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To sum up the previous contributions: Skeleton grain shape (mineral grains or conglomeration), Particle connection form (cementation degree), Particle arrangement (porosity characteristics) can be used as the structure factors of the loess [1].
The soil structure elements’ property depends largely on soil conglomeration single grain mineral properties.
This paper will describe the fractal structure parameters,which are shown in Table 1 Table 1 Algorithm of fractal parameters of microstructure Structural Parameters Mathematical Model Partical Fractal Dimensions Particle Size Num Greater than a Particular particle size Particle Distribution Fractal Dimension Grid Side Length Total Number of Particles Gri Surface Relief Fractal Dimension Measuring Tape Length Measuring Number Steps Aperture Fractal Dimension Aperture Num Greater than a particular Aperture If all the fractal dimensions are taken into account, it will be very complicated.
Set pore radius to , and the number of radius larger than is.

It was suggested that this might be due to the difference of a grain size.
We numbered pixels from lowest column from 11-14, second 19-22, third 27-30 and forth 35-38.
Figure 1 shows the neutron cross-sections as a function of neutron wavelength for the second column, pixel number 19-22, as an example.
The reason is unclear now, but we may have one reason that the larger grain size, namely, single crystal region increases the probability of the forward scattering by multiple scattering.
The former result indicated usefulness of this method to see the crystal structure change in the sample, and the latter suggested that potentiality of this method to observe the grain size of the sample.

The results show as follows: Carbon contents of the samples' surface are 1.28 wt%, 1.36 wt%, 1.51 wt% respectively after W-Mo-Y alloying layer (also called co-penetrated layer) was processed by solid carburizing at 960 ˚C, 980 ˚C, 1020 ˚C respectively; The amount of the carbides in W-Mo-Y alloying layer is obviously more than that of the carbides in W-Mo alloying layer; The granular carbides distribute dispersively and uniformly in alloying layer, and the sizes of carbide particle are less than 1 μm; There is no eutectic carbide at the grain boundaries; With temperatures of carburizing and quenching process rising, the carbides increases in number; After W-Mo-Y alloying layer was carburized and quenched at 1020 ˚C, the phases of alloying layer are Fe2C, W2C, Fe2MoC, MoC, Fe3C, Mo2C and Y2C3; and the types of their carbides are M3C, M2C, and MC, which are different from the types of W-Mo carbides in general metallurgy high-speed steel (HSS).
Fig. 1 ~ Fig. 6 are SEM photos of alloying layer after processed by carburizing and quenching at different temperatures, which show as follows: (1) The granular carbides distribute dispersively and uniformly in alloying layer, and the sizes of carbide particle are less than 1 μm; (2) No eutectic carbide exists at the grain boundaries; (3) carbides increase as the temperatures of carburizing and quenching process rise.
There are more alloying element and more defects at the grain boundaries, where carbides are easy to generate.
(2) The granular carbides distribute dispersively and uniformly in alloying layer, and the sizes of carbide particle are less than 1 μm; There is no eutectic carbide at the grain boundaries; The amount of the carbides in W-Mo-Y alloying layer is obviously more than that of the carbides in W-Mo alloying layer at the same temperature of carburizing and quenching process

The model is consisted of uniformly divided 125 grains.
To represent non-uniform deformation within grains, each grain is sub-divided into 4×4×4 elements with 20 nodes brick shaped element with 8 Gauss points.
For this finite element mesh, α-Mg phase or LPSO phase is allocated to each grain.
While the number of grains are determined in accordance with volume fraction of LPSO phase, the configurations for α-Mg and LPSO are randomly determined.
Acknowledgement This work was supported by JSPS KAKENHI Grant Number 26109717 and 26420020.

