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Many applications of LIBS require the measurement of plasma temperature and electron density, which in turn requires knowledge of the integrated line intensity and the shape of the spectral lines. While the integral intensity is preserved as light passes through the spectrometer, the shape emitted by an individual atom or ion is greatly distorted. This is due, firstly, to the transfer of light through the plasma (self-absorption), secondly, to the influence of the instrumental function of the spectrometer, and, thirdly, to the aberrations of the optical system. In addition, processing of spectral information, such as background removal, noise reduction, deconvolution, and line fitting, introduces additional errors in the reconstructed linewidth and line integral, which leads to erroneous temperature and electron density values.
This communication will be devoted to the general shortcomings of spectral data processing and the resulting inaccuracies in determining the plasma parameters. The analysis is based on the use of synthetic spectra generated by plasma with known temperature and particle density. The estimation of errors caused by inadequate processing of the spectral data is made by comparing the initial and determined plasma parameters. As a result, an improved data processing method will be proposed that takes into account the spectrum distortion by the instrumental function and integration on the pixel detector. The former is accounted for by convolution (instead of deconvolution) of the estimated line profile using a predetermined slit function, and the latter is achieved by piecewise integration of the line profile by the pixel detector, taking into account the pixel size and uniform or non-uniform pixel separation. Recommendations will be made for which analytic function best approximates the observed spectral lines and examples will be given for the application of this routine to calibration-free LIBS using both synthetic and experimental data.
The aim of the project is to develop an adequate model of laser induced plasma for conditions expected in space missions, i.e., vacuum, or low-pressure CO2 atmosphere. Numerical modeling will help to find optimal experimental parameters for the laser ablation under artificial lunar or Martian environments and obtain both qualitative, in terms of a composition, and quantitative, in terms of an elemental abundance, information about interrogated samples based on spectral data generated by the model. The best operational conditions will be found at a low cost without conducting tedious and time-consuming optimization experiments. The modeling approaches will be supported by machine learning to accelerate the optimization.
Back Deposition of Titanium Oxides under Laser Ablation of Titanium: Simulation and Experiment
(2022)
Titanium is widely used in medicine for implants and prostheses, thanks to its high biocompatibility, good mechanical properties, and high corrosion resistance. Pure titanium, however, has low wear resistance and may release metallic titanium into surrounding tissues. Structuring and coating its surface with oxide layers are necessary for high wear resistance and improved biocompatibility. In this work, a combination of theoretical and experimental methods was used to study processes responsible for deposition of titanium oxides during ablation of titanium in air.
The deposition process was modeled via the Navier-Stokes equations that accounted for the material removal and accumulation of the deposit on the ablation surface. The chemical part was based on the equilibrium model embedded into the hydrodynamic code. Simulations showed that the most active zone of production of condensed titanium oxides were at plasma periphery whereas a zone of strong condensation of titanium metal was above the molten pool.
In experiment, a pulsed Yb fiber laser was scanned across a titanium surface. The temperature and composition of the plasma were inferred from plasma emission spectra. The post-ablation surface was analyzed by SEM, TEM, STEM, AFM, and XRD.
The developed model well reproduced the main features of experimental data. It was concluded that the deposition of condensed metal oxides from the plasma is a principal mechanism of formation of nanoporous oxide layer on the metal surface. The method of surface structuring and modification by nanosecond laser ablation can be developed into a useful technology that may find applications in medicine, photonics, and other areas.
Modeling is an important tool for understanding a physical phenomenon. It helps to interpret results of experiments and optimize experimental parameters for obtaining a desirable result. Modeling laser induced plasma is beneficial for many scientific and industrial fields, e.g., analytical chemistry, pulsed laser deposition, plasma enhanced chemical vapor deposition, laser welding, additive manufacturing etc. In this presentation, a personal experience in development of a physical model of laser induced plasma will be given in a chronological sequence starting from early 2000th and until now.
Over the time, the model evolved from its simple analytical form that described plasma emission spectra to its current numerical form that describes plasma dynamics, chemistry, and interaction with a substrate surface. Several examples will be given for the application of the model to practical problems such as spectroscopic chemical analysis, plasma enhanced chemical vapor deposition, and surface modification by laser ablation.
