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Besides, fine second phase is able to suppress grain growth by exerting pinning effect on grain boundaries [9].
Numbers of studies were carried out to determine Table 1.
Meanwhile, recrystallized grain size is extensively fine especially at 948K.
Microstructure at 1108K consists of elongated α grains containing sub-grains in their interior.
It seems that these elongated grains are transformed from the dynamically recovered β grains during gas quenching.

Adding rare earth not only reduced the degree of super-cooling, but also increased the number of nucleation and accelerated crystallization rate.
During the solidification of magnesium alloy, Re widely dispersed on the grain boundaries and prevented grain growing and the grain was refined.
As a result, it was difficult for the Mg17Al12 phase to form a network compound on the grain boundaries and the relative number of the phase decreased.
This was because that the network phrase changed into the grainy shape on the grain boundaries and the grain was also refined.
And also, RE refines grain of the alloy.

The as-deposited films did not show clear grain boundaries, but after thermal annealing, grains grow and form nanocrystalline structure with a grain size of 8 nm.
Color code indicates the coordination number.
The size of a grain is about 8 nm.
For perfect fcc crystals, the coordination number is 12.
Wang: Theoretical tensile strength of an Al grain boundary.

However, the increasing degree of grain number is not directly proportional to inputting voltage.
Grain refining is not obvious with inputting voltage further increasing when the grain size decreases to a certain extent.
Howerer , [5] , thereinto, is the grain number per unit volume.
So, the grain numbers per unit volume become more with cooling rate increasing.
In addition, if stopping stirring temperature is too high, the grains nucleated will regrow, too.

The grain size of the alloys after annealing was 100 ~ 200 mm.
Experimental Results and Discussion Figure 2 shows the torque and the compression load of Gum Metal as a function of the number of turns during HPT.
Fig. 2 In situ torque and compressive load curve as function of number of turns.
For the 25 Nb alloy, the original grains are slightly deformed and have the curved grain boundaries as shown in Fig. 4 (c).
Such localized shear deformation would process grain refinement, resulting in the very fine grains in Gum Metal.

Grain refinement and work hardening remain the most effective methods for improving strength of the material [4].
In the different rolling cycles have been changed the number of the cold rolling passage, the thickness gained with the hot passage and the number of annealing treatment.
After the first hot rolling step it can be noticed that the grains are elongated in the rolling pass direction, while, after the final annealing, the grains undergo a drastic reduction in dimension but at the same time the grains become equiaxed and this fact lead to a reduction of the PLC effect.
This phenomenon also leads to a reduction of the PLC occurrence because there is a smaller number of precipitates that obstructs the dislocation movement during the plastic flow.
In particular, it is well known that the grain boundaries are obstacles for the dislocations movement so by increasing the grain size decreases the occurrence of the PLC effect

A number of studies have been carried out on the use of Holographic optics [4-6], with success demonstrated of the technique in terms of beam control for cutting.
A number of welds ~30 mm length were completed before the sheet was removed.
The grains in this deposit are more equiaxed than in Fig.3(a) with a smaller grain size seen on the side with the lower energy input.
There is clearly a grain refinement with the low energy ORP-HOE with a larger 200µm 200µm grain size seen in the high energy ORP-HOE.
The grain size within the weld bead/deposit can be controlled such that a finer more equiaxed grain structure can be developed.

In a previously proposed model [5] it was discussed that the growth rate of crystallographic planes is influenced by the number of nearest neighbours that a metallic adatom encounters at the growing surface.
The crystallographic plane that offers the highest number of nearest neighbours to a metallic adatom will have the highest growth rate.
Calculating the number of nearest neighbours, it was predicted that the [002] direction will be the resulting out-of-plane orientation in case of YSZ (a fluorite structure) [5].
As such, the grains that catch the largest number of metallic adatoms will be able to overgrow the others.
The higher grains will shadow the other grains more efficiently when the substrate is tilted.

This feature made a number of researchers study experimentally the transformations in Fe–9 %Cr alloys [2–6].
Legend numbers indicate transformation temperatures (in deg Celcius).
The fact that nucleation energy for austenite ® ferrite transformation is small compared to the activation energy of growth also found its confirmation in direct synchrotron radiation measurements of the number of ferrite grains during transformation [10].
Acknowledgements The work was financially supported by the Ministry of Education and Science of the Russian Federation (state assignment No. 3.9660.2017/BCh; publication number 3.9660.2017/8.9).
Cahn, The kinetics of grain boundary nucleated reactions, Acta Metallurgica, 4 (1956) 449-459

Each cell has four state variables: (a) dislocation density: the initial dislocation density of cell is taken as the dislocation density after deformation; and the static recovery and recrystallization make the dislocation density reduce; (b) grain orientation: the new generated recrystallization cell is randomly given number between 1 to 180 as a orientation value.
The same orientation value belongs to the same grain, and different grain is corresponding to different color; (c) recrystallization flag: “0” indicates un-recrystallization state, and “1” indicates recrystallization state; (d) grain boundary sign: it is used to indicate the location of grain boundary cell.
The fraction of static recrystallization can be expressed as follows: (13) where, is the cell number for static recrystallization, is the total cell number for cell space.
The temperature is 1200 ˚C, the initial grain size is about 110.
In Fig. 1(a), the initial grain of un-recrystallization is logoed with gray, and the multicolor grain represents the new generated dynamic recrystallization grain during the first pass deformation, the fraction of dynamic recrystallization is 8.1%.