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Zusammenfassung:
Melting in two dimensions can successfully be explained with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario which describes the formation of the high-symmetry phase with the thermal activation of topological defects within an (ideally) infinite monodomain. With all state variables being well defined, it should hold also as freezing scenario where oppositely charged topological defects annihilate. The Kibble-Zurek mechanism, on the other hand, shows that spontaneous symmetry breaking alongside a continuous phase transition cannot support an infinite monodomain but leads to polycrystallinity. For any nonzero cooling rate, critical fluctuations will be frozen out in the vicinity of the transition temperature. This leads to domains with different director of the broken symmetry, separated by a defect structure, e.g., grain boundaries in crystalline systems. After instantaneously quenching a colloidal monolayer from a polycrystalline to the isotropic fluid state, we show that such grain boundaries increase the probability for the formation of dislocations. In addition, we determine the temporal decay of defect core energies during the first few Brownian times after the quench. Despite the fact that the KTHNY scenario describes a continuous phase transition and phase equilibrium does not exist, melting in polycrystalline samples starts at grain boundaries similar to first-order phase transitions.
