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The grain size is computed assuming the grains to be circular and calculating diameter from the circular grain area.
When the average grain size enlarges and the uniformity of the grain size distribution is improved in Cu lines, the number of grain boundaries and the fraction of triple junctions will reduce, respectively.
We can conclude that the number of grain boundaries in Cu lines with trench aspect ratio of 0.068 and the fraction of triple junctions in Cu lines with trench aspect ratio of 0.176 is the minimum.
Therefore, the number of grain boundaries in Cu lines with line spacing of 1.81 mm and the fraction of triple junctions in Cu lines with line spacing of 0.19 mm is the maximum.
Since Σ3 grain boundaries are twin grain boundaries as well as Σ9 grain boundaries are the twin variant grain boundaries, so it is also easy to exist in annealed Cu lines and Cu blanket films.

The sizes and number densities of dispersoids in at least 20 images from each homogenization condition were measured to ensure high accuracy.
It has been demonstrated that recrystallization and grain growth are inhibited when the migrating recrystallization front encounters a sufficient number of dispersoid particles, as a result of the Zener drag effect [12].
The number density of the dispersoid particles types decreases significantly with the increasing distance toward the grain boundaries.
It is clear that the sizes and number densities of the Zr-containing dispersoid particles change with the homogenization condition.
During homogenization at a given temperature, Figs. 6 (a) and (b), the sizes of dispersoid particles increase slightly, with time while the number density remain almost unchanged.

To date, the number of research work and publications concerning the superplasticity of CP alloys are very limited [11], since the majority of research are concentrated on Ti-6Al-4V alloys.
In the present work, fine grains are defined as grains having a diameter of ≤10 µm.
The volume fraction of fine grain ratio was calculated by dividing the fine grain area by the total image area.
The large grain size is not suitable for grain boundary sliding (GBS), in view of the fact that only grains with an average size of less than 10µm can deform by GBS [12, 13].
However, many coarse grains with grain size larger than 10 µm can still be found in Fig. 7 (d).

Microstructures and mechanical properties of as-received and ECAP deformed samples were investigated as related to the number of ECAP pass for better understanding of the effect of multiple-pass pressing.
Although many grains were already significantly refined after only 2 passes, the grain structure was not homogeneous with very fine grains of 5–8 μm as well as coarse grains of greater than 15 μm.
And there were coarse grains surrounded by fine ones.
Since the grain size decreased monotonously with the number of passes, factors other than grain sizes should be considered.
Fig. 2 Dependence of (a) ultimate tensile strength and (b) elongation on the number of ECAP passes Conclusions (1) AZ61 magnesium alloy was successfully ECAP deformed for up to 8 passes at temperatures as low as 473K and the average grain size was considerably reduced from over 26 μm to below 5 μm

Figure 2 Microstructures of the samples under different deformation temperatures (a) 900℃ (b) 950℃ (c) 1000℃ (d) 1050℃ (e)1100℃ As shown in figure 2, under the same strain rates and deformation dimensions, when the deformation temperature was 900°C, a large number of deformed austenitic grains appeared at the core-area of the sample, and a small amount of recrystal grains also appeared.
When the deformation temperature was 950°C, the number of small recrystal grains increased obviously.
Figure3 Microstructures of the samples under different strain rates (a) =1s-1 (b) =0.1s-1 (c) =0.05s-1 (d)=0.01s-1 As shown in figure 3, under the same deformation temperatures and deformation dimensions, when the strain rate was 1s-1, a large number of deformed austenite appeared at the core-area of the sample, and a small amount of recrystal grains also appeared, the grains’ size were 5~10mm.
When the strain rate was 0.1 s-1, the number of the recrystal grains increased, and the size of the grains also increased.
When the strain rate was 0.05 s-1, the recrystallization was almost completed, and the grains’ size was also uniform, about 20mm, a small number of deformed grains still existed.

