Local orderings in the melting process of a square crystal and in the resulting liquid

Using Brownian dynamics simulations we investigate the melting processes of a square crystalline lattice of colloidal particles interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential. For temperatures slightly lower than the transition one, we found a proliferation of small liquid clusters surrounded by the square lattice. These clusters are not static, quite the opposite, they have an intense dynamics and are continuously formed and destroyed over time. However, no unbound topological defects are observed. At the transition temperature, one of these liquid clusters starts to grow, until the entire system becomes in the liquid phase, then, characterizing a first-order phase transition. The tetratic intermediate phase, as given by the KTHNY theory, was not observed. Moreover, the liquid phase exhibits a considerable number of crystalline clusters having square and triangular orderings, which remain present even when increasing temperature by an order of magnitude. As the temperature increases, structural changes within the liquid phase are analyzed by evaluating the number and sizes of the square and triangular clusters. A transition of the dominant clusters is observed.