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r( eM +σ⋅=ε ), and )r(B and )r(b are the stress concentrations tensors of grain (r), i.e. )r()r()r( bB +Σ⋅=σ , (3) where )r(σ is the average stress of grain (r).
Each of these polycrystals has associated different first- and secondorder moments of the stress field in the grains.
This is the reflection of an effective softer behavior at grain level that occurs when field fluctuations are considered for the determination of the linearized behavior of the grains.
For comparison between the different SC approaches, Fig. 2 shows the compression texture evolution (in terms of the basal texture factor along the axial direction), the effective stress, the relative basal activity, and the average number of active slip systems per grain, for the case of an initially random ice polycrystal, under the assumption of bas20pr τ×=τ and bas200pyr τ×=τ , where basτ , prτ and pyrτ are the critical stresses of the ( ) 11200001 basal, { } 11201010 prismatic and { } 11231122 pyramidal slip modes, respectively, as reported in [11].
However, at around 0.8 strain, the tangent results show a sudden drop in the basal activity, together with an increase in the effective stress (not attributable to geometric hardening only) and in the number of active deformation systems.

The effects of process conditions (grain size, acid species and concentration, leaching time and temperature) are discussed.
Optimal operating conditions are suggested: 75μm of grain size, 80 min of leaching time, 0.28 mol/l of concentration of HF, 80  C of leaching temperature.
The effects of process conditions (grain size, acid species and concentration, leaching time and temperature) are discussed.
Particles with sizes of 150μm, 75μm, 48μm and 38μm, that is 100, 200, 300 and 400 mesh numbers, respectively, were leached in turn under the same conditions.
Optimal operating conditions are suggested: 75μm of grain size, 80 min of leaching time, 0.28 mol/l of HF concentration, 80  C of leaching temperature.

The working principle involves the receptor function played by the surface of each oxide grain and the transducer function played by each grain boundary.
Firstly, we should mill the original monoclinic zirconia prepared before in planetary ball mill for 12 hours to make its original grain size under 1 μm.
Made a number of circular sheet embryos with the diameter of 20mm,a thickness of 5mm and a number of test bar with length of 60 mm, width of 4 mm, height of 3 mm.
From Figure 1, the grains of 5YSZ(yttria untreated) are smaller and more uniform than 5YSZ(yttria 1300°C); On the contrary, the grains of 8YSZ(yttria 1300°C) are smaller and more uniform than 8YSZ(yttria untreated), and the grains of 8YSZ(yttria untreated) are not in the same plane, the performance of 8YSZ(yttria untreated) is bad.

At final stage, the twins are saturated by filling in most part of the grains.
These recrystallized grains grow further with the increase of annealing temperature.
For the homogenized Mg alloy ingots, the orientation of their inside grains is usually distributed randomly, which means some of the grains are favourable for twinning while some are favourable for basal slip.
This can be verified by Fig. 4a, that is, twins were not formed in all of the grains.
Combined analysis of the results, we found that when the strain is very small (e.g. ε = 0.005), the relative intensity between {100} and {0002} diffraction peaks just undergoes a minor change with only a small number of twins emerge (Fig. 3).

Temperature variations Grain size statistics Local compositional changes?
Temperature variations Grain size effects.
The influence of grain size statistics depends upon the number of diffracting grains within the sampling or gauge volume.
From this information one can assess whether grain size will pose a problem.
Oscillating the specimen will increase the effective number of grains 'seen' on the detector.

Non-destructive technique based of X-Ray Diffraction Contrast Tomography also exists [6] but presents some limitations regarding the materials and/or the number of investigated grains.
Figure 3: Grain size distibution of 75 grains with transgranular cracks and of 815 grains without crack.
This crack may have been slowed down by grain boundaries (between grains 38 and 46 in Fig. 2b).
The cracked grain has a complex morphology: it contains two elongated twins which do not cross the full grain in depth.
This individual grain appears as three distinct grains in 2D surface orientation map (grains 37, 44 and 46 in Fig. 2b).

With increasing strain (88%) imposed by CR the number of twin bands decreases at the expense of an increasing fragmentation into subgrains (Fig. 3).
The dislocation density in the interior of the grains is low.
With increasing strain (88%) imposed by CR to the UFG material the number of subgrains getting smaller and smaller increases.
Fig. 4 TEM image of Ti processed by 8 ECAP passes; the equiaxed grains are often bounded by high angle grain boundaries.
After 8 ECAP passes (at 450° C) equiaxed grains with sizes from 300 - 800 nm are observed; most of the grain boundaries are high-angle boundaries.

The oxide films collected from Al-9.4Si-2.3Cu-1.0Zn-0.49Mg alloy melt were not continuous but contained a large number of particles, as shown in Fig. 3a.
Our previous experiments have demonstrated that melt treatment by intensive shearing prior to solidification can result in significant grain refinement in both Al- and Mg-alloys without any addition of grain refiner [8,14-17].
In practice, in order to enhance heterogeneous nucleation and achieve grain refinement, the nucleation substrate not only needs to be potent, but also needs to have an adequate number density, a consistent particle size and a narrow size distribution [18, 19].
The oxide particles dispersed by melt shearing supply a sufficient number of potent substrates to enhance the heterogeneous nucleation prior to solidification, resulting in grain refinement.
MgAl2O4 particles in the oxide films were dispersed by intensive melt shearing to provide a sufficient number of potent particles for enhancing the nucleation process, resulting in grain refinement.

The result showed an insignificant difference between 0 and 90 degrees of grain direction in aramid composite in any properties.
Variables for each treatment were differentiated by the grain direction.
The results are shown in Table 1 that the samples with weft direction (90˚) have a higher number of compressive strength (193.71 MPa) than the ones with warp direction (203.61 MPa).
These numbers explain the reason why the compressive strength of warp direction samples was higher as well.
The samples were varied by their grain direction: warp (0˚) and weft (90˚) directions.

The average grain size (d) was determined by the linear intercept method [15].
The addition of Gd2O3 increased the number of grains and here it acts as a grain inhibitor (Fig 2).
Conclusion In the Gd2O3 substituting of the ceramics, there is an increasing number of secondary phase that inhibited the grain growth and reduced the porosity, thus improving the sample microstructure.
Halim, Grain growth in sintered ZnO–1 mol% V2O5 ceramics, Mater.
Nelson, Lineal intercept technique for measuring grain size in two-phase polycrystalline ceramics.