Unique Indexing Scheme of Decagonal Phases Based on a Six Dimensional Model
- PDF / 1,792,670 Bytes
- 11 Pages / 612 x 792 pts (letter) Page_size
- 94 Downloads / 151 Views
LL1.6.1
Unique Indexing Scheme of Decagonal Phases Based on a Six Dimensional Model R.K. Mandal1, A.K. Pramanick2, G.V.S. Sastry1 and S. Lele1 Centre of Advanced Study, Department of Metallurgical Engineering Institute of Technology, Banaras Hindu University, Varanasi 221 005 (India) 2 National Metallurgical Laboratory, Jamshedpur 831007 (India) 1
ABSTRACT Mandal 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.
INTRODUCTION Decagonal quasicrystals (DQC) exhibit two dimensional (2-d) quasi periodicity and onedimensional (1-d) periodicity perpendicular to the 2-d plane. Many interesting features of these phases have been summarised by Ranganathan et al. (1997) [1]. One of the important characteristics of DQCs refers to variation in periodicities along ten fold axis. DQCs having 2, 4, 6 and 8 layers periodicity are experimentally observed and are designated as T2n phases (for n = 1,2,3,4). Apart from this, they display change in symmetry also. Popularly observed phases show either P10/mmm or P105/mcm symmetries. The indexing of the spots present in the 10-fold (f) zone has posed a problem akin to that of periodic hexagonal phase under 6-f zone [2-3]. It may be recalled that permuted sets of three indices are required in the 6-f plane for indexing symmetry related spots for hexagonal phase. It may be noted here that the rank of the above 2-d hexagonal section is two and choice of three indices in the plane introduces the problem of redundancy. This yields non-uniqueness in the identification of diffracted spots. The triplet of indices for hexagonal phase in the plane can be made unique by exploiting the property of the basis set which leads to h+k+i = 0 (Frank, 1965) in usual notation of Miller-Bravais scheme. It will be argued, in this communication, that 5-d pentagonal planar indexing scheme or 6-d indexing scheme should also be looked into from such a perspective [4-6]. Singh and Ranganathan (1996a,b) [7-8] have presented the most
Data Loading...
