New procedure for CSigma laser induced breakdown spectroscopy addressing the laser-induced plasma inhomogeneity

CSigma laser-induced breakdown spectroscopy (Cσ-LIBS), as the other methods for quantitative elemental analysis by LIBS based on plasma characterization, is negatively affected by the inhomogeneity of laser-induced plasmas. In the present work, we propose a new procedure for Cσ-LIBS which addresses the plasma inhomogeneity problem. The key features of the method are: (1) the extension of the concept of apparent temperature to other plasma parameters (apparent plasma) and its use in both the ionization and excitation equilibria and (2) the addition to the theoretical Cσ curve of a linear contribution arising from the plasma regions of low optical depth. In ionization equilibrium, the inhomogeneity requires separated Cσ graphs and different apparent ionization temperatures for neutral atom and ion emissions. In excitation equilibrium, we account for the inhomogeneity by obtaining a different apparent temperature for each multiplet included in the Cσ graph. In this way, the procedure only requires the fitting of a limited number of parameters to describe the inhomogeneous plasma, as the multiplet temperatures $T_i$ are determined by a straightforward iteration procedure of fast convergence. The improved treatment of plasma inhomogeneity allows to include intense resonance lines in Cσ graphs, which were previously avoided. The development of the method has demanded accurate experimental Cσ graphs, obtained with seven certified aluminum alloys. The laser-induced plasma is generated in air at atmospheric pressure, the most common and versatile ambient gas condition for LIBS, which is known to produce a strongly inhomogeneous plasma. To validate the analytical application of the method, the samples are divided into three characterization samples and four analytical samples. The average deviation of the determined concentrations from the certified values has been 8.5% for elements with concentrations greater than 0.05 wt%.