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Effects of grain sizes and density on removal rate and roughness.
Effect of grain sizes on removal rate and roughness showed as Fig.4.
The change of removal rate drops firstly then rises up with increasing of grain sizes, and the values are greater of the W3.5﹠W14 grain sides.
The explanation of this phenomenon follows as: the numbers of smaller grains participating in lapping are so multiple in unit time that the removal rate improves quickly because of sufficient cutting, and the scratches of smaller grains are shallow that forms the smooth surface.
The experimental results of optimization parameters as shown in Fig. 6: in the number of group two, the removal rate reaching 109.2nm/min with large size (W10) abrasive is higher than that of small size, so its parameters can be used for coarse lapping process of sapphire; in the number of group one, the surface roughness reaching 1nm with small size (W3.5) abrasive is obviously better than that of large size, so its parameters can be used for fine lapping process of sapphire.

(6) The driving force for grain growth is a reduction of grain boundary area.
If secondphase particles are present in the microstructure they exert a pinning effect on grain boundaries, which reduce the rate of grain growth.
The number fractions of precipitates are shown in Fig. 5.
The calculated number fraction is also compared to the measured.
The discrepancies obtained in the number fraction distributions are thought to be partly due to the small number of size groups used in the calculations.

Traditional Cellular Automaton model can only predict the grain structure and grain size.
Free growth of equiaxed grains and the competitive growth of columnar grains were simulated.
Discretized step is ∆x=∆y=∆z=0.01mm, the generated grid number is 1000000.
From modeling results, it was indicated that a nucleated equiaxed grain grows continually to form a fully dendritic grain, which has six primary stems in 3D.
Calculation domain is 1mm×1mm×2mm, mesh is divided by ∆x=∆y=∆z=0.01mm, grid number is 2000000.

The goal of this research was to create a surface topography that would promote cell attachment onto Ultrafine-grained Grade 2 Titanium.
Viewed as a process that can be optimised, definitive results are difficult to find without exhausting a large number of processes and parameters.
Reduced grain size enables pure UFG-Ti to mimic titanium alloys with aluminium and vanadium in strength and lightness, but without toxicity concerns.
Meanwhile, reduced grain size of UFG-Ti also creates denser arrays of 3-point surface grain boundaries – shown to give habitats that encourage denser cell colonisation [9].
Törköly, Microstructure and Mechanical Behavior of Ultrafine-Grained Titanium, Mater.

Special attention was given to the role of hydrostatic pressure and the effectiveness of the process in terms of grain refinement and high angle grain boundaries formation.
There are a number of methods allowing grain size refinement in metals.
Table 1 shows the grain size and the fraction of high angle grain boundaries for pure aluminium processed by various methods.
Grain size and the fraction of high angle grain boundaries for pure aluminium processed by various methods.
In order to avoid excessive influence of the heat, extrusion pressure and thus temperature rise can be decreased by increasing number of passes to achieve the same cumulative strain.

We apply the method to hydrogen diffusion in Si grain boundary.
Hydrogen Diffusion in Si Grain Boundary.
Fig. 2: Atomic positions of (001)Σ5 twist grain boundary of Si with a H atom.
where n is the number of particles, and the two boundary points, Ri (0) and Ri (T), are fixed.
In the discrete representation of the time integration in Eq. (3), the action is redefined as , 1 1 2 ,∑∑== = N k n i kiS ε (4) where tTN ∆≡ / is the total number of time steps.

The FΣ3 parameter has been defined as the relative number of high angle boundary segments, in the range from 15º to 65º misorientation, satisfying a Σ3 relationship within a fixed tolerance.
In-grain level: Different OIM options have been used here to define parameters that can be related to the in-grain microstructure.
θθθθm [º] F[1º,15º] K [º] OSA [º] Related distance ∆d ∆d 2∆d Over the grain Table 2.
Conclusions The effect of monotonic and strain reversal conditions on the microstructure has been studied at two levels (grain boundary and in-grain).
Proceedings of First International Conference Recrystallisation and Grain Growth, Eds.

The topography of the tile was measured before and after the polishing process with particularly grit number.
The results show the evolution of roughness and gloss for each load as a function of abrasive grit number and polishing time, as well as the material removal rate for each grit number and load.
Except of the finest grain size (Lux), which is resin bonded, all these segments are made from silicon carbide grains embedded in Sorel cement matrix.
The gloss graphs are plotted as function of used abrasives and number of passages.
For fine grain sizes the protrusion of the grain is probably smaller than the hcu,crit, and in this case even higher loads cannot force the grains to penetrate the ceramic deeper than hcu,crit , so that the ductile-mode will be kept.

When temperature is relatively low (the thickness of liquid is relatively thin), grains contacted with each other, which produced irregular-shaped grains.
In contrast to the traditional die casting and forging processes, thixoforming has a number of advantages, such as less energy consumption; less solidification shrinkage (low shrinkage porosity); no handling of liquid metal; and prolonged die life due to decreased thermal shock [3].
A large number of liquid droplets formed intracrystalline and grain boundary of two grains during partial remelting (Fig. 6 (a)).
Therefore, recrystallised grain gradually becomes rounded.
When recrystallised grains were not completely surrounded by liquid film, two grains contacted with each other and therefore merged into a new grain with larger size, which resulted in occurrence of irregular-shaped grains, as shown in Fig.2 (c), Fig.3 (c) and Fig.4 (c).

The abrasive mixture was boron carbide powder with grain number F400/17, mixed with kerosene and machine oil with grain concentration equal to m = 0.25.
Normally those two surfaces interact indirectly via abrasive grains.
Grains are cutting tools during lapping.
Hence, the abrasive mixture used in this research was boron carbide powder, grain number F400/17, mixed with kerosene and machine oil with grain concentration equal to 0.25.
Normally two surfaces interact indirectly via abrasive grains.