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With further increase in strain, fine grains are frequently developed in parts of original grain interiors and especially near original grain boundaries.
Under intense plastic deformation at low to moderate temperatures, deformation band are frequently developed and the number and the average misorientation of these boundaries increase with straining [3-9].
The mechanism of fine grains formation may be associate with grain fragmentation process by development of deformation bands.
Repeated deformation leads to increase in the number and misorientation of these bands and finally development of new fine grains in high strain.
Sakai: Ultrafine Grained Materials IV, eds.

On the contrary, when the sintering activity is too high, grain-boundary migration is dominant, so grains grow abnormally.
Illustrations are the grain size distributions.
The Weibull distribution function is generally used to evaluate the BDS, which can be described by the following equations[9]: (1) (2) where n is the total sample numbers for BDS measurement, i is the serial number of samples arranged in ascending order and Ei is the corresponding BDS obtained in experiment.
The formation of nanodomains increases the number of domain walls and reduces the energy barrier of domain inversion, thereby reducing Joule loss and thermal breakdown.
(c) BDS as a function of grain size.

Andersson et al. [9] indicated that Nd 3+/Sm3+ or Pr 3+/Gd3+ co-doped ceria which had an effective atomic number between 61 (Pm) and 62 (Sm) should possess the highest electrical conductivity, and experimental evidences soundly supported the result [4, 10].
The conductivities are measured using ac impedance spectroscopy due to it is possible to study the separate contributions from the grain and the grain boundary to the overall ionic conductivity.
As it is known that the grain size is almost the same for all the SNDC samples with various thicknesses, the number of the grain layers decreases with the decrease of the thickness.
The typical plots of ln(σT) versus 1000/T for the grain and the grain boundary conductivities of the SNDC electrolytes with various thicknesses are shown in Fig. 3 and 4.
They show that the grain conductivity values of all the SNDC samples with different thicknesses are almost same while the grain boundary conductivity increases with the decrease of the electrolyte thickness, which indicates that the enhancement of the total conductivity is not contributed to the grain conductivity but the increased grain boundary conductivity.

Accumulative roll bonding leads to significant grain refinement.
An ultrafine-grained microstructure with an average grain size of ~ 200 nm [17] is produced after six ARB cycles (Fig. 1 c).
Similarly, burst pressure of the accumulative roll bonded aluminium alloy AA6016 without friction stir welding significantly increases with increasing number of ARB cycles.
Maximum von Mises equivalent strain of AA6016 increases with an increase in number of ARB cycles and reaches a maximum value of approximately 10 % after 6 ARB cycles.
Microstructural investigations showed that the grain size decreases after friction stir welding of the conventionally grained material AA6016, but increases after welding the ultrafine-grained material due to dynamic recrystallisation.

The results showed that the microstructures of these two kinds of steels are Equiaxed ferrite grains, but the grain sizes are greatly different.
Respectively the average grain size of steel A and B are 24.85μm and 11.85μm, and the average grain size number are 7.4 and 9.5.
Metallographic image analysis software was used for measuring the photos of the figure 1, we can get the average grain size of steel A and steel B are 24.85μm and 11.85μm , respectively, the average grain number of steel A and B are 7.4 and 9.5.
A large number of experimental studies have shown that, uniform ,fine ferrite grains is conductive to the development of {111} texture in the subsequent cold and annealing process.
Respectively the average grain size of steel A and B are 24.85μm and 11.85μm, and the average grain size number are 7.4 and 9.5

ECAP resulted in significant grain refinement down to the sub micron level and corresponding increase in hardness.
Introduction There has been considerable interest in metals and alloys with an ultra fine grain (UFG) size (100nm to 1µm) as this significant grain refinement leads to considerable increases in tensile strength, hardness, corrosion and wear resistance in comparison to its coarse grained (CG) counterparts [1-6].
In a number of cases, the crack propagated at an angle to the principle stress axis, therefore finite element modelling (FEM) was employed to calculate stress intensity factor ranges.
This suggests that small grain size differences and differences in grain boundary character do not have a significant influence on fatigue crack growth behavior.
Large increases in Vickers Hardness follow from the significant levels of grain refinement.

One more factor of the particular importance for development of the superplastic flow is the total area of grain boundaries, growing with refinement of grains.
For the quantitative estimation of the grain fraction, giving an input into the deformation of material by means of intergranular glide, a number of parameters are calculated by direct texture pole figures.
If p=1 in the point of PF(0001) with angular coordinates (ψ, φ), it signifies that in the studied sample the relative number of grains with the corresponding orientation of basal axis is the same as in the textureless sample.
At that, value p shows, by how many times the number of grains with the corresponding orientation of basal axis is higher or lower, than in the absence of texture.
New finest nuclei of α-grains form and “go away” from β-grains, giving rise to them, by means of the slip by interphase boundary.

In the presenting two-dimensional section, this cluster is constituted of 65 grains which are numbered in Fig. 2(a).
Thus, from grain 1 to grain 33, the route mentioned above can be simplified as 1→4→44→58→21→52→33 (Grain 4 and grain 6, grain 58 and grain 19 have the same orientations respectively.
Grains are numbered in (a) which is the orientation contrasted OIM map of this grain-cluster; Grains with the same orientation (The orientations with difference smaller than 1.5°are here recognized as same orientation.) are listed in (b); (c) Twin chain analyzing of these 65 grains; (d) Twin chain analyzing of these 23 orientations.
Grain boundary between grain 44 and grain 34 seems a random grain boundary, but it is actually a higher order Σ3n type misorientation.
(a) (b) (c) (d) (e) (f) (g) (h) The hollow arrow marked boundary in Fig. 3(c) is the grain boundary between grain 44 and grain 34 in Fig. 2(a).

Grain refiner intensifies the effect of UST, as a result the grain size appears to be additionally reduced.
Al-5Ti-1B decreases the grain size from 150 to 105 µm.
This effect can be a result of the influence of grain refiners and/or involving of larger numbers of grain refining particles into the solidification process.
In all cases grain size is about 130 µm.
Further treatment leads to grain size reduction to 130 µm.

The energy band gap decreases with increasing number of layers but increases with increasing pre-heating temperatures.
Grain growth occurred along the (002) plane for all films irrespective of sol concentration, aging time or number of layers.
The obtained values shown in Table 1, reveal an increase in the grain size, which may be associated with the coalescence of small grains by grain boundary diffusion resulting in major grain growth [27].
Similar morphology is observed but with a decrease in the grain size with increasing thickness.
Taking into account the effect of the number of layers, the film with 10 layers pre-heated at 400°C is the thicker one.