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With the increase of cooling rate, the grain size decreases and there are a large number of microcrystals in the microstructure.
In Fig. 5(a), a large number of spherical quasicrystal phases uniformly distribute in the matrix Mg7Zn3 phase, and the average grain size is less than 0.8 mm.
In Fig. 5 (a), (b), (c), there are a large number of gray white cellular or granular grain, whose size is very small.
With the increase of cooling rate, the grain size decreases, and the number of quasicrystal increases per unit area.
They collide together and form a large number of extremely tiny grains before they all grew up.

The presence of defects in the form of cavities and porosities were also observed at the grain boundaries.
In between, columnar grains are present with different sizes and orientations.
Fig. 3 presents the SEM micrograph of a cracked zone where four cracks, numbered C1, C2, C3 and C4, can be distinguished.
On the other hand, the number of P2 pores is higher than that of P3 pores.
Based on their morphology, they could be considered as grain boundaries and/or secondary microcracks.

Theoretical Analysis It is known that the grains are more even size with the decrease of grain size.
It decreases slowly with reducing grain size.
Then the total polarization of ceramic sample may be written as: (4) Where N is the number of grain in ceramic volume. f0 is determined by formula (1).
N0 is original nuclei number. k’ is a coefficient.
It is obvious that the polarization of each grain is reduced and the coercive field decreases when grain size decreases.

It can be seen from Figure 1 without the pulsed electric field processing of solidification, center grains are coarse , the direction of growth are disorder, right side are mostly small equiaxed grains.
It can be seen from Figure 2 that the pulsed electric field processing of samples solidified, center grains are coarse, the right end are much more tightly packed columnar grains, the direction of growth of columnar crystal are same in the cooling direction.
When the liquid metal was connected with the anode of the pulse, Fe, Mn, Cr atoms will rapidly close to the solid - liquid interface at the role of electric field moment, yet Si atoms will be away from the solid - liquid interface, with the number of solute atoms declining, the number of solute atoms are fewer, nucleation rate has dropped, the resulting grain size to slightly larger.
Thus by the pulsed electric field treated samples, the number of martensite are increased, the number of ε → γ transformation are increased after heat back, which increased the amount of shape recovery. (2) Solidification of pulsed electric field treated are most columnar crystals, most non-treated solidification are nearly equiaxed.
Pulsed electric field is benefit to Fe-Mn-Si-Cr alloys grain refinement.

The fine and pancake-like grains of this alloy lead to the increase of fatigue life and fatigue strength.
The S-N (Stress amplitude-Number of cycles to failure) curves of Al-Mg-Mn alloys with and without minor Sc and Zr are shown in Fig.1 It shows that in the same loading stress amplitude condition, the numbers of cycles to failure of the Al-Mg-Mn-Sc-Zr alloy were significantly higher than those of the Al-Mg-Mn alloy.
Discussion Effect of grain structure on the fatigue properties.
Al-Mg-Mn alloy sheets with Sc and Zr still retain the fine pancake-like grain structure after annealing, but grain structure of Al-Mg -Mn alloy sheets without Sc and Zr is equiaxed coarse recrystallization grains.
Additionaly, the grain-fining enhances the resistance to slip deformation, restrains the formation and development of slip band, the resistance to microcrack propagation from grain boundary also increases [13,14].

Currently, most authors and researchers tend to favour on of the growth selection theories, in particular the Σ9 grain boundary theory, and a number of striking proofs for its validity have been presented.
In the case of Goss grain growth a number of specific theories on oriented nucleation and growth selection have been proposed.
The numbers in the fields correspond to the depth in the sheet.
Up to a temperature of 800°C, when still no abnormal grain growth is observed the numbers do not change significantly.
These numbers suggest that actually Σ9 boundaries do not show any increased mobility which would lead to a decrease of their density.

To consider the effect of grain size refinement, it is instructive to examine the contribution of atomic species residing in the grain boundary relative to that of the total atoms in a nano-grain.
This is shown in Fig. 1, which depicts the percentage of atoms in the grain boundaries as a function of grain size for two assumed thickness values for the grain boundary, 0.5 and 1 nm [5].
As the grain size is reduced, the number of atoms in the bulk (and their contribution) diminishes and becomes zero with the overlapping of the space charge layers.
Grain size dependence of percentage of atoms in grain boundaries assuming boundary widths of 0.5 and 1 nm [5].
Fig. 2.Reduction of the bulk relative to space charge layer and grain boundary as grain size decreases.

The specimens processed by rolling showed only elongated grains and the ones processed by ECAE (Route A) at 2 and 4 times showed elongated grains and partially equiaxial grains and in the samples fabricated by ECAE (Route Bc) at 2 and 4 times, equiaxial grains were found by optical microscopy.
The evaluation of the time until crack initiation and the number of cracks were employed to see the corrosion morphology of the samples.
ECAEed (route A) sample consisted of mainly elongated grains and partially fine equiaxial grain.
So the equiaxial grains were formed by dynamic recrystallization.
ECAEed (route A) sample had largely elongated grains and partially recrystallized grains.

Computer simulation of the interaction of junction disclinations in nanomaterials with grain boundary vacancies A.
Atomic structure of Σ = 5 (310) tilt grain boundary in Ni viewed along the tilt axis [001].
Denote N the number of structural units belonging to a GB section of length r with the left edge on the disclination core and enumerate these units by i.
Assume that the grain size is equal to d=135 nm, then the GB length is L ≈ d/2 ≈ 67 nm.
At least two orders of magnitude increase of the effective grain boundary diffusion coefficient can be expected in both special tilt and general tilt and twist GBs in bulk nanostructured materials with the grain size d ≈ 100 - 200 nm due to disclinations with the strength about ≈ω 5°.

The CNA method uses a ternary number, ijk to denote an inter-atomic bond.
In the ternary number system, i designates the number of common neighbors shared by two atoms, j denotes the number of bonds among those common neighbors, and k indicates the longest path in these bonds.
Within the grain size regime investigated, the yield stress increases with increasing grain size, revealing an inverse Hall-Petch effect.
A number of theories have been proposed to explain the Hall-Petch break-down[18], a recent argument put forward by Louchet [19] and co-workers seems particularly appealing.
However, a peak fraction exists for each grain size with the actual peak value depending on the initial grain size.