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To meet low insertion loss requirement, a lower number of turns is required.
This fact was mainly attributed to that phosphorus ions with high electronic valence could increase cation vacancies in the grain boundary region, as a result, the speed of the grain boundary movement increased, thereby promoting grain size of the ferrites.
Due to the increased pores hindered grain boundary movements, enlarging trend of grain size became tardily as P2O5 addition exceeded 0.06wt%.
Hysteresis loss decreased with increasing grain size, which could be explained by the decrease of domain wall pinning factor, grain boundary, with increasing grain size [6].
Magnetic loss was also influenced by both grain size and porosity.

Fig. 4 shows the relationship between average slip strains and the number of cycles.
In the results of PRI-BSL cyclic with EQ-hardening, activities of both slip systems decrease with increasing the number of cycles (Fig. 4 (a)).
(a) (b) (a) (b) (a) (b) Fig. 4 The relationship between average slip strain and the number of cycles at =0.7 % in the model PRI-BSL cyclic with CRSS ratio of 1:1.1.
If there is any spaces between crystal grains after the deformation, mechanical constraints exist to conform the grain boundary of one grain to that of the other grain.
(a) (b) (c) εyy σyy σyy (a) (b) Grain 1 Grain 2 Grain 1 Grain 2 Fig. 7 Schematic diagrams of deformed shapes of crystal grains when the grains are separated at the grain boundaries.

The initial γ grain size was assumed to be 50-60 µm and a large number of Sigma3 twinning boundaries were observed inside the γ grains.
Equiaxed grains are observed that are much finer than the initial grains along the Sigma 3 twinning boundaries or γ grain boundaries.
Since the SFE in this alloy is very low, the stacking faults are assumed to form with extreme ease, with a result that the matrix grains are partitioned into numerous superfine grains.
In addition, ∑3 annealing twinning boundaries are considered to easily occur in CCMN alloy at high temperature especially after deformation because of the large increase in the number of stacking faults, since we observed large number of ∑3 annealing twinning boundaries even in the starting materials (Fig. 4).
The strain rate exerts a large effect on grain refinement when it is in the range 10 -2 to 30 s-1, and the grain size becomes extremely refined as the strain rate increases.

α-SiC powder grew moderately into plate-shaped grains. β-SiC powder was completely transformed to 6H and subsequently 4H with large grain growth.
Numbers beside circles are relative specimen densities.
The closed circles are the experimental points and the numbers alongside the circles are densities in percentage of a theoretical density, left: α-SiC and right: β-SiC.
This introduced anisotropy in grains and resulted in plate or rod-shaped grain growth.
It is considered that grain growth is driven by surface energy stored in fine grains.

Mechanical characteristics of the initially cast Al-Mg-Zr and Al-Mg-Zr-Sc alloys as a function of the number of ECAP passes.
As seen from the graphs, the strength of the alloys increases with the number of ECAP passes.
The best result in terms of ductility was achieved with the Al-Mg-Zr-Sc alloy by applying 6 passes of ECAP. 100 150 200 250 300 350 0 2 4 6 8 Number of passes YS, MPa 270 290 310 330 350 370 390 410 430 450 0 2 4 6 8 Number of passes UTS, MPa 20 25 30 35 40 45 0 2 4 6 8 Number of passes RA,% 10 12 14 16 18 20 0 2 4 6 8 Number of passes EL,% Al-Mg-Mn-Zr Al-Mg-Mn-Zr-Sc Fig. 11.
This is considered to be the mechanism responsible for the finer grain structure (with the average grain size of 850 nm) in the Al-Mg-Zr-Sc alloy.
Valiev, in: Recrystallization and Grain Growth, edited by G.

The columnar grains changed into equiaxed grains.
The number of the columnar grains was farther smaller in fig.5.
The net-like grains covered around the columnar grains.
There were no columnar grains but equiaxed grains in fig.6.
There were a big number of net-like grains.

Fig.1a illustrates the grain size was about 50-200nm.
These structures were not composed of a single grain, but made of several grains.
It is clear that every cellular structure contains a number of fine particles(grains), four grains having strong diffraction contrast are marked as 1, 2, 3, 4 in the figure.
Fig.3a presents one grain morphology in dark field mode.
Who will be dominant is determined by a number of conditions.

The recrystallized grains are defined by their grain boundaries.
These grain boundaries may separate the recrystallized grains from the deformed volumes or from other recrystallized grains.
(1) where (Sv)rr is the grain boundary area density separating recrystallized grains from other recrystallized grains, i.e. the recrystallized grain contact area resulting from impingement, and (Sv)rd is the grain boundary area density separating the recrystallized grains from the deformed matrix.
Thus, the contiguity ratio measures the fraction of the total grain boundary area of recrystallized grains shared by other recrystallized grains.
Recall that (Sv)rr = 2 nrr / Lt where nrr is the number of recrystallized grain /recrystallized grain boundary intersections measured in the test line length Lt.

At this time the formation of grain roundness is very bad, and the grain size is not uniform.
As shown, at this time the number of dendrites has an observabe ruduction , many dendrites were interrupted, but there are still a few residual dendrites.
A lot of grain shapes have become a long strip, but also there is a little number of spherical or globular classes .
This is because at this time under the conditions of process parameters, the exit temperature is in the range of the semi-solid aluminum alloy, a large number of solid-phase has been made during the flowing process of the aluminum alloy, which makes the interactive shearing between grains to enhance greatly, while the dendrite arm has just been formed, it will be cut off by the interactive shearing between grains, so the growth of dendrites has been restrained.
As can be seen from the Figure 7, at this time a large number of dendrites appear, while other dendrites have been cut off to become a long strip, the grain shape is very rules, size is also very uneven, the roundness of grains is also very poor.

Then the number of grains inside Ninside and number of grains Nintercepted that intercept the test rectangle, ignoring the four grains in corners, were counted.
The number of grains per square millimetre at 1x, NA, was calculated from Eq. 1.
The final ASTM grain size number, G, can be calculated from NA using the Eq. 2.
The number of cycles 2 × 107 was considered as run-out.
The number of grains, NA [mm-2] The average grain area, A [mm2] The mean grain diameter, d [μm] Calculated ASTM grain size No., G Starting stage 11 354.82 8.8 × 10-5 9.38 10.52 After fatigue test 19 517.46 5.1 × 10-5 7.16 11.30 Fig. 3 SEM micrographs for grain size and δ-phase volume evaluation; a) starting stage of IN 718 alloy with ASTM grain size No.