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Its mechanism is that Al4C3 particles can form a large number of dispersed sites for heterogeneous nucleation, and therefore enhance the nucleation rate.
In order to exactly describe the activation efficiency of grain-refiner in the melt, we define that the activation efficiency of the grain-refiner Al4C3 in the magnesium alloy melt, ρ, to be the ratio of the number of grains in unit volume after refinement to the number of particles which in size are bigger than or equal to the critical nucleation size.
(1) In the equation, λ is the number of grains in unit volume after the solidification of the melt and Ф is the number of particles which in size are equal to or bigger than the critical nucleation size.
(2) λ1 is the number of the grains in unit volume when adding Al4C3 grain refiner only. λ2 is the number of grains in unit volume when the Al4C3 grain refiner and the electromagnetic field acting simultaneously.
The number of Al4C3 particles of nucleation, Ф, is recorded as can be expressed as follows:

The results indicated that the hardening behavior of fine grained samples (mean grain sizes in the range of 2.13.8µm) can be described as typical dislocation interactions.
However in coarse grained samples (mean grain sizes in the range of 4.7-38.5µm) where extensive mechanical twinning occurs, another strengthening mechanism is required.
The number of dislocations in the pile-up is related to the resolved shear stress in the slip plane and the distance between the source and the obstacle.
Therefore in coarse grained samples, the operation of primary slip systems during the initial stages of deformation and the formation of an appropriate number of dislocations in the pile-up result in continued plastic deformation with minimum slip systems.
Conversely in the case of fine grained samples (for example with a mean grain size of 2.1µm), since the mean grain size is not sufficient to create the appropriate number of dislocations in pile-up from primary slip systems, secondary slip systems start operating.

The grain boundary diffusion strongly depends on the grain boundary character and structure [1].
The GBCD was shown by the fraction of number of grain boundaries with specific S-value.
Figure 3 shows the change in the average grain size of {111} grains and other grains in gold thin film specimens during annealing at 873 K.
The average grain size of {111} grains became modestly larger than that of the other grains.
The percolation probability is evaluated by the ratio of the maximum number of percolation-susceptible triple junctions connected by random boundaries to the total number of triple junctions.

Fig.2 shows the microstructure after recrystallisation for Cube orientated single crystals with an initial dislocation density of ρ=1014m-2 and number of nuclei w=0.05% at different temperatures (573 K, 673 K, 773 K).
Fig.2: Microstructure of fully recrystallised single Al crystals, number of nuclei w=0.05% and initial dislocation density ρ=1014m-2.
In Fig.3 the number fraction of grain boundaries is shown as function of the misorientation angle for Al single crystals with initial Cube orientation at 573 K, initial dislocation density of ρ=1014m-2 and w=0.05%.
For the case (1) simulation in Fig.3(a) one can see that the number of grain boundaries in the regime below 15° is clearly larger (50%) than in Fig.3(b) for the case (2) simulation.
Fig.3: Number fraction of grain boundaries as function of the misorientation angle for Al single crystals with initial Cube orientation at 573 K, initial dislocation density of ρ=1014m-2 and w=0.05%.

The probability of diffraction spot overlap, which increases with the number of illuminated grains as well as with the orientation spread within the grains.
Unfortunately, it also has the disadvantage of requiring a larger number, Nr, of useful diffraction spots per grain to produce quality reconstructions.
In these the quality of the reconstruction was measured by a function FOM2, defined as the ratio between the number of wrongly assigned pixels and the total number of pixels belonging to the grain.
• In conventional reconstructions the number of projections through a given voxel can be determined at will by adjusting the angular step.
By contrast, in diffraction, the number and directions of the projections giving rise to nonzero intensities is given by the crystallography of the system.

Nanocrystalline materials consisting of nanometer-sized crystallites contain a large number of interfaces, i.e.
Such nanocrystalline electrodeposits are in a high non-equilibrium (metastable) state, i.e. a high energy state due to a large number of interfaces [8, 9].
Journal Title and Volume Number (to be inserted by the publisher) 3 Table 1.
The fronts of the abnoramlly growing Journal Title and Volume Number (to be inserted by the publisher) 5 grains are observed to be not smooth and to consist of individual segments having different misorientations with the adjacent nanostructured matrix.
The fact that the <111>//ND grains are much coarser than the <100>//ND grains in the fully annealed specimen is attributed to the abnormal grain growth of the former in the early stages of grain growth.

