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A large number of strain-induced subboundaries with low-angle misorientations appeared at early deformation.
A great number of planar low-angle boundaries evolved at relatively small strains and form well-defined banded structure during MDF and ECAP (Figs. 2a and 2d).
At early stage of deformation, the formation of a large number of strain-induced low-angle boundaries occurs in the AT samples (Figs. 3a and 3d) that is similar to the ST samples.
On the other hand, the AT samples subjected to ECAP are characterized by almost linear relationships of FHAB and FUFG with number of passes.
Acknowledgements The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.575.21.0005 (ID number RFMEFI57514X0005) is gratefully acknowledged.

The important parameter of ARB is the number of cycles and then the consequent number of layers of the final sample.
The analysis of mean grains size and high angle grain boundaries (HAGB) fraction as a function of the number of cycles showed an early formation of a subgrained structure with low angle boundaries and then the evolution of the microstructure towards an ultrafine-grained structure with an increase of HAGB.
For n = 1, due to the small number of grains in the analyzed zone, no conclusion can be drawn about a predominant orientation, but a large gradient of orientations can be observed inside the grains.
(b) Evolution of the average grain size (♦) with the number of ARB cycles.
In Fig.3 (a), as the fraction of High Angle Grain Boundaries (HAGB) is increasing with the number of ARB cycles, it appears that ultrafine grains are progressively formed after the first cycle (ε1 = 0.8).

This has led to the development of a number of commercially important Zr-containing magnesium alloys.
This complex behaviour of Zr on grain structure with the presence of intensive melt shearing could be explained by the change of the type and number of the heterogenous nucleating particles.
Therefore, when intensive melt shearing was applied to pure Mg melt, the grain structure was transformed from columnar grains to equiaxed grains, contributing to the increasing number of heterogenious nucleating particles (MgO).
Potent nucleating particles can be effective for grain refinement only if they have sufficiently high particle number density in the melt.
When Zr concentration is larger than 0.443%, the un-dissolved Zr particles may experience rapid coarsening under intensive melt shearing, resulting in a rapid decrease in particle number density.

Each region is given a number corresponding to a grain orientation, grain boundary exists between block with different orientation.
The grain volume V is the number of site within a 3D grain, the average grain volume is the total number of lattice points divided by the number of grains.
The increase of the number of neighbours tend to reduce the grain size distribution and avoid the occurrence of abnormal grain growth.
Here we investigate the way the number of neighbouring grains influence the variation of volume of a grain.
For all the grains, we calculate the number of grains with different orientations connected to them and their variation of volume during 1 MCS (dV/dt) .

Its grain output reached 111.41 billion kg in 2011; commodity grain output amounted to 90 billion kg and became the first major grain-producing province beyond Henan.
Meanwhile, Heilongjiang also ranks first in total grain output, commodity grain output and grain self-sufficiency rate. 30 billion kg of 90 billion kg commodity grain is contributed by the Heilongjiang reclamation.
The rate of its commodity grain is as high as 90% and the grain farmers make great contributions to guarantee national grain security in Heilongjiang reclamation.
It includes: the number of labor force, whether have cadre relatives or not, the number of underage children, the number of boys, the number of girls, the highest education in family and the number of non-healthy persons. (1) The number of labor force has a positive impact on farmers’ income.
It includes: the number of land blocks, sown area, the proportion of plain land, deeply plowing the land and land Huancha. (1) The number of land blocks has a negative impact on farmers’ income.

The rate-sensitivity exponent in the rate-type constitutive relation is closely related to the number of active slip systems.
Song and Abe [3] pointed out that, by using instruments such as laser-scanning microscope, r-value can be defined for respective grains in polycrystalline metal from the changes of grain profile or grain area during plastic deformation.
The relation between the shape of yield curves and the number of active slip systems was clarified.
The 12 slip systems in fcc crystal are numbered from k = 1 to 12.
It was shown [6,7] that, by changing the value of , the effects of the number of the active slip systems is studied.

Therefore, those simulations were limited to small grains in order to keep the number of grains adequate for statistically analysis.
Number of faces vs. grain size.
One important topological feature of the microstructure is the correlation between the number of faces s per grain and the relative grain size x (cf.
Figure 1: a - Number of faces vs. relative grain size for all grains together with quadratic leastsquares fit; b - Number of faces vs. relative grain size divided into size classes for three different time steps.
Figure 1a shows the number of faces of the individual grains as a function of the relative grain size for the 500 th MCS.

In this paper, hydroxyapatite was used as a grain growth inhibitor additive to get nano-titania ceramics with different grain size, and the effect of grain size on the bioactivity was studied in vitro.
In this paper, hydroxyapatite was used as a grain growth inhibitor additive to get nano-titania ceramics with different grain size, and the effect of grain size on the bioactivity was studied in vitro.
Ltd, China) were used as grain growth inhibitors.
The result of MTT assay showed that the number of viable cells was not statistically significantly different between the HT and the control (HA) (p<0.05), but the number of cells on the MT was much lower than the number on the control (p<0.05).
Both HA additive and the grain size of HT might be responsible for the bioactivity of HT.

%P) by refining grain size.
Microstructural evolution of the copper alloy with the number of the 3-layers ARB cycles was investigated by optical microscopy (OM), transmission electron microscopy (TEM), and electron back scatter diffraction (EBSD).
Results and Discussion Tensile properties of Cu-0.02P alloy (phosphorus deoxidized copper) as a function of number of 3-layers ARB cycles have been shown in Fig. 2.
Tensile strength of the specimen processed by the 2-layers and 3-layers ARB increased with the number of cycles.
A large number of dislocations and cell structures were observed in the samples after 3 cycles.

During grinding a large number of micrometer or sub-micrometer grains remove material from the surface of a workpiece, acting as cutting tools.
They were able to determine the origins of lattice distortion of the substrate and the dependence of material removal rate on the ratio of sp2 to sp3 phases by conducting analyses of RDF and coordination number.
At a later moment, all grains are involved in the process, with the two back grains removing less material than the two front ones and forming chip in the area between the two rows of abrasive grains.
It can be seen that the number of atoms in a deformed lattice constitute a small part of the total number of atoms, as expected, because depth of cut is less than the 1/10 of total workpiece height and thus, deformation occurs at a few atomic layers beneath the surface.
The number of atoms belonging either to the plastic deformation region or the cutting chip range is larger with larger depth of cut.