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In this formula, M is one of the cations Li, Mg, Ca, Y and most rare earths with valance of +v, m is number of Si-N bonds in α-Si3N4 replaced by Al-N; n is the number of Si-N bonds in α-Si3N4 replaced by Al-O; and and x is the cation solubility (x=m/v) [1].
α-SiAlON grains, that contain a small amount of sintering additive are light gray β-SiAlON grains without any additive are black and the cation rich grain boundary phase appear white.
Some of the α-SiAlON grains are elongated which is believed to be a result of having a high amount of grain boundary phase.
After removing the grain boundary phase, individual α and β-SiAION grains were obtained for SEM and EDX analysis.
α-SiAlON grains are determined according to their morphologies since they are generally considered to occur in equiaxed grain morphology [8].

133 Variant selection in Zr alloys: how many variants generated from one beta grain?
The minimum number of variants needed to reach this minimum is shown to be 6, and in this case, the variants have very specific volume fractions.
We will assume the β grain is spherical, and behaves according to isotropic elasticity.
Volume fractions of variants allowing to reach the minimum energy with the minimum variant number (6).
Concluding remarks It is reasonable to assume that a minimum number of variants will nucleate, to reduce the surface energy of the system.

Quite a number of relaxation effects is connected with the dislocations [9], especially in severely plastically deformed (SPD) materials and alloys with sufficient high dislocation density.
Some grains are deformed and shear bands have evolved, but also areas with equiaxed and round grains exist whereas the rounded grains can be observed at the junctions of larger grains which is in agreement with literature [17].
The inhomogeneous microstructure also occurs when the sample is exposed to a temperature of 400 °C (Fig. 8 b): a mean grain size is 6.7 ± 3.9 µm. 25 µm a) 25 µm b) 0 5 10 15 20 10 20 30 40 50 ECAP-1 fitted data 1h at 250°C fitted data 1h at 400°C fitted data number of grains grain size in µm Fig. 7.
In case of annealing at 250 °C the small grains have grown but areas with small grains still exist.
After annealing at 400 °C a more intensive grain growth sets in which is dominated by the growth of especially small grains leading finally to an increasing homogeneity of the microstructure as shown in Fig. 8 b. 0 5 10 15 20 20 40 60 80 100 120 as received fitted data 1h at 250°C fitted data 1h at 400°C fitted data number of grains grain size in µm 0 30 60 90 120 150 180 210 hardness HV1 initial ECAP 1 ECAP 4 250°C 250°C 250°C 400°C 400°C 400°C Fig. 9.

The effect of a highly dispersed wollastonite-based additive on the physical and mechanical characteristics of fine-grained concrete was studied by uniform test procedure according to regulatory documentation preparing fine-grained concrete samples 40×40×160 mm in size.
It is established that the fine-grained concrete modified with the wollastonite Miwall 05-97 shows the best characteristics.
The compressive strength of the fine-grained concrete modified with the obtained compositions of a highly dispersed additive is given in Figure°3.
It contributes to the production of the effective fine-grained concrete with the Portland slag cement CEM II/A–Ш 42.5H as a binder, having the compressive strength of 50.8 MPa, and an additive content in the composition of fine-grained concrete in the amount of 10% of the cement weight.
Karpikov, Energy-efficient fine-grained concrete with integrated microfill, Construction and reconstruction. 5 (2014) 94–100

Reduced grain size, increased microhardness, rougher and more fractal grain surfaces are observed for the alloy solidified by two-liquid casting in comparison of the microstructure obtained by conventional solidification techniques.
Furthermore, grain size is related with undercooling as 31 ~ Id and )/exp(~ 2 2 TkI ∆− where I is nucleation rate and 2k is nucleation constant[3].
Measured average grain number by ASTM method was 3.91.
Measured average grain number by ASTM method was 6.03.
Comparing Fig. 2(A) and 2(B) it is obviously that the microstructure in the Fig. 2(B) is much more fractal than that of shown in Fig. 2(A), extremely increased grain number proves the supercooling that achieved during two-liquid composite casting.

The fracture modes at this aging temperature are mixed fracture mechanisms of dimple fracture and intergranular fracture, and the number of dimple fractures increases with time.
It can be seen from the figure that the die forging has not undergone recrystallization after 477℃/7.5h solution treatment, and there are a large number of fine sub-grains in the original grain boundaries.
The grains are elongated along the rolling direction, and undissolved second phase particles are dispersed inside the grains and at the grain boundaries.
Overall, the number of dimple fractures increases with time.
When the time was prolonged to 8h, the composition of intergranular fracture decreased significantly than before, and the number of dimples increased.

The reduction in grain size due to the increase of grain density results compressive residual stress.
As shown in Figure 3b, pearlite grains after 6.25% pre-deformation can become barriers for next moving ferrite grain.
The total number of cycles that cause failure is sum of the number of cycles that caused the initial crack and its crack propagation.
The effect of this plastic deformation makes changes in the grain structure become larger, the reaction from the specimen and the environment occurs more in the grain itself, resulting in brittle grains [14].
Number of cleavage surface due to propagation of fatigue crack are found to be many more in number and size (Figures 5c and 5d).

The novelty of the approach stems from incorporating an incubation period in the equations describing the progress of dislocation density with strain; beyond such incubation dislocation free grains form.
During hot rolling, DRX is employed for engineering grain size which further influences mechanical properties via the Hall-Petch effect [1].
At low temperatures, DRX is fundamental in attaining ultra-fine grained and nanostructured ultra-strong pearlitic wire (reaching 5 GPA strength) subject to severe plastic deformation [2].
• C: is the dislocation recovery term; fDRX = Nnucl Ngrowth − 1 = exp ( 6 κckBT ([(1 + x)N]−1T∆S | {z } i + 2xl∗ bκc ∆Gsys | {z } ii − λ 2µb3 | {z } iii )) − 1 depends on the difference between the number of subgrains with sufficient energy for grain nucleation Nnucl (from whom grain growth occurs) and the number of growing grains Ngrowth, divided by Ngrowth. κc is a variable that relates the dislocation density to the formation of cells [8].
Term i incorporates the energy dissipation related to grain boundary motion, and is expressed in terms of the entropy for disocation glide; term ii accounts for the solute/grain boundary interactions; and term iii quantifies the energy required to initiate grain growth.

It is observed that hardness and densification increased significantly with increase in number of ECAP passes.
Although a number of studies have been carried out with ECAP of many wrought metals and alloys, only limited research on ECAP powder consolidation is reported [5, 6] and no studies have been reported so far on ECAP consolidation of nanocrystalline powders.
The microstructure of base alloy having large grains consisting of sub grain network in them, which is shown in Fig. 5(a).
It resulted in a microstructure with small fraction of coarse grains along with large amount of ultra fine grains (300-600 nm).
It is shown that MWNTs were uniformly distributed in the aluminum matrix along less grain growth.

The number of AE events per minute is indicated as a bar chart on each graph (right-handed axes).
The number of AE events per unit of time for both rock samples tended to be higher under conditions of lower stress.
The amplitude and occurrence number of the AE signals might be a function of the amount of grain-boundary shear (mineral slip) between grains and/or the degree of resistance to deformation.
Acknowledgements This work was supported by JSPS KAKENHI [Grant-in-Aid for Young Scientists (B)] Grant numbers 22760651 and 24760691.
Oliver, Investigation of deformation twinning in a fine-grained and coarse-grained ZM20 Mg alloy: Combined in situ neutron diffraction and acoustic emission, Acta Mater. 58 (2010) 1503-1517