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Obviously, accepter dopants Mn2+, Cu2+ and Cu+ ions only distribute near the grain boundaries to form grain-boundary layers.
It plays an important role in the formation of semiconducting grain (n-type)-insulating grain boundary-semiconducting grain (n-type) structure in SrTiO3 ceramics [8].
It made the grain boundary Schottky barrier height increase, the electron depletion layer near the grain boundary thickens, and insulating properties of grain boundary enhance.
CuO doped samples had larger and better homogeneous distribution grain size, higher sintered density, and thinner grain boundary.
Acknowledgements This project is supported by open foundation of Guangxi Key Laboratory for Advanced Materials and Manufacturing Technology (Contact Number: GXKFJ11-12).

The interior of these new grains is free of dislocations; grain boundaries are straight and they have a similar morphology to the already polygonized subgrains.
These can then be the nuclei of new grains with high angle boundaries, Fig. 4.
TEM microstructure analysis results indicate that there is a very low fraction of submicron grains with high angle grain boundaries even in case the strain applied is the highest.
A distinction between the values for the initial state and the deformed plates subjected to CGP straining due to the different number of pressings evident.
In order to clarify the CGP effect on grain refinement, transformation of subgrain boundaries to high angle boundaries and appearance of a small fraction of dynamically recrystallized grains, all these structural changes may substantially contribute to modification of plastic deformation of strained Al specimens, as regards the number of pressings.

The homogeneity of grain size was also improved.
Therefore, a number of scholars have reported various of methods to overcome these shortages and then improve the properties of magnesium alloy.
With FUT treatment, another morphology (acicular β phase) replaces the laminar β phase, and the number of small β phase increases at the same time.
With VUF treatment, the β phase become smaller than FUT treated billet, showing the increased number of dot-like phases.
The homogeneity of grain size was also improved.

Experiments with a number of different steels show that the methodology can be applied to sheet of different formability.
At such high levels of local deformations, grains are elongated extensively and the grain boundaries are severely disrupted.
The 3D nature of the grains that are elongated towards the fracture surface can be clearly observed.
For IF steel, for example, triple grain boundaries are observed to be probable nucleation sites (Fig. 6(b)).
Experiments with a number of different steels show that the methodology can be applied to sheet of different formability.

It is anew nano-surface technology to refine grains to the degree of nanoscale.
The grain size of sample surface is measured by XRD-7000S.
The type of dislocation inside the grains tends to partial dislocation.
Because the grain boundary sliding or crystal rotation is prone to realize when the grain size is nanometer scale from the relationship between grain boundaries sliding and grain size [12-14]. large number of dislocations are very difficult to form in the nanoscale subgrain.
At the time grain boundary can’t absorb large number of dislocations.

Such sub-volumes are called pseudo-grains (Fig. 3).
It is seen from orientation tensor definition that such tensor has to satisfy a number of conditions: (2) Two-step homogenization scheme means that each pseudo-grain is homogenized by one of mean-field homogenization technique, and all pseudo-grain family is homogenized by Voigt scheme.
The failure of all RVE is determined by is weighted fraction of failed pseudo-grains in RVE: (3) Where - is the total number of pseudo-grains; - is the individual pseudo-grain weight, which reflects its relative contribution to the fiber orientation distribution; is a binary failure flag equal to 0 if the pseudo-grain is sane, and 1 if the pseudo-grain has failed.
Pseudo-grains failure model with failure indicator (3) and Tsai-Hill for transversely isotropic failure criterion in strain formulation (4) for pseudo-grains was used for failure prediction.
Such number of elements is necessary for accurate approximation of orientation tensors and to account thereby differences in orientation tensors over the sample’s volume.

The grain size determined from Electron Backscatter Diffraction (EBSD) maps indicate the reduction in average grain size with individual Ca and Ce additions.
The literature has only a limited number of works on squeeze casting of AZ91 alloy containing Ca and Ce and it needs more attention.
A straight line was drawn in a specific location which intersected a bunch of cells all of which were arranged in a row, and the number of cells was calculated by dividing the length of the line.
Grain refinement in AZ91-1 wt.% Ca and AZ91-1 wt.% Ce alloy The average grain size was determined with the help of EBSD analysis.
Also, Al2Ca and Al11Ce3 intermetallics are pinned at the grain boundaries and restrict the grain growth.

There are a number of publications addressing the circumstances under which the interaction is more severe.
The original grains of the core changed due to the liquid film passage to large grains.
Recrystallization of aluminium alloys during a thermal treatment follows a number of steps before reaching its final stage [15].
SIBM involves the bulging of a part of a pre-existing grain boundary leaving a dislocation free region behind the moving grain boundary.
The non-homogenised alloy will form a large number of very small dispersoids during the brazing cycle, responsible for recrystallization inhibition or sub grain structure stabilization.

It was found that the addition of SiO2 increased grain size marginally, and decreased sample density by reducing the amount of grain-grain contact.
The addition of SiO2 also modified the distribution of grain boundary types by systematically decreasing the proportion of low-Σ grain boundaries within the microstructure.
In house software was used to establish the numbers and distributions of Σ = 3, 5, 7, 9 and 11 interfaces present in the thermistor.
The degree of grain-grain contact also decreases and the amount of SiO2-rich second phase present at triple points increases.
PACS number: 85.20.Ea, 85.30.Hi, 85.50.Ly, 73.40.Ty

Homology analysis In this paper, we used the same method to analyze the fracture surface based on out former paper for prior austenite grains in JIS SUJ2. [8] It is noted that the Betti number is topologically invariable, i.e., while the images of fracture surfaces have a variety of shapes, the Betti number is independent of their shapes.
The values b0 and b1 represent the numbers of red areas and their connection numbers, reaspectively.
Comparing the all Betti numbers b1 of all distances, it was found that the Betti number b1 decreased with stress intensity factor.
(a) Betti numbers, b0 Observation No.
Mizobe, Homoogy analysis of austenite grain size of SAE52100 bearing steel processed by cyclic heat treatment, Apple Mechanics and Materials, Vol. 813, pp. 116-119. (2013) [5] K.