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The obtained data are then a set {xi, yi, gi, with 1 ≤ i ≤ N}, N being the total number of measurements and (xi, yi) being the coordinates of the 'points' for which the orientation, gi, has been determined.
The total number of measurements, N, should also be compatible with a good statistics for the quantities calculated from the measured data.
To calculate an ODF for example, one should measure a number of grains similar to the one considered in X-ray pole figure experiments (~ 10,000) which is possible today thanks to the high speed of modern systems.
The number of successfully indexed points decreases with the amount of previous plastic deformation.
The grain boundaries could be easily characterized.

It was revealed that the deformation texture, grain size and fine precipitates (G.P. zone) were almost the same, indicating that the excess Mg in the new alloy was contained as solute atoms in the matrix.
It is seen that many small rectilinear cracks whose length is comparable to that of average grain size (≈ 27 mm) appear on specimen surface.
As shown in Fig. 4, the sub-surface crack penetrates a grain in rectilinear manner.
Indeed, small faceted region whose size was similar to that of a grain was clearly observed at the fracture origin.
Here, N25 is defined as the number of fatigue cycles where surface crack number density, ρ, reaches 25 mm-2. ρ can be regarded as an index representing the resistance against fatigue crack initiation.

Montmorillonite grains split and in the state of “bridge-break”.
There are a large number of hydrophilic groups on its macromolecular chains, such as –COOH, -OH, -CONH2.
Interlayer distance of montmorillonite grains increase, grains that encapsulated on the surface network structure of polyacrylamide expand and become much plumper, the grain layers have a slight angle deflection.
Part of the connetion between the grains is broken and the grains split into small single-particles.
At last, moontmorillonite grains disperse in three direction with the angles closely to 120℃, causing the totally disconnection of moontmorillonite grains.

A number of properties of Al2O3 are closely related to atomic and electronic structures of intrinsic point defect and dopants.
Consistent with previous study [16], YSZ grains and Al2O3 grains are fairly distributed among each other but minor agglomeration is unavoidable.
In general, similar microstructural characteristic are observed in these samples i.e. uniformly sized grains with high degree of grain close packing.
Almost no abnormal grain growth is observed.
Energy dispersive X-ray analysis (EDX) indicates that dark grains are Al2O3 and MgO while lighter grains are YSZ.

The microstructure of the aluminium alloy exist obvious differences at the initial and final compression deformation instant between L and H, as shown in Fig.3, where the grain size of L is larger than H and the grain boundary density of L is lower than H whenever at the initial or final compression deformation instant.
The grain boundary is stronger than grain itself both at room temperature or low temperature, but becomes weak at elevated temperature on the contrary [10].
Recovery mechanism of the alloy is dislocation rearrange and dislocation density decrease under inner stress, the driving force affect by temperature, deformation, grain size and so on.
H has smaller grain with greater extrusion ratio than L before compression, a large number of (sub-)boundaries and mismatch to the matrix alloy allows generating more barriers, which make dislocation slip more difficult and recover driving force increase [14], resulting higher apparent active of H than L commonly.
(2)The flow stress of extruded bar with fine grain decreases faster than that with coarse one in high temperature and low strain rate which was mainly controlled by grain boundary sliding

Table 1 listed the sample number with different running time.
From Fig. 1(a), one can find that the as-received steel have large grains where there are a larger number of martensite lamellae.
Fine precipitated carbides exist inside the grains.
For the S0 samples, it is found from Fig. 3(a) that a number of carbides exist at the martensite lamellae boundaries and grain boundaries.
For the S16B sample (Fig. 3(c)), the precipitated carbides significantly become coarsened and spheroidal along the grain boundaries and inside the grains.

With the increase of O2/Ar ratio, the film surface became smoother and denser, and the angular grains gradually disappeared.
As for the reason for such phenomenon, at lower O2/Ar ratios, a large number of ionized Ar+ with high-energy bombarded the surface of ZnOn target, sputtering a large number of high-energy ions onto the film surface, causing rough and less dense structure on the film surface.
The compositional and structural parameters such as (002) peak FWHM, grain size, lattice constant c, and compressive stress calculated from the XRD patterns are listed in Table 1.
O2/Ar ratio XRD results O/Zn ratio Electrical resistivity (Ω·cm) (002) Peak FWHM Grain size (nm) Lattice constant c (Å) Stress (GPa) 0 0.484 126.1 5.198 0.7542 0.81 0.2 ± 0.1 0.25 0.595 78 5.202 0.3756 0.93 28.7 ± 1.2 0.5 0.634 64 5.213 -0.5366 0.92 2165.1 ± 1.9 1.0 0.661 45.3 5.219 -1.0732 0.88 410.4 ± 1.2 2.0 0.935 13.1 5.254 -4.2568 0.85 317.4 ± 1.3 With the increase in O2/Ar ratio, the grain size decreases.
As for the reason for such variation, it might be attributed to the reduction of argon ion content in the sputtering gas and the presence of a large number of un-ionized neutral O atoms.

The result shows that there are many atomic vacancies and formed a number of point defects in the films.
The increase of grain size leads to reduce the number of grain boundary.
The number of film grain increases with the power further increasing.
Many atomic vacancies forming a number of point defects result in the increase of the film resistivity.
The increase of grain size leads to reducing the number of grain boundary, and then the surface become smooth.

Subsequent warm rolling with a total reduction of 86% led to increased to 0.8-0.85 volume fraction of ultrafine grains with no changes in grain size.
At that, the volume fraction of new ultrafine grains increases to 0.8-0.85, suggesting that additional grain refinement takes place through subdivision of remnant grains.
At that the average grain size in fine-grained regions was about 6.1 mm in the material after warm rolling and 5.6 mm – after cold rolling.
In contrast, the formation of the grained structure in cold rolled alloy can occur during annealing by continuous static recrystallization [13,15], when a great number of strain-induced grains in the heavily deformed matrix transform to potential nuclei for static recrystallization.
Langdon, Influence of scandium and zirconium on grain stability and superplastic ductilities in ultrafine-grained Al-Mg alloys, Acta Mater. 50 (2002) 553-564

The temperature field of Number 1 in different melting periods was shown in Fig. 4.
A thin layer of fine grain region formed on the ingot surface for neighboring grain collided with each other so as not to continue growing.
Thereby the growth of other grains was inhibited.
When smelting power increased from 30 kW to 120 kW, the number of grains decreased from 34242 to 25753 and the mean grain radius increased from 1.01 mm to 1.06 mm.
The number of grains was 30215 and the average grain radius was 1.02 mm.