1 Introduction

Laser-induced breakdown spectroscopy (LIBS) is an analytical promising detection technique for solid, liquid and gaseous samples, and is based on optical detection of certain atomic and molecular species by monitoring their emission signals from the laser-induced plasma (LIP) [1–3]. It is a simple technique as compared to many other types of elemental analysis methods or techniques because of its straightforward experimental setup. In it, one requires a pulsed laser for generating micro plasma on the target surface and the elemental analysis is carried out by studying the emission of the plasma plume. The nature and dynamic of the LIP depend on different parameters such as laser wavelength, spot size, pulse width, ambient environment, etc. Using this technique, experiments can be performed either at atmospheric pressure or in the presence of some ambient gas [4, 5]. During ablation process, laser energy is used in dissipation into the sample through heat conduction, melting, and vaporization of the target material to generate plasma plume. The main advantage of this technique is that it provides direct chemical analysis of sample without its specific preparation.

Barium is a metallic alkaline earth metal and is never found in nature in its pure form due to its reactivity with air. It has few industrial applications in its elemental form. However, it has a number of applications in its compound forms. Barium is a component of some high temperature superconductors as well. This element remained under investigation by many researchers since long. Platisa et al. [6] presented the measurements of electron impact broadening of ionized Be and Ba lines in an electric shock tube plasma and calculated electron number density by laser interferometry, while electron temperature was measured using relative intensities of spectral lines. Bhattacharya [7] used laser-induced fluorescence method for the detection and measurement of ionized barium atoms near the vicinity of a Ba–Sr–Ca oxide coated electrode. Cappelli et al. [8] used laser-induced fluorescence diagnostics technique to expand recombining barium plasmas produced by laser ablation using 532 nm lasers. El-Astal et al. [9] studied temporally and spatially resolved YBa2Cu3O x plasma produced using 280 nm laser in 180 mTorr oxygen at laser fluence of 4 J cm−2 and estimated electron temperature using Cu I lines through the Boltzmann plot method. Dimitrijevic and Sahal-Brechot [10] calculated line widths and shifts for 14 Ba I and 64 Ba II multiplets for perturber densities 1015 to 1018 cm−3 and temperatures from 2,500 to 50, 000 K for Ba I and 5,000 to 100,000 K for Ba II lines using a semi-classical approach. Harilal et al. [11, 12] studied temporal and spatial behavior of electron temperature and its density by placing target material (YBa2Cu3O7) in an evacuated chamber using Q-switch Nd:YAG laser. Suzuki and Kijima [13] reported the successful preparation of well-crystallized BaTiO3 nano particles by the RF plasma CVD method using metal organic sources as source materials. A feasibility study of the laser-induced fluorescence diagnostic using barium ions with the characterization of a tunable dye laser was carried out by Chung et al. [14]. Kalyar et al. [15] presented the photo-ionization cross-section measurements from the 6s6p 1P1 and 3P1 excited states of barium at and above the first ionization threshold. They also reported a systematic line shape analysis study of the 6p7p configuration based 1P1, 3D1 and 3P1 auto-ionizing resonances in barium using Nd:YAG pumped dye laser system in conjunction with a therm-ionic diode ion detector [16]. Planar laser-induced fluorescence was used by Ma et al. [17] to examine the effect of the sampling interface on spatial distributions of barium ions and atoms in an inductively coupled plasma ion source. Study on transformation kinetics in plasma-sprayed barium and strontium-doped alumino-silicate was presented by Harder and Faber [18]. Conductivity study of 10 % yttrium-doped barium zirconate (BZY10) obtained by spark plasma sintering was carried out by Ricote et al. [19].

In the present work, we have employed LIBS technique for the optical emission study of the barium plasma generated at the surface of baryta Ba(OH)2 target placed in the air at atmospheric pressure in front of laser beam using fundamental harmonic (1,064 nm) of a Nd:YAG laser. We report the spatial evolution of the barium plasma in which experimentally observed line profiles of neutral barium (Ba I) have been used to extract the electron temperature (T e) using the Boltzmann plot method. Whereas, the electron number density (N e) has been determined from the Stark broadening parameter. Besides, we have studied the variation of electron temperature and electron number density as a function of laser energy.

