1 Introduction

In the past decades, there has been an increasing interest in laser-induced breakdown spectroscopy (LIBS) in several research fields such as material processing, space applications and diagnostic techniques [1, 2]. LIBS is an essential analytical technique for identification of the elemental composition of a sample [3–6].

In this technique, a highly energetic laser pulses generated from a Q-switched laser source is focused through a suitable focusing lens to generate a plume of plasma rich in atoms, electrons and ions on the surface of the sample. The focused beam results in the evaporation, atomization and ionization of the sample surface material, and the emitted radiations in this process are used for the identification of the elemental composition of the sample [7–9].

LIBS offers many advantages over other spectroscopic techniques such as mass spectroscopy, electrode spark and inductively coupled plasma. Some of LIBS unique advantages include the ability to make in situ analysis even in hostile environment, remote sensing, little or no preparation of the sample, and multi-element analysis [10–12]. Based on these advantages, LIBS has been extensively investigated on several samples including liquids [13], gases [14] and as well from non-conducting and conducting solids [15].

LIBS is also a spectroscopic technique for the determination of the density of electron, electron temperature and number densities of the plasma plume [16, 17]. Laser-induced plasma temperatures are influenced by various experimental conditions such as ambient surrounding, laser energy and laser pulse width. Most of the studies on LIBS temperatures report that the plasma temperature tends to increase with increasing laser energy, pulse width, laser wavelength and ambient pressure [18–21].

Although LIBS has been employed successfully in several experimental and theoretical works, to analyze the spectroscopic composition of the samples, there are still many aspects which need to be investigated [6]. For example, Barthelemy et al. [22] investigated the influence of the laser parameters of an aluminum-induced plasma. They reported that the temperature slightly decreases at the plasma edge and close to the aluminum surface. This decrease in temperature at the plasma edge is basically caused by radiative cooling, while the decrease in temperature at the aluminum surface is as a result of thermal conduction. The authors also found that at the first microsecond of the ablation plume, the electron density was spatially homogeneous.

Zhang et al. [23] also reported on the influence of laser parameters on plasma temperature. Their results predicted a general trend that LIP temperature increases with increasing laser parameters.

In this work, we shall report on laser-induced magnesium plasma with different laser energies and several time delays in order to optimize the spectroscopic performance, and investigate the influence of laser energy on the electron temperature. Section 2 of this work is devoted to the experimental setup and procedure used to obtain the time-resolved emission spectra and the temporal evolution of the electron temperature. The experimental results are presented in Sect. 3. Finally, Sect. 4 gives the conclusion of the results of this work.

2 Experimental setup

The experimental setup of the laser-induced breakdown spectroscopy is shown in Fig. 1. The setup consists of Nd:YAG laser source for plasma formation and vaporization of the target, monochromator and a time-resolved detector. The 1064-nm beam from a Q-switched Nd:YAG laser, with 10 ns pulse width and 1-Hz pulse repetition rate (PRR), emitting a laser pulse with energy of 150, 250 and 350 mJ, which was measured by a pyrometric detector.

Fig. 1
figure 1

Schematic diagram of the experimental setup for laser-induced breakdown spectroscopy

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The laser beam was focused horizontally onto the target surface by a means of a quartz lens with 150 mm focal length. The distance from the lens to the target was set to about 14 cm in order to gain a nearly hemispherical plasma plume and a reproducible breakdown. The plasma was generated in air at atmospheric pressure on ~1-mm2 surface area of the metal target. The content purity of the target was almost 99.99% magnesium plate, which was previously well polished before exposing to the laser beam.

The plasma emission was collected by a fiber bundle, which is coupled to a Mechelle spectrometer built with a gateable intensified charge-coupled device (ICCD) camera with a 1024 × 1024 pixels (istar from Andor Technology). The ICCD detector was synchronized with the trigger of the laser pulse. The synchronization was done using a digital generator (Stanford Research System, model DG645) and the oscilloscope (YOKOGAWA, digital oscilloscope DL9140, Japan). The gate delay was also monitored with the oscilloscope, which was triggered by signals collected by the photodiode. The time delay of the ICCD was varied from 100 to 1000 ns of the different laser energies for the spectra detection. In each measurement, the acquisitions were integrated over a suitable number of accumulations, in order to increase the signal-to-noise ratio. The atomic emission lines were identified using available atomic spectra data compiled in the national institute for standards and technology database [24].