The density of TZS88 aluminum alloy is only 1/3 of ZQSn6-6-3, under the same quality and shape, size conditions, part number of the TZS88 aluminum alloy can be casted is 3 times than that of ZQSn6-6-3 tin bronze.
Majorities of them distribute along the grain boundary, and the rest in the substrate.
B, E, F point on the grain boundaries in Fig. 3, crystals mainly formedby Al, Cu, Mg, Ni.
The proportion of alloying elements in compounds on the grain is far greater than ingredients, in addition to the matrix particles, these elements of in most the region are very low, which shows that these elements often form compounds enriched in the grain boundary, some part distribute in the matrix as diffuse.
Alloys contain a certain number of Ni, it can generate  FeNiAl9 compounds that has hight hardness with Fe, the remaining generate NiAl3 and other compounds, the dispersion particles can  strengthen alloy.

According to the known empirical rules, a high glass-forming ability can be achieved in complex materials composed from a number of dissimilar elements [8].
Martensitic transformation is sensitive to crystal grain size, hence its characteristic temperatures may be different in preexisted bigger grains and newly formed smaller grains.
Martensitic transformations in amorphous-crystalline melt-spun ribbons are affected by a number of factors and can be easily modified applying a special thermal treatment.
Depending on the temperature and time conditions, the amorphous component of the material can crystallize in two ways: by nucleation and growth of new small grains or by growth of existing big grains (with possible formation of peculiar internal structure).
SEM image of crystalline grains with martensite crystals in amorphous matrix. 2 nm2 nm a) b) Fig. 4.

The majority of observed features of p- Zn, as shown in Fig. 2 (a), is composed of spherical shaped grains (2 ~ 100 nm in diameter) with some pseudo-elliptical shaped grains.
A similar corrugation height of 9 nm with pseudo-elliptical shaped grains is also observed for the oxidized p- Zn.
The detected grain size distribution shows one maximum for the oxidized p- Zn, as depicted in Fig. 3 (b).
The image sizes are 770 x 770 nm, respectively. 10 20 30 40 50 Number 0 20 40 60 80 100 120 Diameter (nm) 10 20 30 40 50 Number 0 20 40 60 80 100 120 140 160 (a) p- Zn (b) air annealed p- Zn Diameter (nm) Fig. 3 The size distribution of obtained from (a) anodically etched p- Zn and (b) ambient air annealed p- Zn at 380 o C.
In contrast, p- Zn exhibits mainly spherical shaped grains with slightly larger average diameter of 9 nm.

However, thick Si particle could be observed, the number and size of Si particles diminished sharply compared with Fig. 1(a).
The grain diameter of the primary crystal silicon in composite material with fine SiC granules is rather small, the number of Si precipitated will diminish and distribute more even.
With the decrease of number and size, the expansion of the matrix could not be restricted well by primary crystal silicon[4].
Combined with microstructure in Fig 2(b), the main reason is decreased holding time, number of SiC granules and grain size.
Thus the CTE of the composite is mainly depends on the number and the size of Si.

The spot 1~6 correspond to the oxide layer, where numerous, a few hundred nanometer-size grains are seen (Fig. 5a and b).
Most of grains are TiO2, which formed due mainly to the selective oxidation of Ti.
Fig. 5d corresponds to the TiO2 grain overlapped by the Al2O3 grain (spot X).
Fig. 5e corresponds to the TiO2 grain (spot Y).
No individual Nb-oxide grains were found in the scale, because Nb was dissolved in the scale that consisted of TiO2 and Al2O3.

For metallography the sections were directly cold mounted followed by grinding with increasing grit number in the order of 240, 320, 500, 800, 1000, 2400, 4000 followed by fine polishing.
The optical microscopy was performed on finely polished samples after grinding on the order of increasing grit number grinding paper and final polishing on non-ferrous polishing cloth and images are obtained using a Pax-Cam software.
Further correlation of the micrograph shows that there is an aspect of grain refinement produced by impingement of grain boundaries due to the lower diffusivity of the silica nano-particles in the Titanium-nickel matrix.
This prevents the grain growth thereby increasing the grain boundary area.
From the study it is found that: · Addition of nano-silica produced alteration in the mechanical properties of the TiNi alloy owing to the better hardness of the alloy with grain refinement as result of impingement of diffusion and grain growth in the matrix