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Unimodal distributions with narrow bands were obtained, so the average particle size can be considered as representative of each fraction. Particle size distribution of sieved powder. In table 1 average particle size and specific surface experimental and theoretical of the iron powder fractions are reported. It can be observed in this table, the specific surface, S e , diminishes as average particle size increases; however, this decrease is also affected by particle morphology and microporosity.

Table 1. Physical properties of sieved powder. When the values of theoretical and measured specific surfaces are compared, differences in one order of magnitude are observed. This could be caused by particle morphology and internal microporosity. Smaller disagreements were found in fractions with smaller average particle size. It is in agreement with the nearly spherical shape of this fraction; as shown in figure 2 a.

This higher ratio can be explained in terms of the more irregular morphology of the iron particles; as shown in figure 2 d. In figure 2 it can be observed that all the powder fractions have irregular morphology. It could have been originated by the coalescence of almost spherical particles with several sizes. In table 2 , fluency and apparent density values of the powder fractions without lubricant, are reported. In all the samples small variations of fluency with average particle diameter were found.

Table 2.

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Apparent density and flow rate of the powder fractions without lubricant. As it can be seen in table 2 , the apparent density diminishes when the particle size is decreases, due to internal friction increases. On the other hand, flow rate is not only affected by the number of contacts between particles. It also involves other factors such as: ordering, spatial distribution and morphology of the powder particles.

Lubricant binders small powder particles and acts as a glue restricting particle sliding. In the other fractions no strong effect of lubricant on flow rate was found, once the standard deviation is considered. Only a modest improvement in flow rate was found as a consequence of the lower inter-particle friction. Table 3. Apparent density and fluency of the powder fractions with lubricant.

It can be observed in the table 3 that in the fractions with lubricant, apparent density reduced slightly as average diameter increased.

It could be caused by a better arrangement due to a smaller range of size distribution. Compressibility of the powder fractions is reported in table 4. Compressibility increases with average particle diameter. Bigger particles have less contact surface than smaller ones and then less inter-particle friction is found in the first case. This improves particle mobility in the first reordering step [17] and particles packing increases.

Table 4. Compressibility of the powder fractions with lubricant. Samples of the different powder fractions were compacted to a density of 6.

## Particle-size distribution

Which all have the same porosity. However, porous morphology, size and distribution changed with average particle diameter. This can be observed in the micrographs shown in figure 3. These differences in porosity are a consequence of the changes in grain size distribution in each powder fraction. Porosity is partially created by air or lubricant occlusion of the compacted powder particles. Porous size increases with particle size, but porous number decreases.

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However, porosity percentage remains almost constant when average particle size changes. Micrographs of transverse sections of green compacts pressed at 6.

Differences in porous morphology, size and distribution were quantified by roughness measurements. Results of this parameter, R a , of each fraction are shown in figure 4. It can be observed that R a increases with particle size. Measured roughness in each powder fraction. Results of green strength measurements are shown in figure 5 a.

Green strength reaches a maximum value at intermediate particle sizes due to the effect of particle morphology and number of bonds contact zones during compaction. In fractions with small particle size a more spherical shape causes less interlocking between particles.

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In fractions with large particle size a fewer average number of mechanical bonds between particles produces weaker samples. Then, the maximum in green strength is observed at intermediate particle sizes. In this case the conditions of particle morphology and number of bonds are more favorable to obtain higher mechanical strength [18]. It can also be observed that the maximum in green strength was measured in the sample formed by compaction of the powder fraction having the most irregular shape. Transverse rupture strength decreases as powder diameter increases; as shown in figure 5 b.

This is convenient when the majority of particles in a sample are relatively close to spherical in shape, but can cause problems when equivalent diameters must be used for more arbitrarily shaped particles. Several different attributes can be chosen to determine the size of an "equivalent sphere".

Most commonly particles are modelled as spheres of equivalent volume, which assuming constant density, may be considered interchangeable with mass. It is the diameter which, when all particles in a sample are arranged in order of ascending mass, divides the sample's mass into specified percentages.

## Particulate Systems Analysis: Particle & Particle Systems Characterization: Vol 23, No 2

The percentage mass below the diameter of interest is the number expressed after the "D". The D50 is also known as the "mass median diameter" as it divides the sample equally by mass. This can be most clearly demonstrated using the particle size distribution graph below.

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This shows the particle volume distribution and cumulative volume of the sample. While D-values are based on a division of the mass of a sample by diameter, the actual mass of the particles or the sample does not need to be known. A relative mass is sufficient as D-values are concerned only with a ratio of masses.

This allows the optical measurement systems discussed above to be used without any need for sample weighing. Each particle's diameter is therefore cubed to give its relative mass. These values can be summed to calculate the total relative mass of the sample measured. The corresponding D value for each of these is the diameter of the last particle added to reach the required mass percentage. For a guide to particle sizing techniques and definitions used within the pharmaceutical industry download the PDF below.

This Cookie Policy outlines our policy concerning the use of cookies on www. Determination of particle size distribution by FMR measurements. Walter S. Folly and Ronaldo S. Knowledge of particle size distribution is very important for the study of magnetic fluids, magnetic powders and other magnetic systems. In this work, we describe a simple method for its determination from FMR measurements.