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Thus interference can be observed if the thickness of the film is an even number multiple of the quarter of the wavelength (λ/4).
If the lower velocity of the light in the film is also taken into account, interference will occur at the even number multiple of λ/4n, where n is the refractory index of the film.
The individual grains are numbered on both the color etched image and on the IPF map.
In order to define the colors quantitatively, a number was calculated for each color, applying the YUV color system [4].
Grain No.

It has been postulated that the HPR expression which is valid for coarser grains is not valid for finer grains because the constant of proportionality in the HPR that depends on the resistance of the grain boundary to dislocation movement is no longer a constant as continuing refinement of the grain size occurs [4].
During experiments, the mechanisms of deformations in materials are analysed by monitoring the behaviour along grain boundaries and in the interior of grains.
It was found that nanostructured materials have larger "grain boundary layers"-to-"grain sizes" ratio compared to bulk materials.
Working with a 3-D sample composed of large, possibly infinite, number of grains, is a time consuming and tedious task to gather accurate information about every grain.
Conclusions This paper shows that both average grain size and grain size dispersion play vital roles in the design of specific mechanical properties.

The distinction between various ECAP routes with different number of ECAP passes applied may lead to variations both in the macroscopic distortions of the individual grains and in the capability to develop a reasonably homogeneous and equiaxed ultrafine-grained microstructure.
It has been proved that the effectiveness of the grain refinement depends on angle between two channels, number of ECAP passes and mode of rotation between consecutive passes.
With increasing the number of ECAP passes, the number of shear bands and dislocations was found to be increased.
In our recent work [13] it has been suggested that the coexistence of a dislocation climbing process and grain boundary sliding in creep of ECAPed material may explain the observed decrease of the creep resistance with increasing number of ECAP passes.
Fig. 6 The fraction of HAGBs in the crept samples as a function of the number of ECAP passes.

Introduction Grain boundaries are diffusion short circuits and consequently the major part of material transport will occur by grain-boundary diffusion in nanomaterials where a large amount of atoms can lie on grain or interphase boundaries (about 50% for a grain size equal to 5 nm; 20% for a grain size equal to 10 nm).
It is well known from classical treatments of grain- or interface diffusion that there are three different grain-boundary diffusion regimes: type A, B and C.
-In the A kinetics regime (Dv t) 1/2 >> d), the different diffusion zones overlap with each other resulting in a macroscopic homogeneous diffusing distribution which appears to obey Fick's law as for a homogeneous system with an effective diffusion coefficient (Deff) equal to an average of Dv and Db weighted in the ratio of the number of diffusing atoms in the grains to that in GB [9]: Deff = g Db + (1-g) Dv, (2) where g is the grain-boundary volume fraction (g ≈ δ/d; the factor of proportionality depends on the grain shape, but is in the order of unity).
In fact, owing to the high number of GBs and the synthesis conducted under UHV conditions, the grain boundaries must be purer in the first type of materials (not enough impurities to cover all grain boundaries).
Perraillon: Grain Boundary Structure and Kinetics, (R.

ECAP produced a grain size less than 1 mm, and FSP provides the formation of UFG structures with an average grain size ranging from 0.7 to 2.6 mm [3-8].
The size of the particles was estimated using at least five arbitrarily selected micrographs, the total number of individual measurements for each condition was ~1000.
The grains are completely separated by HABs (Fig. 4a, c, e and g).
The distributions of the grain sizes are shown in Fig.5.
The authors acknowledge with gratitude the financial support received through the German Academic Exchange Service (Funding program number 57048249, Research Grants for Doctoral Candidates and Young Academics and Scientists 2014/15).

In the case of development of a composite without Co and taking into account the demand made, so that it can partially or totally replace the WC-Co based, it is necessary a larger number of analysis and testing to obtain key information that allows some conclusion on the feasibility.
Grains larger than 20 µm.
During sintering of cemented carbides the average grain size increases due to the grain growth.
This phenomenon is called Ostwald ripening .[9], i.e., large grains grow at the expense of small grains, leading to a stepwise increase of the average size every time a small grain vanishes [9].
Abnormal grain growth is observed when a few grains grow more drastically compared to the surrounding grains during the sintering process.

MDF to a total strain of 1.2 results in the formation of large number of strain-induced low-angle boundaries within initial coarse grains.
This process rapidly develops with an increase in the number of turns from 0.5 to 1.
The number of new recrystallized grains and their volume fraction increases upon further straining to 3 turns.
The recrystallized fraction gradually increases when the number of HPT turns increase to 1.
The microstructure contains large initial grains with great number of low-angle boundaries after 1 ECAP pass.

Two different shapes of the grains are introduced in the RVEs of CP-FEM in order to study the effect of the grain morphology.
The grains in each RVE are given different texture and grain shape.
For each texture, 400 orientations are numerically generated using a Gaussian distribution function [4] with a small value of the orientation spread around the ideal component, and mixed with 400 random orientations generated using a random number generator.
It was assumed that this number of grains is enough to predict accurately the stress states at yielding for each texture [4,5].
FC-Taylor model versus CP-FEM with one element per grain, CP-FEM with one element per grain versus eight elements per grain, and CP-FEM with one element per grain versus elongated grains.

The expression of grain mass is used to predict the mass of grains.
According to the concept of fractal, Turcotte proved that the particle number-size fractal model can be expressed as [4].
According to the fractal theory, the number of panes of grains corresponding with measure scale L, N(L), can be expressed as [11], (1) Where is a constant, D is the area fractal dimension of grains.
The incremental number of pores, , is the incremental volume divided by the volume of one pore, (7) Where .
The total number of grains of size r or larger, , is the integral of Eq.(7) taken from the largest pore size, , to grain size r, (8) Where, (9) In Eq.(8), it is easy to confirm that is the density function of pore-size distribution, where is the pore-size distribution fractal dimension which is equal to the area fractal dimension of grains in Eq.(5) suppose the area shape factors of pores are the same.

There were a number of bright second phase particles distributed along rolling direction in the matrix (Fig.1(a)).
Higher magnification shown that there were a number of small bright particles at grain boundaries and in the grains, see Fig.1(c).
After 5s, it seems that GBs and SGBs were attacked slightly, and were decorated by a number of discontinous black pits.
From Fig.3(a), a number of white round or elliptic S phase particles located in a REX grain can be seen.
Due to corrosion of quench-induced η phase particles (Fig.1(c)), a number of black pits could be seen in the REX grains and in some subgrains (Fig.3(a)&Fig.3(c)).