TY - JOUR
T1 - The geometrical structure of 2D bond-orientational order
AU - Bowick, Mark
AU - Travesset, Alex
N1 - Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2001/3/2
Y1 - 2001/3/2
N2 - We study the formulation of bond-orientational order in an arbitrary two-dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, in both the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.
AB - We study the formulation of bond-orientational order in an arbitrary two-dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, in both the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.
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U2 - 10.1088/0305-4470/34/8/301
DO - 10.1088/0305-4470/34/8/301
M3 - Article
AN - SCOPUS:0035794096
VL - 34
SP - 1535
EP - 1548
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 8
ER -