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Rare‐earth Oxides of the Homologous Series R n O 2n–2m : a New Structural Principle
Author(s) -
Bevan D. J. M.,
Martin R. L.
Publication year - 1999
Publication title -
zeitschrift für anorganische und allgemeine chemie
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 66
eISSN - 1521-3749
pISSN - 0044-2313
DOI - 10.1002/(sici)1521-3749(199901)625:1<57::aid-zaac57>3.0.co;2-p
Subject(s) - tetrahedron , octahedron , motif (music) , crystallography , structural motif , homologous series , polyhedron , combinatorics , chemistry , materials science , physics , stereochemistry , crystal structure , mathematics , nuclear magnetic resonance , acoustics
The structures reported by the Eyring school [9–12] for several anion‐deficient, fluorite‐related rare‐earth oxides of the series R n O 2 n–2m are interpreted here in terms of arrangements of vacancy‐centred tetrahedra; specifically, the linkages between nearest‐neighbour, „anti‐phase coordination defects (CDs)”. The CD is an octahedron of corner‐shared OR 4/8 tetrahedra enclosing a □R 4/8 tetrahedron, where □ represents an oxygen vacancy. This description enables unique motifs to be identified for each structure: these comprise (100) n nets, usually puckered and mostly 6 3 , of „anti‐phase” 1 / 2 <210> F CD linkages: only for the reported phase with n = 40; m = 4 does the motif contain more than six such linkages – there are ten present in this case. For the most part, a sub‐motif can be defined by four „anti‐phase” CD linkages of the (100) n net, three of which must be 1 / 2 <210> F (the sub‐motif for n = 40; m = 4 is six‐sided, five of which are 1 / 2 <210> F ): the full motif is then generated by inversion of the sub‐motif through the mid‐point of the fourth (sixth), usually unique linkage. This leads in general to a „chair form” motif . The supercells all have a common a ‐axis which has been chosen traditionally as 1 / 2 [2 1 1] F , and it is the a ‐axis translations of the motif vertices which generate the complete three‐dimensional motif – a generally complex polyhedron. This new motif principle has been used to derive possible models for phases of unknown structure.