Laser-induced plasmas are widely used in many areas of science and technology; examples include spectrochemical analysis, thin film deposition, and material processing. Several topics will be addressed. First, general phenomenology of laser-induced plasmas will be discussed. Then, a chemical model will be presented based on a coupled solution of Navier-Stokes, state, radiative transfer, material transport, and chemical equations. Results of computer simulations for several chemical systems will be shown and compared to experimental observations obtained by optical imaging, spectroscopy, and tomography. The latter diagnostic tools will also be briefly discussed. Finally, a prospective application of laser-induced plasma and plasma modeling will be illustrated on the example of chemical vapor deposition of molybdenum borides and micro processing and coating of titanium dental implants.
The review mainly deals with two topics that became important in applications of laser-induced breakdown spectroscopy (LIBS) in recent years: the emission of halogen- and rare-earth-containing molecules and selective excitation of molecules by molecular laser-induced fluorescence (MLIF). The first topic is related to the emission of alkaline-earth diatomic halides MX, M = Ca, Mg, Ba, Sr and X = F, Cl, Br, and I and rare-earth element (REE) oxides LaO, YO, and ScO. These molecules form in laser-induced plasma (LIP) soon after its ignition and persist for a long time, emitting broad bands in a visible part of the spectrum. They are best detected after relatively long delay times when emission from interfering plasma species (atoms and ions) has already been quenched. Such behavior of molecular spectra allows of using, for their detection, inexpensive CCD detectors equipped with simple electronic or mechanical shutters and low-resolution spectrometers. A main target for analysis by molecular spectroscopy is halogens; these elements are difficult to detect by atomic spectroscopy because their most intense atomic lines lie in the vacuum UV. Therefore, in many situations, emission from CaF and CaCl may provide a substantially more sensitive detection of F and Cl than emission from elemental F and Cl and their ions. This proved to be important in mining and concrete industries and even Mars exploration. A similar situation is observed for REEs; their detection by atomic spectroscopy sometimes fails even despite the abundance of atomic and ionic REEs' lines in the UV-VIS. For example, in minerals and rocks with low concentrations of REEs, emission from major and minor mineral elements hinders the weak emission from REEs. Many REEs do not form molecules that show strong emission bands in LIP but can still be detected with the aid of LIP. All REEs except La, Y, and Sc exhibit long-lived luminescence in solid matrices that is easily excited by LIP. The luminescence can be detected simultaneously with molecular emission of species in LIP within the same time and spectral window. The second topic is related to the combination of MLIF and LIBS, which is a technique that was proved to be efficient for analysis of isotopic molecules in LIP. For example, the characteristic spectral signals from isotopic molecules containing 10B and 11B are easier to detect with MLIF-LIBS than with laser ablation molecular isotopic spectrometry (LAMIS) because MLIF provides strong resonance excitation of only targeted isotopes. The technique is also very efficient in detection of halogen molecules although it requires an additional tunable laser that makes the experimental setup bulky and more expensive.
This course will provide an introduction to plasma diagnostic techniques. The major focus of the course will be on the discussions of the practical procedures as well as the underlying physical principles for the measurements of plasma fundamental characteristics (e.g., temperatures, thermodynamic properties, and electron number density). Particular emphasis will be placed on inductively coupled plasma–atomic emission spectrometry, but other analytical plasmas will also be used as examples when appropriate. Selected examples on how one can manipulate the operating conditions of the plasma source, based on the results of plasma diagnostic measurements, to improve its performance used for spectrochemical analysis will also be covered. Topics to be covered include thermal equilibrium, line profiles, temperatures, electron densities, excitation processes, microreactions, pump and probe diagnostics, tomography, temporal and spatial resolution. Basis of plasma computer modeling will be presented.
