1 Introduction

Laser-induced breakdown spectroscopy (LIBS) is a plasma-based method that combines a powerful laser and atomic emission spectroscopy (AES). It has increased in popularity as an analytical tool due to its various advantages over other AES and non-AES-based techniques. It is able to detect all elements as well as simultaneous multi-element detection. LIBS can be applied on a variety of materials including solids, liquids, and gases both in situ and remotely, without sample preparation, and under extreme temperature and pressure conditions. During the last 4 decades, the applications of LIBS have increased considerably including environmental monitoring [1, 2], space exploration [3, 4], cultural heritage conservation [5, 6] and biomedical research [7].

In 2018, Noll et al. [8] revealed, in an overview of advancements from 2014 to 2018, the two main development directions of LIBS industrial application which are stationary automated LIBS systems for routine use on assembly lines, as well as the evolution of handheld LIBS system markets. Nevertheless, additional efforts are required to establish appropriate materials methodological approaches for an accurate quantitative LIBS analysis. Previously [9], we have demonstrated the feasibility of using LIBS technique for sorting zinc-based alloys, for the first time. We used chemometric methods applied on LIBS spectra registered at a delay and gate times of 2 and 1.5 µs, respectively. In the experimental condition of this contribution [9], it is important to point out that the registered spectra were characterized only by atomic emissions of zinc, aluminum and copper.

In order to increase the accuracy of measurements, a plasma parametric investigation has been conducted in our study. LIBS is generally used for elemental composition studies using either the calibration curves method or the CF-LIBS method. This latter is based on the assumptions of LTE, an optically thin plasma, and stoichiometric ablation of the sample (the composition of the plasma is representative of the alloy composition). Notice that the CF-LIBS method has the capability to accurately quantify the concentration of major elements with a higher level of precision compared to the minor ones. The ease or difficulty of determining plasma parameters depends on the composition of the sample. For instance, in the study by Iqbal [10], the CF-LIBS quantification of Devarda’s alloy, which consists of 50% Zn, 45% Al, and 5% Cu, was performed using a Nd:YAG laser operating at 532 nm with a laser energy of 120 mJ. In this case, the detection of several Cu atomic lines in the spectra was feasible. However, in our sample containing only 0.8% Cu, the quantification of Cu becomes a challenging task.

The laser-induced plasma (LIP) is formed by focusing a high-power pulsed laser on the material surface, which then proceeds to expand and cool down emitting characteristic radiation consisting of atomic and ionic lines of the constituent elements present in the sample under analysis [4]. The spatiotemporal optimization of plasma parameters is necessary for applying the CF-LIBS.

In the present contribution, a spatiotemporal study of spectral intensity, plasma temperature, and electron number density of zinc-based alloy plasma is investigated to identify optimum distances and times where the LIP satisfies the conditions for applying the CF-LIBS.

We explored the effect of optical fiber position along the plasma propagation axis as well as the delay time on the plasma parameters. Laser-induced breakdown spectroscopy of zinc-based alloy is investigated using spatiotemporal resolved measurement in air at a fixed laser energy of 50 mJ. These measurements have been carried out in the delay time range from 0.8 to 12 µs and along the plasma length. The Saha–Boltzmann plot method is employed to estimate the plasma temperature by analyzing copper lines, while the electron number density is determined through the measurement of the Stark broadening of the Hα line profile. CF-LIBS quantification was performed at optimized delay times and axial distances, and the results were compared to the analysis obtained from µ-XRF measurements.

2 Experimental setup

Figure 1 depicts a schematic illustration of the apparatus used in this experiment. It is composed of a Q-Switched Nd–YAG laser operating at its fundamental wavelength (1064 nm) with a pulse duration of 7 ns, having a maximum energy of 200 mJ, at a repetition rate of 10 Hz.

Fig. 1
figure 1

Experimental setup

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A convex lens with a focal length of 100 mm is used to focus the laser pulse, which has an energy of 50 mJ, on the zinc-based alloy target. This latter is placed in a rotating holder during the experiment, leading to the formation of a plasma in the ambient air.

