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Broadening of the resonance Cu I lines in the laser-induced copper spectrum
Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
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Broadening of the resonance Cu I lines in the laser-induced copper spectrum M. Burger, M. Skočić, Z. Nikolić, S. Bukvić n, S. Djeniže University of Belgrade, Faculty of Physics, POB 368, 11000 Belgrade, Serbia
a r t i c l e i n f o
abstract
Article history: Received 17 April 2013 Received in revised form 18 September 2013 Accepted 19 September 2013 Available online 7 October 2013
Broadening of the resonance 324.754 nm and 327.396 nm copper (Cu I) lines have been investigated in the laser-induced copper spectrum in the residual atmospheric pressure of 8 Pa at 19 300 K electron temperature, and electron density of 2.1 1023 m 3. The second harmonic of the Nd:YAG laser at 532 nm was applied for evaporation of atoms from the copper target. The Stark and Doppler broadening were found as the most significant mechanisms in the line shape formation at the actual plasma parameters. Measured Stark widths (W) were compared to existing experimental and theoretical W data. The role of the hyperfine structure (HFS) components in the resonance Cu I line shapes formation was, for the first time, discussed taking also into account the isotope shift (IS). & 2013 Elsevier Ltd. All rights reserved.
Keywords: LIBS Emission spectroscopy Line broadening Stark effect
1. Introduction Copper (Cu) is one of the most exploited elements in the various fields of the industry and technology [1–3]. It has two stable isotopes: 63Cu and 65Cu (69.2% and 30.8% abundances, respectively) with isospins of 3/2. The spectral line characteristics of the copper atoms (Cu I) are affected by both the isotope shift (IS) and hyperfine structure (HFS) due to considerable isospin. The intense resonance 324.754 nm and 327.396 nm lines are good candidates for diagnostic purposes in various applications. Due to different kind of broadenings one can expect a complex profile of Cu I lines, especially the resonance 324.751 nm and 327.396 nm lines. It is of interest to study the shape of these lines in realistic plasma conditions with emphasize on possible application in plasma diagnostics. Broadening mechanisms for certain number of the visible range Cu I spectral lines have been investigated in laser-generated plasma by Song et al. [4] and Man et al. [5]. In the plasmas with electron density (N) higher than 1022 m 3 and electron temperature (T) below 20 000 K the Stark broadenings are dominant broadening mechanisms in the spectral line
n
Corresponding author. Tel: þ381 11 7158 168; fax: þ 381 11 3282 619. E-mail address: [email protected] (S. Bukvić).
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shape formation [6]. However, the other mechanism found to be non-negligible is a Doppler broadening. The literature devoted to the Cu I resonance spectral lines Stark widths is presented in [7] and references therein. Only one experiment [8] deals with 324.754 nm Cu I line Stark FWHM (Full Width at Half Maximum, W). The Stark effect of resonance Cu I lines is considered theoretically in [9–11]. To the knowledge of the authors, the contribution of the hyperfine structure components on the resulting shape of the two Cu I resonance lines is discussed in only one paper [12]. The aim of this work is to present experimental Stark FWHM of the two intense resonance Cu I lines observed in the laser-induced copper plasma in the residual atmospheric pressure. We present, also, the synthetic (computed) profiles of these lines, constructed on the basis of the components in the hyperfine-structure in both of the isotopes, taking into account the isotope shift between 63 Cu and 65Cu for various electron densities. The existing theoretical W values [9–11] were used as input parameters for a superposition procedure. 2. Experimental details The schematic of the used experimental setup is given in Fig. 1. It is a realization of common arrangement used for single pulse laser-induced breakdown spectroscopy
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M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
Fig. 1. The schematic of the experimental setup.
(LIBS). Copper sample (99.9% purity) was placed inside of a closed chamber in order to have controlled atmospheric pressure of 8 Pa attained by means of a mechanical pump. The chamber is mounted on an x–y translation stage which provides motion in small steps so that a fresh target surface is exposed to each consecutive laser shot. The stage itself could also be translated in the z (axial) direction for the purpose of spatially resolved measurements. The surface of the copper target was carefully polished until it was perfectly glossy. A lens of the 100 mm focal length, used for target ablation, was positioned slightly out of focus in order to create the laser spot of 0:6 mm in diameter on the copper surface. The Nd:YAG laser, EKSPLA NL 311, operating at 532 nm (second harmonic) was used as a light source. Laser pulse width was 5 ns, with repetition rate of 1 Hz, delivering 6 mJ of output energy. A McPherson 209 spectrograph (Czerny–Turner geometry, 1.33 m focal length, reciprocal linear dispersion of 0.28 nm/mm in the first order) equipped with a holographic grating with 2400 grooves/mm was used. An Andor DH740-18F-03 iStar intensified CCD camera was employed as a detection system and cooled down to 20 1C for the purpose of thermal noise reduction. The instrumental profile of the spectrograph itself, in the first order measured with a 9789 QB EMI photomultiplier, corresponds to the Gaussian function with a FWHM not higher than 2.8 pm in the UV region, while the overall profile (spectrograph þ ICCD camera) can be approximated by the Voigt function with a FWHM of 8.7 pm at 265 nm. The system was calibrated using a set of pen-light sources (Ne, Ar and Hg) produced by LOT-Oriel. A relative radiometric calibration of the spectrograph þ ICCD camera system was carried out using a deuterium light source (StellarNet SL3-CAL) for the UV region from 200 to 400 nm and a tungsten NIST F-000 lamp for the visible range. The spectroscopic observations were made side-on (at right
angle to the laser beam direction) with a 40 mm diameter quartz lens (1:1 imaging system), used to collect and project plasma image onto a 20 μm wide entrance slit. The recorded Cu I line image is presented in Fig. 2. In order to reduce noise the spectra were acquired by averaging 100 consecutive shots. The detector gate width of 10 ns and appropriate gain were determined experimentally. Furthermore, a series of spatial and time-resolved measurements were also carried out to optimize parameters in terms of best signal-to-noise ratio and low continuum level. A careful analysis was conducted to determine optimal recording parameters and density decay rate, having in mind the possible departures from the LTE distributions in the case of plasma inhomogeneities, temporal variations and self-absorption, as pointed out in [13]. The recorded resonance Cu I line profiles are presented in Fig. 3. The laser-induced plasma is essentially non-homogenous and strongly subjected to temporal variations and ambient conditions [14]. Electron density (N) and electron temperature (T) have values gradually changed along the radial coordinate r (distance from the axis defined by the laser beam) and axial position z, as well. The spectrum, recorded in the image mode of the ICCD camera, provides necessary data to calculate shape of the spectral line at different radial positions. This procedure is based on the inverse Abel transform. While the Abel transform itself is well defined mathematical method, its application to the real-world (noisy) data is known as numerically difficult problem. To accomplish this task number of algorithms were proposed in specialized literature [15–18]. As a background for our numerical procedure we have adopted approach proposed by Ignjatović and Mihajlov [18]. It is an elegant technique adequate for plasmas with undetermined radius, the typical case of laser-induced plasma. Relying on the Abel inverse we found that our plasma at z 2 mm from the target surface emits spectrum, recorded 120 ns after the laser pulse (see Fig. 4), free of self-absorption. Namely, at the specified moment and recording position the intensity ratio of the two commonly investigated Cu I resonance spectral lines was in agreement with theoretical one, confirming absence of self-absorption
Fig. 2. The image of the 324.754 nm Cu I spectral line recorded as a result of averaging 100 consecutive shots.
