Page 66 - Nomenclature of Inorganic Chemistry (IUPAC Recommendations 2005)

IR-11.6 S O L I D S

if the ratio is irrational, the structures a re called non-commensurate or incommensurate.
Commensurately m odulated structures exist in many s toichiometric and non-stoichiometric
compounds; they may be regarded as superstructures a nd be described by the usual rules.
Non-commensurately modulated structures occur in several stoichiometric compounds (and
some elements), usually in a l imited temperature range, e.g. U, SiO 2 , T aS 2 , N bSe 3 , N aNO 2 ,
Na 2 CO 3 and Rb 2 ZnBr 4 .
Many modulated structures c an be regarded as being composed of two or more
substructures. The substructure with the shortest p eriodicity often represents a s imple
basic structure, w hile the other periodicities cause modulations o f t he basic structure. T he
basic structure often remains u nchanged within a c ertain c omposition range, w hile the
other substructures take up the change in stoichiometry. If this change takes place
continuously, a n on-stoichiometric phase with a n on-commensurate structure results. If
the change occurs discontinuously, a series of (essentially stoichiometric) homologous
compounds with commensurate structures (superstructures of the basic structure) m ay
result or, in the intermediate case, a series of compounds with semi-commensurate or
Vernier structures.

Examples:
1. Mn n Si 2n m
The structure is of the TiSi 2 type which has two atom substructures, the Mn array
being identical to that of the Ti array in TiSi 2 and the Si 2 array being identical to
that of the Si 2 array in TiSi 2 . R emoval of Si leads to a c omposition Mn n Si 2n m in
which the Mn array is completely unchanged. The Si atoms are arranged in rows
and, as the Si content falls, t he Si atoms in the rows spread out. In this case there
will be a V ernier relationship between t he Si atom rows and the static Mn positions
which will change as the composition varies, giving rise to non-commensurate
structures.

2. YF 2þx O
The structure is of the fluorite type with extra s heets o f a toms inserted into t he
parent YX 2 structure. When these are ordered, a h omologous series of phases
results. When they are disordered, there is a n on-commensurate, non-stoichio-
metric phase, w hile partial ordering will give a V ernier or semi-commensurate
effect. Other layer structures c an be treated in the same way.

Misfit structures consist of two or more d ifferent, often mutually non-commensurate, units
which are held together b y e lectrostatic or other forces; no basic s tructure can be defined.
The composition of compounds with misfit structures is determined by the ratio of the
periodicities of their structural u nits and by electroneutrality.

Examples:
3. Sr 1 p Cr 2 S 4 p with p ¼ 0.29, where chains of compositions Sr 3 CrS 3 and Sr 3 x S
lie in tunnels of a f ramework of composition Cr 21 S 36 ; t he three units are mutually
non-commensurate.

þ
4. LaCrS 3 , w hich is built from non-commensurate sheets of (LaS) and (CrS 2 ) .
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