LIP emission from tungsten

The LIP spectra of tungsten in air for incident laser fluence of 60 J/cm² in the spectral range of 220–850 nm are shown in Figure 2 as a function of delay with respect to the laser pulse. From this, several atomic and ionic transitions of tungsten are identified using NIST and Kurucz database (https://www.nist.gov; https://www.cfa.harvard.edu/amp/ampdata/kurucz23/sekur.html). In the UV spectral range of 200–300 nm, the spectra are dominated by ionic transitions, whereas in the visible range of 300–850 nm, the emitted spectral lines are attributed to mainly atomic transitions. The expanded view of the temporal variation of the spectra in the range of 267–277 and 429–431 nm is shown in Figure 3a and 3b, respectively, at a laser fluence of 60 J/cm². As an example, the lines of WII at 265.8, 270.2, 258.9, and 276.4 nm are marked in Figure 3a and that of the neutral atomic lines of WI at 429.4, 430.2, and 430.7 nm in Figure 3b. The temporal evolution of the WII line at 276.4 nm and the WI line at 430.2 nm for all the fluences are shown in Figure 4a and 4b, respectively. From these, the decay time of atomic and ionic species are assessed by exponential fitting the respective data and is shown by solid lines in Figure 4. The decay time of ionic and atomic lines is the time over which the initial intensity fall down to a 1/e factor. The variation in decay time for ionic and atomic transitions as a function of incident laser fluence is shown in Figure 5a. From this figure, it is observed that the decay time for the ionic line is 0.60 (±0.02), 0.84 (±0.04), 1.06 (±0.03), and 1.02 (±0.04) μs and that of the atomic line is 1.26 (±0.03), 1.63 (±0.09), 1.65 (±0.01), and 1.59 (±0.09) μs at four incident laser fluences of 60, 120, 180, and 270 J/cm², respectively. The decay time for atomic and ionic lines increases with the increase in laser fluence up to 180 J/cm², and then, there is a marginal fall in it. Initially, with the increase in laser fluence, the mass ablation increases up to the laser fluence of 120 J/cm², but at higher laser fluence of 180 J/cm², the mass ablation of the target decreases due to the plasma shielding at higher laser fluence (Harilal et al., Reference Harilal, Bindhu, Issac, Nampoori and Vallabhan1997; Haq et al., Reference Haq, Ahmat, Mumtaz, Shakeel, Mahmood and Nadeem2015), resulting in the decrease in the intensity of both the atomic and ionic lines as well as their decay time. The ions possess kinetic energy than atoms and recombine with the electrons to form atoms and thus decay faster than atoms.

Fig. 2. Expanded view of the temporal evolution: (a) ionic (267–277 nm) and (b) atomic transitions (429–431 nm) at 60 J/cm² of laser fluence.

Fig. 3. Temporal evolution of the LIP emission of tungsten in air at the laser fluence of 60 J/cm².

Fig. 4. Exponential decay of (a) WII at 276.4 nm and (b) WI at 430.2 nm at four incident laser fluences.

Fig. 5. (a) Decay time for the ionic and atomic tungsten line at 276.4 and 430.2 nm, respectively, with respect to laser fluence and (b) SNR for 430.2 nm line at four laser fluences as a function of delay time.

The signal-to-noise ratio (SNR) of the spectra is estimated using the WI at 430.2 nm transition, by the following equation (Freeman et al., Reference Freeman, Diwakar, Harilal and Hassanein2014; Skrodzki et al., Reference Skrodzki, Becker, Diwakar, Harilal and Hassanein2016):

(1)$${\rm SNR} = \displaystyle{{I_{\max} -I_{{\rm background}}} \over {{\rm \sigma} _{{\rm background}}}}$$

where I _max is the integrated peak intensity for the WI at 430.2 nm line, I _background is the averaged background intensity in the neighborhood of the line under consideration, and σ_background is the standard deviation in the background intensity. The temporal variation of the SNR of the spectra at all the laser fluence is shown in Figure 5b. It is observed that SNR increases with the delay time up to 3.5 µs for all the laser fluence and then starts falling down, similar behavior is found for the other lines too. This is due to the fact that during the initial stage of plasma formation, continuum radiation is dominated and at a later time, the intensity of emitted lines falls down (De Giacomo and Hermann, Reference De Giacomo and Hermann2017). This confirms that for LIBS detection, there is a need to record the spectrum at an appropriate temporal window where the SNR is maximum.