M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
Fig. 3. Experimental data points of 324.7 nm and 327.4 nm Cu I resonance spectral line profiles fitted to the Voigt functions using β2 ¼ 4.6 pm as a Gaussian parameter. Letter I denotes line intensity proportional to area under the Voigt profile and H stands for height.
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Fig. 5. Radial distribution of the line intensity ratio of the 324.754 nm and 327.396 nm Cu I resonance spectral lines. Dashed line represents theoretical value calculated with atomic data taken from NIST. Line profiles were analyzed at the distance of 0:64 mm from the axis defined by the laser beam. Error bars indicate uncertainty magnitude of 12%.
Fig. 4. The zero-order plasma image acquired at 120 ns delay time. The cursor is marking up the distance from the sample surface ( 2 mm), positioned on the left-hand side, where the spectroscopic observations were made.
Fig. 6. The Boltzmann plot in the Cu I spectrum. The atomic parameters, upper energy level (Eu), g (statistical weight) and A (transition probability) were taken from Kurucz [20]. Line intensities (I) represent areas under the line profiles fitted to a Voigt function. Listed wavelengths (λ) are given in nanometers and positioned right above corresponding data points.
(see Fig. 5). Regarding the radial position, we have chosen distance of 0:64 mm from the axis as the point where intensity ratio perfectly coincides with theoretical value. All other spectral lines were processed in similar way, therefore, measured electron temperature and electron density are associated to the same recording position and time delay. The Boltzmann-plot method was used for the excitation temperature determination [19], which corresponds to electron temperature assuming that the LTE conditions are valid. In this manner 12 Cu I line intensities were obtained as values proportional to the area under the line profile fitted to the Voigt function. The necessary atomic data were taken from [20]. The Boltzmann-plot is presented in Fig. 6. The line intensities are measured typically with error of 6%, while uncertainties of transition probabilities (A) are not specified.
Relatively large scatter of data points suggests that transition probabilities are given with considerable errors. Consequently, error in estimated electron temperature, T¼(19 300 72200) K, is mainly due to A value uncertainties. The electron density was determined using well known Saha equation [19] on the basis of the intensity ratios of the 324.754 nm Cu I line to 202.995 nm, 209.840 nm, 214.549 nm and 226.321 nm Cu II lines. Necessary atomic parameters were taken from [21]. The average N value was ð2:1 7 0:3Þ 1023 m 3 . In the case of an optically thin plasma, straight line defined by the points in the Boltzmann-plot implies that all considered levels are in thermal equilibrium with free electrons. Relatively large energy span of 5.5 eV minimizes possibility for obtaining straight line just by chance
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[22]. According to [23], electron density must satisfy the following relation (McWhirter criterion) in order to maintain in LTE condition: Nðm 3 Þ 41:6 1018 p ffiffiffi plasma T ðΔEnm Þ3 , where T is the electron temperature in Kelvins, ΔEnm is the largest gap between adjacent levels expressed in eV. In our case (T ¼19 300 K; ΔEnm 1:16 eV) this value is 3:5 1020 m 3 , therefore, the necessary condition for the LTE existence is also fulfilled.
3. Hyperfine structure components The stable copper isotopes 63Cu and 65Cu have isospin (i) of 3/2. According to [24] and references therein, corresponding nuclear magnetic moments are 1:12 10 26 J=T and 1:20 10 26 J=T, respectively. The energy levels of the electrons, besides the electrical Coulomb interaction (with nucleus and among electrons in the core) are defined, also, through the magnetic dipole (M1) and the electric quadrupole interactions (E2) with the nucleus. The ΔEM1 and ΔEE2 energy corrections can be calculated using simple formulae from [24] knowing the a and b constants (in MHz), related to the (M1)
and (E2) interactions for the particular energy level. On the basis of these corrections, one can obtain the components wavelength in the HFS splitting. Mutual shifting of the HFS components of the two Cu isotopes is a result of the isotope shift [25,26]. In this work we have calculated the HFS components of the 324.754 nm (4s2 S1=2 –4p 2 P 3=2 transition) and 327.396 nm (4s2 S1=2 4p2 P 1=2 transition) Cu I resonance lines for 63Cu and 65Cu isotopes. Values of the magnetic dipole HFS constant a and the electric quadrupole HFS constant b of the 4s2 S1=2 4p2 P 1=2 and 4p2 P 3=2 states of Cu I were taken from [25,26], while the isotope shifts (IS) of the considered states were taken from [27]. The splitting among four HFS components in 4s2 S1=2 –4p2 P 1=2 transition (327.396 nm) is 4.56 pm and 4.87 pm for the 63Cu and 65Cu isotopes, respectively. The isotope shift between two sets of the HFS components is 0.2 pm [25]. The splitting among six HFS components in 4s2 S1=2 –4p2 P 3=2 transition (324.754 nm ) is 4.25 pm and 4.55 pm for the 63Cu and 65Cu isotopes, respectively. The isotope shift between two sets of the HFS components is also 0.2 pm. The HFS components have different intensities. It is known that Cu I and B III (doubly ionized boron) belong to the same homologue sequence,
Fig. 7. Resulting Stark (a and b) profiles of the 324.754 nm and 327.396 nm Cu I resonance lines at N ¼ 2:1 1023 m 3 electron density, calculated as a superposition of Lorentz functions associated to each component in the HFS pattern. The relative positions of HFS components are calculated in present work, while corresponding relative intensities are taken from [28,29]. Each component is indicated by vertical line with height proportional to the relative intensity. Calculation of the relative intensities is based on the natural isotope ratio 63Cu/65Cu¼0.692/0.308. Profiles (a and b) are evaluated relying on theoretical FWHM values (8.0 pm and 7.8 pm for 324.754 nm and 327.396 nm respectively) taken from [11] for T¼ 19 300 K. Next to each synthetic profile estimated value of FWHM is clearly indicated. For the sake of completeness, profiles calculated assuming Doppler width of 4.1 pm are also presented (c and d).