2 Experimental details

2.1 The sample

The sample under this study, barium hydroxide Ba(OH)2 is the chemical compound which is also known as Baryta, and is one of the principal compounds of barium. In its original form, it is a white color powder. A small amount of it was used to prepare a pallet of 13 mm diameter and 3 mm thickness with the help of hydraulic press machine. The powder was pressed by a load of 10-ton for time duration of 5 min. The scanning electron microscope (SEM) photograph of the Baryta is shown in Fig. 1a. The quantitative analysis of the sample conducted by JSM–6490A analytical SEM is shown in Fig. 1b. The mass% of barium in the sample was 85.62.

Fig. 1
figure 1

a SEM Photograph of Baryta Ba(OH)2 sample showing its morphology. b The SEM signals of the Baryta Ba(OH)2 sample

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2.2 The experimental setup

The experimental setup is shown in Fig. 2, and is same as that described in our previous work [20–22]. Briefly, we used a Q-switched Nd:YAG (Quantel Brilliant) pulsed laser having pulse duration of 5 ns and 10 Hz repetition rate which is capable of delivering 400 mJ at 1,064 nm, and 200 mJ at 532 nm. The laser pulse energy was varied by the flash lamp Q-switch delay through the laser controller, and the pulse energy was measured by a Joule meter (Nova-Quantel 01507). The laser beam was focused on the target using convex lens of focal length 20 cm and diameter 30 mm. The estimated area of the laser spot on the target was ≈4 × 10−4 cm2 for the first (1,064 nm) harmonic of Nd:YAG laser which was used in the experiment. The sample was mounted on a three dimensional sample stage, which was rotated to avoid the non-uniform pitting of the target. The distance between the focusing lens and the sample was kept at 18.5 cm, less than the focal length of the lens to prevent any breakdown of the ambient air in front of the target. The spectra were obtained by averaging 10 single data of shots under identical experimental conditions. The radiations emitted by the plasma were collected by a fiber optics (high-OH, core diameter: 600 μm) having a collimating lens (0o–45o field of view) placed at right angle to the direction of the laser beam. The optical fiber was connected with the LIBS-2000 detection system (Ocean Optics Inc.), to measure the plasma emission. The emission signal was corrected by subtracting the dark signal of the detector through the LIBS software. The LIBS-2000 detection system is equipped with five spectrometers each having slit width of 5 μm, covering the range between 220 and 720 nm. Each spectrometer has 2,048 element linear CCD array and an optical resolution of ≈0.05 nm by scanning a narrow bandwidth dye laser. In the experiments, the time delay between the laser pulses and the start of the data acquisition is about 3.5 μs, whereas the system integration time is 2.1 ms. In order to record the emission spectrum, the LIBS-2000 detection system was synchronized with the Q-switch of the Nd:YAG laser. The flash lamp out of the Nd:YAG laser triggered detection system through a four-channel digital delay/pulse generator (SRS DG 535). The LIBS-2000 detection system triggered the Q-switch of the Nd:YAG laser.

Fig. 2
figure 2

Block diagram of the experimental setup

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3 Results and discussion

3.1 Optical emission studies

In the present work, we have studied the Baryta plasma generated by the fundamental (1,064 nm) mode of a Q-switched Nd:YAG laser by placing the target in air. Ba belongs to the group of alkaline earth elements and has its two s electrons in outside filled shells in the ground state. The term 1S0 is the ground term. Figure 3a shows the window of emission spectrum of barium plasma covering the spectral region from 540 to 650 nm. The majority of the lines in this region belong to neutral barium (Ba I). Assignments of these lines are taken from the Moor’s and NIST database [23, 24] and their transitions are shown in Fig. 3b.

Fig. 3
figure 3

a The emission spectrum of Ba plasma generated by first harmonic (1,064 nm) of the Nd:YAG laser at a distance of 0.05 mm from the target surface. b Energy level diagram showing barium transitions

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3.2 Laser-induced plasma emission studies

3.2.1 Calculation of electron temperature (T e)

s important to understand the dissociation, ionization, and excitation processes taking place in plasma. When the laser light interacts with the target surface, outer most electrons of the atoms get excited. When the energy is greater than the binding energy of the target material, bond breaking occurs and evaporation of target material starts. The electron temperature is determined using the Boltzmann plot method from the relative intensities of the observed lines. After observing the well-resolved multiplet structure from a number of excited levels and decaying to a common lower level, it is tempting to extract the plasma parameters from the observed spectra, in particular, the electron number density (N e) and the electron temperature (T e). The spatial behavior of the line intensities has been recorded using the fundamental (1,064 nm) harmonic of an Nd:YAG laser by varying the distance of the detector from the target surface along the plume expansion. The electron temperature is determined using the Boltzmann plot method from the relative intensities of the observed line. The relative intensities are normally proportional to the population of the pertinent upper levels. The following relation has been used to extract the plasma temperature [25]:

