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In the scaling state of grain growth the effective volumetric rate of change VV &3/1− depends only on the relative grain size 〉〈= RRx / [3-5].
That is, )( 3/1 xkHRRVV ζζ == − && , where R is the radius of the grain-volume equivalent sphere, )(tRR 〉〈=〉〈 is the average grain size, )(xH is a dimensionless time-invariant function, k is the kinetic constant of curvature-driven grain boundary motion and 3/12)48( πζ = .
Least-squares fit of Eq. (2) (solid curve) to the MC simulation results (stars with error bars) and plot of Eq. (3) with ( )xs from Eq. (4) (dotted curve); b - Number of neighbouring grains ( )xss = vs. relative grain size x divided into size classes.
A qualitative understanding of the non-linear behaviour of )(xkHRR =& can be gained on the basis of recent results of Hilgenfeldt et al. [10] and Glicksman [11], who have shown by considering three-dimensional space filling polyhedral networks that the average volumetric rate of change of grains of relative size x is solely a function of its average number of faces or neighbours )(xss = .
Acknowledgment The authors would like to thank the Deutsche Forschungsgemeinschaft for financial support under grand number GKMM 828.

Mössbauer Spectroscopy of Grain Boundaries in Ultrafine-Grained Metal Materials V.
The emission Mössbauer spectroscopy expands the number of subjects and physical phenomena to be studied.
Submicrocrystalline materials obtained by severe plastic deformation (SPD) were studied by the absorption NGR spectroscopy only in a number of studies on submicrocrystalline Fe obtained by high-pressure torsion (HPT), with average grain sizes of 220 nm [15-17].
The emission NGR spectroscopy was successfully applied for the studies of the state of equilibrium GBs of recrystallization origin in a number of polycrystalline metals (see e.g. [1, 19, 20]).
Nevertheless, as demonstrated by a number of various examples, the emission Mössbauer spectroscopy enables to reveal real differences in “equilibrium” and “non-equilibrium” boundaries.

Effect of ECAP number passes on grain size and fraction of high angle boundaries after cold rolling was investigated.
Rolling results in grain refinement and HABs fraction increase the more ECAP number passes.
The dependence of average grains/subgrains size with passes number is given in table 1.
The difference between grain/subgrain sizes decreases with increasing passes number.
Subsequent rolling results in grain refinement: grain size decreases, HABs fraction increases.

The pitting corrosion resistance firstly decreases with increasing the cold-rolling reduction from 0% to 30% due to the number of nucleation site increasing.
When the reduction up to 40%, grain boundaries are cut by slip line, partly grain boundaries begin disappear (Fig.1 (e)).
Due to increasing dislocation density during cold working, the number of nucleation site of pitting corrosion increases from 0 to 30% cold-rolling reduction which results in the reduction of pitting corrosion resistance.
Schino [7] suggested that the pitting of coarsely grained steel initiates in limited sites with large and deep individual pits, the increment of pitting corrosion sites number in the ultrafine grained steel leads to a decrease of anodic current density with respect to the coarsely grained steel.
The number of nucleation site of pitting corrosion increases from 0 to 30% cold-rolling reduction which results in the reduction of pitting potential.

It has been established that there is an annual increase in the number of fires at grain elevators.
Silos provide reliable long-term storage of grain with the least losses, as well as a number of technological operations: reception, storage and unloading of grain; low-temperature drying of grain in a silo; cooling of grain mass; grain disinfection; as well as layer-by-layer control of grain temperature [1].
However, immature grains of freshly harvested or grains with high moisture content have a higher activity.
According to the statistical method, the risk is calculated by the formula: R=n/N, where R is the risk for a certain period of time; n is the number of actual manifestations of danger during this period; N is the theoretically possible number of hazards for a given type of activity or at a facility.
The authors [12] established that,according to data from the website Elevatorist.com [13], there is an annual increase in the number of fires in grain elevators.

