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Dpor: diameter of pores measured starting from fracture topography to avoid the artefacts related to polishing (pull out of grains).
Ceramics F and H contain cordierite (Table 2) and have, a priori, a high interface number, thus more traps what leads to a high breakdown strength (14.9 and 14.4 kV/mm).
In the case of ceramics B, in spite of the high number of interfaces, the nature of inter-granular phases, without cordierite, probably leads to other types of interfaces which decrease breakdown strength (13.9 kV/mm).
Indeed, strong breakdown strength at room temperature can be related to strong capacity to trap charges at interfaces localized in the grain boundaries.
At the first steps of wear (low load, short time), the dielectric phenomena seem to have a significant role on the fracturing of alumina grains.

These grains are 4- 7µm thick which is equal to the 2-4 grains thickness at this reduction level.
The recrystallized grains predominantly form at the grain boundaries in 30% rolled material, figure3b.
At 80% rolling, the recrystallized grains formed inside the microbanded grains and become larger by consuming the deformed material of the parent grains.
These shear bands covered several grain widths instead of being confined inside a single grain.
In a detailed investigation of partially recrystallized warm rolled 75% IF steel it was found that double sets shear banded grains which are small in number, were missing in the 8% partially recrystallized stage and replaced by some grains which were completely recrystallized.

It can been seen from Fig.2 that the grain size of the web is minimum , the grain size of R -joint is biggest and the grain size of flange is in the middle.
There are coarse grains and the grain orientation confusion in R-joint.At the rolling deformation, because of difficult deformation, the amount of grain crushing is not the same,resulting in abnormal coarse grains appearing in R-joint .
Because of finer grain of web, there is much more grain boundaries than that of flange.
In engineering application of H-beam, a large number of grain boundaries continue to hinder dislocation movement.
Table 3 Average grain size number PA1 PA2 PA3 PB1 PB2 PB3 PC1 PC2 grain size number 9.6 9.3 9.1 9.8 9.6 9.0 9.8 9.2 average diameter （μm） 11.3 12.8 13.5 10.7 11.7 13.9 10.8 13.1 PC3 PD1 PD2 PD3 PE1 PE2 PE3 grain size number 9.6 9.2 9.3 9.6 9.5 9.5 9.3 average diameter （μm） 11.5 13.4 12.7 11.5 11.2 11.4 11.5 In the rolling deformation of H-beam, the deformation of R-joint is the most complex and heat stored in R-joint is the maximum .So the cooling effect of R-joint is worse than that ofthe flange webs, resulting in uneven grain size in R-joint.

(2) I-current; U-voltage; A-the effective cross-sectional area of the sensing material; Nd-the carriers density; VB0-the grain boundary potential; ε-permittivity of the material; T-temperature; kB-Boltzmann constant; Nbarr-the number of potential barriers.
Obviously, there is no activation source in dark, so the number of electron and hole pairs in dark is the smallest.
Consequently, the number of holes that actually react with as shown in eq.4 raises in the same order, too.
Then the width of the depletion layer decreases as a result of the decrease of the number of around the grain boundary.
And VB0 is the grain-boundary potential, Nbarr means the amount of grains of the material tested.

The films were not smooth, with grains and porosity in between them, and become denser as film thickness increased.
Figure. 3 presents the average of the surface roughness and the grain size of the prepared ZnO thin films.
ZnO grains size and the surface roughness were gradually increase as result to increase the numbers layers.
Crystallization probably encourage large grains and moderate defects and dangling bonds.
Fig. 3 The grain size and average surface roughness of ZnO thin films as a function of the layers number obtained via AFM.

When the extrusion temperature is up to 390°C, the grain size increases significantly, but the second phase precipitation along grain boundaries transforms into continuous and uniform-distribution precipitation within the grain.
When the temperature is 300ºC, big grains in magnesium alloy form new grains under the influence of stress; at the same time, relative rotation among grains causes imperfect dynamic recrystallization of the deformed structure, which eventually forms fine particles.
At 330 ºC, some black second phase begin to precipitate along the boundary of the grains.
Since the pinning effect of the black second phase on the grain boundary prevents the grains from growing big, the grains becoming finer, which accounts for the increase of tensile strength.
When the extrusion ratio is 60, the grain has the smallest size (being about 3-5μm), the second phase in diffusion precipitation refines gradually and increases in number, and the tensile strength reaches to its highest.

Meanwhile, a large number of small scattered martensite-austenite (M-A) islands are observed in the color optical micrograph (Fig. 3).
It indicates that a large number of large angle grain boundaries exist in the investigated steel.
It is seen that a large number of sub-grains exist in the tested steel.
In this work, the microstructures predominantly consist of a large number of acicular ferrite and polygonal ferrite grains plus a small proportion of scattered M-A constituents.
In the present work, the microstructures mainly consist of a large number of acicular ferrite.

When the extrusion temperature is 1080℃, there is still some region of unrecrystallization, but the number of fine recrystallization grain become more.
The recrystallization grain is very fine and grain size is about 4～5μm.
Some finer recrystallization grain lie the uniform grain and the grain size is about 1µm.
The γ' phase lie the grain boundary inhibit the free growth of grain.
When the heat time reach 90min, some grain with γ' phase is still fine, but little grain without γ' phase grow rapidly and grain size reach 8µm.

Many numbers of experimental studies and simulation models have been conducted in order to understand the texture development in pure magnesium and its alloys [4].
However, it was showed a large change of grain size and texture in extruded AZ80 magnesium alloy at stress of 15-20MPa.
The grain boundaries with a misorientation higher than 15° are expressed by the black lines.
The uniform grain structure is shown in specimen before deformation, and the grain size is about 42μm.
Also, although not shown here, the grain size increases with an increase of true strain.

During the operation of the automaton, in each step the cells need to have a status obtained from a determined, finte number set of states.
The excess energy arising from the fact, that the atoms situated inside the grains have less energy than the ones situated at the grain boundaries, is called boundary energy.
By taking stereological principles [9] into consideration, besides the transformed proportion, the change of the average grain size and the distribution of the grain size can also be determined.
If the number of cells is divided by the total number of cells than the value of the Avrami exponent (n) is maximum 2, while if this operation is carried out with the second power of the cells the result is n = 3, respectively by raising to the third power and carrying out the division the value of the Avrami exponent is n = 4.
The calculated grain size distribution.