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Preferred misorientations, Dg, between nuclei and deformed grains, correspond to high mobility of grain boundaries.
Compromise Function The compromise function is defined as a volume fraction of all deformed grains, which can be potentially 'consumed' by a nucleus of a given orientation: (2) where Vj is the volume of the j-th deformed grain and the following condition has to be fulfilled: the i-th nucleus can grow into j-th grain with the migration rate exceeding some minimal value, i.e., .
The volume DVij of the j-th deformed grain consumed by the i-th nucleus is: (4) where Vj is the initial volume of the j-th grain and the summation on k is done on growing nuclei (those which fulfill the compromise condition).
The total volume of the deformed matrix, 'consumed' by i-th nucleus is: (5) where N is total number of deformed grains.
Acknowledgment This study was financed by the Polish National Centre for Science (NCN) under decision number: DEC-2011/01/B/ST8/07394.

It has been demonstrated that below a critical size, the grain interiors contain no significant dislocation source.
Thus, only grain boundaries act as significant dislocation sources and sinks.
Specimens cut from the processed billets were prepared by standard metallographic techniques and etched in a solution of 30 ml NH4OH, 25 ml H2O2 and 45 ml C2H5OH to identify grain boundaries and some crystal features within the grain interiors.
In figure 2(a) the trend of assessed dislocation density (ρ) is plotted as a function of ECAP pass number.
Further comparative analyses of tensile behaviour between ultrafine grained 99,97% purity silver and ultrafine grained Al-Mg-Si alloy was carried out by calculating the cumulative true plastic strain of the ECAP processed and tensile strained materials.

Grain structure was observed in polarised light after anodising in Barker's reagent.
The number of dispersoids is much larger in alloy 5049, which corresponds to the higher Mn content.
Figure 3 Grain sizes in RD (a) and ND (b) in as-cast, homogenised and 1.0 mm samples.
The grains in alloy AA5049 are coarser than in alloy AA5754.
On the other hand, uniform and fine grain size is obtained in the non-homogenised alloy AA5754, whereas the homogenised sample has slightly coarser grains at surface.

The film deposited at 4800 s owned a mixed texture of (111) and (200), showing an anisotropy distribution of (111)-oriented and (200)-oriented grains, while film deposited at 7200 s owned a strong (200) texture, displaying an isotropy distribution of (200)-oriented grains.
The competitive growth between (111)-oriented and (200)-oriented grains was responsibility for alternating texture.
The number of intrinsic stress also alternately change with deposition time.
Furthermore, it is notable that the number of intrinsic stress for NbN films will increase when the growth face change from (200) to (111).
The film deposited 4800 s displays an anisotropy distribution of (111)-oriented and (200)-oriented grains, and shows an isotropy distribution of (200)-oriented grains while the deposition time of film was 7200 s.

Mg96Zn2Y2 base alloy had extended LPSO phase along extruded direction in α-Mg grains.
At the nugget, net-like secondary phase was produced in the Mg grains.
Net-like secondary phase is observed inside of a single Mg grain.
In the grain, large number of Mg17Al12 particles with small quantity of Zn precipitated.
Grain size of Mg in the nugget was about 30μm and net-like fine dispersed 14H, 18R-type LPSO phases were produced in the grains.

The numbers of cycles werе: 1,2,4,6,8,10,12,20 and 40.
The final, grain radius after thermal cycling, similarly to the discounting operation, can be calculated by the formula (1) (1) where – relative reduction in grain radius as a result of a single processing cycle; n – number of thermal exposure cycles.
We also theoretically and experimentally found that the more processing cycles the alloy undergoes, the smaller the grain sizes in its structure become, while the grinding intensity decreases with an increase in the number of cycles.
With a further increase in the number of cycles, the sizes of their grains do not decrease.
Dependences of the relative elongation δ of VT20 and OT4 alloys on the number of TCT cycles Thermal cycling of titanium pseudo-α-alloys VT20 and OT4 causes a significant increase in their impact strength (Fig. 9).An increase in the impact toughness of the samples under study is observed up to 10 TCT cycles, as well as an increase in strength.This is obviously associated with the nature of the structure formed in alloys with such a number of thermal cycling cycles: a fine grain of the α-phase with interlayers of the β-phase and a high density of dislocations in fine grains of the α-phase.

The mean grain size was 20 µm; the grains were rather equiaxed.
At large strains (0.25 and 0.36) the dislocation arrangement is similar, but the number of grains with equiaxed cells rises with increasing deformation.
TEM images showing twin - grain boundary interactions.
However, twins are more frequently observed in rolling than in tension (for a strain value of 0.30 in rolling, the number of twins is significantly smaller than for 0.25 in tension).
Observed grains have a <011> normal to the sheet plane.

The abrasive grains which contact with the electrode will eventually fall off because their holding forces become weakened.
In the experiments of Number 1 and 2, the run-out of the grinding wheel hardly decreased by the truing.
It was the same in the experiment of Number 3.
After the experiment of Number 3, the black colored layer formed on the wheel surface was removed by grinding a GC grinding stone (75 mm length × 35 mm width, grain size #800).
On and after the experiment of Number 3, the additional truing was implemented.

The SEM images also showed a reduction in grain size which can be due the fact that Nd doping induces Sr and Ti vacancies in the system which inhibits the grain growth.
These vacancies react with the oxygen vacancies already present, thus reduces the total number of vacancies.
The theoretical density can be calculated by Eq. 1, where, M is the molecular weight of ceramic material, n is the number of molecular units in a unit cell, V is the volume of the unit cell and NA is the Avogadro number which is 6.022x1023.
From the micrographs, it is clear that the grain size of the ceramics reduced with the addition of Nd into the host SrTiO3.
The SEM images also showed a reduction in grain size which can be attributed to the inhibition of grain growth due to the presence of Sr and Ti vacancies in the system induced as a result of Nd doping.

Table 3 The gradual change of grain composition in slaking testing of soaking sample dry-wet circle number/time grain content/% <0.25mm 0.25～0.5mm 0.5～2mm 2～5mm >5mm 1 2.57 2.04 6.65 25.15 63.59 3 6.31 3.7 12.02 42.61 35.36 5 7.89 5.25 16.9 60.75 9.21 7 11.2 5.37 20.48 55.29 7.66 9 13.09 5.95 22.4 52.81 5.75 11 14.27 6.12 32.63 42.4 4.58 13 15.91 6.76 32.68 40.92 3.73 Table 4 The gradual change of grain composition in slaking testing of soaking sample ② dry-wet circle number/time grain content/% <0.25mm 0.25～0.5mm 0.5～2mm 2～5mm >5mm 1 0.55 0.28 0.76 1.61 96.80 3 3.00 0.93 3.22 20.02 72.83 5 4.30 1.56 6.73 61.91 25.50 7 6.11 1.93 9.83 71.94 10.19 9 7.26 2.35 11.55 71.66 7.18 11 8.22 2.65 16.10 66.72 6.31 13 9.33 2.96 19.37 62.71 5.63 Carbonaceous mudstone slaking particle distribution characteristics The slaking process and experimental data, it is known that the drying than the original rock slaking characteristics were ambitious, And the slaking of particle size particles that the
In the process of slaking of Carbon Mudstone, the composition of grain is changing continuously.
When slaking stops, The main thing apart grain diameter in 0.5 ~ 5 mm.
Figure 2 for test obtained two groups of different size particles sample the content of dry-wet cycle number change curves.
Conclusions In the process of slaking of Carbon Mudstone, the composition of grain is changing continuously.