3 Results and discussion

3.1 The spectra of the magnesium-induced plasma

The emission spectrum of the laser-induced magnesium plasma is shown in Fig. 2. The plasma emission was collected by a fiber bundle, which is coupled to a Mechelle spectrometer built with an intensified charge-coupled device (ICCD). The spectra were taken at a delay time of 100 ns and pulse energy of 350 mJ. The characteristic intensity of the Mg emission rapidly decreases with a larger delay time, due to bremsstrahlung emission and radiative recombination between the ions and electrons [25], and this is as a result of plasma quenching. At a delay time of 100 ns, a strong continuum is observed. The MgI 518.4-nm spectral line reaches the highest intensity with laser energy of 350 mJ, and this is fitted into the Lorentz profile in Fig. 3. In order to estimate the electron temperature of the laser-induced magnesium plasma, we study different emission spectra at several delay times. Figure 4 depicts a time-resolved emission spectrum of laser-induced magnesium plasma at different delay times.

Fig. 2
figure 2

a LIBS spectra of laser-induced magnesium plasma at a delay time of 100 ns and laser energy of 350 mJ. b LIBS spectra of laser-induced magnesium plasma at a delay time of 100 ns and laser energy of 350 mJ in the spectral region of 515.97–519.22 nm

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Fig. 3
figure 3

Lorentz fit of MgI 518.4-nm spectral line at a delay of 100 ns and laser energy of 350 mJ

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Fig. 4
figure 4

Time-resolved emission spectra of a laser-induced Mg plasma at different delay times, in the spectra region of 515.97–519.22 nm with a laser energy of 350 mJ

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3.2 The local thermodynamic equilibrium and the optical thinness of the plasma

The determination of the plasma temperature by the Boltzmann plot method requires the plasma to be in the state of thermodynamic equilibrium (LTE) and also must be optically thin. The Mg-induced plasma was optically thin for the line intensities used in the determination of the plasma temperatures [26]. This was observed from the peak intensities of the ratio of the Mg lines used. The experimental data and the stimulation validate that the local thermodynamic equilibrium condition is satisfied with plasmas of longer delay times. This depends on the plasma parameters such as the ambient gas, laser energy and pulse duration used in the experiments [27, 28]. The most commonly used method to warrant the existence of LTE is the electron energy distribution function (EEDF) Maxwell distribution, and the McWhirter criterion [23, 29–31]. The McWhirter criterion defines the minimum electron number density which must be present in order for LTE to exist, which can be expressed mathematically as [3]:

$$N_{e} \ge 1.6 \times 10^{12} T^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} \left( {\Delta E_{mn} } \right)^{3}$$
(1)

where N e is the electron density (cm−3), T is the plasma temperature (K) and \(\Delta E_{mn}\) is the higher energy difference (eV) between the upper and lower energy states of the Mg lines used.

Research recently has revealed that the McWhirter criterion is necessary but insufficient to assess the existence of LTE [32], since it is derived for stationary and homogenous plasmas. From this work, we established that the LTE is satisfied because the electron density deduced from the stark broadening is higher than 1016 cm−3.

3.3 Theoretical model of the electron temperature

Assuming plasma in LTE, the population of the energy levels of the species obeys the Boltzmann’s distribution law [17, 23], which can be given by the expression:

$$N_{m} = N\frac{{g_{m} e\frac{{E_{m} }}{kT}}}{U\left( T \right)}$$
(2)

where the subscript m stands for the upper energy level of the transition, N m and g m are the population (m−3) of the energy levels and the statistical weight of the upper energy level, respectively, \(E_{m}\) is the energy (eV) of the upper energy level, N is the number density (m−3), k is the Boltzmann’s constant (eV k−1), T is the electron temperature (k) and U(T) is the partition function. The emissivity \(\varepsilon_{mn} \left( {{\text{W}}\,{\text{m}}^{ - 3} } \right)\), of a particular transition of the species, can be written in the form:

$$\varepsilon_{mn} = \frac{hc}{{\lambda_{mn} }}A_{mn} N_{m}$$
(3)

where the subscript n represents the lower energy level of the transition, c is the speed of light (m s−1), h is the Planck’s constant (Js), A mn is the transition probability (s−1) and λ mn is the transition wavelength (m). From the expression of the emissivity, substituting the population of the energy levels N m into Eq. (2), we will obtain:

$$\varepsilon_{mn} = \frac{hc}{{\lambda_{mn} }}A_{mn} N\frac{{g_{m} e\frac{{E_{m} }}{kT}}}{U\left( T \right)}$$
(4)

