Cell, unit planes

In this diagram, a series of hexagon-shaped planes are shown which are orthogonal, or 90 degrees, to each of the corners of the cubic cell. Each plane connects to cuiother plane (here shown as a rectangle) on each fiace of the unit-cell. Thus, the faces of the lattice unit-cell and those of the reciprocal unit-cell can be seen to lie on the same pltme while those at the corners lie at right angles to the corners. 

Figure 2.1 6 Small volume element m within the unit cell, one of many elements formed by subdividing the unit cell with planes parallel to the cell edges. The average electron density within m is pm(x,y,z)- Every volume element contributes to every reflection in the diffraction pattern, as described by Eq. (2.4).

The lines on Figure 5.33(A) represent planes in a cubic crystal parallel to the c axis, which is normal to the plane of the page. The circles mark the comers of the cubic unit cell. Index planes (a)-(d). 

X-Ray diffraction observations of E-V powders and fibers showed an expansion of the unit-cell basal plane, mainly in the a-direction, and a constant fiber period, respectively, as their chlorine content increased. Together these observations indicate that at least some V units, with their attendant Cl atoms, are incorporated into the crystals, resulting in an increase in interchain separation, but no alteration in the M-trans, planar zigzag conformation found for crystalline PE. 

Fig. 2.7. Different possible shapes of unit cells of plane lattices...

The most important finite size error comes from the interaction of the two interfaces and the expected plateau of the FES appears gradually by increasing the cell dimension along z and hence the distance between the interfaces. The minimum length of the supercell along z yielding a reasonable plateau was determined to be around 8 cell units. The variation of the width of the xy-plane showed that the residual slope of the plateau vanished if the lattice constants along x and y exceeded... 

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

W L Bragg [7] observed that if a crystal was composed of copies of identical unit cells, it could then be divided in many ways into slabs with parallel, plane faces whose distributions of scattering matter were identical and that if the pathlengths travelled by waves reflected from successive, parallel planes differed by integral multiples of the... 

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