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The varistor voltage increases with increasing number of ZnO grain boundaries between the electrodes.
Therefore, to fabricate varistors with low breakdown voltages, it is necessary to reduce the number of ZnO grain boundaries between the electrodes.
Adding only Ba to Bi-based ZnO varistors promotes grain growth, which enables large ZnO grains to be obtained [2].
This is because compounds containing both Ba and Mn do not form at grain boundaries between ZnO grains.
Excess Zn2+ ions at interstitial sites in ZnO grains have been reported to diffuse from inside the grains to the grain boundaries during annealing at approximately 700 °C [7].

Superplastic behavior and cavitation were investigated for WC-15 mass % Co cemented carbides with the WC grain sizes of 0.7 µm (A) and 5.2 µm (B), WC-10 mass % Co cemented carbide with the WC grain size of 1.5 µm (C) and WC-5 mass % Co cemented carbides with the WC grain sizes of 0.5 µm (D) and 2.5 µm (E) by tensile tests at 1473 K.
The WC grain size, dWC, and the mean free path of Co phase, λCo, are given by [9] s L WC N N d ⋅= π 4 (1) L Co N f− = 1 λ (2) where NL is the number of the carbides intercepted per unit length, Ns is the number of the carbides included per unit square and f is the volume fraction of carbide.
Values of the WC grain size, the free path of Co phase and the WC contiguity for the cemented carbides.
WC grain size, µm Mean free path of Co phase, nm WC contiguity Fine-grained WC-15 mass. % Co cemented carbide (A) 0.7 55.7 0.51 Coarse-grained WC-15 mass. % Co cemented carbide (B) 5.2 154.4 0.31 Medium-grained WC-10 mass. % Co cemented carbide (C) 1.5 533.4 0.27 Fine-grained WC-5 mass. % Co cemented carbide (D) 0.5 23.4 0.56 Coarse-grained WC-5 mass. % Co cemented carbide (E) 2.5 109.8 0.49 Results and Discussion SEM photograph of A annealed at 1473 K for 1.8 ks are shown in Fig. 1, where the specimens were polished mechanically and then etched with Murakami reagent.
The WC contiguity, which is one of parameters representing the number of the WC grain in direct contact with the WC grain without the Co phase, is given by [10] WCWC CoWC WCWC WC NN N C / / / 2 2 − = (3) where CWC is the WC contiguity, NWC/WC is the number of interfaces between WC grains intercepted per unit length and NWC/Co is the number of interfaces between WC grains and Co phase intercepted per unit length.

To illustrate the effects, the average grain stack model was introduced.
The breakdown electrical field EB of the varistors is determined by barrier density n per unit length and barrier voltage Vb [11]: EB=n ·Vb (1) where n also presents the average grain number per unit length.
The resistivities and capacitances of grains are much lower than those of grain boundary layers.
The capacitance Cgb of single grain boundary Cgb=εBε0 d 2/t (4) where εB is the relative permittivity of the grain boundary material, ε 0 is vacuum permittivity. d and t are mean grain size and grain boundary thickness, respectively.
The thickness of grain boundary dielectric layer is normally in the range of 10~100nm, while the grain size d is in the magnitude order of µm.

(a) strong axial orientation columnar grain, and (b) equiaxed grain Rolling experiment.
When the cold deformation further increased to 61.86%, a number of fine bending deformation bands formed with the axial of the tube to be 15- 45° in the columnar grain, as shown in Fig. 2e.
Grain boundary strengthening effect depends on the grain boundary misorientation.
When the cold deformation further increased to 61.86%, a number of deformation bands were clearly observed, as shown in Fig.3e and 3f.
Axial Radial Axial Axial Radial Radial There were a large number of grain boundaries in the pure copper with equiaxed grain than columnar grain, leading to a more obviously prevent effect on dislocations during plastic deformation.

