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The S-Parameter reflects the number of photons with a low momentum shift (<3 x 10-3moc) [9] and is defined as the ratio of the counts in the central region of the peak to the total counts in the peak.
The number of different vacancy-type positron traps in the material can be studied by investigating the linearity between the annihilation S- and W-Parameters.
The grain size as a function of irradiation doses is depicted in figure (7).
Grain size of about 180 nm is obtained at 10 kGy of irradiation doses.
The measured S-parameter values can be used to determine the grain size of the alloy under investigation Grain size of about 90 nm is obtained at 70 kGy of irradiation doses.

In addition, it has to contain titanium to promote equiaxed grains nucleation.
Figure 3: Evolution of volumic fraction of equiaxed grains for 3 grains densities corresponding to the micrographs A (ng=65 mm-3), B (ng=300 mm-3) and C (ng=2000 mm-3) Figure 4: Evolution of volumic fraction of equiaxed grains for a grain density of 300 mm-3 and for the two welding speeds Fig. 3 shows the evolution of the equiaxed grains fraction feg for the 3 grains densities deduced from the micrographs (Fig 1).
However, the real situation is more complex because a change in welding parameters simultaneously affects the temperature field around the weld pool and the content of transferred Ti, and then the number of nucleation sites.
Thermal numerical modelling of a welding operation allows predicting qualitatively the microstructure type, columnar or equiaxed, and shows that the number of nuclei in the supercooling region is very important.
A slight increase of Ti (and N) should be then increase the number of nuclei, and then produce a better grain refinement.

The σr max value decreases noticeably with the increasing number of thermomechanical cycles, then this reduction slows down, and stabilizes after reaching N=30 cycles..
Thus, the grain size decreases from 5-10 microns down to 35 nm (Table 1).
The effect of the number of ECAP passes (N) at 450oC for Ti-50.2%Ni alloy and PDA temperature for Ti-50.6%Ni alloy on characteristic temperatures is shown in Fig. 2a,b.
Characteristic temperature dependences as a function of number of ECAP passes (at 450°С) for alloy 2 (a) and as a function of the annealing temperature for alloy 3 (b).
Ultrafine Grained Materials IV.

With removal from the active zone of deformation the grain size increases, and microhardness decreases.
At the same time these alloys possess a number of advantages the major of which is an opened single-phase α-area along with an economy of cobalt.
In the top part of the samples, near to fixed head, the of grain size was maximum and in the middle part it has an average value.
The fraction of special grain boundaries sharply decreased and the fraction of low angle boundaries considerably rose.
It was shown that application of the method of complex loading allows obtaining gradient microstructure with minimum grain size near to mobile head and a constant increase in a grain size along the vertical axis of the sample. 2.

In presence of grain boundaries (GBs), the grain size effect (GSE) is traditionally described as τGB=τ0+kHPdg-1/2 [11,12], where τ0=τCRSS for an infinitely large grain and kHP the empirical Hall-Petch (HP) parameter.
Simplified calculations with straight dislocation segments permit varying the number of dislocations in the pileup and the GB and the degree of dissociation, for different geometries of slip plane and GB.
Dislocation pileups in small grains. 
Dislocation interactions with grain boundaries.
Grain boundaries and interfaces in slip transfer. 

Yin [4] studied the tamping effect of cold spraying by number simulation.
Borchers [6,7] studied the influence of continuous bombardment from sprayed particles on microstructure of the coating; the results showed that dislocation walls, sub-grain boundaries had been formed in the coating, and the grains even are refined via sub-boundary by dislocation propagation.
In the present work, work hardening effect generated during dynamic formation of Al-based coating on ZM5 magnesium alloy was investigated by combination of number simulation and experimental analysis; and microstructure of Al-Si coating was also researched.
Meanwhile, a large number of equated grains with approximate diameter of 0.3~0.5μm also be observed in the coating.
And with increase of micro-strain, the high density dislocation might convert to sub-grain boundary to refine the grains in the coating further.

JIS G 0551 requires the magnification which can catch the number of grains more than 50 in the intercept method, but we counted it with magnification ×300 in order to measure the PAG sizes in both areas.
We counted the number of grains which were intercepted by the test lines from a microscope image (magnification ×300).
(1) where L is an average grain size [µm], L is a length of the test line [µm] and N is the number of grains intercepted a unit length.
Prior austenite grains.
Prior austenite grain boundaries were observed in both areas.

Grain Boundary Faceting Phase Transition and Thermal Grooving in Cu B.B.
Grain 1 in this bicrystal is completely surrounded by grain 2.
The grain 1 in this bicrystal is completely surrounded by the grain 2 forming the Σ9 <110>tilt GB.
The <110> axes in both grains are parallel to the growth axis.
Westmacott and Dahmen observed that a small Al grain embedded in another Al grain had a polyhedral shape at low temperatures [26].

Multiple scattering theory for acoustic waves, proposed by Foldy [5], was represented following heuristic integral equation by Lax [6], , (1) where is conditional number density of scatterers at if a scatterer is known to be at , and is a T-matrix.
Grain size distribution of each sample of S3 and S5 Table 1.
For the bimodal grains, however, dispersions are slightly different.
And the attenuation of larger size grains increase more steeply.
For, grains can be considered as scatterers.

The grain of graphite consists of a stack of parallel hexagonal net planes as schematically shown in Fig. 1.
(3) It is assumed that the crack will extend at a grain size, a, if the entire low with n grains fail.
When N is the number of pores per unit volume and V is the specimen volume, the total survival probability of the volume V under stress σ having 2NV flaw tips is (Ps) 2NV.
Input parameters such as pore size, grain size etc. are required in the analysis same as the uniaxial ones.
Fig. 3 Analytical flow of strength prediction under multiaxial stress Table 1 Input parameters of PGX graphite [8] Parameter Value Mean grain size (μ m) 762 Bulk density (g/cm3) 1.74 Mean pore size (μ m) , S0 238 Standard deviation parameter of pore size, Sd 1.73 Number of pores per volume (m-3) 0.187x10 8 Grain fracture toughness (MN/m3/2) 0.225 Results and discussions Biaxial strength prediction.