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Abstract

We use super-paramagnetic colloidal particles confined by
gravitation to a flat water-air interface as a model system to study the
non-equilibrium liquid-solid phase transition in two dimensions. The
system temperature is adjustable by changing the strength of an external magnetic field perpendicular to the water-air interface. Increasing
the magnetic field on a timescale of milliseconds quenches the liquid to a
strongly super-cooled state. If the system is cooled down out of equilibrium the solidification differs drastically from the equilibrium melting
and freezing scenario as no hexatic phase is observable. The system
solidifies to a polycrystalline structure with many grains of different
orientations. Since the local closed packed order in two dimensions is
sixfold, in both the fluid and the crystalline state, sensitive measures
have to be developed. In the present manuscript we compare different
methods to identify crystalline cluster locally and motivate the threshold values. Those are chosen in comparison with the isotropic fluid
on one hand and large mono-crystals in thermal equilibrium on the
other hand. With the given criteria for crystalline cluster the cluster
are found not to be circular and fractal dimensions of the grains are
given.