Plasma temperature and electron density

The most widely used method to determine the plasma temperature in LIP is the Boltzmann plot method. In this, plasma is assumed to be in local thermodynamic equilibrium (LTE) and optically thin. In LTE, the line intensity of a transition, I_nm, from an upper level n to the lower level m is related to the upper energy state E_n, and is given by the following relation (Zhang et al., Reference Zhang, Wang, He, Jiang, Zhang, Hang and Huang2014; Gao et al., Reference Gao, Liu, Song and Lin2015):

(2)$$\ln \left( {\displaystyle{{I_{nm}{\rm \lambda}_{nm}} \over {g_nA_{nm}}}} \right) = -\displaystyle{1 \over {k_{\rm B}T_e}}E_n + \ln \left( {\displaystyle{{hcN} \over {4{\rm \pi} U(T_e)}}} \right)$$

where λ_nm is the wavelength of the radiation emitted due to the transition from the upper level n to the lower level m, g _n is the statistical weight of the upper level, A _nm is the transition probability, k _B is the Boltzmann constant, T _e is the plasma temperature, h is the Planck constant, c is the velocity of light, and N and U(T _e) are the number density and partition function of the element under consideration. The plot of the left-hand side of the equation against E _n for several number of transitions is a straight line. The temperature of the species can be thus obtained from the slope of the equation, that is, 1/k _BT _e without the involvement of any partition function. The accuracy of temperature measurement from the Boltzmann plot method depends on the selection of the lines. The selection criteria are (1) the line's transition probability should be low so as to neglect the self-absorption, (2) the lines should not be a resonant line (terminating to the ground state), and (3) spread in the upper energy level as large as possible. The plasma temperature for the LIP of tungsten is estimated using atomic transitions and ionic transitions. The six atomic lines at 430.7, 449.4, 468.0, 484.3, 505.3, and 524.2 nm and that of the three ionic lines at 251.0, 227.9, and 357.2 nm are selected for the estimation of plasma temperature from Eq. (2). The upper energy levels of all these selected lines for the Boltzmann plot are widely apart, and all these possess low values of transition probability. All the WI lines are non-resonant lines. The spectroscopic parameters required for these ionic and atomic transitions are taken from Kurucz database (https://www.cfa.harvard.edu/amp/ampdata/kurucz23/sekur.html) and NIST database (https://www.nist.gov), respectively, and are listed in Tables 1 and 2, respectively.

