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Accuracy of calibration-free (CF) methods in laser-induced breakdown spectroscopy (LIBS) depends on experimental conditions and instrumental parameters that must match a CF LIBS model. Here, the numerical study is performed to investigate effects of various factors, such as the optical density, plasma uniformity, line overlap, noise, spectral resolution, electron density and path length on the results of CF-LIBS analyses. The effects are examined one-by-one using synthetic spectra of steel slag samples that fully comply with the mathematical model of the method. Also, the algorithm includes several new features in comparison with previously proposed CF algorithms. In particular, it removes limits on the optical thickness of spectral lines that are used for the construction of the Saha-Boltzmann plot; it retrieves the absorption path length (Plasma diameter) directly from spectral lines; it uses the more realistic Voigt line profile function instead of the Lorentzian function; and it employs the pre-calculated and tabulated thin-to-thick line ratios instead of approximating functions for selfabsorption correction.
Two calibration-free (CF) LIBS approaches are used for the quantitative analysis of cement samples: the CF-LIBS based on the Boltzmann plot method and the Monte Carlo (MC) LIBS based on the iterative spectrum fitting. In CF-LIBS, the inverse problem is solved, i.e. the elemental concentrations are determined by the reconstruction of plasma parameters from spectra. The MC-LIBS technique solves the direct problem by finding the highest correlation between the model-generated and experimental spectrum. The accuracy of both calibration-free LIBS methods suffers from factors such as inaccurately determined instrumental function, the deviation of experimental plasma from the mathematical model used, not taking into account the collection geometry, and from the uncertainty of spectroscopic data. The both calibration-free LIBS approaches are first applied to synthetic spectra which perfectly suit the mathematical model of the method, i.e. the model of the uniform, isothermal, and stationary plasma. This test yields the accuracy of both the approaches for the ideal case. In addition, the accuracy of both the methods is investigated for non-uniform and non-isothermal plasma, because real laser-induced plasma often has high gradients in temperature and particle number densities. Finally, both calibration-free LIBS approaches are applied to experimental spectra obtained from cement samples. The figures of merits of two approaches are compared when working with both synthetic and experimental spectra.