Size Measurements

Various techniques are used to measure the size of irregularly shaped particles when viewed through a microscope. This has resulted in different measurements, which are used to classify these two-dimensional particle images in terms of an equivalent spherical particle. Accepted measurements (Fig. 1) include:

• Feret's diameter (F): The maximum length of the particle measured in a fixed direction

• Martin's diameter (M): The length of a line that bisects the area of the particle image; all particles measured in the same direction

• Project area diameter (da): The diameter of a circle with the same area as the two-dimensional image of the particle

• Longest dimension: The maximum Feret's diameter for each particle: no set direction

• Perimeter diameter (dp): The diameter of a circle having the same circumference as the perimeter of the particle

• Maximum horizontal intercept: The length of the longest line that can be drawn through the particle in a fixed direction

Fig. 1 Techniques for measuring sizes of irregularly shaped particles. See text for identification of variables.

Feret's diameter is the easiest to measure manually. The average Feret's diameter is related to the perimeter of the convex hull of the particle, as shown in Fig. 2, by the relationship:


where PCH is the perimeter of the convex hull. Martin's diameter is related to the specific surface Sv of the particle by:

The projected area diameter gives the best estimate of the true cross-sectional area of the particle.



Fig. 2 Feret's diameter

Generally, the three diameters above are related to one another by the expression M < da < F. Their ratios remain fairly constant for a given material. The expression F/M has been used as a shape function, which is equal to 1 for spherical particles and increases in magnitude as particle shape becomes more acicular. Perimeter diameter and maximum horizontal intercept (or longest chord) are measured easily by some of the automatic particle sizing analyzers.

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