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Due to the f(amin) represents the number of the boxes of the same maximum height probability (NPmax(e) = Namin(e) ~ e--f(amin)), while f(amax) reflects the number of the minimum one (NPmin(e) = Namax(e) ~ e--f(amax)), the Df describes the ratio of the number of the maximum probability and that of the minimum one: NPmax(e)/NPmin(e) = e -Df.
Experimental results indicate that the number of lowest valleys of all HfO2 films is larger than that of the highest peaks (at e = 1/512, NHmax/ NHmin » 3, 77, 11, 29 for HfO2 grown at RT, 200 oC, 400 oC and 600 oC, respectively).
The grain sizes become larger with the increasing temperature.
As listed in table1, it is important to recognize that d spacing (d-111) decreases with increasing grain size below 7 nm, but becomes larger with grain size of 14.8 nm.
Fig.3 (b) also shows the relationship of Da and the grain size of HfO2 films.

Abrasive grain was estimated as a sphere with diameter d0.
Spacing of abrasive grain.
If abrasive grains of the number m grind the space between A1 and Am until the Am cuts the same line of B1 cutting, then the average spacing scratch generated by abrasive grain b becomes b =(ω/m)cosθ.
The abrasive grain mesh of the diamond wheel used three kinds of grain numbers; 100, 270 and 500.
The hardness of the diamond wheel is expressed as the strength of a bonding agent supporting each diamond grain.

At R/2, the number of residual deformed grains increases significantly, and the deformation is elongated along the 45° direction.
With the increase in torsion amount, the recrystallization degree of the microstructure at the center of the sample gradually decreases, resulting in an increase in the number of residual deformed grains.
Blue represents recrystallized grains, yellow represents substructure grains, and red represents deformed grains.
It can be seen that not all small grains belong to recrystallized grains with low distortion energy.
Additionally, the deformation uniformity improves within and along the grain boundaries of large grains.

Grain orientation has a great influence on the formation of twins.
Zhao[10] states that the increased densities of twins make great contributions to finer grain size and higher microhardness besides for large number of dislocations when CP Ti sample is processed by ECAP with the angle of 120° between channels at room temperature.
The average grain size of annealed Ti is 90μm (see fig.1a).
It may relate with grain orientations.
At even small strain, there are a large number of twins in samples processed by DPD.

DRX grain size and volume fraction were simulated using the CA model.
It was observed that DRX kinetics depends on both thermo-mechanical parameters and initial grain sizes.
The number of particles is predefined by the actual situation, and dispersed second-phase particles are distributed stochastically throughout the CA domain.
The model of grain growth.
The simulated results also indicate the DRX is prone to occur for the finer initial grain size.

The final grain size and recrystallization texture depend on many factors including thermomechanical history.
The area and the size of the recrystallized grains generally increase as the annealing time increases.
It is observed that some deformed grains are completely consumed by new grains, whereas other deformed grains are partially replaced by new grains .Specimen 1 and specimen 2, 22 seconds annealing recrystallization did not occur, When annealing 24 seconds the specimen 2 had the approximately 35% deformation band to form the recrystallization, but the specimen 1 basic has not formed the recrystallization.
Annealing process conditions in the specimens are complete recrystallization and grain growth occurred.
These differences may be related to the number of shear bands formed in the cold rolled state, In the equiaxial-grained specimen, Gauss texture and rotateds the Gauss texture of the with the certain deviation are significantly strengthened

After rolling, Al8Cu4Er phase could be fragmentated into dispersed particle which leaded to an increase of the grain boundary strengthening .
Some coarse bright particles were present in grain-boundary eutectic structure.
After hot rolling , Al8Cu4Er particles were crushed up along with the grain boundary (Fig.5b) .
The precipitation of Ω phase also includes the nucleation and coarsening .The number of nucleation site and coarsening force affect the distribution and the size of Ω precipitate .
As discussed above , addition of Er in alloy decreased the number of Ag/Mg co-clusters.

These fine grains are produced by dynamic recrystallization at the grain boundaries of original grains.
Smaller grains a few microns in size are mainly distributed surrounding original large grains in the form of either necklace or colony.
However, the number (or the volume fraction) of the recrystallized grains increases significantly with strain.
Microstructures in the fractured samples consisted of small recrystallized grains and non-recrystallized large grains.
The recrystallized grains were grouped in a necklace structure around large grains.

It reveals that the melt spinning gives rise to the obvious broadening of the major diffraction peaks of the alloys, to be ascribed to the refined grain and the stored stress in the grains by melt spinning.
Fig. 3 shows the evolution of the discharge capacities of the Mg20Ni9M1 (M=Cu, Co) alloys with the cycle number.
On the other hand, the refined grain by melt spinning is favourable to the discharge capacity because the grain boundaries possess the distribution of the maximum hydrogen concentrations [7].
Fig. 4 presents the cycle number dependence of the SN values of the Mg20Ni9M1 (M=Cu, Co) alloys.
The enhanced D value by the melt spinning is ascribed to the refinement of the grains of the alloys due to that the huge numbers of the grain boundaries available in the nanocrystalline materials provide easy pathways for hydrogen diffusion and accelerate the hydrogen absorbing/desorbing process.

In order to deform the material to a large total strain, the billet is pressed through the die a number of times, since its cross sectional area remains unchanged during ECAE.
Second, the initial grain size was smaller (200 µm) and the authors did not report the presence of recovered grains in the starting condition.
TD ED 0 10 20 30 40 50 60 70 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Number fraction Misorientation angle (deg) as-deformed 400°C for 15 min Fig. 5.
Fine equiaxed grains coexist with coarser areas where grain fragmentation is less pronounced.
The mean grain size in the deformed state is 650 nm.