Martin’s diameter

Ferefs diameter (Fig. 20-5) is the perpendicular projection, in a fixed direction, of the tangents to the extremities of the particle profile. Martin s diameter is a hne, parallel to a fixed direction, which divides the particle profile into two equal areas. Since the magnitude of these statistical diameters varies with particle orientation, these diameters have meaning only when a sufficient number of measurements are averaged. 

The microprocessor is programmed to recognize length and width, but the question of the correct diameter of irregular particles has remained controversial. For example, Martin s diameter is defined as the shortest line which divides the area of the image in half. A depiction of this is shown as follows ... 

To obtain a value for the dimensions of an irregular particle, several measurement approaches can be used Martin s diameter (defined as the length of a line that bisects the particle image), Feret s diameter (or end-to-end measurement, defined as the distance between two tangents on opposite sides of the particle parallel to some fixed direction), and the projected area diameter (defined as the diameter of a circle having the same area as that of the particle observed perpendicular to the surface on which the particle rests). With any technique, a sufficiently large number of particles is required in order to obtain a statistically valid conclusion. This is best accomplished by using a... 

Image analysis can be used to determine a variety of morphometric parameters including area, Feret s diameter, Martin s diameter, aspect ratio (ratio of minimum to maximum Feret diameter), perimeter, length, width, and form factor (the ratio of area/[perimeter]2), which can be related to specific particle shapes. Some of these functions are illustrated in Fig. 10 [14]. In addition, quantitative methods have been developed to measure particle shape [2,15,16]. 

As we just suggested, particle size and shape are important physical properties influencing powder flow and compaction. Particle size is a simple concept and yet a difficult one to quantitate. Feret s diameter, Martin s diameter, projected area diameter, specific surface diameter, Stokes diameter, and volume diameter are but several of the measurements that have been used to quantify particle size using a variety of methods. 

Martensitic reaction, 13 511 Martensitic stainless steels, 23 305 Martin s diameters, 18 147 Martin Lake supercritical furnace, 12 325, 326... 

Feret s diameter, l.) (the mean value of the distance between pairs of parallel tangents to the projected outline of the particle), and Martin s diameter, Du (the mean chord length of the projected outline of the particle[96] D DM=I 7.1. S A//b) are used in automated analysis of microscopic images [49,50],... 

Martin s diameter and Feret s diameter of a particle depend on the particle orientation under which the measurement is made. Thus, obtaining a statistically significant measurement for these diameters requires a large number of randomly sampled particles which are measured in an arbitrarily fixed orientation. Since Martin s diameter, Feret s diameter, and projected area diameter are based on the two-dimensional image of the particles, they are generally used in optical and electron microscopy. The principles of microscopy as a sizing method are discussed in 1.2.2.2. 

Two commonly encountered definitions of particle size are Feret s diameter and Martin s diameter. These refer to estimates of approxi-... 

Feret s diameter = 15 scale units Martin s diameter = 10 scale units Projected area diameter = 13 scale units... 

This measurement problem can be simplified somewhat by using the projected area diameter instead of Feret s or Martin s diameter. This is defined as the diameter of a circle having the same projected area as the particle in question. Figure 1.1 illustrates these three definitions. In general, Feret s diameter will be larger than the projected area diameter which will be larger than Martin s diameter. 

Figure 1.1 Illustration of three common definitions of particle diameter. In general, Martin s diameter is less than the equivalent area diameter, which in turn is less than Feret s diameter.

Martin s Diameter Proiected Area Diameter Maximum Horizontal Intercept... 

Microscopy Projected Area diameter Feret s diameter Martin s diameter Perimeter diameter Uiuolled diameter... 

Fig. 2.2 The projected area of a particle is orientation dependent. Martin s diameter (i/ ) is 246 pm, the Feret diameter dp) is 312 pm and the projected area diameter in stable orientation d ) is 252 pm (the particle is the same as in Figure 2.1)...

Martin s diameter df ) is the length of the line which bisects the area of the particle s projected area. The line may be in any direction, which must be maintained constant throughout the analysis [60,61 ]. 

It has been shown [63,64] that the relationship between specific surface and Martin s diameter is ... 

Since the surface-volume diameter is inversely proportional to S, the constant of proportionality being a minimum of six for spherical particles, Martin s diameter is systematically different to the surface-volume diameter. Experiments confirm that, on the whole, d/ shape function. For example dp/dj = 1.2 for Portland cement and 1.3 for ground glass [65]. 

Martin s diameter (dm). This is defined as the length of a line that dissects the image of the particle. 

Fig. 1 Influence of particle orientation on statistical diameters. The change in Feret s diameter is shown by the distances, df. Martin s diameter (dm) corresponds to the dashed lines.

Feret s Diameter A statistical particle diameter the length of a line drawn parallel to a chosen direction and taken between parallel planes drawn at the extremities on either side of the particle. This diameter is thus the maximum projection of the particle onto any plane parallel to the chosen direction. The value obtained depends on the particle orientation thus, these measurments have significance only when a large enough number of measurements are averaged together. See also Martin s Diameter. 

Martin s Diameter The length of a line which divides the projected outline of the particle into two equal areas and is paiallel to a given direction (nomially the hoiizomal cross-hait in a microscope field of view)... 

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