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Where 8 represents the number of molecules in a unit cell of spinal lattice, M is the molecular weight of the sample, "a" is the lattice constant and N is the Avogadro's number.
It is also useful to interpret the amount of porosity and find out the size of grains and their positions in the crystal.
In all the samples the morphology of maximum grain structure as seen from the scanning electron microscopy (SEM) consist of cellular type grains size varying from 5 to 10 µm and confirm the formation of Cu Zn ferrite structure.
In determining the grain size, the interaction of grain boundary and porosity along with sintering temperature is important [17,18].
In our case grains were grow smaller and shows the phenomenon of continuous grain growth where grain size increases with the increase of Cu content.

It is found from the experiments that the grain size and the layers of FAB may have great influence on the removal rate of polishing; the surface roughness is mainly decided by the ball diameter and the layers of FAB.
The results of experiments are discussed and analyzed, it indicates that the efficiency and quality depend on flotage and the number of active grains when the velocity of workpiece is assigned.
In this case, the cutting depth of a grain is defined by the following equation:[3] απσ α 2 s e tan 2F = (mm) (1) here, F is the pressure of a grain acting on the workpiece in N, α is half vertex angle in °and σs is yield-point of material in MPa.
Fig.2 is the developed model of FAB; abrasive grains are distributed in the FAB.
In this study, it is also found that the removal-rate of big diameter of FAB is not obviously higher than that of small diameter of FAB, the reason is that the bigger the diameter of FAB, the less the active grains acting on the workpice .

The TMP consists of the following two parts; the first part is grain refinement and the second the creation of recovered structure stabilized by fine particles.
Particle length and number density of particles were measured using image processing software.
Thus, a hot deformation with coarse particles, leading to intense deformation around particles and thereby PSN, is an important process to obtain fine grain size.
High angle grain boundary is also denoted by white lines in (b).
The TMP consists of two parts; the first part is grain refinement and the second the creation of recovered structure stabilised by fine particles.

§ collection of samples before drawing reduction of tubes, after drawing reduction of tubes, § metallographical analysis – definition of grain orientation [5].
The described process of calculation is used by microstructures of particular planes: § addition of points of intersection boundaries of area orientated grain boundaries of microstructure with parallel (horizontal) experimental lines labelled as (Pp), in the case of microstructure, where the number of points of intersection is 422; § addition of points of intersection boundaries of area orientated grain boundaries of microstructure with vertical experimental lines (Po) is 432; § calculation of points of intersection of surface grains with parallel experimental lines related to the length unit of an experimental line (PL)P with the unit [mm-1] according to the relation § calculation of points of boundary intersection of surface grains with parallel experimental lines related to the length unit of the experimental line (PL)O with the unit [mm-1] according to a relation PL=PoLoz=4321330426=138.36mm-1 PLφ= PφLφz=4221528426=117.6mm-1 where Lo – is the total length of orthogonal
Orientation of grain boundaries – the first draw ∅57 x 5 mm Orientation of grain planes is significant according to measured and calculated values in direction of longitudinal experimental lines in all planes.
(External surface O = 1.78, middle O = 1.83 and internal surface O = 1.83) Orientation of grain boundaries – the second draw ∅50 x 3.75 mm In the longitudinal plane of the analysed sample there is an increase of grain limits orientation after the second draw in the direction from an external surface to an internal surface of the tube.
(External surface O = 3.09, middle O = 3.51 and internal surface O = 3.63) Orientation of grain boundaries – the third draw ∅44 x 3 mm Total grain orientation for the longitudinal plane of the analyzed sample is an increase of grain boundary orientation in the direction from an internal surface to an external surface of tube.

The size of TiC grains are about 3- 6 μm.
With TiC content in the layers increasing, Ti2AlC grains gradually decrease.
The lathy Ti2AlC grains of the FGM have a length of about 10 μm and a width of about 4 μm.
Results and Discussion Fig.1 Samples of the energy spectrum (EDS) The samples of the energy spectrum (EDS) are shown in Fig.1, energy spectrum analysis of the sample of the 1300°C sintering can get Ti: Al: C atom number 2.06:1:1.08, compared with Ti2AlC chemical measurement, explains the in situ synthesis method of synthesized Ti2AlC at 1300°C.
It can be seen from the figure, as the TiC in Ti2AlC volume fraction is reduced, the grain size of Ti2AlC gradually increased, Ti2AlC is the main material gradient layer microstructure, TiC powder particles distribution in Ti2AlC network structure.

Introduction Granular materials, which are composed of grains and quite common in nature, are generally treated as continuum in the classical framework of geomechanics.
Coordination number and void ratio.
The contact displacements are generally characterized in terms of the translations of the particle centers, and the rigid-body rotations of the grains around their centers.
Powders and Grains, Rotterdam, 1989, 319-322
Powders and Grains, 1993, 129-134

With the raising of the quenching temperature, the original austenite grain size increases and the martensite platelet gradually coarsens.
It is because that lath martensite is formed in the original austenite grains and the number of lath is certain in austenite grains and the size of the martensite platelet increases with increasing of austenite grain size [2].
When the quenching temperature increased, the grain size of prior austenite grew, and the martensitic laths become wide and the hardness gradually decreased.
As the rising of tempering temperature, the lath martensite gradually become thin, the austenite grains coarsens with increasing tempering temperature (figure 5), and the size of the lath martensite increases with increasing of austenite grain size.
The size of martensite platelet is coarsened and the size of original austenite grains increases from 9.2μm to 63.6μm with increasing of quenching temperatures.

Ho2O3 dopant can hinder ZnO grain growth and make the crystal grains more uniform.
That means doping of Ho2O3 can hinder ZnO grain growth.
We believe this new phase has restrained the ZnO grain growth.
Pattern a clearly shows the diffraction peaks of the spinel phase of Zn(Zn,Co,Sb)2O4 (PDF Number: 82-1101).
Ho2O3 can inhibit the ZnO grain growth.

The catalysts with small grain size of Cu had higher activity than those with big grain size.
Activities of some Cu-based catalysts and their Cu grain sizes were given in table 1.
The number in this column denotes the weight percentage of each element in the final catalyst.
The catalyst with small Cu grain size obtained by impregnation method had a higher activity than the one with big Cu grain size obtained by co-precipitation method.
The activity of the Cu-based catalyst was related to the grain sizes of Cu.

It is worth noting that the grain size of the AM60 alloy matrix is reduced to around 50 μm in the composites due to the grain refinement effect of the fibres.
Arrow A-fibre is heterogeneous nucleation substrate Grain Refinement Mechanisms.
Obviously, the supercooling of magnesium alloys can be correlated to their grain structure.
Metals that would give coarse grains yield high supercooling, and melts with low or no super- cooling give rise to fine grains.
With the reinforcement addition, the number of nuclei and the nucleation rate increases.