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**Up:** 4. Interpretation of Powder Photographs
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For a cubic structure only one quantity is involved, the cell edge or the
*lattice parameter* .

Equation (1) can be expressed in the form

(5) |

From the observed values of , a table of values of should be
prepared. For a cubic structure these should be in simple numerical proportion.
The highest common factor should be /4*a ^{2}*, and hence

Not all values of *h ^{2}* +

For small values of *N*, the values of *h*, *k* and *l* are easily deduced. Thus
*N* = 1 corresponds to 100, 2 to 110 and 3 to 111. For some values of *N*, more
than one set of indices exists: 9 is both 300 and 221. For values of *N* (up to
100) see Lipson and Steeple (1970) Table 5.

The intensities of the lines depend upon the arrangement of atoms in the unit
cell, but they also depend upon the number of possible ways of combining the
indices - the *multiplicity factor* . For simple structures, this factor is
dominant. Thus 100 includes 010, 001, 00, 00,
00; the multiplicity factor is 6, corresponding to the six faces
of a cube. For *N* = 14 (321) however there are 48 arrangements, and line 14
will usually be much stronger than line 1, even if the decrease in intensity
with is allowed for.

If the lattice is not primitive, some values of *N* are not possible. For the
lattice *F* (face-centred), the indices must be all odd or all even: thus the
first few lines are *N* = 3(111), 4(200), 8(220), 11(311), 12(222),
16(400)These are shown diagrammatically in Fig. 4. For the body-centred lattice,
*I*
(Innenzentiert), *N* must be even, and so the possible lines are 2(110), 4(200),
6(211), 8(220), 10(310)

This raises the difficulty mentioned earlier: for a body-centred structure the
common factor is 2/4*a ^{2}* and not /4

**Copyright © 1984, 1998 International Union of
Crystallography**