film sample, the larger number of triple junctions allowed a more detailed analysis to be performed.
The resultant system of linear equations for all the triple junctions in the dataset is solved using a statistical multiscale method, described in detail elsewhere.[4-7] For the cube-textured Al foil, the number of triple junctions analyzed was 297.
This reduced the number of triple junctions analyzed from 8694 to 7367.
Table 1 - Annealing time, mean grain size (equivalent circular diameter), standard deviation in grain size, and number of grains measured for 100 nm-thick Al films annealed at 400 °C.
Support from the MRSEC program of the National Science Foundation under award number DMR-0079996 is gratefully acknowledged.

However, the intensity of shear texture components decreased with increasing number of ECAR passages.
Observations by TEM and EBSD revealed that the degree of misorientations within the deformed grains increased with increasing number of ECAR passages.
The annealed sheets comprising of ultra-fine grains were successfully produced in the samples deformed by a large number of ECAR passages.
The new isolated grains developed frequently at prior grain boundaries.
With increasing number of ECAR passages, the further decrease in grain size was not pronounced.

A large number of studies have been realised concerning the stabilisation of nanocrystalline grain structures in many materials and the number of factors influencing the grain boundary mobility in nanocrystalline alloys, like grain boundary segregation, solute drag, pore drag, second phase (Zener) drag and chemical ordering.
The high number of observed grains makes statistical analyses possible.
Number and arrangement of the lattice points regulate only the accuracy of the calculations.
The high number of small grains implies also a high number of small triple junction distances (compare Fig. 3a).
The data of vs. x for all grains with a certain number of faces s show a strict linear relationship.

The larger size of island grains is their dominant characteristic, and grains which become island grains may have been incipient abnormal grains.
These grains grow excessively, consuming the matrix grains, resulting in a bimodal grain size distribution.
Of the total number of island grains observed, around 75% possessed either low angle (<20o ) or high angle (>45o ) grain boundaries.
The number of low and high misorientations observed at these island grain boundaries is therefore substantially higher than the number found in the uniform structure.
The existence of a number of island grains with mid-range misorientations (20 o -45o ) to the abnormally large grain may be explained by the presence of a Σ5 (36.9 o <100>) boundary misorientation.

A number of deformation microstructure maps are developed to aid the discussion.
There are now a large number of research groups and approaches [1-24].
Having said this it must be noted that a number of factors intervene to cause the grain size in reality to exceed the values of those predicted from simple analyses such as those presented here.
Figure 3 shows the time to 50% softening as a function of strain for a number of different steels and deformation conditions.
Figure 4: Variation of average recrystallized grain size for IF grade with strain at s/1=ε& and 900°C Dynamic Strain Induced Transformation A number of groups have shown the potential for dynamic strain induced transformation to refine the grain size to around 1µm.