Particle histograms

The particle histograms show peaks in N50 and N100 concentrations during spring of over 1,000 particles cm-3. Another smaller mode of low concentrations was also visible around 500 particles cm 3 in both N50 and N10o... 

It will be convenient to deal first with the distribution aspect of the problem. One of the clearest ways in which to represent the distribution of sizes is by means of a histogram. Suppose that the diameters of SOO small spherical particles, forming a random sample of a powder, have been measured and that they range from 2-7 to 5-3 pm. Let the range be divided into thirteen class intervals 2-7 to 2-9 pm, 2-9 to 3-1 pm, etc., and the number of particles within each class noted (Table 1.5). A histogram may then be drawn in which the number of particles with diameters within any given range is plotted as if they all had the diameter of the middle of the... 

Fig. 1.12 Histogram showing the distribution of particle sizes for the sample of powder referred to in Table 1.5. (After Herdan )...

The distribution curves may be regarded as histograms in which the class intervals (see p. 26) are indefinitely narrow and in which the size distribution follows the normal or log-normal law exactly. The distribution curves constructed from experimental data will deviate more or less widely from the ideal form, partly because the number of particles in the sample is necessarily severely limited, and partly because the postulated distribution... 

Bulk particulates of various sizes can be analysed to display their particle size distribution and a frequency histogram plotted, as shown in Figure 1.8. 

Fig. 2. TEM images and the corresponding particle size distribution histograms of (a) 6 nm, (b) 7 nm, (c) 8 nm, (d) 9 nm, (e) 10 nm, (f) 11 nm, (g) 12 nm, and (h) 13 nm sized iron nanoparticles showing the one nanometer level increments in diameter. The scale bars at the bottom of the TEM images indicate 20 nm...

Particle size data are usually represented by a histogram, where the dimensions of the particles are plotted against their frequencies of occurrence. 

Figure 1 represents a particle size distribution histogram. Where a preponderance of smaller particles occurs, the curve is right skewed and where a preponderance of larger particles occurs, the curve is left skewed. The symmetrical histogram is rarely found in practical applications. 

For the analysis, we developed a new method that makes it possible to observe correlated potentials between two trapped particles. The principle is shown in Figure 7.5. From the recorded position fluctuations of individual particles (indicated by the subscripts 1 and 2), histograms are obtained as a function of the three-dimensional position. Since the particle motion is caused by thermal energy, the three-dimensional potential proflle can be determined from the position histogram by a simple logarithmic transformation of the Boltzmarm distribution. Similarly, the... 

Since the histogram gives a probability density function of the particle position, the correlation in the velocities Vy and V2j in the j-direction causes the change in the shape of the histogram plotted against Vy and V2j, due to the different coefficient y — Pj in... 

Figure 3. Transmission electron microphotographs and histograms of the particle size distribution for Pd nanoparticles synthesized at Wo 3 (a) and 7 (b) [23] and isolated via the proposed method.

Histograms of gold particle size distributions are shown in Figure 4. 

Figure 4. Particle size histograms for the gold deposited onto various carbon samples. (Partially reprinted from Topics in Catalysis, 122 (1) 2007, pg 248, with permission from Elsevier Science).

Pt particle size distributions (histograms) measured directly from TEM images are shown in Figure 6. 

Figure 4. Electron micrographs and relative histograms of the particle size distribution of commercial Rh/y-Al203 (Bl) and Rh/y-Al203 (MVS) (B2). (Reprinted from Ref [24], 2003, with permission from Elsevier.)...

Figure 6. Electron micrographs and relative histograms of the particle size distribution of Pd/PDMP (MVS).

Figure 7. Electron micrographs and relative histograms of the particle size distribution of 5% (w/w) of Pt/y-Al203 systems obtained (a) from the solution containing Pt particles with hydrodynamic diameter of 0.9 nm (b) from the solution containing Pt particles with hydrodynamic diameter of 1.5 nm.

Figure 2. Comparison of the simulated velocity distribution (histogram) with the Maxwell— Boltzmann distribution function (solid line) for kgT —. The system had volume V — 1003 cells of unit length and N = 107 particles with mass m = 1. Rotations (b were selected from the set Q — tt/2, — ti/2 about axes whose directions were chosen uniformly on the surface of a sphere.

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