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The number of grains for D301 is consistently over all cycles.
The grain area ratio increases with increasing number of cycles.
In the bottom diagram the number of grains for D601 is constant.
Thereafter, the number of grains decreases.
At the end the number of grains decreases again.

High-amplitude and thin-pulse electricity accelerated the nucleation and restrained the growth of the crystalline grains, and as a result nano-sized nickel grains homogenous in size were obtained, which are shown in Fig. 3(b).
The following explanation is as follows: (1) When pulse electricity was employed, existence of the pulse interval hindered the growth of the crystalline grains and changed the growth direction, thus prevented the grains from growing into bulks [4-6]. (2) The size of grains of the deposited layer depended on the velocity of nucleation and growth.
According to the theories in electrodepositing, when the cathode polarization is stronger, the rate of crystal nucleate will increase, and the number of nucleuses will multiple.
However, under the direct current electrodepositing condition, the cathode polarization is weaker, and the numbers of nucleuses are fewer, which will cause the grains to grow bigger and form a rough surface.
SEM shows that the average diameters of Ni grains and AlN particles are smaller.

Evidently, the average NKLN grain size grows up gradually when temperature increasing.
NKLN powders annealed at 600°C show outstanding combination property, and the average grain size is the smallest.
Fig.4 SAED image of a typical NKLN particle Grain size and lattice constants of NKLN powders.
(1) (2) (3) Table. 1 Grain size and lattice constants of NKLN powders Calcined temperature/°C a=c/nm b / nm β/° Grain size/nm 600 0.4034 0.3976 90.5212 40.78 650 0.3981 0.3974 89.5925 50.56 700 0.3978 0.3963 90.2614 65.52 Table 1 showed the grain size and lattice constants of NKLN powders.
NKLN powders annealed at 600°C distributed uniformly, the mean grain size was 40.78nm.

But at 700°C the grain size and translucency were both increasing and grain boundaries cannot be clearly distinguished, which means the initial integration.
Therefore, it can be inferred that Vita Alpha powder contains a large number of ceramic components, rather than the glass-based composition.
From the microstructure of sintered ceramic as shown in Figure 3.2, we can see the grains have began to fuse.
The transparency and grain size were also gradually increased.
At 700°C, the Vita Alpha porcelain has showed initial integration and it's individual grains has unable to be distinguished.

(The average width of the α-SiAlON grains is the mean of the minimum distance passing the geometric center of each grain).
Since the backscattered electron intensity depends mainly on the mean atomic number, the differences in the amounts of neodymium presented in the α, β SiAlON and grain boundary phases make them easily identified.
Grain growth during post heat treatments.
A grain growth was observed in α-SiAlON grains related to high temperature heat treatment and holding time.
Additionally, results of measurement of grain size according to LSW theory showed that grain growth mechanisms are different for width and length of grains.

The reduction in grain size due to the increase of grain density results compressive residual stress.
As shown in Figure 3b, pearlite grains after 6.25% pre-deformation can become barriers for next moving ferrite grain.
The total number of cycles that cause failure is sum of the number of cycles that caused the initial crack and its crack propagation.
The effect of this plastic deformation makes changes in the grain structure become larger, the reaction from the specimen and the environment occurs more in the grain itself, resulting in brittle grains [14].
Number of cleavage surface due to propagation of fatigue crack are found to be many more in number and size (Figures 5c and 5d).

The reduction of the carbide grain average size was found as well (owing to nanoparticles blocking influence on re-crystallization).
Introduction Strength and tool life of hard metals correlated with their microstructural parameters: volume content of binder and carbides, carbide sizes, mean free path between carbide grains, intercarbide boundaries.
Conventional notions regarding the failure of hard metals composites indicate that the boundaries between carbide grains are very weak structural elements [3,4].
Introducing nanoparticles also inhibits the growth of carbide grains and recrystallization by mass transfer through the cobalt layer, while preventing the formation of intercarbide WC–WC boundaries.
(2) The probability of structural parameters l1 and l2 emergence was determined from: ; , (3) where: n0 – number of particles with volume; n2 – total number of nanoparticles.

The TRC plate shows a very coarse dendritic grain structure with an average grain size of 600 mm (Fig. 1a).
It has been confirmed that intensive melt shearing is capable of dispersing the oxide films in the alloy melts, and increases the number of active nucleating particles, resulting in a much finer grain size after solidification.
Both the large number of dispersed MgO particles and the high cooling rate ensure an enhanced heterogeneous nucleation during solidification, resulting in a very fine weld microstructure (Fig. 3).
Liquation cracks at the grain boundaries in the HAZ of the TRC plate.
Yoshida, Effect of grain refiner and grain size on the susceptibility of Al-Mg die casting alloy to cracking during solidification, J.

With the continuous martensitic transformation, the dislocation density increased further, which results in the formation of a large number of dislocation intertangles within the austenite grains.
According to grain size, the austenite grains can be divided into two parts: coarse ones and fine ones.
According to this, we assume that grains of different grain sizes come from different initial structure [18].
The coarse grains came from deformed austenite grains without phase transition.
In addition, as the amount of deformation increased, the austenite grains without strain-induced transition were elongated, and the dislocation density increased, providing a large number of austenite nucleation points during the annealing process, leading to grain refinement.

Homology analysis In this paper, we used the same method to analyze the fracture surface based on out former paper for prior austenite grains in JIS SUJ2. [8] It is noted that the Betti number is topologically invariable, i.e., while the images of fracture surfaces have a variety of shapes, the Betti number is independent of their shapes.
The values b0 and b1 represent the numbers of red areas and their connection numbers, reaspectively.
Comparing the all Betti numbers b1 of all distances, it was found that the Betti number b1 decreased with stress intensity factor.
(a) Betti numbers, b0 Observation No.
Mizobe, Homoogy analysis of austenite grain size of SAE52100 bearing steel processed by cyclic heat treatment, Apple Mechanics and Materials, Vol. 813, pp. 116-119. (2013) [5] K.