M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
consequently, we assume that the total transition probabilities (Einstein's A coefficient) for both species have very similar distribution among the HFS components. Following this idea we adopted that distribution of the A values for 324.754 nm and 327.396 nm Cu I lines is equivalent to the distribution of the 206.5 nm and 206.7 nm B III resonance lines, see Table 3 in [28]. The obtained intensities are consistent with the ones presented in [29]. 4. Results and discussion By knowing the component pattern within HFS splitting and corresponding intensities, one can evaluate line profiles induced by Stark effect. We have calculated the resulting Cu I resonance line profiles as a superposition of the Lorentz contributions originating from each component in the HFS pattern. The Lorentz (Stark) FWHMs were taken from [11] for T¼19 300 K and N ¼ 2:1 1023 m 3 plasma parameters. The values of 8.0 pm and 7.8 pm for the 324.754 nm and 327.396 nm Cu I lines were calculated on the basis of the semi-classical perturbation method [30] and include electron and ion contribution to the Stark broadening (total Stark widths). The calculated synthetic profiles are presented in Fig. 7. For each synthetic profile estimated value of FWHM (as the full width of the overall distribution at the half of its maximum) is clearly indicated. It is evident that due to HFS and IS effects Cu I resonance lines are asymmetric and additionally broadened. However, recorded lines appear symmetric (see Fig. 8) due to further Doppler and instrumental broadening. The splitting pattern for both Cu I resonance lines can be approximated just by two components (see Fig. 7), under assumption that Stark width is at least one picometer in magnitude. This simplifies our task to estimate Stark width relying on experimentally recorded profiles. By knowing separation between these two groups and relative A values for both, one can fit experimental profile to the sum of two Voigt profiles. This fit has the same number of free parameters as the single Voigt function, therefore, it is of the same quality, but more adequate than only one profile. In this way gap of 4 pm between
Fig. 8. Profile of 324.75 nm Cu I line at r 0:64 mm from the axis defined by the laser, obtained by adopted inverse Abel procedure. Solid line is fit to the sum of two Voigt functions, separated by 4 pm, with β2 ¼ 4.6 pm Gauss parameter.
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two groups of components, due to HFS, is correctly excluded from inferred Stark widths. Standard deconvolution procedure based on the least-squares method [31–33] is applied in order to evaluate spectral line parameters. The best fit profile for sum of two Voigt functions for the 324.754 nm line is presented in Fig. 8. Applying foregoing procedure, we have obtained the experimental Stark FWHM (Wm) values at T ¼19 300 K and N ¼ 2:1 1023 m 3 electron density. The values are (12.5 71.3) pm and (11.9 71.2) pm for the 324.754 nm and 327.396 nm Cu I lines, respectively. Fig. 9 illustrates effect of fair broadening on the complex structure of resonance Cu I lines. If the lines appear to be symmetric, due to considerable Stark, Doppler or instrumental broadening, then FWHM of the overall distribution overestimates the width of the single component. For distributions narrower than 15 pm error in FWHM associated to Stark broadening, introduced by considering this profile as a single line, is over 10% and underlying HFS/IS structure must be treated correctly. However, if the recorded distribution is broader then 25 pm exact calculation will improve Stark width attributed to the single component in just few percent. In this case correct approach is meaningful only if the noise in recorded line is minimal. To illustrate considered analysis suppose that dominant broadening is due to Stark effect. Relying on the recent theoretical values from [11] it follows that for T 20 000 K and N≳7 1024 m 3 Stark width of the single component is W≳30 pm, which is the least value of overall distribution, thus the HFS structure can be neglected according to Fig. 9. In Table 1 we summarize available results regarding Cu I resonance lines. One can notice that our results agree well with theoretical predictions made by Grishina et al. [9]. Regarding the results presented by Babina et al. [10] and Zmerli et al. [11] the agreement is less favorable, within the
Fig. 9. Rough estimate of HFS/IS impact on the Cu I resonance lines widths for different levels of broadening. Numbers on abscissa, W SINGLE , are FWHM values estimated by considering line as a single distribution, without any structure. The ordinate values are ratio W SINGLE =W HFS where W HFS is FWHM value of each component inferred by two component model detailed in the text. The analysis is done under assumption that profiles are of the Voigt type with equal contribution of Lorentz and Gauss.
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M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
Table 1 Our measured Wm Stark FWHM at T ¼ 19 300 K, N ¼ 2:1 1023 m 3 and values WG [9], WB [10] and WZ [11] normalized to the same plasma parameters. Asterisk (*) indicates value, normalized to actual plasma parameters and additionally corrected according to analysis summarized in Fig. 9, from experiment Skuljan et al. [8] which is originally carried out at T ¼ 17 000 K and N ¼ 6:6 1022 m 3 . Transition 1=2
4s2 S
1=2
4s2 S
–4p2 P –4p2 P
3=2
1=2
λ (nm)
Wm (pm)
WG (pm)
WB (pm)
WZ (pm)
W G =W m
W B =W m
W Z =W m
324.754
12.5 71.3
12.4
8.8
8.0
0.99
0.70
0.64
327.396
25n 11.9 71.2
12.6
8.9
7.8
1.06
0.75
0.66
range of 35%, but still acceptable having in mind experimental uncertainties and limited accuracy of the theory. The Stark width of the Cu I 324.754 nm line has been measured twenty years ago in a completely different experiment by Skuljan et al. [8]. Originally reported value of 9.5 pm is obtained at T¼17 000 K and N ¼ 6:6 1022 m 3 without taking into account complex structure of the line, therefore, quoted result is associated to the whole distribution regarded as Lorentzian. Hence, FWHM value of 9.5 pm can not be simply normalized to the actual electron density measured in our plasma. From Figure 2 in Ref. [8], one can read width of the unprocessed line; it was 19.6 pm. According to foregoing discussion and Fig. 9 this value, reduced for 6%, corresponds to the raw width (convolution of the Stark, Doppler and instrument) of the single component in the HFS/IS structure. To estimate just Stark contribution we rely on approximative relation [34] for width of the Voigt function W V 0:5346W L þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:2166W 2L þ W 2G expressed via Lorentz (WL) and Gauss (WG) component. Solving this relation in respect to WL we get corrected FWHM value for Stark width of the Cu I 22
324.754 nm at T¼ 17 000 K and N ¼ 6:6 10
m
3
. This
value, W Corr 7:86 pm, can be normalized to our actual S electron density of N ¼ 2:1 1023 m 3 for final comparison. Eventually, result measured twenty years ago, after necessary corrections becomes W Final 25 pm; it is twice S above the actual value Wm ¼12.5 pm. The procedure that we have applied in analyzing old results is of a limited accuracy, nevertheless, considerable discrepancy regarding the actual value can not be attributed just to incomplete access to the original data measured by Skuljan et al. The main characteristic of the setup, employed only in the mentioned experiment [8], was pulsed discharge superimposed on continuous glow discharge. Large broadening of the Cu I 324.754 nm line could be explained by non-negligible amount of self-absorbtion present in plasma due to permanent sputtering caused by glow discharge. Later, we have switched to the pulsed discharge with floating auxiliary electrodes providing better control of sputtered metal atoms. 5. Conclusion Broadening of the resonance 324.754 nm and 327.396 nm copper lines has been investigated in the laser-induced copper spectrum in the residual atmospheric pressure of 8 Pa. The role of the hyperfine structure components in the resonance Cu I line shapes
formation was, for the first time, discussed taking also into account the isotope shift. It is shown that hyper-fine structure and isotope shift additionally broad profile of the Cu I resonance lines. This should be taken into account in various calibration procedures based on these lines, especially in the case when measured electron densities are below 1024 m 3.