Table 1. Spectroscopic parameters for WII lines for the Boltzmann plot

Table 2. Spectroscopic parameters for WI lines for the Boltzmann plot

The Boltzmann plot for WII at a delay time of 0.5, 3.0, and 5.0 µs for the laser fluence of 60 J/cm² shown in Figure 6a–6c and that of the WI lines in Figure 7a–7c, respectively, as an example. The correlation coefficient for the fitted straight line by Eq. (2), for the measurement of the temperature, is found to be in the range of 0.98–0.99. The high-value correlation coefficient in the Boltzmann plot indicate the absence of self-absorption in LIP. The variation in plasma temperature as a function of delay time for all the four laser fluences estimated from ionic and atomic transitions are shown in Figure 10a and 10b, respectively. It is observed that with the delay time, the plasma temperature decreases but increases with the increase of incident laser fluence in both the cases. It is found that the plasma temperature from WII lines is higher than that of neutral atom in the delay time range of 0.5–1 µs, but at a later time and in the temporal window of 1.5–4.0 µs, both the temperatures are nearly same indicating the coexistence of thermal equilibrium among tungsten atoms and ions. During an early phase of plasma evolution, LIP mainly consists of highly energetic ions having higher kinetic energy, and thus, the temperature value is higher compared with that of atoms in the early phase of LIP, indicating the nonexistence of LTE among WII and WI lines (Aguilera and Aragón, Reference Aguilera and Aragón2004). It is found that plasma temperature from WII lines varies from 1.622–0.840 (±0.034), 1.696–0.985 (±0.033), 1.805–1.001 (±0.045), and 1.913–1.182 (±0.044) eV and that for WI lines from 1.208–0.971(±0.042), 1.304–0.985 (±0.041), 1.308–1.104 (±0.042), and 1.312–1.094 (±0.035) eV as the delay time increases from 0.5 to 5 µs at four incident laser fluences of 60, 120, 180 and 270 J/cm², respectively. In general, there is an increase in plasma temperature with the laser fluence.

Fig. 6. Boltzmann plot for WII lines at a delay time of (a) 0.5, (b) 3.0, and (c) 5.0 µs for the incident laser fluence of 60 J/cm².

Fig. 7. Boltzmann plot for WI lines at a delay time of (a) 0.5, (b) 3.0, and (c) 5.0 µs for the incident laser fluence of 60 J/cm².

The electron density of plasma is extracted using the Stark-broadened profile of the spectral line and given by (Radziemski and Cremers, Reference Radziemski and Cremers2006; Singh and Thakur, Reference Singh and Thakur2007; Haq et al., Reference Haq, Ahmat, Mumtaz, Shakeel, Mahmood and Nadeem2015; Wermer et al., Reference Wermer, Lefkowitz, Ombrello, Bak and Im2018)

(3)$$\Delta {\rm \lambda} _{{1/2}} = 2w\left( {\displaystyle{{N_e} \over {{10}^{16}}}} \right) + 3.5A\left( {\displaystyle{{N_e} \over {{10}^{16}}}} \right)^{1/4}\lsqb {1-1.2N_{\rm D}^{-{1 / 3}}} \rsqb \left( {\displaystyle{{N_e} \over {{10}^{16}}}} \right)$$

where Δλ_1/2 is the full-width at half-maximum, N_e is the electron number density, w and A are the electron impact width and ion broadening parameter, respectively, and N _D is the number of particles in the Debye sphere. Considering the small contribution of ion to Stark-broadening, Eq. (3) simplifies to the following (Cowpe et al., Reference Cowpe, Pilkington, Astin and Hill2009; Haq et al., Reference Haq, Ahmat, Mumtaz, Shakeel, Mahmood and Nadeem2015):

(4)$$\Delta {\rm \lambda} _{{1 / 2}} = 2w\left[ {\displaystyle{{N_e} \over {{10}^{16}}}} \right]$$

In the present study, the electron density is determined using the Stark-broadened profile from the atomic tungsten transition at 430.2 nm using Eq. (4). The value of the electron impact parameter for this line is taken from the literature (Nishijima and Doerner, Reference Nishijima and Doerner2015). The Stark-broadened line of WI at 430.2 nm is fitted using the Lorentzian function and is shown in Figure 9a at a delay of 0.5 µs and the fluence of 60 J/cm² as an example. The correlation coefficient for the fitted Lorentzian function, for the measurement of the electron, is found to be 0.99.

The variation in the electron density as a function of delay time for all the four laser fluences is shown in Figure 11b. The electron density is varying from 2.40−1.70 (±0.15), 2.33−1.76 (±0.13), 2.44−1.84 (±0.16), and 2.54−1.82 (±0.07) × 10¹⁷ cm⁻³ as the delay time increases from 0.5 to 5 µs, respectively, in the increasing order of fluence (Surmick and Parigger, Reference Surmick and Parigger2015).

