A Novel Method for the Determination of the Lateral Dimensions of 2D Rectangular Flakes.

We present a novel method for the determination of the lateral dimensions of thin rectangular flakes, as they exist randomly dispersed in flake composites. Knowledge of flake size and shape is essential for the correct prediction of the mechanical, electrical, thermal and barrier properties of flake composites. The required information is the distribution function of lengths of the lines representing the intersection of flakes with a sectioning plane, as seen in cross-sections of composite samples used in optical or electron microscopy or obtained using tomographic imaging techniques. The key observation is that the major peak of the distribution function coincides with the short dimension S of the flake while a secondary peak corresponds to its long dimension W. These observations are explained using Monte-Carlo simulations, as well as deterministic, geometry-based modeling and probability analysis. Since the strength of the secondary peak diminishes with increasing flake aspect ratio r=W/S, we develop two additional methods for the determination of W. The first finds W from the maximum intersection length; this procedure is justified by computing the relevant probability fields through Monte-Carlo simulations. The second method finds r from the average intersection length and is valid in the range 1