Laser-induced plasma electron number density: Stark broadening method versus the Saha Boltzmann equation

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1 Plasma Science and Technology PAPER Laser-induced plasma electron number density: Stark broadening method versus the Saha Boltzmann equation To cite this article: Arnab Sarkar and Manjeet Singh 2017 Plasma Sci. Technol Related content - Characterization of laser induced plasmas by atomic emission spectroscopy Diego M Díaz Pace, Graciela Bertuccelli and Cristian A D'Angelo - Time-Resolved Emission Spectroscopic Study of Laser-Induced Steel Plasmas M. L. Shah, A. K. Pulhani, B. M. Suri et al. - Spectroscopic characterization of laser ablated silicon plasma Hira Shakeel, M Mumtaz, S Shahzada et al. View the article online for updates and enhancements. Recent citations - Qualitative and quantitative analysis of human nails to find correlation between nutrients and vitamin D deficiency using LIBS and ICP-AES M.A. Almessiere et al - Time-resolved evaluation of uranium plasma in different atmospheres by laserinduced breakdown spectroscopy Manjeet SINGH and Arnab SARKAR This content was downloaded from IP address on 30/10/2018 at 14:39

2 2017 Hefei Institutes of Physical Science, Chinese Academy of Sciences and IOP Publishing Printed in China and the UK Plasma Science and Technology Plasma Sci. Technol. 19 (2017) (9pp) doi: / /19/2/ Laser-induced plasma electron number density: Stark broadening method versus the Saha Boltzmann equation Arnab SARKAR and Manjeet SINGH Fuel Chemistry Division, Bhabha Atomic Research Centre, Mumbai , India Received 2 June 2016 Accepted for publication 19 August 2016 Published 19 January 2017 Abstract We report spectroscopic studies on plasma electron number density of laser-induced plasma produced by ns Nd:YAG laser light pulses on an aluminum sample in air at atmospheric pressure. The effect of different laser energy and the effect of different laser wavelengths were compared. The experimentally observed line profiles of neutral aluminum have been used to extract the excitation temperature using the Boltzmann plot method, whereas the electron number density has been determined from the Stark broadened as well as using the Saha Boltzmann equation (SBE). Each approach was also carried out by using the Al emission line and Mg emission lines. It was observed that the SBE method generated a little higher electron number density value than the Stark broadening method, but within the experimental uncertainty range. Comparisons of N e determined by the two methods show the presence of a linear relation which is independent of laser energy or laser wavelength. These results show the applicability of the SBE method for N e determination, especially when the system does not have any pure emission lines whose electron impact factor is known. Also use of Mg lines gives superior results than Al lines. Keywords: plasma parameter, laser induced plasma, plasma electron density, Saha-Boltzmann method, Stark broadening method (Some figures may appear in colour only in the online journal) 1. Introduction The optical emission spectroscopy (OES) of laser-induced plasma (LIP), which is also known as laser-induced breakdown spectroscopy (LIBS) has become a powerful tool for the fundamental studies of laser material interaction and for many practical applications, e.g., the application of pulsed laser deposition for thin film growth, etc. LIBS is a unique technique in the modern analytical science world, which allows fast and standoff analysis of any type of material for diverse practical analytical problems. Apart from LIBS s analytical application, a distinguishing feature of LIBS is its capability to carry out characterization of the LIPs by studying the fundamental plasma parameters, such as excitation temperature (T ex ), electron density (N e ), their temporal character, effect of the laser energy (E L ) or laser irradiation wavelength etc. These data are essential for understanding the energy transport mechanism into the plasma. The interest and importance of LIPs characterization are based on the fact that, the spectral line intensity and continuum emission of the LIPs depends on the plasma parameters. Improvements of these two factors improve the quality of LIBS analytical results. A detailed systematic discussion of plasma characterization was reported by Griem [1, 2], Lochte-Holtgreven [3] and Bekefi [4]. Adrain et al and Cremers et al described the principles for characterization of LIPs by OES [5, 6]. The principles of these characterizations are mainly based on the assumption of local thermodynamic equilibrium (LTE). The Boltzmann distribution law is usually used to measure the T ex [3]. For N e measurement, three different methods were reported in the literature: the Stark broadening (StB) method [7 14], the Stark shifting (StS) method [15 17] and the use of the Saha Boltzmann equation (SBE) [18 21] /17/ $

