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The number of components required defines the order of the tensor since the kinetic coupling occurs between all recrystallizing and all deformed components.
Firstly, it reduces the number of deformed and newly formed recrystallized orientations to only a small number of discrete components.
The number of discrete texture components typically required for instance for the case of low carbon steel sheets amounts to 5-10.
It is also possible to increase the number of components for higher precision.
In the model essentially three types of grain boundaries have been used, namely, low angle grain boundaries which have a low mobility, high angle grain boundaries which have a larger mobility, and one type of special grain boundary (27°<110>) with a very high mobility.

The influence of covered area, number of measurement points and grains on the validity of texture analysis are also discussed.
Thus, the number of grains probed and the total covered area should be considered for the statistical reliability of EBSD based texture analysis.
CI) of the austenite phase, number of austenite grains and number of points included of each map in comparison are shown in Table 1.
The number of probed grains depends on the step size and average grain size of the material for scans with the same total number of measurement points.
These studies suggested the number of probed grains to be in the range of 200 – 3000 for reliable EBSD based texture analysis.

However, as for the fine-grained cassiterite, flotation and joint processing techniques are generally selected to improve the low recovery from gravity separation.
According to the studies of a number of tin ore bodies, tin can be classified into three major groups [2]: Cassiterite contained in pegmatite veins contain significant quantities of (Nb,Ta)2O5 with traces of wolframite and manganese.
The commonly used beneficiation method for coarse-grained cassiterite is gravity separation and for fine-grained is flotation.
Carrier Flotation Carrier flotation is that floatable coarse mineral particles are added into the pulp as a carrier, fine-grained particles adhere to the carriers or fine-grained particles themselves flocculate together, then the coarse particles are collected out.
Conclusions Though various flotation regents can be used for cassiterite separation, a number of difficult problems still cannot be avoided due to bad selectivity, high cost of the reagents, low index and serious environment pollution.

Critical nanometer grain sizes and deformation mechanisms The nanometer area a grain size approaches to the thickness of grain-boundary layers.
The polycrystalline grains are numbered.
In grains 3 and 4, the dislocation sources are triple grain junctions, whereas in grain 2, these are steps in the boundary between grains 1 and 2.
In Table the critical intervals of grain sizes from nano to mezo grains.
The stages with even numbers (II, IV, VI) have a constant value Θ, the stages with odd numbers (III, V) have the value of Θ decreasing with deformation.

According to the mechanical and microstructure test results, increasing in welding pass number causes reduction in grain size and increasing in average hardness of HAZ.
Also inter-pass slag inclusion defect occurred in high number of passes.
For example increasing welding current intensity causes increasing in heat input which leads to grain growth in HAZ and then reduces mechanical properties of weldments.A105 and A106parts joined together with TIG method by changing current intensity and pass numbers, then macro and microscopic evaluations, hardness, tensile, impact and bending tests accomplished.
Due to the increase of heat input with increasing of current from 80 to100am, the grain size of the HAZ in the S3 increased then hardness decreased from 149 in S2 to 141HV in S3.
(b) is clear that the HAZ grain size in the S4(80amps-5pass) (S2) is smaller than in S2(80amps- 3 passes ).

The number and the size of the recrystallized grains generally increase as the annealing temperature increases.
The total number of grains used for this calculation were as follows: 2663 grains at 790°C, 1144 grains at 850°C, 1037 grains at 900°C and 954 grains at 950°C.
The number of grain boundaries used for the calculation was 650 and 512 for Goss and {111}<112> orientations, respectively.
Average grain diameter of grains with various orientations with annealing temperature during the progress of grain growth.
Consequently, {111}<112> grains have a much higher frequency of high angle grain boundaries than Goss grains.

Goss grains({011}<100>) are nucleated within shear bands in deformed {111}<112> and{111}<110> grains. {111}<112> grains nucleate in deformed {111}<110> grains and new{111}<110> grains nucleate in deformed {111}<112>grains. {111}<112> grains have an evident advantage both in number and growth rate over α grains, thus the controlling of annealing time can contribute to the increase of {011}<100> texture.
With the increasing of annealing time, as shown in Fig.1 (b), new Goss grains({011}<100>) are nucleated within shear bands in deformed {111}<112> and{111}<110> grains and the number of shear bands is the highest in deformed {111}<112>grains.
Since {111}<112> grains have an evident advantage both in number and growth rate over α grains, when the annealing time increasing to 180s, the area fraction of {011}<100> component drops down to 0, while {111}<112> component is the dominant component.
(2) {111}<112> grains nucleate in deformed {111}<110> grains and new {111}<110> grains nucleate in deformed {111}<112>grains.
Few Cube grains ({100}<001>) are nucleated within shear bands in deformed {111}<112> grains

As the power increased, the size of the nano silver grains increased and the number of grains decreased.
It is apparent that the silver films were composed of compact nano size grains, and the surface shape of the grains varied with the power.
As sputtering power increased, the size of the nano silver grains increased and the number of grains decreased.
As sputtering power increased, some nano grains aggregated to form larger islands, thus the number of the grains appeared to be smaller and their diameter larger.
We measured the number of Staphylococcus aureus bacteria of samples at dilution ratios 10 -1, 10-2 and 10-3.

We want now to adapt it to the grain boundary precipitation.
No deformation of lattice and no disorientation between the two grains are taken into account.
At long time (fig. 2a), one observes approximately the same number of NbC precipitates on the GB and in the bulk.
Figure 3 : Evolution of the size of the precipitate in number of atoms by precipitate during a thermal aging at T=900K and the concentration CC=CNB=0.5%at.
Figure 4 : Evolution of the size of the precipitate in number of atoms by precipitate during a thermal aging at T=900K and the concentration CC=CNB=0.5%at.

The number of cyclic treatment was varied from 0 to 20 cycles.
With increasing the number of heat treatment cycles, the W/W grain boundary area is changed to W/matrix boundaries by the penetration of matrix phase.
Variations of measured impact energy with number of heat treatment cycles.
This anisotropy of plastic deformation in the W grain may be increased with increasing the number of heat treatment cycles.
Residual stresses in W grains measured by XRD were also increased with increasing the number of heat treatment cycles.