Marx str., Ufa 450000 Russia RZValiev@mail.rb.ru Keywords: Severe plastic deformation, ultrafine grains, grain boundaries, mechanical properties.
Introduction Ultrafine-grained (UFG) materials with a grain size in the submicrometer (100-1,000 nm) or nanometer (less than 100 nm) range possess much higher length of grain boundaries than usual coarse-grained counterparts; that is why the properties of UFG materials depend considerably on the structure and behavior of internal interfaces - grain boundaries (GBs).
The concept of grain boundary engineering or grain boundary design was introduced by T.
Results The evidence available to date shows that both ECAP and HPT processing provide an effective procedure for achieving different misorientation distributions because there is a high fraction of low-angle boundaries after a small number of passes but a lower fraction of low-angle boundaries when the number of passes is increased [2, 4, 9].
Misorientation Number of Misorientations Angle (deg) 0 200 400 600 800 1000 3.4 9.2 14.9 20.6 26.4 32.1 37.8 43.6 49.3 55.0 60.8 66.5 72.2 78.0 83.7 89.4 (a) (b) Fig. 3.

Egb is the elastic modulus of the grain boundary region.
Fv is the vacancy formation energy at grain boundaries.
Thus it can be determined that Cb(σ=σ) and Cb(σ =0) are 0.683 at.% and 0.482 at.% according to Auger peak height ratio curve, and the increased grain-boundary concentration of sulfur induced by tensile stress is Cb(σ=σ) - Cb(σ=0) = 0.201 at.%. 3.2 Molar volume of grain boundary and vacancy formation energy at grain boundaries Fv In order to transform the increase of sulfur in molar fraction into that in atomic number, the average grain-boundary density to be about 50% of the lattice density was adopted.
So, the increased number of sulfur atoms in 1 m3 volume of grain boundary induced by the applied tensile stress is 6.02×10 23 ×7.04×10 4×0.201% = 8.52×10 25 .The vacancy formation energy at grain boundaries has been selected to be 1.5 eV in present paper. 3.3 RESULT OF ELASTIC MODULUS AT GRAIN BOUNDARIES The applied stress σ is 35kg / mm 2 = 3.43×108 Pa in Misra's experiment. 5 For polycrystalline material, the normal directions of grain boundaries are oriented randomly to the direction of applied stress over angles ranging from 0 o to 90o.
The Cb-curve is in grain boundary concentration (Ref. 2-4).

The number and effectiveness of the abrasive particles during grinding depends on factors such as the abrasive concentration and the extent of particle protrusion from the wheel’s surface.
The number of active abrasives of the effectively removal materials is only very small part of the total grains, the redundant grits not only increase the cost of tools and waste a large number of abrasives, but also seriously interfere with the work of effective abrasives, increase the grinding temperature, decrease the chips volume, the manufacture efficiency and the service life [1-2].
Fig. 6 shows the grain pattern parameters for the third grain distribution pattern.
After cooling the buried height of grains is 30% by alloy solder or grains protrusion rate are about 70%.
American patent application number US 4925457, US 5049165, US 5092910 researched the mesh screen technique [12-14].

Since Grain yield prediction is significant for regulating grain prices, the research on the accurate prediction of grain output has great value.
The meaning of Markov transition probabilities )(mpij are: System consists of state i transferred to the system state j of the transition probability )(mpij only depends on the time interval m (step number) of the length of time, and has nothing to do with the starting.
(2) Division of the state Using (k)Yˆ curve as a benchmark, according to the specific circumstances of each prediction object is divided into a number of parallel bar area, each bar area to form a state.
Case study 1.Grain Output In Jiangsu Province According to Statistical Yearbook of Jiangsu Province, the main grain production show in Table 1.
The exact prediction of grain output has positive function for provide prevention and cure grain failure and regulate and control grain prices.