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With the increase of the pressure, the number of the voids in the materials decreased, the density and the hardness increased, the change of the grain size was not obvious.
As shown in Fig. 3, there were coarse grain zones and fine grain areas after hot pressing.
After thermal deformation, the grain grown in orientation, the width of the grains decreased and the grains changed to flat morphology.
When height reduction was low, the grain orientation was not obvious.
The equiaxed grains were oriented in the direction of the pressure direction after deformation.

Therefore several grain-orientating techniques have been examined to modify piezoelectric properties in BLSFs [1,2,3].
It has been recently reported that the grain orientating improved the TCF in the thickness shear vibration mode for the CaBi4Ti4O15 (CBT) ceramics fabricated by the templated grain growth (TGG) method [6].
TCF is defined as a positive number in the case where the resonance frequency increases with temperature increasing, and as a negative number in the case where the resonance frequency decreases with temperature increasing.
Plate-like grains aligned parallel to the stacking direction.
These results support that the aligning main surface of plate-like grain in which the remanent polarizations lie originates the increase of k15.

Results and Discussion Measurement for Materials with Fine Grains.
The material of the specimen is S45C as a material with fine grains.
(a) Measured diffraction angle (b) Coarse grain going through gauge volume Fig. 4: Strain scanning method of material with coarse grains using 2D detector.
As shown in Fig. 4 (a), the number of diffraction spots obtained was only eight because of the coarse grains.
In the DSTM, the role of the gauge volume is to determine the centre of the crystal grain.

The workpiece and abrasive grain are assumed to consist of monocrystalline Si and diamond, respectively.
If the number of neighbors (�n) is four, the specific Si atom takes the diamond structure.
Fig. 7 shows the time variation of number of workpiece atoms in amorphous state. 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Number of atoms in amorphous state Time ps (b) Chemo-mechanical grinding (CMG) (a) Diamond grinding Fig. 7 Variation of number of workpiece atoms in amorphous state 2 nm (a) Diamond grinding (b) Chemo-mechanical grinding (CMG) 0 Traveling distance 0.1 nm Fig. 5 Cross sectional view of scratch groove at solid lines shown in Fig. 4, where broken line shows contour of abrasive grain in initial condition.
r1 r2 R 2 21 rr R + = (Si: R = 0.3095 nm) :n� :4 :4 > = n n � � Diamond structure Amorphous state Number of atoms within R Fig. 6 Index for crystallinity of silicon The stress caused by Si-C interaction is relatively small for all the cases shown here, because the abrasive grain size and cutting depth is very small.
According to Fig. 7, it is easily understood that the deformation volume or the number of atoms in amorphous phase becomes larger in diamond grinding than that in CMG.

As a reference, samples of base metal were also analyzed, revealing a homogeneous ASTM grain size number of 8.78±0.17 (corresponding to an average grain diameter of 17.3±1.0µm).
By means of optical microscopy and grain size measurements, this increase is attributed to dynamic recovery and recrystallization, leading to the formation of very fine grains.
In the weld area, measured values of matrix grain size combined with conditions of temperature (around 1200°C at the interface) can reasonably be attributed to grain growth mechanisms.
Fig. 4 - Grain size variation across the weld.
The maximum ASTM grain size number is observed for z=1mm and corresponds to a nominal diameter of 5.6±0.4µm while the base met al value is 17.3±1.0µm. 8 9 10 11 12 0 1 2 3 4 5 6 7 8 Distance from weld (mm) ASTM Grain size number Weld centerline.

In some places heterogeneity of plastic deformation is observed even within one austenitic grain.
In some grains micro areas were revealed with the signs of heavy as well as weak deformations.
The latter initiates a formation of new slip bands in the neighboring grains (or subgrains) so that the direction of the new slip bands differ from that in the primary grain.
The microcracks, stopped at grain boundaries, behave unlike slip bands.
Increase in number of loading cycles leads to the addition of external and internal stresses in individual microstructure volumes.

If the ultrafine-grained materials are indeed manufactured industrially, it may offer a great advantage to a wide range of industry, such as light weighting of structures and components, rationalizing a large number of current steel grades, aiding recyclability, and reducing alloy costs.
The optimized SSMR condition provides the ultrafine-grained ferrite of about 1 µm in grain diameter except for a region near the thichness center of the sheet.
The center of the sheet consists of ferrite and bainite with cementite precipitation both at grain boundaries and inside grains.
Summary Ultrafine-grained C-Mn steel sheets with 1µm in average grain size have been obtained by SSMR process, in which the finish rolling temperature is around Ae3.
In addition, more than 80% of ferrite grain boundaries are of high-angle, consequently assuring the increase in strength by grain refinement according to Hall-Petch relationship.

In contrast SPDprocessed materials possess a granular structure containing a significant number of high angle grain boundaries [2, 3].
Within a various number of different SPD-techniques [2] the most utilized are Equal Channel Angular Extrusion (ECAE) and High Pressure Torsion (HPT).
The smallest grains have a diameter of ~30 nm that is well in the nanocrystalline range [2].
The SAED shows concentrations suggesting the coexistence of low- and high-angle grain boundaries.
According to the comprehensive results in [18] the SRS of bcc metals decreases with a reduction of grain size, since new grain boundaries act as long-range obstacles that can not be overcome by thermal activation.

We should calculate the differences between the two sides of Eq. (1) in Eq. set(1) and that of Eq.(2~11) in Eq. set(1), and then let (a¢=2, 3, ¼ , 11), we can obtain (2) According to the EET theory we can know that the total number of covalent electron ånc of all atoms in a structure unit should be equal to the sum of the number of covalent electron of all covalent bonds in the same structure unit, i.e. ånc=n1+n2+¼+n11= n1åIa¢ra¢.
In ref.[9], the PSF of sN was defined as the number of atom state groups which satisfying the bond length difference DDa<0.005 nm, it is considered that the larger the number of probable atom state groups sN in a phase, the stabler the phase.
In ref.[10], the PSF F was defined as F=åna[(fu+fv)/2]Ia, where, na is the number of covalent electron pairs on the covalent bond a, Ia is the equivalent bond number of bond a, fu and fv are forming-bond abilities of the two forming-atoms u and v, their values were shown in ref.[7].
From the VESs of Al8Fe4Ce and Al4Ce in Table 1 and 2, We can see the numbers of covalent electron pairs n1 in their strongest bond are =0.9611 and ＝0.6189 separately, they are bigger than that of the matrix α-Al (=0.2086), so they can hinder the movement of dislocation and the slipping of the grain boundary strongly.
That with one another seizes Ce atoms with the center of Al atoms and restricts the growth of grains result in the quantity of crystal nucleus increased and the difficulty of the grains growth.

The number of elements in the mesh is 4200 and the shape of element is quadrangle.
The change of copper grain size.
But in general, the copper layer is composed by united grains and the grain size is about 4μm.
We also know if steel is hardened by laser and its temperature is up to 1300 K, a large numbers of acicular martensite will be observed[14].
In Fig 8(b), the number of twins is not so much and their orientations are random.