The spatial heterodyne spectrometer (SHS) concept, which is based on an interferometricoptical setup, boasts both the Fellgett and Jacquinot advantages. Theoretically it can provideboosted sensitivity and spectral resolution with respect to dispersion spectrometers in acompact, reasonably cheap arrangement without any moving components – this set ofcharacteristics can be attractive to a number of industrial, space and other field applications. The potential of SHS has already been demonstrated in IR and Raman spectroscopies(e.g.), and more recently also in LIBS. The scientific goal of our present project is toapply the SHS concept to the development of an optimized, but practical dual-grating,tunable SH-LIBS setup, which would possess appealing spectroscopic characteristics.During this development, we extensively rely on the computer-based simulation of theoptical setup, which is an efficient approach that we found to have been missing from earlierSHS efforts published. It can provide application-specific optimization of the SHS systemand predict the performance of the final system. In particular, we use optical simulation tostudy the effect of various important parameters on the relevant spectroscopic figures ofmerits of the system. We used the non-sequential ray-tracing mode of the Zemax/OpticStudio software for optical modelling of the SH-LIBS setup (Optical distortions were studiedin sequential mode). Characteristics of the setup and interferograms were calculated with atleast one million rays. All calculations were carried out for the visible spectral range(400-700 nm), using stepwise extension of monochromatic simulations with 5 nm steps.Wherever applicable, characteristic discrete visible wavelengths from the emissionspectrum of Hg discharge lamps (404.7 nm, 435.8 nm, 546.1 nm, 579.0 nm) were used for thecalculation of spectroscopy figures of merit and for the validation of simulation.
Asymmetrical laser-induced plasmas were investigated by a tomography approach based onthe inverse Radon transform. Two distinct sources of asymmetricity were investigated:double-pulsed laser-induced plasmas in the orthogonal configuration and single-pulsedlaser-induced plasmas under an inclined incidence angle. Both cases were observed atvarious delay times. The optical thinness of the laser-induced plasmas was achieved byappropriately adjusting the pulse energies. High temporal resolution was achieved by agated intensified charge-coupled-device camera. The asymmetrical laser-induced plasmaswere investigated in terms of their total emissivity, spectrally resolved emissivity, andtemperature. The latter was obtained by the Saha–Boltzmann plot method. The imagesrequired for the inverse Radon transform technique were obtained with a high angularaccuracy and reproducibility provided by mounting the spectrometer on a high-precisionnano-positioning rotary stage. The plasmas were induced in the center of rotation of thestage. This arrangement enabled the reconstruction of emissivity which was integrated overthe full spectral range (200–800 nm) or over a desired spectral range selected by a bandpassfilter (~10 nm). It also allowed for the reconstruction of spectrally-resolved emissivity ineach cross-sectional plasma slice by scanning the plasma across a spectrometer slit. The 3Dmaps of the temperature and electron density were thus obtained for different types ofasymmetric plasmas. The work will provide a more detailed description of the twoasymmetrical laser-induced plasmas. This might help with the development of LIBSinstrumentation using the orthogonal double-pulse geometry, or remote LIBS applicationswhich inherently rely on inclined-angle ablation.
A goal of this work is to apply the model, which was initially developed for laser induced plasmas, to plasmas used in chemical reactors, in particular, the inductively-coupled-RF discharge plasma. The model predicts equilibrium chemical compositions of reaction mixtures as functions of plasma temperature and stoichiometry of reactants. The mixtures investigated are BCl3/H2/Ar and BF3/H2/Ar where Ar serves as the plasma-forming gas and H2 as a binding agent which binds the active species Cl and F and Cl- and F-containing intermediates to produce gaseous B and its condensate. An additional goal is to obtain information about intermediate reaction products for different ratios of BCl3/H2 and BF3/H2 and at different temperatures and different Ar flow rates. Also, chemical reactions in laser induced plasmas (LIPs) created on calcium hydrate and calcium carbonate targets in argon are modeled. The results are compared with those obtained by means of the equilibrium model based on the minimization of Gibbs free energy.
Molecule formation in calcium carbonate and calcium hydroxide libs plasmas: model and experiment
(2019)
Analysis of calcium hydrate and calcium carbonate samples and their mixtures is important for archeology, anthropology, and geology. Laser-induced plasma spectroscopy (LIBS) is a suitable tool for such the analysis as it allows for in- and on-line real time chemical assays. LIBS is inherently a technique for atomic analysis; however, since recently, it is also used for molecular analysis. The information attained by the latter is mainly related to “secondary” chemistry that deals with re-association of atoms and ions into molecules at long delay times (≥10 μs) after the initial breakdown. Even though the direct information about the initial molecular content in the target may be lost, the molecular analysis by LIBS can still be useful to assess the composition of samples.
