**Dr Richard Rousseau**601 Booth St., Room 707

Ottawa, Ont., K1A 0E8

Canada

Dr. Rousseau is an X-Ray Fluorescence Analyst working at Geological Survey of Canada. His has published numerous scientific papers and book chapters on XRF. He got his Ph.D. with Dr. Fernand Claisse, from 1969 to 1973. From 1976 to now, he has worked at the Geological Survey of Canada as the Head of the XRF laboratory. He has also been teaching intensive XRF courses, acting as consultant many times in the private sectors.

Title:

How to solve the Sherman equation in practice

Abstract:

In X-ray fluorescence (XRF) analysis, the Sherman equation enables one to calculate theoretical net X-ray intensities emitted by each element from a specimen of known composition when a polychromatic X-ray beam irradiates it. This equation is of vital importance in XRF analysis for two main reasons. Firstly, it enables us to calculate what we measure: line intensities. This feature is unique to X-ray spectrometry. No other analytical technique allows for such a combination of theoretical physics and experimental results. Secondly, the Sherman equation can provide the theoretical basis of all modern models for the correction of matrix effects.

The two earliest well-known methods proposed for solving the Sherman equation are the ones of Beattie-Brissey (1954) and Criss-Birks (1968). In the opinion of the author, both methods failed to provide valid solutions. That is why, in 1984, 30 years after the publication of Beattie-Brissey, Rousseau proposed a new mathematical model, the Fundamental Algorithm (FA), which is the original Sherman equation expressed in a different mathematical form, but respects it in every detail: algebraically, mathematically and physically. The FA is thus theoretically exact, and completely and accurately corrects for all matrix effects that modify the measured net intensity emitted by the analyte i in a given specimen. When the first estimate of the sample composition is calculated with the Claisse-Quintin algorithm, when the FA is associated with its efficient calibration procedure, and when an iteration process without any normalization is applied to the FA, it becomes a mathematical method that corresponds to the modern needs for speed and accuracy in XRF analysis.

The aim of this presentation is to explain the true nature of the problems associated with the solution of the Sherman equation and to describe the three essential characteristics that any valid solution must have, i.e.,

1. how to transform the Sherman equation in order to facilitate its practical use;

2. how to solve it (or its only true equivalent model, the FA) for obtaining a valid solution in practice. It is not enough to propose a model that is theoretically valid. In addition, it must be solved in such a way that the solution does not violate any mathematical rule, converges all the time, and therefore calculates accurate sample compositions;

3. how to calibrate it in order to adapt theory to experimental data of each XRF spectrometer.

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**Ms. Maggi Loubser**

Analyst Scientist, X-Ray Analytical Facility, Geology Department, University of Pretoria, Pretoria, 0002, South Africa. E-mail: mloubser@postino.up.ac.za

Over the past ten years she has been involved in building up the X-Ray laboratory to a state of the art facility with a Thermo Electron ARL9400XP+ XRF spectrometer, with Win-XRF3.1-2, as well as UniQuant software. Together with Dr. Sabine Verryn, she has been presenting an introductory course in XRF and XRD to Geology honours students since 1998. She has been on the executive of the South African Spectroscopic Society since 1997 in the portfolio of secretary, and organise most of the SASS meetings. She has presented numerous papers at international conferences and national symposia.

She will present the following paper:

Lithium borate fusion: Some physical and chemical aspects involved

Maggi Loubser, X-ray Analytical Facility, Geology Department, University of Pretoria, Pretoria, 0002, South Africa. E-mail: mloubser@postino.up.ac.za

Peet H van Rooyenb, Chemistry Department, University of Pretoria, Pretoria, 0002, South Africa. E-mail: phvr@up.ac.za

Johan PR de Villiersc, Department of Materials Science and Metallurgical Engineering, University of Pretoria, Pretoria, 0002, South Africa. E-mail: jpdev@postino.up.ac.za

Fused glass beads as a sample preparation method for XRF spectroscopy were introduced in 1957 by Claisse; it soon became the preferred method to introduce oxide samples to the spectrometer, because heterogeneity, mineralogical and particle size effects are eliminated during the fusion process. Matrix effects are largely reduced by the resulting dilution.

After 48 years of fused bead use in XRF analysis, certain matrices remain problematic. Although many fusion methods for chromite-, sulphide- and cassiterite-rich materials have been published, routine methods for these still elude analytical chemists. Lengthy fusions at temperatures >1100ºC are often prescribed for refractory materials and ores, and until recently one of the biggest challenges was a metal-bearing sample eg. slags or certain refractory materials.

In this study, different analytical techniques were used to investigate the reactions occurring during the fusion process and, based on this, an attempt was made to postulate methods for the different problematic materials, based on theoretical glass-making principals rather than the much used "hit and miss" technique. As a starting point, Thermo Gravimetric Analysis was used to evaluate the reactions occurring during the fusion of a lithium borate glass. Observed reactions were modelled in a muffle furnace to produce identical material in larger quantities, and this material was then investigated using X-ray Powder Diffractometry, Raman Spectroscopy and Electron Microprobe Analysis.

Some of the problems addressed using this approach were metallic content in samples. XRF spectroscopy is one of the major tools used in evaluation of refractory failures, but pressed powder briquettes have analytical limitations when metal particles are present in the interface between the refractory and melt phases. Fused bead preparation of such samples has always been problematic due to reaction of metal with platinum crucibles. XRD was used to evaluate a pre-oxidation step, which was included into the preparation. This method was further developed to fuse pure metallic samples with a simple pre-oxidation step. Sample preparation for sulphide-bearing matrixes was also optimised using TGA and XRD to evaluate the pre-oxidation step. The next problem evaluated using the insight gained from investigating the temperature behaviour of fluxes, was difficult to fuse materials including rutile, zircon and chromite-bearing ores. Successful fusion recipes were compiled with much lower dilutions than used in the past.

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**Colleen Frazer**

Dr. Frazer is working with Materials Characterization at Sandia National Laboratories Albuquerque, NM.

Title:

Rietveld Refinements: Theory and Application

Abstract:

As the amount of information obtainable from powder diffraction techniques increases, so does the need for greater accuracy in structural determinations and subsequent analyses. Full-pattern refinement techniques allow for increased accuracy by significantly reducing the inherent errors resulting from peak-to-peak analyses. Among the accessible full-pattern refinement techniques, the Rietveld Method, named after the originator Dr. Hugo Rietveld, is routinely used to obtain systematic structural results. In this presentation, the refinement parameters and steps involved in performing skillful Rietveld Refinements on single and mixed phase materials will be discussed, along with interpretations of the results and approaches for large datasets. Various examples of how the results were applied to actual materials projects will also be highlighted.