The principle of emerging two-dimensional Voronoi crystalline grain structure is: (1) in certain area, some geometry points are sown some points of geometry to define the grain embryo at random.
According to the grade characteristic of crystalline grains in national standard GB/T6394-2002，when grade of crystalline grain is offered，for the calculating formula: (1) we can obtain density of crystalline grains, that is number of crystalline grains on an area equaling to 1,by which we can simulate polycrystal models through Voronoi algorithm.
Fig.4.Metallographic picture of aluminum alloy The shape and area of the crystalline grain, as the visualized indices of the character, can reflect detailed geometry view of material structure; therefore, the side number and area of the every polygon under different grades from 2 to 4 of crystalline grain are statistical analyzed.
Mean value of the side number of every grain under different grades of crystalline grain is shown in Table 1.
Table 1.Statistic of crystalline grain polygon Project Grade 2 Grade 3 Grade 4 Mean value 5.314 5.322 5.346 Theory value 5.148 Above all ,we can conclude that the meso-scale model based on Voronoi algorithm has met the metallurgy principle through the mathematical information and geometric simulation，and have good consistency with actual structure in main characters such as grain shape, side number, area, etc, which can offer the good structural form for meso-scale calculating.

Meanwhile, the Nd-rich grain boundary phase was precipitated at the grain boundary of the main phase to form a distinct phase separated from the main magnetic phase.
Materials and methods The sintered cylinder of Nd-Fe-B permanent magnet with the serial number of N38SH and the size of Φ10mm×8mm was used in this study.
So the main phase grains are more thoroughly isolated from each other.
In this work, the domain wall pinning effect was enhanced in the two aging treated samples, in which a large number of the thinner and more continuous Nd-rich phase formed along the grain boundaries, so as to significantly increase the intrinsic coercive force. 4.
Acknowledgments This work was supported by the national major special project for the rare earth and rare metallic materials with the project approval document number: (2012) 1743.

Furthermore, the grain orientation effects of BNTV-y ceramics on their piezoelectric properties are discussed using the grain-oriented ceramics prepared by the hot forging (HF) method.
Grain-oriented samples were prepared by the hot-forging method (HF).
RESULTS AND DISCUSSION X-ray diffraction patterns for (OF) BIT-Nd, BIT-V and BNTV ceramics show single phase of bismuth layer structured compounds with the layer number, m=3.
It is considered that these small grains prevent large grains from being orienting.
On the other hand, the number of small grains of the (HF) BNTV-y0.25 ceramic� shown in (a) are fewer than those of the (HF) BNTV-y0.75 ceramic.

Fig. 5a-b shows the histograms of the internal stresses σ in grains with simple and complex grain bending for the deformation degree ε = 14 %.
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.

In this study, a fine nanocrystalline structure with an extremely number of α-Fe grains with the similar size of ~ 30 nm was obtained.
Fe-based nanocrystalline powders particularly usually show low power loss on the high frequency band, higher performance with a thinner layer due to higher saturation magnetization because of a large number of α-Fe grain precipitation as well as higher permeability than those of the conventional materials.
An extremely large number of α-Fe grains with very fine grain size of ~ 25 nm were precipitated in the amorphous matrix.
On the other hand, the crystallization degree became larger as a large number of α-Fe nanocrystalline grains precipitated from amorphous phase with increasing Tq.
It can be observed that these samples have a fine nanocrystalline structure with an extremely number of α-Fe grains with the similar size (28, 27 and 20 nm when Tq is 773, 798 and 823 K, respectively) below 30 nm in general dispersed in amorphous phase.

Research indicates that grain size and concentration of abrasive material should be reasonably selected based on the surface roughness.
And Inhomogeneity of concentration distribution along wheel circumference will result in heterogeneity of insulator layer state, which will bring difference in the number of abrasive grain in the grinding area, thereby changing the actual cutting depth of every abrasive grain.
Selection of grain size and abrasive material concentration It is known well enough that grain size and concentration of abrasive material should be choiced rightly based on the surface roughness and maching efficiency.
Inhomogeneity distribution of various components on the surface of abrasive tool will result in heterogeneity of insulator layer state, which will bring difference in the number of abrasive grain in the grinding area, thereby changing the actual cutting depth of every abrasive grain.
Main conclusions of this paper are as follow: 1) Abrasive grain size and diamond wheel concentration should be reasonably selected based on the demand of surface roughness, and each grinding depth and feed frequency in vertical direction of maching surface should always be scientifically determined. 2) Inhomogeneity of concentration distribution along wheel circumference will result in difference in the number of abrasive grain, thereby change the actual cutting depth of every abrasive grain.