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The improved Monte-Carlo (MC) method for standard-less analysis in laser induced breakdown spectroscopy (LIBS) is presented. Concentrations in MC LIBS are found by fitting model-generated synthetic spectra to experimental spectra. The current version of MC LIBS is based on the graphic processing unit (GPU) computation and reduces the analysis time down to several seconds per spectrum/sample. The previous version of MC LIBS which was based on the central processing unit (CPU) computation requested unacceptably long analysis times of 10's minutes per spectrum/sample. The reduction of the computational time is achieved through the massively parallel computing on the GPU which embeds thousands of co-processors. It is shown that the number of iterations on the GPU exceeds that on the CPU by a factor > 1000 for the 5-dimentional parameter space and yet requires > 10-fold shorter computational time. The improved GPU-MC LIBS outperforms the CPU-MS LIBS in terms of accuracy, precision, and analysis time. The performance is tested on LIBS-spectra obtained from pelletized powders of metal oxides consisting of CaO, Fe2O3, MgO, and TiO2 that simulated by-products of steel industry, steel slags. It is demonstrated that GPU-based MC LIBS is capable of rapid multi-element analysis with relative error between 1 and 10's percent that is sufficient for industrial applications (e.g. steel slag analysis). The results of the improved GPU-based MC LIBS are positively compared to that of the CPU-based MC LIBS as well as to the results of the standard calibration-free (CF) LIBS based on the Boltzmann plot method.
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
A collisional-dominated model of a laser induced plasma will be presented which 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, C, SiC, CaCl2 in N2 or Ar atmospheres with the formation of molecules N2, C2, Si2, CN, Cl2, SiN, SiC, CaCl, CaCl2 and their corresponding positive and negative ions1,2. The initial conditions are specially chosen to emulate the plasma state on the onset of expansion just after the laser pulse had ended.
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. The model and experiment serve to elucidate mechanisms of molecular formation in LIPs, the topic which has recently received much attention in the LIBS community.
A collisional-dominated model of a laser induced plasma will be presented which 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, C, SiC, CaCl2 in N2 or Ar atmospheres with the formation of molecules N2, C2, Si2, CN, Cl2, SiN, SiC, CaCl, CaCl2 and their corresponding positive and negative ions. 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. The model and experiment serve to elucidate mechanisms of molecular formation in LIPs, the topic which has recently received much attention in the LIBS community.
The lasing effect is demonstrated in laser plasmas induced on various metal targets and pumped by a laser tuned in resonance with a strong optical transition of a metal. The intense, polarized and lowdivergent radiation is emitted from a longitudinally pumped plasma plume in forward and backward directions with respect to the pump beam. Lasing occurs only within duration of the pumping pulse. The effect is found for elements of 13th and 14th groups and for Ca, Ti, Zr, Fe and Ni. The Einstein coefficients for spontaneous emission of all lasing transitions are higher than 10⁷ s⁻¹. For some elements like Al and In, a three-level lasing scheme is realized. For others, like Tl, both three- and four-level lasing schemes are realized. It is found that the longitudinal pump geometry is more efficient than the transversal one.
Tomography of a laser-induced plasma in air is performed by inverse Radon transform of angle-resolved plasma images. Plasmas were induced by single laser pulses (SP), double pulses (DP) in collinear geometry, and by a combination of single laser pulses with pulsed arc discharges (SP-AD). Images of plasmas on metallurgical steel slags were taken at delay times suitable for calibration-free laser-induced breakdown spectroscopy (CFLIBS). Delays ranged from few microseconds for SP and DP up to tens of microseconds for SP-AD excitation. The white-light and the spectrally resolved emissivity ε(x,y,z) was reconstructed for the three plasma excitation schemes. The electron number density Ne(x,y,z) and plasma temperature Te(x,y,z) were determined from Mg and Mn emission lines in reconstructed spectra employing the Saha-Boltzmann plot method. The SP plasma revealed strongly inhomogeneous emissivity and plasma temperature. Re-excitation of plasma by a second laser pulse (DP) and by an arc discharge (SP-AD) homogenized the plasma and reduced the spatial variation of ε and Te. The homogenization of a plasma is a promising approach to increase the accuracy of calibration-free LIBS analysis of complex materials.