Laser-induced breakdown spectroscopy (LIBS) is widely used in various fields, such as agriculture, industry, national defense, energy, aerospace, natural science, and interstellar physics, because of its unique advantages. However, low detection sensitivity and accuracy have hindered the expansion of LIBS, and many researchers have worked to improve the detection sensitivity and reduce measurement errors. Optimizing the experimental parameters is important in LIBS. The maximum intensity or signal-to-noise ratio of a LIBS signal under the optimal experimental parameters is an important means of improving the LIBS detection sensitivity. However, studies on the effect of sample matrix properties on the optimal detection system, which we call the matrix effect of the optimal experimental parameters, are scarce. Therefore, the matrix effect of the optimal experimental parameters must be studied for selecting the standard samples in the calibration method and improving the LIBS characteristics. The distance between the focal position of the laser beam and sample surface (defocus distance) is an important experimental parameter of a LIBS system during LIBS analysis. Optimizing this parameter ensures that the LIBS signal has the strongest intensity. Therefore, the intrinsic connection between the physical properties of the matrix and optimal defocus distance must be studied to select a suitable matrix for enhancing the LIBS signal and selecting a reference sample for the calibration method. We could not find other studies focusing on the correlation between the metal matrix and optimal experimental parameters.

Considering that the interaction of nanosecond pulsed laser and metallic materials to form a plasma involves the evaporation of metallic materials, interaction of vapors with laser, and plasma radiation, this work studies the influence of the matrix physical properties (density, hardness, optical absorption coefficient, ionization energy, electric conductivity, thermal conductivity, specific heat capacity, melting point, boiling point, latent heat of melting, and latent heat of vaporization) on the optimal defocus distance. Twelve metal matrix samples with considerable differences in the physical properties, i.e., Co, Ni, V, Nb, Cr, In, Sn, Cu, Er, Gd, Bi, and Zn, were selected, and the LIBS signals of these samples were measured. The appropriate metal element spectral lines were selected as the analytical spectral lines for optimizing the experimental parameters. The optimal defocus distances of the metal samples were obtained from the experimental results (Table 3). Based on the linear correlation hypothesis between the change in matrix physical parameters and optimal defocus distances, 11 equations were created and solved using the Mathematica program. For the first time, the correlation coefficients between the optimal defocus distance and matrix physical parameters were obtained.

According to the correlation coefficients obtained and the nature of the matrix physical parameters, a rational correlation analysis was conducted to investigate the matrix effect mechanism of the optimal defocus distance. This study will be useful for developing a laser beam focusing on an optimization method in LIBS quantitative analysis.

The correlation properties between the physical property parameters of the matrix and optimal defocus distance were obtained (Table 4). The density and hardness in mechanical property parameters are negatively correlated with the optimal defocus distance, and the hardness has a higher correlation coefficient than density. The optical absorption in optical properties parameters exhibits a positive correlation with the optimal defocus distance, whereas the ionization energy is negatively correlated with the optimal defocus distance. The conductivity of the matrix has a negative correlation with the optimal defocus distance. The influence of the thermodynamic properties of the substrate on the optimum defocus distance is prominent. The thermal conductivity, specific heat capacity, latent heat of melting, latent heat of vaporization, and boiling point of the matrix are positively correlated with the optimal defocus distance. Conversely, the melting point of the matrix is negatively correlated, with the high correlations for thermal conductivity and specific heat capacity. In the absence of previous studies on the matrix effect on optimal defocus distance for comparison, the results of existing LIBS breakdown threshold matrix effect studies and our speculation of the correlation between LIBS breakdown threshold and optimal defocus distance were used to explore the physical mechanism of the optimal defocus distance matrix effect.

The matrix effect of the optimal defocus distance of metal samples was investigated. The correlation rules between the optimal defocus distances and physical properties of metal matrix elements were initially revealed, which was corroborated with the results of the previous study on the LIBS breakdown threshold. Results show that the mechanical, optical, electrical, and thermal properties of the metal matrix influence the optimal defocus distance. However, the influence of thermal properties is more obvious, especially the thermal conductivity and specific heat capacity having the greatest influence on the optimal defocus distance, both of which show a positive correlation. A preliminary analysis of the mechanism of the optimal defocus distance matrix effect was also conducted based on the physical parameters of the matrix elements. The study results provide basic support for further understanding and correcting matrix effects, improving the quality of LIBS analysis.