JAAS

PAPER

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article OnlineView Journal

A new method fo

aDepartment of Physics, K. N. Toosi Univer

Iran. E-mail: Fh_rezaei@yahoo.com; h-tavabLaser and Plasma Research Institute, Shahi

Evin, Tehran, Iran

Cite this: DOI: 10.1039/c4ja00237g

Received 21st July 2014Accepted 8th October 2014

DOI: 10.1039/c4ja00237g

www.rsc.org/jaas

This journal is © The Royal Society of

r calculation of thick plasmaparameters by combination of laser spectroscopyand shadowgraphy techniques

Fatemeh Rezaei*a and Seyed Hassan Tavassolib

In this paper, a new method is introduced for studying optically thick plasma in local thermodynamic

equilibrium condition by laser induced breakdown spectroscopy (LIBS) technique. The method presented

here is very simple, exact, and appropriate for simultaneously quantifying the plasma parameters and

instrumental function of the experimental system from self-absorbed spectral lines. A LIBS experiment is

performed on an aluminum target in air atmosphere by combination of two techniques of

shadowgraphy and spectroscopy, and by utilizing a theoretical approach. In this work, plasma

parameters can be accurately calculated when the electron density, plasma length and intensities of

three spectral lines are experimentally known. This model suggests that instead of using two spectral

lines in thin plasmas, three lines are required in thick plasmas for exactly estimating the plasma

temperature. In this paper, the temporal evolution of plasma dynamics, such as the number densities of

the emitting species, plasma length, velocity of plasma expansion and its temperature variation is

obtained by the presented procedure.

1. Introduction

Laser induced breakdown spectroscopy is an analytical tech-nique characterized according to the spectral analysis of theradiation that is emitted by a plasma created by focusing thelaser source on the target surface. The characterizations oflaser-induced plasmas (LIPs), as the spectroscopic sources, areacquired by the determination of the main plasma parameters,such as number densities of different species, temperature, andelectron density, from spectral emissions.1,2 The most usualmethods for evaluating the plasma parameters in LIBS tech-nique are Boltzmann plot, line-to-continuum intensity ratio ortwo lines ratio analysis. Furthermore, Stark broadening, Sahaequations and Boltzmann equation are utilized for the estima-tion of number densities of electrons and different species inLIBS plasmas.3–6 It should be noted that all the mentionedmethods are formulated for thin LIBS plasmas, while for almostall the strong lines of a spectrum and for the concentrations ofhigher than approximately 3% in sample,7,8 the LIBS plasma islocated in the thick plasma category.

Generally, the self-absorption phenomenon is a limitingeffect for exact quantitative measurements at high concentra-tions, which appears as nonlinearity in calibration curves andleads to a thick plasma condition. In LIBS plasmas, the self-

sity of Technology, 15875-4416, Tehran,

ssoli@sbu.ac.ir

d Beheshti University, G. C, 1983963113,

Chemistry 2014

absorption of spectral lines sometimes appears as peak heightreduction and it is not obvious to be recognized, while in othercases, such as strong resonance lines, self-absorption isobserved as a self-reversal shape and a central dip in spectrallines is observed due to the cold absorbing atoms from the outerparts of the plasma plume compared to the interior hot part ofthe plasma. Various research groups have proposed severalmethods, such as duplicating mirror,9 line ratio,10,11 curve ofgrowth (COG),12–15 and calculation models,16–20 for the identi-cation and evaluation of the self-absorption of the analyzedspectrum. Aer diagnostic stages, suitable corrective methodsutilized the intensity of the self-absorbed spectral lines beforeusing them for analytical goals. Consequently, they calculatedthe plasma parameters aer appropriate correction methods.For example, Aragon et al.3,12–15 tted the theoretical curve ofgrowth to the experimental data, and then they extractedplasma parameters, such as damping constant and numberdensity of neutral atoms. Furthermore, this group outlined theCOG curves for the evaluation of the magnitude of self-absorption parameter and for the determination of theconcentration at which transition from thin to thick plasmaoccurs. They characterized the temporal and spatial evolution ofplasma parameters for analytical purposes. In addition, theysubstantially investigated the effects of optical depth variationon spectral lines radiation. Nevertheless, it should be noted thatin many studies, the self-absorbed lines are disregarded forexact quantication as an undesirable effect in LIBS experi-ments. In spite of the complication of spectrally self-absorbedlines, few investigations have used these specic lines for the

