INDEX orthorhombic distortion

The index usually indicates the sequence cubic (3), hexagonal (2), or double hexagonal (4) for the ABAC sequence. The Pearson symbols (Table 2.5) can clarify cases such as hexagonal structures with an ABC sequence and a = 3 for the index. The symbols t for tetragonal, o for orthorhombic, m for monoclinic, and h for hexagonal, rhombohedral, or trigonal indicate the type of distortion of an idealized structure. Without distortion, a = 3 is for a cubic structure and a = 2 is for a hexagonal (or rhombohedral) structure. 

X-ray diffraction analysis reveals two different vacancy distributions without the detection of a two-phase domain in every system. For low values of y S 0.25, the symmetry of the perovskite remains which indicates that the vacancies are apparently disordered. At higher values of y = 0.25 X-ray patterns give evidence of a distortion. For y = 0.25, they can be indexed with the theoretical parameters (orthorhombic symmetry) deduced from the vacancy ordering previously described. As a consequence, an order-disorder transition takes place around y 0.25. This phenomenon is illustrated in Fig. 4, which shows a discontinuity of the unit cell volume Vm around this value for each system. 

The many magnetic transitions below room temperature in the rare earth metals are discussed in ch. 6. The ferromagnetic ordering of Tb at 220 K was shown to be accompanied by a transition from an hep to an orthorhombic symmetry by Darnell (1963) who measured the lattice parameters versus temperature of single crystal Tb and found the hOO and hkO reflections were each split into two components. These components were indexed on the basis of an orthorhombic cell which showed an exj>ansion along the b direction from 6.244 A at 220 K to 6.263 A at 77 K and a contraction along the a direction from 3.605 A to 3.588 A over the same temperature interval. This distortion corresponds to the positive magnetostriction observed in Tb by Belov et al. (1961). 

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