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The traditional methods of getting the grain size depend on artificiality.
When the grain size was measured through intercept method, the relationship between average diameters (L) and grain size (G) just as the Eq.5
Fig.7 The average diameters Table.1 Grain sizes A B C Manual 12.951585 12.64429 12.299873 Computer 12.833637 12.725512 12.372498 Table.2 shows the average time consumed in the process of scanning an image at different number of sampling.
Table.2 Consumed Time Number of sampling in an image 1600 2000 Time（ms） 22 37 Form the data Table.2, we can see that the consumption of time in level of ms.
Metal-methods for Estimating the Average Grain Size.

Mössbauer investigations of grain-boundary diffusion and segregation V.V.
In particular, Mössbauer investigations make it possible to evaluate directly the grain-boundary segregation factor, to determine the grain-boundary diffusion mechanism, to estimate the rate of the diffusant pumping from a grain boundary core into the bulk, etc.
In particular, Mössbauer investigations can give information on the grain-boundary diffusion mechanism and enable to determine the grain-boundary segregation factor, to evaluate the rate of the diffusant pumping from a grain boundary into the bulk, and to obtain some data on composition of a grain-boundary core and near-boundary areas.
Let's consider this model of grain-boundary diffusion (Fig. 4).
Number 1 denotes component 1, and number 2 - component 2.

The fraction of nanoscale grains increases with strain.
New grains grow consuming deformed ones.
It is seen that relatively large recrystallized grains are surrounded by fine grains.
Schematic presentation for variation of structural mechanisms responsible for new grain development during annealing of cold-worked Ni-20%Cr alloy, where Nrex.nuclei – number of recrystallization nuclei, Nsubgrains – number of subgrains.
In this case the continuous grain growth leads to the formation of homogenous structure with a grain size of 60 nm.

Novel Approaches to the Thermodynamics of Grain Boundaries and Grain Boundary Junctions Lasar S.
Three recent investigations in the field of thermodynamics of grain boundaries and grain boundary junctions are presented. 1.
Expressing µ through the thermodynamic characteristics of the volume of the grain and taking into account that 0s s as s= Γ , where sas is the surface excess of the entropy per atom at the boundary surface we arrive at [11] ( )0 0 s v a a a d s s dT dp γ= −Γ − − Γ Ω (3) A grain boundary separates two thermodynamically identical phases, and one peculiarity of grain boundaries consists of the fact that for a system with a grain boundary the number of degrees of freedom is by one greater than for an interphase [10], which is completely determined at constant temperature.
The three line tensions of the three grain boundaries are indicated in Fig. 3 by γi-j with the indices i and j denoting the two grains on both sides of the grain boundary.
For an equilibrium grain size, if it exists, the derivative d G d ∆ S must equal zero at T = const ( ) ( ) ( ) 2 2 2 2 0 2 2 2 sold G c d cdc dc d G V c d dc d dc d γ γ ∆∆ = + + S S S (11) grain 1 grain 2 grain 3 grain 1 grain 1 grain 3 grain 2 grain 3 grain 2 For positive grain boundary energy and positive adsorption ( 0Γ > ), when the concentration of impurities at grain boundaries is higher than in the bulk, the derivatives ( ) ( )22 2 2 2 , , sold G c d cdc dc d dc γ ∆ S in Eq. (11) are negative.

Grain refinement.
However, understanding of the mechanism of the grain refinement process is still an open problem.
High-pressure torsion(HPT) is one of the methods highly suitable for experimental and theoretical studies of formation of the ultra-fine grain substructure: very high strain can be achieved without interruption and one can look at various amount of strain in one specimen.Due to relatively simple loading conditions strain can be defined approximately as simple shear.The large number of recent publications reviewed in[1,2] indicates that the research is still mostly empirical.
The basic assumption is that the lattice rotation is impeded in grains mostly near grain boundaries.
On the other hand,the observed non-equilibrium boundaries are wider than δ≈10-9 m of standard grain boundaries.

