Lattice rods

Figure 5.78 Comparison of square lattice rod bundle data from different sources and CISE-3 correlation, Eq. (5-148). Data sources X, A, , 9-rod bundle (Hench and Boehm, 1966) 0, 16-rod bundle (Janssen et al., 1969) V, 16-rod bundle (Evangelisti et al., 1972) , 16-rod bundle (Israel et al.,...

This intensity distribution means that each reciprocal lattice point is effectively extended into a rod that is normal to the thin crystal specimen. Due to this extension of the reciprocal lattice points and to the fact that the radius of the Ewald sphere is large compared with the spacing between reciprocal lattice points, the Ewald sphere usually intersects many reciprocal lattice rods, as shown in Figure 3.12(a). Thus, many diffracted... 

Figure 3.12. Facing page, (a) Diagram showing the Ewald sphere cutting the reciprocal lattice rods of zero and higher order Laue zones and (b) a schematic diagram of the corresponding diffraction pattern.

Fig. 3 Ewald construction. The white half-circle indicates the Ewald sphere in two dimensions. The points of intersection between the reciprocal lattice rods and the Ewald sphere form the set of reciprocal lattice points (bright) which obey Bragg s law and appear as diffraction spots in the diffraction pattern. Zero-, first- and second-order Laue zone are indicated. Eor electron diffraction in TEM, the ratio between the radius of the Ewald sphere and the reciprocal lattice unit is larger than visualized in the figure. (View this art in color at www.dekker. com.)...

Unit cell effective multiplication factor for selected fuel diameters/lattice rod pitches ... 

Figure 8.2.9 Ewald construction for elastic and inelastic scattering of a particle with initial and final wave vectors kj and kf. Six crystal truncation rods perpendicular to the crystal surface are indicated as solid lines, (a) Five conditions of elastic Bragg reflection are marked as gray dashed arrows, which are defined via the intersection of the Ewald sphere with the reciprocal lattice rods. Spheres for different final energies are marked as dashed circles with a constant increase in energy between the circles. An enlargement is shown in (b), which emphasizes the relation between both the energy loss AE and the momentum transfer hAq (short solid arrows) due to phonon excitation or annihilation, to allow scattering into a defined detector direction given by the long dashed arrow.

Y. Murao and T. Hojo, Numerical Simulation of Reflooding Behavior in Tight-Lattice Rod Bundles, Nuclear Technology, Vol. 80, 83 (1998)... 

In many cases the surface is reconstructed (see Section 10.8) which breaks the periodicity in the surface plane. For example, for the (2x1) surface reconstruction in Figure 10.13, the repeat unit for the surface is one atom spacing along the rows of dimers and two atom spacings perpendicular to the rows. Doubling the periodicity in the surface plane halves the reciprocal lattice rod spacing. This leads to the appearance of extra spots in the diffraction pattern. Counting the spots shows the surface reconstruction. Thus, a Si (111) surface that reconstructs with a 7x7 structure... 

Typically the substrate is not cut exactly on a low-index plane. When the diffraction spots are sharp enough, the spots may be split along the reciprocal lattice rod direction (vertically on the pattern) into two spots when the beam is aligned up or down the staircase of surface steps causing the miscut. The separation of these spots reflects the miscut of the sample surface relative to the low index planes. This is useful to know because miscut is used in some cases to enhance heteroepitaxy. 

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