Saha-Eggert Equation Research Articles

Gold fineness measurement using single-shot spark assisted laser-induced breakdown spectroscopy.

Here, a homemade gold fineness analyzer is fabricated based on calibration-free spark assisted laser-induced breakdown spectroscopy (CF SA-LIBS). The experimental arrangement consists of a Q-switched Nd:YAG laser combined with a spark generator and a single-channel CCD spectrometer. The well-arranged optical system, coupled with an electrical setup, allows us to successfully run SA-LIBS even at low energy single shots. The electric discharge contributes LIBS to reheat and promote more energetic plasma. Subsequently, plasma temperature elevates up to ∼20%, and its lifetime is elongated as much as 6 times. As a consequence, the relative signal intensity is enhanced up to 1 order of magnitude against that of LIBS at the same pulsed energy. Furthermore, the electron density is also measured based on the broadened spectral width of the intensified Hα line. The latter is used to obtain the ionic species concentrations more accurately according to the Saha-Eggert equation. As a result, we have assessed the gold karat with an analytical error less than 0.5% using CF SA-LIBS. In addition, the surface patterns recorded by the stylus profilometer reveal that the single-shot SA-LIBS benefits a smaller ablative mass against standard LIBS.

Truncation of a nanosecond CO2 laser pulse by following of the temporal characteristics of the plasma parameters in laser ablation model

The evolution of laser-induced plasma for an aluminum target in a helium ambient gas at different pressures of 100, 300, 500, 700, and 1000 mbar is numerically studied. A thermal model of laser ablation is utilized for calculation of plasma parameters which comprise heat conduction, Euler equations, Saha–Eggert equations, Knudsen layer boundary condition, mass and energy balance relations, and optical shielding effects. In addition, in order to determine the temporal parameters of aluminum's plasma, the hydrodynamic equations are computed for calculation of the plasma absorption due to inverse Bremsstrahlung and photoionization. A CO2 laser pulse at a wavelength of 10.6 μm with different pulse durations of 50 and 100 ns is irradiated on laser induced Al plasma for truncation of the transmitted CO2 laser pulse. The laser intensities irradiated on the Al sample for producing plasma and generation of a shortened pulse are considered as 1016, 1017, and 5 × 1017 W/m2. Furthermore, for validation of the theoretical calculations, some experimental results are presented. Results showed that higher helium gas pressures caused the critical density attained at earlier delay times which caused the CO2 laser beam became efficiently truncated. Moreover, it is concluded that pulse duration has an inverse relation with ambient gas pressure and laser intensity which means that the higher gas pressure or laser intensity induces less pulse duration.

Study of material ablation and plasma radiation in double-pulse laser induced breakdown spectroscopy at different delay times: Modeling and numerical simulation

A one-dimensional numerical model is presented on a copper sample to investigate double-pulse laser induced breakdown spectroscopy (DP-LIBS). The effect of the inter-pulse delay time on the material ablation, plasma homogeneity, and signal enhancement is examined. The dynamics of laser ablation, plume expansion, plasma formation, and plasma radiation of the ionized and neutral atoms in the presence of helium background gas at a pressure of 1 atm are studied. A heat conduction equation is solved in the sample and is coupled to the fluid dynamic equations through the Knudsen layer relations. Saha-Eggert equations are utilized to investigate the plasma formation. The influence of plasma shielding, due to the photoionization and inverse bremsstrahlung processes, is considered. Continuous radiation, bremsstrahlung and recombination radiations, and spectral emissions of the plasma are examined. The optimum inter-pulse delay time for maximizing the neutral and ionized spectral emissions is determined. The results reveal that the ablation rate in DP-LIBS is significantly higher than that of single pulse laser induced breakdown spectroscopy (SP-LIBS) and reaches its maximum at an optimum inter-pulse delay time due to the decrease in the recondensation of the ablated plume. Furthermore, it is demonstrated that in DP-LIBS, the ablation profile is smoother and its continuous radiation decreases much earlier than that of SP-LIBS. Although the double-pulse mode improves the signal to background ratio, it leads to more inhomogeneity in the plasma.