Acknowledgments This work is part of the “Determination of atomic parameters on the basis of spectral line profiles” (ON 171008) project supported by the Ministry of Science, Education and Technological Development of the Republic of Serbia. References [1] Boraa B, Wongb CS, Bhuyana H, Leeb YS, Yapb SL, Favrea M. Understanding the mechanism of nanoparticle formation in wire explosion process. Journal of Quantitative Spectroscopy and Radiative Transfer 2013;117:1–6. [2] Gonomea H, Baneshib M, Okajimac J, Komiyac A, Maruyamac S. Controlling the radiative properties of cool black-color coatings pigmented with CuO submicron particles. Journal of Quantitative Spectroscopy and Radiative Transfer, http://dx.doi.org/10.1016/j. jqsrt.2013.02.027, in press. [3] Liang L, Gao W, Zhou C. Photoionization cross section of Ne-like Cu XX with J ¼ 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2012;113:2018–22. [4] Song K, Cha H, Lee J, Lee Y. Investigation of the line-broadening mechanism for laser-induced copper plasma by time-resolved laserinduced breakdown spectroscopy. Microchemical Journal 1999;63: 53–60. [5] Man BY, Dong QL, Liu AH, Wei XQ, Zhang QG, He JL, et al. Linebroadening analysis of plasma emission produced by laser ablation of metal Cu. Journal of Optics A: Pure and Applied Optics 2004;6: 17–21. [6] Griem HR. Spectral line broadening by plasmas. New York: Academic Press; 1974. [7] NIST. Atomic Spectra Database. 〈http:physics.nist.gov〉; 2013. [8] Skuljan LJ, Bukvić S, Djeniže S. Measured Stark width of the 324.75 nm Cu I resonance spectral line. Publications of the Astronomical Observatory of Belgrade 1995;50:127–9. [9] Grishina NA, Il'in GG, Salakhov MKh, Sarandaev EV. The estimation of Stark broadening parameters for the spectral lines of 0 0 4s 2 S 4p 2 P and 4s2 2 D 4p 2 P multiplets of neutral copper atoms. In: SPIG conference proceedings; 1998. p. 361–4. [10] Babina EM, Il'in GG, Konovalova OA, Salakhov MKh, Sarandaev EV. The complete calculation of Stark broadening parameters for the neutral 0 0 copper atoms spectral lines of 4s 2 S 4p 2 P and 4s2 2 D 4p 2 P multiplets in the dipole approximation. Publications of the Astronomical Observatory of Belgrade 2003;76:163–6. [11] Zmerli B, Ben Nessib N, Dimitrijević MS, Sahal-Bréchot S. Stark broadening calculations of neutral copper spectral lines and temperature dependence. Physica Scripta 2010;82:1–9.
M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
[12] Bonifacio P, Caffau E, Ludwig HG. Cu I resonance lines in turn-off stars of NGC 6752 and NGC 6397 Effects of granulation from CO5BOLD models. Acta Astronautica 2010;524:96. [13] Cristoforetti G, De Giacomo A, Dell'Aglio M, Legnaioli S, Tognoni E, Palleschi V, et al. Local thermodynamic equilibrium in LaserInduced breakdown spectroscopy: beyond the McWhirter criterion. Spectrochimica Acta Part B 2010;65:86–95. [14] Yalcin S, Crosley DR, Smith GP, Faris GP. Influence of ambient conditions on the laser air spark. Applied Physics B 1999;68:121–30. [15] Nestor H, Olsen H. Numerical methods for reducing line and surface probe data. SIAM Review 1960;2:200–7. [16] Aguilera JA, Aragón C, Bengoechea J. Spatial characterization of laserinduced plasmas by deconvolution of spatially resolved spectra. Applied Optics 2003;42:5938–46. [17] Djurović S. Fitting and Abel inversion of experimental data using Jacobi polynomials. Journal of Research in Physics 1999;28:155–64. [18] IgnjatovićLj M, Mihajlov AA. The realization of Abel's inversion in the case of discharge with undetermined radius. Journal of Quantitative Spectroscopy and Radiative Transfer 2002;72:677–89. [19] Griem HR. Plasma spectroscopy. New York: McGraw Hill Inc; 1964. [20] Kurucz RL. Atomic spectral line database from CD-ROM 23; 1995. [21] Ortiz B, Mayo R, Biémont É, Quinet P, Malcheva G, Blagoev K. Radiative parameters for some transitions arising from the 3d94d and 3d84s2 electronic configurations in Cu II spectrum. Journal of Physics B 2007;40:167–76. [22] Quintero MC, Rodero A, Garcia MC, Sola A. Determination of the excitation temperature in a nonthermodynamic-equilibrium highpressure helium microwave plasma torch. Applied Spectroscopy 1997;51:778–84. [23] McWhirter RWP. In: Huddlestone RH, Leonard SL, editors. Plasma diagnostic techniques. New York: Academic Press; 1965.
595
[24] Radcing AA, Smirnov BM. Spravocnik po atomnoj i molekularnoj fizike. Moscow: Atomizdat; 1980. [25] Wagner S. Zur Isotopieverschiebung im Cul-Spektrum. Zeitschrift für Physik 1955;141:122–45. [26] Hannaford P, McDonald DC. Determination of relative oscillator strengths of the copper resonance lines by atomic absorption spectroscopy. Journal of Physics B 1978;11:1177–91. [27] Song SQ, Wang GF, Ye AP, Jiang G. Multi-configuration Dirac–Fock calculations of the hyperfine structure constants A and B of neutral Cu, Ag and Au. Journal of Physics B 2007;40:475–84. [28] Proffitt CR, Jönsson P, Litzén U, Pickering JC, Wahlgren GM. Goddard high-resolution spectrograph observations of the B III resonance doublet in early B stars: abundances and isotope ratios. Astrophysical Journal 1999;516:342–8. [29] White HE, Eliason AY. Relative intensity tables for spectrum lines. Physical Review 1933;44:753–6. [30] Sahal-Bréchot S. Impact theory of the broadening and shift of spectral lines due to electrons and ions in a plasma. Acta Astronautica 1969;1:91–123. [31] Davies JT, Vaughan JM. A new tabulation of the Voigt profile. Astrophysical Journal 1963;137:1302–5. [32] Bukvić S, Spasojević Dj. An alternative approach to spectrum base line estimation. Spectrochimica Acta B 2005;60:1308–15. [33] Bukvić S, Spasojević DJ, Žigman V. Advanced fit technique for astrophysical spectra: approach insensitive to a large fraction of outliers. Acta Astronautica 2008;477:967–77. [34] Olivero J. Empirical fits to the Voigt line width: a brief review. Journal of Quantitative Spectroscopy and Radiative Transfer 1977;17: 233–6.
