The softening of two-dimensional colloidal crystals

According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory a two-dimensional (2D) crystal melts when bound pairs of dislocations dissociate into single dislocations. The temperature at which dislocation pairs unbind can be identified by means of the Young's modulus K passing through 16 pi. In a previous paper (von Grunberg et al 2004 Phys. Rein Lett. 93 255703) we analysed video-microscopy data of 2D colloidal crystals, obtained elastic constants from normal-mode band-structures, and confirmed that the unbinding temperature is indeed close to the melting temperature. Processing the same data we now obtain elastic constants directly from an analysis in real space by computing relative mean-square displacements as a function of the lattice site separation. We have also carried out Monte Carlo simulations to check for the thermal softening of the colloidal crystal. Both studies confirm our previous results. We finally compare our results to the corresponding curves for a 2D electron solid on the surface of liquid helium.