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The sample with high transparency is fewer mineral composition numbers, similar mineral compositions and bigger crystal particles.
The typical samples were numbered according to its transparency.
The number of mineral compositions also affects the transparent degree of Shoushan Stone.
The more the number of mineral compositions is, the more the reflection is and the less the transparency is.
The number of mineral compositions in the sample also affects its transparent degree.

The non-ohmic properties of ZnO varistors originate from the grain boundaries and highly depend on the grain size [4].
There are connected pores around the grains.
Some grains are about 1µm in size, which means that the grains begin to nucleate and grow.
Thus, there are shortcuts for currents which contain only a small number of insulating intergranular layers.
The ZnO grains as well as the spinel phase are obvious in the image, and the average grain size is 3 to 4 µm.

Microstructural observation showed that the increasing in mixing time has increased the number of AC particles to become agglomerated.
The black particles indicate AC particles which located at the grain boundaries.
The AC particles such as showed in Fig. 2(a) had been well-structured along the grain boundaries.
Reinforcement concentration between the grains will hold the grains and preventing from grain dislocation and slow down the grain growth [12].
It can be observed that the number of AC particles become agglomerated with the increasing of mixing times where the size of AC particles increased with the increasing of mixing time.

T. (001)- and (212)-oriented recrystallized grains mainly nucleate, and (001)-oriented grains mainly grow up.
Although the nucleation of (111)-oriented grains was also observed, the size of such grains is at most of μm order and is smaller than that of (001)-oriented grains.
In contrast, (111)-oriented grains hardly grow with increasing storage time, although the number of nucleated grains increases.
Except (111)- and (001)-oriented grains, (212)- and (112)-oriented grains were also observed.
The grains nucleated in the growth direction of recrystallized grains and (001)-oriented grains mainly grew up to a maximum grain size of approximately 40 μm.

The traces of grain boundaries were parallel to the ED and TD.
Despite the texture of the initial state was dominated by cube-oriented grains, the grains with orientation forming copper-type texture are also well-marked.
For both metals the development of deformation microstructure and texture as a function of the number of passes was analysed using the SEM/EBSD system on the ND/ED and ND/TD sections.
(i) The number of applied passes had a strong impact on the global deformation behaviour and on the intensity of grain refinement.
Two types of boundaries between the grains are observed in the present copper and AA1050 alloy samples: the boundaries that separate the grains placed inside a particular layer and the boundaries between the grains of adjacent layers.

The change of size and shape of dimples fracture from larger and irregular shape dimples in initial sample to much smaller and grains-look like dimples in ECAPed sample indicating the grain refinement occurred after ECAP.
Introduction The grain refinement is one of the strengthening method of the metal alloys based on the Hall Petch formula which relates the strength with the inverse of the grain sizes, the finer the grains the stronger the alloys.
However, small number of larger dimples still can be observed in a small area.
It is clear from Fig. 4 that the small size dimples have more regular shape (looks like grains), where the initial voids might initiate at grain boundary as the strain concentrator.
The change of size and shape of dimples fracture from larger and irregular shape dimples in initial sample to much smaller and grains-look like dimples in ECAPed sample indicating the grain refinement occurred after ECAP.

Grain size.
Total number of cell state variables.
depends on the total number of cells in each array, and .
The distribution of grains size was analysed in terms of the ferret diameter, and Weibull analysis was performed to obtain Weibull grain size parameters, in order to incorporate the distribution of grains size in CAFE model using random number generators.
A misorientation angle of grains was incorporated in the brittle cells of CAFE model using random number generators, with following Weibull parameters: shape parameter = 1. 1931, scale parameter = 39.832.

The average grain size of sample 1 is the greatest of all the samples.
And the fully recrystallized grain is the main structural feature for sample 1.
Since it is difficult to distinguish high-angle grain boundary and the low-angle grain boundary in optical microscope, further observation is conducted with EBSD.
For grain boundaries with grain boundary misorientation that is more than 15 degrees are defined as high-angle boundary.
Fig. 3 Grain boundary map of 7055 aluminum alloy samples in various conditions obtained by EBSD: (a) sample 1; (b) sample 3; (c) sample 4; (d) sample 5 Table 2 Fraction and length of different grain boundaries measured by EBSD Sample Number Fraction and length of different grain boundaries 2°～5° 5°～15° 15°～180° Fraction Length (cm) Fraction Length (cm) Fraction Length (cm) 1 0.321 4.98 0.225 3.49 0.454 7.03 3 0.324 3.78 0.216 2.51 0.460 5.35 4 0.359 5.45 0.200 3.04 0.441 6.69 5 0.302 4.42 0.199 2.91 0.499 7.29 Relation between fracture toughness and microstructure.

Typical Journal Title and Volume Number (to be inserted by the publisher) 3 microstructures and pole figures from EBSD analysis are presented in Figure 3 for the three steels after hot torsion at 900 and 1050°C and a strain rate of 1 s-1.
At the onset of straining, sub-boundaries form near the original grain boundaries.
Above this temperature range, the energy stored by deformation is lower (higher recovery) and the pinning effect by precipitates ( NbCN, TiN or TiC) Journal Title and Volume Number (to be inserted by the publisher) 5 is also observed [6].
Moreover, after the plateau, the grains and subgrains with D2 orientation grow and the overall grain and subgrain size increase.
Jonas: Acta Metall., vol. 32, 1984, p. 2077 Journal Title and Volume Number (to be inserted by the publisher) 7 [5] J.

The SiO2 additives have significant effect on grain sizes.
The nonferroelectric phase of twinned ZrO2 and PbSiO3 also tend to segregate on the grain boundary, which enhances the bond energy of grain boundary.
In general, the great improvement of fracture strength with SiO2 dopant added to PMS-PZT ceramics should be attributed to two reasons: (1) the segregatation of the second phase on grain boundary inhibites the growth of grain sizes and reinforces the bond energy of grain boundary, which leads to the fracture mode change from the mixture of transgranular and intergranular to predominantly transgranular; and (2) the reduction of the number and distribution of pores in the specimens enhance the bond energy of grain boundary.
The great improvement of fracture strength with SiO2 dopant added to PMS-PZT ceramics mainly due to the secondary phase segregating on grain boundary inhibites the growth of grain size and reinforces the bond energy of grain boundary.
Acknowledgements The authors gratefully thank the support of National High Technology Research and Development Program of China (grant number: 2001AA325030) and Jiangxi Nature Science Foundation.