J. Anal. At. Spectrom.

JAAS Paper

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

accurate estimation of plasma parameters.21–23 For instance,Karabourniotis et al.24 have determined the plasma temperatureof arc plasma from two self-reversed lines in spatially inhomo-geneous plasma. They calculated the population of the lowerlevel of specic transition, as well as the electron density fromthe model introduced by them. Cristoforetti et al.25 calculatedthe columnar density of the reactive species and plasmatemperature from the information of the self-absorbed spectrallines in a homogeneous plasma. They extracted the opticaldepth of spectral lines from the self-absorption coefficient andthen calculated the laser-induced plasma composition. More-over, some studies have thoroughly investigated the evolutionof optically thick plasmas26–28 by appropriate theoretical modelswithout applying the special corrections. For example, Gor-nushkin et al.28 have utilized a simplied theoretical approachfor the evaluation of plasma parameters for an optically thickinhomogeneous plasma. They estimated the electron tempera-ture of the plasma using a second order polynomial function,which has the maxima in the center of the plasma. Moreover,they calculated the temporal and spatial evolution of differentspecies number densities, variation of optical thickness andline prole from the proposed model.

The purpose of this work is to consider the thickness ofplasma in LIBS spectral lines for more accurate evaluation ofplasma parameters. The present work has the capability ofobtaining the absolute number density of emitting species andplasma temperatures by a newmethod without the constructionof calibration curves or Boltzmann plots. Furthermore, theplasma length and its velocity are estimated from the diagnosticmethod of optical shadowgraphy.29 Generally, the main advan-tage of this method is that it comprises both the conditions ofoptically thin and thick plasmas. Because the self-absorptioncoefficient is not directly quantied in the presented model,whenever the selected lines are located in thin regimes, thecalculations automatically convert from optically thick to thinconditions.

2. Theoretical background: opticallythick plasma in LTE2.1. Self absorption effect in radiation equations

The detailed theoretical description of the self-absorption effectis explained in the literature.30 In this section, a summary of thefundamental equations that prevail in the optically thickhomogeneous plasma is illustrated using a proposed model.Spectral intensity along the line prole corresponding to thetransition between the two levels of u and l under the conditionof optically thick plasma is expressed as follows:18

Ithick ¼ SA � Ithin (1)

With the assumption that local thermal equilibrium (LTE)condition is maintained, the population of each energy level canbe obtained by Boltzmann distribution. In abovementionedequation, Ithin represents thin plasma intensity in the absenceof the self-absorption effect, which can be dened as follows:

J. Anal. At. Spectrom.

IthinðnÞ¼CguNAlAulhn0

Ze� Eu

kBTLðn; n0;gulÞ (2)

where gu, kB, Eu, T, h, Z and Aul are the degeneracy of upper levelu, Boltzmann constant (J K�1), energy of upper level u (J),plasma temperature (K), Planck's constant (J s), partitionfunction and transition probability (s�1), respectively. NAl, Cand n0 are the total density of a specic ion or neutral atom,instrumental function and central frequency (s�1), respectively.L(v, n0, gul) is the Lorentzian line prole (s) due to Starkbroadening effect. Because there are high ion and electronconcentrations in an LIBS experiment, Stark broadening has thedominant inuence compared to other broadeningmechanisms.31,32

Lðn; n0;gulÞ¼gul

4p2

� �

ðv� v0Þ2 þ gul

4p

� �2(3)

gul is the decay rate, which has a direct relation with line widthas follows:31

gul ¼ 2p(c/l02)DlStark (4)

DlStark is full width at half maximum (FWHM) of the spectralline due to Stark broadening which is dened as follows33:

DlStark ¼ 2une

nref(5)

here, ne and u are electron number density and electronimpact parameter, respectively. nref is reference electron density(here 1016 cm�3) at which u is calculated.

