Minimization of Microabsorption Effects in Complex Mixtures

In using X-ray diffraction (XRD) and the Rietveld method there are many factors that affect the results and the interpretation of the data that are collected. One of these is microabsorption. Microabsorption has historically been ignored or accounted for using the Brindley correction. This correction has come under much debate in recent years. A recent Round Robin study on quantitative analysis included data that was less accurate overall when the correction was used. This study focuses on examining factors that will aid in minimizing microabsorption effects and assessing microabsorption effects under various conditions; including absorption characteristics of the sample, absorption characteristics of the internal standard and particle size of the internal standard. The data was examined using the Rietveld refinement method, and the results were then compared with and without the Brindley correction. INTRODUCTION The goal of any quantitative procedure is to obtain the most accurate results possible. Within XRD, there are a number of factors that influence the accuracy of the results. One of the more problematic factors, particularly when dealing with complex mixtures such as coal combustion by-products (CCBs), cements/concretes and geologic materials, is microabsorption. Microabsorption stems from differences in the interactions of each material with the X-ray radiation. Each material will absorb the X-ray radiation to a different extent depending on its linear absorption coefficient for the particular wavelength (energy) of radiation being used. In many complex mixtures the differences in linear absorption coefficients are typically large (for instance, CCBs have linear absorption coefficients ranging from 81cm for quartz to 1153cm for magnetite using copper radiation). Microabsorption is not a new concept in XRD. G.W. Brindley described microabsorption and developed a method for correcting for its effect in quantitative XRD in the mid-1940’s [1]. His work derived a correction factor, τ, for microabsorption based on the difference in the linear absorption coefficient for a given analyte (μa) and the mean linear absorption coefficient of a mixture (μ ), and the average particle radius of that analyte, R, by numerical integration of ∫       − − = Va