It is observed from Figures 4, 8, and 9 that the intensity of the spectral lines, the plasma temperature and electron density are falling down with respect to delay time and increase with the increase of laser fluence. The plasma temperature and electron density are found to be maximum at 0.5 µs delay (initial recording time) at each of the incident laser fluence. Immediately after the commencement of the LIP, it starts expanding into the surrounding medium and loses its energy. The overall process of LIB can be divided into three stages: first one is the initial laser-target interaction to form plasma, second one is plasma-laser interaction, and the last stage is plasma cooling and particulates formation (Singh and Thakur, Reference Singh and Thakur2007). The rising part of the laser pulse generates the plasma, while the trailing part heats the plasma. During the laser pulse, the plasma expands isothermally, but after the termination of the laser pulse, its expansion is adiabatic, as there is no means to supplement the energy further to the plasma. Thus, it loses its energy due to thermal conduction to the ambient and target sample, the conversion of the thermal energy to the kinetic energy via work done by the expanding plasma and the various radiative as well as non-radiative processes involved in it along with the collisional mechanism. Due to all these energy dissipative processes with the time, the temperature and electron density fall down (Harilal et al., Reference Harilal, O'shay, Tillack and Mathew2005; Hussein et al., Reference Hussein, Diwakar, Harilal and Hassanein2013). The emission of radiation from the plasma is interrelated with the plasma temperature and electron density and exhibited the similar trend in temporal behavior as that of plasma parameters (Figs 4, 10, and 11). The fall in plasma parameters is faster during 0.5–1.5 µs as compared with that of the later time of 2–5 µs. The possible reasons behind this are three-body recombination and the effect of surrounding atmosphere particularly at a later stage. In the three-body recombination process, the energy is released due to the recombination of ions and electrons, which compensate the energy loss due to plasma expansion (Shaikh et al., Reference Shaikh, Hafeez, Rashid, Mahmood and Baig2006a; Freeman et al., Reference Freeman, Harilal, Diwakar, Verhoff and Hassanein2013).

Fig. 8. Temporal variation of plasma temperature at all the four laser fluences from (a) WII and (b) WI lines.

Fig. 9. Stark-broadened line of WI at 430.2 nm fitted using the Lorentzian profile at a delay time of 0.5 µs for the laser fluence of 60 J/cm² and (b) temporal variation of electron density at all the four laser fluences.

Fig. 10. Comparison of the experimental intensity ratio with the theoretical intensity ratio for optically thin plasma as a function of delay time and laser fluence.

Fig. 11. Temporal evolution of minimum required electron density required from the McWhirter criteria for LTE at various laser fluences.

The LIP radiation and plasma parameters are strongly influenced by the laser fluence. The target absorbs the energy mainly from the initial rising part of the laser pulse, and this absorption increases with the increase in the laser fluence, thus furnishing the higher plasma temperature and electron density. However, at the laser fluence above the plasma shielding effect (Harilal et al., Reference Harilal, Bindhu, Issac, Nampoori and Vallabhan1997; Haq et al., Reference Haq, Ahmat, Mumtaz, Shakeel, Mahmood and Nadeem2015), the absorption of energy by the target is curtailed, and thus, the plasma parameters exhibit hardly any variation with the impinging laser fluence. Figures 4, 10, and 11 clearly indicate that the variation in the intensity of the spectral lines, the plasma temperature and electron density with the laser fluence are more prominent up to 180 J/cm², and beyond this fluence, there is not much significant difference in the plasma characteristics with further increase in the laser fluence (Farid et al., Reference Farid, Harilal, Ding and Hassanein2014; Haq et al., Reference Haq, Ahmat, Mumtaz, Shakeel, Mahmood and Nadeem2015).

