Determination of Cr particle sizes in thin dilute Cr-in-Cu films from measurement statistics

A variance-based method of analysis is described in which the clump size (average number of solute atoms aggregated together) of one atomic species (solute) in a matrix can be determined from a set of composition measurements taken from volumes which contain a much greater number of solute atoms than the clump size. The observed variance of the solute concentration measurements, each of which is computed from a discrete number of counts, is compared to an expected variance derived from a statistical model, assuming a random distribution of solute atoms measured with the same number of counts. The difference between the expected and observed variance indicates the clump size. This method is used to determine the degree of segregation of Cr in thin films of Cr in Cu. The films are produced by evaporation of bulk billets of the desired composition, and the concentration of Cr is measured with high resolution electron beam induced X-ray spectroscopy in a scanning transmission electron microscope (STEM). Cr is practically insoluble in Cu at room temperature: the degree of segregation is determined by the kinetics of the evaporation. From sets of composition data taken from small volumes (tens to hundreds of thousands of atoms total, and a few hundred atoms of Cr), we calculate an average Cr clump size of eight atoms or less, and we conclude that the average Cr clump size is less than 20 atoms.