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The specimens of 3 and 4 passes ECAE have extremely fine-grained with 200-300 nm of the grain size.
The hardness of ECAE processed Al-3%Mg alloys increased with increasing the number of passes and finally reached up to 150 HV at 4 passes.
The relationships between the grain size, dislocation density and the number of passes of Al-3%Mg alloy were shown in Fig. 2.
The grain size decreased with increasing the number of passes until 2 passes.
On the other hand, the Figure 1 IPF maps of ECAE processed Al-3%Mg alloy dislocation density, of course the hardness, increased with increasing the number of passes beyond the microstructure was saturated.

The total number of atoms was 5,103,926.
This is less than the number that would be present in a single crystal of this volume due to the lower density of atoms at the grain boundaries.
This provides a computationally efficient way to estimate the average grain size at a given time by simply counting the number of non-crystalline atoms.
The most obvious feature is that there are a significant number of twin boundaries in the system.
It is also observed that vacancies and a large number of twin boundaries are produced during the growth consistent with recent experimental observations.

Diffusion in an Ensemble of Intersecting Grain Boundaries A.N.
Grain boundary (GB) diffusion in an ensemble of three grain boundaries intersecting in the point of GB triple junction is described on the basis of quasi-steady Fisher’s model.
Two versions of the configuration of the ensemble are considered, namely, with different number of GBs adjacent to the surface covered with a diffuser source and with different angle between GB and surface.
It has been found that Zn diffuses along TJ lines in a coarse-grained aluminium with a columnar grain structure much faster than along GBs that form a TJ line [6, 7].
There are, however, a number of diffusion problems where a triple junction manifests itself as a singular point of space where the diffusion fluxes along GBs intersecting in TJ point merge or separate.

On the other hand, the calculation domain must also contain a large number of grains in order to obtain statistically reliable results.
Similarly, it has been shown ‎[12] that for 3D grains the number of neighbours is on average close to 14.
To keep a sufficient number of grains in the domain, simulations were repeatedly interrupted to rescale the domain size, number of grains and grid size.
This technique effectively reduces the numerical cost of the 3D simulations while maintaining a statistically significant number of grains in the calculation domain.
Figure 4 -Variation of with number of grains in the simulation domain at the various simulation stages with different grid sizes, dx, for the grain growth case shown in Figure 2 a.

Figure 6 shows the stress-strain curve of the cemented coarse-grained soils and the coarse-grained soils.
Additional, the residual strength of the cemented coarse-grained soils are very close with that of the coarse-grained soils because the cemented coarse-grained soils material become similar to the coarse-grained soils material after all cement bonds broken.
Microscopic mechanism analysis Fig. 7 presents the cumulative number of cracks during the loading process.
The added number of cracks reached the maximum when the strain reached 1.5% ,which was the strain corresponding to the peak stress, and the number of cracks produced in the unite time reduced gradually until it reached a constant value.
Fig.9 shows the energy stored in the parallel-bond, it has the same evolution as the number of cracks.

The position of the 6 nuclei (also shown in Fig. 1) is marked by numbers in (b).
In Fig. 5 is the number of neighbors for each grain in the initial condition plotted versus the grain volume.
Number of grain neighbors for all grains in the initial condition (see Fig. 4a).
The number of neighbors increase with grain volume largely as should be expected theoretically [22].
The figure further shows that also the number of neighboring grains does not seem to explain which grain will grow.

Finally, the mean grain size and the fraction of high angle grain boundaries were determined as a function of the number of cycles.
To characterize the formation of ultrafine grains, the evolution of both microstructure and texture has been analyzed by EBSD and the microhardness measured, as a function of the number of ARB cycles.
Fig. 3 illustrates the results obtained for the mean grain size and the fraction of HAGB as a function of the number of ARB cycles.
As the number of cycles increases, the average grain size decreases, reaching a value of 580 nm for n = 7, and the fraction of HAGB increases, reaching a saturated value after 5 cycles.
Fig. 3: Evolution of the mean grains size and the fraction of High Angle Grain Boundaries (HAGB) as a function of the number of ARB cycles n.

Therefore, the properties of polycrystalline materials strongly depend on the number, the structure as well as the character of the grain boundaries.
The fractions of grain boundaries of different types were determined in terms of the length fraction by dividing the number of pixels of a particular boundary with that of the entire grain boundaries [11].
And the maximum number of grains was obtained in the stage of complete recrystallization.
The absolute number of the low-Σ boundaries in the recrystallized specimens increased due to the number of grains multiplied.
Moreover, a large number of random boundaries and low-Σ boundaries were both generated, the number of random boundaries increased faster than the low-Σ boundaries during the recrystallization stage.

Sulphides may show a different value of the contact angle within individual grains, which is probably caused by heterogeneity of particles [7].
Each sample was grinded on a LaboPol-21 grinder (Struers, USA) by a rotating abrasive paper with a grit size of 600, 800, 1200 and 2500 (number of grains per inch) under running water, followed by polishing on a Phoenix 3000 (Buehler, USA) by a fine textile polishing cloth using aluminum paste without ultrasonic cleaning of the surface after each step.
Compared to the other pyrite samples, the areas of pyrite grains were much smaller and surrounded by other minerals.
The number of outliers, arithmetic mean and standard deviation for each deposit is given in Table 2.
The number of outliers in the whole set for a given type of genesis deposit did not exceed 4%.

The initial grain was about 200µm.
(Phosphorus deoxidized copper) Number of Passes Strength (MPa) 10 20 30 40 50 60 Elnogation(%) Fig. 3 Tensile properties of oxygen free copper with respect to the number of ECAP passes.
Journal Title and Volume Number (to be inserted by the publisher) Results and discussion The microhardness as a function of number of ECAP pass was presented in Fig. 2.
Then, microhardness increases gradually up to 3 pass and saturated with further number of pass.
A large number of dislocations are observed within these bands.