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Broadening of the resonance Cu I lines in the laser-induced copper spectrum M. Burger, M. Skočić, Z. Nikolić, S. Bukvić n, S. Djeniže University of Belgrade, Faculty of Physics, POB 368, 11000 Belgrade, Serbia
a r t i c l e i n f o
abstract
Article history: Received 17 April 2013 Received in revised form 18 September 2013 Accepted 19 September 2013 Available online 7 October 2013
Broadening of the resonance 324.754 nm and 327.396 nm copper (Cu I) lines have been investigated in the laser-induced copper spectrum in the residual atmospheric pressure of 8 Pa at 19 300 K electron temperature, and electron density of 2.1 1023 m 3. The second harmonic of the Nd:YAG laser at 532 nm was applied for evaporation of atoms from the copper target. The Stark and Doppler broadening were found as the most significant mechanisms in the line shape formation at the actual plasma parameters. Measured Stark widths (W) were compared to existing experimental and theoretical W data. The role of the hyperfine structure (HFS) components in the resonance Cu I line shapes formation was, for the first time, discussed taking also into account the isotope shift (IS). & 2013 Elsevier Ltd. All rights reserved.
Keywords: LIBS Emission spectroscopy Line broadening Stark effect
1. Introduction Copper (Cu) is one of the most exploited elements in the various fields of the industry and technology [1–3]. It has two stable isotopes: 63Cu and 65Cu (69.2% and 30.8% abundances, respectively) with isospins of 3/2. The spectral line characteristics of the copper atoms (Cu I) are affected by both the isotope shift (IS) and hyperfine structure (HFS) due to considerable isospin. The intense resonance 324.754 nm and 327.396 nm lines are good candidates for diagnostic purposes in various applications. Due to different kind of broadenings one can expect a complex profile of Cu I lines, especially the resonance 324.751 nm and 327.396 nm lines. It is of interest to study the shape of these lines in realistic plasma conditions with emphasize on possible application in plasma diagnostics. Broadening mechanisms for certain number of the visible range Cu I spectral lines have been investigated in laser-generated plasma by Song et al. [4] and Man et al. [5]. In the plasmas with electron density (N) higher than 1022 m 3 and electron temperature (T) below 20 000 K the Stark broadenings are dominant broadening mechanisms in the spectral line
n
Corresponding author. Tel: þ381 11 7158 168; fax: þ 381 11 3282 619. E-mail address: [email protected] (S. Bukvić).
0022-4073/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2013.09.022
shape formation [6]. However, the other mechanism found to be non-negligible is a Doppler broadening. The literature devoted to the Cu I resonance spectral lines Stark widths is presented in [7] and references therein. Only one experiment [8] deals with 324.754 nm Cu I line Stark FWHM (Full Width at Half Maximum, W). The Stark effect of resonance Cu I lines is considered theoretically in [9–11]. To the knowledge of the authors, the contribution of the hyperfine structure components on the resulting shape of the two Cu I resonance lines is discussed in only one paper [12]. The aim of this work is to present experimental Stark FWHM of the two intense resonance Cu I lines observed in the laser-induced copper plasma in the residual atmospheric pressure. We present, also, the synthetic (computed) profiles of these lines, constructed on the basis of the components in the hyperfine-structure in both of the isotopes, taking into account the isotope shift between 63 Cu and 65Cu for various electron densities. The existing theoretical W values [9–11] were used as input parameters for a superposition procedure. 2. Experimental details The schematic of the used experimental setup is given in Fig. 1. It is a realization of common arrangement used for single pulse laser-induced breakdown spectroscopy
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Fig. 1. The schematic of the experimental setup.
(LIBS). Copper sample (99.9% purity) was placed inside of a closed chamber in order to have controlled atmospheric pressure of 8 Pa attained by means of a mechanical pump. The chamber is mounted on an x–y translation stage which provides motion in small steps so that a fresh target surface is exposed to each consecutive laser shot. The stage itself could also be translated in the z (axial) direction for the purpose of spatially resolved measurements. The surface of the copper target was carefully polished until it was perfectly glossy. A lens of the 100 mm focal length, used for target ablation, was positioned slightly out of focus in order to create the laser spot of 0:6 mm in diameter on the copper surface. The Nd:YAG laser, EKSPLA NL 311, operating at 532 nm (second harmonic) was used as a light source. Laser pulse width was 5 ns, with repetition rate of 1 Hz, delivering 6 mJ of output energy. A McPherson 209 spectrograph (Czerny–Turner geometry, 1.33 m focal length, reciprocal linear dispersion of 0.28 nm/mm in the first order) equipped with a holographic grating with 2400 grooves/mm was used. An Andor DH740-18F-03 iStar intensified CCD camera was employed as a detection system and cooled down to 20 1C for the purpose of thermal noise reduction. The instrumental profile of the spectrograph itself, in the first order measured with a 9789 QB EMI photomultiplier, corresponds to the Gaussian function with a FWHM not higher than 2.8 pm in the UV region, while the overall profile (spectrograph þ ICCD camera) can be approximated by the Voigt function with a FWHM of 8.7 pm at 265 nm. The system was calibrated using a set of pen-light sources (Ne, Ar and Hg) produced by LOT-Oriel. A relative radiometric calibration of the spectrograph þ ICCD camera system was carried out using a deuterium light source (StellarNet SL3-CAL) for the UV region from 200 to 400 nm and a tungsten NIST F-000 lamp for the visible range. The spectroscopic observations were made side-on (at right
angle to the laser beam direction) with a 40 mm diameter quartz lens (1:1 imaging system), used to collect and project plasma image onto a 20 μm wide entrance slit. The recorded Cu I line image is presented in Fig. 2. In order to reduce noise the spectra were acquired by averaging 100 consecutive shots. The detector gate width of 10 ns and appropriate gain were determined experimentally. Furthermore, a series of spatial and time-resolved measurements were also carried out to optimize parameters in terms of best signal-to-noise ratio and low continuum level. A careful analysis was conducted to determine optimal recording parameters and density decay rate, having in mind the possible departures from the LTE distributions in the case of plasma inhomogeneities, temporal variations and self-absorption, as pointed out in [13]. The recorded resonance Cu I line profiles are presented in Fig. 3. The laser-induced plasma is essentially non-homogenous and strongly subjected to temporal variations and ambient conditions [14]. Electron density (N) and electron temperature (T) have values gradually changed along the radial coordinate r (distance from the axis defined by the laser beam) and axial position z, as well. The spectrum, recorded in the image mode of the ICCD camera, provides necessary data to calculate shape of the spectral line at different radial positions. This procedure is based on the inverse Abel transform. While the Abel transform itself is well defined mathematical method, its application to the real-world (noisy) data is known as numerically difficult problem. To accomplish this task number of algorithms were proposed in specialized literature [15–18]. As a background for our numerical procedure we have adopted approach proposed by Ignjatović and Mihajlov [18]. It is an elegant technique adequate for plasmas with undetermined radius, the typical case of laser-induced plasma. Relying on the Abel inverse we found that our plasma at z 2 mm from the target surface emits spectrum, recorded 120 ns after the laser pulse (see Fig. 4), free of self-absorption. Namely, at the specified moment and recording position the intensity ratio of the two commonly investigated Cu I resonance spectral lines was in agreement with theoretical one, confirming absence of self-absorption
Fig. 2. The image of the 324.754 nm Cu I spectral line recorded as a result of averaging 100 consecutive shots.
