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Within each melt pool, the grain size is not uniform and some finer grains are distributed around the large elongated grains.
The degree of grain refinement generated is evaluated by estimating the ASTM grain size number and then correlated to the average grain diameter of the weld section.
Fig. 5 SEM microstructures of the welds produced at different heat inputs and cooled under normal condition: (a) 432 J/mm; (b) 518.4 J/mm; and (c) and 1296 J/mm Fig.6 SEM microstructures of weld samples produced by cryogenic cooling and then welding at different heat inputs (a) 432 J/mm; (b) 518.4 J/mm; and (c) and 1296 J/mm Fig.7 EDX spectroscopy of welds produced under different welding conditions: (a) welds cooled under normal condition; (b) samples cooled in liquid nitrogen prior to welding Effect of cryogenic Cooling on the Grain Size of Weld The grain diameter is evaluated through intrapolation within the spectrum of the ASTM grain size number and is given in Fig.8.
The grain structure of welds is primarily determined by the time spend above the grain coarsening temperature.
The grain refinement was between 14% and 36% compared to the grain size of the welds cooled in normal condition.

Above seven extrusions the grain size decreases and grains seem to be broken.
Sharpness of the grain boundaries decreases with increasing pressing number.
It refers the increasing diffusivity of the grain system.
Higher number of pressing caused decreasing in hardness.
Higher number of pressing caused decreasing in hardness. 7.

Vickers Hardness vs. mean grain size.
(a) CG Ni with a mean grain size larger than 10 µm; (b) as-deposited NC Ni with a mean grain size smaller than 30 nm and heat-treated NC Ni with a mean grain size of about 60 nm.
The length of the dislocation source may be some fraction of and proportional to the grain diameter, because they are associated with individual triple lines or grain/grain interfaces.
As l scales with the grain size, the AV value increases with increasing grain sizes.
The shear strain, γ, is defined as tnr /2πγ = where n is the number of turns, r is the radius and t is the thickness of the specimen [58].

For this aim, a number of ways such as alloying, heat treatment, transformation of silicon particles into spherical form with the help of elements such as sodium and strontium, and grain size reduction with grain refiners have been tried [2-4].
In addition, the E% of the homogenized sample shows a continuous increase with increasing pass number.
As seen in this figure, microhardness and hardness decrease with increasing pass number.
Principles of equal-channel angular pressing as a processing tool for grain refinement. 
Ultra-fine grained bulk aluminum produced by accumulative roll-bonding (ARB) process. 

The microstructure evolution of AA 3103 with growing number of ECAP passes is presented in Fig. 3.
During annealing similar trends were observed irrespective of the number of ECAP passes.
Apparently, the precipitation kinetics are sped up in samples after higher number of ECAP passes (N>4), most likely due to the high fraction of high angle grain boundaries and therefore accelerated diffusion processes.
ECAP deformation up to eight passes in route Bc led to the formation of an ultra-fine grained structure with a mean grain size of about 500 nm.
ECAP processed AA 3103 showed increased stability against discontinuous recrystallization with growing number of passes due to accelerated dispersoid formation at higher number of passes.

Cast alloys are designated using three digits along with a decimal designation as Xxx.x, in which first digit shows the major alloying elements and the second and third are the arbitrary numbers given to specify the alloy.
The decimal number with “0” identifies it as casting and “1” or “2” identifies as ingot structure [2].
Mark Easton et al. has derived a relation between grain size (d) and solute content , considering a growth restriction factor Q, potency and number density of nucleant particles, The term a is related to the maximum density of active TiB2 nucleant particles within the melt, while b is related to their potency [23]
Ramesh et al. has studied on the mechanical properties of multi directional cryoforged Cu-Ti Alloy and confirms that Grain size reduces to 2 µm after 3 cycles of MDF, Density of the shear bands increases and width of the shear bands decreases as the number of MDF passes increase and shows that yield, ultimate strength, Hardness increase by increasing number of passes as strain hardening [33].
[23] Mark Easton And David Stjohn “An Analysis of the Relationship between Grain Size, Solute Content, and the Potency and Number Density of Nucleant Particles” Metall.

A large number of pores, high water consumption, and weak supersaturation of the solution characterize the concrete made of such cement and lead to decrease in the strength.
The sand fineness modulus Mfn = 1.29: no grains larger than 5 mm; the share of grains with a diameter of less than 0.16 mm is 8.7%; the content of pulverized and clay particles is 0.84% [7].
Research Results The cement grains have sizes from 1 to 100 μm [8, 9].
Ivanov-Gorodov believes [10] that uniform and rapid hardening of cement is achieved with the following grain compositions: grains smaller than 5 μm compound no more than 20%, grains of 5-20 μm in size are about 40-45%, grains 20-40 microns in size - 20-25%, and grains larger than 40 microns - 15-20%.
Concrete obtained using cement mechanically activated in the activator Pulverizette-6, has a more loose structure with a large number of different forming elements.

Then local textures around holes were estimated in EBSD-OIM system above because the number of grains with orientations of Goss and diagonal-Cube ({100}<011>, D-Cube hereafter) were very small and these grains should then be identified before the TEM observation.
On the other hand, many dislocation densities were observed in grain (c) while their densities were not so high in grain (d) though both grains have D-Cube orientations.
Microstructures in grains after 5% strain; (a) a Goss grain within 6.8 degrees, (b) a {111}<112> grain within 8.0 degrees, (c) a D-Cube grain with 7.3 degrees from ideal one and (d) another D-Cube grain with 14.8 degrees (a) (b) (c) Fig. 3.
Microstructures in grains after 9% strain; (a) a {111}<112> grain with 13.9 degrees, (b) a D-Cube grain with 14.3 degrees, (c) a Goss grain with 12.2 degrees from ideal orientations.
Stripe patterns also can be seen in a Goss grain; grain A is the same as the one in Fig.3(c).

Averaging the properties in all directions is based on a large number of grains and random orientations of their crystal lattice.
Otherwise, if the models contain too small number of grains, the obtained properties do not represent the entire system and are representative for the specific grains configuration.
Reduction of dimensionality decreases the number of degrees of freedom in Eq. 11.
This, on the other hand, allows to simulate much higher number of geometrical details of the analysed structures.
First, the number of the modelled grains needs to be sufficiently large, assuring that the results do not depend on the number of grains used.

Phase material microstructure and grain area ratio directly affects the material uniformity, uniformity of material differences caused by different grain characteristics which ultrasound parameters.
Thus, studying further on the changing relationship between velocity and grain size is also necessary.
Figure 5-1 Proportion of the α phase of the sample grain and trend of the ultrasonic velocity The relationship between the area ratio of α phase of sample and acoustic attenuation coefficient When the acoustic wave spreads in the medium of uniform grain material, the scattering due to the grain boundaries will cause the attenuation of sound waves.
In the heat treatment process, with the α-phase single area ratio and the ratio of the number increases, the scattering when sound wave spreads in media aggravates, resulting in the increase acoustic attenuation coefficient.
With the increase of the ratio of α phase of the grain, it will lead to the variation in elastic modulus and density.