Order–disorder in sapphire, aenigmatite and aenigmatite-like minerals

The chemically very different minerals aenigmatite and sapphirine are crystallographically closely related, being ordered members of isomorphous families of OD structures consisting of equivalent layers. The symbol of the OD-groupoid family characterizing their symmetry is P1(2/n)l {1(22/c1/2)1 }. Formulae for the structure factor are deduced for the general member of the family and then specialized to explain the diffraction pattern of some members of interest. The twinned structures of aenigmatite, rhonite and krinovite are explained as OD twins; the constituting twin individuals are structures of maximum degree of order corresponding to the OD-groupoid family quoted above.