MICROSCOPIC INVESTIGATIONS OF THE SINGLE-PARTICLE DYNAMICS IN COLLOIDAL CRYSTALS

In this paper we investigated the single particle dynamics in a colloi dal crystal by means of video microscopy and digital imaging methods. To obtain the self term of the van Hove function G(s)(x, tau) with a r easonable good statistical accuracy we analyzed up to two million part icle displacements per time channel tau of G(s)(x, tau), which corresp onds to the analysis of 3000 video frames, each with approximately 100 0 particles. It was found that the Gaussian approximation almost perfe ctly accounts for the experimental results, so that the time evolution of G(s)(x, tau) can solely be described by the mean square displaceme nt [x(2)(tau)]. The measured mean square displacements were compared w ith the model of a Brownian particle bound in a harmonic potential [Ph ysica A 157, 705 (1989)]. The experimental curves approach the plateau value [x(2)(tau-->(infinity))] Of the mean square displacement much s lower than is predicted by the model. From the plateau value of the me an square displacement the Lindemann parameter was determined for vari ous samples. (C) 1996 American institute of Physics.