Statistical study of two-dimensional colloidal crystals based on microscopic images and optical diffraction

Through the direct measurement on the microscopic image of a two-dimensional (2-D) colloidal polycrystalline array, the statistical distribution profiles of the crystalline grain size and the defect density were determined. At the same time, an optical diffraction analysis method was developed to extract the mean values of these two parameters from the measured diffraction pattern. Results from the two methods were compared. We found that both parameters obey the Poisson distribution. For grain size, the discrete unit of the distribution is the average distance between the neighboring defects. It implies that the growth of crystalline grains displays a process of increasing grain size with this quantum value. A possible reason for this distribution is discussed based on the atomic force microscopy (AFM) images.