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The varistor voltage increases with increasing number of ZnO grain boundaries between the electrodes.
Therefore, in order to fabricate varistors with low breakdown voltages, it is necessary to reduce the number of ZnO grain boundaries between the electrodes.
The varistor voltage is determined by the number of ZnO grain and/or the barrier height formed at the boundaries of the ZnO grains.
Figure 4 shows the ratio of the number of ZnO grain boundaries with spot- and sheet-like deposits to the total number of grain boundaries on the fractured surfaces for samples with added 0.10 mol% Si.
Before annealing, the ratio of the number of ZnO grain boundaries with sheet-like deposits was significantly more than those with spot-like deposits.

According to the phase field model for grain growth [5], a large number of phase field variables η1(r,t), η2(r,t), …., ηQ(r,t), is used to distinguish the different orientations of the recrystallization grains.
In the following discussion, length and volume are expressed in number of grid points (g.p.) and time in the dimensionless time (t.s.).
Particles appear as black spots, grains are bright and grain boundaries grey.
The radius of a grain is calculated as /R A π= , with A the number of grid points within the grain.
They reduce the mobility of the grain boundaries and, when a critical grain size is reached, arrest grain growth eventually.

In many respects, diffusion, determines physical and mechanical characteristics for new materials with fine-dispersed matter and a large number of grain boundaries and phases.
With reduction of grain sizes the volume of material, presenting a grain boundary layer, increases.
This fact can be connected with the grain size decrease.
Acknowledgment This work was supported by Russian Foundation for Basic Research, grant number 13-01-00444.
Sauvage, et al., Grain boundaries in ultrafine grained materials processed by serve plastic deformation and related phenomena Mat.

This paper deals with the cavity formation and growth behavior of fine-grained 1420 Al-Li alloy during superplastic forming.
With the strain and temperature increasing, the total number and the average size of cavities increased.
The average grain size was about 10µ m.
Result Microstructure of fine-grained 1420 Al-Li alloy Fig.2 (a) showed the SEM micrograph of fine-grained 1420 Al-Li alloy.
Among them, the larger particles were crushed in the process of hot rolling and the broken particles randomly distributing both within the interior of grains and along the grain boundaries.

This happens because the driving force for grain growth is the decrease in energy caused by the reduction of the number of grain boundaries per unit volume.
The total surface area of boundaries is decreased as grain size is increased, causing a reduction in the surface energy, i.e., when grains grow, the number of their boundaries is decreased and their total surface area energy decreases.
This is due to the number of grain boundaries.
It is clear then that the number of grain boundaries was probably the main cause for the difference found between the machining strengths in these two groups of specimens.
Coppini Index values are sensitive enough to characterize distinct values of machining strength in solid solutions with different number of grain boundaries; d. machining strength test may be performed preliminarily to discover the minimum number of steps in order to get more accurate results.

The mean grain area was used as a parameter characterising grain growth.
In calculation of the mean grain area, a grain was considered as a circle.
The median position of grain diameter distribution corresponds the mean grain area.
The statistic treatment of grain size revealed the log-normal distribution of grain size and self-similar (scaling) character of grain growth.
(1) Where S is the area of a grain, Agb is GB reduced mobility equal to the product of GB mobility, mgb, on GB surface tension, γgb, and n is the topological class of a grain, the number of triple junctions per grain perimther.

Effect of Chemical Composition on Grain Refinement of AlxCoCrFeNi High Entropy Alloys with NiAl Grain Boundary Precipitates Hiroyuki Y.
In this way, grain boundary precipitation is effective in obtaining ultrafine-grained microstructure in HEA.
Thus, the grain refinement by the NiAl grain boundary precipitates is effective in the improvement of strength-ductility balance.
Summary The effect of x on grain refinement of AlxCoCrFeNi alloys was investigated focusing on the NiAl grain boundary precipitates.
Acknowledgement This work was supported by Grant-in-Aid for Challenging Exploratory Research (JSPS KAKENHI Grant Number 17H03415) in Japan.

Although the traditional methods could reduce the average size of grain the potential of grain refinement still need to be developed further.
It has been shown in large number of experiments [7] that the phenomenon of grain refinement in melt solidification organization will appear atand.
It means the grain size starts to be refined, and grain refinement of Ni99.45B0.55 alloy occurs in a very narrow temperature range.
Grain Refinement Mechanism of Uniform Alloys.
Both methods can get fine grains.

Solute Interaction in Grain Boundary Segregation and Cohesion LEJČEK Pavel Institute of Physics, AS CR, Na Slovance 2, 182 21 Praha 8, Czech Republic lejcekp@fzu.cz Keywords: Interfacial segregation; Grain boundary embrittlement; Solute interaction; Modeling Abstract.
Introduction Most of the materials used in technical practice (e.g. steels, duralumin and nickel-base superalloys) are complex alloys composed of a number of elements.
Under attraction (aIM>0) the grain boundary is enriched by I.
In fact, increasing XIGB enhances the number of the strong M–I bonds and the number of the weakened surrounding M–M bonds increases thus increasing the probability of the embrittlement.
Lejček: Grain Boundary Segregation in Metals (Springer, Heidelberg, 2010)

Gorlenkoc Magnitogorsk State Technical University, Magnitogorsk, Russia avdovin@magtu.ru; bfna87@mail.ru: cgorldima@mail.ru Keywords: high-manganese steel, wearability, hardness, microhardness, grain number, proeutectoid constituent.
The ability of the alloy to wear resistance depends on the parameters of the cast structure, namely, austenite grain size, the number and morphology of the carbide phase, its location relative to the austenite grain boundaries.
Increased cooling rate in the crystallization range results in increased number of grains from 3 to 5.
Summary table of the parameters of the microstructure containing high-manganese steel formed under different cooling conditions № VCryst, [°С/sec] Vpc, [°С/min] Grain number Number of carbides, [%] The temperature of the start of carbide precipitation, [°С] The temperature of the end of carbide precipitation, [°С] The temperature range of carbide precipitation, [°С] The thickness of grain boundary carbides, micrometers 1 1.1 14.4 3 14.80 788 693 150 ~ 30 2 1.9 21 3 6.70 782 632 149 <30 3 3.7 24 4 4.88 771 624 147 <30 4 4.5 60 4 4.26 763 617 146 ~ 1 5 8.9 108 4 2.83 757 613 144 ~ 1 6 13.6 196 4 2.63 731 591 140 ~ 1 7 17.6 255 5 2.37 711 575 136 ~ 1 8 25 327.6 5 2.10 694 563 131 ~ 0.3 The most uniform grain size structure of austenite is formed at the cooling rate of the alloy in the temperature range of crystallization of 4.5° C/sec.
Conclusion The cooling rate of the alloy affects the parameters of the cast primary structure of Hadfield steel: grain size, the number and morphology of the carbide phase.