Comparison between some common influence coefficient algorithms

Abstract

The quality of the results obtainable from a number of different algorithms available in modern manufacturers' software has been compared using data for a single sample of Ni–Fe–Cr, for considerations of space. The conclusions reached are based on similar comparisons using many samples of different compositions. The aim was to demonstrate that, when all criteria (variable theoretical influence coefficients; total concentration of all elements equals 100%; homogeneous, flat and infinitely thick samples) relating to emission theory are met, a number of valid mathematical expressions are available to the user. The mathematical expressions (algorithms) examined are Lucas-Tooth and Price, Rasberry–Heinrich and Lachance–Traill, all using empirical influence coefficients; Claisse–Quintin and COLA using linear and hyperbolic variable theoretical influence coefficients, respectively; and Broll–Tertian, Rousseau, Lachance–Claisse and de Jongh, using variable theoretical influence coefficients based on fundamental parameters. The last four algorithms give exactly the same results, despite the fact that the ‘structures’ of the algorithms are all very different and that the magnitudes of the influence coefficients are also very different (except that the magnitudes and signs of influence coefficients are the same for the Broll–Tertian and Rousseau algorithms). If any of the four algorithms is used correctly, each will give acceptable results. Copyright © 2004 John Wiley & Sons, Ltd.