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The maximum grain growth rate was observed to be around Nb2O5/CoO = 0.25.
In this case, since the donor additives reduce the number of oxygen vacancies, the diffusivity of the oxygen ions become reduced.
The grain growth of the sintered body can be described by the rate equation )( o n o n ttkRR −=− , where R is the average grain size after heat treatment for time t, Ro is the initial grain size, n is the grain growth exponent and k is the rate constant, inclusive of grain boundary segregation, interface energy (γ) and diffusion coefficient (D) terms [6].
This grain growth behavior can be explained by the occurrence of a solute segregation at grain boundaries since the segregate concentration is hard to obtain.
Another concern about grain growth behavior is grain boundary energy.

Based on the protrusion depth, this study found that only small number of grains can be considered as active grains.
The ground surface profile from the UVAG with DET was analyzed [2] and the possibility that only a small number of grains, probably one, are active during the grinding process was highlighted, but it has not yet been known how the 3D grain protrusion parameters were related to the ground surface.
Fig. 4 shows typical successful samples for the possible active grains identification where the number bullet shows the highest grains in sequence for the top 5 µm.
All successful samples only have a small number of possible active grains while some only have one possible active grain.
All successful samples have some of their possible active grains located within the estimated active grain locus.

This method introduces three-dimensional compression and shear stresses and the process can be repeated for a certain number of passes until the desired accumulated strain has been introduced.
The present work investigates the effects of both particle numbers and the type of particles on the microstructure development.
Also, in alloy AZ31-1Si the grain size distribution exhibited a bimodal nature although the coarse grains dominated over the finer grains (Fig. 2b).
These observations indicate that additional alloying in the AZ31 alloy system do not increase the number fraction of fine grains, hence larger amounts of second phase particles seemed to promote less bimodality.
(4) The grain size, grain shape and grain boundary structures in the present alloys seemed to be little affected by the coarse phase Mg2Si.

Additional rolling after ECAE also enhances grain refinement [6-8].
Mean intercept length of recrystallized grains was evaluated as grain size.
The starting material had equiaxed recrystallized grains, with a mean grain size of 16µm.
In the specimen s1, deformed grains remained.
The change in deformation route may increase the stored energy and produces finer recrystallized grains. 500 520 540 560 580 600 620 640 8 10 12 14 16 18 20 22 s1 s0.8 s0.6 s0.3 s0 Annealing temperature, T/K Recrystallized grain size, d/ m µ Fraction of shear strain Fig.5 Effect of annealing temperature on recrystallized grain size. 0 0.2 0.4 0.6 0.8 1 8 10 12 14 16 18 20 22 Recrystallized grain size, d/ mµ Fraction of shear strain 533K 543K 553K 573K 623K Annealing temperature Fig.6 Effcet of deformation route on recrystallized grain size. 0 100 200 300 400 500 600 s1(1.28) s0.8(1.28) s0.6(1.28) s0.3(1.28) s0(1.28) Sample name Number of high angle boundaries /mm-1 15-30° 30-40° >40° Fig.7 Effect of deformation route on number of high angle boundaries.

Grains Ultra-refinement of Materials Imposed by Pulse Laser M.
Accordingly, the mechanisms of grains refinement are explored.
Fig.1 Experimental schematic of grains ultra-refinement induced by pulse laser.
Results Grains ultra-refinement had happened on the sample top layer after LSP.
(a) Elongated subgrains perpendicular (b) Equiaxed subgrains to the direction of τ1 Fig.3 SEM micrographs of treated zones after LSP (a) Original grains about 20~30µm in size; (b) Parallel streak-like grains; (c) Parallel dislocation walls in a streak-like subgrain; (d) Numbers from 1 to 6 denote subgrains with high misorientation angles.

It shows that grain coarsening would occur after annealing as the grain size increases from 600 µm to 859 µm.
Fig. 5 The mean grain size values versus the number of ECAP passes for commercially pure aluminum [10].
Fig. 6 shows the variations of the Vickers hardness with the number of ECAP passes performed on pure aluminum at room temperature [11].
By performing TE the grains of about 150 µm was developed.
Although post-rolling resulted in elongated grains, it lessened the mean grain size to 80 µm. 2.

The range of the flight of a particle depends on a number of factors: its mass, the centrifugal force acting on it, the force of friction on the wall of the hull and the aerodynamic resistance of air during flight.
In turn, the vibration method has a number of disadvantages that can be eliminated by improving its design.
The upper 3 and lower 4 electrodes are located in the same plane and the distance between them varies from 0.2 to 0.3 times the width of the loaded strand of the inclined endless sheet, depending on the number of grinding grains poured from the feeder per unit time, and sorting accuracy.
The reliability of the measurement results in this case is ensured by a large number of scanned grains in comparison with the three-dimensional system.
The curve is plotted as follows: the points corresponding to the numbers of the separator cells are laid off as abscissa, and the shape factor values of the grinding grains are laid off as ordinate.

The grain size is strongly related to the number of nuclei.
Different pulse number of laser.
In this section, different pulse numbers are investigated.
Fig. 4 shows the average grain sizes of different pulse numbers and laser intensities.
This could increase the nucleus number, which leads to the smaller grain size.

Relatively higher grain refinement rates are observed during initial passes.
Linear intercept method was employed to estimate the average grain sizes and the ambiguity in grain size measurement arising from deformed microstructure is minimized by measuring the number of intercepted grains from superimposition of grids on the image in different orientations (00,450,900).
The photograph of constrained groove pressed OFE copper sheet after different number of passes shown in Fig.1 clearly reveals rough surface finish marked with waviness caused by the sharp corners present in the grooved die profile during repetitive pressing of sheets.
The average grain sizes obtained in CGP processed OFE copper sheets as a function of accumulated plastic strain shown in Fig. 3a clearly indicates the reduction in grain sizes with increasing number of CGP process.
As the accumulated strain increases, the grain refinement reduces significantly (Fig.3a) and the average grain sizes obtained at the end of third pass is 39mm (Fig. 2b) which are comparable to grain sizes reported earlier in CGP processed commercial purity copper [7].

In production of superfine-grained grades, one of the main obstacles is to retard and control the grain growth during sintering [3-5].
The WC grain sizes in specimens added with Pr6O11 were fine and their average grain sizes were lower than 0.5um, without abnormal growth of WC grain found in them.
In specimen VI with 3.5% of Pr6O11 doping content, some nearly quadrate large-size grains, which were the undissolved Pr6O11 grains, were found.
Studies have shown that the flexural strength will increase with the reduction of WC grain size when WC grain size reaches the superfine-grained range for WC-Co cemented carbide.
This means that a large number of pores appeared in the sinter.