On the Madelung Part of Lattice Energy

Abstract

Abstract The Born-Haber Cycle (BHC) is critically reviewed, the origin of severe limitations in its appli­ cation is shown. Partly this is based on the construction of the third step, partly it is connected with the fact that most of the "classical" anions of inorganic chemistry are instable, "unobservable" gaseous entities. The Madelung Part of Lattice Energy, MAPLE*, is extentionally analyzed (e.g. TiO 2 ) to demonstrate that the similarity of thermodynamical properties like ΔH° 298 of all modifica­ tions, reflected in MAPLE, is non-trivial. The analogous analysis with e.g. BaTiO 3 proves that neither the classical "central ion" (here Ti 4+ ) nor the "completing" cation (here Ba 2+ ) but the "anions" coordinating the last mentioned cation BaO gain energy and, in this sense, "stabilize" the complex. Even simple compounds (e.g. A-La 2 O 3 ) show surprising geometrical arrangements, in striking contrast to often used but simple minded concepts like "Bond Length/Bond Strength" and its derivatives like CHARDI, whereas such "oddities" are explained by MAPLE. The application of the theorem of additivity of MAPLE (MAPLE polynary = Σ MAPLE binary ), that passes even in the case of hydrates, and its limitations are discussed. Guided by MAPLE, surprisingly complicated structures (e.g. Cs 2 Li 3 I 5 ) of polynary derivatives of structurally exceedingly simple binary com­ pounds become "understandable". If "molecular" entities like SO 3 are involved, limitations can be excluded using "increments". Last not least, MAPLE is the first known guide to a multi-dimen-sional but strict scheme of characterisation of Solid State Structures in the sense of Linne's ideas, based on geometrical facts only.