3 Both the StB and StS methods are based on the Stark effect phenomenon in plasmas, which is due to the collisions of the emitting atoms/ions with electrons and ions. The electric field generated by these fast moving electrons/ions in the plasma perturbs the energy levels of the individual atoms/ ions, thereby broadening the resultant emission lines (StB). This perturbation is also unsymmetrical in nature and hence there will be small shifts of the intensity maxima of line profiles (StS) produced by the Stark effect. In a LIP, the LTE assumption is based on the fact that the characteristic collision time is much less than the characteristic time of radioactive decay. In this scenario, it is valid to assume that the StB is the dominant broadening mechanism in the LIP, in comparison with the natural broadening and/or Doppler broadening. Hence broadening of an emission line along with the shift of intensity maxima can be correlated with the electron and ionic density as described by Griem [1, 2]. For non-hydrogen neutral atoms and singly ionized atoms, the FWHM (full width at half maximum) (Δλ 1/2 ) of an emission line due to StB is expressed as equations (1) and (2) for lines of neutral atoms and singly ionized atoms respectively. - 2W N A N 3 N W D 1 3, 4 ( 1) 5 4 e e D l1 2= W N A N 6 N W D ( 2) 5 4 e e D l1 2= W is the electron impact parameter, A is the ion broadening parameter and N D is the number of particles in the Debye sphere. Δλ 1/2 is in Å unit and N e is in cm 3 unit. The right-hand sides of equations (1) and (2) consist of two contributions, the first part is the electron contribution and the second part is the ion correction to the StB. Since StB of well isolated lines from species is predominantly caused by electron impact, the expression can be simplified as: 10 D W N e ( 3) The limitation of this technique is the availability of the W value database which is very limited [1, 2, 22, 23]. Again no uncertainties have been reported for W values in the literature for Al lines, but Ortiz et al reported an uncertainty of 20% for W values of Au(I) lines [24]. Assuming the same error level on W, and 5% uncertainty in the FWHM measurement, a simple uncertainty propagation calculation shows 20% uncertainties on the N e value determined by the StB method. For high Z elements (Z > 20) only a few W data are available. Hence, if the system under study does not have an emission line whose W is known then the use of the StB method is not possible. The same argument is valid for the StS method also, which also correlates the shift of peak maxima with N e. The N e determination based on the SBE used the wellknown Saha ionization equation, with the T ex determined by Boltzmann plot [20, 21]. N Iij z e = + Iij z ij z 1 z 1 gi lij z p 3 2 mkbte + A g l h ij z z i ij z E - E - E i z i z 1 z kbte 2 A 2 exp. ( 4) Here, ionization states of a species are represented by superscript Z (0 for neutral and 1 for singly ionized species). I ij is the observed intensity of wavelength λ ij, A ij is the Einstein coefficient of transition probability for spontaneous transition. E i, g i, h, c, m, k B and E are the energy of the upper energy level, the degeneracy of the upper energy level, the Planck constant, the speed of light in a vacuum, mass of electron, Boltzmann s constant and the ionization energy respectively. In the SBE method, one only needs to know the intensity of two emission lines of the different ionization level and the T ex. Other parameters are constant for a set of emission lines and are available for almost all prominent emission lines in the database. But a simple error propagation calculation reveals that, if the determined intensity, transition probability and T ex all have 15% 30% error, the N e value by the SBE method will have 65% 80% error. This clearly shows the reason for the unpopularity of the SBE method. The aim of the present work is to study and compare the temporal behavior of N e determined by the StB as well as SBE methods, in LIP generated on a nuclear grade Al sample. The effect of choosing different emission lines on the overall behavior of N e determined by the StB and SBE methods are also studied. The effect of laser wavelengths (266, 532 and 1064 nm) as well as different E L (35, 45 and 60 mj) on this temporal profile was also evaluated. 