Newton approximation method for linearization of calibration curves in Zeeman graphite furnace atomic absorption spectrometry

Abstract

An algorithm previously developed by L'vov et al. [ Spectrochim. Acta 47B, 889 (1992), and Spectrochim. Acta 47B, 1187 (1992)] was extended to allow for improved linearization of the upper end of the calibration curves of Zeeman graphite furnace atomic absorption spectrometry (GFAAS). The theoretical model of L'vov et al. described the effect of stray light on the calibration curves, and was based on three parameters: the rollover absorbance, A r, the limiting absorbance, A lim, and the Zeeman sensitivity ratio, R. Their theoretical treatment did not have an exact mathematical solution; rather, they used a simplifying assumption that the Zeeman sensitivity ratio had unity value and this made it possible to linearize the calibration curves. An extension of the algorithms of L'vov et al. is described here, which used Newton's method of successive approximations to approach a solution to the theoretical expression of L'vov et al., while still allowing the sensitivity ratio at the rollover point, R', to be taken into account along with the rollover absorbance. Both the extended algorithm and the algorithm of L'vov et al. were used for the linearization of the calibration curves of copper, silver, manganese, bismuth and thallium in Zeeman GFAAS. The characteristic mass values [cf. Microchem. J. 48, 278 (1993)] obtained from the linearized parts of the calibration curves of both models were compared to test the validity of each algorithm. The experimental and theoretical values of the characteristic masses of both models nearly coincided (±7%) for elements with R ⩾ 0.6. However, for copper ( R ⩽ 0.5) the differences between the theoretical and experimental characteristic masses values were 2% and 25% for the extended algorithm and that of L'vov et al., respectively. Overall, these results indicated the general validity of the L'vov et al. linearization algorithm and assumptions, but the case of copper demonstrated some limitations of the L'vov algorithm that could be mitigated by the extension described here.