Mathematical Modeling of XRF Matrix Correction Algorithms With an Electronic Spreadsheet

Abstract

AbstractIt will be demonstrated that the Lachance-Traill, and Lucas-Tooth and Price matrix correction algorithms can easily be applied to spreadsheet stored XRF data.The structure of spreadsheet stored data in Quantitative XRF Analysis, the utilization of built-in spreadsheet functions essential for data processing and the utilization of Spreadsheet Graphics for plotting of corrected and uncorrected XRF data will be presented.Development of modern Electronic Spreadsheets has reached the point where they can readily be used for almost any type of laboratory task, including: Data Plotting, Statistical Data Analysis, Report Writing and Publishing, Slide Presentations, etc. This valuable tool can easily be added to older equipment that usually lacks sophisticated XRF software. It can also become an auxiliary tool to modern XRF spectrometers equipped with advanced XRF software.The spreadsheet approach gives the analyst freedom of choice to process data according to personal/analytical preferences circumventing the rigidity of software supplied with the equipment. The spreadsheet approach also possesses educational value since it presents the basic ingredients of Matrix Correction in clear and concise table fashion. Addrtionaliy, the spreadsheet program is an excellent tool for demonstrating and evaluating different matrix correction models commonly used in X-ray Spectroscopy.It will also be shown tliat Spreadsheet Graphics are capable of handling the two-theta scans of XRF or XRD data gathered from older DEC/PDP-11 based Rigaku Equipment. This results in excellent hard copies of the two-theta scans, regardless of the output device.A mathematical background leading to the spreadsheet approach was partially presented in the paper “A mathematical comparison of the Lachance-Traill Matrix correction procedure with statistical multiple linear regression analysis in XRF applications” (41st Annual Denver X-ray Conference, Colorado Springs, 1992).