2. Experimental procedures 2.1. LIBS system and measurements A common configuration for a laboratory LIBS system described elsewhere was used for the present study (figure 1) [25]. In short, a Nd:YAG laser equipped with the 1st (1064 nm), 2nd (532 nm) and 4th harmonic (266 nm) was focused using a plano-convex lens ( f = 25 cm) to produce a LIP. Three different E L were used in the present study, 35, 45 and 60 mj. Laser pulse energy was measured with a pre-calibrated energy meter (Ophire Photonics, Israel). The plasma emission was collected at a 45 angle with respect to the laser beam direction, through a collimator. A collimator is a light collection system consisting of UV grade quartz lenses/mirrors (CC52, Andor, UK), and it images the plasma onto a high resolution echelle spectrometer (Mechelle, ME5000, Andor, UK) by using an optical fiber (core diameter 200 μm). The spectrograph is attached with an intensifier charge coupled device (ICCD), (istar, Andor, UK) embedded with a delay generator. The detector is in synchronization with the Q-switch of a laser pulse, to control acquisition time delay (t d ) and gate width (t w ). Intensity and wavelength calibrations of the spectrograph-iccd were carried out using NIST certified 2

4 Figure 1. LIBS experimental set up used for the present study. deuterium quartz tungsten halogen [DH2000, Ocean Optics, USA] and Hg Ar lamps [HG-1, Ocean Optics, USA], respectively. The samples were placed on an XYZ-translator stage (Velmex, USA) and analyzed in ambient atmosphere here. An in-house written program in LabVIEW was used, which can analyze LIBS spectra to report the background subtracted area under a peak and also fit the peaks in the Lorentzian profile Analysis The Indian nuclear research reactor, Dhruva, uses Al as a cladding material. Specifically Al-1S is used for the cladding for uranium metal fuel. For the present study this Al sample obtained from the Atomic Fuel Division, BARC was used. The material is 99.5% pure Al with impurity of Cu (500 ppm), Mg(300 ppm), Mn(500 ppm), Si(1000 ppm), Fe (1700 ppm), Ti(300 ppm) and Zn (800 ppm). The sample was analyzed at three different E L, 35, 45 and at 60 mj using 532 nm laser to compare the effect of E L.To compare the effect of different laser wavelengths, samples was analyzed at 60 mj using 266, 532 and 1064 nm in air at atmospheric pressure. A constant t w of 2.5 μs was chosen for getting an adequate signal at the highest delay time while still maintaining a good temporal resolution. To get a good signalto-noise ratio and keeping in mind that only 300 ppm Mg (which was used in N e calculation, discussed later) is present in the sample, the acquisition of the spectra was carried out by accumulating 50 single shot spectra (>50 accumulations was causing the strongest emission peak to reach near detector saturation). To avoid any local inhomogeneities in the sample surface or any other factor, in every experimental condition, five replicate analyses were carried out at five different positions randomly selected on the sample surface. The Hampel outlier procedure was applied to remove any outlier from replicate analysis of T ex or N e [26]. The plasma emission spectrum was recorded at several t d while varying the pulse energy and/or laser wavelength. The acquisition delay times used were in the range of 50 ns 4 μs. 3. Results and discussions One of the utmost important factors for LIP characterization by LIBS is to find out emission lines of interest with good signal-to-noise ratio having known spectroscopic constant values. Carefully studying the LIBS spectrum of the Al-1S sample, eight atomic Al emission lines, one each of Al ionic, Mg atomic and Mg ionic emission lines were selected based on spectral purity and intensity, which were used for T ex and N e calculation. The NIST and Kurucz database was used to identify these emission lines tabulated in table 1 [27, 28]. To check the existence of self-absorption, the line pair Al(I) nm and Al(I) nm was chosen as these two lines have the same upper energy level and with a change of t d,if there is self absorption the intensity ratio will change, which was not observed at any E L of t d. A typical LIBS emission spectrum generated by the 532 nm laser at a t d of 1.5 μs and 60 mj energy is shown in figure Excitation temperature (T ex ) Effect of laser energy. As mentioned previously, the T ex is determined by Boltzmann plot. The atomic emission lines of Al, tabulated in table 1 are used for the estimation. Figure 3 shows a typical Boltzmann plot for T ex determination in the Al- 1S sample at different t d. The temporal profile of T ex at different E L measured at 532 nm is shown in figure 4. Irrespective of the E L,theT ex was found to