grain I grain II <111>II <111>I <112>II <112>I a ϕ a <111>I <111>II <112>II <112>I grain II grain I ϕ (a) (b) Fig. 1.
For sake of convenience we will consider the effect of the "lateral" Journal Title and Volume Number (to be inserted by the publisher) 3 and "top/bottom" surface triple lines (Fig. 2) separately.
(a) Measured inclination angle θ versus time for a moving 37.5° <111> grain boundary at 440°C and (b) calculated criterion Λ vs. temperature (circle symbols - 37.5° <111> grain boundary, square symbols - 40.6° <111> grain boundary).
Journal Title and Volume Number (to be inserted by the publisher) 5 Discussion Since grain boundary migration is a drift motion to reduce the total free energy of the system, the boundary velocity has to be proportional to the driving force = bV m p (6) and bm is referred to as the grain boundary mobility.
For all temperatures, at which grain boundary motion was measured in the current experiments (a ≅550 µm), the criterion Λ was calculated to be about 22=Λ for the 37.5°<111> grain boundary and 29=Λ for the 40.6°<111> grain boundary (Fig. 4b).

Effects of grain size on fatigue crack propagation in copper film K.
The fatigue crack propagation in the film with large grains was often decelerated, so the crack propagation rate of the film with the large grain was lower than that of the film with the small grain.
When the crack propagation was decelerated, the crack opening displacement obtained from the film with large grain size was smaller than that obtained from the film with small grain size.
Especially, a grain size in the film is considered to have a greater effect on fatigue fracture properties than in the bulk materials because of a small number of crystals against to its thickness.
As a result, the fatigue crack propagation rate of the film with the large grain was lower than that of the film with the small grain. 2) When the crack propagation was decelerated, the crack opening displacement distribution obtained from the film with large grain size was smaller than that obtained from the film with small grain size. 3) The relationship between the fatigue crack propagation rate and the stress intensity factor estimated from the crack opening displacement was identical for the cracks in the film with the large grain and the small grain.

An alternative method could be the use of ultra-fine grained materials in which the grain size effects may become insignificant.
A number of non-conventional methods such as rapid solidification, power metallurgy and vapour condensation can be used to produce very small grains in metals.
Without the reduction of the initial billet cross-section, the process can be repeated a number of times and the billet is rotated by different routs (A, Ba, Bc and C) [17] between consecutive passes in order to obtain uniform strain.
Grain Size and Hardness.
Sections of extruded cups heat treated to obtain a fine-grained microstructure with a grain size of about 4 µm.

The dependences of the number of dislocations emitted by a crack on grain size (ranging from 10 to 300 nm) in Cu and 3C-SiC (the cubic phase of silicon carbide) are calculated which characterize the grain size effect on crack blunting that crucially influences ductility of these materials.
Effect of grain size on crack blunting Let us calculate the number � of dislocations emitted from a crack along one slip plane as a function of grain size d.
The number � characterizes crack blunting induced by lattice dislocation emission.
With this calculation procedure, we have calculated the number � of lattice dislocations emitted along the same plane as a function of grain size d, for the typical nanocrystalline metal (Cu) and ceramic (3C-SiC) (Fig. 2).
The maximum number � of edge dislocations (that can be emitted from the crack tip along one slip plane) as a function of grain size d in nanocrystalline Cu (a) and 3C-SiC (b). 34] that some nanocrystalline fcc metals exhibit a ductile-to-brittle transition with decreasing grain size.

This paper deals with the influence of the coarse aggregate grain size on the frost resistance of concrete.
Frost resistance of concrete is influenced by a number of factors with a significant part of them being related to the composition of fresh concrete.
Results and Discussion Fig. 1 presents the results of RDM in relation to the number of F-T cycles.
The higher the maximum aggregate grain size, the better the resistance of concrete to cyclic freezing.
The smaller the maximum grain size of the used coarse aggregate, the lower the frost resistance of concrete.