In this work, chemical reactions in laser induced plasmas (LIPs) created on calcium hydrate and calcium carbonate targets in argon are modeled and compared to experiment. The model is based on the assumption that all ionization processes and chemical reactions are at local thermodynamic equilibrium. A chemical composition of argon-calcium-oxygen and argon-calcium-hydrogen plasmas is studied as a function of plasma temperature and pressure. It is established that more than twenty simple and composite molecules and ions can be formed in the course of chemical reactions. The results are compared with those obtained by means of the equilibrium model based on the minimization of Gibbs free energy.
A goal of this work is to apply the model, which was initially developed for laser induced plasmas, to plasmas used in chemical reactors, in particular, the inductively-coupled-RF discharge plasma. The model predicts equilibrium chemical compositions of reaction mixtures as functions of plasma temperature and stoichiometry of reactants. The mixtures investigated are BCl3/H2/Ar and BF3/H2/Ar where Ar serves as the plasma-forming gas and H2 as a binding agent which binds the active species Cl and F and Cl- and F-containing intermediates to produce gaseous B and its condensate. An additional goal is to obtain information about intermediate reaction products for different ratios of BCl3/H2 and BF3/H2 and at different temperatures and different Ar flow rates. Also, chemical reactions in laser induced plasmas (LIPs) created on calcium hydrate and calcium carbonate targets in argon are modeled. The results are compared with those obtained by means of the equilibrium model based on the minimization of Gibbs free energy.
The elemental analysis of seawater is often critical to the understanding of marinechemistry, marine geochemistry, and the deep-sea ecosystems. Laser-induced breakdownspectroscopy (LIBS) with the advantage of rapid multi-elements detection, has a greatpotential for in-situ elemental analysis of seawater. In practice, it is crucial to create acompact, low cost and power saving instrument for the long-term deep-sea observation. Arecently appeared diode-pumped solid-state (DPSS) laser seems to be a promising candidateas it is both compact and robust. Additionally, its high repetition rate up to hundreds of kHzcan provide a considerable throughput for LIBS analysis. However, the DPSS lasers operateat moderate pulse energies, usually less than one mJ, which cannot sustain stablebreakdowns in bulk water. To ensure stable laser-induced plasmas underwater with such aμJ-DPSS laser, we introduced an ultrasound source to assist the breakdown process. Thephase interface and mass flow generated by the near-field ultrasound can greatly reduce thebreakdown threshold and enhance element-specific emissions. Meanwhile, the highrepetition-rate pulses can also improve the breakdown probability and generate uniqueemission lines originated from the water molecule. We further demonstrate that the highrepetition-rate DPSS laser combined with the Echelle spectrometer can provide effectivequantitative analysis for metal elements in bulk water.
In this paper experimental temperature and density maps of the laser induced plasma in water during Pulsed Laser ablation in Liquid (PLAL) for the production of metallic nanoparticles (NPs) has been determined. A detection system based on the simultaneous acquisition of two emission images at 515 and 410 nm has been constructed and the obtained images have been processed simultaneously by imaging software. The results of the data analysis show a variation of the temperature between 4000 and 7000 K over the plasma volume. Moreover, by the study of the temperature distribution and of the number densities along the plasma expansion axis it is possible to observe the condensation zone of the plasma where NPs can be formed.
Finally, the time associated to the electron processes is estimated and the plasma charging effect on NPs is demonstrated. The set of observations retrieved from these experiments suggests the importance of the plasma phase for the growth of NPs and the necessity of considering the spatial distribution of plasma parameters for the understanding of one of the most important issues of the PLAL process, that is the source of solid material in the plasma phase.
An improved algorithm for calibration-free laser induced breakdown spectroscopy (CF LIBS) is presented which includes several novel features in comparison with previously proposed similar algorithms. In particular, it allows using spectral lines with arbitrary optical thickness for the construction of Saha-Boltzmann plots, retrieves the absorption path length (plasma diameter) directly from a spectrum, replaces the Lorentzian line profile function by the Voigt function, and allows for self-absorption correction using pre-calculated and tabulated data rather than approximating functions. The tabulated data embody the solutions of the radiative transfer equation for numerous combinations of optical thicknesses and line widths. The algorithm is used to analyze 100 low alloy steel spectra.
