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ISRN Condensed Matter Physics
Volume 2012 (2012), Article ID 342642, 7 pages
Research Article

Ordering in Two-Dimensional Lennard-Jones Clusters

Experimental Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Bidhannagar, Kolkata 700064, India

Received 1 December 2011; Accepted 27 December 2011

Academic Editors: H. D. Hochheimer, L. Pusztai, and V. Stephanovich

Copyright © 2012 Barnana Pal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cluster formation in a two-dimensional Lennard-Jones system under different conditions of temperature ( 𝑇 ) and particle concentration ( 𝑐 ) has been studied using the Monte-Carlo method with the introduction of real thermal motion of the constituent particles through a modification of the conventional Metropolis algorithm. The 𝑐 - 𝑇 phase diagram determined from the study of the root mean square displacement of the particles shows features characteristics of the 𝑃 - 𝑇 diagram for phase equilibrium in real systems. The solid-like to liquid-like transition takes place when the average nearest neighbour distance increases by ~1% of the equilibrium value in the low-temperature solid-like configuration. The Lindemann parameter ( 𝛿 ) is found to decrease with the increase of 𝑐 to reach a steady value of 𝛿 = 0 . 0 1 0 6 Β± 0 . 0 0 0 4 for 𝑐 β‰₯ 0 . 6 .