# Reflection conditions

(Difference between revisions)
 Revision as of 06:40, 19 April 2006 (view source)← Older edit Revision as of 07:10, 19 April 2006 (view source)Newer edit → Line 12: Line 12: *''Glide planes''. *''Glide planes''. The resulting conditions apply only to twodimensional sets of reflections, ''i.e.'' to reciprocal-lattice nets containing the origin (such as hk0, h0l, 0kl, hhl). For this reason, The resulting conditions apply only to twodimensional sets of reflections, ''i.e.'' to reciprocal-lattice nets containing the origin (such as hk0, h0l, 0kl, hhl). For this reason, - they are called ''zonal reflection conditions''. They are listed in Table 2.2.13.2 of ''International Tables of Crystallography, Volume A''. + they are called ''zonal reflection conditions''. For instance, for a glide plane parallel to (001): + + +
type of reflectionreflection condition glide vector glide plane
0''kl'' ''k'' = 2 ''n'' '''b'''/2 ''b''
''l'' = 2 ''n'''''c'''/2 ''c''
''k'' + ''l'' = 2 ''n'''''b'''/2 + '''c'''/2 ''n''
''k'' + ''l'' = 4 ''n''
''k'', ''l'' = 2''n''
'''b'''/4 ± '''c'''/4 ''d''
+ + + + + + + + + + + The zonal reflection conditions are listed in Table 2.2.13.2 of ''International Tables of Crystallography, Volume A''. *''Screw axes''. *''Screw axes''. - The resulting conditions apply only to onedimensional sets of reflections, ''i.e.'' reciprocal-lattice rows containing the origin (such as h00, 0k0, 00l). They are called ''serial + The resulting conditions apply only to onedimensional sets of reflections, ''i.e.'' reciprocal-lattice rows containing the origin (such as h00, 0k0, 00l). They are called ''serial reflection conditions''. For instance, for a screw axis parallel to , the reflection conditions are: - reflection conditions''. They are listed in Table 2.2.13.2 of ''International Tables of Crystallography, Volume A''. + + +
type of reflectionreflection condition screw vector screw axis
00''l'' ''l'' = 2 ''n'' '''c'''/2 21; 42
''l'' = 4 ''n'''''c'''/4 41; 43
000''l'' ''l'' = 2 ''n'' '''c'''/2 63
''l'' = 3 ''n'' '''c'''/3 41; 31; 32; 62; 64
''l'' = 6 ''n'''''c'''/661;65
+ + + + + + + + + + + + The serial reflection conditions are listed in Table 2.2.13.2 of ''International Tables of Crystallography, Volume A''. (2) ''Special conditions'' (‘extra’ conditions). They apply only to special Wyckoff positions and occur always in addition to the general conditions of the space group. (2) ''Special conditions'' (‘extra’ conditions). They apply only to special Wyckoff positions and occur always in addition to the general conditions of the space group.

## Revision as of 07:10, 19 April 2006

Conditions de réflexion (Fr).

## Definition

The reflection conditions describe the conditions of occurence of a reflection (structure factor not systematically zero). There are two types of systematic reflection conditions for diffraction of crystals by radiation:

(1) General conditions. They apply to all Wyckoff positions of a space group, i.e. they are always obeyed, irrespective of which Wyckoff positions are occupied by atoms in a particular crystal structure. They are due to one of three effects:

• Centred cells.

The resulting conditions apply to the whole three-dimensional set of reflections hkl. Accordingly, they are called integral reflection conditions. They are given in Table 1.

• Glide planes.

The resulting conditions apply only to twodimensional sets of reflections, i.e. to reciprocal-lattice nets containing the origin (such as hk0, h0l, 0kl, hhl). For this reason, they are called zonal reflection conditions. For instance, for a glide plane parallel to (001):

type of reflectionreflection condition glide vector glide plane
0kl k = 2 n b/2 b
l = 2 nc/2 c
k + l = 2 nb/2 + c/2 n
k + l = 4 n
k, l = 2n
b/4 ± c/4 d

The zonal reflection conditions are listed in Table 2.2.13.2 of International Tables of Crystallography, Volume A.

• Screw axes.

The resulting conditions apply only to onedimensional sets of reflections, i.e. reciprocal-lattice rows containing the origin (such as h00, 0k0, 00l). They are called serial reflection conditions. For instance, for a screw axis parallel to , the reflection conditions are:

type of reflectionreflection condition screw vector screw axis
00l l = 2 n c/2 21; 42
l = 4 nc/4 41; 43
000l l = 2 n c/2 63
l = 3 n c/3 41; 31; 32; 62; 64
l = 6 nc/661;65

The serial reflection conditions are listed in Table 2.2.13.2 of International Tables of Crystallography, Volume A.

(2) Special conditions (‘extra’ conditions). They apply only to special Wyckoff positions and occur always in addition to the general conditions of the space group.