Page 67 - Nomenclature of Inorganic Chemistry (IUPAC Recommendations 2005)

S O L I D S IR-11.6

IR-11.6.3 Crystallographic shear structures
Crystallographic s hear planes (CS planes) are planar faults in a c rystal that separate t wo
parts of the crystal which are displaced with respect to each other. The vector describing the
displacement is called the crystallographic shear vector (CS vector). Each CS plane causes
the composition of the crystal to change by a s mall increment because the sequence of
crystal planes that produces the crystal matrix i s c hanged at the CS plane. (From this it
follows that the CS vector must be at an angle t o t he CS plane. If it were parallel to the plane,
the succession of crystal planes would not be altered and no composition change would
result. A p lanar boundary w here the displacement vector is parallel to the plane is more
properly called an antiphase b oundary.)
Because e ach CS plane c hanges t he composition of the crystal slightly, the overall
composition of a c rystal containing a p opulation of CS planes will depend upon the number of
CS planes present and their orientation. If the CS planes are disordered, the crystals will be
non-stoichiometric, the stoichiometric variation being due to the CS plane ‘defect’. If the CS
planes are ordered into a parallel array, a s toichiometric phase with a c omplex formula r esults.
In this case, a change in the separation of the CS planes in the ordered array will produce
a n ew phase with a n ew composition. The series of phases produced by changes i n t he
spacing between CS planes forms an homologous series. The general formula of a p articular
series will depend upon the type of CS plane i n t he array and the separation between the CS
planes. A c hange in the CS plane may change the formula o f t he homologous series.

Examples:

1. Ti n O 2n 1
The parent structure is TiO 2 (rutile type). The CS planes are the (121) planes.
Ordered arrays of CS planes can exist, producing an homologous series of oxides
with formulae Ti 4 O 7 , T i 5 O 9 , T i 6 O 11 , T i 7 O 13 , T i 8 O 15 and Ti 9 O 17 . T he series formula
is Ti n O 2n 1 , w ith n between 4 and 9.
2. (Mo,W) n O 3n 1
The parent structure is WO 3 . T he CS planes are the (102) planes. Ordered arrays
of CS planes can form, producing oxides with formulae Mo 8 O 23 , M o 9 O 26 ,
(Mo,W) 10 O 29 , ( Mo,W) 11 O 32 , ( Mo,W) 12 O 35 , ( Mo,W) 13 O 38 and (Mo,W) 14 O 41 . T he
series formula i s ( Mo,W) n O 3n 1 , w ith n between 8 a nd 14.

3. W n O 3n 2
The parent structure is WO 3 . T he CS planes are the (103) planes. Ordered a rrays of
CS planes can form, producing oxides with formulae W n O 3n 2 , w ith n between
approximately 16 and 25.

IR-11.6.4 Unit cell twinning or chemical t winning

This is a s tructure-building component in which two constituent parts of the structure are
twin-related across the interface. T he twin plane changes t he composition of the host crystal
by a d efinite amount (which m ay be zero). Ordered, closely s paced arrays of twin planes will
lead to homologous series of phases. Disordered twin planes will lead t o n on-stoichiometric
phases i n w hich the twin planes serve a s t he defects. There is a c lose parallel between
chemical twinning and crystallographic shear (see Section IR-11.6.3).

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