Plasma emissions are collected and focused on the entrance of a 400 µm optical fiber using a lens of 100 mm focal length (the plasma image is reproduced with a magnification of 1:1 on the entrance of the optical fiber). The optical fiber placed at an angle of 45° is connected to the Echelle spectrometer array (LTB Lasertechnik Berlin Aryelle 200) with a focal length of 200 mm and a spectral resolution of 24–90 pm, covering the spectral range from 200 to 790 nm. The spectrometer is equipped with an ICCD camera (ANDOR iStar33418F-03) with 1024 × 1024 pixels and a 13 × 13 mm2 surface detection. The spectra are displayed on a computer using the SOPHI software. The spectrometer was calibrated in wavelength and intensity using an Hg, and Deuterium-Halogen lamps, respectively. LIBS spectra were registered at a fixed gate width of 500 ns and an exposure time of 901 ms that corresponds to an accumulation of ten spectra in order to improve the signal-to-noise ratio. The spatially and temporally resolved plasma was collected by varying the delay time from 0.8 to 12 µs and the collecting position on the plasma plume along the propagation axis (perpendicular to the target) from 0 to 3 mm by different steps of 100, 200 and 400 µm.

The Zn-based alloy under investigation is known for its robustness, endurance, and ability to withstand corrosion even under severe environmental conditions. These properties make it a highly desirable option for numerous industrial applications, such as automotive, construction, electrical, and electronics manufacturing. Accurately determining the elemental composition of this alloy is crucial to ensure its quality and performance.

On Table 1, we present the elemental composition of the studied zinc-based alloy using the µ-XRF analysis.

Table 1 The elemental composition determined by the µ-XRF
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3 Results and discussion

The optimization of LIBS spectra and the understanding of physical processes are crucial for the quantification of any material using the CF-LIBS approach. In this sense, we have carried out the study of spatiotemporal evolution of plasma emissions (lines intensities) and plasma parameters such as plasma temperature Te and electron number density Ne and the evaluation of LTE.

3.1 Spectra acquisition and analytical lines selection

Several spectra are recorded along the propagation axis at different delay times in the range of 0.8–12 µs. Figure 2 shows a representative emission spectrum for ZnAlCu alloy recorded at a delay time of 1.5 µs. The emission spectra were characterized by various atomic and ionic transitions of Zn, Al and Cu identified using NIST [11] and Kurucz [12] database and presented in Table 2. The accuracy of the transition probabilities are: A ≤ 3%, AA ≤ 1%, A +  ≤ 2%, B ≤ 10%, B +  ≤ 7%, C ≤ 25, C ≤ 18%, **: not available.

Fig. 2
figure 2

Zoomed part of the emission spectrum of Zn-based alloy at delay time of 1.5 µs

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Table 2 Spectroscopic data of the identified lines present in our alloy
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3.2 Spatiotemporal evolution of the emitted species

For the signal collection in this study, an optical fiber with a diameter of 400 µm was employed. Consequently, the recorded spectrum represents only a portion of the emitted plasma. We moved the optical fiber along the plasma propagation axis at different increments of 100, 200, and 400 µm to investigate the influence of its position on the spectra.

Figure 3 shows the spatial evolution of the intensities of a pair of ionic and atomic lines of the alloy components: Zn, Al, and Cu recorded at a delay time of 1 µs. The intensities of the emitted couples (Zn I, Zn II), (Al I, Al II), and (Cu I, Cu II) show the same behavior as a function of distance in all cases of moving steps. According to Fig. 3, the emissive plasma length is approximately 3000 µm with a maximum intensities occurring at propagation distances of 800 µm for ionic species and slightly shifted at 1200 µm for atomic species. This shift is due to the fact that atomic emissions are enhanced by the ionic species recombination effect. These results are noticed independently of the moving steps.

