Classical multivariate least-squares methods have been applied to the quantitative analysis of boron oxide in bulk borosilicate glasses using transmission infrared spectroscopy. However, molecular interactions in the glass result in deviations from Beer's law and cause the analytical B-O overtone band at ~2680 cm<sup>−1</sup> to shift to higher energy with increased boron concentration. Therefore, in order to account for the molecular interactions and achieve higher quantitative accuracy, one must use a nonlinear model relating absorbance and concentration. It has been found that if a quadratic correction term is added to the Beer's-law equation, the observed 15 to 25 cm<sup>−1</sup> shift in frequency of the B-O overtone band can be modeled to within the spectral noise. With the use of a model quadratic in boron oxide concentration, the least-squares analysis of boron in glass was determined with an average relative error of 3.3% for glasses with boron oxide concentrations ranging from 0.88 to 2.58%. This compares favorably with the 3% accuracy claimed for ion chromatography exclusion used for calibration. The methods described in this paper are general, and a variety of nonlinear models can be applied whenever Beer's-law deviations are present.
David M. Haaland, "The Quantitative Analysis of Boron Oxide in Borosilicate Glasses by Infrared Spectroscopy," Appl. Spectrosc. 40, 1152-1156 (1986)