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Abstract
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Local order parameters for the characterization of liquid and different two- and three-dimensional
crystalline structures are presented. The order parameters are expressed in terms of the angular
correlations between a vector (defined in terms of the spherical harmonics, identifying the local
environment around a central particle) and its neighboring vectors. For the three-dimensional systems,
we have undertaken simulation of the Lennard-Jones (12-6) particles and metallic systems at the
melting temperature. The proposed order parameters are shown to accurately discriminate between
liquid, fcc, hcp, and bcc phases. The simulated two-dimensional systems consist of liquid, Kagome,
square, honeycomb, and hexagonal phases formed from a solution of triblock Janus colloidal particles,
sedimented on the top of a supporting surface. The presented order parameters resolve all phases.
A comparison was made between the predictive ability of the present order parameters and the popular
three-dimensional [Lechner and Dellago, J. Chem. Phys., 2008, 129, 114707] and two-dimensional
[Mermin, Phys. Rev., 1968, 176, 250] order parameters in the literature in the identification of crystal
structures. In both cases, advancements in the present scheme, over the existing methods in the
literature, are seen.
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