Small Ion Distortions and Rattling

Up till now, the distortions from cubic symmetry that we have discussed have all been attributed to various features of the electronic structure of the metal ion which lack spherical symmetry and which hence lead to more or less strongly directional electrostatic interactions with the environment. In other words, these deviations from ideal ionic packing result from the breakdown, in a number of cases, of the assumption made on p. 2 that ions can be regarded as spheres. 

We now consider a quite different type of distortion, a good example of which occurs in the structure of vanadium pentoxide, V206 (27). The environment of the V6+ ion is illustrated in Fig. 24. Each V6+ ion has five 

Somewhere between these two extremes there must be a radius of the metal ion for which the potential energy curve is flat for small displacements from the center of the octahedron (Fig. 25c). We call the corresponding interionic distance the maximum contact distance L0, for insofar as analogies with classical particles are permissible, the flatness of the potential energy curve may be said to correspond to contact between compressible spheres. If the interionic distance increases the metal ion becomes free to rattle if it is decreased the metal ion is subjected to compression. Note 

Our assumption that the anions are fixed and form part of a rigid extended framework within whose octahedral interstices the cations are free to move is not, of course, very realistic except, perhaps, when the anions form a close-packed arrangement. For some other structures it would seem equally plausible (or implausible) to assume that the cations were rigid and that the anion environment could be distorted, though only in such a way as to make an extended framework possible. Neither of these models is in any sense complete but they are distinct in that they may lead to rather 

We now consider the consequences of continuously reducing the size of the central cation in an octahedrally coordinated structure. First, there may be another structure, perhaps quite unrelated and involving tetrahedral or other coordination, which becomes stable relative to the octahedral structure before the latter becomes unstable with respect to small displacements, that is, before the maximum contact distance is reached. In this case there is a sudden change from regular octahedral to regular tetrahedral coordination, as shown in Fig. 26a. The oxides of the divalent transition-metal ions have structures in accord with this model, for, in the absence of Jahn-Teller effects, they are either octahedrally or tetrahedrally coordinated. 

---