decrease as the t d was increased. The error bar on the temperature is calculated from the standard deviation of five replicate analyses, which varies from 3% to 8% for all energies. At a very early stage of plasma evaluation (<500 ns) the plume emits a strong continuum radiation due to mechanisms involving free electrons (inverse Bremsstrahlung (IB), radiative recombination and photoionization). So, information obtained about the plasma is inaccurate because of the overwhelming continuum emission for short acquisition delay times and hence was not used in this work. The plasma temperature follows the power law decay pattern [13, 21]. The plots for 35 mj ( T = t ex d 0.008), 45 mj ( T = t ) and 60 mj ( T = ex d ex 3

5 Table 1. Chosen emission lines for Al and Mg, and their respective spectroscopic data. Energy level Elements Ionization state Wavelength (nm) Transition coefficient (A ij )(s 1 ) Lower (E j )(cm 1 ) Upper (E i )(cm 1 ) g i Al I a a II Mg I II a Values were obtained from Kurucz database, the rest are from NIST. Figure 2. A typical LIBS emission spectrum generated by the 532 nm laser at a t d of 1.5 μs and 60 mj energy in the wavelength region nm of the Al-1S sample used in the present study. Figure 4. Plasma temperature (T ex ) as a function of acquisition time delay (t d ) at different laser energy of 532 nm for an Al LIP. t d ) with fittings are also shown in figure 4. The power law decay pattern indicates that the temperature diminishes rapidly with time in the early phase of plasma life. It then slows off and then levels off. The fast decay rate can be attributed to the plasma temperature gradient with atmosphere, while the slowing and leveling off at longer delay may be due to recombination processes. This implies the rate of decay in T ex, i.e., dt ex /dt d at a particular t d is faster at high E L.Thefaster T ex decay at high E L can be explained by the presence of a large difference between T ex and ambient temperature, which allows theenergytransfertobefaster.againhighert ex means faster expansion of plasma leading to faster decrease of T ex. For all the E L, after 2 μs acquisition delay, there were almost no variations in T ex. Figure 3. Boltzmann plot at E L 60 mj and 532 nm laser wavelength at different acquisition time delay Effect of laser wavelength. Similar to the study of E L, a study using different laser wavelengths at 60 mj E L was carried out. Figure 5 shows the temporal profile of T e at 266, 532 and 1064 nm. T ex is always higher for the 1064 nm LIP than 532 and 266 nm lasers. A high value of the T ex is 4

6 Figure 5. Plasma temperature (T ex ) as a function of acquisition time delay (t d ) at 60 mj E L using different laser wavelength for an Al LIP. attributed to the behavior of the main laser energy absorption procedure, i.e., IB. The IB coefficient has a λ 3 dependency (λ = wavelength of laser), which results in a higher IB effect in 1064 nm LIP than 532 nm and 266 nm. The high IB effect means more laser light absorption and hence more T ex. The rate of decay of T ex. i.e., dt ex /dt d (given in the inset of figure 5) increases with decreasing laser wavelength at any particular t d. This feature is more prominent in the <1 μs region. At larger delay small changes in temperature irrespective of the laser wavelength make this pattern very fussy. Contrary to the observation in figure 4, where LIP with high T ex decay faster, in the case of figure 5 where the effect of laser wavelength has been shown, the decay rate of high T ex plasma caused by 1064 nm laser is slower than the decay of 266 nm LIP. This effect can be explained by the fact that the 266 nm LIP is consisting of a higher N e than the other two wavelengths LIP (discussed later). A high N e implies a small time to dissipate energy to neighboring species and thereby faster decay of energy or the T ex of the plasma Electron density (N e ) Effect of laser energy. The N e was determined by both the StB and by the SBE method. H α ( nm) and H β ( nm) lines for N e determination is also reported by a few studies [29 32]. But in these reports the samples were either pure hydrogen gas or hydrogen rich compounds, which emit strong H α and H β emission lines. In the present study the sample does not contain any hydrogen, hence the only source of hydrogen is air (the hydrogen content in air is %). Moreover due to the use of a low throughput echelle spectrograph, in the spectra recorded in different conditions, both the H α and H β lines were very weak and in some cases were equivalent to the background signal. Hence the use of H α and H β lines were not performed in the study. By the StB method, both the Al(I) nm and