Computer Modeling and Description of Nonstoichiometric Apatites Cd5−η/2(VO4)3I1−η and Cd5−η/2(PO4)3Br1−η as Modified Chimney–Ladder Structures with Ladder–Ladder and Chimney–Ladder Coupling

✍ Scribed by Andrew G. Christy; Peter Alberius-Henning; Sven A. Lidin

• Book ID: 102974931
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 566 KB
• Volume: 156
• Category: Article
• ISSN: 0022-4596
• DOI: 10.1006/jssc.2000.8967

✦ Synopsis

Di4raction patterns from apatite-structure compounds Cd 5؊ /2 (TO 4 ) 3 X 1؊ with T ‫؍‬ P, V and X ‫؍‬ Br, I show sheets of di4use scattering normal to c* at incommensurate l ‫؍‬ q (q ‫؍‬ 1.63 for Cd+V+I apatite and q ‫؍‬ 1.78 for Cd+P+Br apatite), because the c repeat of the average unit cell is shorter than two X diameters. The equilibrium X.. X spacing along c de5nes the incommensurate periodicity c/q and stoichiometry (1؊ ) ‫؍‬ q/2. The layers show a honeycomb texture for the Cd+V+I apatite, which is condensed into discrete spots for the Cd+P+Br compound. In both phases, X.. X repulsions along 11002 force neighboring rods of X atoms out of phase. In the Cd+P+Br phase, additional 12102 attractions drive incipient formation of a rhombohedral superstructure. Average structure site occupancies and the observation of second-order di4use layers at both l ‫؍‬ 2q and l ‫؍‬ q؉2 imply the existence of strong Cd.. X in addition to X.. X interactions. A three-dimensional computer model was used to produce 5nite-temperature structure simulations as a function of X.. X interactions along 10012, 11002, and 12102, and X..Cd interactions, from which di4raction patterns were calculated. The experimental patterns were 5t and approximate values for the interaction energies obtained (hundreds to thousands of joules per mole). It was apparent that lock-in to commensurability caused by the X..Cd term and the formation of nonprimitive incommensurate modulated structures driven by X.. X interactions were mutually antagonistic, and the actual structures are compromises between the two.