Measurements of ultra-violet titanium lines in laser-ablation plasma

    Measurements of Ultra-Violet Titanium Lines in Laser-Ablation Plasma Christian G. Parigger, Alexander C. Woods, David M. Surmick, Lauren D. Swafford, Michael J. Witte PII: DOI: Reference:

S0584-8547(14)00118-9 doi: 10.1016/j.sab.2014.06.014 SAB 4716

To appear in:

Spectrochimica Acta Part B: Atomic Spectroscopy

Received date: Accepted date:

29 December 2013 5 June 2014

Please cite this article as: Christian G. Parigger, Alexander C. Woods, David M. Surmick, Lauren D. Swafford, Michael J. Witte, Measurements of Ultra-Violet Titanium Lines in Laser-Ablation Plasma, Spectrochimica Acta Part B: Atomic Spectroscopy (2014), doi: 10.1016/j.sab.2014.06.014

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Measurements of Ultra-Violet Titanium Lines in Laser-Ablation Plasma

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Christian G. Parigger, Alexander C. Woods, David M. Surmick, Lauren D. Swafford, Michael J. Witte

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The University of Tennessee Space Institute, Center for Laser Applications, 411 B.H. Goethert Parkway, Tullahoma, TN 37388-9700, U.S.A.

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We present Stark broadened atomic titanium lines recorded following laser-induced optical break during ablation of a 99.999 % pure titanium sample. The UV lines reveal electron density on the order of 20 to 60 ×1023 m−3 , and the electron temperature is estimated to be on the order of 40,000 K some 200 ns after the ablation process. In our study of the modified semi-empirical approach, we conclude that our results favor the standard Gaunt factor without the requirement of introducing an additional effective Gaunt factor, that others appear to use. c 2013 Published by Elsevier Ltd.

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Keywords: Atomic Spectroscopy, Laser-Induced Plasma, Laser-Induced Breakdown Spectrometry, Plasma Diagnostics

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1. Introduction

Research involving laser ablation of titanium has long been studied from the perspective of laser-induced breakdown spectroscopy (LIBS)[1] and garners interest for various applications[2, 3, 4, 5, 6]. While the processes involved in the evolution of plasma resulting from laser ablation of a titanium target are generally understood, a more comprehensive and detailed understanding of titanium particles in a laser ablation plume is desired[7]. Of particular importance in this endeavor is the understanding of the plasma environment to which the titanium particles are exposed. A sufficient understanding would include the composition and temporal evolution of the titanium species in the plasma. The analysis of spectral lines emitted from plasma provides a means of quantifying the parameters of the plasma. The current communication investigates various Ti II and Ti III emission lines located between 237 and 245 nm, as observed no later than 500 ns after plasma formation. Initially, just after plasma formation, spectra gathered from the laser-induced plasma will represent the characteristic spectral continuum provided by the processes (inverse Bremsstahlung, radiative recombination, photoionization) of the many free electrons[8, 9]. Nanoseconds after the laser pulse interacts with the surface and induced-plasma, atomic and ionic lines will become prominent. This occurrence corresponds to the expansion and recombination Email addresses: [email protected] (Christian G. Parigger), [email protected] (Alexander C. Woods), [email protected] (David M. Surmick), [email protected] (Lauren D. Swafford), [email protected] (Michael J. Witte)

