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Through a large number of experiments, n(citric acid):n(ethylene glycol)=2:1, n(citric acid):n(Nb5+)=1.5:1 is the best equipped ratio.
Figure (a)-(e) can be clearly observed that sintering at low temperatures, ceramics has fine grain size and large number of pores.
When T=1100℃℃, grains are well growed, particles are uniform distributed, size is relatively uniform,and density is better.
When sintering temperature reached 1140℃℃,grains melt, which is due to higher sintering temperature.
(a) (b) (c) (e) (d) Figure 2 T=1100℃℃, SEM photographs of 0.992KNN-0.008BF at different PH: (a)1-2 (b)2-3 (c)3-4 (d)4-5 (e)5-6 As can be seen from figure 2 from (a) to (c), quartet blocky grains gradually regularization, pores gradually smaller and fewer, organization densification improved; in photographs (a) and (b), abnormal grains growth in serious and grains have different sizes; the grain size gradually homogenizing and regularization in photographs (c) and (d); particles have good uniformity and density, and the shape is tetragonal blocky structure.

Grain size decreased with decreasing in cooling rates.
Three major regions were observed; the dynamically recrystallized (DRX-ed) α-Mg fine-grains region, the hot- worked α-Mg coarse-grains region, and the kink-deformed LPSO phase region.
Although average grain size of the DRX-ed grains in the extruded alloys was ~ 4 µm regard- less of different SDAS, area fraction of the DRX-ed region increased with decreasing SDAS.
To describe the change in a dispersion of LPSO quantitatively, dispersion level, DL (mm-1), was defined for discussion by the following expression in this study, DL = Σ v / ΣLv, (2) where Lv (µm) is length of a segment L that is vertical line drawn against extruding direction in Fig. 3, and v is number of LPSO phase that intersects with a segment L.
The DRX-ed α-Mg fine-grains largely contributed to the improve- ment of the ductility of the alloys.

The distribution of abrasive grains on the grinding tape is represented by number density, and the material existence probability that is represented by Abbott-Firestone curve is modified by considering machining parameters.
(ii) Cutting edges are distributed "uniformly at random" in the surface layer, and the number density of them is ρ.
(iii) Abrasion, fracture or falling-off of abrasive grains are negligible.
By substituting C1 for C0, C2 can be obtained, and Cn of an arbitrary number n can be calculated recursively.
The number of calculation cycle Nc was decided that Nc = 2fot where fo is the oscillation frequency and t is the process time.

Conversely, good ductility in austenite is associated with high grain boundary mobility that produces fine, recrystallised grains and subsequent dimple fracture after plastic tensile stress.
Glodowski, Fine-grained practice – revisited, Proc.
Precipitation sizes were measured and the distributions calculated when particle numbers exceeded 100.
This marked difference in flow behaviour suggests higher austenite grain mobility in Al-free steel F.
Grain boundary sliding (GBS).

Meanwhile, the crystalline grain had a uniformity distribution, and the grain size was about 9.5~10 grade.
When the tempering temperature rose continuously to 680℃, a large number of supersaturated precipitation carbides happened along the grain boundaries, and began to gather and grow forming black network microstructure, as shown in Figure 3(c).
The number of club-shape precipitates increase at the beginning and reach peak number at the tempering temperature about 625℃ then decrease to a certain quantity at 680℃.
Figure 7 shows particle number of precipitation in different temperatures.
Consequently, the reduction in the number of M3C carbides leads to an improvement in the fracture toughness [6].

Our attention is drawn to the partition of deformed grains hosting the emblematic component.
The orientation of the banded-type orientation gradient was analyzed in a cluster of two neighbouring rotated cube grains, grains A and B in Fig.2a, and in a grain of orientation (-1 2 4)<11 8 -1>, grain C in Fig.2b.
Present data showed the development of a substructure in {001}<110> grains but also in grains of which the orientation does not belong to the a- nor the g-fibre.
The {311}<136> components appeared both in the vicinity of the grain boundaries as well as in the grain interior of these orientations.
Acknowledgements This research was carried out under the project number MC5.07294 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl).

The average SiC grain size and bonding area of SiC grain increase during heat treatment at 1850°C.
A crack propagating before failure may have to go round SiC grains, and the number of grains it will go around depends on the size of the intergranular silicon and the SiC grains.
There are some smaller SiC grains surrounding larger primary SiC grains in the two samples before heat treatment (Fig. 2(a), (b)).
This could be due to the fact that in the case of a specimen containing grains of a far smaller size than their average size, the smaller grains grow to some limiting grain size close to the uniform grain size.
In addition, the fine SiC grains disappear.

To prevent abnormal grain growth, 0.25 wt% MgO was also added.
Influence of alumina grain size and volume fraction of SiC.
For alumina, the pullout dimensions increased with grain size.
around 2µm, and was independent of grain size.
Inspection of Fig. 2 suggests two sources of the reduction in grain pullout on adding SiC to alumina: (i) a reduction in size of each individual pullout, and (ii) a reduction in the number of pullouts present at any given time.

Then, from each ODF, a new list of discrete orientations is generated, and the ratio between the absolute numbers of entries in these lists is chosen equal to the respective volume fractions of the recrystallized and the deformed grains.
The total number of grains in this new list is chosen to fulfill the standard input for the GIA and CORe grain pool.
The median of the size distribution of the previous grains after a CORe calculation is assigned to the reconstructed grain list as the new grain size.
Generally, the simulated grain structure is consistent with experimental observations with respect to both the recrystallized volume fraction and the grain size.
Acknowledgement This research was carried out under the project number M42.5.09375 in the framework of the Research Program of the Materials innovation and institute M2i (www.m2i.nl).

The polishing wear of the diamond grain is showed in Fig.3.
Fig.2 Diamond grain with whole crystalline form Fig.3 The polished diamond grain Partial breakage is showed in Fig.4.
The whole breakage will take place when the cutting force acting on one diamond grain surpasses the pressure strength of diamond grain.
The sharpness of the saw would decline with the polished grain number increasing and the saw appeared low cutting ability
(4) Partial fall off is that the diamond grains broken fall off from the nickel-plate layer because the bonding force is not enough to hold grain onto the nickel layer.