M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
Fig. 3. Experimental data points of 324.7 nm and 327.4 nm Cu I resonance spectral line profiles fitted to the Voigt functions using β2 ¼ 4.6 pm as a Gaussian parameter. Letter I denotes line intensity proportional to area under the Voigt profile and H stands for height.
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Fig. 5. Radial distribution of the line intensity ratio of the 324.754 nm and 327.396 nm Cu I resonance spectral lines. Dashed line represents theoretical value calculated with atomic data taken from NIST. Line profiles were analyzed at the distance of 0:64 mm from the axis defined by the laser beam. Error bars indicate uncertainty magnitude of 12%.
Fig. 4. The zero-order plasma image acquired at 120 ns delay time. The cursor is marking up the distance from the sample surface ( 2 mm), positioned on the left-hand side, where the spectroscopic observations were made.
Fig. 6. The Boltzmann plot in the Cu I spectrum. The atomic parameters, upper energy level (Eu), g (statistical weight) and A (transition probability) were taken from Kurucz [20]. Line intensities (I) represent areas under the line profiles fitted to a Voigt function. Listed wavelengths (λ) are given in nanometers and positioned right above corresponding data points.
(see Fig. 5). Regarding the radial position, we have chosen distance of 0:64 mm from the axis as the point where intensity ratio perfectly coincides with theoretical value. All other spectral lines were processed in similar way, therefore, measured electron temperature and electron density are associated to the same recording position and time delay. The Boltzmann-plot method was used for the excitation temperature determination [19], which corresponds to electron temperature assuming that the LTE conditions are valid. In this manner 12 Cu I line intensities were obtained as values proportional to the area under the line profile fitted to the Voigt function. The necessary atomic data were taken from [20]. The Boltzmann-plot is presented in Fig. 6. The line intensities are measured typically with error of 6%, while uncertainties of transition probabilities (A) are not specified.
Relatively large scatter of data points suggests that transition probabilities are given with considerable errors. Consequently, error in estimated electron temperature, T¼(19 300 72200) K, is mainly due to A value uncertainties. The electron density was determined using well known Saha equation [19] on the basis of the intensity ratios of the 324.754 nm Cu I line to 202.995 nm, 209.840 nm, 214.549 nm and 226.321 nm Cu II lines. Necessary atomic parameters were taken from [21]. The average N value was ð2:1 7 0:3Þ 1023 m 3 . In the case of an optically thin plasma, straight line defined by the points in the Boltzmann-plot implies that all considered levels are in thermal equilibrium with free electrons. Relatively large energy span of 5.5 eV minimizes possibility for obtaining straight line just by chance
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[22]. According to [23], electron density must satisfy the following relation (McWhirter criterion) in order to maintain in LTE condition: Nðm 3 Þ 41:6 1018 p ffiffiffi plasma T ðΔEnm Þ3 , where T is the electron temperature in Kelvins, ΔEnm is the largest gap between adjacent levels expressed in eV. In our case (T ¼19 300 K; ΔEnm 1:16 eV) this value is 3:5 1020 m 3 , therefore, the necessary condition for the LTE existence is also fulfilled.
3. Hyperfine structure components The stable copper isotopes 63Cu and 65Cu have isospin (i) of 3/2. According to [24] and references therein, corresponding nuclear magnetic moments are 1:12 10 26 J=T and 1:20 10 26 J=T, respectively. The energy levels of the electrons, besides the electrical Coulomb interaction (with nucleus and among electrons in the core) are defined, also, through the magnetic dipole (M1) and the electric quadrupole interactions (E2) with the nucleus. The ΔEM1 and ΔEE2 energy corrections can be calculated using simple formulae from [24] knowing the a and b constants (in MHz), related to the (M1)
and (E2) interactions for the particular energy level. On the basis of these corrections, one can obtain the components wavelength in the HFS splitting. Mutual shifting of the HFS components of the two Cu isotopes is a result of the isotope shift [25,26]. In this work we have calculated the HFS components of the 324.754 nm (4s2 S1=2 –4p 2 P 3=2 transition) and 327.396 nm (4s2 S1=2 4p2 P 1=2 transition) Cu I resonance lines for 63Cu and 65Cu isotopes. Values of the magnetic dipole HFS constant a and the electric quadrupole HFS constant b of the 4s2 S1=2 4p2 P 1=2 and 4p2 P 3=2 states of Cu I were taken from [25,26], while the isotope shifts (IS) of the considered states were taken from [27]. The splitting among four HFS components in 4s2 S1=2 –4p2 P 1=2 transition (327.396 nm) is 4.56 pm and 4.87 pm for the 63Cu and 65Cu isotopes, respectively. The isotope shift between two sets of the HFS components is 0.2 pm [25]. The splitting among six HFS components in 4s2 S1=2 –4p2 P 3=2 transition (324.754 nm ) is 4.25 pm and 4.55 pm for the 63Cu and 65Cu isotopes, respectively. The isotope shift between two sets of the HFS components is also 0.2 pm. The HFS components have different intensities. It is known that Cu I and B III (doubly ionized boron) belong to the same homologue sequence,
Fig. 7. Resulting Stark (a and b) profiles of the 324.754 nm and 327.396 nm Cu I resonance lines at N ¼ 2:1 1023 m 3 electron density, calculated as a superposition of Lorentz functions associated to each component in the HFS pattern. The relative positions of HFS components are calculated in present work, while corresponding relative intensities are taken from [28,29]. Each component is indicated by vertical line with height proportional to the relative intensity. Calculation of the relative intensities is based on the natural isotope ratio 63Cu/65Cu¼0.692/0.308. Profiles (a and b) are evaluated relying on theoretical FWHM values (8.0 pm and 7.8 pm for 324.754 nm and 327.396 nm respectively) taken from [11] for T¼ 19 300 K. Next to each synthetic profile estimated value of FWHM is clearly indicated. For the sake of completeness, profiles calculated assuming Doppler width of 4.1 pm are also presented (c and d).
