Bond-orientational Order in Melting of Colloidal Crystals
  Using Brownian dynamics simulation, we study the orientational order in melting transition of colloidal systems with $'$soft$'$ Yukawa potential. The bond-orientational order parameter $\Phi_{6}$ and the bond-orientational order function $g_B(r)$ are calculated in two-dimensional systems. It is found that a two-stage transition and the hexatic phase are indeed existent in two-dimensional melitng, which is consistent with the prediction of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For comparing with the melting process in three-dimensional systems, the probability distribution of single-particle local order parameter is introduced. Based on the extensive simulations, it is qualitatively suggested that the breakdown of local order only occurs on the fractional part of the colloidal systems for the two-dimensional melting, but in three-dimensional melting, this breakdown takes place on the whole systems at the same time. 
Xin Qi, Yong Chen, Yan Jin, and Yao-Hui Yang