Fig. 3
figure 3

Spatial evolution of couples of ionic and atomic emission lines related to the ablation of ZnAlCu alloys at delay and gate time of 1 µs

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On Fig. 4 (contours), we present the spatiotemporal evolution of the three ionic and atomic couple lines: (Zn I, Zn II), (Al I, Al II), and (Cu I, Cu II). We observed that strong emissions occurred at 1 and 2 µs for all ionic and atomic species, respectively. This is because the plasma is confined at this stage, and it goes through an adiabatic expansion, in which its thermal energy is converted to kinetic energy, allowing the LIP to expand in both time and space. The Zn I emission line is detectable for a longer time (about 10 µs) than the Al I and Cu I emission lines, which have maximum durations of 7 and 5 µs, respectively. Contours related to ionic emission lines indicate more confined structures, with maximum delay times of 4, 2.25, and 1.8 µs for Zn II, Al II, and Cu II, respectively. The fact that Zn is the major element in ZnAlCu alloy explains the persistence of the zinc emission lines all over distance and time when compared to Al and Cu. The intensity of ionic emission for the same species decreases significantly at early time compared to atomic lines and this is attributed to the recombination mechanism.

Fig. 4
figure 4

Spatiotemporal representation of three couples of ionic and atomic lines

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It was observed that the intensity of all emission lines decreases towards the peripheries and target surface along the propagation axis. The highest intensity was recorded at the plasma plume core. This phenomenon can be attributed to thermal conduction between the plasma and both the solid target and the surrounding atmosphere.

Table 3 provides the corresponding distance and time ranges for the maximum intensity of the three species.

Table 3 The distance and time ranges that correspond to the maximum emission intensities
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3.3 Plasma electron temperature

The spatiotemporal evolution of plasma temperature is crucial because it allows us to select the time when the plasma is in LTE and to obtain an accurate quantification of materials. Boltzmann and Saha–Boltzmann plots are the most commonly used methods in LIBS to estimate plasma temperature. The Boltzmann plot calculates the excitation temperature based on the emission lines of a single species. The simplest version of this plot uses only two emission lines with enough difference in upper level energy. When the plasma spectrum has a large number of emission lines, the Boltzmann plot shows a good correlation of the experimental data to a linear fitting, showing the Boltzmann equation validity. For the Saha–Boltzmann plot method, the ionization temperature is obtained from the emission lines of the neutral and singly ionized lines of a single element. This method, well described by Aragon et al. [13], can improve the sensitivity by selecting lines from successive ionization stages of the same element, here the difference in energy levels is enhanced by the ionization energy, which is much greater than the thermal energy [14]. This method permits a large extension of the range of upper energy level and, therefore, an improvement in temperature precision.

In case of the studied alloy, we encountered many difficulties in precisely determining Te values due to the limited availability of atomic line emissions in the spectra of the zinc-based alloy. These emissions are primarily resonant lines or lines with same or small gap in upper energy levels (Table 2). The plasma temperature is determined using the Saha–Boltzmann plot method applied on Cu lines (the used Cu atomic and ionic lines are shown in Table 2 in bold). For that, only distances and times containing atomic and ionic emission lines with a good signal-to-noise ratio were chosen. For t > 6 µs, the spectral intensity of ionic Cu lines is too weak for the measurement of temperature. Consequently, the Te values were calculated only for times ranging from 0.8 to 6 µs and for axial distance from 0.6 to 2.6 mm.

A representative Saha–Boltzmann plot is depicted in the Fig. 5 for a delay time of 1.5 µs.

Fig. 5
figure 5

Representative Saha–Boltzmann plot at a delay time of 1.5 µs and an axial distance of 1.6 mm

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Figure 6 shows the spatiotemporal evolution of the electron temperature of the plasma (a) and the variation of electron temperature as function of delay time at a distance of 1.6 mm approximated by two functions, the exponential function and t−1 function (b). The estimated electron temperature falls from 1.3 eV at 0.8 µs to 0.74 eV at 6 µs. It decreases rapidly as the time increases from 0.8 to 2.5 µs due to the cooling of the LIP, and then it decreases slowly in the range from 2.5 to 6 µs due to the energy released by recombination which compensates the cooling due to the expansion processes. In the literature [15,16,17,18,19], the authors used different functions to fit the electron density and plasma temperature. Bai [15] used an exponential function, whereas [16,17,18,19] used t−n function. Rumsby et al. [18] fitted, for the first time, the evolution of the electron temperature and electron density as function of time and distance. They presented a theoretical model describing the adiabatic expansion of the plasma, in which the electron temperature is directly proportional to Neγ−1. The authors found fitting functions as t−2 and t−3 for Te and Ne, respectively. In our case where the plasma is induced in atmospheric pressure, the function t−1 as well as the exponential function fitted well the evolution of the electronic temperature as function of time.

