Electrical sensing zones, low-angle laser light scattering, field flow fractionation, photon correlation spectroscopy, hydrodynamic chromatography, and laser obscuration time are just some of the latest high-tech methodologies currently being used for particle size analysis. Unfortunately, in our quest to embrace the ultramodern, we sometimes dismiss the traditional methods such as microscopy and sedimentation. However, we do so at our cost because both of these techniques now offer the highest resolution and widest size range available today, extending the lower limits down to nanometer sizes. This application note looks at the importance of calibration and particle orientation in microscopy and image analysis.
The vital statistics
The most well-known parameter in powder metrology is the equivalent spherical diameter of the particles. However, this rather limited descriptor is sometimes inadequate to explain some major differences between two particles that apparently have exactly the same size. For example, the equivalent spherical diameter of the human body is not that informative, and more “vital statistics” give a better impression of size. Similarly, weight alone as a guide to obesity is not a good definition, and shape (height) must be brought into the equation in the form of the body mass index. One would never dream of describing a giraffe by its equivalent spherical diameter, yet that is exactly what we often do in the field of particle size analysis.
Particle shape is therefore being recognized increasingly as an important parameter, and enormous technological developments have been made in recent years. These include advances in microscope and lens design coupled with increased computer power, and the development of high-performance digital cameras. It is now possible to capture, process, and store images in seconds rather than hours so that millions of particles can now be mapped in detail, giving excellent repeatability.
In any particle metrology technique, results without calibration have limited value, and microscopy is no exception. However, in microscopy there are more elements than most that need calibrating; for example, the planarity of the lenses, the uniformity of the illumination source, and the influence of ambient light.
In addition, the aspect ratio of the pixel array in the charge-coupled device (CCD) camera needs to be known; otherwise any distortion could be falsely attributed to the particle shape. Some detectors have been found to have differences of up to 10% between the X and Y directions.
As particles decrease in size, other factors such as focusing, edge detection, and diffractional enlargement (an aberration based on physical size) also need to be considered. These factors can easily add a further 10% uncertainty in the measurement.
Figure 1 - Image analysis reference graticule (NPL).
A useful calibration starting point is the National Physical Laboratory (NPL) stage reference graticule from the U.K. There are several very useful fields on this graticule that are invaluable to image analysis (see Figure 1).
First, the certified grid must be used for correcting any pixel array distortion (Figure 1a). Depending on the magnification being used, an appropriate square grid should fill the field of view and the X and Y dimensions compared. Having made any necessary axial compensation, the calibration of each lens can begin. Either the NPL or NIST may be used.
The uniformity of the illumination source and/or the planarity of the lenses can be checked using the array of 15-μm spots (Figure 1b). Any deviation from the certified values indicates poor-quality lenses or uneven illumination.
Finally, for sizes from 48 μm down to 3 μm, there is a root 2 array of certified spots (Figure 1c). These are especially useful for setting the threshold or the exact shade of gray that corresponds to the particle edge.
Usually, for spots down to about 11 μm, there will be good correlation using the calibration from the large grid or linear scale, but below 10 μm, allowances must be made for other factors intruding on the calibration, for example, particle enlargement by edge diffraction or thresholding issues mentioned above.
Figure 2 - Polydisperse reference standard.
The final check on the calibration of the image analyzer, especially when working at high magnifications, is to use NIST-traceable latex standards. Unlike the 2-D spots on the NPL graticule, the monodisperse latex standards are 3-D and thus are a better model for particles being measured by microscopy. However, for calibrating over the expected dynamic range of the powder being analyzed, polydisperse standards should be used (see Figure 2).
Although microscopy can provide a measure of shape, it must be remembered that, despite its advantage over single-dimension methods, microscopy is still only operating in two dimensions. In the case of asbestos fibers, for example, the fibers are essentially circular in cross-section; therefore, provided they are constrained between the microscope slide and the coverslip, they are always in a good orientation for measurement. Similarly, if the particles are orientated in a liquid flow field for continuous analysis, accurate length-to-diameter ratios can be obtained.
Figure 3 - Rotating a rod out of the measuring plane can produce a range of aspect ratios when measuring in two dimensions.
A problem arises, however, when trying to analyze a random orientation of fibers, for example, when they are dropped or carried in an air current through the measuring zone. A single rod can have an infinite number of 2-D sizes from the end-on cross-section to the maximum rod length (Figure 3); hence a false range of shapes could be reported if, for instance, air curtains are not used to align the particles in the analysis zone.
In principle, microscopy with image analysis is an easy-to-understand method of particle size analysis—after all, “seeing is believing.” However, we all know the doubts cast on that other old adage, “the camera never lies.”
In the latest evolution, desktop electron microscopes no bigger than a computer now offer magnifications up to 20,000. In practice, the technique can be difficult to implement because of the large number of uncertainties associated with the various elements of the system. Nevertheless, if all the areas of calibration are rigorously observed, the technique is an unparalleled tool for detailed analysis in particle metrology.
Dr. Rideal is with Whitehouse Scientific Ltd., The Whitehouse, Whitchurch Rd., Waverton, Chester CH3 7PB, U.K.; tel.: +44 (0) 1244 332626; fax: +44 (0) 1244 335098; e-mail: [email protected]