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Assuming that all grains never stop growing and that new grain hypothetically nucleate also in the transformed material: the extended transformed volume is introduced, i.e. at this stage, hard impingement is ignored.
Thus, the number of prevailing nucleus density increase with increasing the cooling rates and thus the grains of specimens will be refined, as shown in Table 2.
It decrease with the increase of cooling rate, which may also ascribe to the increase of the number of vacancies and dislocation leading to the average distance of atomic jumps become short.
The QG and v0 reflect the mean values of all grains’ growing process in matrix.
Consequently, by increasing the density of high angle boundaries, cooling rates influences the process of grain growth.

Select the nano-Al2O3 as the reinforcing phase to improve WC grain boundary’s strength.
Select VC as Inhibitor to inhibit the growth of grain and impurities in the composite materials.
By contrast, the size of grain of YG8-b and YG8-b-Re is greater, and the organizational structure is not uniform.
The number of cracks is small.
The number of cracks is lager.

Macro cracks resulted from stress concentration were also visible on grain boundaries.
Metallographic Examination Result from the metallographic examination shows macro cracks on grain boundaries as shown in Fig. 8.
These macro cracks are caused bystress concentration initiated by a single cavity at the grain boundaries.
A growing number of cavity formed numbers of combined cavities which finally formed the macrocracks [14].
Result from metallographic examination showed there were macrocracks on grain boundaries.

An overwhelming number of ceramic materials are reported to fulfill such requirement and equation (1) is found to account for the experimental outputs satisfactorily.
This is an additional technique to assess that the grain size distribution is really within the nanoscale (i.e. the average grain size is well below 100 nm).
Equiaxially-shaped grains have been found in all samples.
No detectable grain growth has been measured after deformation neither a change in the grain aspect ratio.
As an alternative explanation, grain boundary sliding could be invoked: Ashby and Verrall proposed a model for high-temperature plasticity [8] based upon grain rearrangement through translation and ulterior accommodation by means of grain boundary motion controlled by diffusion.

The graph shows that the number of monolayers deposited at each cycle is approximately 0.5 ML/cycle.
The ratio of Pb:Te is 1 which means that number of atoms of Pb and Te deposited are equal.
The ratio of Cd:Te is 0.9 which means that number of atoms of Cd is approximately equal to the number of Te atoms deposited.
The average grain size is estimated to be 165nm.
The average grain size is estimated to be 23 nm.

The microstructure was analyzed by scanning electron microscopy (SEM), and the grain size became bigger after the addition of BaO.
A number of studies on crystallization behavior and other physical properties in glass–ceramics of the lithium zinc silicate (LZS) system have been carried out [2-7].
Compared with other glass–ceramics, LZS glasses offer a number of distinct advantages.
As shown in Fig. 3(a), the grain size of sample L0-2 is very fine, and they bunching into a radial-pattern.
The size of crystalline grains is bigger due to the addition of BaO.

In the Al-18Si-4Fe alloy, the structure could be modified from a coarse needle-like structure into a fine grained structure.
In 6%Si and 12%Si, a grain refinement or the formation of a rectangular parallelepiped from the coarse platelets intermetallic compounds is present.
b),d):b,973K~923K ultrasonic vibration is added. 0 25 50 75 100 Aria of intermetallic compound A,vol% 0 20 40 60 80 Inverse number of cooling speed 1/V, Without Vibration With Vibration 0 25 50 75 100 Aria of intermetallic compound A,vol% 0 20 40 60 80 Inverse number of cooling speed 1/V, Without Vibration With Vibration Fig.4 Relation between aria of intermetallic compound and inverse number of cooling speed.
The application of ultrasonic vibration in this temperature range including the liquidus line, where the intermetallic compound crystallizes, makes it possible to achieve grain refining.
However, when the ultrasonic vibration was applied to dendrites or grains of already crystallized Si, it was not possible to refine the structure.

The rest of the area is the β-phase and the secondary sheet-like α phase. β grains and grain boundaries can be clearly identified in T3 and T4.
The Widmanstatten structure (T4) owns larger β grains, with continuous secondary sheet-like α phase distributed at β grain boundaries.
In contrast, T3 and T4 own visible β grain boundaries and large volume fraction of secondary sheet-like α, which have led to a large number of interfaces and finally become barriers to the movement of dislocation.
Plastic deformation is mostly carried out by a number of slip systems.
Aging response of coarse and fine-grained β titanium alloys[J].

Fine grained microstructure was found for all the deposited films.
However they are still less in number as compared to those of bulk CoNiAl samples.
From the figures we find that the samples possesses fine grained microstructure and compared to as-deposited films, the annealed samples have slightly larger grain size.
As compared to the sample no. 3, sample no. 4 has finer and more uniform grains.
In case of the second sample, the increase in magnetization was evidently due to higher number of magnetic ions, but even then the sharp increase of high field magnetization below 300 K is striking.

Nucleation of eutectic grains in hypoeutectic Al-Si alloys is important as it modify the plate-like Si phase to fibrous.
Hence, modifying and controlling grain growth of eutectic is important to improve the ductility and strength of the alloy [2].
In the unmodified Al-12.6Si alloy, the eutectic silicon exists as the lamellar-like shape, while the number of lamellar-like eutectic silicon significantly decreases in the modified Al-12.6Si-0.3Er alloy [11].
Further propagation was possbile through grain boundaries with α-Al phase caused by debonding of Si particles [14].
Al-Si alloys Shape of primary Si Shape of eutectic Si Grain size of Si (µm) Tensile strength (MPa) Friction coefficient Ref.