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It can be attributed to fact that grain growth phenomena are more likely for smaller grain (i.e. 3 nm grain size) as compared to larger grain (i.e. 6 nm grain size).
Discussion on vacancy formation during creep Plots of number of vacancy formed during creep deformation versus time for nanocrystalline nickel specimens having 3 nm and 6 nm grains are shown in Fig. 10.
On the other hand, number of vacancy curves is observed to be shifted towards downward with decreasing grain size of specimens at 1400 K and 1500 K operative temperatures (refer Figs. 10(c) and 10(d) respectively).
It is observed that formed vacancy number versus time plots also supports the nature of creep curves (as evident from Fig. 2, Fig. 3 and Fig. 10).
Fig. 10 The plots of evaluated number of vacancy vs. creep time for 3 nm and 6 nm grain size NC Ni at (a) 1100 K, (b) 1200 K, (c) 1400 K and (d) 1500 K 3.7.

The structural changes can be characterized by the evolution of many mutually crossing kink bands at low strains followed by increase in their number and misorientation, finally resulting in a fully developed fine-grains at high strains.
The total number of boundaries was 80 to 100 in each sample.
This leads directly to the evolution of a new fine-grained structure with medium-to-high angle grain boundaries.
The numbers in insert indicate the misorientations in degrees. 20 40 60 80 0.1 0.2 0.3 0 Misorientation angle,θ /deg Frequency, AZ31 T=463K Σ ε =3.2 θ =38° ε =3× 10 -3 s -1 fkink bands as well as full development of new grains hardly take place even at high strains [8].
The misorientation and the number of boundaries of kink band rapidly increase with deformation, finally followed by the evolution in-situ of new grains with high angle boundaries in high strain

The 3D fractographs illustrated that the numbers of the dimples decrease with the increase of the grain size.
A minimum of 500 grains was measured for the determination of grain diameter for a given annealing condition.
The numbers of the dimples in the fracture surfaces decrease with the increase of the grain size.
The dimple size depends on the grain size.
The 3D fractographs illustrated that the numbers of the dimples decrease with the increase of the grain size.

The grains became thinner and elongated to the rolling direction with increasing the number of ARB cycles.
In addition, the fraction of high-angle grain boundaries increased with the number of ARB cycles and reached about 0.7 after 8 cycles.
Figure 4 shows the variation of mean spacing and the fraction of high-angle grain boundaries with the number of ARB cycles.
Summary The grains became thinner and elongated to the rolling direction with increasing the number of ARB cycles.
In addition, the fraction of high-angle grain boundaries increased with the number of ARB cycles, reached about 0.7 after 8 cycles.

Grain growth model Grain growth model(GGM) is the model for calculating grain growth speed model essentially, generally, which use the rate of average grain radius to characterize grain growth speed.
Grain growth model of solid phase sintering.
It is well known that the grain growth process at the end of the single-phase SPS is such process as the grain boundary migration between pores and grain boundary reaction; and the grain growth of polycrystalline material is the result of surface diffusion or grain boundary migration due to the system energy reduce.
When particles dissolve in the liquid phase, the number reduced.
Because LSW theory had not considered the solute concentration change around particles, and the effect of diffusion distance decrease due to the increase of the number of particles, then Ardell modified LSW theory by introducing volume fraction, the MLSW is given by Eq. 11

Grain Size Analysis.
A circle was drawn on the image, the grains that were located entirely inside the circle were counted and then the grains intercepting the circle were counted separately and the average grain size was calculated by using the following formula: n1 = number of grains completely inside the test circle n2 = number of grains intercepting the circle NA = f [n1 + (n2/2)] f = Jeffries multiplier (magnification2/circle area) A = Average Grain Area (A = 1/NA) d - The average grain size d is defined by d = (A)1/2 G = 3.322(Log A) – 2.955 G is the ASTM grain size number (Note that NA is the number of grains/mm2 at 1X) Fig.2, shows the analysis and quantification of grain size by Jeffries planimetric method Total Grain Counting Method.
The numbers of grains were counted by hand and the total surface area of the tube cross-section was also calculated.
Then the total number of grains was dived by the area of the tube cross-section to give the average grain size in millimeters squared.
So the grains within the structure re-crystalize into many fine grains.

The samples exhibited a large number of intermetallic particles on polished sections in each case.
No appreciable difference was found in the number density of particles between the base alloy sample and the grain-refined sample.
A total of 63 such particles were captured from a large number of randomly selected viewing fields and probed at 20 kV.
It can be inferred from the Al-Mn phase diagram [7] that this master alloy splatter may contain a large number of metastable intermetallic phase particles such as ε-AlMn.
Therefore, we can make the assumption that the nucleant is ε-AlMn in commercial AZ alloys, a b c d although the number density of these ε-AlMn particles is much lower than for Al8Mn5.

Kanga Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea asjkang@kaist.ac.kr Keywords: grain boundary structure, grain boundary migration, microstructural evolution, grain growth model, abnormal grain growth, nonstationary grain growth Abstract.
If the deposition of an atom from the neighboring grain onto the growing grain is not stable, the atom should detach from the grain and return back to the neighboring grain.
Experimental Observations and Practical Applications There are a number of experimental results that demonstrate the correlation between grain growth behavior and grain boundary structure: normal in systems with rough boundaries and non-normal, in particular abnormal, in systems with faceted boundaries [9, 15, 16, 18-22, 24].
The number in a circle on the figure shows the percentage of the rough boundaries in the sample prepared under the corresponding oxygen partial pressure and donor concentration.
The number in the circle denotes the measured percentage of rough boundaries at the respective conditions.

This method gives the average grain size but no information is provided about the grain size distribution.
Ma et al [5] have observed the presence of a small number of grains with clearly larger sizes than the average.
The large amount of defects, the lack of clear grain boundaries and the superposition of grains (in the width direction) do not help in measuring the grain size.
Bright-field and corresponding SAD (a) and dark field (b) TEM images showing the grain structure in samples consolidated at 425ºC. 0 20 40 60 80 100 120 140 160 50 100 150 200 250 300 350 400 450 Number of grains Grain size (nm) CONSOLIDATION TEMPERATURE : 425ºC Number of grains: 422 Figure 4.
Bright-field TEM image and corresponding SAD showing grain structure of a sample consolidated at 475ºC. 0 20 40 60 80 50 100 150 200 250 300 350 400 450 Number of grains Grain size (nm) CONSOLIDATION TEMPERATURE : 475ºC Number of grains: 550 Figure 6.

In recent years, it has been developed on the grain design for the solid rocket motor and complete star grain design is found in [2].
The star grain configuration considered is defined by the seven independent geometric parameters: grain outside radius, R, number of star points, N, web thickness, W, fillet radius, r1, cusp radius, r2, star angle, ζ, and star point semiangle, η.
To ensure neutral burning, for a given number of star points, the star point semiangle can be solved by using (2).
η = π/2 + π/N – tan (π/2 – η) (2) Star point semiangle with respect to the star point number is expressed in table II.
Grain outside radius, R = 150 mm Web thickness, W = 60 mm Fillet radius, r1 = 10 mm Cusp radius, r2 = 8 mm Number of star points, N = 6 Star angle, ζ = 25˚ Star point semiangle, η = 33.5295˚ As shown in table III and table IV, the numerical method gives close result as the geometrical method which gives the exact result.