As shown in a number of papers, this results in acceleration of diffusion processes, and, consequently, the processes of structure transformation start at lower temperatures than in traditional coarse-grained materials.
Its initial grain size was 50 µm.
Subgrains are observed within coarse grains.
Note that the coarse grain size achieves 2 µm, and the volume fraction of grains, 1-2 µm in size, is 40%.
As a result, the activation energy of grains is decreased essentially and the additional stage of rapid grain growth appears on the grain size-temperature curve (Fig. 2).

Development of initial structures similar to the real ones by simulating the grain-coarsening We began by developing a one-phase grain structure (Fig. 2.a) by using a simulation suitable for calculating the grain coarsening [6].
So-called smaller sub-grains could be developed by further grain-coarsening (Fig. 2.b) in these grains by modifying the simulation.
The boundaries of the earlier grains indicate the former grain boundaries of austenite while the boundaries of the above smaller grains indicate the boundaries of pearlite colonies.
b) a) Fig. 2. a, b Grain structures developed by the simulation of grain coarsening (a, one-phase grain structure, b, sub-grains in the previous structure) The ferritic-pearlitic initial structures are developed from these pearlitic structures in such a way that the former austenite grain boundaries „are thickened” after the second step so the proeutectoid ferrite can be obtained (Fig. 4).
The cementite balls with different sizes and numbers were drawn in this ferritic matrix by the software.

The results show that the as-cast microstructure of the Mg-Zr alloys was composed of non-dendritic, equiaxed Mg grains, with a few Zr particles within the Mg grains and along grain boundaries.
A few zirconium particles are distributed within the Mg grains and along grain boundaries.
The number of large particles(e.g.>1μm)also increased with increasing in Mn concentration.
Summary Solidification of dilute Mg-Zr alloys produced equiaxed grains, with a small number of Zr particles within the Mg grains and along grain boundaries.
The Mg- Mn alloys solidified as columnar grains.

In diamond wheel precision grinding process, the grinding force of nano-ceramic coating materials can be divided into single grain grinding force and wheel unit area grinding force, this paper studied the two grinding force, results showed that, with the increase of grinding depth, grinding wheel per unit area grinding force and single grain grinding force increased.
Grinding Wheel Particle Size Effects on Grinding Force The unit area normal grinding force in large size abrasive grinding wheel is bigger than it in small grit size grinding wheel, This is because the grinding forces are generally composed of two components of the chip deformation force and sliding frictional force. the number of effective abrasive grains is large , which involved in grinding in small grain size grinding wheel, in the grinding process, three kinds of sliding friction effection is large among wheel binder, wear debris, and the milled workpiece, so the unit area of grinding force is larger ( the tangential grinding force increases larger ).
The grinding force in per unit area of different particle size under different gringing conditions is discriminate , under the same kind of binder, the smaller the grain size number is, the smaller the grinding force of the unit area is , and this is because the unit area number of effective sharpening is different from different granularity number wheel, the more smaller the size number in per unit area is , the more less grinding sharpening is, per unit area total grinding force is low.
However, the more smaller the grain size number is, the more larger the single abrasive grit grinding force is, this is because the particle diameter is larger, single grain grinding depth increases, the contact area of the grinding wheel and the workpiece increases, which leads to a single mill grain grinding forceincrease .
When the abrasive grain size is reduced, the total grinding force increase in the grinding process, but single abrasive grinding force decreases .

Influence of Nanoparticle Reinforcement on the Mechanical Properties of Ultrafine-Grained Aluminium Produced by ARB Christian W.
The so-produced composite material showed about 17 % higher tensile strength than unreinforced aluminium after the same number of ARB cycles.
With this method a strengthening of 12.6 % related to the unreinforced reference condition after the same number of ARB cycles was achieved.
The additional strengthening was reported to reach up to 12.6 % and was shown to be caused by additional plastic strain around the hard embedded nanoparticles leading to an acceleration of microstructural evolution in the first ARB cycles as well as reduced grain sizes after a high number of ARB cycles.
The grains are clearly elongated in rolling direction (RD) and have a median grain size in the range of 0.4 µm.