Laser-produced uranium plasma characterization and Stark broadening measurements

This work reports the spatiotemporal diagnostics of uranium species in plasma plumes produced by nanosecond near-infrared laser pulses in a low-pressure environment. Spatially and temporally resolved emission spectroscopy experiments are combined with the modeling of uranium emission for investigating the dynamics of the plume. The Saha-Eggert equation and Boltzmann plots generated from numerous U I transitions are used to infer temperature. This work also reports the measurements of uranium Stark broadening parameters for U I 499.01 nm and U II 500.82 nm transitions. The Stark widths of select U transitions were measured by comparing their linewidths with the broadening of the O I 777.19 nm line. The electron density was found to be of the order of 1016 cm−3, while the temperature was found to be in the range of 3000–9000 K. In addition to enhancing the fundamental understanding of high-Z plasmas in reduced-pressure environments, the knowledge of Stark broadening parameters could improve the modeling capabilities and analytical performance of techniques that rely on emission plasma spectroscopy.

A simple finite element model to study the effect of plasma plume expansion on the nanosecond pulsed laser ablation of aluminum

In this paper, a simple model was proposed using finite element analysis (FEA) with a commercial FEA software ABAQUS to simulate the two-dimensional (2-D) laser heat transfer in an aluminum material. Without relying on the conventional hydrodynamic model, the proposed model not only predicts the evolutions of the temperature field and ablation profiles in the target material, but also provides an estimation on the evolutions of electron density, plasma temperature, and plasma absorption coefficient. The assumptions used in the model include the local thermal equilibrium and additional assumptions regarding the average plasma temperature and vapor density. The assumptions allowed the laser heat transfer equation to be solved together with the Saha–Eggert equation and conservation equations of matter and charge. When compared to the existing hydrodynamic models, the proposed model solves a less number of nonlinear equations and hence is computationally more efficient. The proposed FE model was employed to study the plasma-shielding effect on PLA produced by a 193 nm Excimer laser and a 266 nm Nd:YAG laser. The predictions of ablation depths, electron density, and plasma temperature agree well with the experimental data. Moreover, effects of the laser intensity and the average plasma temperature on the efficiency of the plasma shielding during PLA were also investigated and discussed in this study.

Characteristics of a plasma flow field produced by a metal array bridge foil explosion

To improve the energy utilization efficiency of metal bridge foil explosion, and increase the function range of plasmas, array bridge foil explosion experiments with different structures were performed. A Schlieren photographic measurement system with a double-pulse laser source was used to observe the flow field of a bridge foil explosion. The evolution laws of plasmas and shock waves generated by array bridge foil explosions of different structures were analyzed and compared. A multi-phase flow calculation model was established to simulate the electrical exploding process of a metal bridge foil. The plasma equation of state was determined by considering the effect of the changing number of particles and Coulomb interaction on the pressure and internal energy. The ionization degree of the plasma was calculated via the Saha–Eggert equation assuming conditions of local thermal equilibrium. The exploding process of array bridge foils was simulated, and the superposition processes of plasma beams were analyzed. The variation and distribution laws of the density, temperature, pressure, and other important parameters were obtained. The results show that the array bridge foil has a larger plasma jet diameter than the single bridge foil for an equal total area of the bridge foil. We also found that the temperature, pressure, and density of the plasma jet’s center region sharply increase because of the superposition of plasma beams.

