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D=i=1N4AπN (1) Fs=Ni=1NP24Aπ (2) where D, Fs, A, N and P are the average equivalent grain diameter, shape factor, area, number of grains and perimeter of the primary α-Al grains, respectively.
After liquid 6061 aluminum alloy flowed through the serpentine channel, the semi-solid slurry contained a large number of spherical primary α-Al grains.
When injected into the die mould, the slurry was chilled by the die mould, and so the residual liquid immediately solidified, resulting in a large number of secondary solidified α2-Al grains.
There are a large number of tiny dimples at the edge of the tensile specimen in Fig. 5(d).
Due to the chilling effect of the mould wall, the residual liquid rapidly solidified, and a large number of fine grains were distributed on the edge, as shown in Fig. 6(f).

Moreover, it is noted that RE addition in 316LN steel promotes to precipitate a great number of fine Laves particles within grains.
Xu et.al [5] have reported that the segregation of Ce on grain boundaries increased the grain boundaries cohesion, thus restrained the grain boundaries sliding during creep deformation and resulted in improving creep strength of P91 steel.
Under 200MPa, larger size cavities and a number of cracks are found in NRE steel, as shown in Fig. 4 (a).
While the size of cavities and the number of cracks decreased, the number of cavities also increased in 32RE steel under 200MPa, as shown in Fig. 4 (b).
(the black lines in fig. 6 represent large angle grain boundary).

Notice: each grain misorienting with the neighbour grains was differentiated by certain colour in Fig. 3.
It was found that the grain boundaries in the original steel were consisted of the high angle grain boundaries (HAGB).
The variation of the average misorientation decreased from 38.71˚ (original steel) to 37.54˚ (after one period service) and 32.12˚ (after 30 days service), and correspondingly, the fraction of the LAGB increased from 17% to 24% and 36%. 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 Number Fraction Misorientation Angles (degrees) 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Number Fraction Misorientation Angles (degrees) 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Number Fraction Misorientation Angles (degrees) Fig. 5 Corresponding profiles for grain orientations a. original steel; b. after 150 hours service; c. after 30 days service Comparing to the service temperature below 900ºC, the present "recovery and recrystallization" process was accelerated due to the dislocation fast movement and their intensive interaction during 1200ºC super high temperature servicing.
Generally, grain boundary is a contact region between nearby grains which exhibits different orientation and is consisted of dislocations.
However, the grain growth mechanism still met the well-accepted dislocation model of subgrain combination induced grain growth.

Effect of hot-deformation on micro-texture in ultra-fine grained HSLA steel S.
(d) Grain boundary misorientation histograms of SP-samples showing UFF grains.
EBSD measurement revealed that majority of the UFF grains in the SP-samples (63-75%) and MP-samples (60-80%) were surrounded by high angle grain boundaries.
In general, the investigated samples represented random texture, Fig. 1 and Fig. 2, however, quantitative analysis has been carried out to determine the fraction of different texture components from statistically significant number of grains (at least 1000 grains) in each sample.
Cube component in a-grains comes after the transformation of recrystallised g-grains and is known to cause delamination problem in the steel [4, 5, 8].

Only a small number of grains are <100>//ND and <110>//ND orientation texture.
And it has an in-homogenous grain size distribution with an average grain size of 10μm or so when the sample annealing 180sec.
The deformed stored energy of {111}<110> orientation grains is higher than {111}<112> grains.
The deformed bands and grain boundaries are benefit for the nucleation of {111}<110> and {110}<001> orientation grains.
The low angle grain boundaries are higher for the sample annealing 60sec and the high angle grain boundaries are higher for the sample annealing 90sec.

Besides, the average grain size of alumina ceramic is about 2.8μm, and the effect of inhibition on grain growth of alumina ceramics was obvious.
Therefore, the grain boundary migration speed was reduced, and the growth of the grain boundary was prevented.
The grain size of the samples was about 2.8μm and the grain size distribution was uniform (refer with: Fig.7 (c)).
When the speed of grain boundary migration was greater than that of the pores, the pores were wrapped in the grain.
Hot-Pressed Sintering of Fine Grained Alumina Ceramics [J].

The ASTM standard grain number is defined by the ASTM E112 [6]
The grain size of the microstructure can be estimated by grain number of per area.
Frequency Grain number [N] Deviation No.
A line is drawn for each microstructure picture to indicate where the intercept method was used to compute the grain number.
The result shows that the grain size (inverse of grain number along a line) of samples deposited with vibration is smaller than that of the samples deposited without vibration.

With traditional methods, Numbers of repetitive experiments will have to do, thus the research work for grinding mechanisms become heavy [3-5].
There are large numbers of abrasive grains whose geometric characteristics and space position are uncertain distributing on the grinding wheel and the cutting characteristics of each grain are different [9-12].
Considering the number of active grains and their radial distribution in actual grinding process, the arithmetic average roughness is modified as followed:                   R d s m R R 8.0 s 0 a 2 1 2 1 (4) where m is the ratio of Rt to Ra, R0 is a empirical constant.
Abrasive grains are numbers of cubes which side length are l.
Interference model between grain and workpiece surface is expressed with grain j and node i, as shown in Fig 1b.

SEM/EBSD local orientation measurements on partly recrystallized samples demonstrate the appearance of a specific number of new orientation groups of recrystallized grains, which resulted from rotation of the deformed crystal orientations around axes lying near (but rarely at) selected the <111> directions.
Despite the scatter of the recrystallized grain orientations, it can be claimed with certainty that only a finite number of their groups were observed.
‘Incoherent’ twin boundaries between growing grains.
They appeared between the growing grains.
Therefore, for lightly annealed samples the number of recrystallized grains significantly decreases as the middle sample section approaches; this may reduce the ‘quality’ of performed analysis.

While H80 and H65 brass have larger grain sizes, more small-angle grain boundaries obviously than copper, the proportion of their low ∑CSL grain boundaries are 48.2% and 45%.
Sample D has the highest ratio of low ΣCSL grain boundaries, and there are a number of Σ3 n grain boundaries forming into 3-3-9 or 3-9-27 triple junctions.
The sizes of grain clusters decrease with the reducing of proportion of low ΣCSL grain boundaries.
Sample D has the maximum grain cluster, while sample F has the minimum low ΣCSL grain boundaries, and the smallest grain clusters.
(4)The reasons of sample which has a high proportion of low ΣCSL grain boundary has higher corrosion resistance are relevant to the kind of Σ3 grain boundary and the size of grain clusters.