Validity of the optical thin condition of plasma

The use of OES for the measurement of plasma temperature and electron number density demands that plasma emission should be optically thin and plasma should be in LTE. Optical thin plasma means that plasma should not absorb its own radiation. If the plasma is not optically thin, then the lines involved in the characterization of plasma undergo self-absorptions. Due to this, the spectral line profile exhibits distorted line shape leading to enormous error in the determination of electron density and plasma temperature. To verify the condition of optically thin plasma in the present case, the theoretical branching ratio is compared with the experimental intensity ratio of the emitted lines. The branching ratio of two atomic lines originating from the same upper energy level is defined by the following equation (Shaikh et al., Reference Shaikh, Rashid, Hafeez, Jamil and Baig2006b; Zhang et al., Reference Zhang, Wang, He, Jiang, Zhang, Hang and Huang2014):

(5)$$\displaystyle{{I_1} \over {I_2}} = \displaystyle{{g_1A_1{\rm \lambda} _2} \over {g_2A_2{\rm \lambda} _1}}$$

For this, the intensity ratio of atomic transitions of WI at 468.0 and 500.6 nm having the same upper energy level, that is, 3.247 eV is calculated as a function of time at all the four fluences. The theoretical branching ratio from Eq. (5) for these lines is 1.26. The experimental values of the branching ratio are varying from 1.25–1.40, 1.26–1.25, 1.25–1.25, and 1.34–1.25 for the time range of 1–3.5 µs at 60, 120, 180, and 270 J/cm² of the laser fluence, respectively, as shown in Figure 10.

The temporal evolution of the branching ratio shows that the deviation in experimental values is minimum in the delay range of 1–3.5 µs, but for 0.5 and 4–5 µs, there is a large deviation from the theoretical value. Thus, the optimum temporal window in which the plasma can be assumed to be optically thin is 1–3.5 µs.

Validity of LTE in LIP of tungsten

The LIP is of high density and high temperature along with being highly transient and inhomogeneous in nature (Shaikh et al., Reference Shaikh, Hafeez, Kalyar, Ali and Baig2008; Zhang et al., Reference Zhang, Wang, He, Jiang, Zhang, Hang and Huang2014). Due to all these, the total ideal thermodynamic equilibrium state for LIP can never be completely attained. Thus, the concept of LTE is introduced (Cristoforetti et al., Reference Cristoforetti, Lorenzetti, Legnaioli and Palleschi2010b; Zhang et al., Reference Zhang, Wang, He, Jiang, Zhang, Hang and Huang2014). The LTE condition in the plasma is studied under three different conditions (Zhang et al., Reference Zhang, Wang, He, Jiang, Zhang, Hang and Huang2014), that is, the first case, plasma is assumed to be stationary and homogeneous, the second case, it is considered to be transient but homogeneous, and third case, the plasma is regarded as stationary but inhomogeneous. In the first case, in order to satisfy the LTE condition, the collisional processes between electron-atom and electron-ion should be very fast and dominating over the radiative processes, former of which requires a sufficiently large electron density (Shaikh et al., Reference Shaikh, Hafeez, Kalyar, Ali and Baig2008). The lower limit of electron density for which plasma can be described in LTE is given by the McWhirter criterion given by the following equation (Mortazavi et al., Reference Mortazavi, Parvin, Pour, Reyhani, Moosakhani and Moradkhani2014; Zhang et al., Reference Zhang, Chen, Wang, Li, Wang, Sui, Jiang and Jin2017):

(6)$$N_e \ge 1.6 \times 10^{12}T_e^{1/2} (\Delta E)^3$$

where N _e (cm⁻³) is the electron density, and ΔE (eV) is the energy difference between the states expected to be in LTE. The lower limit for electron density in the present case is estimated using energy gap ΔE = 2.487 eV between the ground level and the first excited level of WI-498.2 as a function of delay time and is shown in Figure 11, which varies from 2.91–1.61, 3.02–2.63, 3.03–2.78, and 3.04–2.77 × 10¹⁵ cm⁻³ for the incident laser fluence of 60, 120, 180, and 270 J/cm², respectively, and this range of minimum electron density is nearly similar for all the laser fluences.

