INDEX interplanar distances

The X-ray patterns taken from the two sections of the intermetallic layer adjacent to the Ni phase were also closely comparable, though this layer is visually seen in Fig. 3.13 to consist of three sublayers. One of these sections corresponded to a layer composition of 16.0 at.% Ni and 84.0 at.% Zn, while the other to 19.0 at.% Ni and 81.0 at.% Zn. The experimental interplanar distances were found to be in better agreement with the calculated values from the orthorhombic lattice parameters of =3.3326 nm, b=0.8869 nm and c=1.2499 nm reported by G. Nover and K. Schubert,279 rather than from the cubic lattice parameter =0.892 nm. Moreover, a few diffraction lines, including the strong line corresponding to the interplanar distance 0.207 nm, could not be indexed on the basis of the cubic structure. 

The XRD patterns of MCM-41 and Al-MCM-41 are shown in Fig. 4. The crystallinity of the MCM-41 samples decreases in the Al-containing sample. The patterns can be indexed in a hexagonal unit cell. From the interplanar distance, dioo, the hexagonal unit cell parameter (a = 2 dioo / " 3) are calculated and reported in Table 2. From the pore size diameter, Dp, reported in Table 1, the thickness of the silicate walls (s) are obtained by using the equation s = a - Dp (see Table 2). 

Each point of the reciprocal lattice represents, as we have said, a family of crystal planes. The different families of planes define the crystal system, which is therefore determined by assigning a triplet of Miller indices to each diffraction spot or in diffraction on a polycrystalline sample, to each diffraction peak. This is referred to as the indexing of the diffraction peaks. The interplanar distance associated with a family of planes with indices (hkl) is a function of these Miller indices and of the cell parameters. We can write ... 

Figure 10.4 also shows the existenee of two sets of refieetions for the thiek-est sample direet evidenee of polymorphism. The seeond form indexed with (100) appears at higher Q y = 0.525 A eompared with (100) Qj, y = 0.405 A ). This reflects an interplanar distance of = 12.0 A compared with the main form with the tf = 15.6 A. The appearance of higher-order peaks such as (200) and (300) in addition to (200) and (300) gives evidence for well-pronounced ordering of both polymorphs. Interestingly, such dual form is not observed for thinner films. Such polymorphism was also found in powder samples [17]. 

Miller s index system is similar to the lattice plane index system but with the difference that the hkl values are the lowest possible integer values. The Miller s index notation for both the sets of planes with the lattice plane indices (010) and (020) is simply (010). Miller s indices thus provide information only about the orientation of the planes and disregard the interplanar distances involved. 

Further, from the definition of by Miller indexing, there is clearly how the family of planes (200) cuts the axis Oa at distance /ra and therefore will be characterized, on the same normal as that of the family of (100) planes, by the interplanar distance But this distance will be... 

This model is purely geometric and does not require any knowledge of the crystal structure of the solid, merely the unit cell dimensions need to be known. The smaller the interplanar distance, the larger the relative growth rate, and as the low index faces are those with the largest interplanar distances, it is these that are expressed in the crystal habit. 

FIGURE 9.6 X-ray diffractograms of DND (a) and CVD diamond film on silicon substrate (b) and diamond particles produced from HPHT diamond by milling method (c). Positions for interplanar distances are marked. The corresponding intensities are given by the lengths of the dashed lines. Positions of diffraction maxima are marked by corresponding Miller indexes. The asterisk identifies an impurity diffraction maximum. The (b, c) curves are received with CoK and CuK radiation. 

Solution Bragg s law should be used to solve this problem (refer to Section 6.3.5 and eq. (6.3.11), Figure 6.20). In the equation mentioned, 9 is the incident angle and (p is the deflection angle. The picture is repeated here to make the situation clearer (Figure E6.14 an atomic arrangement is not depicted substituted by two reflected planes with interplanar distance d ). It is seen in the picture that cp = 26. The crystallographic plane s index is (600), in fact there is no such plane in the crystal this should be understood as a 6th order of reflection from the plane (100) (i.e., at distance... 

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