SA is self-absorption coefficient that determines the magni-tude of intensity reduction and saturation of a specic spectralline. It is substantially a quantity between 0 and 1. For opticallythin plasma, it is nearly unity, while it equals approximatelyzero for the case of severely thick plasma:34,35

SA ¼ ð1� e�klÞkl

(6)

l is plasma length and k (m�1) is absorption coefficient, whichincludes both the stimulated emission of upper level and theabsorption of lower level in the international system of units (SI)as follows:34,36

k ¼ guAulNAll02

8pZe� El

kBT

�1� e

� hn0kBT

�Lðn; n0;gulÞ ðSIÞ (7)

El and l0 are the energy of the lower level l (J) and the wavelength(m) of the transition, respectively. Z is the partition function,which is calculated by two and three levels method. In thismethod, by grouping different atomic levels to some virtualstates, thermodynamic properties and partition functions ofatomic particles are calculated. It should be noted that in thismethod, an atom is constituted of a ground state and single ordouble excited states with level energies of 30, 31, 32 anddegeneracies of g0, g1, g2, respectively.37

This journal is © The Royal Society of Chemistry 2014

Paper JAAS

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

Z ¼ g0e� 30

KBT þ g1e� 31

KBT þ g2e� 32

KBT

¼ g0e� 30

KBTð1þ G1e�w þ G2e

�awÞ (8)

The degeneracy g and energy of the grouped levels 3 areexpressed by summing or averaging the energy and statisticalweight of all different levels – which is inserted from the NISTdatabase – as follows:

g ¼ Pgi (9)

3 ¼ 1

g

Xgi3i (10)

For further simplication of calculations, the dimensionlessparameters of G1, G2, w and a are introduced as follows:

G1 ¼ g1

g0G2 ¼ g2

g0(11)

w ¼ ð31 � 30ÞkBT

(12)

a ¼ ð32 � 30Þð31� 30Þ (13)

Finally, by substituting all of the abovementioned equationsin eqn (1), the thick plasma radiation can be evaluated asfollows:

Ithick ¼ ð1� e�klÞ�1� e

� hcl0

1kBT

� C8p

l02e� ðEu�El Þ

kBT ðSIÞ (14)

As is clear, eqn (14) is a complicated and nonlinear relationsuch that the parameter extraction from it is rather difficult. Thedetails of the calculation of the plasma dynamic are explainedin the subsequent section.

2.2. Calculation of plasma parameters

The main purpose of the present paper is the calculation ofplasma parameters utilizing a newmethod and using three self-absorbed spectral lines instead of the traditional techniques ofthin plasmas. In this calculation, it is assumed that the selfabsorption coefficient is an unknown parameter because theplasma temperature is unknown, but it is parametricallyinserted in the measured intensity from experiment, accordingto its dependence on the absorption coefficient k.

Generally, self-absorption effect is an unavoidable phenom-enon in LIBS experiments, which causes certain errors in thequantitative measurement and is usually neglected for quanti-tative analysis. In this paper, the self-absorbed lines can providebenecial information about the composition of LIBS plasmaand instrumental function of an experimental device. Here, by arealistic approach for optically thick plasma, a new method is

This journal is © The Royal Society of Chemistry 2014

introduced for attaining more accurate quantitative measure-ment by taking into account the self-absorption effects.

As seen in eqn (14), there are three unknown parameters,namely, T, NAl (which appeared in the equation for absorptioncoefficient k) and C, which will be obtained by considering threeequations similar to eqn (14) for three arbitrary spectral lines,either self-absorbed or not, affected by self-absorption. Thebasic goal of the present work is that by knowing the electrondensity, three line intensities, and plasma size (from experi-ment and other constant parameters from NIST database),38 theplasma temperature, total number densities of specic elementin plasma and instrumental function can be evaluated. Thesethree equations are simultaneously solved by an appropriatenumerical method.

