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There tends to be a higher density of dispersoids near the grain boundaries than in the centre of the grains, and this non-uniformity is found to be due to the presence of the cored dendritic structure after casting[4, 6], as there is not enough time to level out the microsegregations through diffusion before nucleation begins.
After grinding, the samples were polished with a fabric with diamond spray with grain sizes down to 1 µm.
These were taken in a straight line through the alloys, covering a distance of 1500 µm, crossing approximately 18-22 grains.
Results Number Density and % Area.
Fig.2 shows results for the number density and % area of both alloys.

We used the same inelasticity and friction coefficients for grain−grain and grain−wall collisions including the horizontal base.
The variation of the packing fraction ρ(t) with the number of shakes t for several tapping intensities ξ is presented in Fig. 1, where more dissipative grains (disks (A)) have been used.
In this study we work with the following definition of the grain mobility: ( ) ( ) ( ) ,1 1 1∑= −+ −= N i i i d tyty N tµ (3) where N is the number of particles, yi(t) is the y−coordinate of the ith particle at time t and the angular brackets denote an average over independent runs.
When compaction goes on, the grain mobility decreases.
An example is given in Fig. 3 where we have plotted both mobility µ(t) and density ρ(t) as functions of the number of taps t.

Fig.1 shows the clustered sand grains movement track.
This SUFA will take off only the sand grains which are satisfied critical velocity value of sand grains to jump.
With this contrary, on the sheltered lee-face, the sand grains have lots of open air and sand grains respectively relax, so fly far.
In this study, for the numerical simulation, the average clustered sand grain field density (2.65 g/cm3) and air stream field density (0.00129 g/ cm3) are assumed to be constant, and the average clustered sand field grain size and shape are set by the random number during the simulation in the whole field, then the whole sand field surface roughness are obtained automatically by using this manner.
However, for the detailed analysis needs to consider concrete influence factors and number of simulations results and should be compared with experiment.

Spherical grains are excessive alumina after burning or dissolvable phase.
The results showed that rod-like Crystal is very likely the CaCO3 and MgCO3 [9].The reactions are as follows: As shown in Fig. 3g the rod-like crystals become thick but the number of them is reduced after hydration for 24h.
Instead there appear a large number of mesh or beard shape crystals.
The stick big grains are not appeared.
The stick big grains are not appeared.

Thereby it reduces the number of shutdown to ensure the safe operation of the boiler and create the favourable vield and social benefits.
It clearly shows there is a clear boundary line and discontinuous columnar crystal in sample 1.The organization is uneven and there is a large number of bright coarse-grain on the left side.
And the grain is very small.
And the grain tapered from the inside out.
Then it is coarse-grained zone and fine-grained zone.

EBSD results showed that after five cycles of ARB, sheets were found to contain ultra-fine grains with high fraction of high angle grain boundaries.
Fig. 2 shows that the mean spacing of the lamellar boundaries decreased by increasing the number of the ARB cycles, but, the fraction of high angle boundaries increased during the ARB process continuously.
Fig. 3 shows the weight loss of the ARBed 6061 aluminum sheets versus number of ARB cycles.
Variation of weight loss of the ARBed 6061 Al alloy as a function of number of ARB cycle (under applied load of 4.2 N).
- A coarse grain structure formed under subsurface which had a strain incompatibility regarding to the fine grain structure and non-equilibrium ultra-fine grains (ARB structure)

The sample with high transparency is fewer mineral composition numbers, similar mineral compositions and bigger crystal particles.
The typical samples were numbered according to its transparency.
The number of mineral compositions also affects the transparent degree of Shoushan Stone.
The more the number of mineral compositions is, the more the reflection is and the less the transparency is.
The number of mineral compositions in the sample also affects its transparent degree.

Grain size.
Total number of cell state variables.
depends on the total number of cells in each array, and .
The distribution of grains size was analysed in terms of the ferret diameter, and Weibull analysis was performed to obtain Weibull grain size parameters, in order to incorporate the distribution of grains size in CAFE model using random number generators.
A misorientation angle of grains was incorporated in the brittle cells of CAFE model using random number generators, with following Weibull parameters: shape parameter = 1. 1931, scale parameter = 39.832.

The traces of grain boundaries were parallel to the ED and TD.
Despite the texture of the initial state was dominated by cube-oriented grains, the grains with orientation forming copper-type texture are also well-marked.
For both metals the development of deformation microstructure and texture as a function of the number of passes was analysed using the SEM/EBSD system on the ND/ED and ND/TD sections.
(i) The number of applied passes had a strong impact on the global deformation behaviour and on the intensity of grain refinement.
Two types of boundaries between the grains are observed in the present copper and AA1050 alloy samples: the boundaries that separate the grains placed inside a particular layer and the boundaries between the grains of adjacent layers.

The change of size and shape of dimples fracture from larger and irregular shape dimples in initial sample to much smaller and grains-look like dimples in ECAPed sample indicating the grain refinement occurred after ECAP.
Introduction The grain refinement is one of the strengthening method of the metal alloys based on the Hall Petch formula which relates the strength with the inverse of the grain sizes, the finer the grains the stronger the alloys.
However, small number of larger dimples still can be observed in a small area.
It is clear from Fig. 4 that the small size dimples have more regular shape (looks like grains), where the initial voids might initiate at grain boundary as the strain concentrator.
The change of size and shape of dimples fracture from larger and irregular shape dimples in initial sample to much smaller and grains-look like dimples in ECAPed sample indicating the grain refinement occurred after ECAP.