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The as-cast alloy consists of face-centered cubic (FCC) solid-solution with equiaxed matrix and network grain boundaries.
According to the Gibbs phase rule F=C-P+1 (F-degree of freedom, C-number of components, and P-number of phases) [6], the value of F equals to six for single phase or five for the two-phase region in the present six-component alloy system.
It means that the maximum equilibrium phase number of Al0.5CoCrCuFeNi alloy allowed by the Gibbs phase rule is much higher than the total number of phases.
As shown in Fig. 2 (a) and (c), typical equiaxed grain structure was observed.
The grain matrix and grain boundary denoted as “GM” and “GB” in Fig. 2 (b, d) is composed of only one simple FCC phase (see Fig. 1).

Too much or too less of dopants (both Pr6O11 and TiO2) in the varistor cannot obtain regular shapes of ZnO grains, and the grain boundaries are neither clearly observed.
The results reveal that the Pr- and Ti-rich phases were distributed at grain boundaries, triple point junctions or embedded in ZnO grains, which is an inhibitor for ZnO grain growth.
The inhibitors for ZnO grain growth include the secondary phases PrTiO3 and Zn2TiO4, and the praseodymium ions segregated in the region of grain boundaries [8].
The increase of varistor voltage can be explained by the increase in the number of grain boundaries owing to the decrease of the average ZnO grain size [9].
This is attributed to the increase of the number of grain boundaries caused by decreasing average ZnO grain size.

Compared HE1/E-TMB with HE2/E-TMB, the results showed that although they formed smaller grain crystals instead of spherulites with bigger size and complete structure, the grain crystals size of the former were bigger.
As can be seen from fig. 3, with the increasing of elastomer content of HE1/E-TMB blends, the number of the crystals increased gradually, and the size of grain crystals decreased, which induced the extent of the refining of crystalline increased.
They strengthen the heterogeneous nucleation and inhibit the growing of crystals. therefore, the number of the crystals in the blends increased, and the size of grain crystals decreased, which enhanced the refining extent of crystal gradually.
Furthermore, with the content of butylbenzenne elastomer N increasing, the number of crystals increased and the size of grain crystals decreased, the refining extent of crystalline reamrkably increased.
When E-TMB had the same composition, with the increasing of elastomer content of HDPE/E-TMB blends, the number of crystals of the blends increased and the size of grain crystals decreased, the refining extent of crystalline remarkably increased.

One element in the cellular automata model represents one grain.
The alive cell models a grain which does not contain a large foreign particle (inclusion).
One cell represents one grain.
The average size of the grain is 10 µm.
The number of the failed inclusions is a function of an effective plastic strain and such a relation was established experimentally.

Next, cool down to 800˚C by respectively taking the cooling rate of roller as 6˚C /min （water quenching，serial number A1）,600˚C（water quenching，serial number B1），and cool down to 400˚C by taking the stack cooling rate as 0.3˚C /min（water quenching，serial number C1）.
Wherein, stands for the volume fraction of precipitated particles; stands for the number of precipitated particle; stands for the average diameter of precipitated particle; stands for the measurement area.
As a result, the precipitated particles rapidly precipitates along austenite grain boundary (ferrite omentum), and thus destroys the strength of austenite grain boundary.
As shown in Figure 7, after the entry into furnace, the thermal stress received by austenite grain transforms into pulling stress, and produce grain boundary sliding under the action of thermal stress.
Following the solution of precipitated particles, the continuous holes form tiny cracks along austenite grain boundary.

The ferrite grains have irregular grain boundaries and often show etching evidence of dislocated substructure.
Boundary distribution and equivalent grain size The complexity of the fine-scale microstructure of low carbon bainite is further exemplified with detailed determinations of the numbers and nature of the boundaries in the microstructure.
The larger is the number of boundaries the smaller is the effective grain size.
The number and nature of boundaries in the microstructure obtained by EBSD mapping provides a means of distinguishing between different forms of bainite as well as determining the effective grain size.
<15° 60° Misorientation Angle Lower Bainite Granular Bainite Upper Bainite Number Fraction Fig. 13 Definition of bainite based on distribution of misorientation angles between grains/laths.

In addition, it is an alternative grain refinement approach that , nanoscale twins can generate nanosized grains[11].
Apparently, twin thickness, in addition to the number of twins, is a crucial structure parameter for the twinned materials.
A number of researches have shown that the improvement in mechanical properties and fatigue life of the stainless steel was directly related to the generation of dislocations and micro-structural deformation near the surface during the LSP process [14].
The grain size was determined to be 2μm～5μm, the average grain size is about 3.2um shown as Fig.2(b), the grain boundary (GB) is distinct and few twins can be seen in it shown as Fig.2(a).
It can be clearly seen from Fig. 5g and h that there are a large number of MT–MT intersections in three directions.

Over time, this "competitive diffusion" results in an increase in the average size of the particle population, and in a concomitant decrease in the number density of particles.
In order to take into account the effects of non-zero volume fraction, a number of mean-field theories of coarsening have been developed over the past 40 years [4].
In the following, particle and grain can be interchangeable.
Where σgb is the energy of a planar grain boundary and σin is the interphase boundary energy, more detail about grain boundary energy σgb and interphase boundary energy σin are described in [9].
The number of orientation field variables is 30.

At the microscale, a small number of grains are directly involved in the forming process, so that size, orientation, and position of a single grain can influence the process[1-2].
The repeat number was 22.
The grains of the larger pin are more elongated while the grains in the smaller one are more rounded.
As recrystallization tends to round the grains, the grains in the smaller pin were rounded rather than elongated.
The grains in the larger pin were elongated, while the grains in the smaller one had rounded shapes.

The volume of their application is currently about 70% of the total number of structural materials in the airframe [3].
In recent years, ultra-fine-grained aluminium materials have been of great interest to researchers of materials science.
This confirms the results of the well-known studies [5] that under the action of ultrasonic smoothing, the grain sizes of the source material are reduced to nano-sizes.
Therefore, subsequent studies should be conducted for a larger number of layers of experimental samples.
Grabovetskaya, et al, Grain boundary diffusion and properties of nanostructured materials, Novosibirsk, Nauka, 2001.