Topological Signatures of Medium Range Order in Amorphous Semiconductor Models
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Topological Signatures of Medium Range Order in Amorphous Semiconductor Models M. M. J. Treacy*, P. M. Voyles*† and J. M. Gibson# *NEC Research Institute, Inc. 4 Independence Way, Princeton, NJ 08540 † Dept. of Physics, University of Illinois, 1110 W. Green St., Urbana, IL 61801 # Materials Science Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, IL 60439 ABSTRACT The topological local cluster (or Schläfli cluster) concept of Marians and Hobbs is used to detect topologically crystalline regions in models of disordered tetrahedral semiconductors. We present simple algorithms for detecting both Wells-type shortest circuits and O’Keeffe-type rings, which can be used to delineate alternative forms of the Schläfli cluster in models. INTRODUCTION Fluctuation microscopy experiments have shown that evaporated amorphous silicon and germanium exhibit a paracrystalline-type structure [1], in which some regions possess the bonding topology of the crystal, but are strained so that the component atoms do not lie on a lattice. This discovery was aided by comparison of the fluctuation microscopy data to simulations from molecular dynamics structures, and has highlighted the need for effective tools for characterizing medium range order in structural models. To address this need, useful topological analysis tools for characterizing models have been developed [2-6]. In this paper, we describe how the local cluster (or Schläfli cluster) concept of Marians and Hobbs [2] can be used to detect paracrystalline regions in models of disordered materials. We also outline a simple algorithm for detecting these topological clusters. TOPOLOGICAL REPRESENTATION OF NETWORK STRUCTURES Because of their periodicity, crystals can be completely defined by the positions of a small asymmetric unit of atoms and a group of symmetry operators. In principle, the bonding topology of covalent materials, such as perovskites and zeolites, can also be represented unambiguously by a graph. Atoms define the graph vertices and bonds define the graph edges. Such a topological approach has advantages for disordered models because it is insensitive to local strain and symmetry breaking. One useful topological descriptor that is used extensively in zeolite studies is the circuit symbol [7-9], which is an ordered list of all the shortest closed paths that pass through each vertex and all the pairwise combinations of that vertex’s first nearest neighbors. If there are N nearest neighbors, there are N(N-1)/2 distinct sets of circuits. The shortest meaningful circuit is of length 3. The circuit symbol itself does not give a unique description of any given topology. However, when used in conjunction with other topological descriptors such as the coordination sequence, there is a very high likelihood that graphs with the same descriptors represent the same topology. The coordination sequence is a list of the number of vertices Np in coordination shell p around each atom [8-10]. However, coordination sequences are less useful for describing local topology in am
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