On comparing Figures 9b and 11, it is obvious that the required minimum electron density as per Eq. (6) is less than that of the experimentally estimated for all the four laser fluences, confirming the LTE for LIP of tungsten in the present case.

In the case of inhomogeneous and transient plasma, the temporal evolution of the plasma parameters should be sufficiently slow in order to allow the plasma sufficient time to reach the thermodynamic equilibrium. This requires that the plasma relaxation time, t _rel, the time required to establish excitation and ionization equilibrium should be much shorter than the time of variation of plasma parameters, that is (Cristoforetti et al., Reference Cristoforetti, De Giacomo, Dell'Aglio, Legnaioli, Tognoni, Palleschi and Omenetto2010a),

(7)$$\displaystyle{{T_e(t + t_{{\rm rel}})-T_e(t)} \over {T_e(t)}} \ll 1\quad \displaystyle{{N_{e}(t + t_{{\rm rel}})-N_{e}(t)} \over {N_{e}(t)}} \ll 1$$

The relaxation time is estimated by the following equation (Cristoforetti et al., Reference Cristoforetti, De Giacomo, Dell'Aglio, Legnaioli, Tognoni, Palleschi and Omenetto2010a):

(8)$$t_{{\rm rel}} = \displaystyle{{6.3 \times {10}^4} \over {N_{e}f_{mn}\left\langle g \right\rangle}} \Delta E_{nm}(kT_e)^{1/2}\exp \left( {\displaystyle{{\Delta E_{nm}} \over {kT_e}}} \right)$$

where t _rel is the relaxation time (s), ΔE _nm is the energy difference between the levels, f _nm is the transition oscillator strength, g is the effective gaunt factor, and N_e is the electron density. The WI-498.2 nm transition having ΔE _nm = 2.487 eV and f _nm = 0.0046 is used to estimate the relaxation time. The variation in the relaxation time as a function of delay time with respect to laser pulse is shown in Figure 12a. The relaxation time in the present experimental conditions is found to be of the order of 10⁻⁹ s, which is much smaller than decay time of plasma parameters, estimated to be of the order of microsecond (Fig. 5a), thus satisfying the second criteria for the LTE condition.

Fig. 12. Assessment of LTE at various delay times as a function of incident laser fluence: (a) relaxation time and (b) diffusion length parameters.

The third condition for LTE demands the diffusion length during the relaxation time should be small compared with the dimension of the plasma (Cristoforetti et al., Reference Cristoforetti, De Giacomo, Dell'Aglio, Legnaioli, Tognoni, Palleschi and Omenetto2010a):

(9)$$\displaystyle{{T_e(x)-T_e(x + \Lambda )} \over {T_e(x)}} \ll 1\quad \displaystyle{{N_e(x)-N_e(x + \Lambda )} \over {N_e(x)}} \ll 1$$

where Λ is the diffusion length (cm) during the relaxation time given by the following equation (Cristoforetti et al., Reference Cristoforetti, De Giacomo, Dell'Aglio, Legnaioli, Tognoni, Palleschi and Omenetto2010a):

(10)$$\Lambda = 1.4 \times 10^{12}\displaystyle{{{\lpar {kT} \rpar }^{{3 / 4}}} \over {N_e}}\left( {\displaystyle{{\Delta E_{nm}} \over {M_Af_{nm}^{}}}} \right)^{1/2}\exp \left( {\displaystyle{{\Delta E_{nm}} \over {2kT_e}}} \right)$$

In Eq. (10), M _A is the atomic mass of element emitting the transition. The variation in the diffusion length as a function of time is shown in Figure 12b and is of the order of 10⁻⁵ cm. The inhomogeneous plasma will fulfill the LTE condition provided the plasma size is at least 10 times larger than Λ. In the present experimental condition, the size of the plasma is of the order of 10⁻¹ cm confirming the validity of the third criteria of LTE.