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With the increase of the number of deformation passes, refinement effect becomes weakened gradually, the grain size tends to stabilize and the organization is more uniform.
Currently, this technology has been successfully used to refine grain of pure metals of aluminum, copper, but the study on the grain refinement of alloy is rarely reported.
Initial grain size of the material: 90.
The grain size is refined from the initial 90 to 31 or so, but the grain size of the billet is inhomogeneous.
The grain size becomes more uniform in the follow-up passes.

In the pole figures, the numbers are the grain 1 2 3 1 1 1 2 2 2 2 3 3 3 3 1 numbers in the orientation map, the lines in d are the orientation distribution ranges of the deformed grains taken from b, and the solid circles show the orientation of the nucleus.
The nucleus/grain has a <111> pole in common with grain 6.
Even more it has a misorientation of 39.8º/[-0.61 0.51 -0.61] to a few pixels near grain boundary in grain 6.
If the grain boundaries after annealing are overlapped onto the grain boundaries before annealing (Fig. 5), it can be observed that the nucleus mainly has grown into grain 4, which has a misorientation of 20.3º/[-0.43 0.88 0.18] to the new grain.
In the pole figures, the numbers are the grain numbers in the orientation map, the lines in d are the orientation distribution ranges of the deformed grains taken from b, and the solid circles show the orientation of the nucleus.

The grain boundary surface is the excess energy of the grain boundary as the lattice on one side of the grain is translated relative to the lattice on the other side of the grain.
Grain boundary sliding is characterized by the relative translation of two adjacent grains parallel to the grain boundary plane driven by applied shear stress.
Figure 2 contains two grains jointed along the grain boundary plane.
In Fig. 4, we present the relative strains (percentage) of the interlayer spacing normal to the grain boundary plane as a function of the number of layers away from a given layer for the ]110)[211(3Σ tilt grain boundary before the sliding.
Interlayer strain (percentage) as a function of the number of layers away from a given layer.

N, Dv and c eq, denote the number of atoms per unit volume, the vacancy diffusivity and the thermal equilibrium vacancy concentration, respectively.
This implies that vacancies generated at grain boundaries have to travel across a grain before they get absorbed by a grain boundary and further transported to a free surface via grain boundary diffusion.
This yields for the vacancy concentration eq cc λ= , (6) where Journal Title and Volume Number (to be inserted by the publisher) 3 ( )     += βδ γ λ NkT4 1
The linear grain growth stage extends to the grain sizes for which vacancy sinks other than the grain boundaries will emerge.
Journal Title and Volume Number (to be inserted by the publisher) 5 It should be stressed that in contrast to the classical diffusion creep that does not show a primary stage, the present model predicts a transient behaviour that is effectively tantamount to primary creep followed by a steady state creep stage.

In this case, a number of grains to thickness would be one or two.
It is reported that the mechanical properties of thin metallic films are dependent upon the number of grains per thickness, if there are < 10 grains per thickness.
Thus, in the general thin films with very fine grains, the film thickness plays as a dominant role rather than the grain size.
Fig.6 Grain size dependence of yield strength (a) and ratio of thickness to grain size dependence of yield strength (b) Size effects in fracture strain of thin films were found by a number of authors [1, 5, 11-13].
Therefore, an increase of a number of grains per thickness would increase a resistance to necking fracture.

Furthermore, in calcia added samples, grain growth was much faster and lots of micro-pores were left in coarse pure yttria grains.
This procedure was repeated until the destruction of the sample, and the number of quenches was taken as the measure of thermal shock resistance.
Moreover, the EDS results revealed that grains less than 1μm on the grain boundaries were calcia contained yttria solid solution and coarser grains about 5μm or 30μm were pure yttria.
Simultaneously, because of the increased high grain boundaries mobility, micro-pores were inevitably left in coarse yttria grains.
Because of the existence of calcia, the migration of yttria grain boundaries was increased and micro-pores were left in coarse yttria grains.

This is explained by considerable relaxation of the internal stresses in the deformed steel caused by appearance at ε > 20% of a great number of microtwin packages.
The dotted line shows the average internal stress values The distribution analysis showed that both at simple and complex grain bending of a grain one sees the inhomogeneous polycrystal grain deformation.
Consequently, the number of more stressed sample sections (σ > 2 GPa) is insignificant.
It should be also pointed out that the total area of the second and the third mode for a grain with complex bend is greater than for a grain with simple bending, i.e. the number of sample sections with the internal stress increasing 2 GPa is greater at complex grain bending than in grains with simple bending.
This is explained by considerable relaxation of the internal stresses in steel caused by appearance at ε > 20% of a great number of microtwin packages in the deformed material.

A number of authors, including one of the present writers, have suggested that this effect is due to the influence of grain size on mechanical twinning (e.g. [4]).
Grain size control through recrystallization A number of workers have pointed out that the static recrystallization of magnesium and its alloys is enhanced by the presence of deformation twins [5, 6].
An example of the rate at which the grain size evolves with annealing time for a number of different alloys is shown in Figure 5.
It is assumed here that this evolution is reflective of the kinetics of a recrystallization reaction. 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) AZ11 AZ21 AZ31 AZ61 (a) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) AZ11 AZ21 AZ31 AZ61 (a) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) Mg-0.3Zr Mg-0.5Zr Mg-1Zr Mg-1Zn-0.5Zr Mg-6Zn-0.5Zr (b) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) Mg-0.3Zr Mg-0.5Zr Mg-1Zr Mg-1Zn-0.5Zr Mg-6Zn-0.5Zr (b) Grain Size (µm) Figure 5.
The more solute rich alloys display the finer grain sizes.

Modeling Ostwald ripening remains inexact because of the large number of thermodynamic, kinetic and spatial variables which must be simultaneously considered and the former coresponding models make assumptions about the grain shape, diffusion field around the grains or concentration of the matrix phase to make the problem tractable.
The number of iterations is given in units of Monte Carlo step, MCS.
The total number of states that A-sites could assume was Q = 32, the mole fraction of A was 0.80, and simulation temperature was kBT = 0.7.
Under these conditions, it is not possible for a grain boundary atom from the first grain to jump across several atoms of the liquid phase to the next grain.
Without liquid phase, some grains became larger at the expense of other smaller grains and grain growth occurred almost entirely by the direct exchange mechanism.

Accordingly, two numbers are given in Table 2.
Two numbers are given in table 1 because the determination of GBC is ambiguous.
Table 2 Number of GBC with and without a precipitate.
Table 3 Number of precipitates at various types of GBCs.
Type Total number of GBCs examined Number of GBCs with precipitate Number of GBCs without precipitate Fraction with precipitate A 10 7 3 70% B1 5 2 3 40% B2 4 1 3 25% C1 4 0 4 0% C2 1 0 1 0% D 3 1 2 33% Total 27 11 16 41%