Reciprocal lattice axes

Thus the reciprocal lattice axes are perpendicular to the (100), (010) and (001) planes in the real-space lattice. In cubic, tetragonal and orthorhombic crystals it is also trae that they are parallel to the [100], [010] and [001] directions, but this is not tme in other crystal classes. The general formulae for the reciprocal space... 

Recall from Chapter 5, Section IV.C, that for a twofold screw axis along the c edge, all odd-numbered 001 reflections are absent. In the space group P 21212, the unit cell possesses twofold screw axes on all three edges, so odd-numbered reflections on all three principle axes of the reciprocal lattice (M)0, OfcO, and 00/) are missing. The presence of only even-numbered reflections on the reciprocal-lattice axes announces that the ALBP unit cell has P2,2121 symmetry. 

Often one has several options for choosing the net, or reciprocal lattice axes. The rule is that an axial system is always chosen that preserves the highest symmetry of the diffraction pattern. That is, the axes are chosen to be consistent with the real unit cell of highest symmetry. Sometimes, before the diffraction symmetry is fully clear, incorrect axes may be chosen. The axial system, or reciprocal lattice net, can, however, always be reassigned and the hkl indexes of the reflections reindexed at a later time. The choice of axes determines the crystal class. 

Figure 2.10 The construction of a reciprocal lattice (a) the a-c section of the unit cell in a monoclinic (mP) direct lattice (b) reciprocal lattice axes lie perpendicular to the end faces of the direct cell (c) reciprocal lattice points are spaced a = 1 /do o and c = 1 /V/0oi (d) the lattice plane is completed by extending the lattice (e) the reciprocal lattice is completed by adding layers above and below the first plane...

The reciprocal lattice of a crystal is easily derived from the unit cell. For cubic cells, the reciprocal lattice axes are parallel to the direct lattice axes, which themselves are parallel to the unit cell edges, and the spacing of the lattice points hkl, along the three reciprocal axes, is equal to the reciprocal of the unit cell dimensions, I/aq = l/ o = /co (Figure 5.11). For some purposes it is convenient to multiply the length of the reciprocal axes by a constant. 

SVD-Index. This is a commercial indexing program belonging to the TOPAS suite from Bruker AXS. The reciprocal-lattice relationship defined in Equation (8) is solved via the iterative use of the Singular Value Decomposition (SVD) approach. This method is recommended for cases in which there are more equations than variables. ... 

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