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The relative intensities, positions and shapes of the D and G peaks are related to the number of graphene layers.
Specially, the nature of the D peak is related to the degree of edge chirality and the G peak is affected by the number and nature of defects associated with doping [20].
The increase of grain boundaries is mainly due to the pinning effect of graphene on copper, which can effectively inhibit grain growth.
With the addition of graphene, the growth of some grains is hindered to a certain extent, and the increase of the content of graphene increases the hindrance of grain growth [15].
Lavernia, Tougher ultrafine grain Cu via high-angle grain boundaries and low dislocation density, Applied Physics Letters 92(8) (2008) 54

The average grain size was determined using the linear intercept method employing the relation [26] Gavg=1.5L/MN (4) where L is the total test line length, M the magnification and N the total number of intercepts.
The patterns also revealed the spinal ferrite phase, these XRD patterns match with the JCPDS card number 89-3084 for magnesium ferrite powder and peaks of Sm and Dy are marked in the XRD, which match with the JCPDS card number 26-593.
The grain size of the each sample was calculated using Eq. (4).
The effect of grain size on initial permeability and found a linear relation between the initial permeability and grain size in Dy3+–Sm2+ doped magnesium ferrite.
The calculated grain size increases with increasing Dy-Sm ion concentration.

The microstructure analysis (SEM) showed cubic-like grain shape in which excessive sample possessed greater average grain size than other.
Microstructure analysis showed cubic-like grain with approximately 1-2mm in size as depicted in Figure 3.
Average grain size of non-excessive composition (1.15mm) was smaller than other one (1.96mm).
It was the consequence of secondary phase existence in former composition which inhibited grain growth.
The increasing of dissipation factor as increasing of temperature indicating the increasing number of charge carriers was also observed on both materials.

Productivity of internal grinding Productivity of grinding operation could be estimated using total number of machined parts per minute (per hour) or it could also be estimated using volume of material removed from workpiece per minute per 1 mm of width of grinding wheel.
Both parameters are connected to each other and by knowing the volume of removed material per minute the number of parts machined per minute (or per hour) could be found.
Productivity of new grinding method could be calculated using the following equation: (1) kc – coefficient considering the impact of grain trace matching; ky – grains packing coefficient; w3, wK – angular velocity of workpiece ring and grinding wheel respectively (– for unidirectional rotation, + for opposite rotation); B – width of abrasive segment; Ro – outside radius of abrasive segment; n – number of segments; N – abrasive material size according to standard classification; Rз – radius of workpiece ring; Sпр, Sр – axial and radial feed respectively; lп – length of wheel-workpiece overpass; aср, bср – average values of height and width of cutting part of abrasive grains respectively; Uo – relative wear of abrasive grain; Dз – diameter of workpiece ring; nк, nз – grinding and workpiece spindle speed respectively (– for unidirectional rotation, + for opposite rotation); t – grinding time.
Heat evacuation and coolant pressure According to [2, 3] in order to increase heat evacuation during grinding it is necessary to: - raise the speed of turbulent flow of cutting fluid on surface of workpiece material; - increase heat exchange area between workpiece (abrasive tool) and coolant fluid; - increase pressure of cutting fluid in the cutting zone in order to help to supply coolant and lubrication to contacting surfaces of abrasive grains and workpiece material.
Cross sectional shape deviation due to influence of cutting data: (8) Cross sectional shape deviation due to centrifugal force: , (9) Cross sectional shape deviation due to w3/wK ratio: , (10) , – height and width of cutting profile of abrasive grain from number i elementary profile having number j in the arc of contact between abrasive segment and workpiece ring; a – arctangent of Sр /Sпр ratio; Qc – inertial centrifugal force applied to abrasive segment; m – mass of abrasive segment; – radius of center of mass of abrasive segment.

Lack of oxidation will make the p-type layer between n-type grains very thin and therefore the barrier has not fully grown.
Barrier can reduce the number of electrons overcome it, so as to reduce the number of carriers.
Grain sizes (DC) of the films were calculated with Scherer formula：
Grain size decreases with increasing of oxygen ratio.
The number of carriers and the migration rate increase with increasing temperature.

The main cause of creep failure is the nucleation, growth and coalescence of cavities on the grain boundaries (Leckie and Hayhurst, 1984; Huddleston, 1985; Kassner and Hayes, 2003; Goodall and Skelton, 2004) [6].
It indicates that grain boundary is the most severe type of creep damage mechanism and will result in considerable reduction in the creep rupture life of the material [8].
Dyson’s cavitation equation Grain boundary creep cavitation is a damage mechanism that can not only soften the materials, but can also be the mechanistic cause of fracture.
Dyson’s grain boundary creep cavitation equation considered at high stress during unconstrained cavitation and low stress during constrained cavitation.
It is also to be noted from the exponential powers that the rupture ductility is more sensitive to increases in void volume fraction as compared with the void number density.

While increase the preheated temperatures, the grains grow gradually.
The grain sizes increase to a large extent at temperatures above 700°C, and decrease the numbers of grain boundary eventually.
So the few number of grain boundary contribute the lower dielectric constant.
Similarly, the prohibition of grain growing during heating by La modification improves the dielectric properties.
The d33 increase with the temperatures and La amount owing to the increase of grain sizes by higher temperatures and La modification.

Eleven RBS samples have coarse-grained gritting, four RBS have fine-grained gritting and three RBS are without gritting.
Characteristics of the test sample / number of test sample 2 3 4 6 7 9 10 13 14 flow resistance [°C] 155 155 120 115 125 160 160 155 125 Characteristics of the test sample / test sample number 15 16 17 18 22 23 25 26 28 flow resistance [°C] 100 110 125 130 160 160 125 140 110 Results of the Statistical Evaluation.
In the second step, we conducted the evaluation separately for the RBS mass modified by plastomers and the coarse-grained scattering, in which the linear dependence was most apparent.
Following the observations and above commented results, we have performed the same analysis only for the plastomers with coarse-grained gritting.
This would mean that in the case of coarse-grained plastomers gritting, there would be a direct proportionality between the amount of the flow resistance and the softening point.

This paper presents a 2D model of grain/bed impaction under consideration of random distribution of contact points of the grains in the bed, pattern of the granular bed, initial velocity and angle accordingly.
For the former case, the sand particle B contacts with four sand particles on the bed, while on the latter bed only two sand grains contact with particle B.
In practice, the pattern of grains in sand bed is complex and variable, here, we select α to behavor it.
Let n be the total number of elements in X.
Divide the region [ ]εε +− ba , into m equi-elements, where ε is a small positive number.

Zr has been used as grain refiner in Mg alloys [9-14].
This is shown in Fig. 3a which shows the number of samples “n” withdrawn from the crucible.
The sample numbers in Table 2 correspond to the sample numbers in Fig. 3b.
Das, Grain refinement of magnesium alloys by zirconium, Formation of equiaxed grains, Scripta Mater. 54 (2006) 881-886
Hildebrand, Grain refinement of magnesium alloys, Metall.