Comparison of 2D melting criteria in a colloidal system

TL;DR

This study compares various criteria for identifying phase transitions in a 2D colloidal system, confirming the effectiveness of specific structural and dynamical measures in detecting melting points consistent with KTHNY theory.

Contribution

It systematically evaluates multiple melting criteria in a 2D colloidal system, highlighting the most effective measures for phase transition identification.

Findings

Bond order correlation function and susceptibility best identify the hexatic-liquid transition.

2D dynamic Lindemann parameter clearly detects the crystal-hexatic transition.

Certain criteria outperform others in systems with long-range repulsion.

Abstract

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal - hexatic and hexatic - isotropic liquid phase transition for the same experimental data of the given setup. Those criteria are the bond orientational correlation function, the Larson-Grier criterion, 2D dynamic Lindemann parameter, the bond-orientational susceptibility, the 2D Hansen-Verlet rule, the L\"{o}wen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long range repulsion, the bond order correlation function and bond order susceptibility works best to identify the hexatic - isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic - crystalline transition.