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The solution with the greatest number of votes is deemed the most likely.
Comparisons are then made of the number of observed spots in the RDP with those predicted in a simulation of the pattern using the mean orientation.
Numerous studies have been made using the DFC procedure to form OIM images on a large number of materials most of which were single-phase materials.
The number of spots observed was also less than what was seen in a selected are diffraction pattern recorded from the same area.
Hence grain map 6b is a better representation of the grain contiguity than that shown in figure 6a.

At 20 % deformation a relatively large number of voids can be observed.
At 70 % cold work the number of voids is smaller than at 20 %, but their shape is again almost spherical.
They number is not different from that recorded at 70 % cold work.
Continuous deformation leads to new grain formation, and the number of the grains increases as the forming degree increases.
From figure 3, it is also observable that the number of the grains is not changing appreciably, only the shape of the grain become more elongated.

In either case, the scale of the structure is determined in the first instance by the number density of effective nucleation sites.
In the case of grain structure, grain growth must subsequently be controlled to sustain refinement and ensure thermal stability.
Control and Stability of Grain Structure Cast Alloys.
Effective grain refinement is considered to correspond to an average grain diameter of <200µm and normal cast grain sizes are typically not less than 150-200µm [7].
Refinement of grain size and stabilisation of refined grain structure remain key research targets in wrought Al alloys [9].

The nucleation rate is the number of grains nucleated within a given time in the untransformed unit part of the parent phase.
It was assumed that after the transformation the grain size number (m) of the finest austenite grain structure would be a maximum of 10, NA = 8192 grain/mm2 (Eq. (11)), and thus on the simulated area the maximum number of developed austenite grains can be 1/2.84*10-3≈23.
The average areas of grains were 23.28 µm2, 36.41 µm2 and 76.76 µm2, the number of grains/mm2 (NA) were 42957, 27464 and 13028, and the grain size numbers (m) were ~12, ~11 and ~10.
A linear curve is kept for the nucleation rate as a function of grain size number (m) (Fig. 7b).
a) b) Fig. 7. a: Number of nuclei in a unit area as a function of time, b: nucleation rate as a function of grain size number The effect of carbon concentration.

An experiment, in which a lengthy number billet at a temperature of 500 °C rolled from a diameter of 30 mm to a diameter of 15 mm in the mill SVP-08, was conducted.
All industrially used metal materials have a coarse-grained structure with grain-crystallite dimensions of the order of 20-80 μm or more.
The periphery of the rod is an equiaxial ultrafine-grained structure with grains size 300-600 nm.
In the initial state, titanium grade VT-1 has a coarse-grained structure with an average grain size of 70-80 µm.
Acknowledgments This work was partially supported by Ministry of Science and Education Republic of Kazakhstan, grant number AP05131382 - “Development and research of the technology for producing ultrafine-grained materials with improved mechanical properties and increased radiation resistance for using them as materials of the first wall of fusion reactors and in nuclear energy” (2018-2020).

The initial grain size distribution before vibration is shown in Fig. 3.
The main grain sizes of the crushed rock sample range from 25 to 45 mm.
Then, the water weight of each layer was measured via draining away the pore water of each layer in order of hole Number 1, 2, 3 and 4, as shown in Fig. 1.
Finally, the relevant porosity in each layer of the crushed rock sample from the sequence as a function of the cycle numbers was measured.
The grain sizes of the crushed rock sample are relatively smaller than the initial garin sizes due to fracturing edge angles of crushed rock grain during vibration.

The HPT made samples exhibit ultra fine grained (UFG) structure with grain size around 100 nm.
Recently it has been demonstrated that ultra fine grained (UFG) metals with grain size around 100 nm can be produced by high pressure torsion (HPT) [2].
A number of UFG metals exhibit favorable mechanical properties consisting in a combination of a very high strength and a significant ductility.
Results and Discussion Coarse-Grained Specimens.
Similar behavior of HV was observed also in HPT deformed Cu [9] and it seems to be typical for a number of HPT deformed metals.

The rotating bending processes carried out with various conditions show that the grains in cross-section and longitudinal section of magnesium alloy tube were refined for all samples by the rotating bending process with rotation speed of 20r/min for different rotation numbers and temperatures.
It can be seen that the grain number increased significantly in the relative area after rotating bending process.
After plastic deformation at low temperature region (150 and 200°C), the dense dislocation piled up in the interior of grains accompanied by the forming of a large number of twins.
The average grain size was reduced due to the newly formed fine grains.
As the grain size is small, the strong deformation had little effect of on the grain shape as well as grain boundaries.

Phase material microstructure and grain area ratio directly affects the material uniformity, uniformity of material differences caused by different grain characteristics which ultrasound parameters.
Thus, studying further on the changing relationship between velocity and grain size is also necessary.
Figure 5-1 Proportion of the α phase of the sample grain and trend of the ultrasonic velocity The relationship between the area ratio of α phase of sample and acoustic attenuation coefficient When the acoustic wave spreads in the medium of uniform grain material, the scattering due to the grain boundaries will cause the attenuation of sound waves.
In the heat treatment process, with the α-phase single area ratio and the ratio of the number increases, the scattering when sound wave spreads in media aggravates, resulting in the increase acoustic attenuation coefficient.
With the increase of the ratio of α phase of the grain, it will lead to the variation in elastic modulus and density.

During homogenizing treatment, a large number of dispersive Mg2Si phase appeared inside grains, and large number of the phases containing Er were dissolved into the matrix.
Fig. 2(a) shows that the grain size is non-uniform.
In addition, the bright granular phases appeared inside grains.
The bright granular phases inside the grains and the bright strip-liked phase in the grain boundary were complex compounds rich in Al, Mg, Si, Fe and the rare earth elements of Er (called Er-rich phase).
Besides, Er-rich phases on the grain boundary became smaller or even disappeared, while in the grain boundary Er-containing phases became discontinuous and sparseness.