Analytische Chemie
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The equation of state for plasmas containing negative atomic and molecular ions (anions) is modeled. The model is based on the assumption that all ionization processes and chemical reactions are at local thermal equilibrium and the Coulomb interaction in the plasma is described by the Debye–Hu¨ckel theory. In particular, the equation of state is obtained for plasmas containing the elements Ca, Cl, C, Si, N, and Ar. The equilibrium reaction constants are calculated using the latest experimental and ab initio data of spectroscopic constants for the molecules CaCl2, CaCl, Cl2, N2, C2, Si2 , CN, SiN, SiC, and their positive and negative ions. The model is applied to laserinduced plasmas (LIPs) by including the equation of state into a fluid dynamic numerical model based on the Navier–Stokes equations describing an expansion of LIP plumes into an ambient gas as a reactive viscous flow with radiative losses. In particular, the formation of anions Cl-, C-, Si-, Cl2, Si2, C2 , CN-, SiC-, and SiN- in LIPs is investigated in detail.
Under the assumption of local thermal equilibrium, a numerical algorithm is proposed to find the equation of state for laser-induced plasmas (LIPs) in which chemical reactions are permitted in addition to ionization processes. The Coulomb interaction in plasma is accounted for by the Debye–Hückel method. The algorithm is used to calculate the equation of state for LIPs containing carbon, silicon, calcium, chlorine, nitrogen, and argon. The equilibrium reaction constants are calculated using the latest experimental and ab initio data of spectroscopic constants for the molecules N2, C2, Si2, CN, Cl2, SiN, SiC, CaCl, CaCl2 and their positive and (if existed) negative ions. The algorithm is incorporated into a fluid dynamic numerical model based on the Navier–Stokes equations describing an expansion of LIP plumes into an ambient gas. The dynamics of LIP plumes obtained by the ablation of SiC, CaCl2, solid silicon, or solid carbon in an ambient gas containing N2 and Ar is simulated to study formation of molecules and molecular ions. A particular attention is paid to formation of anions Cl−, Cl2−, Si2−, C2−, CN−, and SiN− in LIPs.
Two topics will be addressed: (1) calibration-free LIBS based on Monte Carlo spectral optimization and (2) insight into the possibility of simultaneous elemental and molecular analysis by LIBS. Both topics heavily rely on modeling of laser induced plasma and are closely connected to experiment. In Monte Carlo LIBS (MC LIBS), concentrations are found by fitting model-generated synthetic spectra to experimental spectra. The model of a static uniform isothermal plasma in local thermodynamic equilibrium is employed. Many configurations of plasma parameters and their corresponding spectra are simultaneously generated using a graphic processing unit (GPU). Using the GPU allows for the reduction of computational time down to several minutes for one experimental spectrum that presents the significant progress in comparison with earlier versions of MC LIBS. The method is tested by analyzing industrial oxides containing various concentrations of CaO, Fe2O3, MgO, and TiO2. The agreement within several percent between found and certified concentrations is achieved. Next, a newly developed collisional-dominated model of a laser induced plasma is introduced. The model includes the coupled Navier-Stokes, state, radiative transfer, and material transport equations and incorporates plasma chemistry through the equilibrium approach based on the use of atomic and molecular partition functions. Simple chemical systems are modeled including ablation of Si and C in N2 and Ar atmospheres.The model is used to study evolution of number densities of atomic and molecular species in the expanding plasma plume. The distribution is compared to experimental observations obtained by optical imaging and tomography. To further verify the model, dynamic plasma
Data processing in the calibration-free laser-induced breakdown spectroscopy (LIBS) is usually based on the solution of the radiative transfer equation along a particular line of sight through a plasma plume. The LIBS data processing is generalized to the case when the spectral data are collected from large portions of the plume. It is shown that by adjusting the optical depth and width of the lines the spectra obtained by collecting light from an entire spherical homogeneous plasma plume can be leastsquare fitted to a spectrum obtained by collecting the radiation just along a plume diameter with a relative error of 10−11 or smaller (for the optical depth not exceeding 0.3) so that a mismatch of geometries of data processing and data collection cannot be detected by fitting. Despite the existence of such a perfect least-square fit, the errors in the line optical depth and width found by a data processing with an inappropriate geometry can be large. It is shown with analytic and numerical examples that the corresponding relative errors in the found elemental number densities and concentrations may be as high as 50% and 20%, respectively. Safe for a few found exceptions, these errors are impossible to eliminate from LIBS data processing unless a proper solution of the radiative transfer equation corresponding to the ray tracing in the spectral data collection is used.
Kinetic model of stimulated emission created by resonance pumping of aluminum laser-induced plasma
(2017)
Stimulated emission observed experimentally in an aluminum laser induced plasma is modeled via a kinetic approach. The simulated emission at several cascade transitions is created by a pump laser guided through the plasma at several microseconds after its creation and tuned in resonance with the strong 3s²3p-3s²4s transition at 266 nm. A two-dimensional space-time collisional radiative plasma model explains the creation of the Population inversion and lasing at wavelengths of 2100 nm and 396.1 nm. The population inversion for lasing at 2100 nm is created by depopulation of the ground 3s²3p state and population of the 3s²5s state via the absorption of the resonant radiation at 266 nm. The population inversion for lasing at 396.1 nm occurs during the laser pulse via the decay of the population of the pumped 3s²5s state to the excited 3s²4s state via cascade transitions driven optically and by collisions. In particular, efficient are the mixing transitions between neighboring states separated by small gaps on the order of kT at Plasma temperatures of 5000–10 000 K. The model predicts that the population inversion and corresponding gain may reach high values even at very moderate pump energy of several lJ per pulse. The efficiency of lasing at 2100 nm and 396.1 nm is estimated to be ~3% and 0.05%, correspondingly with respect to the pump laser intensity. The gain for lasing at 396.1 nm can reach as high as ~40 cm⁻¹.
The polarization effect that the pump radiation at 266 nm imposes on the stimulated emission at 396.1 nm is discussed. The calculated results are favorably compared to experimental data.