2.3. Calculational method

As noted above in eqn (14), for the spatially integrated plasmaemission, the radiances of the three self-absorbed spectral linesper unit volume, per unit time and per unit frequency areexpressed by the following relations:

Ithick_1 ¼�1� e�k1 l

��1� e

� hcl01kBT

� C8p

l012e� ðEu1�El1Þ

kBT (15)

Ithick_2 ¼ ð1� e�k2 lÞ�1� e

� hcl02kBT

� C8p

l022e� ðEu2�El2Þ

kBT (16)

Ithick_3 ¼ ð1� e�k3 lÞ�1� e

� hcl03kBT

� C8p

l032e� ðEu3�El3Þ

kBT (17)

The absorption coefficient k is a function of T and NAl, asmentioned in eqn (7). As clearly seen, there are three unknownparameters: NAl, T, and C in the above relations. The depen-dency of the eqn (15)–(17) on NAl is because of the presence ofthe absorption coefficient k in the mentioned equations. Tosolve the equations, they are divided by each other and thenumber of relations is reduced to two equations by omitting thevariable of instrumental function C as follows:

Ithick_1

Ithick_2�

�1� e�k1 l

��1� e�k2 l

���1� e

� hcl02

1kBT

��1� e

� hcl01

1kBT

�� l022

l012

�e1

kBTðEl1 � Eu1Þ

e1

kBTðEl2 � Eu2Þ ¼ 0 (18)

Ithick_1

Ithick_2� ð1� e�k1 lÞ

ð1� e�k2 lÞ ��1� e

� hcl02

1kBT

��1� e

� hcl01

1kBT

�� l022

l012

�e1

kBTðEl2 � Eu2Þ

e1

kBTðEl3 � Eu3Þ ¼ 0 (19)

J. Anal. At. Spectrom.

Fig. 1 Contour plot of neutral density and temperature at 50 mJ laserenergy and 1 ms delay time. Red colors refer to various contour plots ofeqn (18) and blue colors indicate the several contour plots of eqn (19).

Fig. 2 A schematic of the experimental set up.

JAAS Paper

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

At specic T and NAl, both eqn (18) and (19) equal zero (i.e.right hand side of above equations) and these values satisfyboth the equations. Therefore, the cross of two equations (i.e.le hand side of equations) at the contour of zero (i.e. righthand side of equations) is the answer. Therefore, by plotting thecontour of the above equations and crossing them, as illus-trated in Fig. 1, the unknown parameters, T and NAl, will beobtained at a specic delay time and certain laser energy. Then,by substituting the cross point data (answer) in one of the eqn(15), (16) or (17), the instrumental function C will be computed.This procedure can be repeated for other optical delay timesand pulse energies. Consequently, the temporal behavior of theplasma parameters, such as T and NAl can be attainted.

It can be noted that this simple procedure can be used forthe evaluation of the self-absorption magnitude.

Fig. 3 A typical spectrum of aluminum sample at delay time of 1 msand laser energy of 50 mJ.

3. Experimental set up

An experimental set up combining shadowgraphic and spec-troscopic techniques is schematically shown in Fig. 2. Thepump laser for plasma generation is a Q-switched Nd:YAG(yttrium aluminum garnet) laser (Continuum, Surelite III) with10 ns pulse width, 1064 nmwavelength and 2 Hz repetition rate.The laser pulse is focused on the sample in air atmosphere byapplying a lens with 180 mm focal length. The aluminumstandards (1100 series) are used throughout the experiment.These samples are supplied from the Razi metallurgicalresearch center in Iran. The incident laser energies on the Alsurface are adjusted to 30 and 50 mJ. The probe laser for theillumination of the plasma is a frequency doubled Nd:YAG laserwith 532 nm wavelength, 2 Hz repetition rate, and 10 ns pulsewidth. Two beam splitters are used to direct the illuminationand excitation lasers to the fast photodiodes of PDi and PDe,respectively. Photodiodes are connected to a digital oscilloscopeto monitor the temporal behavior of the pump and probe pulsesduring the experiment. A digital delay generator (Stanford DSG

J. Anal. At. Spectrom.

535) adjusts the acquisition timing of the intensied CCDcamera and the delay between two laser pulses. The delay timesbetween the pump and probe lasers for the acquisition ofplasma evolution are continuously varied from 100 ns to 1 mswith the time steps of 100 ns.

