Abstract

In this physical chemistry laboratory, the students develop experience in using Laser-Induced Breakdown Spectroscopy (LIBS) to analyze spectral emission data from to determine lifetimes of neutral and singly-ionized titanium species in LIBS plasmas. LIBS is a spectroscopic technique that focuses a high power laser on a surface. The laser heats, ablates, atomizes, and ionizes the surface material which creates a plasma. The light from the plasma is then spectrally resolved and detected. For LIBS experiments, the data can be collected using gated (using time delays and gate widths) or non-gated detection; this experiment uses gated detection taken at various time delays. The time delays used ranged from 0 to 60 μs to create the time decay curves. After creating the time decay curves for the titanium species used in this experiment, the students were able to examine the curves which illustrated the behavior of the neutral and singly-ionized titanium species and also gained experience calculating lifetimes.

1. Introduction

In laser-induced breakdown spectroscopy (LIBS), a high power laser is focused onto a surface. The focused laser pulse heats, ablates, ionizes, and atomizes the surface material and causes the formation of a plasma. The plasma emits light, which is spectrally resolved and detected. The subsequent spectrum can provide both quantitative and qualitative information regarding the sample. LIBS has many advantages including multi-element detection, little or no sample preparation, analysis of solids, liquids, and gases, real time analyses, and a requirement of only optical access to the surface. ^{1, 2} There are also many applications of LIBS, some of which include metal sorting, heavy metal determination, fissile material detection, geochemical fingerprinting, space exploration, and explosive detection ^{3, 4, 5, 6, 7, 8}.

As the laser is focused onto the sample, its energy couples into the sample, leading to its evaporation. The plasma is formed within the sample’s vapor and the surrounding gas atmosphere which causes excitation of the species in the sample and leads to their spontaneous emission. This further produces a continuum of light which is seen in the first few nanoseconds of plasma formation and causes rising backgrounds LIBS spectra. This continuum decays faster than the spectral emission lines in the plasma. Thus, by delaying the signal collection, the continuum background can be rejected; this is called the time delay, t_d. ⁹ The species primarily atomized or ionized in the plasma tend to exist in their neutral or singly-ionized forms, whereas doubly- or triply-ionized species are not likely to be observed in air due to their higher ionization potentials. Neutral or singly-ionized lines are signified by (I) or (II), respectively. Neutral species tend to have a longer lifetime in the plasma over singly-ionized species due to electron-ion recombination, which causes neutral species to remain longer in the plasma, and the decrease in both electron density and plasma temperature at the longer time delays. ¹ This lab experiment is designed for students to observe the behavior of neutral and singly-ionized atomic species in the LIBS plasma.

Two LIBS laboratory experiments have been published previously in the Journal of Chemical Education and are in current use at Alvernia. ^{10, 11} One was designed for an Analytical/Instrumental Analysis course and shows how LIBS can be used to obtain quantitative data through the use of calibration curves. ¹⁰ The other was designed for a Physical Chemistry lab where students learned how to calculate plasma temperature and electron density using the spectral information. ¹¹ This lab is also designed for a Physical Chemistry laboratory experiment. It shows the students how singly-ionized and neutral species behave in the plasma and allows them to calculate pseudo-lifetimes of the species for comparative purposes. The actual lab handout supplied to the students is included in the Supplemental Materials Section under Directions for Students. The learning objectives for this experiment are (1) to gain experience using LIBS and work up spectral data, (2) to visually see the difference between singly-ionized and neutral species’ behavior in the plasma, and (3) to learn how to calculate lifetimes using time decay curves.

2. Materials and Methods

There is no sample preparation for this laboratory experiment. A metal titanium electrode (Metal Electrodes, product code: METELECT12, Miniscience Inc., Clifton, NJ) was used as the sample.

The experimental set-up remained constant throughout this lab experiment. A Nd:YAG laser (λ=1064 nm, pulse width 6 ns) (Surelite II, Continuum, Santa Clara, CA) was operated at 100 mJ per pulse and 10 Hz. The laser pulse was focus onto the sample by a 50 mm focal length lens. The spot size on the sample was approximately 0.080 cm; this produced an approximate power density of 2.5 GW/cm². The light emitted by the plasma was collected with an optical fiber (QP1000-2-UV-VIS, Ocean Optics, Dunedin, FL) and it was then spectrally dispersed and detected with an echelle spectrograph and ICCD (echelle: SE200, Catalina, Tucson, AZ and ICCD: DH-734-18F-03, IStar, Andor Technology, Belfast, Ireland); the approximate resolving power of the echelle/ICCD is 1700. The data was taken at atmospheric pressure using various time delays ranging from 0 to 60 µs and a constant gate width of 500 ns. The time delay is the time the detector waits to view the pulse and the gate width is how long the detector views each pulse. A 3 second exposure time was used and the signal was integrated on the detector chip, and thus 30 pulses were averaged per trial since the laser was operated at 10 Hz. The timing between the laser and detector were controlled using a digital delay generator (BNC Model 575-4C Digital Delay and Pulse Generator, Berkeley Nucleonic Corp., San Rafael, CA). A typical LIBS set up has been shown previously ¹⁰.

