Equivalent Projection Area of a Circle

Equivalent Projection Area of a Circle Equivalent projection area of a circle (Fig. 21-3) is widely used for the evaluation of particle sizes from the projection area A of a nonspherical particle. 

Note that the projected area is the area of the object projected on the perpendicular to the flow plane for a sphere, this is equivalent to the area of a circle with the same radius. Thus, the following well-known definition is derived (Perry and Green, 1999) ... 

Particle shape index is defined as the projected area of the particle divided by the area of a circle having a diameter equivalent to the maximum projected length of the particle. 

The equivalent circle diameter (the diameter, in microns, of the circle with the same area as the projected area of a particle) is plotted in (A). 

Comparing the projected area of the particle with a series of circles, the equivalent spherical diameter is obtained, which describes the particle for the orientation in which it is measured. 

An irregular particle can be described by a number of sizes. There are three groups of definitions the equivalent sphere diameters, the equivalent circle diameters and the statistical diameters. In the first group are the diameters of a sphere which would have the same property as the particle itself (e.g. the same volume, the same settling velocity, etc.) in the second group are the diameters of a circle that would have the same property as the projected outline of the particles (e.g. projected area or perimeter). The third group of sizes are obtained when a linear dimension is measured (usually by microscopy) parallel to a fixed direction. 

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed direction (29) Feret diameter, the projected length with respect to a reference direction (30) and the diameter of equivalent surface area, the diameter of a circle the area of which is equivalent to the projected area of the partide in question (3). 

Equivalent projected area diameter The diameter of a circle having the same area as the projected area of the species, while lying in a stable position... 

Figure 25 shows the projection areas of growing particles after 0, 20, 40, and 60 min of polymerization (Fig. 25a) and demonstrates the particle growth evaluation (Fig. 25b). These collected images are processed to determine the projection area of each catalyst particle. Although the projection area is the primary quantity measured, it is easier to comprehend the size of the particles in terms of their diameter and volume. Hence, the projection area is used to estimate the diameter of a circle of equivalent area (equivalent circle diameter, BCD) and from that the volume of a sphere having an equivalent projection area (equivalent sphere volume, ESV).

Two important morphological parameters characterizing ball-milled powders are the particle and grain size of constituent phases within the powders. In our laboratory, the size measurement of the powder particles is carried out by attaching loose powder to sticky carbon tape and taking pictures under secondary electron (SE) mode in the SEM. The images are then analyzed by an image analysis software. The size of the powders is calculated as the particle equivalent circle diameter, ECD = AA/nf, where A represents the projected particle area. Usually from -300 to 700 particles are analyzed for each batch. 

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