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In order to simulate the normal force of grains on die surface, the indentation of a symmetric, cone-shape grain with the rough surface is used as the model of the single-grain polishing.
Since the interval between every pair of grain is commonly large than the diameter of the plastic deformation zone generated during the indentation of the cone-shape grain, the plastic deformation zones do not meet each other.
ABC section presents the axial plane of the cone-shape grain with the cone angle 2�; h is the depth of the grain in the workpiece.
Using a vidicon with 20 times magnification, and the photographs are uploaded into a computer, and count the number of grains at any 5 regions, then the even grain density is obtained.
Since all acting grains are not on the same plane of the polishing head, when the force is small, the total number of acting grains is less, and the depth is larger.

While numbers of technologies have been developed to enable full densification, maintaining the nanometric microstructure remains a challenge [3-5].
Fig. 6 pH value dependence of grain size of PZT 52/48 powders calcined at 600°C for 3h.
Effect of pH value of the sol and calcination temperature on the grain size.
The grain boundary is clear without any precipitate.
The difference of grain sizes of the powders is wiped by the high sintering temperature.

The meso-mechanical model allows for inclusion of all microdefects in the polycrystalline structure that exists at the grain boundary interfaces and inside the grains.
(3) where: - are local strains due to existence of single “s” defect (meso- or wing cracks), A – surface area of the RSE, Ncr – a number of specified cracks (meso- or wing) inside the RSE.
Acknowledgement 1) Financial support of Structural Funds in the Operational Programme - Innovative Economy (IE OP) financed from the European Regional Development Fund - Project "Modern material technologies in aerospace industry", No POIG.0101.02-00-015/08 is gratefully acknowledged (RT-10: Modern barrier covers on critical engine parts). 2) This work was financially supported by Ministry of Science and Higher Education within the statutory research number S/20/2013.
Golewski, Effect of aggregate kind and graining on modelling of plain concrete under compression, Comput.

The structure has a large number of pores and cracks.
Irradiation mode was 18 keV, the energy density of the electron beam was 40 J/cm2, the pulse repetition rate was 0.3 s-1, the pulse duration was 200 ms and the number of pulses was 20.
Primary grains of silicon reach a size of about 100-120 microns (Fig. 1a).
X-ray diffraction data for initial samples of hypereutectic silumin The structure of the hypereutectic silumin after irradiation with an electron beam does not contain primary silicon grains.
The primary silicon grains size can reach 100 µm.

The temperature-time evolution of the grain-size distribution and microstrain can be monitored in detail at specimen-relevant scales.
This type of nanocomposite microstructure provides an efficient averaging of the magneto-crystalline anisotropy and magnetostrictive coefficients of the nanophase over a large number of grains within the nanomaterial.
While the evolution with temperature and the average volumeweighted grain-sizes are rather similar for both as-quenched and as-milled specimens (Fig. 5), the widths of the grain-size distributions vary significantly (Fig. 6).
Fig. 5 Temperature evolution of the average grain size and microstrain for the bcc Co(Fe) main phase of the CoFe-Zr-B alloy.
Information on nanocrystallization and grain-growth is essential to the guidance of sintering experiments; for instance, sintering rates were already shown to vary significantly with the grain-size distribution widths [18].

The heat treatment process and coding number of every sample are listed in Table 2.
The austenitic grain size of 840°C × 60 min sample is 8-9 level, and the austenitic grain size in zero time holding is 9-10 level.
The grain size in zero time holding is smaller than that with holding time (60 min), which may be resulted from no time for the austenite grain to grow up.
According to the Hall-Patch equation, σ = σ0 + Kd-1/2, σ is the strength of materials (MPa); σ0 is the strength of crystal grain inside(MPa); K is constant, d is the diameter of the grain, fine grain contributes to strength and hardness of the steel.
This may be ascribed to the smaller austenitic crystal grain and the uneven distribution of the carbon concentration in austenitic crystal grain.

The mean grain size is about 10 μm.
As shown in Fig. 1(b), large amounts of the new fine grains appear at the initial grain boundaries, especially at triple junctions, which may be the consequence of recrystallization during hot extrusion[7,8].
Moreover, non-recrystallized regions in the original grains are remained and the mean grain size is about 5 μm.
The nucleus will grow by the process of grain boundary migration.
As illustrated in the Fig.3a, numbers of smaller crystallines about 5 nm in different orientations are around Mg2Si particle.

The microstructure also shows segregation free grains with clearly visible grain boundaries.
The microstructure consists of fairly uniform, equi-axed and fine grains.
The grains are slightly oriented in the longitudinal direction (rolling direction).
These figures reveal that the grains are not fully recrystallized and with decrease in temperature from 350°C to 300°C, the number of grains with serrated grain boundaries has increased and recrystallized grains have formed.
Large numbers of scattered secondary cracks are found to be present and these appear unusually deep.

In addition, the half-width of this Raman spectrum curve is about 67cm-1, which is similar to the theoretical half-width (50cm-1) of the two layers of graphene, so the graphene used is a multi-layer number.
After extrusion deformation, the crystal grains are elongated along the extrusion direction.
The grain boundaries are blurred and present a fibrous structure.
Finally, the hardness drops monotonously at the terminal stage of the retrogression mainly due to the gradual coarsening of η′ (MgZn2) particles both inside the grains and along grain boundaries.
In addition, there are a large number of GP zones (spherical particals) uniformly distributing within the grain, and the η′ (MgZn2) phases which are able to form within the grain and along the boundary.

The electron backscatter diffraction (EBSD) technique was used to evaluate the size of grains, grain orientation and grain boundary.
The size of grains was very small, and most of grains were equiaxed.
The main grain orientation was cube orientation, this grain orientation was useful to stamping for the alloy.
The combination of Si atom and vacancy was easy, which consumed large numbers of vacancies of supersaturated solid solution in the matrix.
The number of vacancy that can move was reduced, leading to the combination of Zn and Mg atom became difficult.