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phase of the laser-induced plasma. Due to the high degree of ionization at such time delays from plasma formation, when compared to their neutral atomic counterparts, the ionic titanium lines will be more intense. Thus, the higher ionized species will be observable first, followed by the lower ionized species, neutral atoms, and molecules. The majority of the line broadening observed in laser-induced plasma is attributed to Stark broadening due to the many electron collisions. The system is expected to undergo an overall cooling, as the maximum electron temperature should occur shortly after being exposed to the laser pulse intensity. According to theory, the decreasing temperature will correspond to decreasing electron density. Thus, the emission lines will become progressively more narrow. The assumption of local thermodynamic equilibrium (LTE)[10] is a convenient approach in the study of laserinduced breakdown spectroscopy (LIBS). The LTE assumption asserts that the loss of radiative energy is small compared to the energy exchange between particles. Thus, such relations as Saha and Boltzmann will be valid locally. Therefore, the LTE assumption makes it possible to infer the temperature and electron density within the plasma[11]. However, such an assumption cannot be taken for granted. For a laser-induced plasma, the excitation energy used to generate the plasma is, in this case, applied for a time on the order of ten nanoseconds. A great deal of this initial energy is converted to the kinetic energy of the particles which will comprise the plasma. The system will then evolve quite spontaneously for many microseconds, so as the plasma evolves, the LTE assumption might not always be valid. Therefore, it is important to understand the applicability and constraints of theory applied to such systems[12, 13]. For a homogeneous, optically thin plasma in LTE, the radiation transfer equation can be solved and immediately rewritten as the Boltzmann equation for the integral intensity over a line profile. The Boltzmann equation can then be manipulated to take the form of a line. This particular form of the Boltzmann equation is known as the Boltzmann plot equation. By assuming an electron density, ne , this equation can be used to infer the electron temperature, T e , of plasma. This procedure involves plotting the natural logarithm of the measured intensity of transitions as a function of their respective energy levels. The slope of the resulting line will be inversely proportion to −kB T e , where kB is Boltzmann’s constant. It is noted that the accuracy of this method can be dependent on the number of spectral lines used and if the spectral lines display significant differences in upper energy levels. As a means of increasing the amount of spectral lines available, the so-called Saha-Boltzmann plot method can be used to provide more reliable temperature inferences[14]. This technique employs the same strategy as the Boltzmann plot method, however, now the Saha equilibrium relationship for the number density of the neutral and/or ionic species is used. Because the Boltzmann plot method requires electron densities in order to infer electron temperature, it is necessary to measure another parameter to infer the electron density before using the Boltzmann plotting technique. This can be accomplished by measuring the Stark width of a spectral line and using this width to infer electron density. The Stark broadening of an observed spectral line is determined by measuring the full-width at half maximum (FWHM) of the line and properly evaluating the instrumental broadening involved.

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Table 1. Atomic data for Ti III and Ti II lines that were observed[15].

λ (nm) 237.4986 241.3989 244.0165 244.2685

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A (107 s−1 ) 40 38 5.1 5.1

El (cm−1 ) 41,704.27 41,704.27 12,628.8455 12,628.8455

Eu (cm−1 ) 83,796.86 83,116.93 53,597.2664 53 554.9903

Configurations 3p6 3d4s - 3p6 3d4p 3p6 3d4s - 3p6 3d4p 3d3 - 3d(2 D)4s4p(3 Po ) 3d3 - 3d(2 D)4s4p(3 Po )

Terms 1

D - 1 Po D - 1 Fo 2 b D2 - w2 Do b2 D2 - w2 Do 1

2. Experimental Procedure A 13 ns Q-switched Nd:YAG Quanta-Ray DCR-2A(10) laser providing 160 mJ per pulse is used as the excitation source. The laser beam is focused to approximately a 1 mm spot size vertically downward onto a Ti sample at rest in laboratory air. The ablation plume is imaged onto the slit of a Jobin−Yvon HR 640 spectrometer equipped with an 1800 groove/mm grating by a field lens chosen to match the f # of the spectrometer. As a means of gated detection, the spectrometer is equipped with an intensified linear diode array (model 1460 Princeton Applied Research 2

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3. Results

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Figure 1 illustrates six instances of collected data, observing the Ti III and Ti II lines, demonstrating the evolution of the laser ablation plasma. At a ∆τ = 50 ns, the Ti lines are hardly discernible, as the the plasma emissions are dominated by free electrons. As the plasma evolves in time, the two Ti III lines (237.49 nm and 241.40 nm) can be observed prior to the Ti II lines (244.01 nm and 244.27 nm). Also, the free electron radiation, providing the sloped baseline, gradually lessens, lowering this slope with increased time delay. The top row and the bottom row of Fig. 1 represent data collected from two separate experimental runs. Notice the presence of the Ti II at 244.01 nm in the top row is replaced by the Ti II line at 244.27 nm on the bottom row. As seen in Table 1, both Ti II lines share the same lower energy level. The difference in upper energy level is a factor of J = 3/2 and J = 5/2 for 244.01 nm and 244.27 nm Ti II lines[15], respectively.

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detector/controller optical multichannel analyzer). The detection is gated such that spectra are gathered with a 6 ns gate width. The 6 ns gate is provided by a Model 1302 Fast Pulser (EG& G Princeton Applied Research). The laser is operated at a 10 Hz repetition rate, and each measurement is an accumulation of 100 individual laser events. All of the collected data are wavelength and sensitivity corrected. The sensitivity correction utilized a calibrated Ocean Optics (DH-2000-BAL) deuterium-halogen light source. Spectra from the ablation plume of the titanium sample in the wavelength region of 237 to 245 nm were collected to infer temperature by means of the Boltzmann plot method. These measurements were gathered at 10 ns intervals at delay times ranging from 20 to 100 ns after the laser event. The same spectral region was then examined at 20 ns intervals from 100 to 200 ns. Three additional measurements were then taken at 300, 400, and 500 ns times delays. The spectrometer was then adjusted in order to observe the N II line at 399.5 nm. The N II transition was observed in the titanium ablation plume at the same time intervals as before, ranging from 20 to 200 ns. The N II line was then fit with a Lorentzian profile. The full-width at half maximum (FWHM) was then used to infer the electron density, ne , of the plasma.