$$ \ln \left[ {\frac{{\lambda_{ji} I_{ji} }}{{hcA_{ji} g_{j} }} \times \frac{Q(T)}{N(T)}} \right]\, = - \left[ {\frac{{E_{j} }}{kT}} \right] $$
(1)

where λ ji (m) is the wavelength of the transition lines, I ji (W m−3) the integrated line intensity of the transition involving an upper level (j) and a lower level (i), Q(T) the partition function (dimensionless), h (J s) Plank’s constant, c (m s−1) the speed of light, A ji (s−1) the transition probability, g j (s−1) the statistical weight of level (j), N (T) (m−3) the total number density, E j (J) the energy of the upper level, k (J K−1) the Boltzmann constant and T(K) is the electron temperature. A plot of ln(λI/gA) versus the term energy E j gives a straight line with a slope equal to (−1/KT). Thus, the electron temperature can be determined without the knowledge of the total number density or the partition function. Errors are bound to be present in the determination of the electron temperature by this method. Therefore; the electron temperature is determined with ≈10 % uncertainty, coming mainly from the transition probabilities and the measurement of the integrated intensities of the spectral lines. The line identifications and different spectroscopic parameters such as wavelength (λ), statistical weight (g), transition probability (A) and term energy (E) are listed in Table 1.

Table 1 Spectroscopic parameters of Ba I lines used in Boltzmann plot
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For the determination of electron temperature of the plasma through Boltzmann plot method, we have used the five barium (Ba I) lines at 551.90, 577.76, 582.62, 599.70 and 606.31 nm as shown in Fig. 4. Errors are bound to be present in the determination of the plasma temperature by this method; therefore, the temperature is determined with ≈10 % uncertainty, coming mainly from the transition probabilities and the measurement of the integrated intensities of the spectral lines. We have also studied the spatial behavior by moving detector from the target material along the line of propagation of plasma plume. The electron temperature of the plasma close to the target surface (0.05 mm) is estimated as 12,378 K that varies to 10,720 K at a distance of 2 mm from the target as shown in Fig. 5. The region near the surface of the target material constantly absorbs radiation during the time interval of the laser pulse, causing a higher temperature near the target. This higher value of the temperature is due to absorption of the laser radiation by the electrons via the inverse bremsstrahlung absorption process. A decrease in the temperature may be attributed to the thermal energy which is rapidly converted into kinetic energy when the plasma is attaining maximum expansion velocities, causing the temperature to drop for the expanding plasma.

Fig. 4
figure 4

Boltzmann plot for the Ba I spectral lines emitted by the laser-induced plasma at 0.05 mm from the target surface at energy 172 mJ using first harmonic (1,064 nm) of the Nd:YAG laser

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Fig. 5
figure 5

Variation of the electron temperature along the direction of propagation of the plasma plume at energy 172 mJ using first harmonic (1,064 nm) of Nd:YAG laser

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3.2.2 Calculation of electron number density (N e)

During the evolution of LIP, excitation and ionization of the evaporated material occur, so that the depositing material is energetically suitable for the film formation. It is then important to determine the thermodynamic parameters of LIP such as electron number density (N e) and electron temperature (T e). One of the most reliable techniques to determine the electron number density is from the measured Stark broadened line profile of an isolated line of either neutral atom or singly charged ion. The electron number density (N e) related to the full-width at half maximum (FWHM) of the Stark broadening lines is given by the relation [1, 3, 25]:

$$ \Updelta \lambda_{1/2} = 2\omega \left( {\frac{{N_{\text{e}} }}{{10^{16} }}} \right) + 3.5A\left( {\frac{{N_{\text{e}} }}{{10^{16} }}} \right)^{1/4} \left[ {1 - \frac{3}{4}N_{\text{D}}^{ - 1/3} } \right]\omega \left( {\frac{{N_{\text{e}} }}{{10^{16} }}} \right) $$
(2)

where ω is the electron impact width parameter, A the ion broadening parameter, N e the electron number density and N D is the number of particles in the Debye sphere. The first term in Eq. (2) refers to the broadening due to the electron contribution, whereas the second term is attributed to the ion broadening. Since the contribution of the ionic broadening is normally very small, therefore, it can be neglected. The electron number densities have been determined from the line profiles of the isolated barium neutral line (Ba I) at 585.37 nm using the above relation (2) by neglecting the contribution of the ion impact broadening and Doppler broadening:

$$ \Updelta \lambda_{1/2} = 2\omega \left( {\frac{{N_{\text{e}} }}{{10^{16} }}} \right) $$
(3)

The value of ω corresponding to different electron temperatures is obtained from Ref. [10].

