On the construction of the lattice of ionic crystals from the viewpoint of close packing II. AX2

Abstract

This paper deals with the construction of crystal lattiees of ionie compounds of composition AX 2 based on close packing. If the ratio of the ionic radii satisfies the inequality rA/rx ~ 0,732, then the construetion is very similar to that of CsCI and the lattice is built up from close-packed ionic planes which contain both the anions and cations, respectively, in the adequate ratio. In this case only one solution is possible, namely the CaF 2 lattice. Ir the ratio of the ionie radii satisfies the inequality 0,732 > rA/rx > 0,414 the solution can be found by investigating several possibilities of uniform eationie distributions in the octahedral cavities of the different spatial close-packed anionic frames which satisfy PAULING's coordination principle. Many such solutions can be found, several of them giving the lattice of rutile and its sister lattices with different chemical composition and cationic distribution, the lattiee of brookite and anatase. However, no actual crystal lattices have been found till now, corresponding to some of the possibilities.The actual erystal lattices ate almost always distorted and dilated eompared to the ideal ones built by close packing, but for the isotypie lattices forming a group the differenee volume associated with one anion has to be the same. With this supposition the author was able to show that a deviation from this rule oecurs in the crystal lattices of compounds ABaX s when the divalent A cations are Fe, Co, Ni of Mn. The most serious deviation can be found in the case of Fe. Another deviation can be found in the compounds AAs20 ~ which has to be attributed to the influenee of As +5 causing ah apparent decrease of the ionic radii of the divalent cations A.