Developing the model of laser ablation by considering the interplay between emission and expansion of aluminum plasma

In the present study, the ablation behavior of aluminum target and its plasma radiation in noble ambient gases by a laser pulse with wavelength of 266 nm and pulse duration of 10 ns are numerically studied. A thermal model of laser ablation considering heat conduction, Euler equations, Saha-Eggert equations, Knudsen layer, mass and energy balance relations and optical shielding effects are used for calculation of plasma parameters. Effects of excitation energy on plasma expansion and its emissivity are investigated. Time and spatial-resolved plasma emission including bremsstrahlung, recombination and spectral emission at early delay times after laser irradiation is obtained. Effects of two ambient gases (He and Ar) as well as different gas pressures of 100, 300, 500, and 760 Torr on plasma expansion and its spectrum are studied. Results illustrate that at initial delay times, especially at high noble gas pressures, ionic lines have the maximum intensities, while at later times neutral lines dominate. When the pressure of ambient gas increases, a confinement of the plasma plume is predicted and the intensity of neutral lines decreases. Continuous emission increases with wavelength in both ambient gases. Spatially resolved analysis shows that an intense continuous emission is predicted next to the sample surface decreasing with distance from the latter.

Simulation of nanosecond pulsed laser ablation of copper samples: A focus on laser induced plasma radiation

A thermal model for nanosecond pulsed laser ablation of Cu in one dimension and in ambient gas, He at 1 atm, is proposed in which equations concerning heat conduction in the target and gas dynamics in the plume are solved. These equations are coupled to each other through the energy and mass balances at interface between the target and the vapor and also Knudsen layer conditions. By assumption of local thermal equilibrium, Saha–Eggert equations are used to investigate plasma formation. The shielding effect of the plasma, due to photoionization and inverse bremsstrahlung processes, is considered. Bremsstrahlung and blackbody radiation and spectral emissions of the plasma are also investigated. Spatial and temporal distribution of the target temperature, number densities of Cu and He, pressure and temperature of the plume, bremsstrahlung and blackbody radiation, and also spectral emissions of Cu at three wavelengths (510, 516, and 521 nm) are obtained. Results show that the spectral power of Cu lines has the same pattern as CuI relative intensities from National Institute of Standard and Technology. Investigation of spatially integrated bremsstrahlung and blackbody radiation, and also Cu spectral emissions indicates that although in early times the bremsstrahlung radiation dominates the two other radiations, the Copper spectral emission is the dominant radiation in later times. It should be mentioned that the blackbody radiation has the least values in both time intervals. The results can be used for prediction of the optimum time and position of the spectral line emission, which is applicable in some time resolved spectroscopic techniques such as laser induced breakdown spectroscopy. Furthermore, the results suggest that for distinguishing between the spectral emission and the bremsstrahlung radiation, a spatially resolved spectroscopy can be used instead of the time resolved one.

Survey analysis by inductively coupled plasma mass spectrometry without the use of standard reference materials

The reference-free analysis of a standard solution containing 21 elements was performed on an inductively coupled plasma mass spectrometer. The relative sensitivity coefficients of the elements were calculated taking into account the absolute electronegativities of atoms in accordance with the new approach that was developed previously for single-element solutions. The accuracy was evaluated. The results obtained using the new approach were compared with the data calculated by the Saha–Eggert equation and a quasi-equilibrium model, which use ionization potentials.

Nonlinear effects of laser-plasma interaction on melt-surface temperature

A plume consisting of vapour and ionized particles of the workpiece is usually formed during various types of laser materials processing. The characteristics of this plume depend on a large number of parameters such as the laser power, spot size, scanning speed, material properties and shielding gas. The height, radius, temperature and absorption coefficient of the plasma are calculated for various values of process parameters. The surface temperature of the melt pool and the vaporization rate are also calculated on the basis of the Stefan condition at the liquid-vapour interface. The absorption coefficient of the plasma given by the Kramers-Unsöld relation and the ionization fraction given by the Saha-Eggert equation are used to model the laser beam propagation through the plasma. A detailed analysis of the plasma stability indicates that absorption of the laser beam by the plasma affects the melt-pool surface temperature nonlinearly.

Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum

The interaction of pulsed laser irradiation of nanosecond duration with a metal surface is studied by numerical simulation. The heat transfer in the solid substrate and the melted liquid is modeled as one-dimensional transient heat conduction using the enthalpy formulation for the solution of phase change problems. A discontinuity layer is assumed just above the liquid surface. Mass, momentum, and energy conservation are expressed across this layer, while the vapor across the discontinuity is modeled as an ideal gas. The compressible gas dynamics is computed numerically by solving the system of Euler equations for mass, momentum, and energy, supplemented with an isentropic equation of state in a two-dimensional axisymmetric system of coordinates. The excimer laser-beam absorption and radiation transport in the vapor phase are modeled using the discrete ordinates method. The rates for ionization are computed using the Saha–Eggert equation assuming conditions of local thermal equilibrium. The inverse bremsstrahlung mechanism is considered as the main mechanism of plasma absorption. Results show that a thin, submicron vapor layer is formed above the target surface in the duration of laser pulse while thermal radiation plays the key role for plume cooling during the period of strong absorption by the plasma. The release of a very strong shock wave, propagating with a speed of 104 m/s, is observed in the evaporating plume.

Simulation of Positive Secondary-Ion Emission from Ar+-(or O2+-)Bombarded Fe-Based Alloys by Local Thermodynamic Equilibrium Model.

Low-alloy and stainless steels of known composition were Ar+-(or O2+-) bombarded, and the secondary ion currents were converted to elemental concentrations with a help of the Saha-Eggert equation. When the secondary ions are emitted from the surface layer which contains as many oxygen atoms as possible, the calculated concentrations were sufficiently close to the specified values for most constituent elements. This indicates that the secondary ion emission from the surface layer of steels can be simulated by the local thermodynamic equilibrium model when the layer contains many oxygen atoms.

Analytical characterization of sample entraining multi-electrode plasma sources for atomic emission spectroscopy–II. Interelement effects and excitation temperature measurements

Interelement effects are reported for a vertical 4-electrode plasma source. The magnitude and direction of the interelement effects are influenced by the experimental conditions. For a 30-mm plasma length, the interference effect of either phosphate or aluminum on calcium emission is insignificant over the entire vertical region of the plasma observed. Ionization interference effects on Ca(II) emission produced by an easily ionized element (EIE) are in general agreement with observations in an inductively coupled plasma (ICP). Nine Fe(I) lines were used to determine the excitation temperature from the slope of a Boltzmann plot. The excitation temperature in the center of the 25-mm plasma at 6mm above the quartz tube is 5800 ± 600 K. As the plasma length increases from 25 to 30 mm, the maximum excitation temperature in the sample aerosol channel increases by 2000 K and changes spatially. The electron number density increases by a factor of 10. Under the assumption of local thermal equilibrium (LTE), the electron number density obtained from the Saha-Eggert equation is about 1.0 × 10 15 cm −3 for a 30-mm plasma. As the sample carrier gas flow rate decreases from 0.85 to 0.711/min, the maximum excitation temperature for a 30-mm plasma increases by 1000 K.

Role of electronic partition function in quantitative SIMS using the Saha-Eggert equation

Methods of obtaining the electronic partition functionsZ were discussed with an intention to use them for the Saha-Eggert quantification in SIMS. The Lagrange's interpolation formula and the least-squares method were applied to the published values ofZ to obtain the expression for calculatingZ at arbitrary temperatures. With the aid of the Saha-Eggert equation, the secondary-ion currents from Ni-Cr and Fe-Ni-Cr alloys were converted into the elemental concentrations for the two types ofZ: those obtained with the above methods and those with the approximate fifthorder polynomials presented by de Galan and others. It was proved, from the comparison of the calculated concentrations, that the latter are valid for the quantification in SIMS using the Saha-Eggert equation. The largest error in the elemental concentrations was 22% for the Ni-Cr alloy and 7% for the Fe-Ni-Cr alloy.

