ANSWER

For nearly all crystalline materials, the reflection conditions are determined solely by the symmetry elements of the space group as shown by the space group symbol, e.g. the 21 and c in space group P21/c give rise to the reflection conditions 0k0: k = 2n and h0ll = 2n, respectively. This results from the fact that one or more atoms are sited on a general position, x,y,z within the unit cell of the material.

However, for a few materials (and silicon is one of them), the atoms in the crystal structure lie only on special positions, i.e. they are sited on positions with a specific point-group symmetry. The additional symmetry provided by some special positions in some space groups results in additional reflection conditions that are not immediately obvious from the space group symbol itself. For the case of silicon, (which has the so-called diamond structure in which the Si atom is sited at 1/8,1/8,1/8 in space group Fd-3m relative to the centre of inversion at the origin,) the additional reflection conditions are hkl: h + k + l = 2n + 1 or 4n.

Given these additional special reflection conditions, one can deduce that 111 is allowed (sum is odd), but that 222 (sum is even, but indivisible by 4) is forbidden. Hence the absence of a peak at about 58.9°. The other missing peak at about 116.6° is due to a similar extinction condition for the 442 reflection.


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© Copyright 1995-2006.  Birkbeck College, University of London. Author(s): Jeremy Karl Cockcroft