The probe beam is collimated by a beam expander to passthrough the plasma region. Then, the light pulse is guided to apin hole to select the homogeneous part of the Nd:YAG laser. Inthis experiment, the probe laser energy is attenuated at differentstages by (a) combination of polarizer and a Glan–Taylor prismas an optical attenuator, (b) dichroic mirror by discarding someparts of laser emissions in IR region, and (c) an attenuatorbefore recording the camera image to avoid the saturation ofthe CCD. Moreover, a green lter is placed between the plasmaand CCD camera to discriminate and block the plasma emis-sions from probe beam light.

For the spectroscopic analysis, spatially integrated plasmaemissions are collected using a quartz lens accompanied by anobjective lens. Then, by transmitting the radiations to an opticalber, which is connected to an Echelle spectrograph (Kestrel,SE200), a spectrally resolved light is obtained. The temporalanalysis of the recorded spectra is performed by adjusting the

This journal is © The Royal Society of Chemistry 2014

Paper JAAS

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

gate and delay time of the ICCD camera (Andor, iStar DH734).For illustration, a typical spectrum of aluminum sample at 1 msdelay time at energy of 50 mJ is shown in Fig. 3. Each spectrumis an accumulation of 10 laser pulses and each data pointillustrates the mean value of three measurements.

Fig. 5 The temporal behavior of plasma expansion at different laserenergies after pulse irradiation.

4. Results and discussion

In one of the previous studies,34 the temporal behavior of self-absorbed lines in different noble gases was reported by anumerical approach. The temporal and spatial variation ofplasma temperature with laser energy at two noble gases wascarefully investigated. Furthermore, it supplied a comparisonbetween thin and thick aluminum plasmas under differentlaser energies. In this paper, collisional dominated plasma atLTE condition is assumed for the line intensity calculation ineqn (14). Plasma characterization is attained by a semi-empir-ical model such that some parameters are acquired from theexperiment and other information is obtained from calculation.The presented model can be very useful for the verication ofplasma dynamics. For quantitative analysis, the applicability ofthe theory is evaluated by the investigation of the effects of timeevolution and laser energy variation. To illustrate the capabil-ities of this model, initially the plasma size is measured by thediagnostic method of shadowgraphy in the experimental set uputilizing a pump and probe lasers. The shock wave propagationis diagnosed by backlightening with Nd:YAG laser by the illu-mination of the breakdown area. Two of the shadowgramimages captured by a usual CCD camera at delay times of 200 nsand 1 ms during plasma evolution are shown in Fig. 4. Accordingto the shock wave images, the plasma length (width) is depictedin Fig. 5 as a function of delay time and laser pulse energy. Theimage processing enables us to measure the plasma length bycomparison with a reference object of known length. The errorbars in this gure illustrate the deviation from averagemeasurements. As expected, because of plasma expansion bytime progressing, the plasma length increases, which isconsistent with the previous results.39–41 Moreover, the temporalbehavior of plasma length is in agreement with the Sedovequation at intermediate laser energy such that the shock

Fig. 4 The shadowgraphic images at delay times of (a) 200 ns with0.28 mm length and (b) 1 ms with 0.45 mm length, during plasmaevolution, at 30 mJ laser energy.

This journal is © The Royal Society of Chemistry 2014

length varies proportional to t0.4 during a spherical expansion.In general, the ablation mechanism of metal samples under nspulse laser irradiation for plasma formation is normal evapo-ration. At these laser irradiance regimes under study (i.e., about1 GW cm�2), by increasing laser energy, the ablation rate andthe amount of ablated mass increases6,42–45 and consequentlythe plasma length increases. It must be noted that as laserenergy increases, the irradiance grows and spectral linesintensify. Accordingly, the temporal behavior of the axialaverage velocity of laser induced plasma shock wave toward thepump laser is shown in Fig. 6 as a function of laser pulse energy.It is approximately in order of 103 m s�1 in these laser energiesintervals. As clear in this gure, the shock velocity is faster athigher pulse energy. Furthermore, the plasma shock waveexpansion slows down at a later delay time due to collision withair atmosphere. The plasma loses its energy because of emis-sion and expansion; it subjects to recombination, and thendecays and forms clusters and particles. The obtained result isin acceptable agreement with the prediction of ref. 46 and 47.

