Diameter equivalent circle

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. 

Fig. 2.3 (a) Scanning electron micrograph of the morphology of as-received Tego Magnan MgH powder and (b) powder particle size distribution (equivalent circle diameter, ECD)... 

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. 

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).

The particles in Fig. 30 represent an excellent replica of the catalyst particle distribution through the polymer particle distribution the spherical form of the initial particles is retained and the equivalent circle diameters are enlarged from about 90 pm to about 360 pm after 190 min polymerization time. Their dependence on time indicates a very active catalyst system with a fast copolymerization rate and a fast particle expansimi caused by the loosely agglomerated MgQ2 support and the volume increase of the amorphous copolymer. It seems that this copolymerization system follows the multigrain model. 

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). 

It is interesting to note that where differences are apparent, the TSA and TKA particles are similar to one another and generally larger (as shown by the equivalent circle diameter data) and more elongated (as shown by the aspect ratio and elongation data) than THA particles. 

An irregular particle can be described by a number of sizes depending on what dimension or property is measured. There are basically three groups of sizes equivalent sphere diameters , equivalent circle diameters and statistical diameters . 

Table 2.2 A list of definitions of equivalent circle diameters ...

Beside the porosity, also the pore size distribution plays a decisive role for granule stability. One approach is the determination of spatial relationships between the particles. This parameter can be described by the surface spacing Dnn-surf and can be calculated in simplified form with (11.9) with the help of the center of gravity spacing center and the equivalent circle diameters (BCD) of two particles ( /particle,... 

In addition, more detailed measurements of equivalent circle diameter (ECD), which is defined as the diameter of a circle with an area equivalent to the area of the particle, and has units of length ... 

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