Number density distributions of (a) Nb- and (b) Al-rich particles in the solute-rich and solute-depleted regions after reheating at 1150 °C.
From the number density distribution of Nb-rich particles it can be seen (Figure 8 (a)) that there is almost no change in number density of the particles in the solute-depleted regions compared to 1150 °C as predicted by Thermo-Calc.
However, a greater number of finer particles of AlN is present in the solute-depleted regions.
(a) Number density distributions of Al-rich particles (b) prior austenite grain size distribution after reheating at 1125 °C for 2 and 8 hours.
Increased numbers of Al-rich particles more uniformly distributed can offset difference in pinning behaviour due to Nb segregation. 2.

,)1() 2 ( 1 2 ∑ ∫ ∑ =< −+∇∇− = n i i ji V nji ij jiij dV F φλφφ ε φφω (1) where i and j represent the orientations of grains, n is the number of distinguishable orientations, ω is the height of double-well potential, ε is the coefficient of the phase field gradient energy term and λ is a Laglangian multiplier.
One iteration corresponds to the calculations of the total number of grids in system multiplied by 11 loops, where 11 is an upper limit of the number of phase fields which can share simultaneously in a grid.
For this, the simulation system was filled with cubic grains of 9×9×9 grid 3 with each grain of a random orientation number ranging from 1 to 1,000,000.
To determine the size of individual grains, the volume V of each grain at a given simulation time was estimated from the microstructure by counting the number of grids inside a grain.
(a) The grain size distribution data at t = 1000(initial), 2000, 3000, 4000, and 5000 iterations, compared with three dimension Hillert distribution (solid curve). n in the inset of Fig. 2(a) refers to the total number of grains in the simulation system.

Fine-Grained Concrete with Nanodispersed Silica Additive N.P.
The maximum number of particles of up to 100 nm in the additive is observed at the age of 10 days, and then their number decreases.
The maximum number of particles of up to 100 nm in the additive is observed at the age of 10 days, and then their number decreases.
Porosimetric characteristics of fine-grained concrete
The maximum number of particles of up to 100 nm in the additive is observed at the age of 10 days, and then their number decreases.

Furthermore, the number of effective nuclei is typically around 1% or less of the number added to the melt for the case of TiB2, so the efficiency of particle addition is limited.
This study [11] has led to the development of Eq. 2, on the basis of Eq. (1), for the prediction of grain size as a function of Q, nucleant particle type and number, and/or cooling rate as follows   2 1 3 .1 TQ Tb NTf d n v      (2) where d is the grain size, Nv is the number of nucleant particles added, f is the fraction of nucleant particles that are able to nucleate grains at the cooling rate, T (f is a function of T ), nT is the nucleation undercooling and ''b is a fitting constant.
There are a number of semisolid casting techniques that use this as a method of producing slurries for rheocasting or billet for thixocasting [14-16].
The increase in the number of active particles is probably due to the fact that the origin of the extra grains is from on or near the mould walls due to thermal undercooling rather than constitutional undercooling [12].
Summary A number of approaches to controlling grain size and thus the morphology for semisolid processing have been examined using a new and simple analytical model.

To complete this analysis we need a relationship between the number of faces of a grain of radius RS and the mean grain radius .
This can be determined, again approximately, from the work of Rhines and Craig [12], who serial sectioned single phase aluminum undergoing rapid grain coarsening to determined the frequency of grains with different numbers of faces, fig. 6.
So using eq. 5 we obtain: RF = RS 2 / N 1/2 = 2 / 81/2 = 0.707 (5a) NGC -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0 20 40 60 80 100 Number of Grain Faces (N) sin Ф' .
The variation of sin φφφφ' as a function of the 3D number of neighbors N [16].
The sin φ' curvature determined by the grain neighbor number 10 min 60 min 10 20 1 min 2 min 30 min 40 30 Faces Per Grain Number of Grains/ cm 3 x 104 12 4 8 makes grains with N> 14 grow more slowly than grains with N < 14 shrink.