Unique Indexing Scheme of Decagonal Phases Based on a Six Dimensional Model

Abstract

ABSTRACTMandal and Lele (1989) have proposed a six dimensional model for the structural description of the decagonal phases. The integral linear combination of six basis vectors for indicating a physical vector in their model, however, leaves the problem of redundancy in indexing. While revisiting their model, we have noted that the condition of a null vector in physical space permits the formulation of unique indexing scheme both in physical reciprocal and direct spaces, we will demonstrate that our scheme, unlike all previously discussed ones, relies only on the information contained in the model. It will also be shown that diffracted spot having equivalent indices possesses identical intensity. This aspect, though equally important, has been totally ignored in the past. We shall substantiate our claim by taking examples from the known decagonal phases. We shall also present parity condition on indices that will be helpful in discussing subtle features of diffraction patterns. The notion of weak and strong diffracting conditions is explained based on the zone rule in physical space in terms of Cartesian components of direct and reciprocal vectors.