For experimental systems, we can replace the emissivity by the line intensity, and by taking the natural logarithm of Eq. (4), we obtain the expression in the form:

$$\ln \left( {\frac{{I_{mn} \lambda_{mn} }}{{A_{mn} g_{mn} }}} \right) = - \frac{{E_{m} }}{kT} + \ln \left( {\frac{hcN}{U\left( T \right)}} \right)$$
(5)

By plotting the magnitude on the left side against the energy of the upper level in Eq. (5), yields a linear fit with a slope of \(- 1/kT\). The electron temperature can be calculated from the slope of the Boltzmann’s plot without knowing the partition function. The magnesium atomic lines at wavelength of 383.2, 470.3 and 518.4 nm were used to calculate the electron temperature. The spectroscopic data of \(A_{mn} ,E_{m}\) and \(g_{m}\) of the MgI spectral line can be retrieved from the NIST database. The spectroscopic data of the MgI spectra lines are listed in Table 1.

Table 1 The spectroscopic data of \({\text{Mg I and Mg II}}\) lines used, from the NIST database [24]
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The Boltzmann plot at a delay time of 100 ns and energy of 100 mJ is shown in Fig. 5, and the slope of the plot yielded an electron temperature of 8810 K. The temporal evolution of the electron temperature is shown in Fig. 6, with a delay time varying from 100 to 1000 ns at three different laser energies. The error bars depicted the standard deviations in determining the value of the electron temperature. In Fig. 7, the electron temperature reaches their highest value at 10164 K, with a delay time of 100 ns and laser energy of 350 mJ, and then decreases slowly up to 8833.6 K at 500 ns. Figure 8 depicts a plot of the electron temperature against the energy of the laser. As evident from the figure, the electron temperature increases with increasing laser energy.

Fig. 5
figure 5

Boltzmann plot obtained from MgI lines at a delay time of 100 ns and laser energy of 100 ns, using the spectral data of MgI 383.2, MgI 470.3 and MgI 518.4 nm

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Fig. 6
figure 6

Temporal evolution of the electron temperature of the magnesium-induced plasma, with laser energies of 100, 200 and 300 mJ

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Fig. 7
figure 7

Temporal evolution of the electron temperature of the magnesium-induced plasma, with laser energies of 150, 250 and 350 mJ

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Fig. 8
figure 8

Plot of the electron temperature against laser energy, at three different delay times, 100, 300 and 500 ns

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4 Conclusion

The emission spectroscopy of the laser-induced magnesium plasma in atmospheric air was investigated. The emission spectral lines were resolved at different delay times. From the time-resolved emission spectra of the laser-induced Mg plasma, we observed that the characteristic intensities of the spectral lines rapidly decrease with a larger delay times, this was as a result of bremsstrahlung emission and radiative recombination between the ions and electrons, and this is due to plasma quenching. At a delay time of 100 ns, a strong continuum was observed. The MgI 518.4-nm spectral line reaches the highest intensity with energy of 350 mJ. The electron temperature was determined from the Boltzmann plot method, using the magnesium atomic lines at wavelength of 383.2, 470.3 and 518.4 nm. A plot of \(\ln \left( {\lambda I/A} \right)\) against \(E_{m}\) gave a slope of \(- 1/kT\). At a delay time of 100 ns and laser energy of 350 mJ, the electron temperature attained their highest value at 10164 K. The electron temperature then decreases slowly up to 8833.6 K at a delay time of 500 ns. At laser energies of 100, 200 and 300 mJ at a delay time of 100 ns, the electron temperatures were found to be 8810, 9303 and 9724 K, respectively. We found that the electron temperature of the Mg plasma increases rapidly with increasing laser energy.