In Lecture 2 we went through the three cubic 1:1 structures possible: CsCl(8,8 coordinate , i.e. the coordination number of both the cation and the anion is 8) NaCl(6,6 coordinate) and ZnS (4,4 coordinate). In this lecture, we will look in more quantitative detail at some of the concepts already outlined i.e. lattice energies, packing radius ratios, a detailed look at structure selection (first: stoichiometry, then either extent of covalency, or radius ratio, or both). And finally, we will cover some stoichiometries other than 1:1. By taking the electronegativities on page 3 of handout one and plotting points on a Van Arkel-Ketelaar Triangle, with colour coding according to the type of structure adopted, for a wide range of binary XY solids, the following pattern emerges: Using this method, there is a remarkably clear distinction between the 6,6-coordinate , more ionic NaCl-type structures (dark grey diamonds), and the more covalent 4,4 zincblende structures (pale grey squares). To define the triangle, Cs metal and F 2 are shown along the bottom as black diamonds, and also along the bottom (zero electronegativity difference) Si, C, Ge and Sn are shown as zincblende structures because of the identical 4,4 tetrahedral coordination , though the fact that both types of position " cation " and " anion " are identical in those cases means that they are not strictly describable as zincblende structures. This diagram is persuasive of the notion that electronegativity difference, directly correlated with extent of covalency, is a powerful director and predictor of structural preference: More covalent: lower coordination number. You will not find this point discussed in Chem 3 nor in any other text in existence, though there is some discussion of bonding triangles on page 295-296. However, there is one 1:1 structure yet to be included: CsCl structure is surprisingly rare, being more rarely observed than would be predicted on the basis of radius ratio (see below). Though it is the ideal way for ionic 1:1 solids to pack in terms of maximizing the electrostatic attractive terms, it is only adopted by CsCl, CsBr, and CsI amongs all the alkali halides. All others are Rocksalt, NaCl lattice. In so doing these three define the outer edge of the Van Arkel Triangle. There are other compounds which fit less-well, but there are questions over the accuracy of the assumptions on bonding: TlCl, TlBr and TlI also adopt CsCl structures, despite TlI being predicted NaCl.
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