Mg(II) nm were used to calculate N e. The W values used in this work are tabulated in table 2. For the StB method the required FWHM was obtained by fitting the emission lines to a Lorentzian peak. Figures 6(a) and (c) show the Lorentzian fitting of both the emission lines at different E L at 1 μs acquisition delay. The Stark line width Δλ 1/2 was extracted from the measured line width Δλ 1/2(observed) by subtracting the instrumental line broadening Δλ 1/2(instrument). In our case Δλ 1/2(instrument) was nm for Mg(II) nm and nm for Al(I) nm determined by measuring the FWHM of the Hg lines emitted by a standard low pressure Hg lamp. It was seen from figures 6(a), (c) that irrespective of the E L used, the FWHM remains almost constant for a particular emission line. This indicates a very similar N e. Figures 7(a), (b) show the temporal profile of N e determined at different E L by both the emission lines mentioned previously by the StB method. In the SBE method, both the Al and Mg line pairs were used for N e determination. The Mg line pair Mg(II) nm/mg (I) nm was used. In the case of Al, the ionic line Al(II) nm is paired with all the other eight atomic Al lines tabulated in table 1 and an average of the resultant N e was used. These eight N e values have 70% RSD among them as indicated by the error bar. Figures 7(c), (d) show the temporal profile of N e determined using both the Al and Mg line pair using the SBE method at different E L. The temporal profile of N e is shown in figure 7 and shows that irrespective of the method or emission lines used N e decreases with the t d following a power law. Because of the decay of the line intensity, the statistical errors in the determination of the FWHM increase from 3% to 10%, thus introducing a larger scatter of the data of N e in the high delay condition. The obtained values of N e in the present study are in the same range reported by Drogoff et al [33], Colan et al [34], and Ferrero et al [35]. Irrespective of the emission line used the magnitudes of the N e differ slightly from one E L to another, but within the same order of magnitude and within the range of the experimental errors (figures 7(a) (d)). The presence of a systematic difference between the N e temporal curves (determined by StB method) in magnitude could be attributed to the uncertainties of W of Al and Mg. A similar observation was also reported by Galmed et al [36]. It can be seen that the SBE method (figures 7(c), (d)) generates a little higher value N e (within one magnitude difference) than the StB method (figures 7(a), (b)) for both the emission lines, Al and Mg lines. But considering an uncertainty of 60% 80% on the SBE method s values of N e, the difference is within the experimental uncertainty range. In all cases power law decay was observed. After 1.5 μs t d, there were almost no variations in N e. To examine the equality or the presence of some relation in the temporal pattern of N e determined by either of the methods a comparison plot was constructed as shown in figures 8(a), (b). Fromfigure 8(a) it can be seen that the N e determined by the StB method using an Al line has a linear relation with the same determined using the SBE method, with a slope of 0.35 ± This relation is also true for N e determined using Mg lines, with a slope of 0.60 ± This indicates that the temporal profile of N e determined by the SBE method is not only good to compare relative changes but is true for magnitude with 60% 80% uncertainty. Also the use of the Mg line gives better results 5

7 Table 2. Electron impact factor (W) of the line used in this study for N e determination. Emission line Temperature (K) Electron impact factor (nm) N e o (cm 3 ) Reference Al(I) nm [22] Mg(II) nm [1, 2] Figure 6. Lorentzian fitting of Al(I) nm (a) & (b) and Mg(II) nm (c) & (d) emission line at three different E L (a) & (c) and at three different laser wavelengths (b) & (d) at 1 μs acquisition delay and 2.5 μs gate widths. than the Al line if we consider the StB method is the standard method. This relation is again independent of E L used to produce Al LIP Effect of laser wavelength. To evaluate the validity of the relation between N e determined by StB and SBE methods observed in different E L, the same was analyzed by producing Al LIP by different laser wavelengths. It was found that the N e produced by the 266 nm laser wavelength has always been higher than the same produced by 532 and 1064 nm. This is a reverse character to that of T ex. This can be explained on the basis of the fundamental difference in physics between IR, Vis and UV laser ablation. One of the fundamental processes in laser ablation is IB and its