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Projection effects in electron micrographs of three-dimensional fractal aggregates: theory and application to gas-evaporated specimens

The authors analyse electron micrographs which show projections of three-dimensional fractal aggregates. Shadowing and finite size effects in the projection are treated by calculations for two model systems, namely a single aggregate and a connected aggregate. The calculations allow the authors to obtain the fractal dimension of the aggregates from the measured effective dimensions on the micrographs. Aggregates of metal particles were produced by gas evaporation and studied by electron microscopy. The authors analysed the structure of the specimens by the connected-aggregate model. Fractal dimensions in the range 1.9 to 2.0 were found. This is in good agreement with the cluster-cluster aggregation model if the aggregating particles follow linear trajectories.