ASYNNNI model

The superstructures with wave vectors at x fa 6.65 and 0.37 at 6.71 found by Beyers et al. (1989) were not identified. The diffuse streaks at xf 6.85 indicate a series of very similar superstructures, which were considered by de Fontaine et al. (1990a) as the result of their structure combination branching mechanism (sect. 5.2). They also considered the 0.37 as a I which according to their ASYNNNI model could give a chain sequence (11011010) of full (1) and empty (0) chains. 

Fig. 44b. Superstructures of 123-0 in the T-x field, as determined by hard X-ray diffiaction. The larger parabolic curve (dotted line) shows the prediction of the ASYNNNI model. The experimentally determined curve lies 200 K lower. After von Zimmermann et al. (1999).

It is a matter of interpretation whether one follows the Gibbs picture with miscibility gaps or the ASYNNNI model based on the CVM method and discussed in sect. 5.2. The first was followed by Beyers and Shaw (1989), and the results of the lattice constants of equilibrium samples seem to support it. The ASYNNNI model is nearer to the ideas of von Zimmermann et al. Much more work (with many more stoichiometric compositions) is necessary to find out whether there are miscibility gaps between ortho-V, ortho-VIII and 3 o- Also, the single-phase character of the ortho-V and ortho-VIII phases should possibly be better supported. 

Fig. 46b. Cul-oxygen coordinations discussed by the ASYNNNI model. For a discussion see the text. After...

Although the ASYNNNI model reproduces excellently the temperature and composition dependence of the O-T transition and the existence of the O-II phase, as we have seen it is 200 K wrong in the prediction of the O-I to O-II transition temperature. Further, it does not account for the appearance of the up to now observed higher superstructures (O-V and O-VIII, sect. 5.1.1) and it predicts always long-range order... 

In conclusion it can be said that, even with the above-mentioned drawbacks, the ASYNNNI model has considerably helped to understand the difficulties of the superstructure problem. The delicate balance resulting from eqs. (3) and (4) indicates the strong dependence on preparation conditions to be expected. The complexity of superstructures dictates extremely slow cooling and low-temperature annealing. Here, however, the freezing of the mobility of oxygen puts a natural limitation. 

The ofiier early model (ASYNNNI, de Fontaine et al. 1987), followed the opposite approach, using short-range effective pair interactions despite its simplicity it succeeded in accounting correctly for the formation of the chains, the appearance of the tetragonal and orthorhombic phases, and the locus of their transition in the T-x phase diagram. It also succeeded in predicting superstrucmres but - as we have seen above (sect. 5.1.1) -it gave a quite erroneous critical temperamre for the ortho-II phase. 

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