The compressible ion studies on ionic solids, ionic melts and solified gases

Abstract

In this chapter, the compressible?ion theory of repulsion has been applied to the alkaline?earth chalcogenides using a simplified formulation of the polyhedral cell approach. The theory correctly predicts that most of these crystals should occur in the NaCl structure. The repulsion parameters of the chalcogen ions were then used to derive hard?sphere radii for divalent ions. The theory has also been extended to the rutile and perovskite structures, where the interionic distances and compressibilities were satisfactorily predicted. These results indicate that the theory, which is based on a purely ionic picture, is quite valid for divalent ions in crystals. However, a mild discrepancy exists in the relative stabilities of different crystal structures. The present approach appears to overestimate the stability of the NaCl structure and underestimate the binding energies of the competing ZnO (or ZnS) structure. It is generally believed that some degree of covalency is present in these crystals, which might explain the discrepancy. The repulsion parameters derived in this chapter are subsequently used in the following chapters. The highlight of the present chapter is that, for the first time, a theory has satisfactorily explained the observed centre?of?mass structures of all the ammonium halides. The key feature of the approach is the distributed?charge model of the ammonium ion, which causes significant changes in the relative stabilities of the ZnO, NaCl, and CsCl structures. In contrast, a point?charge model predicts only the NaCl structure for all the crystals considered. As pointed out earlier, with the distributed?charge model, the Madelung constant becomes a function of the nearest?neighbour distance (r). Because of this effect, the modification introduced by the distributed charge is maximum in NH?F (which has the smallest r) and reduces progressively for larger anions. Consequently:

NH?F adopts the ‘anomalous’ ZnO structure NH?Cl and NH?Br both prefer the CsCl structure over the NaCl structure, though NH?Cl is stable in CsCl only over a larger temperature range NH?I remains in the NaCl structure at room temperature, requiring only a small pressure to convert it into the CsCl structure

The pressure and thermal transitions among the centre?of?mass structures in ammonium halides are all qualitatively explained by the present theory, except for the NH?FI phase, which was not included due to insufficient data. It is significant that the theory correctly predicts that there is no NaCl phase in NH?F at room temperature. To appreciate the discrepancies between calculated and observed transition pressures and temperatures, one should note that the calculations involve several approximations. Additional effects may also be relevant:

Garland and Jones (1964) suggested that d?/dV is negative in ammonium halides. Thus ? decreases with increasing temperature and increases with pressure. A smaller ? corresponds to a more stable NaCl phase. This tends to reduce the transition temperature in NH?F and NH?Cl and the transition pressure in NH?I, improving the agreement with experiment. In NH?Cl, the ion may rotate more freely at higher temperatures (Gutowsky et al., 1954), reducing electrostatic binding in the CsCl structure.

With these added effects, better quantitative agreement might be obtained. The ZnO structure of NH?F deserves special mention. In the usual ionic?crystal picture, this structure is expected only at very low radius ratios (~0.4). For NH?F, the radius ratio is ?0.55. For this reason, hydrogen bonding has often been invoked in this crystal. The nearest?neighbour distance in NH?F has also been considered anomalously low, further motivating hydrogen?bond models. The present calculations, however, explain the stability of the ZnO structure and give good agreement in the nearest?neighbour distance (see Table 3.4) using only ionic theory with no hydrogen bonding. A substantial part of this success is due to the distributed charge on the NH?? ion, which simulates hydrogen bonding through increased electrostatic binding. However, one should also note the arguments of Narayan (1979b), who showed that ZnO and ZnS structures can occur in purely ionic crystals, even at relatively high radius ratios, provided the ions are sufficiently compressible. The equilibrium value of r in a 4?coordinated structure can be much smaller than in NaCl (particularly for compressible ions), compensating for the reduction in the Madelung constant. In the above calculations, the complex nature of the ion has been introduced only for the electrostatic?energy calculations; the repulsive energy was computed using the compressible?ion model in the same way as for simple ions.

This chapter has extended the concept of ionic compressibility to rare?gas atoms, thus unifying repulsion in closed?shell ions and neutral atoms. The compressional behaviour of rare?gas atoms was predicted from earlier results on monovalent and divalent ions and used to explain the properties of rare?gas crystals. The results show that this unification is meaningful and that the physical picture of compressible ions and atoms is quite valid. While the above results are not very conclusive, they raise interesting questions:

The irreversible transformation observed at high temperatures is intriguing. Earlier experiments (Kukkonen et al., 1981) on other Ti–S compositions such as TiS??? (x ? 0.1) did not show such transitions. The present transition is unlikely to be due to oxidation, since Al?Aluray et al. (1977) showed that chemical decomposition and oxidation of TiS??? occur only above 595°C. TiS? exists in several polytypic modifications (Palosz, 1983), and interpolytypic transformations are always irreversible. X?ray structure determination of the transformed phase is needed but could not be carried out because sample retrieval after the pressure run was difficult.

The thermopower changes by ~30% in the range 100–250°C, and the resistance nearly doubles in this range. Such large changes over a small temperature span suggest that carrier?scattering mechanisms in the crystal are quite complicated. The pressure?dependent anisotropy in electrical properties would also be interesting to explore, but this would require thicker crystals to avoid damage during high?pressure electrical contacts. Measuring thermopower parallel to the c?axis is another challenge, requiring very small thermal gradients across specimens. As discussed earlier, the experiments were mainly carried out to explore the feasibility of high?pressure studies on layered compounds. The results indicate that the study is justified, as it has produced interesting observations and identified the difficulties that must be overcome before such studies can be carried out on a larger scale.