LASER Diffraction

The LASER diffraction (LAS) method involves the detection and analysis of the angular distribution of light produced by a LASER beam passing through a dilute dispersion of particles. Typically, a He-Ne LASER (=632.8 nm) in the 5 mW to 10 mW range is employed as the coherent light source, but more recently solid-state diode LASERs have come into use and provide a range of available wavelengths in the visible and UV spectrum. Since the focal volume of the beam senses many particles simultaneously, and thus provides an average value, it is referred to as an ensemble technique. With the exception of single particle optical scattering (SPOS), all scattering methods are ensemble techniques, and only ensemble methods will be considered here. There are a number of different diffraction and scattering phenomena that can be utilized for particle sizing. Likewise, there are a number of different ways to define and classify these methods, depending on the underlying principle or its application. We have chosen here to classify all time-averaged scattering and diffraction phenomena involving LASER optics, under the general heading of LASER diffraction; however, it should be noted that "LASER diffraction" is often used in a more narrow way to refer to techniques that utilize only low-angle scattering. See Table 1 for a list of equivalent or related methods.

Strictly speaking, one can differentiate between light waves that are scattered, diffracted or absorbed by the dispersed particles. The scattered light consists of reflected and refracted waves, and depends on the form, size, and composition of the particles. The diffracted light arises from edge phenomena, and is dependent only on the geometric shadow created by each particle in the ballistic light beam: diffraction is therefore independent of the composition of the particles. In the case of absorption, light waves are removed from the incident beam and converted to heat or electrical energy by interaction with the particles; absorption depends on both size and composition.

The influence of composition is revealed through the complex refractive index, m = n - ik, where . For nonabsorbing (i.e., transparent) particles, k = 0, where k, the imaginary component of the refractive index, is related to the absorption coefficient of the material. Both the real part of the refractive index, n, and the imaginary part, k, are wavelength-dependent. Scattering arises due to differences in the refractive index of the particle and the surrounding medium (or internal variations in heterogeneous particles). Therefore, in order to use a scattering model to calculate the PSD that produced a specific scattering pattern, one must first know the complex refractive index of both the particles and the medium (typically, the latter is selected such that k = 0). Values of n have been published for many bulk materials [3], but in the case of cement, n is routinely estimated based on a mass average of the refractive indices for the individual material components [4]. The imaginary refractive component is more difficult to determine and/or find in the published literature [5, 6], and this often represents a significant challenge to the use of scattering methods for fine particle size measurements [7].

The influence of absorption becomes more important as the particle size decreases, and is therefore more likely to impact the range below the micron of the cement PSD. As a general rule of thumb, the darker or more colored a specimen appears, the higher the imaginary component. For white powders, such as high-purity alumina, k = 0. Cement, on the other hand, is generally gray to off-white in color, and therefore one can anticipate a finite, but relatively low value for the imaginary component (k = 0.1 is often reported for cement, although this value is unverified and will likely vary for different formulations).

Mie theory, which describes scattering by homogeneous spheres of arbitrary size, is the most rigorous scattering model available, and is used in many commercial instruments. For non-spherical particles like cement, Mie theory provides a volume-weighted equivalent spherical diameter. Mie theory has been applied with mixed success to the analysis of fine powders with diameters from several 100s of micrometers down to several tenths of micrometers. An accurate representation of the "true" size distribution by Mie scattering is dependent on a knowledge of the complex refractive index, and will be impacted by the degree of asymmetry present in the particles and the dispersion procedure used to prepare the test sample. 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.

For very large particles (relative to the wavelength of light), the diffraction effect can be exploited without reference to 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 related to particle size, again assuming spherical geometry. The range of validity for this method is limited on the low end to particle diameters a few times greater than the wavelength of the incident light for particles that are opaque or have a large refractive index contrast with the medium [8]. For somewhat more transparent particles, or particle with a moderate refraction contrast, the lower limit is increased to about 40 times the wavelength of light. For a He-Ne LASER, this corresponds to about 25 μm. The benefit of using Fraunhofer diffraction is that the interpretation is not dependent on the absorptive or refractive properties of the material. A totally absorbing black powder, a translucent glass powder, and a highly reflective white powder, having the same particle size and shape, will produce identical Fraunhofer patterns within the valid size range. On the other hand, inappropriate use of the Fraunhofer approximation outside of the valid range can lead to large systematic errors in the calculated PSD [4, 5]. These errors are especially prevalent in the range below the micron size, where errors exceeding 100 % are possible. Partial transparency can lead to the appearance of "ghost" particles. These are virtual particles, generally in the range below the micron size, produced as an artifact of refractive dispersion of light within the transparent particles. The refracted light is registered at large scattering angles as anomalous diffraction, and is therefore interpreted by the Fraunhofer analysis as being produced by very small particles.

In general, the LAS method requires that the particles be in a dispersed state, either in liquid (suspension) or in air (aerosol). The former is commonly referred to as the "wet" method (LAS-W) while the latter is termed the "dry" method (LAS-D). In Fraunhofer diffraction, the pattern does not depend on the refractive index, so there is no theoretical difference between using a liquid or a gas as a dispersing medium. For Mie scattering, the higher refractive index contrast in air, compared with most liquids, may somewhat impact the scattering pattern, but should not alter the results in any way.

Differences between LAS-D and LAS-W methods arise primarily from the different ways in which the particles are dispersed in each case. In liquid, it is possible to modify solution conditions, by changing pH or adding chemical dispersing agents for example, or to break up aggregates using mechanical or ultrasonic energy. Thus, in general, a better state of dispersion can be achieved in an appropriately selected liquid medium. For silicates and most metal oxides, water is an excellent dispersing medium. However, due to the reactive nature of cement in water, alcohols, such as isopropanol, methanol, and ethanol, are commonly used in its place. In the LAS-D method, a stream of compressed air (or a vacuum) is used to both disperse the particles and to transport them to the sensing zone. This method of dispersion works well for large, non-colloidal-phase spheroids, where the interfacial contact area is small and the physical bonds holding the individual particles together are relatively weak. For the particles smaller than a micron and highly asymmetric, the higher surface-to-volume ratio results in more intimate and numerous contact points and, as a consequence, a greater driving force is needed to separate aggregated particles.