Fig. 6
figure 6

a Spatiotemporal evolution of electron temperature. b The variation of electron temperature as a function of delay time at an axial distance of 1.6 mm. The line in blue represents a decay exponential fit and the line in red represent a t−1 fit

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3.4 Plasma electron density

One of the most important values to be calculated in LIP is the electron density. It can be calculated using the Stark broadening of various emitted spectral lines from neutral atoms or ions [14, 20,21,22,23,24]. According to El Sherbini et al. [20], the precise estimation of electron density is frequently performed using the Hα line which comes from the low concentration of water present in the surrounding humid air. The Stark broadening parameter of Hα line is provided by Griem [25].

In this section, we present the spatiotemporal evolution of electron density which was calculated through the determination of the Stark broadening of the optically thin Hα line according to the relation given by Gigosos [24]:

$$N_{{\text{e}}} = 10^{23} \left( {\frac{{\Delta \lambda_{1/2} \left[ {{\text{nm}}} \right]}}{1.098}} \right)^{1.471} {\text{m}}^{ - 3} .$$
(1)

Here, Ne is the electron density and Δλ1/2 is the full width at half maxima (FWHM) of the Hα line profile obtained from a Voigt fit.

Figure 7a reports on the spatiotemporal evolution of the electron density for the ZnAlCu plasma and Fig. 7b depicts the variation of Ne as function of delay time at a distance of 1.6 mm approximated by the t−1 function. The estimated electron density falls from 3.54 × 1017 at 0.8 µs to 4.9 × 10 16 at 6 µs. It is found to rapidly decrease as the time increases from 1 to 2.5 µs, primarily due to the cooling of the LIP, then it decreases slowly until it remains nearly constant at 5 µs as a result of the energy released by recombination, which offsets the cooling effect caused by expansion processes.

Fig. 7
figure 7

a Spatiotemporal evolution of electron density. b The variation of electron density as a function of delay time. The solid line represents t−1 fit

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3.5 Evaluation of LTE in transient and heterogeneous plasma

Only under the LTE condition, the description of the plasma state and the evaluation of its parameters, such as Te, Ne and the total number density of the species Ns, can be possible especially when using the CF-LIBS approach [26]. The McWhirter criterion [27] is given by the relation 2. It defines the minimum electron number density required in a plasma to guarantee the existence of LTE. This criterion is achieved by requiring collisional depopulation rate for electronic levels to be at least ten times greater than the radiative depopulation rate. It is important to note, however, that this criterion was originally established for plasmas that are both homogeneous and stationary. Therefore, it is essentially a necessary but not sufficient condition when dealing with other forms of plasmas, such as laser-induced plasma:

$$N_{{\text{e}}} \left( {{\text{cm}}^{{ - 3{ }}} } \right) \ge 1.6{ }.{ }10^{12} T^{\frac{1}{2}} \left( {\Delta E_{nm} } \right)^{3} ,$$
(2)

where \({\Delta E}_{{nm{ }}}\) is the largest energy gap of the transition lines and it is expressed in eV, and T is the temperature expressed in Kelvin.