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consequently, we assume that the total transition probabilities (Einstein's A coefficient) for both species have very similar distribution among the HFS components. Following this idea we adopted that distribution of the A values for 324.754 nm and 327.396 nm Cu I lines is equivalent to the distribution of the 206.5 nm and 206.7 nm B III resonance lines, see Table 3 in [28]. The obtained intensities are consistent with the ones presented in [29]. 4. Results and discussion By knowing the component pattern within HFS splitting and corresponding intensities, one can evaluate line profiles induced by Stark effect. We have calculated the resulting Cu I resonance line profiles as a superposition of the Lorentz contributions originating from each component in the HFS pattern. The Lorentz (Stark) FWHMs were taken from [11] for T¼19 300 K and N ¼ 2:1 1023 m 3 plasma parameters. The values of 8.0 pm and 7.8 pm for the 324.754 nm and 327.396 nm Cu I lines were calculated on the basis of the semi-classical perturbation method [30] and include electron and ion contribution to the Stark broadening (total Stark widths). The calculated synthetic profiles are presented in Fig. 7. For each synthetic profile estimated value of FWHM (as the full width of the overall distribution at the half of its maximum) is clearly indicated. It is evident that due to HFS and IS effects Cu I resonance lines are asymmetric and additionally broadened. However, recorded lines appear symmetric (see Fig. 8) due to further Doppler and instrumental broadening. The splitting pattern for both Cu I resonance lines can be approximated just by two components (see Fig. 7), under assumption that Stark width is at least one picometer in magnitude. This simplifies our task to estimate Stark width relying on experimentally recorded profiles. By knowing separation between these two groups and relative A values for both, one can fit experimental profile to the sum of two Voigt profiles. This fit has the same number of free parameters as the single Voigt function, therefore, it is of the same quality, but more adequate than only one profile. In this way gap of 4 pm between
Fig. 8. Profile of 324.75 nm Cu I line at r 0:64 mm from the axis defined by the laser, obtained by adopted inverse Abel procedure. Solid line is fit to the sum of two Voigt functions, separated by 4 pm, with β2 ¼ 4.6 pm Gauss parameter.
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two groups of components, due to HFS, is correctly excluded from inferred Stark widths. Standard deconvolution procedure based on the least-squares method [31–33] is applied in order to evaluate spectral line parameters. The best fit profile for sum of two Voigt functions for the 324.754 nm line is presented in Fig. 8. Applying foregoing procedure, we have obtained the experimental Stark FWHM (Wm) values at T ¼19 300 K and N ¼ 2:1 1023 m 3 electron density. The values are (12.5 71.3) pm and (11.9 71.2) pm for the 324.754 nm and 327.396 nm Cu I lines, respectively. Fig. 9 illustrates effect of fair broadening on the complex structure of resonance Cu I lines. If the lines appear to be symmetric, due to considerable Stark, Doppler or instrumental broadening, then FWHM of the overall distribution overestimates the width of the single component. For distributions narrower than 15 pm error in FWHM associated to Stark broadening, introduced by considering this profile as a single line, is over 10% and underlying HFS/IS structure must be treated correctly. However, if the recorded distribution is broader then 25 pm exact calculation will improve Stark width attributed to the single component in just few percent. In this case correct approach is meaningful only if the noise in recorded line is minimal. To illustrate considered analysis suppose that dominant broadening is due to Stark effect. Relying on the recent theoretical values from [11] it follows that for T 20 000 K and N≳7 1024 m 3 Stark width of the single component is W≳30 pm, which is the least value of overall distribution, thus the HFS structure can be neglected according to Fig. 9. In Table 1 we summarize available results regarding Cu I resonance lines. One can notice that our results agree well with theoretical predictions made by Grishina et al. [9]. Regarding the results presented by Babina et al. [10] and Zmerli et al. [11] the agreement is less favorable, within the
Fig. 9. Rough estimate of HFS/IS impact on the Cu I resonance lines widths for different levels of broadening. Numbers on abscissa, W SINGLE , are FWHM values estimated by considering line as a single distribution, without any structure. The ordinate values are ratio W SINGLE =W HFS where W HFS is FWHM value of each component inferred by two component model detailed in the text. The analysis is done under assumption that profiles are of the Voigt type with equal contribution of Lorentz and Gauss.
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Table 1 Our measured Wm Stark FWHM at T ¼ 19 300 K, N ¼ 2:1 1023 m 3 and values WG [9], WB [10] and WZ [11] normalized to the same plasma parameters. Asterisk (*) indicates value, normalized to actual plasma parameters and additionally corrected according to analysis summarized in Fig. 9, from experiment Skuljan et al. [8] which is originally carried out at T ¼ 17 000 K and N ¼ 6:6 1022 m 3 . Transition 1=2
4s2 S
1=2
4s2 S
–4p2 P –4p2 P
3=2
1=2
λ (nm)
Wm (pm)
WG (pm)
WB (pm)
WZ (pm)
W G =W m
W B =W m
W Z =W m
324.754
12.5 71.3
12.4
8.8
8.0
0.99
0.70
0.64
327.396
25n 11.9 71.2
12.6
8.9
7.8
1.06
0.75
0.66
range of 35%, but still acceptable having in mind experimental uncertainties and limited accuracy of the theory. The Stark width of the Cu I 324.754 nm line has been measured twenty years ago in a completely different experiment by Skuljan et al. [8]. Originally reported value of 9.5 pm is obtained at T¼17 000 K and N ¼ 6:6 1022 m 3 without taking into account complex structure of the line, therefore, quoted result is associated to the whole distribution regarded as Lorentzian. Hence, FWHM value of 9.5 pm can not be simply normalized to the actual electron density measured in our plasma. From Figure 2 in Ref. [8], one can read width of the unprocessed line; it was 19.6 pm. According to foregoing discussion and Fig. 9 this value, reduced for 6%, corresponds to the raw width (convolution of the Stark, Doppler and instrument) of the single component in the HFS/IS structure. To estimate just Stark contribution we rely on approximative relation [34] for width of the Voigt function W V 0:5346W L þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:2166W 2L þ W 2G expressed via Lorentz (WL) and Gauss (WG) component. Solving this relation in respect to WL we get corrected FWHM value for Stark width of the Cu I 22
324.754 nm at T¼ 17 000 K and N ¼ 6:6 10
m
3
. This
value, W Corr 7:86 pm, can be normalized to our actual S electron density of N ¼ 2:1 1023 m 3 for final comparison. Eventually, result measured twenty years ago, after necessary corrections becomes W Final 25 pm; it is twice S above the actual value Wm ¼12.5 pm. The procedure that we have applied in analyzing old results is of a limited accuracy, nevertheless, considerable discrepancy regarding the actual value can not be attributed just to incomplete access to the original data measured by Skuljan et al. The main characteristic of the setup, employed only in the mentioned experiment [8], was pulsed discharge superimposed on continuous glow discharge. Large broadening of the Cu I 324.754 nm line could be explained by non-negligible amount of self-absorbtion present in plasma due to permanent sputtering caused by glow discharge. Later, we have switched to the pulsed discharge with floating auxiliary electrodes providing better control of sputtered metal atoms. 5. Conclusion Broadening of the resonance 324.754 nm and 327.396 nm copper lines has been investigated in the laser-induced copper spectrum in the residual atmospheric pressure of 8 Pa. The role of the hyperfine structure components in the resonance Cu I line shapes
formation was, for the first time, discussed taking also into account the isotope shift. It is shown that hyper-fine structure and isotope shift additionally broad profile of the Cu I resonance lines. This should be taken into account in various calibration procedures based on these lines, especially in the case when measured electron densities are below 1024 m 3.
