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It seems that the final size of the colonies at the end of the transformation is correlated to the number of α-alumina seeds in the starting γ-alumina powder.
But the above observations suggest that a grain rearrangement process is coupled with the phase transformation.
Unfortunately, at the end of the sintering, the microstructure is always composed of micrometric grains.
For higher contents, the excess of the dopant has to be rejected to the surfaces and grain boundaries of α-particles which grow at the expense of γ-grains.
To benefit from this effect and with the goal of producing sub-micrometric grain size dense ceramics using isothermal sintering, further work with controlled density of nucleation sites and co-doping to limit grain growth is planned.

After FEG–SEM observations, these overestimates are mainly due to additional intergranular cavitation along grain boundaries.
It is expressed in term of the number of cavities per unit grain boundary area and per unit time and given by: N0=α'εmin with α'=Naεfin , Na=dgNmπdH (2) For various stress and temperature values, the parameter α' is determined using the image processing software of FEG-SEM micrographs which allows us to measure the area fraction of creep void and the cavity size distributions.
Ten FEG-SEM images (about 250 observed grains) with magnification X500 were analyzed to determine the number of cavities per unit area of polished section, Nm.
The number of cavities per unit grain boundary area, Na, was then deduced using Eq. 2. with dg the average diameter of austenitic grains and dH the harmonic mean of intersected cavity diameter.
The upper and lower bounds of the time to failure can thus be predicted by: 0.301 h(α)kbTΩDbδ∑n2/5ωf0.5164N03/5≤ tf≤0.354 h(α)kbTΩDbδ∑n2/5ωf2/5N03/5 (3) with Ω the atomic volume (1.21·10-29m3 [6]), h(α) the factor which depends on angle formed at the junction of a void and the grain boundary (0.697 [6]), Dbδ the self-diffusion coefficient along grain boundaries times the grain boundary thickness δ (Db°δ = 7.7·10-14m3s-1 and Qb=159kJ/mol [6]) and ωf the critical area fraction of cavities in grain boundaries (0.04 [7]).

The number of primary Si increases obviously and the average grain size of primary Si decreases largely, less than 50μm.
Also the number of the primary Si particles increased significantly and the average grain size of primary Si decreased substantially(shown in Table.3）.
This is because that a large number of AlP compound had formed in Al-Fe-P master alloy, which has a lower melting point.
So the average grain size of primary Si maintains 40μm or less in 5 hours.
The number of primary Si increases obviously and the average grain size of primary Si decreases less than 50μm respectively.

But the alloys commonly used for thixoforming are limited to a few casting alloys and only a limited number of trial have been carried out on wrought alloys.
One coarsening mechanism is the coalescence of the grains, joining together and leaving an entrapped liquid pool in between the two grains.
Another grain coarsening mechanism is likely to be the ripening [4], in which the large grains grow and the small ones remelt.
The grains grow and turn into globular ones through the movement of the grain boundaries.
When the specimens were reheated at 609℃ and 622℃ for 0-30min, the average grain size of grains was 106-124㎛ and 82-91㎛, respectively.

The lamellar g¢ phase in the cellular grains was radial, and perpendicular to the cellular grain boundary.
During the manufacturing process of single crystal blades, a number of processes can occur and result in plastic deformation in the material.
When heating time was about 16 h, the depth of CRX was about 35 mm, and the number of lamellar g¢ phases in the CRX increased and the lamellar g¢phases was almost perpendicular to the boundary of CRX.
It can be seen clearly that the CRX consisted of cellular grains, and the interface between different cellular grains was obvious.
The lamellar g¢ phases in the cellular grains were radial and perpendicular to the cellular grain boundary[21].

Mechanical milling can bring about grain refining and change of lattice parameters.
Cu grain sizes are characterized by the peak of the XRD points of the composite.
The peak 1 and 2 of Cu the grain size peak changing with milling time.
After a long time of ball milling, grain was introduced in serious grain distortion, high density defects and nanometer fine structure, grain at high distortion stored energy state and the sintering activity improved which facilitating sintering densification.
For the composites being milled the grain continued to be refined and grains boundaries increase.

The size of recrystallized grains having orientations of the rolling texture was considerably smaller than the size of grains having other crystallographic orientations.
Such grains were, on average, smaller than grains of other orientations (see Fig.4).
The largest average size was recorded for P- and CubeND-oriented grains.
The larger number of nucleation sites in the A6.4 sample resulted in a smaller average recrystallized grain size, 13 µm, compared to that in the recrystallized A3.6 sample, 19 µm (see Fig.4).
Once formed, P and CubeND grains were able to grow to a significantly larger average size than grains of other orientations (see Fig.4).

The next is that diamond grains are plated and then nickel is plated again.
If the feed load is permanent, the diamond grains density decreases and the depth of the diamond grains into granite increases as the diamond grain size increases.
Table 2 Effect of diamond grain size on slicing process Grain size [Mesh] 170～200 200～230 230～270 Cutting force [N] 3.25 2.99 2.81 Cutting efficiency [mm/min] 8.04 7.68 7.50 Effect of Wire Speed.
If the pressure is permanent, as the wire speed increases, the number of cutting diamond grains increases per second and the depth of the diamond grains into granite decreases.
The depth of the diamond grains into granite increases and cutting efficiency rises as the diamond grain size increases.

This simulation model can be used to optimize forging process chains with respect to grain size distribution as well as cost effectiveness and energy consumption.
Outside of the deformation zone, only marginal changes occur in the modeled physical values, allowing for a simulation that uses a coarser mesh, and thus, reducing the total number of nodes and elements.
The use of the multi-mesh method for this example has lowered the number of nodes and subsequently, the number of degrees of freedom by 48 % when compared to a mesh with uniform element size distribution.
The time saving is lower than the reduction of the number of the degrees of freedom to be simulated because of the additional data transfer operations and the additional memory required by the multimesh method.
The models describing the kinetics of recrystallization as well as the grain size development due to recrystallization and grain growth, introduced by Sellars et. al [5-7], are applied.

However, increasing the number of grains leads to longer computational time.
The VPSC-FLD predictions based on the IF steel texture represented by various numbers of grains, i.e., spanning from 100 to 20000, are demonstrated in Figure 3.
As shown in the previous Section, the predicted FLD is affected significantly by the number of sampled grains in the statistical population.
Results shown in Figure 5b also indicate that the computational speed reduces when increasing the number of CPU cores in use (in this case a population consisting of 100 grain was used for 10 different ψ0 for 7 paths.
Note that the re-0 5000 10000 15000 20000 Number of grains in the population 0 5 10 15 20 25 30 35 40 Computation time [hour] (a) Various numbers of grains in the population (b) Number of CPU cores in use 0 10 20 30 40 50 Number of CPU cores in use [N] 0 2 4 6 8 10 12 14 Speed-up Time(1)/Time(N) 100 grains with 70 independent runs (c) Linear scaling of the results in (b) Fig. 5: Computation time spent for VPSC-FLD calculation sults illustrated in Figure 5a may be significantly sensitive to the technical specifications of computing hardware.