Aer the estimation of the plasma length from the shad-owgraphic portion of the designed experimental set up and theextraction of electron density and spectral intensities from thespectroscopic section, and using above theoretical relations,other plasma parameters are calculated. Electron density isevaluated through line width measurement of the magnesiumspectral line at 280.27 nm from the knowledge of its electronimpact parameter. The main reason for selecting magnesiumemission is that it is a very weak line (with low concentration in

Fig. 6 Axial velocity of aluminum plasma at pulse laser energies of 30and 50 mJ as a function of time evolution.

J. Anal. At. Spectrom.

Fig. 8 Time evolution of neutral aluminum density at laser energy of50 mJ.

JAAS Paper

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

sample), which can be observed inside the plasma plume.Moreover, it is not affected by self-absorption, thus it yields aprecise estimation of plasma electron density. In principle, self-absorption is remarkable for the lines having low excitationenergy of upper levels and high transition probabilities, inparticular for the resonant spectral lines. Therefore, using eqn(5) and inserting Stark parameter from the literature.,48,49 ne iscalculated to be 1023 m�3 at delay time of 1 ms and at laserenergy of 50 mJ. Consequently, for other delay times, ne will becalculated by this procedure.

Then, by substituting the measured ne and plasma length,obtained from experiment, in eqn (14) and by inserting all thetransition parameters from the NIST atomic spectra database,38

the temporal variation of plasma temperature and neutralaluminum density at laser energy of 50 mJ is obtained. Byrepetition of the experiment and using the average experimentaldata, the calculated plasma parameters are obtained. Thecharacteristics of the transition parameters of Al spectral linesin experiment are given in Table 1.

In Fig. 7, the time evolution of plasma temperature illus-trates that as time passes, the plasma gradually cools down. Inthe selected time window, plasma temperature T, decays from9.1 � 103 to 7.7 � 103 K, at laser energy of 50 mJ. Similarly, forthe neutral aluminum density NAl, in Fig. 8, in the time windowinvestigated, T varies from 4 � 1021 to 1.7 � 1022 at 50 mJ laserpulse energy. These behaviors are coherent with the resultsreported in the literature.18,50 The physical mechanism involvedin this growth behavior is that as the temperature decreases, theelectrons recombine with ions and the neutral species are

Table 1 Spectral transition parameters of Al lines from NISTdatabase.38

ElementsWavelength(nm) gl gu El (cm

�1) Eu (cm�1) Aul (s

�1)

Al II 281.62 3 1 59 852 95 351 3.8 � 108

Al I 237.31 4 6 112 42 238 8.6 � 107

Al I 308.22 2 4 0 32 435 6.3 � 107

Al I 309.27 4 6 112 32 437 7.4 � 107

Al I 309.28 4 4 112 32 435 1.2 � 107

Al I 394.40 2 2 0 25 348 4.9 � 107

Al I 396.15 4 2 112 25 348 9.8 � 107

Fig. 7 Temporal variation of plasma temperature at laser energy of50 mJ.

J. Anal. At. Spectrom.

considerably formed. Therefore, plasma parameters along theline of sight are determined using shadowgraphic and spec-troscopic approaches. Furthermore, aer the substitution ofdensity and plasma temperature in eqn (14), the averagemagnitude of the instrumental function of the presented set upis evaluated to be 1.5 � 108. It should be noted that the calcu-lated parameters will be integral over all the plasma volume,and obviously it cannot be used to be a measure of local values.

Generally, the presented method tends to demonstrate thatthe thickness of plasma is a substantial factor for the accurateevaluation of plasma characterization. In addition, anotherpractical application of this model can be utilizing it forquantitative analysis, such as determination of the concentra-tion of an element in a sample without using standard samples.It should be noted that when the selected lines are not affectedby self-absorption, the self-absorption coefficient SA automati-cally approaches to unity and the thin conditions will beattained. The identication of the self-absorbed spectral lines inLIBS plasmas is a complicated way; thus, this method is pref-erable over other traditional techniques because it does notneed to nd specic spectral lines, either self-absorbed or notself-absorbed.

5. Conclusion

In summary, in this paper by starting from the basic equationrelating to the intensity of the self-absorbed spectral line andsubstituting other relations in it, an exact theoretical equationfor experimentally measured intensity was derived. Moreover,by devising an appropriate experimental set up, some of theinput parameters were extracted and other transition parame-ters were inserted in the mentioned theoretical equation (eqn(14)) to characterize the plasma dynamic. The experimentalparameters were electron density, plasma length and threespectral lines, which were measured by a combination ofspectroscopic and shadowgraphic set ups.