Figure 6a shows the line profile of the Ba II line at 493.70 nm recorded from the plasma generated by the first harmonic (1,064 nm) of Nd:YAG laser. The laser energy was varied from 138 to 172 mJ for the various corresponding values of Q switch delay. The width of the line profile increases as the laser energy is increased and its value is maximum at 20 μs delay. Figure 6b shows the Stark broadened profile of Ba I line at 585.37 nm recorded from the plasma along with the least squares fit of a Lorentzion line shape which yields the width ∆λ 1/2 of this line. The full line represents the Lorentzian fit to the experimental data points. The full widths at half maximum (FWHM) of the spectra are used to estimate the electron number density. The spatial behavior of the electron number density in the plume is determined using the above relation (3). The electron number densities at a distance 0.05 mm from the target surface, in the case of fundamental (1,064 nm) harmonic laser with pulse energy 172 mJ, are found to be 2.84 × 1018 cm−3 that decreases to 4.74 × 1017 cm−3 at a distance of 2 mm from the target surface as shown in Fig. 7. The decrease in the number density at large distance is mainly due to the recombination of electrons and ions. As is evident from Figs. 5 and 7, the electron temperature and the electron number density both close to the target (0.05 mm) are maximum, since the region close to the surface continuously absorbs the laser radiation during the laser pulse. When the plasma expands, it thermalizes by transferring the energy to its surroundings and is transparent to the laser pulse; therefore, the temperature and the number density decrease along the direction of expansion of the plume. Moreover, the electron temperature and number density decrease rapidly within a short distance from the target surface, while at a large distance, they exhibit little variation. The variation in the electron temperature is lesser as compared with that of number density. The internal energy of the plasma is distributed in its thermal and ionization energy. The particle density in the plasma depends on the degree of ionization, evaporation rate and the plasma expansion velocity. Because of the high expansion velocity of the leading plasma edge, the electron density decreases, makes the plasma transparent to the laser beam at larger distance away from the target surface. The absorption in the plasma mainly occurs by an inverse bremsstrahlung and photo ionization process.

Fig. 6
figure 6

a Variation in the signal intensity and width of the Ba II line at 493.40 nm correspond to several Q-Switch delays using first (1,064 nm) harmonic of the Nd:YAG laser. b Stark broadening profile of Ba I line at 585.37 nm. The dots represent the experimental profile and the solid line is Lorentizion fit

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Fig. 7
figure 7

Variation of the electron number density with the distance using the first harmonic (1,064 nm) of the Nd:YAG laser

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3.3 Variation of plasma parameters with laser energy

In the second set of experiments, we have determined the electron temperature and electron number density for different values of the laser energy. It is observed that the intensities and widths of the spectral lines increase with the increase in the laser energy. Figure 8a shows the variation of the electron temperature for the laser-produced plasma with respect to the laser energy at a distance of 0.05 mm from the target surface. The electron temperature varies from 9,675 to 11,330 K for the energy range from 138 to 172 mJ. Evidently, the electron temperature increases with the increase in the laser energy which in turn increases the mass ablation rate [26], hence the spectral line intensities and the widths increase as well. Figure 8b shows the variation in the electron number densities as a function of the laser energy. The variation in the electron number density with the laser energy also shows a similar behavior. The energy varies from 138 to 172 mJ, whereas electron number densities vary from 1.02 × 1018 to 2.19 × 1018 cm−3. At higher laser energies, the increase in the plasma temperatures and electron densities increases very slowly, this may be attributed to the plasma shielding. The observed increase in N e and T e by the increase of the laser energy is due to the absorption and/or reflection of the laser photon by the plasma, which depends upon the plasma frequency. In our experiment, the corresponding frequency is 2.8 × 1014 Hz, whereas the plasma frequency is V p = 8.9 × 103 √N e. The electron number density is N e ≈ 2.19 × 1018 cm−3; therefore, V p = 1.30 × 1013 Hz which is less than the laser frequency (≈1014 Hz). This shows that the energy loss due to the reflection of the laser radiation from the plasma is insignificant. It means that practically insignificant energy loss occurs due to the reflection of the Nd:YAG laser from the plasma. By increasing the laser energy, more excited species, ions and free electrons are generated. The laser pulse interacts with these species, resulting in further heating and ionization and consequently further increased consumption of incoming laser energy.

