2 D Lattices on Substrates with Randomly Distributed Pinning Centers: A Possible Scaling Law for Domain Sizes
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ABSTRACT We consider 2D lattices which are disordered by an external field, in this case by a dense, random distribution of attractive pinning centers of an underlying substrate. The preferred configuration of the 2D system with screened-Coulomb two-body interactions and a fixed number of particles is a triangular lattice configuration.The pinning centers strongly affect the triangular lattice configuration. By keeping the location and the density of the pinning centers fixed, we study the effects of pinning strength on the structural properties of the lattice. We find that the strongly disordered lattice prefers to form irregular domains of size s which are composed entirely of topological defects. The distribution of sizes of these domains, D(s) suggest that s- for sufficiently large s. Our results are consistent with -r > 2 in the solid phase and r < 2 in the liquid phase. We present a general argument in support of our findings and suggest that the physics which dictates the structure of 2D lattices on substrates with randomly distributed pinning centers is the same as that for a broad range of problems in which an external field strongly influences the behavior of an interacting physical system.
INTRODUCTION 2D lattices on randomly distributed pinning potentials are realized in a variety of circumstances [1-2]. The most common examples in physical systems include solid films with quenched impurities and/or on rough substrates and flux-line lattices in layered typeII superconductive films [1-2]. At present, however, very little appears to be known about the structural properties of two-dimensional lattices in random potentials. In the present study, we address the problem of determining the structural properties of 2D lattices in the presence of long-ranged repulsive inter-particle interactions with fixed total number of particles in the system and in the presence of a large number of randomly distributed attractive pinning sites. In a set of previous studies we have studied the structural properties of a repulsive screened-Coulomb system in the presence of a substrate described by a strong but uniform corrugation potential [3-6]. These studies were formulated in the context of the structure of Rb ions on the graphitic substrates found in alkali-metal graphite intercalation compounds. It is well known that in the absence of a substrate corrugation potential, a 2D lattice prefers to form a triangular lattice (see for instance in Ref. [7]). The corrugation can affect the triangular lattice structure significantly. In the case of RbC 24 .5 7, where 24.57 reflects a "magic density" of the system, the Rb ions make nanodomains of 17 ions surrounded by thick domain walls. At slightly different stoichiometries, the structure can be viewed as essentially the same as that in the "magic" stoichiometry with regions in which the domains are smaller or larger and there are associated distortions in the domain walls [3-5]. 441 Mat. Res. Soc. Symp. Proc. Vol. 455 © 1997 Materials Research Society
Building on these earlier s
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