The theoretical considerations and experimental results inthe presented paper illustrate that utilizing three spectral linesin LIBS experiment has several features as follows:

(i) Major elements can be used for the calculation of plasmaparameters, in contrast to the methods of analytical calibrationcurve or curve of growth.

This journal is © The Royal Society of Chemistry 2014

Paper JAAS

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

(ii) It allows the evaluation of plasma dynamic without thenecessity of the identication of the self-absorbed spectral linesbecause this technique is helpful for both thin and thickplasmas without the estimation of optical depth.

(iii) It directly uses a simple equation for thick plasmas, thusit does not need direct correction of spectral lines and utilizethem for analysis aer evaluating SA parameters.

Acknowledgements

The authors are very grateful to friends: Gharaje, Sa, Mehrvarand Rasooli for helping us perform this experiment.

References

1 M. Corsi, G. Cristoforetti, M. Giuffrida, M. Hidalgo,S. Legnaioli, V. Palleschi, A. Salvetti, E. Tognoni andC. Vallebona, Spectrochim. Acta, Part B, 2004, 59, 723–735.

2 G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti,E. Tognoni and P. Tomassini, Spectrochim. Acta, Part B,2005, 60, 888–896.

3 C. Aragon and J. A. Aguilera, Spectrochim. Acta, Part B, 2008,63, 893–916.

4 D. A. Cremers and L. J. Radziemski, Handbook of Laser-Induced Breakdown Spectroscopy, John Wiley & Sons, WestSussex, England, 2006.

5 A. W. Miziolek, V. Palleschi and I. Schechter, Laser inducedbreakdown spectroscopy: Fundamentals and Applications,Cambridge University Press, 2006.

6 J. P. Singh and S. N. Thakur, Laser-induced breakdownspectroscopy, Elsevier Science, Amsterdam, 1st edn, 2007.

7 M. Sabsabi and P. Cielo, Appl. Spectrosc., 1995, 49, 499–507.8 C. Aragon, J. A. Aguilera and F. Penalba, Appl. Spectrosc.,1999, 53, 1259–1267.

9 H.-Y. Moon, K. K. Herrera, N. Omenetto, B. W. Smith andJ. D. Winefordner, Spectrochim. Acta, Part B, 2009, 64, 702–713.

10 H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto andP. Matheron, J. Quant. Spectrosc. Radiat. Transfer, 2002, 75,747–763.

11 H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto andM. Ripert, J. Quant. Spectrosc. Radiat. Transfer, 2003, 77,365–372.

12 J. Aguilera and C. Aragon, Spectrochim. Acta, Part B, 2008, 63,784–792.

13 J. Aguilera, J. Bengoechea and C. Aragon, Spectrochim. Acta,Part B, 2003, 58, 221–237.

14 C. Aragon, J. Bengoechea and J. Aguilera, Spectrochim. Acta,Part B, 2001, 56, 619–628.

15 C. Aragon, F. Penalba and J. Aguilera, Spectrochim. Acta, PartB, 2005, 60, 879–887.

16 J. Ben Ahmed and J. Cowpe, Appl. Opt., 2010, 49, 3607–3612.17 D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli,

V. Palleschi, A. Salvetti and E. Tognoni, Spectrochim. Acta,Part B, 2002, 57, 339–353.

18 A. El Sherbini, T. M. El Sherbini, H. Hegazy,G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini,

This journal is © The Royal Society of Chemistry 2014

A. Salvetti and E. Tognoni, Spectrochim. Acta, Part B,2005, 60, 1573–1579.

19 V. Lazic, R. Barbini, F. Colao, R. Fantoni and A. Palucci,Spectrochim. Acta, Part B, 2001, 56, 807–820.

20 L. Sun and H. Yu, Talanta, 2009, 79, 388–395.21 I. S. Fishman, G. G. Il'in and M. K. Salakhov, J. Phys. D: Appl.

Phys., 1987, 20, 728.22 T. Sakka, T. Nakajima and Y. H. Ogata, J. Appl. Phys., 2002,

92, 2296–2303.23 J. Hermann, C. Boulmer-Leborgne and D. Hong, J. Appl.

