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Lumped capacitance model is valid when the value of the Biot number is smaller than 0,1.
A polycrystalline material contains a large number of grain boundaries, which represent a high-energy area due to inefficient packing of atoms [10].
Lower overall energy is obtained in the material if the amount of grain boundary area is reduced by grain growth.
Grain growth involves the movement of grain boundaries, permitting growth of larger grains at the expense of smaller grains.
We can conclude that the driving force for grain growth is reduction in grain boundary area.

Oxides materials with perovskite structure are well stabilized by its high dielectric constant (κ) that leads these classes of materials for a large number of technological applications.
On the other hand, the uS samples presents smaller and square grains, without a visible grain boundary phase formation as presented in the cS ceramics.
Figure 4 shows the EDS microanalyses of the a) grain and the b) grain boundary phase of the 1150/24h cS sample.
EDS analyses of a) grain and b) grain boundary of the sample presented in the Fig.3c.
The grain size of the cS samples was higher than those for uS samples, it can be due to the copper-rich phase formation in the grain boundary, which contributes to the grain growth.

In the course of annealing, these nuclei increase in their sizes, their number increases as well, and gradually they form continuous fine-grained layers.
In the dark-field images taken in the reflections of Nb and Nb3Sn the grains of the superconducting phase (upper right corner) are adjacent to the residual Nb densely populated with a large number of very fine (10-20 nm) nuclei of the Nb3Sn.
Compared to the previous sample, a greater number of second-phase particles are observed (indicated with arrows in Fig. 14c).
The number of these particles is not very great and not enough for the pinning force enhancement, but the Nb3Sn grains in the vicinity of these particles grow coarser.
Here, it is important to remember that wide zones of fine equiaxed grains are of great importance for high performance of the wires not only from the viewpoint of greater number or uniformly distributed pinning centers (grain boundaries).

It is evident that the stronger ACB synthetic diamonds provide the maximal number of the cutting edges on the working surface of the grinding wheels.
The grain size of the diamond wheels has a significant influence on the forming of the roughness of the surface, since with increase of the dimension of the synthetic diamonds the micro-profile of the cutting surface of the wheel changes because of the reduction of the number of the diamond grains per unit working surface of the wheel.
With increase of the grinding wheel speed from 18 m/sec to 32 m/sec (vw = 25 m/sec; Sах = 10 m/min; Str =1.5 mm/stroke and t = 0.03), the parameter Ra decreases from 0.32 µm to 0.2 µm, which is associated with the increase of the number of the cuts by the diamond grains per unit time, and also with the decrease of the thickness of the cut that is performed by the individual grain, i.e., because of the specimens surface "sparking-out" effect.
The weakening of the bonds between the neighboring surface grains of the nitride ceramic leads to brittle fracture of the surface with the subsequent mechanical action from the active grains.
It was established that the specific number of the craters, the grooves, and the cracks on the surface of the specimens that are ground by the diamond wheel depends on the characteristic of the wheel and the grinding regime -and intensification of the grinding regime leads to increase of the number of these defects.

A number of studies have reported that compressive residual stress may develop in the DXZ of FSWed Al alloys due to complex thermal and rigid clamping used in FSW.
Table 1 show that the average grain size in the DXZ for the FSWed specimen is approximately 1/3 smaller than that for the PM specimen.
The intergranular fatigue crack path caused by grain refinement in the near-threshold ∆K regime may further reduce the resistance to FCP.
Average grain size and transverse residual stress for FSWed 6061-T651 measured in PM and DXZ.
Location PM DXZ Average grain size (µm) 25.3 8.7 Transverse residual stress (MPa) 0 -15.7 Fig. 4.

AZ grain is produced by mixing alumina grains with zirconia grains of 30%wt., which is about 1300 in knoop hardness [4].
And the stock removal with AZ grain is larger than that with WA grain that is similar to that with GC grain.
That is, the interference intensity of GC grain is larger than of WA grain because of higher hardness of GC grain.
AZ grain acts on the workpiece surface stronger than WA grain, as the result that AZ grain including zirconia abrasive is softer than WA grain but its specific gravity is larger than that of WA grain.
The number of acting abrasive grain on the workpiece surface is estimated to be proportional to the abrasive concentration, but stock removal at 30%wt. is remarkably larger than those at other concentrations.

And the Al2O3 nanoparticles and Ni grains diameters in thin films are about 40nm and 80nm, respectively.
It is explained that Ni-Al2O3 films obtained by pulse current electrodepositing showed compacter surface and less grain size, while those obtained by direct current electrodepositing were rougher in surface and bigger in grain size.
According to the theories in electrodepositing, the stronger the cathode polarization is, the faster the rate of crystal nucleation, and the more the number of nucleuses.
Therefore, the film can be obtained with a compact surface and fine grains.
And the Al2O3 nanoparticles and Ni grains diameters were about 40nm and 80nm, respectively.

Substantially larger grains could be recognized for sintered samples with the addition of BaF2 (Fig. 3(B)) and CaF2 (D), indicative of the promotion of grain growth in the presence of these additives.
Liquid phase has been cited as a major causes of this kind of abnormal grain growth [11].
Activation energy for oxide ion conduction tended to increase as the number of cation vacancies decreased for the LSO samples with oxygen stoichiometry (No. < 1 > → < 4 > → < 5 >).
Ba3Al2F12 additive had similar effects on the densification and grain growth but a stepwise sintering (1400ºC/5 h → 1450ºC/5 h) brought about the inhibition of abnormal grain growth at 1450ºC.
On the contrary, the BaF2 addition positively assisted both the densification and grain growth.

The {001} oriented grain centre gradually rotates around a <110> axis in small incremental steps when nearing the edge of the grain.
The role of variant selection and thus the number of product variants that actually appear after transformation still remains unclear.
The inverse pole figure (grey scale) in figure 3 shows a single layer of surface grains with specific grain morphology (elongated along RD).
The surface grains are very large in size (~200 µm) with irregular grain boundaries of which the majority exhibits the 3 (<111>60°) orientation relation which is generally connected with a reduced grain boundary energy [9].
grain 1.

The grain refinement theory.
For 125K ≤∆T≤195K, dendrites are regenerated, but the grain size is reduced (Figs.1c).
According to Karma’s model for dendrite fragmentation, the grain refinement of undercooled Ni-11%Si alloy was in good agreement with the experimental data, and the grain size was reduced with the increasing ΔT.
Karma, Model of grain refinement in solidification of undercooled melts, J.
Herlach, Physical mechanism of grain refinement in undercooled melt, Phys.