Particle Size Distributions from Electron Microscopy Images: Avoiding Pitfalls

An important property of heterogeneous catalysts is the size distribution of the catalytically active phase. This is typically obtained form a long list of particles sizes (manually) compiled from electron micrographs. These raw data are then represented as histogram to approximate the underlying continuous distribution. Selecting the proper bin width, w, for the histogram is important as one has to balance resolution with statistical significance of the bin count in each bin. For most published particle size distributions, the selection criterion for w is not reported transparently. In this contribution, it is demonstrated how operator's bias can be avoided by using estimators for w that are based on the raw data only. First, synthetic data are analyzed to illustrate the importance of selecting a proper value for w. Then a survey of published data is presented which reveals that the values for the bin width w was chosen too large in many cases. By using statistically founded bin width estimators not only is operator's bias avoided but also hidden features in the distribution are sometimes revealed; in one case, a distinct bimodal distribution was missed in the original report. Finally, a work-flow is suggested which avoids operator's bias to generate particles size distributions from a list of experimentally determined particle sizes.