Impact of intensity error on temperature estimation in laser-induced breakdown spectroscopy: a numerical study

Abstract

Laser-induced breakdown spectroscopy (LIBS) is a cutting-edge technique for the compositional analysis of multi-element materials. Under standard circumstances for laser-induced plasma (T _e = 1 eV and N _e = 10¹⁶ cm⁻³), we simulated the emission spectrum of a binary alloy (with 70 wt.% Cu–30 wt.% Al). We used the Saha ionization equilibrium formulas to calculate the population of neutral and ionized species of each constituent element, and the Boltzmann distribution to estimate the intensities of emission lines with radiative transition probabilities. The Stark broadening equation is then used to determine the line broadening, yielding a Lorentzian profile for each line. The sum of line emissions of all constituent species will approximate the alloy’s LIBS spectra in an assumption of ideal analytical plasma. Then, we generated random errors in the intensities of spectral lines ranging from 5% to 35%. To investigate temperature estimation accuracy, we utilized three well-established approaches: the Boltzmann plot (BP) method, the Saha–Boltzmann plot (SBP) method, and the Multi-elemental SBP (MESBP) method. As intensity error increases from 5% to 35%, the estimated temperature in the BP method deviates from 0.25% to 18.3%. Whereas the intensity error is almost unaffected using the SBP method and the MESBP method. The temperature deviation is less than 2% in both situations. This study is relevant to calibration-free LIBS, in which the exact temperature determination is crucial for the abundance estimation of trace, major, and minor elements.