Anion Contact and Double Repulsion

The radius ratio for lithium fluoride is 0.44. In this crystal each anion is approaching contact not only with the surrounding cations but 

It is seen that the radius ratio is an important quantity in influencing the properties of ionic crystals. Its significance in the chemistry of ionic substances was first pointed out by Magnus24 and was emphasized by Goldschmidt25 in the field of crystal chemistry. The effect of the ra- 

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Anion Contact and Double Repulsion.2 —The explanations of the deviations from additivity are indicated by Figure 13-6, in which the circles have radii corresponding to the crystal radii of the ions and are drawn with the observed interionic distances. It is seen that for LiCl, LiBr, and Lil the anions are in mutual contact, as suggested in 1920 by Land6.14 A simple calculation shows that if the ratio p = r+/r of the radii of cation and anion falls below /2 — 1 = 0.414 anion-anion contact will occur rather than cation-anion contact (the ions being considered as rigid spheres). A comparison of apparent anion radii in these crystals and crystal radii from Table 13-8 is given in Table 13-7. 

A Detailed Discussion of the Effect of Relative Ionic Sizes on the Properties of the Alkali Halogenides.—A simple detailed representation of interionic forces in terms of ionic radii has been formulated that leads to complete agreement with the observed values of interionic distances for alkali halogenide crystals and provides a quantitative theory of the anion-contact and double-repulsion effects. 0... 

In lithium chloride, bromide and iodide, magnesium sulfide and selenide and strontium chloride the inter-atomic distances depend on the anion radius alone, for the anions are in mutual contact the observed anion-anion distances agree satisfactorily with the calculated radii. In lithium fluoride, sodium chloride, bromide and iodide and magnesium oxide the observed anion-cation distances are larger than those calculated because of double repulsion the anions are approaching mutual contact, and the repulsive forces between them as well as those between anion and cation are operative. 

It is to be emphasised that equilibrium interionic distances are less well defined than covalent bond lengths their values depend not only on ligancy, but also on radius ratio (anion contact, double repulsion), amount of covalent bond character, and other factors, and a simple discussion of all the corrections that have been suggested and applied cannot be given. On the other hand, we have a reliable picture of the forces operating between ions, and it is usually possible to make a reliable prediction about interionic distances for particular structures. 

In the derivation of these ionic radii, it has been assumed that the repulsion coefficient B depends only on the coordination number that is, on the number of anion-cation contacts, but if the radius ratio is close to or less than the lower limit, anion-anion contact occurs and the additional Bom repulsion will lead to equilibrium with the attractive Coulomb forces at a larger distance than that given by the sum of the ionic radii. This phenomenon of double repulsion is shown (see tabulation) by the lithium halides especially. In a more detailed treatment, Pauling 112, 114) has... 

The process of deposition of particles at interfaces which occurs in many industrial processes, such as surface coating, is described at a fundamental level. Particle deposition can be conveniently split into three major steps (i) transfer of particles from the bulk dispersion over macroscopic distances to the surface (ii) transfer of the particles through the boundary layer adjacent to the interface (hi) formation of a permement adhesive contact with the surface or previously deposited particles leading to particle immobilization (attachment). The role of interparticle interactions on deposition is described in terms of double layer repulsion and van der Waals attraction. Particular attention is given to the effect of addition of electrolytes on particle deposition. The measurement of particle deposition using rotating disc and cyhnder techniques is described. The effect of nonionic polymers and polyelectrolytes (both anionic and cationic) on particle deposition at interlaces is described. The most universal and convenient methods for measuring particle deposition are the indirect methods. 

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