Electron density characterization of 27.1 and 50 MHz inductively coupled plasmas by means of Abel corrected Stark broadened H β line profiles

Stark broadened profiles of the H β line were employed to obtain spatially resolved electron number densities in 27.12 and 50 MHz inductively coupled plasmas emission sources. A computerized system was developed for measuring the H β line profile with two stepping motors, which together provided a wavelength scan of the H β line profile, as well as a lateral displacement of the plasma image across the entrance slit. This system thus enables the spatially integrated Stark broadened H β line profile radiances to be converted to radially corrected profiles by using Abel integral equations. The fractional Stark widths (α 1 2 ) calculated by Griem were used to obtain electron density values from the halfwidths of the radially resolved H β line profile. Electron number densities were obtained at various heights and gas flows to characterize the electron number density gradients, which ranged between 1 × 10 21 and 5 × 10 21 m −3 for these investigations and agree very well with values obtained by methods based on continuum measurements and the Saha-Eggert equation.

Improvement in quantitative correction in SIMS using Saha-Eggert equation

Improvement in Quantitative Correction in SIMS Using Saha-Eggert Equation A quantitative conversion of the secondary-ion current intensities into the elemental concentrations using the Saha-Eggert ionization equation was tried with a 78Ni-18Cr-1Ti-1Fe-1Cu-1Zr (each in at %) alloy. Improvements were made on the best-fit search of fitting parameters (T andN e). It proved to be important for the success in the conversion (1) to use the secondary-ion intensities from the sample in oxygen gas of >1.5×10−3 Pa, (2) to add the molecularion intensities to those of mother atomic ions even when the former are small and (3) to search for the fitting parameters considering the relative errors of concentrations not only for the internal standards but for as many elements as possible. With these procedures the largest error of elemental concentration could be reduced to 22% (Ar+ bombardment), 31% (O2 + bombardment) and 19% (N2 +bombardment).

Molecular rearrangement and cluster formation in the secondary ion mass spectra (SIMS) of fluoride salts

Secondary ion clusters with mass greater than 700 amu, e.g., K(KF) 12 + and up to 27 atoms, e.g., Na(NaF) 13 +, have been observed in the static SIMS spectra of MF (M = Li, Na, K), NaBF 4, and KPF 6. The long series of detected cluster ions of the type M(MF) n + indicates that there is a high degree of stability associated with these clusters. The observation of such clusters in the NaBF 4 and KPF 6 spectra suggest that there is significant molecular rearrangement occurring in the secondary ion emission process from such salts. The secondary ion Intensities provide a crude fit to the Saha-Eggert equation, yielding an electron temperature of ~12,000 K. The data are consistent with the plasma model of surface ionization in which rearrangement and cluster formation occur in the plasma.

The measurement of electrode vapour concentration from light-scattering experiments in a high-current arc plasma in air

In the arc discharge in air with copper electrodes, the characteristics are very strongly affected by the local density of the electrode vapour, because of its lower ionisation potential compared with those of the components of air, nitrogen and oxygen. In this paper, from the assumption of local thermodynamic equilibrium, the Saha-Eggert equation is solved and the copper vapour effect on the laser light scattering profile is determined so that the copper concentration may be obtained.

Quantitative Analysis of Compound Semiconductors with an Ion Microanalyzer

The quantitative correction procedures of an ion microanalysis based on the Saha-Eggert equation was applied to Si doped GaAs Samples to examine validity of the appli-cation. The Si concentrations in GaAs measured by means of Emission Spectroscopy were used as standard values. The agreement between calculated and standard concentrations was very good, especially in the case of the measurement with an O2+ beam. In this calculation, the SUMT method was adopted as a minimum seeking method. A mechanism of secondary ion emission from GaAs samples was also discussed on the basis of the LTE plasma theory. The results;(i)the secondary ion intensities don't increase with introduction of oxygen gas into a target chamber, which shows the mechanism of secondary ion emission is not “Chemical Process”.(ii)The target atoms are ionized by “Chemical Process” with energetic O2+ion bombardment.

On the use of the saha-eggert equation for quantitative sims analysis using argon primary ions

Samples of known composition have been bombarded by Ar + ions. The resulting secondary ion mass spectra, obtained with two different types of SIMS instruments, were used to check the validity of the Saha-Eggert equation for the case of Ar + ion bombardment.