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The results show that the greater the crystal grain is, the more uniform and regular the orientation is; and the more compact the arrangement is, the greater the fractal box dimension is.
log log )logN( max LL L D − = (2) It is obvious that the number of box N(L) is a key to compute the dimensions of box.
The number of box according to a method brought forward by Voss R.L. [4] in our study.
It is found that the greater the crystal is, the more uniform and regular the orientation is, the more compact the arrangement is, the greater the number of fractal box is.
It is found that the greater the crystal grain is, the more uniform and regular the arrangement is, and the more compact the arrangement is, the greater the fractal box dimension and the resistivity are.

Although, during recent years a number of sophisticated microstructure process models have been developed, e.g. for hot-rolling [[] C.M.
This is regardless of the extent of the prior ferrite formation, i.e. the carbon content and grain size of the remaining austenite.
Good agreement is achieved except for the larger austenite grain size, i.e. 62mm for the CP steel.
The number of potential nucleation sites for bainitic ferrite is related inversely to grain size of remaining austenite, i.e. = where h is a geometrical parameter.
The model can capture most of the experimental kinetics reasonably well, however, there are a number of points that have yet to be improved.

Introduction A large number of researchers have been focused on improving the electrochemical properties of the Mg2Ni-type alloys in recent years [1-3].
After milling, a large number of tiny particles appear on the surface of the alloy, which greatly increases the surface area of the alloy.
In the milling process, the energy of balls is transferred to the alloy particles, leading to both particle and grain size refinement.
The reduction in particle size increases the surface area of the alloy and the refinement in crystallite size, leading to an increase in volume of grain boundaries.
The increased surface area and grain boundaries make magnesium more likely to be corroded in a strong alkaline solution.

As seen from the figure, the S-N curve bends sharply at the fatigue limit of 710 MPa and number of cycles to failure of Nf = 10 5.
The average grain diameter at the crack initiation site (σa = 730 MPa, N/Nf=22.5 %) was measured, and was found to be 4 µm.
Figure 4 shows the relation between the crack length 2a and the number of cycles N, for stress amplitudes of 730 MPa and 760 MPa.
The variation of the crack length as a function of the number of cycles N can also be calculated by integrating Eq. (3).
Conclusions The conclusions reached based upon the present study can be summarized as follows: (1) Both fine-grained (hard) and coarse-grained (soft) micro-structures were present in the extruded Ti-6Al4V alloy.

Moreover, conventional recycling is characterized by high energy consumption, high operating costs and a large number of operations [1-6].
Grain size [13,14] of the specimens were captured by using Optical Microscope (Olympus BX60M).
The grain size decreases with the increasing of the operating temperature.
At 430°C as stated in Fig. 2(a), the grain size was revealed coarser because of the temperature is below the recrystallization temperature.
At 430°C, the grain size was revealed coarser because of the temperature is below the recrystallization temperature.

(a) Spatial distribution of the grain orientation angle as indicated in each grain, (b) the morphology of grain boundaries by using shape function .
Each grain is energetic equivalent.
Thus, we consider the coarse-grained model of dislocation, see Fig. 4.
Each mesoscopic cell contains a large number of crystal dislocations.
If finite number of discrete slip systems with specific b are considered, the net Burgers vector B is expressed as (40) where is the number of dislocations in line with the Burgers vector in slip system .

Using the KBr pellet method, FTIR spectra were recorded at room temperature between wave number ranges 4000-400 cm-1 on a FTIR spectrometer (Bruker Tensor 27).
FTIR Analysis: FTIR spectra of Ba3Co2-xCaxFe24O41 with x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 in wave number ranges of 400 - 4000 cm-1 are shown in Fig. 2.
At lower frequency, large value of dielectric constant is due to the predominance of species like Fe2+ ions, interfacial dislocation pile-ups, oxygen vacancies and grain boundary defect [22].
The value of tan δ depends on a number of factors such as stoichiometry, Fe2+ content and the structural homogeneity [21].
The first layer consists of conducting ferrite grains, which is separated by a thin layer of weakly conducting grain boundary.

For this reason, the growth mechanism of Al2O3 scales is being a subject of a number of investigations [3-6].
It is commonly accepted that the scales comprising the unstable aluminas, being cation-deficient, grow mainly due to the outward lattice diffusion of the Al3+ cations, while the α-Al2O3 scale grows essentially due to the inward grain-boundary diffusion of oxygen [7,8].
It might be related to the more irregular (blade-like grains) morphology of the scale surface in the former case (Fig. 4C) than in the latter one (Fig. 4A).
The presence of the latter in the outermost part of the scale is related to the unstable aluminas, while its penetration to the deeper parts of the oxide layer is associated with the oxygen inward transport via α-Al2O3 grain boundaries.
The new oxide is then formed : at the scale-gas region due to the presence of unstable aluminas and at deeper parts of the scale due to the oxygen diffusion towards the scale-substrate interface via grain boundaries of α-Al2O3.

RF sputtering produces the most uniform films, that have reduced internal stresses as compared to other techniques and a lower number of voids [9].
Ideally the best optoelectronic properties are obtained in a film which has low number of internal stresses and larger grain sizes, since that reduces the grain boundary scattering of electrons.
Measurements regarding electronic properties such as resistivity, number of charge carriers and electron mobility were done using Hall effect sensing.
Post deposition annealing increased the grain size which reduces the grain boundary, hence less effect of grain boundary scattering and more carrier mobility [13].
This is explained confirmed from the results where the number of charge carrier decreases when the ZnO thin film is oxidized.

It was found that fatigue crack initiation of materials is sensitive to the dislocation structures formed in the cyclic deformation process as well as to the grain boundary structures.
A cold-rolling and annealed sheet, 10 mm thick, with a mean grain size of few microns was subsequently annealed in vacuum at 500°C for 1.5 hours to obtain an equiaxed grain structure with 32 µm mean grain size.
At the early stage of cyclic deformation, for annealed specimens, a large number of dislocations are multiplied.
In the present work, for the specimens with tension pre-straining, in the subsequent cyclic deformation, with increasing cyclic number, the not well-developed cell dislocation structures formed during preloading in tension gradually gives place to a typical fatigue structure, as explained in the following.
However, with the increasing cycle number, the dislocation structure developed during tension preloading gives place to another dislocation structure, which is typical of fatigue without pre-strain and leads to identical saturation stress no matter the angle between the two sequential loading directions.