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Diffusion Mechanisms in Grain Boundaries A.
Under such conditions, the number of point defects in the simulation block is not conserved and the use of Eqs. (1) and (2) is not justified.
Hence, the total number of atoms in the GB core is conserved and it can only contain an equal number of vacancies and interstitials.
Filled symbols mark the upper grain, open symbols the lower grain.
In Cu GBs studied here, the number of nearest neighbors can be as small as � or as large as � � .

Since it included large number of high-misorientation grain boundaries, the foil was miserably brittle with no sign of plastic deformation in the tensile test [15].
However, after the grain growth at 1273K/0.5h, most of grains had {110} textures (green-colored) with few high-misorientation grain boundaries.
Other types of grains exist but are minor.
Note that among these minor grains only the grains with the cold-rolled texture are surrounded by the special, high-mobility grain boundary in the 40˚{TTP}730 <111> rotated recrystallization texture.
Then, in the next stage, i.e. in the grain growth, only the grains with the cold-rolled texture have the advantage of growing faster over the other grains, yielding the texture returning to the original, cold-rolled texture.

The effect of grain composition, replacement ratios and chemical activator of recycled aggregate on compressive strength of concrete small hollow block was studied.
Results and Discussions The effect of grain composition of recycled aggregate on compressive strength.
Table 3 The effect of grain composition of recycled aggregate on compressive strength of samples No.
The main reason for this trend was that on one hand, there were a large number of microcracks in the surface and interior of recycled aggregate.
In addition, there were a large number of microcracks in recycled aggregate.

The shape were labeled as follows: No type – color ( e.g.: 1p - red) were No means the number that the grains had in the order table (this number is given beginning from 1 and finishing with the last value of the counted grains), type can have three values, and represent the type of the grain (p – droplet shape grain, L - elongated shape and N - the nondefine shape) and last the color, that also can take three values (red - droplet shape grain, blue - elongated shape and green - the nondefine shape) (Fig. 6).
The first thing is to count the total number of grains from each picture.
When this number is known the type of grain (droplet shape, elongated shape and undefined shape) must be analyzed in order to build a map of the distribution of grain shapes in the part (Table 1 and Table 2).
Another value that differs between the two strategies is total number of grains, and this is grater in the 30 [µm] (336 grains) while in the 50 [µm] is lower (214).
In other words using the 50 [µm] manufacturing strategy the part will have bigger grains and less of them with a droplet shape, while using the 30 [µm] manufacturing strategy the grains will be smaller and the number of droplet shape ones will be grater.

A large number of slip bands can be clearly observed.
The data on αexp of each grain are classified into four groups based on the number of active slip planes: grains with one slip plane, double slip planes, triple slip planes, and no slip bands.
The numbers parenthesized indicate the quantity of each type of cracks.
However as the fatigue loading proceeds, TC cracks grow so dominantly that a large number of them are even found cutting through grain boundaries.
On the other hand, in Fig. 7(a), (d) the values of h and SB show at sharp increase at some cycle numbers corresponding to crack initiation.

The tetragonal grain size decreases with increased amounts of alumina.
Usually, the cell parameters start to increase with a grain size below 30 nm [22,23].
Initial calculation of the attractive potential for a one dimension ion arrangement, as a final segment, shows that there is a sharp decrease in the attractive potential, when the number of pairs is below 100 (See Fig. 8). 0.50 0.55 0.60 0.65 0.70 1 10 100 1000 10000 2N (N is number of pairs) Factor Fig. 8: Half of Madelung constant as a function of number of cation/anion pairs for a line of alternating cations and ions.
For an infinite number of pairs this number is ln2.
The gradual transitions versus grain size can be attributed to non-uniform grain size.

The dislocation density is the inverse of the number of points np in the Poisson process and value of rτ defines the stress through Eq. (5).
A higher value of np corresponds to a higher dislocation density or a larger grain size.
Examples of τ-γ curves for different grain sizes and particle densities.
Self-energy, line tension and bow-out of grain boundary dislocation sources.
Dislocation pileups in small grains. 

The porosity decreased and the grain size increased with increasing the number of coatings.
The thickness of the PZT-6(6: number of coatings) films was about 60~65µm.
The grain size and the densification of the thick films increased with increasing the number of sol coating.
It can be understood in terms of the effect of the increment of grain size and the decreasing porosity, as shown in Fig. 2.
These properties can be understood in terms of the effect of the increasing densification and the ferroelectric grain growth with increasing the number of 0 2 4 6 30 40 50 60 70 Atomic percent [%] Number of coatings Zr Ti (a) PZT-0 (b) PZT-2 (c) PZT-4 (d) PZT-6 (e) PZT-0 (f) PZT-2 (g) PZT-4 (h) PZT-6 0 2 4 6 250 300 350 400 450 500 550 Relative dielectric constant Number of coatings PZT(30/70) precursor solution coatings[7].

The film width can be quantified and its relationship with atomic GB structure can be clarified by studying the thermodynamic properties of premelted GB because the order parameter of PFC is the periodic local number density of atoms.
Mishin, Atomic mechanisms of grain boundary diffusion: Low versus high temperatures, J.
Gleiter, Amorphous structure of grain boundaries and grain junctions in nanocrystalline silicon by molecular-dynamics simulation, Acta Mater 45(1997) 987-98
Cannon, Grain boundary transitions in binary alloys, Phys Rev Lett 97(2006) 075502
Plapp, Phase-field crystal study of grain-boundary premelting, Phys Rev B 78(2008) 184110.

But this method owns a limitation in simulation of high Reynolds number, which is [2], when LB method is used to derive Navier-Stokes equation, one of errors is O (M2), where M is the Mach number.
It permits a reduction in error in exchange for a smaller Mach number which leads to a smaller Reynolds number, but in the engineering application of hydro turbine, turbulent exists in most of the practical flow phenomenon and high Reynolds number is often encountered.
Simulations of high Reynolds number fluid flow based on entropic Boltzmann method.
Stabilization of the Lattice Boltzmann Method Using the Ehrenfests’Coarse-Graining Idea.
Research on Lattice Boltzmann Method with High Renolds Number. 2008, 56-58