Acknowledgments This work is part of the “Determination of atomic parameters on the basis of spectral line profiles” (ON 171008) project supported by the Ministry of Science, Education and Technological Development of the Republic of Serbia. References [1] Boraa B, Wongb CS, Bhuyana H, Leeb YS, Yapb SL, Favrea M. Understanding the mechanism of nanoparticle formation in wire explosion process. Journal of Quantitative Spectroscopy and Radiative Transfer 2013;117:1–6. [2] Gonomea H, Baneshib M, Okajimac J, Komiyac A, Maruyamac S. Controlling the radiative properties of cool black-color coatings pigmented with CuO submicron particles. Journal of Quantitative Spectroscopy and Radiative Transfer, http://dx.doi.org/10.1016/j. jqsrt.2013.02.027, in press. [3] Liang L, Gao W, Zhou C. Photoionization cross section of Ne-like Cu XX with J ¼ 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2012;113:2018–22. [4] Song K, Cha H, Lee J, Lee Y. Investigation of the line-broadening mechanism for laser-induced copper plasma by time-resolved laserinduced breakdown spectroscopy. Microchemical Journal 1999;63: 53–60. [5] Man BY, Dong QL, Liu AH, Wei XQ, Zhang QG, He JL, et al. Linebroadening analysis of plasma emission produced by laser ablation of metal Cu. Journal of Optics A: Pure and Applied Optics 2004;6: 17–21. [6] Griem HR. Spectral line broadening by plasmas. New York: Academic Press; 1974. [7] NIST. Atomic Spectra Database. 〈http:physics.nist.gov〉; 2013. [8] Skuljan LJ, Bukvić S, Djeniže S. Measured Stark width of the 324.75 nm Cu I resonance spectral line. Publications of the Astronomical Observatory of Belgrade 1995;50:127–9. [9] Grishina NA, Il'in GG, Salakhov MKh, Sarandaev EV. The estimation of Stark broadening parameters for the spectral lines of 0 0 4s 2 S 4p 2 P and 4s2 2 D 4p 2 P multiplets of neutral copper atoms. In: SPIG conference proceedings; 1998. p. 361–4. [10] Babina EM, Il'in GG, Konovalova OA, Salakhov MKh, Sarandaev EV. The complete calculation of Stark broadening parameters for the neutral 0 0 copper atoms spectral lines of 4s 2 S 4p 2 P and 4s2 2 D 4p 2 P multiplets in the dipole approximation. Publications of the Astronomical Observatory of Belgrade 2003;76:163–6. [11] Zmerli B, Ben Nessib N, Dimitrijević MS, Sahal-Bréchot S. Stark broadening calculations of neutral copper spectral lines and temperature dependence. Physica Scripta 2010;82:1–9.
M. Burger et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 589–595
[12] Bonifacio P, Caffau E, Ludwig HG. Cu I resonance lines in turn-off stars of NGC 6752 and NGC 6397 Effects of granulation from CO5BOLD models. Acta Astronautica 2010;524:96. [13] Cristoforetti G, De Giacomo A, Dell'Aglio M, Legnaioli S, Tognoni E, Palleschi V, et al. Local thermodynamic equilibrium in LaserInduced breakdown spectroscopy: beyond the McWhirter criterion. Spectrochimica Acta Part B 2010;65:86–95. [14] Yalcin S, Crosley DR, Smith GP, Faris GP. Influence of ambient conditions on the laser air spark. Applied Physics B 1999;68:121–30. [15] Nestor H, Olsen H. Numerical methods for reducing line and surface probe data. SIAM Review 1960;2:200–7. [16] Aguilera JA, Aragón C, Bengoechea J. Spatial characterization of laserinduced plasmas by deconvolution of spatially resolved spectra. Applied Optics 2003;42:5938–46. [17] Djurović S. Fitting and Abel inversion of experimental data using Jacobi polynomials. Journal of Research in Physics 1999;28:155–64. [18] IgnjatovićLj M, Mihajlov AA. The realization of Abel's inversion in the case of discharge with undetermined radius. Journal of Quantitative Spectroscopy and Radiative Transfer 2002;72:677–89. [19] Griem HR. Plasma spectroscopy. New York: McGraw Hill Inc; 1964. [20] Kurucz RL. Atomic spectral line database from CD-ROM 23; 1995. [21] Ortiz B, Mayo R, Biémont É, Quinet P, Malcheva G, Blagoev K. Radiative parameters for some transitions arising from the 3d94d and 3d84s2 electronic configurations in Cu II spectrum. Journal of Physics B 2007;40:167–76. [22] Quintero MC, Rodero A, Garcia MC, Sola A. Determination of the excitation temperature in a nonthermodynamic-equilibrium highpressure helium microwave plasma torch. Applied Spectroscopy 1997;51:778–84. [23] McWhirter RWP. In: Huddlestone RH, Leonard SL, editors. Plasma diagnostic techniques. New York: Academic Press; 1965.
595
[24] Radcing AA, Smirnov BM. Spravocnik po atomnoj i molekularnoj fizike. Moscow: Atomizdat; 1980. [25] Wagner S. Zur Isotopieverschiebung im Cul-Spektrum. Zeitschrift für Physik 1955;141:122–45. [26] Hannaford P, McDonald DC. Determination of relative oscillator strengths of the copper resonance lines by atomic absorption spectroscopy. Journal of Physics B 1978;11:1177–91. [27] Song SQ, Wang GF, Ye AP, Jiang G. Multi-configuration Dirac–Fock calculations of the hyperfine structure constants A and B of neutral Cu, Ag and Au. Journal of Physics B 2007;40:475–84. [28] Proffitt CR, Jönsson P, Litzén U, Pickering JC, Wahlgren GM. Goddard high-resolution spectrograph observations of the B III resonance doublet in early B stars: abundances and isotope ratios. Astrophysical Journal 1999;516:342–8. [29] White HE, Eliason AY. Relative intensity tables for spectrum lines. Physical Review 1933;44:753–6. [30] Sahal-Bréchot S. Impact theory of the broadening and shift of spectral lines due to electrons and ions in a plasma. Acta Astronautica 1969;1:91–123. [31] Davies JT, Vaughan JM. A new tabulation of the Voigt profile. Astrophysical Journal 1963;137:1302–5. [32] Bukvić S, Spasojević Dj. An alternative approach to spectrum base line estimation. Spectrochimica Acta B 2005;60:1308–15. [33] Bukvić S, Spasojević DJ, Žigman V. Advanced fit technique for astrophysical spectra: approach insensitive to a large fraction of outliers. Acta Astronautica 2008;477:967–77. [34] Olivero J. Empirical fits to the Voigt line width: a brief review. Journal of Quantitative Spectroscopy and Radiative Transfer 1977;17: 233–6.