Fig. 8
figure 8

a Variation of the electron temperature with the laser energy using the first harmonic (1,064 nm) of Nd:YAG laser at a distance of 0.05 mm from the target surface. b Variation of the electron number density with the laser energy using first harmonic (1,064 nm) of Nd:YAG laser at a distance of 0.05 mm from the target surface

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3.4 Validity of local thermodynamic equilibrium (LTE) condition

The basic assumptions for the validity of the LTE include: collisionally recombination rate exceeds the radiative rate, velocity obeys the Maxwell distribution, energy distribution is Boltzmann distribution, heavy particles temperature (T h) is close to the plasma temperature (T e) and the intensive parameters are varying in space and time, but are varying so slowly that for any point, one can assume thermodynamic equilibrium in some neighborhood about that point [27]. In the present work, the estimated experimental results reveal that the decrease of electron number density (N e) is mainly due to recombination between electrons and ions in the plasma. When the electron and ion recombine with each other, the electron–ion system goes from initial charged state to the neutralized state of the lower energy. In the case of electron–ion recombination, the most likely processes are the radiative recombination, and the three-body or collisional recombination. The dependence of the recombination rate for the radiative and the three body recombination on the ion charge \(\bar{Z} \), electron density N e, ion density N i and plasma temperature T e is N e N i \(\bar{Z}^{2} \) T −3/4e and N 2e N i \(\bar{Z}^{3} \)  T −9/2e ln \(\sqrt{\bar{Z}^{2} + 1} \), respectively [27]. Among the two recombination processes considered here, the three-body recombination seems to be dominant in the present reported work. Besides that, we have also estimated the ion temperature using the Saha equation as discussed by De Giacomo et al. [27]. We observed that the ionization temperature using Saha equation is higher than the plasma temperature estimated using Boltzmann plot method, but the LTE plasma is characterized by a single temperature. This difference in the plasma and ionization temperatures is due to the uncertainties in the transition probabilities as well as the uncertainties in the measurement of the integrated line intensities used in the calculations. The use of the emission spectroscopy for the determination of the plasma temperature and electron number density requires optically thin spectral lines. The self absorption depends on the oscillator strength, level energies degeneracy, broadening parameters and also on the plasma parameters. The condition that the atomic states should be populated and depopulated predominantly by electron collisions, rather than by radiation, requires an electron density which is sufficient to ensure the high collision rate. The corresponding lower limit of the electron density is given by McWhirter criterion, which is the necessary (but not sufficient condition) for attaining the minimum number density to check the validity of LTE [28–30]:

$$ N_{\text{e}} \ge 1.6 \times 10^{12} T^{1/2} (\Updelta E)^{3} $$
(4)

where T (K) is the plasma temperature and ∆E (eV) is the energy difference between the states, which are expected to be in LTE. At ~12,378 K, Eq. (4) yields N e ≈ 2.7 × 1014 cm−3. The electron number densities determined in our experiments are in the order of 1018 which is higher than the required number density to satisfy the LTE condition. When we focus the laser on the target, the ablation of target takes place and due to the density gradient, plasma rapidly expands. Moreover, the conditions for the LTE have also been critically discussed by Cristoforetti et al. [31], and we have observed that one of the necessary conditions for LTE is higher density, which is fulfilled. In the Boltzmann plot (Fig. 4), all the lines lie on a straight line which also indicates that the system was in LTE. Moreover, we have not observed any self absorption in the spectral lines.

4 Conclusion

We have used a Q-switched Nd:YAG laser at its first harmonic (1,064 nm) to study the barium plasma produced at the surface of baryta Ba(OH)2. The optical emission spectrum of the barium plasma reveals transitions of neutral and singly ionized barium. The electron temperature and the electron number density have been determined along the axial positions of the plasma plume. It is observed that the spatial behavior of the electron temperature and electron density close to the target (0.05 nm) is maximum, and decreases along the distance from the target. Variations of the electron temperature and the electron number density with the laser energy show that both these parameters increase with the increase in the laser energy.