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Estimation Model Since MnZn soft ferrite is a kind of polycrystalline material composed of a great number of grains, the eddy-current losses of single grains in the micro-structure of this material are calculated, and then the eddy-current loss per unit volume of the core is deduced.
Generally, the grains of MnZn ferrite are polyhedrons, but the simplified model in this paper simplifies the grains as spheres.
If the mean radius of the grain (sphere) is, then the time-varying eddy-current loss of a grain, can be found by , (5) in which the grains per unit volume, excluding the grain boundary, is [12].
In this figure, , and represent grain resistance, grain-boundary resistance and grain-boundary capacitance, respectively.
Grain-boundary resistance dominates the impedance of the sample at low frequencies, while grain resistance dominates at high frequencies.

But a large number of surface acidic sites of Pd/γ-Al2O3 are covered by highly fragmented Pd-grain, it causes DME selectivity reduced.
The internal heat of the catalysts was uneven, it casese a large number of cracks during the heating in muffle.
And more Pd loading makes larger Pd grains increase and worse Pd dispersion.
The author learns that when the loading is within 2%, the reduction of surface acid is mainly because of acidic sites covered by Pd metal; when the loading is between 2% and 3%, the dispersion of Pd drops severely, the grain particle size increases slightly and the number of grain nearly unchanged, the covered area just increases slightly, therefore the amount of surface acid reduces slightly; but when the loading is more than 3%, some γ-Al2O3 pores are blocked by the excessive metal Pd grains, it makes that the amount of acid in pore can not be detected, and the amount of surface acid reduces significantly again.
Besides, a large number of Pd grains have spread and mounted to the pore of γ-Al2O3 carrier, it leads to that the Pd activity surface and the acid activity surface of catalyst reduce simultaneously, and finally leads to the activity of catalyst reduced.

Sr as modifier and TiB as grain refinement elements.
The grain size was measured by Grain Size Planimetri method.
While the addition of TiB on the Al matrix as grain refiner and worked efficiently with higher reinforce particles especialy for Al/SiC composites as seen in Fig.4, where grain size slightly dereased from 5.6 to 6.01 ASTM Grain Number, while for Al/Al2O3 composites the grain size is also decreased from 5.3 to 6.02 ASTM Grain Number (see Fig.5).
ASTM Grain Number of Al/SiC and Al/Al2O3 composites on Fig.4.
The higher ASTM Grain Number the lower grain size of the mirostruture and generated higher strength and hardness.

Therefore, due to the significant disordered grain boundary regions, nc-materials are thermally unstable and are subjected to a strong driving force for grain growth.
Equiaxed grains were usually found in consolidated nc-Cu and nc-Ni while grains were usually crystallized along specific direction in electrodeposited nc-Ni and nc-Cu.
But the average grain size of the as-prepared specimens is about 100 nm.
However, the melting point is lower than that of coarse-grained aluminium by 14 K.
The reasons are that: firstly, the adsorbed gas can be desorbed easily when the nano-particles are heated; the number of micro-pores became less.

With this level of moisture, the grain is susceptible to deteriorate rapidly.
Further, surface temperature of grain was measured using an infrared thermometer.
Air Rough rice grain T (oC) RH v (m/s) Mo(d.b.)
In this experiment, it was found that in a sample of 30.4 g of rice (BRSMG CONAI), 52 hours after drying, the number of grains presenting cracks and fissures increased from 2.73% to 8.9%.
Moreover, short-grain rough rice was very susceptible to fissure whereas long-grain rough rice with a high amylose content was much more fissure-tolerance.

It is well known that number of zirconium alloys present a breakaway of the oxidation kinetics that is associated to the development of lateral cracking within the oxide [1,2] with microcracks parallel to the metal-oxide interface.
A previous work [7] showed that a mesh with 512 grains is large enough to be a representative volume element, and the grain morphology has no effect on the microstress distribution; classical Voronoï tessellation is then used to obtain equiaxed grains.
In order to compare the second order stresses given by the both approaches, 500 different crystalline orientations have been considered for the modeling of the heterogeneity within the EHM; this is about the number of grains of the polycrystalline aggregate.
The normal stress in the x-direction varies from grain to grain as in the case of the extension in the x-direction.
Number of studies reports the presence of a tetragonal ZrO2 phase (ZrO2t) within the oxide of Zr alloys, even at moderate temperatures [2,4,5].

It can be seen that the microstructures of steels are composed of polygonal ferrite and pearlite, the grain size number is 10.
These particles which can hinder the motion of dislocation upon deforming and bring grain bounbary strengthening precipitate in ferrite or along grain boundary.
In this test, a large number of dispersive-fine carbonitrides are found in ferrite and along grain boundary, which can increase the strength and improve the impact energy of steel by hindering the migration of austenite grain boundary, refining grain size and precipitation strengthening.
The ralationship between mechanical properties and grain size is expressed as Hall-Petch equation[4].
In this test, the microstructures of experimental steels are composed of polygonal ferrite and pearlite, the grain size are very fine, compared with vanadium-free steel, Adding vanadium does not change the microstructure and grain size of normalized steel.

It is difficult to control the increasing number of variables because more and more new materials are added into the concrete, along with new properties to be considered.
The high performance concrete usually involves a low w/c ratio has a high content of unhydrated cement grain.
The hardness of cement grain is nearly 10 times higher than that of hydrated C-S-H gel, as shown in Table 2.
Therefore the phases with penetration depth in the range of 0 to 100 nm are preliminarily determined as cement grain, and the phase corresponds to the slope beside the cement grain along with a rapid increase rate of penetration depth is the interface.
Then the HD C-S-H gel gradually forms in the gap between the unhydrated cement grain and the LD C-S-H.

Depending on number of distinct X and Y coordinates, fictitious grid lines are assumed: see figure 1.
Undeformed Grain Deformed Grain Y X Schematic showing the fictitious grid assumed in the grain structures along Y-direction.
Deformed Grain Undeformed Grain Y X (b) Figure 1.
Undeformed Grain Y X Deformed Grain Figure 2.
(a) Estimated in-grain von-Mises strain and (b) in-grain kernel average misorientation.

It can be noted that a large number of corrosion spots were generated throughout the surface of the HAZ.
The precipitate free zone (PFZ) width range is 50~100 nm and evident along grain boundaries.
In the TMAZ (Fig. 5c), the matrix precipitates completely dissolved, while the grain boundary precipitates (GBPs) partially dissolved and a small amount of fine precipitates (40 ~70 nm) were detected on grain boundary.
GBPs are continuously distributed on the grain boundary.
Therefore, corrosion crack initiates and propagates along grain boundaries.