its diameter (D). However, as a particle is rarely a perfect sphere, there are many different techniques that have been devised for determining particle size distribution; for a metal powder, screening techniques and laser diffraction have become the preferred choices.
a) Screening Method
The most common method used for measured particle size is the use of screens (sieves) of different mesh sizes. The term mesh count is used to refer to the number of openings per linear inch of screen.
The basic principle of sieving techniques is as follows. A representative sample of a known weight of particles is passed through a set of sieves of known mesh sizes. The sieves are arranged in downwardly decreasing mesh diameters. The higher the mesh size number, the smaller is the opening in the screen. For example, a mesh size No. 200 has an opening of 74 µm, size No. 100 has an opening of 149 µm, size No. 10 has an opening of 2.00 mm. The sieves are mechanically vibrated for a fixed period of time. The weight of particles retained on each sieve is measured and converted into a percentage of the total sample. This method is quick and sufficiently accurate for most purposes.
b) Laser Diffraction Method
Laser diffraction, alternatively referred to as low angle laser light scattering (LALLS), can be used for the nondestructive analysis of wet or dry samples, with particles in the size range of 0.02 to 2000 µm; this method has inherent advantages which make it preferable to other options for many different materials.
Laser diffraction-based particle size analysis relies on the fact that particles passing through a laser beam will scatter light at an angle that is directly related to the particles’ size. As particle size decreases, the observed scattering angle increases logarithmically. Scattering intensity is also dependent on particle size, diminishing with particle volume. Large particles, therefore, scatter light at narrow angles with high intensity, whereas small particles scatter light at wider angles but with low intensity (Fig. 4.1).
A typical system consists of: a laser, to provide a source of coherent, intense light of fixed wavelength; a series of detectors to measure the light pattern produced over a wide range of angles; and some kind of sample presentation system to ensure that the material being tested passes through the laser beam as a homogeneous stream of particles in a known, reproducible state of dispersion. The dynamic range of the measurement is directly related to the angular range of the scattering measurement, with modern instruments making measurements from around 0.02 degree to beyond 140 degrees (Fig. 4.2). The wavelength of light used for the measurements is also important, with smaller wavelengths (e.g., blue light sources) providing improved sensitivity to sub-micron particles.
Fig. 4.1 Light scattering patterns observing for: a) large particle; b) small particle.
Fig. 4.2 Typical laser diffraction instrument layout.
In laser diffraction, particle size distributions are calculated by comparing a sample’s scattering pattern with an appropriate optical model. Traditionally, two different models are used: the Fraunhofer approximation and the Mie theory.
The Fraunhofer approximation was used in early diffraction instruments. It assumes that the particles being measured are opaque and scatter light at narrow angles. As a result, it is only applicable to large particles and will give an incorrect assessment of fine-particle fractions.
The Mie theory provides a more rigorous solution for the calculation of particle size distributions from light scattering data. It predicts scattering intensities for all particles, small or large, transparent or opaque. The Mie theory allows for primary scattering from the surface of the particle, with the intensity predicted by the refractive index difference between the particle and the dispersion medium. It also predicts the secondary scattering caused by light refraction within the particle. This is especially important for particles below 50 µm in diameter, as stated in the international standard for laser diffraction measurements.
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