Stimulated emission observed experimentally in 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 transition at 266 nm. A two-dimensional space-time collisional radiative plasma model explains the creation of the population inversion and lasing at wavelengths 2.1 μm and 396.1 nm. The population inversion for lasing at 2.1 μm is created by depopulation of the ground state and population of the upper state via absorption of 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 upper state to the lasing state via cascade transitions driven optically and by collisions. The model predicts that the population inversion and corresponding gain may reach high values even at moderate pump energies of several μJ per pulse. The efficiency of lasing at 2.1 μm and 396.1 nm is estimated to be on the order of a percent of laser pump energy. 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 experiment.
Laser-induced plasmas are widely used in many areas of science and technology; examples include spectrochemical analysis, thin film deposition, material processing, and even jet propulsion. Several topics will be addressed. First, general phenomenology of laser-induced plasmas will be discussed. Then, a chemical model will be presented based on a coupled solution of Navier-Stokes, state, radiative transfer, material transport, and chemical (Guldberg-Waage) equations. Results of computer simulations for several chemical systems will be shown and compared to experimental observations obtained by optical imaging, spectroscopy, and tomography. The latter diagnostic tools will also be briefly discussed.
The spatial heterodyne detection principle has a great potential in spectroscopy. It has an optical setup similar to that of a Michelson interferometer, with the mirrors replaced by diffraction gratings positioned at fixed, equal distances from the beamsplitter and are slightly tilted. The resulting interference pattern is recorded by a digital camera and the spectrum is recovered by using Fourier transformation. Although SHS was initially developed for astronomical and satellite-based atmospheric measurements, but in recent years it has been started to be applied in other branches of spectroscopy too. Recently the area of laser-induced breakdown spectroscopy (LIBS) has also discovered the potential of SHS. The main appeal of SHS detection in LIBS includes the compactness and robustness of the setup (in view of field applications) and the flexibility to optimize the setup for either high sensitivity or for high resolution, which can be benficially exploited in applications like stand-off measurements, quantitative analysis with isotope resolution, etc.
In the present work, we have improved and further optimized our initial LIBS-SHS setup described in a previous conference. By using optical simulations, we have modelled the light transmission efficiency, instrumental function and imaging properties of the system. We significantly improved and automated the spectral and image data processing sequence. The optimizations carried out resulted in an improved spectral resolution and repeatability, a lower spectral background and the elimination of the central line artifact originating from the Fourier transformation procedure. A detailed characterization of the LIBS spectroscopy performance (e.g. resolution, spectral coverage, tuning range, linearity, etc.), including a comparison with that of a LIBS setup based on a conventional dispersion CCD spectrometer was also performed.
A goal of this work is to extend the model, which was initially developed for laser induced plasmas, to plasmas used in chemical reactors, in particular, the inductively-coupled-RF discharge plasma. The model predicts equilibrium chemical compositions of reaction mixtures as functions of plasma temperature and stoichiometry of reactants. The mixtures investigated are BCl3/H2/Ar and BF3/H2/Ar where Ar serves as the plasma-forming gas and H2 as a binding agent which binds the active species Cl and F and Cl- and F-containing intermediates to produce gaseous B and its condensate. An additional goal is to obtain information about intermediate reaction products for different ratios of BCl3/H2 and BF3/H2 and at different temperatures and different Ar flow rates.
It is found that the desired components B and B2 appear at appreciable concentrations of >0.1% and ~0.01% respectively only at temperatures above 3000 K. It is also established that the effect of charged species on the reaction products is miniscule for temperatures below 5000 K. The expected yield of boron as a function of the original mole fraction H2/BCl3 and H2/BF3 is calculated. The mole fractions are varied in the range 0.1-1000 and the temperature in the range 1000-10000 K. It is shown that the yield of boron increases with increasing the molar ratio H2/BCl3 and H2/BF3 up to ~100 in the temperature range 2000-5000 K. At higher temperatures, T>5000 K, the boron concentration reaches its maximum and does not depend on the concentration of hydrogen; all molecules dissociate and chemical reactions proceed only between charged particles (mostly elemental ions) and electrons. The calculated plasma parameters and composition are compared with experimental data obtained by optical emission spectroscopy. The calculated plasma temperature and electron density are shown to be in good agreement with the measured ones.