The students took data on titanium metal using time delays of 0.5, 0.75, 1, 5, 10, 15, 20, 30, 40, 50, and 60 µs. Three spectra were recorded at each time delay, corresponding to a total of 33 spectra. The spectra were saved as text files and supplied to the students. The students used Microsoft Excel for their data work up. Emission line data for two titanium species (a singly-ionized specie and a neutral species) were used for comparison, as shown in Table 1. Time decay curves were created by plotting peak height versus time delay. By creating double exponential fits for the curves using Solver in Microsoft Excel, lifetimes were easily calculated. More information on this is supplied in the Results and Discussion Section.

3. Results

The students completed this lab in a two week period. In week 1, students took the LIBS data on their titanium sample but then worked on a different lab. In week 2, the students were given the lab time to do their data analysis during the scheduled lab period. All of the data analysis was compiled in Microsoft Excel. It will take each group approximately 30 minutes to take and save all of their data; therefore, if the lab section is large, it might be hard to complete the whole lab one 3 hour lab period.

The students were directed to create a spreadsheet with all of the raw spectral data. Instead of integrating areas under the emission peaks, the peak heights were used to analyze this data because this can be easily accomplished in Microsoft Excel. The students measured the peak height for each of the titanium lines in each of the replicate trials and recorded an average and standard deviation for each time delay. To view the comparison between the two titanium lines chosen, the students normalized their data sets. Time decay curves were created from this data, plotting the average normalized titanium emission height versus the time delay for each line type on the same graph. The students calculated standard deviations for their normalized data points and the error bars represent the normalized standard deviation from the three trials.

Typical time decay curves are shown in Figure 1. To produce a better predication of the lifetime measurements, double exponential fits were used on the data. Double exponential fits were calculated using the Solver Add-in on Microsoft Excel. Directions are supplied on how to add Solver to Microsoft Excel and how to use Solver for the double exponential fits in the Supplemental Materials. The double exponential fit yields an equation in the form of Equation 1.

(1)

where A and C are considered the amplitudes and B and D are the constants related to the average lifetime. The double exponential fit produces two different lifetimes (τ₁ and τ₂); τ₁ and τ₂ are determined by Equation 2 and 3, respectively. Please note: the negative sign is not included with B and D for the lifetime calculation; the negative sign symbolizes that the signal is decreasing as the time delay gets longer, which creates the time decay curve.

(2)

(3)

The average lifetime (< τ >) can be calculated using Equation 4. ¹²

(4)

The double exponential fits were verified in MATLAB. The slopes, the individual lifetimes, the R² values, and the overall average lifetimes are shown in Table 2.

It should be noted that the double exponential fit is not necessary for the singly-ionized titanium line data since a single non-linear exponential fit would produce the same lifetime results for the singly-ionized line data. However, the single non-linear exponential fit does not accurately predict the mid to tail end of the time decay curve for the neutral line, which ultimately skews its lifetime, and therefore, it is necessary to perform a double exponential fit on the neutral line data for a better predicted lifetime prediction. The double exponential fit matches the mid to tail end of the time decay curve for the neutral line and produces a better prediction of results. Ionized lines are excited during the initial formation of the plasma, when the plasma temperature and electron density are the highest, and thus decay quickly and exponentially as the plasma cools, which decreases the plasma’s temperature and electron density. The double lifetime for neutral lines is due to (1) the initial plasma formation which excites both neutral and ionized lines and (2) the electron-ion recombination which causes the neutral lines to remain longer in the plasma. ^{1, 13} To create less confusion for the students, both sets of data were modeled using the double exponential fits.

4. Conclusion

This experiment shows the basic behavior difference between neutral and ionized atomic lines in the LIBS plasma. As expected, the students could visually determine that the ionized titanium line decayed quicker than the neutral titanium line by plotting the normalized data on the same graph. The students were also able to discuss the trends in the time decay curves which show as the time delay was increased and the emission peaks subsequently decreased. At the conclusion of the experiment after the results were submitted, the instructor explained why the neutral lines last longer in the plasma.

In summary, the students gained a valuable experience using LIBS and learned about the differences between neutral and ionized lines and their behavior in a LIBS plasma. They were taught how to compile the data, learned how to normalize data sets as well as to calculate a standard deviation for the normalized average values, and learned how to use Solver to perform the double exponential fits, which enabled them to calculate lifetimes for the species. These results are relevant for any physical chemistry course. Moreover, this experiment presents an additional way to incorporate LIBS into the undergraduate laboratory. This laboratory experiment met all of its learning objectives.

Acknowledgements

This work was funded through U.S. Department of Energy, Office of Science, and Alvernia University. The authors would also like to thank Arthur Halpern for his advice on single exponential linear and single & double nonlinear exponential fits.

References