cross-section is related to the wavelength as [1 exp( hc/λkt]λ 3, and hence the plasma will be much more absorbing in the IR than in the UV [37]. Again reflectivity of laser light from the sample surface increases with an increase in laser wavelength [38]. Asa consequence the IR plasma is hotter than the UV plasma and less energy in the laser beam interacts directly with the sample surface in the IR laser case. Since more E L is used for ablation in 266 nm hence the amount of material is more in 266 nm created LIP and hence high N e. Figure 9 shows the temporal profile of N e for different laser wavelengths obtained using StB and SBE methods. The temporal profile was fitted with the power law equation for 1064 nm, 532 nm and 266 nm, (N e = t - d 0.481), (N e = t d ) and (N e = t d ) respectively. It can be seen that the rate of decay of N e is faster in 1064 nm LIP than that for 266 nm LIP. This can be explained by the presence of more amounts of ablated material on 266 nm LIP than 1064 nm LIP, which help to sustain the N e for a longer time. Similar to figures 8(a), (b), a comparison plot for N e determined in the different laser wavelength is constructed as shown in figures 8(c), (d). It is interesting to find that the 6

8 Figure 7. The plasma electron number density (N e ) as a function of acquisition time delay (t d ) at different E L for an Al LIP obtained by the SBE method (c) & (d) and the StB method (a) & (b) using Al (a) & (c) and Mg (b) & (d) lines. Figure 8. Correlation plot of the plasma electron number density (N e ) determined by SBE method and StB method using both Al (a) & (c) and Mg lines (b) & (d) at different energy (a) & (b) and different wavelength (c) & (d) in Al LIP. 7

9 Figure 9. The plasma electron number density (N e ) as a function of acquisition time delay (t d ) at different laser wavelength for an Al LIP obtained by SBE method (a) & (b) and StB method (c) & (d) using Al (a) & (c) and Mg (b) & (d) lines. relation between the StB and SBE methods is also applicable in the different laser wavelength originated Al LIP. In case of the use of Al lines the slope is 0.33 ± This relation is also true for N e determined using Mg lines, with a slope of 0.58 ± These values are almost identical to the one obtained at different energy ablated LIPs at 532 nm. The presence of such an identical relation between the N e determined by the StB method and SBE method clearly shows the applicability to use the SBE method for studying the N e temporal profile in a system where the use of the StB method is not possible because of the non-availability of emission line with known W values. But due to the high error associated with the N e values determined by the SBE method, the use of the SBE method for temporal profiling is advisable rather than calculating for a particular condition. 4. Conclusions LIBS was used to characterize the LIP of a nuclear grade Al sample. The temporal profile of LIP parameters (T ex and N e ) was studied at different E L and also against different laser wavelengths. Both T ex and N e show a power law decay pattern with increasing acquisition time delay. The T ex was found to increase with E L. It was also observed that the rate of decay of T ex has a positive correlation with E L and wavelength. StB and using the SBE were used to N e calculation by using both Al and Mg emission lines. Irrespective of the method or emission line used, the magnitudes of the N e remain constant with varying E L, while it decreases with the t d following a power law. Comparisons of N e determined by the two methods show the presence of a linear relation with coefficient, which is independent of E L or laser wavelength. These results show the applicability of the SBE method for N e temporal pattern determination, especially when the system does not have any pure emission lines whose electron impact factor is known. Acknowledgments The authors are thankful to Dr S Kannan, Head, Fuel Chemistry Division, Professor B S Tomar, Associate Director, Radiochemistry and Isotope Group and Professor K L Ramakumar, Director, Radiochemistry and Isotope Group, B.A.R.C. for their constant support and encouragement in LIBS work. All authors contributed equally to the present paper. References [1] Griem H R 1964 Plasma Spectroscopy (New York: McGraw-Hill) [2] Griem H R 1974 Spectral Line Broadening by Plasmas (New York: Academic) [3] Lochte-Holtgreven W 1968 Plasma Diagnostics (New York: Wiley) [4] Bekefi G 1976 Principles of Laser Plasma (New York: Wiley) [5] Cremers D A and Radziemski L J 1987 Laser Spectroscopy and its Applications (New York: Dekker) 8

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