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The grain size is strongly related to the number of nuclei.
Different pulse number of laser.
In this section, different pulse numbers are investigated.
Fig. 4 shows the average grain sizes of different pulse numbers and laser intensities.
This could increase the nucleus number, which leads to the smaller grain size.

Over 1500 grains were analyzed for each UFG sample.
Distributions of grains on size and grain boundaries (GBs) between the adjacent grains on their misorientation angle q were determined from the EBSD maps.
The samples in the initial coarse-grained state with a grain size of about 100 µm failed.
The samples in the coarse-grained state with a grain size of about 100 µm failed.
Edalati, Room-temperature superplasticity in an ultrafine-grained magnesium alloy, Scientific Reports. 7 (2017) Article number: 2662

The sample 1, of which the RE content was 0.0048 wt.%, was also ferrite, but duplex grain structure, there were ferrite with small grain size along the original grain boundaries.
(a) and (b) Ultrafine grain size ferrite at grain boundaries.
First, there were large numbers of dislocation walls, as Fig 4a shown, and this was typical specialty of the recovery and recrystallization.
(b) Clean grains with few dislocations.
(c) Second phase at grain boundaries.

Dislocation models of noneqiulibrium GBs have been developed in a number of works.
Along x direction numbers of type 1 and type 2 GB were chosen in a way to obtain a period close to 15 nm and disclination dipole separation (arm) of about 8 nm.
Li, Energy of grain boundaries between cusp misorientations, Surf.
Vladimorov, Disclination-structural unit model of grain boundaries, Philos.
Baudelet, Microstructures and hardness of ultrafine-grained Ni3Al, Acta Metall.

Plasticity and fracture mechanism of refine-grain AZ31 magnesium alloy sheet was discussed.
Research has shown that the organization of the annealing processing, the second phase number is greatly reduce in the substrate and in grain boundary [4-12].
The relationship of annealing temperature and grain size as shown in Fig. 3 at a certain annealing time, along with the annealing temperature increases, annealing grain size increase gradually.
This is because the relationship between the interface migration rate B (grain boundaries migration velocity was produced by units driving force) and the grain boundaries diffusion coefficient D grain boundaries is[14]：B=D grain boundaries /KT.
Grain boundaries diffusion coefficient increase with temperature into index [D = D0exp (Q grain boundaries P/KT)] ，Because its effects exceeds 1 / T in the type, with the rise of temperature the speed of grain boundaries move increases rapidly, and the trend of the grain growth also more and more quickly.

With shear stress increasing, a large number of dislocations, twins, and other defects are formed in the crystal lattice, and the lattice distortion can also increase.
At the same time, due to the formation of nano-crystals, there have been more grain boundary and sub-grain boundary.
As the rotate rate increases, the powder size decreases gradually, meanwhile, the uniformity of particle distribution is improved and the number of aggregated powder decreases.
After the powders absorb the energy of impact, they break and a large number of small particles are generated.
Acknowledgements The financial support provided by the key program for Heilongjiang province Natural Science Foundation (contract number: ZJC 0604) and"973"program of China (Project NO.: 2008CB617604) is gratefully acknowledged.

The energy band gap decreases with increasing number of layers but increases with increasing pre-heating temperatures.
Grain growth occurred along the (002) plane for all films irrespective of sol concentration, aging time or number of layers.
The obtained values shown in Table 1, reveal an increase in the grain size, which may be associated with the coalescence of small grains by grain boundary diffusion resulting in major grain growth [27].
Similar morphology is observed but with a decrease in the grain size with increasing thickness.
Taking into account the effect of the number of layers, the film with 10 layers pre-heated at 400°C is the thicker one.

Grain A, B and C share the grain boundaries each other.
dV wF n i i V nji ji ij jiij       −+         ∇∇− = ∑ ∫ ∑ =< 1 2 1 2 φλφφ ε φφ , (1) where i and j represent the orientations of grains; n is the number of distinguishable orientations and � is a Laglangian multiplier.
The number of distinguishable orientations is 1,000,000.
One iteration corresponds to 540 ™ 540 ™ 8 calculations, where 540 ™ 540 is the number of grids and 8 is the maximum kind of orientations which each grid has.
The grain boundary between the black grain and the two type I grains has the energy of 0.3 whereas the grain boundary between the two type I grains has the energy of 1.0.

Traces of crystallographic sliding appear inside some grains.
With an increase in the number of impacting pulses, accumulation of damage is observed.
The energy and the number of impacting laser pulses were changed.
Grain boundaries appeared.
Grain boundaries and traces of crystallographic sliding within grains were observed.

This is the natural boundary condition when a fixed number of particles diffuse, each for some time t.
A random number is generated to determine the outcome.
The lattice model with a variable lattice spacing for addressing the problem of diffusion from an instantaneous tracer source at y = 0 in the presence of a grain boundary slab (normal to the surface) ; (a) shows a small mesh size in the vicinity of the grain boundary, (b) shows a large mesh size for the grains except in the immediate vicinity of the grain boundary slab.
(Care must be taken for problems with a changing number of particles introduced into the system so that the 'clock' is suitably rescaled.)
(In the parlance of grain boundary diffusion, this would be the Hart Equation.)