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The double Scohottky barriers at the grain boundaries between every two ZnO grains have been validated as the origin of the nonlinear characteristics.
Generally, Newton iterative method is used to solve above equations, which will become quite time-consuming when the number of equations is large.
In subarea III, two ZnO grains are touched directly.
The values of above impedances depend on the actual sizes of ZnO grains and grain boundaries.
Pores and twin grains.

Grain size.
Figure 2 is the macro grain degree photos of the Nimonic 90 alloy by different remelting casting into test specimens, grain size characteristics are shown in Table 3.
As a consequence, the number of nucleation rate increased, average grain size tended to be smaller and smaller, which ranged from 127μm to 15.9μm.
a)1# b) 2# c) 3# d) 4# Fig. 2 Macro-photographies of samples for different remelting processes Table 3 Grain grade of the Nimonic90 Serial number 1# 2# 3# 4# Grain size(μm) 120~130 60~70 30~33 14~17 Grain grade 3 5 7 9 Microstructure.
Same researches pointed out the number of the γ ' in superalloy usually increases with Al+Ti, and the Ti / Al ratio has little effect relative to the number of γ ' [6].

The grains are elongated along the direction parallel to RD.
The selected area iffraction patteren indicates those grains are high-tilge grain boundaris.
(b) grain-refined sample by ARB
Hirsch pointed out that the BDT temperature depends on the number of dislocation sources and spacing along a crack front.
It indicates the BDT temperature decreases with decreasing the dislocation source spacing, that is, when the number of dislocation sources increases, the BDT temperature deceases.

But after T6 or annealing treatment, its dimple number increases evidently.
And the grain size of AZ91 alloy is obviously refined because of the occurrence of the dynamic recrystallization during hot extrusion.
And the T6 treatment of as-extruded alloy makes the grain size homogeneous and grows lightly.
The fracture of extruded sample is obviously ductile because there are a lot of dimples at the fracture surface, and after T6 treatment or annealing treatment, its dimple number increases evidently.
But after T6 or annealing treatment, its dimple number increases evidently.

The addition of number of SiC particles to Al2O3 was able to significantly increase the hardness properties.
In this study, a number of composite manufacturing methods were compared from the results of properties by accumulative press bonding (APB), accumulative roll bonding (ARB), and repetitive press roll forming (RPRF).
Microstructure’s analysis behaviour used microscope optic was traced to determine the grain morphology and deployment precipitates on grain.
The movement of grain occurs due to the incorrect energy of high-alloying aluminium.
The movement of the grain to slip due to dislocation movement.

The ultimate tensile strength increases with the number of CGP passes from 767 (solution annealed) to 1162 MPa (after 2 cycles), similarly, yield strength increases from 269 (as received) to 328 MPa (after 2 cycles).
Some researchers have successfully processed low carbon steels [17-19] via CGP for obtaining fine grained structured materials.
This graphs reflect the increase in hardness number with the increasing the number of CGP cycle.
Langdon,The process of grain refinement in equal-channel angular pressing, 46(9), (1998), Acta Mater., 3317-3331
Park, Constrained groove pressing and its application to grain refinement of aluminum, 328, (2002), Mater.

Grain size on the magnetic properties The more grain boundary, the greater hysteresis loss and coercive force, because the lattice distortion, more energy at grain boundary for the movement of domain wall are caused by the grain defects and internal stress in grain boundaries during the magnetization process.
The relationship between the optimum grain size, chemical composition, the number of inclusions and the external applied magnetic field during magnetization is also apparent.
Silicon or aluminum in silicon steel can increase the specific resistance of the steel and reduce core loss and the magnetic induction, the content of Si or Al reaching a certain number will cause grain coarsening and increase optimum grain size.
And the inclusions can hinder grain growth during annealing, so the finished grain size is less than optimal grain size.
Chemical composition systems also have a significant effect on inclusions, the increase of Si or Al content reduce obviously the number of oxide inclusions [12].

The flat grain boundary (Fig. 2 a) included, for example, the grain boundaries in which {100}<011> grain was adjacent to {111}<112> grain.
Grain boundaries with fine grains (Fig. 2 c) comprised the various combinations of differently oriented neighboring grains as shown in Table 1; expressly, grains of {111}<011> and {111}<112>.
With a focus on the fine grains in the grain boundary (type 3), an attempt was made to statistically examine the relationship between the characteristics of the grain boundary and the formation of fine grains.
It was found that in the examination of the 84 grain boundaries, 22 grain boundaries formed fine grains.
The number of grain boundaries with fine grains, in particular having ND//<111>, is counted. g1, g2, a1, and a2 stand for orientation of {111}<112>, {111}<011>, {100}<011> , and {211}<011>, respectively [11].

Dependence of the density of samples from fine-grained concrete on the amount of calcium stearate 3.5.
Dependence of the strength of samples from fine-grained concrete on the amount of calcium stearate 4.
By creating a hydrophobic film around the pore space, firstly, it reduces the permeability of large pores, and secondly, it reduces the number of pores with a size of 10-100 microns.
It increases the workability of the mortar mixture, reduces the size and number of pores, and therefore slows down water absorption, practically does not affect the strength characteristics.
Study of the kinetics of water absorption of fine-grained concrete.

Grain Boundary Velocities, v.
Sub-grain Boundary Growth.
The sub-grain mobilities were estimated from the average growth rates of large numbers of sub-grains during more standard annealing experiments outside the SEM.
Grain boundary velocities and mobilities.
ii) Sub-grain mobilities in the same alloys measured during sub-grain growth using a FEG-SEM gave mobilities one or two orders of magnitude lower than the grain boundaries but, quite surprisingly, mobilities close to those of a similar Al-Si alloy.