International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 14.3, p. 874

Section 14.3.5. Incorrect space-group assignment

W. Fischera and E. Kocha*

aInstitut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail:  kochelke@mailer.uni-marburg.de

14.3.5. Incorrect space-group assignment

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In the literature, some crystal structures are still described within space groups that are only subgroups of the correct symmetry groups. Many such mistakes (but not all of them) could be avoided by simply looking at the lattice complexes (and their descriptive symbols) that correspond to the Wyckoff positions of the different kinds of atoms. Whenever the same (or an analogous) lattice-complex description of a crystal structure is also possible within a supergroup, then the crystal structure has at least that symmetry.

Examples

  • (1) The crystal structure of β-LiRhO2 has been refined in space group [F4_{1}32] (cf. Hobbie & Hoppe, 1986[link]).[\openup3pt\matrix{\hbox{Rh} \hfill &16c \hfill &.32 \hfill &{1 \over 8}{1 \over 8}{1 \over 8} \hfill &T\hfill \cr \hbox{Li} \hfill &16d \hfill &.32 \hfill &{5 \over 8}{5 \over 8}{5 \over 8} \hfill &{1 \over 2}{1 \over 2}{1 \over 2}\ T\hfill\cr \hbox{O} \hfill &32e \hfill &.3. \hfill &xxx \hfill &..2\; D4xxx \hfill\cr}] The same atomic arrangement is possible in the supergroup [Fd\bar{3}m] of [F4_{1}32], as can easily be read from Table 14.2.3.2[link] :[\openup3pt\matrix{\hbox{Rh} \hfill &16c \hfill &.\bar{3}m \hfill &{1 \over 8}{1 \over 8}{1 \over 8} \hfill &T\hfill\cr \hbox{Li} \hfill &16d \hfill &.\bar{3}m \hfill &{5 \over 8}{5 \over 8}{5 \over 8} \hfill &{1 \over 2}{1 \over 2}{1 \over 2}\ T\hfill\cr \hbox{O} \hfill &32e \hfill &.3m \hfill &xxx \hfill &..2\; D4xxx\hfill\cr}] Therefore, β-LiRhO2 should be described in [Fd\bar{3}m].

  • (2) KIAs4O6 (Pertlik, 1988[link]) has been described with symmetry P622.[\openup3pt\matrix{\hbox{I} \hfill &1a \hfill &622 \hfill &000 \hfill &P\hfill\cr \hbox{K} \hfill &1b \hfill &622 \hfill &00{1 \over 2} \hfill &00{1 \over 2}\ P\hfill \cr \hbox{As} \hfill &4h \hfill &3.. \hfill &{1 \over 3}{2 \over 3}z \hfill &G2z\hfill \cr \hbox{O} \hfill &6i \hfill &2.. \hfill &{1 \over 2}0z \hfill &N2z\hfill \cr}] Space group [P6/mmm] allows the same atomic arrangement:[\openup3pt\matrix{\hbox{I} \hfill &1a \hfill &6/mmm \hfill &000 \hfill &P\hfill\cr \hbox{K} \hfill &1b \hfill &6/mmm \hfill &00{1 \over 2} \hfill &00{1 \over 2}\ P\hfill\cr \hbox{As} \hfill &4h \hfill &3m. \hfill &{1 \over 3}{2 \over 3}z \hfill &G2z\hfill\cr \hbox{O} \hfill &6i \hfill &2mm \hfill &{1 \over 2}0z \hfill &N2z\hfill \cr}] Therefore, KIAs4O6 should be described in [P6/mmm].

References

Hobbie, K. & Hoppe, R. (1986). Über Oxorhodate der Alkalimetalle: β-LiRhO2. Z. Anorg. Allg. Chem. 535, 20–30.
Pertlik, F. (1988). The compounds KAs4O6X (X = Cl, Br, I) and NH4As4O6X (X = Br, I): Hydrothermal syntheses and structure determinations. Monatsh. Chem. Verw. Teile Anderer Wiss. 119, 451–456.








































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