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Exceptions are constituted by rather rare cases, when registered profiles of the X-ray line (hkl) are obtained as reflections from families of crystallographic planes {hkl} belonging to the same grain or to the group of grains with the same orientation.
Thus, the total number of points in obtained diagrams is equal to that in each GPF or in some of its region of interest.
The same number of points is contained in the correlation diagrams.
Grains with the too "spoiled" crystal lattice lose the ability to deform by means of crystallographic mechanisms, so that their final orientations prove to be occasional; texture minima contain only such grains.
Since the rolling texture of Ti-Ni single crystal is very sharp [8], its GPF contains a relatively small number of experimental points, but the indicated tendency is seen distinctly.

The grains on the top surface of Fe3Al are refined to nanocrystallines and the grain size of nanocrystallines is about 35nm.
It is obviously that the grains were refined to nanometer range and the grain boundaries of nanocrystallines were blurry.
The grain boundaries of these ultrafine grains were wide and high density dislocations piled up among the grain boundaries area.
The grain boundaries with high density dislocations subdivided the ultrafine grains.
A large number of dislocations are induced by high strain.

An increased number of BCC phases resulted from high laser scanning speed.
However, when the scanning speed increased to 1.2 m/min, the number and size of pores decreased.
As the power level grew to 2200W, the number of cracks found decreased even more.
This is further corroborated by the improved microstructure and decreased number of visible macro fractures.
The number of cracks found decrease with increase in laser power.

The results show that morphology and number of ferrite change with the increase of subcritical quenching temperature.
The shape of ferrite evolved from block to thin strip, and the number decreased.
Moreover, temperature of subcritical quenching was lower than that of conventional quenching, which resulted in slow grain boundary migration and was not conducive to the austenite grain growth [2].
The reasons for that are as the following: Firstly, the subcritical quenching temperature is relatively lower, the austenite grain refinement result in the grain refinement of microstructure after subcritical quenching [4].
This paper is supported by Guiyang Municipal Science and Technology Project (Contract Number (2012101)2-5, (2012207)03), and Guizhou Industrial Research Project(Contract Number〔2014〕3018).

Also, there was a positive correlation between surface roughness and wedge feed per stroke cycle and grain size.
Honing is a cutting process with bonded grain[5,6].
The orthogonal table reduces the total number of trials and increases the amount of information of the tested points.
It was found that the increase in grain size lead to the increase in both Ra a and Rz.
The increase in grain size would result in the decrease in the number of grain per unit area and increase of the pressure on each grain under the same radial expansion (wedge feed per stroke cycle).

Two types of diamond grain, SMD35 and DMD was used.
Besides, the bit outer diameter was 20mm; the working length was 6mm; wall thickness was 2mm and water entry number was 2.
The more numbers of the complete shape diamond grains, the better the bit drilling performance.
When the diamond concentration is fixed and the processing conditions remain unchanged, the number of coarse grains in the bond surface is smaller than that of fine ones, so the averaging load acting on each grain becomes heavier which leads to a increasing cutting depth, so the armor ceramic is broken more easily and a higher efficiency is achieved.
When the grain size is small, the grain number in the bond surface grows, which will make an effective reduction to the bit abrasion rate.

The average grain size was measured by the OIM software, and the average (sub)grains size was measured by the mean linear intercept method.
The number of dislocations emitted by sources was less than the number of dislocations consumed for the formation of new GNBs and increasing misorientation of GNBs existed at e~0.22.
Upon further strain the spacing between GNBs decreases and the number GNBII increases (Fig. 2e).
It is obvious that at high strains, the number of dislocations emitted by sources was significantly higher than the number of dislocations consumed for the formation of new deformation-induced boundaries or increasing misorientation of GNBs existed at e~0.91.
The fraction of new fine grain with an average size of ~1 µm increases to ~19%.

Due to the limited number of slip systems, Mg alloys have poor formability which hinders their widespread application.
The grains in the FS zone are equiaxed and recrystallized (Figure 3a), and the grain size (average 12 µm) is significantly decreased compared to that in the BM.
The grain size in the HAZ is comparable to that in the BM, and no significant grain growth was observed.
The average grain size in the TMAZ is also comparable to that in the BM, but it contains a number of recrystallized grains (as determined from the grain size) similar to that shown in the FS zone, which indicates that the TMAZ has suffered plastic deformation and frictional heating during FS processing.
Conclusions (1) For the AZ31 Mg alloy sheet, after the FS processing, the recrystallized grains in the FS zone were formed; the average grain size is ~ 12 µm, which was significantly refined compared to the grain size (25 µm) of the original material.

The results show that the NLEMC can obtain the fine and uniform equiaxed grains structure, its average-area-circle grain diameter is 28.5μm, and its rheoforming parts, hardness is 129Hv.
The non-dendritization of alloy is mainly due to the increasing number of crystal nuclei in melt and elimination of the conditions under which the dendrites grow up.
With respect to the problem of increasing number of crystal nuclei, Fleming etal[13] reckoned that it is resulting from the secondary dendritic branches which will be broken under the action of electromagnetic field, while other experts[11] reckoned that it is mainly due to the increasing number of free crystal grains moving from crystallizer wall under the action of electromagnetic field.
If applying an electromagnetic field to the quasi-solid alloy at the same time, the temperature filed in melt tends to homogenize, and the over-cooled homogenization of the leading-edge portion of crystal grain growth will lead crystal grains to grow in form of uniaxial crystal, as shown in Fig. 3(c).
If applying an electromagnetic field to the quasi-solid alloy at the same time, the temperature filed in melt tends to homogenize, and the over-cooled homogenization of the leading-edge portion of crystal grain growth will lead crystal grains to grow in form of uniaxial crystal.

The final solidification structure often appears coarse grains, large numbers of flaw and grievous internal stress, so it is not suitable for conventional casting [2].
As a result, the effective nucleation number was increased; ultimately, cast structure was refined [6-7].
The crystal structure similarity is the major reasons for grain refinement.
Moreover, aluminum alloy melt with Sc generate abundant number of Al3(Sc, Zr) particles, these particles have important roles to play in grain refining.
Use squeeze casting could refine grains and reduce defect. 2.