Machinery's Handbook, 31st Edition
1524 Characteristics of Metal Powders samples, with particles in the size range from microscopic up to 0.080 in. (2 mm). This method has inherent advantages that 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. Typically, an He-Ne laser (l = 632.8nm) in the 5 mW to 10 mW range is used as the coherent light source. 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 inten sity, whereas small particles scatter light at wider angles but with low intensity. 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, re- producible 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. 1). 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. 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 Mie theory and Fraunhofer approximation. The Mie theory describes scattering by homogeneous spheres of arbitrary size, and pro- vides 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 0.002 in. (0.05 mm) in diameter, as stated in the international standard for laser diffraction measurements. The Mie approach does not work well for extremely fine particulates in the range below 100 nm, possibly because of increased sensitivity to changes in the refractive index that occur with these materials.
Wide Angle Detection System
Laser Light Source
Obscuration Detector
Focal Plane Detector
Focusing Lens
Sample Cell
Fig. 1. Typical Laser Diffraction Instrument Layout Fraunhofer Diffraction: For very large particles (relative to the wavelength of light), the diffraction effect can be exploited without reference to the Mie theory or the complex index of refraction. Diffracted light is concentrated in the forward direction, forming the so-called Fraunhofer diffraction rings. The intensity and distribution of diffracted light around the central beam can be re- lated to particle size, again assuming spherical geometry. The benefit of using Fraunhofer diffraction is that the interpretation is not dependent on the absorptive or refractive prop- erties of the material. On the other hand, 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.
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