High purity halides of III-VI group elements, especially chloride and fluorides, are used in gas phase technologies for obtaining high purity materials and coatings. The reduction of halides in hydrogen-halide mixtures can be achieved in various discharge plasmas, e.g. inductively coupled, ark, and even laser-induced plasmas. Existing models of such plasmas are not sufficiently accurate to predict a yield of the targeted compounds and to describe the plasma processes involved in formation of these compounds. Besides, a construction of costly plasma-chemical reactors can be alleviated by the prior modeling of plasma processes that may occur in such reactors.
A goal of this work is to extend the model, which was initially developed for laser induced Plasmas, to plasmas used in chemical reactors, in particular, the inductively-coupled-RF discharge Plasma. The model predicts equilibrium chemical compositions of reaction mixtures as functions of plasma temperature and stoichiometry of reactants. The mixtures investigated are BCl3/H2/Ar and BF3/H2/Ar where Ar serves as the plasma-forming gas and H2 as a binding agent which binds the active species Cl and F and Cl- and F-containing intermediates to produce gaseous B and its condensate. An additional goal is to obtain information about intermediate reaction products for different ratios of BCl3/H2 and BF3/H2 and at different temperatures and different Ar flow rates.
It is found that the desired components B and B2 appear at appreciable concentrations of >0.1% and ~0.01% respectively only at temperatures above 3000 K. It is also established that the effect of charged species on the reaction products is miniscule for temperatures below 5000 K. The expected yield of boron as a function of the original mole fraction H2/BCl3 and H2/BF3 is calculated. The mole fractions are varied in the range 0.1-1000 and the temperature in the range 1000-10000 K. It is shown that the yield of boron increases with increasing the molar ratio H2/BCl3 and H2/BF3 up to ~100 in the temperature range 2000-5000 K. At higher temperatures, T>5000 K, the boron concentration reaches its maximum and does not depend on the concentration of hydrogen; all molecules dissociate and chemical reactions proceed only between charged particles (mostly elemental ions) and electrons. The calculated plasma parameters and composition are compared with experimental data obtained by optical emission spectroscopy. The calculated plasma temperature and electron density are shown to be in good agreement with the measured ones.
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.
An improved algorithm for calibration-free laser induced breakdown spectroscopy (CF LIBS) will be presented which includes several novel features in comparison with previously proposed similar algorithms. In particular, it allows using spectral lines with arbitrary optical thickness for the construction of Saha-Boltzmann plots, retrieves the absorption path length (plasma diameter) directly from a spectrum, replaces the Lorentzian line profile function by the Voigt function, and allows for self-absorption correction using pre-calculated and tabulated data rather than approximating functions. The tabulated data embody the solutions of the radiative transfer equation for numerous combinations of optical thicknesses and line widths. The algorithm is thoroughly verified using synthetic spectra.
The equation of state for plasmas containing negative and positive ions of elements and molecules formed by these elements is modeled under 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–Hückel theory. The hierarchy problem for constants of molecular reactions is resolved by using three different algorithms for high, medium, and low temperatures: the contraction principle, the Newton–Raphson method, and a scaled Newton–Raphson method, respectively. These algorithms are shown to have overlapping temperature ranges in which they are stable. The latter allows one to use the developed method for calculating the equation of state in combination with numerical solvers of Navier–Stokes equations to simulate laser-induced Plasmas initiated in an atmosphere and to study formation of molecules and their ions in such plasmas. The method is applicable to a general chemical network. It is illustrated with examples of Ca–Cl and C–Si–N laser-induced plasmas.
Laser induced plasma (LIP) is a highly dynamic, short living event which presents significant difficulty for both diagnostics and modeling. The former requires precise spatially- and time-resolved measurements on a micron-nanosecond scale while the latter needs numerous descriptive parameters; many of them can only be obtained from experiment. Diagnostics and modeling should always complement each other for obtaining a truthful picture of LIP.
In this presentation, a newly developed collisional-dominated model will be presented. The model is based on the coupled Navier-Stokes, state, radiative transfer, material transport, and chemical equations. The model incorporates plasma chemistry through the equilibrium approach that relies on atomic and molecular partition functions. Several chemical systems are modeled including Si-C-Cl-N and B-H-Cl systems.