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Figure 1. Top: Experimental data observing the Ti III and Ti II lines by laser ablation of a Ti target at 50, 100, and 200 ns after the laser pulse. Bottom: Experimental data observing the Ti III and Ti II lines by laser ablation of a Ti target at 100, 200, and 300 ns after the laser pulse.

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Tables 2 and 3 list the measured widths of the N II 399.5 nm line along with the corresponding inferred electron densities for various delay times following laser-induced plasma formation in air and laser ablation of a titanium target in air, respectively. Due to the electrons provided by the Ti surface, the N II line observed in the laser ablation plasma of Ti indicates a greater electron density than the N II line observed in laser-induced plasma of air. However, the electron density inferred from each plasma behaves similarly as a function of time after the laser event. The first one or two data points for each inference do not follow the exponential decay of the other data points, but rather show a rapidly increasing electron density.

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ne (1023 m−3 ) 43 58 44 40 36

∆τ (ns) 120 140 160 180 200

N II width (nm) 0.97 0.89 0.82 0.76 0.71

ne (1023 m−3 ) 32 30 27 25 24

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N II width (nm) 1.29 1.44 1.33 1.20 1.07

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∆τ (ns) 20 40 60 80 100

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Table 2. Widths of N II 399.5 nm lines and inferred electron densities Ne for specific time delays ∆τ. Data was collected in laser-induced plasma of laboratory air.

∆τ (ns) 220 240 260 280 300

N II width (nm) 0.68 0.64 0.61 0.58 0.56

ne (1023 m−3 ) 23 21 20 19 19

Table 3. Widths of N II 399.5 nm lines and inferred electron densities Ne for specific time delays, ∆τ. Data was collected from resulting plasma of laser ablation of a titanium target.

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ne (1023 m−3 ) 43 53 53 48 43

∆τ (ns) 120 140 160 180 200

N II width (nm) 1.15 1.03 0.96 0.87 0.81

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N II width (nm) 1.30 1.59 1.58 1.44 1.28

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∆τ (ns) 20 40 60 80 100

ne (1023 m−3 ) 38 34 32 29 27

∆τ (ns) 220 240 260 280 300

N II width (nm) 0.78 0.73 0.69 0.64 0.64

ne (1023 m−3 ) 26 24 23 21 21

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Figure 2 compares the inferred electron densities from the tables with an exponentially decaying function. The horizontal error bars of Fig. 2 represent the 6 ns gate width used in the measurement. The vertical error bars represent ± 30 % of the inferred value, in accordance with previously estimated accuracy for electron density inferences utilizing the N II 399.5 nm line given the inferred electron temperatures of the current measurements[16].

Figure 2. Left: Inferred electron density from measured Stark widths of the N II line at 399.5 nm as a function of delay time from laser-induced plasma formation in air. Right: Inferred electron density from measured Stark widths of the N II line at 399.5 nm as a function of delay time from titanium laser ablation plasma formation. 87

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3.2. Gaunt Factor The modified semiempirical (MSE) approach[17] based on electron impact Stark broadening[18, 19] is often useful in calculating the FWHM of a spectral line and its Stark shift[20, 22]. When calculating the spectral line widths within the MSE approach,  !2 r ! X !  E E 2m π X 2 8π ~  , + R2f ′ f g (1) w MS E = ne √  R ′ g ′ 3 m πkB T e 3  i′ i i ∆Ei′ i ∆E f f ′ f

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3.1. Boltzmann Plot The electron excitation temperature, T e , at early time delays following formation of the plasma was found by considering titanium atomic emissions. At early time delays following laser ablation of the titanium sample, Ti II lines are observed with emissions at 244.01 nm and 244.27 nm, and Ti III lines are observed with emissions at 237.49 nm and 241.40 nm. Using a combination of the Ti II and Ti III lines, Saha-Boltzmann plotting methods may be used to determined the electron temperature, which relates the integrated intensity of each emission line to the electron excitation temperature. The integrated intensities were determined by fitting Lorentzian line profiles to each titanium emission. Using this method, initial temperature calculations are found to be in excess of T e = 40,000 K for a time delay of 200 ns following laser-induced breakdown. Further measurements and analysis would be required to determine the temperature as function of delay time due to uncertainties in the sensitivity of the detector in the specified spectral region and calibrations of background emission contributions. Despite these limitations the order of magnitude temperature of 40,000 K may be determined within an accuracy of 10,000 K.

