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In this model, it is assumed that a huge number of defects are located at the grain boundary and these defects catch free carriers in the polycrystalline grains.
They were re-crystallized by ELA (XeCl, wave number: 308 nm, energy density: 460 mJ/cm2 x 5shots) at room temperature (RT) in a vacuum chamber.
The determination of the grain boundary in the TEM observation is not easy [13], but we decided that the grain boundary is the boundary between grains with different orientations.
(A) (B) insufficient to orient the poly-Si grains, so the stress might not be induced in the poly-Si grains.
In this model, a huge number of defects are located at the grain boundary, and these defects catch free carriers in the polycrystalline grains.

These superior mechanical properties of UFG rare metals can be studied under cyclic loading at very high number of cycles [14] with shear bands [15] forming.
It has not grains and grain boundaries (GB) also.
Light optical microscopy (Fig. 2, a) show that at first pass the grain boundaries forming was started.
Large number of slip system were activated, resulting in the formation of deformation shear bands as observed in Fig.3, b.
At very first pass of ECAP in single crystal start the initial grain boundaries forming.

Figs. 2(d)–(f) show the results for the specimens with large crystal grains.
The stress is smaller in the larger-grain specimen owing to the Hall–Petch effect.
Figs. 3(a)–(c) show results for the specimens with smaller crystal grains.
Figs. 3(d)–(f) show the results for the large-grain specimens.
Acknowledgement Authors gratefully acknowledge support from JSPS Grantsin-Aid for Scientific Research, Grant Numbers 18K03844.

The grain size is controlled by the MCS.
The average grain area is defined as the total lattice site 300×300 divided by the total number of grains.
So the unit of grain area is the number of lattice site.
Then the average grain size is the square of the average grain area.
However, owing to the periodic boundary conditions, the two half grains are actually one entire grain.

The main aim of the present paper is 1) to identify some general trends in dependency of eutectic temperature on the chemical nature of components, 2) to describe of a number of specific sintering parameters of the multiphase eutectiс ceramics, as well as 3) to understand the dependency of eutectic temperature on the number of components in a given system.
Fig. 5 Microstructure of solidified eutectic in system LaB6-B4C-W2B5 Fig. 6 Decrease of melting point (liquid phase formation temperature) with increasing number of components in a system Analysis of the experimental data on the decrease in Teut with increasing number of components in a system shows liquid formation temperature that is almost half of that for individual phases.
As noted above, there is a correlation between the temperature of liquid formation, on one hand, and a number of components in a system (n≥2), on the other hand.
Minimization of the grain size in a sintered material at equivoluminar compositions confirms the screening effect: pure component phases after sintering show grain diameters of ~12 to 18 μm (growth factor 120 to 180), whereas two-phase sintered materials have grain diameters of ~2 to 4 μm (growth factor 20 to 40).
As the number of component phases n increases, grain growth intensity is decreased at all sintering temperatures considered (see Fig. 7).

Results and discussion The metallographic microstructure of as-extruded ZA 31 magnesium alloy consists of α-Mg and the small quantity of MgZn distributed along grain boundary, with average grain size of about 10.3μm.
As the Figure shows, a large number of cavities take shape along grain boundary, and obviously, there are more cavities in sample tensile structure at temperature of 623 K than around sample fracture at temperature of 608K.
When superplastic deformation is conducted by dint of grain boundary sliding mechanism, micro cavities will shape between gains and then expand into crack, which will thus lead to the fracture of deformation sample along grain boundary [4, 5].
Some literatures point out that a certain quantity of cavities which exist independently in scattered state and small size will effectively adjust grain boundary sliding in plastic deformation process and further the grain sliding process [6].
When grain boundary encounters the difficulty in moving in triangular grain boundary, cavity can be used for relaxation and enhancement of plasticity.

This in-turn causes grain recrystallization and refined zone.
They also find increase in abnormal grain growth with an increase in number of pass of FSP.
El-Rayes et al.[9] found that 100 % overlapping of FSP lead dynamic recrystallization with equiaxed grains as number of passes of FSP are increased in case of Al alloy 6082.
A series of FSP runs were conducted perpendicular to the rolling direction at constant process parameters with varying number of FSP passes.
The number of FSP passes are carried out according to Table 1.

In order to solve the problem of the toughness with high heat input, a number of reasonable solutions have been put forward.
The total number of inclusions is the largest in the Ti-0.032%mass sample but the number is the smallest in the Ti-0.048%mass sample, the value is 3186 and 1835 respectively.
Table 3 Grain size statistics Sample Count Number[mm2] Deq [µm] B1 393 6653 13.8 B2 544 9214 11.8 B3 419 7098 13.4 B4 504 8545 12.2 B5 299 5068 15.9 Fig. 4 Relationship between Inclusion density and grain density In these five samples, the average equivalent diameter reaches the minimum 11.8 µm and the grain density reaches 9214 per square millimeter when Ti content is 0.032%.
The grain growing rate caused by grain boundary curvature can be counteracted by particles’ pinning in grain boundary [6], so the grain can be refined by appropriating inclusions around the grain boundary.
So the main grain equivalent diameter is smallest in B2 sample.

The results indicate that surface melting and grain refinement were found in the melted surface layer.
Remelting and grain refinement in the surface layer is mainly responsible for healing fatigue damage and fatigue life improvement.
Fig.1 reveal that fatigue damage was healed completely under conditions 1, selected different pulse numbers and conditions 2, pulse number of 1.
The small grains are, the more grain boundaries of copper film specimens have.
Plenty of grain boundaries could hinder the generation and movement of dislocations, which delay fatigue crack initiation.

But the grain size increases somewhat with further addition of Al5Ti1B.
Grain size can influence the precipitation kinetics and grain boundaries are preferential places for precipitate nucleation [8].
As shown in Fig. 1c, the volume fraction of grain boundaries of Al-5wt.
The grain size increases somewhat with further addition of Al5Ti1B.
The grain refinement of α-Al is mainly resulted from the existence of a large number of heterogeneous nuclei.