The model is used to study the equilibrium states of the systems as functions of the concentrations of plasma species and plasma temperature. The model also predicts the evolution of number densities of atomic and molecular species in the expanding plasma plume.
This course will provide an introduction to plasma diagnostic techniques. The major focus of the course will be on the discussions of the practical procedures as well as the underlying physical principles for the measurements of plasma fundamental characteristics (e.g., temperatures, thermodynamic properties, and electron number density). Particular emphasis will be placed on inductively coupled plasma–atomic emission spectrometry, but other analytical plasmas will also be used as examples when appropriate. Selected examples on how one can manipulate the operating conditions of the plasma source, based on the results of plasma diagnostic measurements, to improve its performance used for spectrochemical analysis will also be covered. Topics to be covered include thermal equilibrium, line profiles, temperatures, electron densities, excitation processes, microreactions, pump and probe diagnostics, tomography, temporal and spatial resolution. Basics of plasma computer modeling will be presented.
An improved algorithm for calibration-free laser induced breakdown spectroscopy (CF LIBS) is presented which includes several novel features in comparison with previously proposed similar algorithms. In particular, it allows using spectral lines with arbitrary optical thickness for the construction of Saha-Boltzmann plots, retrieves the absorption path length (plasma diameter) directly from a spectrum, replaces the Lorentzian line profile function by the Voigt function, and allows for self-absorption correction using pre-calculated and tabulated data rather than approximating functions. The tabulated data embody the solutions of the radiative transfer equation for numerous combinations of optical thicknesses and line widths. The algorithm is thoroughly verified with synthetic spectra.
Laser-induced plasmas are widely used in many areas of science and technology; examples include spectrochemical analysis, thin film deposition, material processing, and even jet propulsion. Several topics will be addressed. First, general phenomenology of laser-induced plasmas will be discussed. Then, a chemical model will be presented based on a coupled solution of Navier-Stokes, state, radiative transfer, material transport, and chemical (Guldberg-Waage) equations. Results of computer simulations for several chemical systems will be shown and compared to experimental observations obtained by optical imaging, spectroscopy, and tomography. The latter diagnostic tools will also be briefly discussed. Finally, a prospective application of laser-induced plasma and plasma modeling will be illustrated on the example of calibration-free MC LIBS (Monte Carlo Laser Induced Breakdown Spectroscopy), in which concentrations of elements in materials are found by fitting model-generated and experimental spectra.
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.
A novel technique based on laser induced plasma imaging is proposed to measure residual pressure in sealed containers with transparent walls, e.g. high voltage vacuum interrupter in this paper. The images of plasma plumes induced on a copper target at pressure of ambient air between 10−2Pa and 105Pa were acquired at delay times of 200ns, 400ns, 600ns and 800ns. All the plasma images at specific pressures and delay times showed a good repeatability. It was found that ambient gas pressure significantly affects plasma shape, plasma integral intensities and expansion dynamics. A subsection characteristic method was proposed to extract pressure values from plasma images. The method employed three metrics for identification of high, intermediate and low pressures: the distance between the target and plume center, the integral intensity of the plume, and the lateral size of the plume, correspondingly. The accuracy of the method was estimated to be within 15% of nominal values in the entire pressure range between 10−2Pa and 105Pa. The pressure values can be easily extracted from plasma images in the whole pressure range, thus making laser induced plasma imaging a promising technique for gauge-free pressure detection.
We found cascade IR generation in Al laser induced plasma. This generation includes doublet transitions 3s25s 2S1∕2→ 3s24p 2P1∕2,3∕2 → 3s24s 2S1∕2; corresponding to strong lines at 2110 and 2117 nm, and much weaker lines at 1312–1315 nm. The 3s25s2S 1∕2 starting IR generation level is directly pumped from the 3s23p 2P3∕2 ground level. The starting level for UV generation at 396.2 nm (transitions 3s24s 2S1∕2 → 4p 2P3∕2) is populated due to the fast collisional processes in the plasma plume. These differences led to different time and special dependences on the lasing in the IR and UV spectral range within the aluminum laser induced 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 least-square 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.
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.
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
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.