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where ne is the electron density, m is the electron mass, kB is the Boltzmann and T e is the electron temper constant, ature. E = 32 kB T e is the energy of the perturbing electron and ∆E j′ j = E j′ − E j is the energy difference between levels j and j′ . Here, R2i′ i is the square of the coordinate operator matrix element summed over all components of the operator, the magnetic substates of total angular momentum J ′ , and averaged over the magnetic substates of J. The matrix element can be estimated using the hydrogenic ion value

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R2j′ j ≈

 i 1 1  n j 2 h 2 h j|r2 | ji = 5n j + 1 − 3l j l j + 1 . a0 2 Z

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1.1 + g(x), (3) Z is employed in addition to the Gaunt factor, g(x)[21]. Note that in the above equations, Z −1 provides the ionic charge. The Gaunt factor is suggested to have a lower threshold value of g(x) = 0.2[17, 22]. Given the electron density and temperature values we have inferred for the plasma at our experimental delay times, our measured Stark widths show agreement with the MSE approach by assuming a Gaunt factor at threshold, g(x) = 0.2, without requiring an effective Gaunt factor.

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4. Conclusions

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e g(x) = 0.7 −

Ultra-violet Ti III and Ti II emission lines are measured in a laser ablation plasma as a function of delay time from plasma generation. The spectral widths of the lines are analyzed with respect to Stark broadening, in order to infer electron density. The Ti III and Ti II lines are further investigated by use of the Boltzmann plot method, to infer temperature. The N II 399.5 nm emission line is also measured in a titanium laser ablation plasma as well as in a laser-induced plasma of laboratory air. The measured Stark widths of the N II line are used to infer the electron density of each plasma. Utilizing the temperatures obtained from the Boltzmann plot, the inferred electron densities for laser ablation plasma are compared with widths calculated by the MSE approach. The N II 399.5 nm line was chosen because of the early plasma delay times involved in this investigation. Typically, the hydrogen Balmer series lines are an excellent choice for inferring electron density[10]. Their accuracy and 5

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5. Acknowledgments

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availability in laser-induced plasma in laboratory air is well understood, with an accuracy of the inferred electron density utilizing the Hα line typically within 20 % and Hβ inferences slightly more accurate[10]. However, at the earliest delay times of this experiment, the Balmer lines proved to be so broad that the N II line became the more appropriate option. Given our determined temperatures and line widths, our inferred electron density agrees with previous investigations into Stark broadening of the N II 399.5 nm line, providing accuracy between 20 and 30 %[16]. The exponentially decreasing behavior of the inferred electron density as a function of time, implies a consistent exponential cooling for both the laser ablation plasma and the laser-induced plasma in air. The first one or two data points for the inferred electron density of the N II line imply the rapid contribution of free electrons in the plasma. This agrees with the observed Ti III and Ti II lines of the laser ablation plasma, as the free electron radiation is overpowering. For the gathered titanium emission lines, the Boltzmann plot method was successful in providing electron temperature estimates, but such estimates contained considerable error. The error is mainly attributed to inaccuracies in the sensitivity corrections made for the detector at the wavelength region. When compared with previous, reliable sensitivity corrected measurements made by this detector, the lower wavelength region of our collected Ti spectra typically displays a factor of two smaller sensitivity. When compared to a similar investigation into Ti III Stark broadening[21], the current experiment resulted in greater electron excitation temperatures and lesser inferred electron densities. Considering the differences in the laser excitation energy and the spectral grating implemented in each investigation, the experimental data appears to agree. However, the previous investigation utilizes the effective Gaunt factor of Equation (3) to enhance the threshold Gaunt factor[21]. For the current investigation, comparison with calculated values of Stark widths from the MSE approach demonstrate agreement when replacing an effective Gaunt factor with simply the Gaunt factor value at threshold. The semi-empirical Gaunt factor, at threshold, has been interpreted as accounting for the first truly quantum mechanical effect in electron impact broadening[17]. Further comparison with the MSE approach was made utilizing Table IV[20] reported by Tankosi´c et al., and it also shows agreement.

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We would like to thank Center for Laser Applications and UTSI for support for both fundamental experimental research and analysis, and for communicating research results with various national and international research groups.

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We present LIBS results of titanium ablation plasma.

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We discuss the modified semi-empirical approach.

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Use of the standard Gaunt factor is preferred.