The study of incommensurate structures as a probe to reveal atomic interactions in crystals

Abstract

Abstract The structure of aperiodic crystals which in cludes incommensurate, quasi- and composite crystals is usu ally described in spaces of higher dimension, the so called su perspace. The main advantage of the superspace formalism is that an aperiodic structure in three dimensions recovers its full periodicity in higher dimensions. The symmetry prop erties of aperiodic crystals are obviously more convenient to describe in superspace too. The origin of the incommensurate nature of structures can often be found in competing inter atomic interactions. From molecular dynamics simulation of a simple three dimensional model with close-packed layers and a single degree of freedom for each particle, it is pos sible to find the existence conditions of commensurate and incommensurate phases. Incommensurate phases can already be predicted on the basis of nearest and next nearest neigh bour particle interactions only. We illustrate this principle of interactions with two examples of structures, Na2CO3 and K3In(PO4)2. These examples shows clearly the importance of non-oxygen interactions i.e. next nearest interactions for the formation of incommensurate structures.