Bond-orientational order in melting of colloidal crystals

Using Brownian dynamics simulation, we study the orientational order in the melting transition of a colloidal system with a 'soft' Yukawa potential. The bond-orientational order parameter φ ₆ and the bond-orientational order function g _B(r) are calculated in two-dimensional systems. We found that a two-stage transition and a hexatic phase indeed exist in two-dimensional melting, which is consistent with the prediction of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For comparing with the melting process in three-dimensional systems, we introduce the probability distribution of the single-particle local-order parameter. Based on extensive simulations, the breakdown of local order is qualitatively suggested only to occur on the fractional part of the colloidal system for the two-dimensional melting, but in three-dimensional melting, that breakdown takes place on the whole system at the same time.