The OD interpretation of the crystal structure of kettnerite CaBiOFCO3.

The mineral kettnerite, CaBi(OFCO(3)), is a rare example of an order-disorder (OD) structure with a quadratic net. The lattice parameters of the simplest possible 1O polytype are a = 5.3641 (1), b = 5.3641 (1), c = 13.5771 (2) A, and the space group is Pbaa. There are three kinds of OD layers, identical to structure-building layers. Two of them are non-polar: the Bi-O and Ca-F at z = 0 and z = 1/2, respectively, with the layer-group symmetry C2/m2/m(4/a,b)2(1)/m2(1)/m. The third kind of OD layer of CO(3) groups (located between the Bi-O and Ca-F layers) is polar, with alternating sense of polarity. The layer group is Pba(4)mm. Triangular CO(3) groups are parallel to (110) or (110) planes with one O atom oriented towards the Bi-O layer and the remaining two O atoms oriented towards the Ca-F layer. The orientations of CO(3) groups alternate along the [110] and [110] directions. As a result, each group parallel to (110) is surrounded by four nearest neighbors parallel to (110) and vice versa. These positions can be interchanged by an (a + b)/2 shift or by pi/2 rotation; thus stacking of the layer onto adjacent ones is ambiguous. Instead of OD layers, the polytypes are generated by stacking of OD packets, comprising the whole CO(3) layers and adjacent halves of the Bi-O and Ca-F layers. They are polar, with alternating sense of polarity; the layer group is Pba(4)mm. Stacking sequences are expressed by ball-and-stick models, with the aid of symbolic figures, and by sequences of orientational characters. There are two maximum-degree-of-order (MDO) polytypes, 1O (really found and described, see lattice parameters and space group above) and 2O, with doubled c parameter and space group Ibca (not yet found). The derivation of the MDO generating operations of both polytypes is presented in this paper. The stacking rule also allows another, non-MDO, polytype with doubled c, i.e. the 2Q polytype, space group P4(2)bc (tetragonal, not yet found). Various kinds of domains can exist: (i) out-of-step domains shifted by (a + b)/2, (ii) twin domains rotated by pi/2 around local tetrads of odd or even packets, and (iii) upside-down domains in the polar 2Q polytype. Stacking sequences of 16 possible domains of the polytypes mentioned above are listed. Also 60 domains of four distinct six-packet polytypes are theoretically possible.