Phys., 1998, 83, 691–696.24 D. Karabourniotis, E. Drakakis and B. Zacharopoulos, J.

Phys. D: Appl. Phys., 1992, 25, 188.25 G. Cristoforetti and E. Tognoni, Spectrochim. Acta, Part B,

2013, 79, 63–71.26 C. A. D'Angelo, D. M. Dıaz Pace, G. Bertuccelli and

D. Bertuccelli, Spectrochim. Acta, Part B, 2008, 63, 367–374.

27 C. A. D'Angelo, D. M. Dıaz Pace and G. Bertuccelli,Spectrochim. Acta, Part B, 2009, 64, 999–1008.

28 I. Gornushkin, C. Stevenson, B. Smith, N. Omenetto andJ. Winefordner, Spectrochim. Acta, Part B, 2001, 56, 1769–1785.

29 G. S. Settles, Schlieren and Shadowgraph Techniques:Visualizing Phenomena in Transparent Media, Springer-Verlag, New York, 2001.

30 R. D. Cowan and G. H. Dieke, Rev. Mod. Phys., 1948, 20,418.

31 W. T. Silfvast, Laser fundamentals, Cambridge Universitypress, New York, 2nd edn, 2004.

32 F. Rezaei and S. H. Tavassoli, Phys. Plasmas, 2013, 20,013301.

33 H. R. Griem, Plasma spectroscopy, McGraw-Hill, New York,1964.

34 F. Rezaei, P. Karimi and S. H. Tavassoli, Appl. Opt., 2013, 52,5088–5096.

35 F. Rezaei, P. Karimi and S. H. Tavassoli, Appl. Phys. B, 2014,114, 591.

36 W. Lochte-Holtgreven, Plasma diagnostics, North-Holland,Amsterdam, New York, 1968.

37 G. D'Ammando, G. Colonna, L. Pietanza and M. Capitelli,Spectrochim. Acta, Part B, 2010, 65, 603–615.

38 Y. Ralchenko, NIST atomic spectra database, 2005, vol. 8, p.96.

39 M. Hauer, D. Funk, T. Lippert and A. Wokaun, Appl. Phys. A,2003, 77, 297–301.

40 M. Hauer, D. Funk, T. Lippert and A. Wokaun, Appl. Surf.Sci., 2003, 208, 107–112.

41 J. F. Y. Gravel and D. Boudreau, Spectrochim. Acta, Part B,2009, 64, 56–66.

42 A. Bogaerts and Z. Chen, J. Anal. At. Spectrom., 2004, 19,1169–1176.

43 W. T. Chan and R. E. Russo, Spectrochim. Acta, Part B, 1991,46, 1471–1486.

44 A. Fernandez, X. Mao, W. Chan, M. Shannon and R. Russo,Anal. Chem., 1995, 67, 2444–2450.

J. Anal. At. Spectrom.

JAAS Paper

Publ

ishe

d on

08

Oct

ober

201

4. D

ownl

oade

d by

Uni

vers

ity o

f C

hica

go o

n 29

/10/

2014

20:

40:1

9.

View Article Online

45 R. Russo, X. Mao, W. Chan, M. Bryant andW. Kinard, J. Anal.At. Spectrom., 1995, 10, 295–301.

46 P. Gregorcic, J. Diaci and J. Mozina, Appl. Phys. A, 2013, 112,49–55.

47 I. B. Gornushkin and U. Panne, Spectrochim. Acta, Part B,2010, 65, 345–359.

J. Anal. At. Spectrom.

48 M. Cvejic, M. R. Gavrilovic, S. Jovicevic and N. Konjevic,Spectrochim. Acta, Part B, 2013, 85, 20–33.

49 A. M. El Sherbini, A. A. Saad Al Amer, A. T. Hassan andT. M. El Sherbini, Opt. Photonics J., 2012, 2, 278–285.

50 W. Sdorra and K. Niemax, Microchim. Acta, 1992, 108,1–10.

This journal is © The Royal Society of Chemistry 2014