There are two additional requirements for time-dependent and inhomogeneous plasma that must be fulfilled. The first criterion reports on the transient behavior of the plasma. The temporal variation of thermodynamic parameters should be slower than the relaxation time [28]; this can be expressed as

$$\frac{{T_{{\text{e}}} \left( {t + \tau_{{{\text{rel}}}} } \right) - T_{{\text{e}}} \left( t \right)}}{{T_{{\text{e}}} \left( t \right)}}{ } \ll 1\;{\text{and }}\frac{{N_{{\text{e}}} \left( {t + \tau_{{{\text{rel}}}} } \right) - N_{{\text{e}}} \left( t \right)}}{{N_{{\text{e}}} \left( t \right)}}{ } \ll 1,$$
(3)

where \(\tau_{{{\text{rel}}}}\) is the relaxation time, i.e., the time needed for the establishment of excitation and ionization equilibrium and it is given by the relation 4:

$$\tau_{{{\text{rel}}}} = \frac{{6.3 10^{4} }}{{n_{{\text{e}}} f_{mn} \langle \overline{g}\rangle }}\Delta E_{nm } \left( {KT_{{\text{e}}} } \right)^{\frac{1}{2}} e^{{\frac{{\Delta E_{nm } }}{{KT_{{\text{e}}} }}}} ,$$
(4)

where \(f_{{mn{ }}} { }\) is the absorption oscillator strength, \(\langle \overline{g}\rangle\) is the Gaunt factor averaged over the electron velocity distribution and over all frequencies, the estimation of this factor from the Sommerfeld formulation gives a value close to unity for temperatures above 1 eV [26].

For inhomogeneous plasma, in addition to the McWhirter criterion, another criterion must be satisfied, which requires that the variation length of the plasma temperature and electron number density should be larger than the diffusion length [28]. This is given by the following inequalities:

$$\frac{{T_{{\text{e}}} \left( {x + \lambda } \right) - T_{{\text{e}}} \left( x \right)}}{{T_{{\text{e}}} \left( x \right)}}{ } \ll 1\;{\text{and}}\;{ }\frac{{N_{{\text{e}}} \left( {x + \lambda } \right) - N_{{\text{e}}} \left( x \right)}}{{N_{{\text{e}}} \left( x \right)}}{ } \ll 1.$$
(5)

where \(\lambda { }\) is the diffusion length and is given by the relation 6:

$$\lambda = 1.4 10^{12} \frac{{KT_{{\text{e}}}^{3/4} }}{{n_{{\text{e}}} }} \left( {\frac{{\Delta E_{nm } }}{{\langle \overline{g}\rangle f_{mn } M_{A } }}} \right)^{1/2} e^{{\frac{{\Delta E_{nm } }}{{2KT_{{\text{e}}} }}}} ,$$
(6)

where \(M_{A}\) is the atomic mass of the element emitting the transition.

The LIP is a laboratory plasma which is by nature heterogeneous and transient, thus for the validation of LTE, all the criteria cited above must be fulfilled.

3.6 Evaluation of LTE in the studied plasma

  1. 1.

    The LTE condition is evaluated using the McWhirter criterion given by relation (2), and we used the Al I 308.21 nm transition for the calculation of the minimum electron density. Figure 8 illustrates a comparative presentation of the plasma electron density and the calculated McWhirter limit value as function of delay time at a fixed distance of 1.6 mm. The electron number density in our experiment was found to be nearly three orders of magnitude bigger than the minimum electron number density given by the McWhirter criterion thus validating the existence of the LTE condition.

    Fig. 8
    figure 8

    Comparison between the plasma electron density and the calculated McWhirter limit value as function of delay time at a fixed distance of 1.6 mm

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  2. 2.

    For temporal evolution of the LIP, the fulfillment of the LTE condition is assessed, along with the McWhirter criterion, through a second condition represented by relation 3. For this condition to be satisfied, we calculated the relaxation time given by expression 4 as a function of delay time and we compared it with the decay time of the LIP. We found that the relaxation time is of the order of 1.5 × 10–9 s, which is shorter than the decay time (expansion time), which is of the order of 1.4 × 10–6 s, thus confirming the existence of LTE in a transient LIP (Fig. 9).

    Fig. 9
    figure 9

    A comparison between the relaxation time (a) and the decay time (b), for the validation of LTE in the transient LIP

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  3. 3.

