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Conventional shape descriptors, formed from a ratio of two particle size measurements, are among the simplest of the many methods used for quantitative particle shape characterization. However, a significant limitation of using one of these shape descriptors is that its value is often not unique to a specific shape. Use of several different shape descriptors may circumvent this problem but, as particle size can be defined in a large number of ways, a similarly large number of shape descriptors can be defined. While some differ substantially, others are only subtly different, conveying similar information. Thus, it is not obvious which of the many possible descriptors should be utilized. In this paper, two-dimensional particle shape descriptors obtained by image analysis of six different commercially sourced powders were considered. Techniques of cluster and correlation analysis were applied to assist in identifying redundant descriptors for shape characterization of these powder particles, allowing for efficient description of shape using a reduced set. It was found that at least two descriptors are required: aspect ratio and the square root of form factor. Significantly, each descriptor is most sensitive to a different attribute of shape: elongation and ruggedness, respectively.

The quantitative use of atomic force microscopes in lateral mode for friction measurements has been limited by uncertainty about reliable calibration techniques. This article describes a comparison of three methods that have been proposed for the calibration of the lateral sensitivity of atomic force microscopes: (a) one based on movement of the photodiode assembly, (b) one based on the slope of the friction-loop while the contacting surfaces are in static contact, and (c) one based on a comparison of the lateral force signal on a surface with changing slopes of known orientation. All three methods gave comparable results thereby confirming their robust nature, and also confirming the validity of atomic force microscope methods for lateral force measurement. However, (b) indicated that for the commercial instrument used here, the lateral signal sensitivity is load dependent. A simple extension to (a) revealed the nature of this dependence: a misalignment of the four-quadrant photodiode detection system with respect to the alignment of the reflected beam path resulting in a coupling of the normal and lateral signals. The result is that the lateral signal does not scale directly with friction, requiring that for friction versus applied load studies, lateral signal calibration be performed across the full range of applied loads of interest. To a greater or lesser extent, this shortcoming will be evident in a wide range of commercial instruments. All three methods studied here have special advantages: (a) provides the most complete information about the detector response, (b) provides a calibration method when friction characteristics of colloid probes of a wide range of possible materials are of interest, and (c) has the advantage of also providing information about the state of the tip geometry.

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