    Alongside the McWhirter criterion, the condition for ensuring LTE in a heterogeneous plasma involves the plasma plume diameter being at least ten times greater than the diffusion length determined by Eq. 6. The diffusion length is calculated based on the emission line of Al I at 308.21 nm. The variation of the diffusion length along the axial distance is given in Fig. 10.

    Fig. 10
    figure 10

    The variation of the diffusion length as a function of axial distance

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As it is shown in the figure above, the diffusion length is of the order of 10–5 cm, which is shorter than the length of the plasma plume (the emissive plasma length is approximately 0.3 cm) thus confirming the existence of LTE in our inhomogeneous plasma.

The McWhirter criterion as well as the two other conditions, which take account for the inhomogeneous and transient nature of the LIP, were validated for the range of delay times from 0.8 to 6 µs and the range of axial distances from 0.6 to 2.6 mm, making this region an optimum condition for CF-LIBS quantification.

3.7 Compositional analysis of the Zn–Al–Cu alloy using CF-LIBS

The compositional analysis of Zn–Al–Cu alloy was carried out using CF-LIBS method which is discussed in detail in the literature [29, 30]. This method is based on the assumption of LTE, stoichiometric ablation, and optically thin plasma. The LTE was verified in the previous section, while the stoichiometric ablation was validated using a power density of 9.1 × 1010 W/cm2 that exceeds the power limit of 109 W/cm2 defined by Chan and Russo [31]. To confirm the optically thin plasma condition, we used the branching ratio method that compare the experimental and theoretical intensity ratios [32]. We have validated this method using several pairs of spectral lines, (308.21 nm, 309.27 nm), (394.4 nm, 396.15 nm) and (224.26 nm, 224.72 nm). The validation of these conditions makes the plasma ideal for the application of the CF-LIBS technique.

On Table 4, we display the CF-LIBS quantification result for various delays and distances, which were then compared to the concentration acquired through the µ-XRF technique. The average relative errors, relative to XRF measurements, of Zn, Al, and Cu elements were 0.8%, 15.42%, and 20.55%, respectively.

Table 4 Quantitative results of the zinc-based alloy at various delay times and distances
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Based on these error values, it can be concluded that the application of CF-LIBS for compositional analysis of zinc-based alloys is feasible and yields satisfactory results.

4 Conclusion

In the present contribution, we have carried out a spatially and a temporally resolved study of the emission spectra of zinc-based alloy plasma generated in air at atmospheric pressure. The impact of optical fiber position along the propagation axis on emission intensities of neutral and singly ionized Zn, Al, and Cu lines at different increments of 100, 200, and 400 µm was investigated. The maximum intensity occurred at the same axial distance (800 µm and 1200 µm for ionic and atomic species, respectively) independently of moving step and element.

The temperature was calculated using the Saha–Boltzmann plot method applied on copper lines, and the electron number density was determined using the Stark broadening of the Hα line profile. Both temperature and electron number density were higher at early delay times, then they start decreasing with the increase of delay time due to the expansion of the LIP.

The LTE was warranted for our inhomogeneous and transient plasma using the McWhirter criterion and two other conditions that take into account the transient and heterogeneous nature of the plasma. The relaxation time computed was found to be shorter than the decay time of the plasma, and the diffusion length was found to be smaller than the plasma diameter, further confirming the LTE condition for the range of delay times from 0.8 to 6 µs and the range of axial distances from 0.6 to 2.6 mm. The validation of LTE and the spatiotemporal characterization of plasma parameters makes the plasma suitable for the implementation of the CF-LIBS approach on the recorded spectra.

The results of this study validate the potential of CF-LIBS in accurately determining the concentration of major elements (Zn, Al) with a higher level of precision, in contrast to minor elements (Cu). Although minor elements may exhibit weaker emission lines and encounter potential interferences and noise, CF-LIBS still allows for reasonably accurate estimations of their concentrations under favorable conditions. Thus, CF-LIBS emerges as a valuable analytical tool for the precise quantification of major elements, while also providing insights into the concentrations of minor elements in specific conditions. This finding provides an opportunity for the engineering and industrial sectors to develop cost-effective LIBS instruments for the sorting of zinc-based alloys.