Measurements of Plasma Electron Temperature Utilizing Magnesium Lines Appeared in Laser Produced Aluminum Plasma in Air

doi:10.4236/opj.2012.24034

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Optics and Photonics Journal, 2012, 2, 278-285

http://dx.doi.org/10.4236/opj.2012.24034 Published Online December 2012 (http://www.SciRP.org/journal/opj)

Measurements of Plasma Electron Temperature Utilizing

Magnesium Lines Appeared in Laser Produced

Aluminum Plasma in Air

Ashraf M. El Sherbini1,2, Abdel Aziz Saad Al Amer1, Ahmed T. Hassan1,2, Tharwat M. El Sherbini2

1Department of Physics, Collage of Science, Al Imam Muhammad Ibn Saud Islamic University (AIMSIU),

Al Riyadh, KSA

2Laboratory of Lasers and New Materials (LLNM), Department of Physics, Faculty of Science, Cairo University, Giza, Egypt

Email: [email protected]

Received August 14, 2012; revised September 16, 2012; accepted October 2, 2012

ABSTRACT

We have utilized the relative intensity of magnesium lines originated from the Mg I at 285.2 nm and Mg II at 280.27,

279.55 nm to measure the plasma electron temperature. The plasma was produced via interaction of Nd:YAG laser with

solid aluminum target contains traces of magnesium. The magnesium lines were found to suffer from optical thickness

which manifests itself on the form of scattered points around the Saha-Boltzmann line. We have utilized a simple

method used for rapid calculation to the amount of absorption to these lines via comparison of the electron densities as

deduced from magnesium lines to that evaluated from the optically thin hydrogen Hα line at 656.27 nm appeared in the

same spectra under the same condition. A correction to the magnesium spectral lines intensities was carried out; hence

the corrected temperatures were re-evaluated. The measurements were repeated at different delay times ranging from 1

to 5 μsec. This work emphasizes on the importance of correcting the emitted spectral line intensity against the effect of

self absorption before using them in the calculation of plasma electron temperature in laser induced breakdown spec-

troscopy (LIBS) experiments.

Keywords: LIBS; Self Absorption; Mg-Lines; Plasma Parameters

1. Introduction

The LIBS technique is one of the potentially growing

applied techniques used in the field of elemental analysis,

because of its simplicity and non-contact nature [1-10].

Its basic principle is based on exciting matter (solid, liq-

uid or gas) to plasma state through irradiation by high

power laser pulses.

The diagnostics of the plasma can be done through the

measurements of electron density (ne) and temperature

(Te). The optical emission spectroscopy (OES) is the tool

by which the plasma can be diagnosed [11]. The meas-

urement of the electron density through Stark broadening

effect requires a line which is free from self absorption

[12,13]. Self absorption occurs in general in any kind of

system capable of emitting radiation, such as plasma.

Moreover, the formation of the plasma in air shows, in

general, a strong gradient of temperature due to the cool-

ing effect of the surrounding air [14]. These cold periph-

eries of the plasma contain a high concentration of the

atoms at the low laying atomic states which can cause a

strong re-absorption to the emitted radiation lines [15-

17]. It was found that, especially the resonance and

strong lines are more likely to be subjected to self ab-

sorbed. The Mg II ionic lines are a good example of this

effect because they are either a resonance lines like; the h

and k lines at 279.55 and 280.27 nm respectively, or they

are relatively intense. However, these lines would be

good candidates for calculating the plasma electron tem-

perature. The wavelength separation is very small as well

as their separation in the upper excited states is relatively

large with respect to the expected plasma temperature (~

1 eV) [11,18,19]. Moreover, the h and k resonance lines

belong to the most exploited lines in astrophysical

plasma diagnostics [18] and therefore, they are also of

the interest in astrophysical plasma at large temperatures.

Moreover, the Stark broadening of these lines are well

known at electron density higher than 1015 cm–3 [18]. On

the other hand the appearance of the Mg I-resonance line

at 285.2 nm provides a assurance chance to construct the

Saha-Boltzmann plot with the help of the Mg II lines, but

unfortunately this line is a resonance line, hence one

should expect that it may be subjected to the effect of self

absorption.

It was suggested in Ref’s [12,20,21], that the use of the

A. M. EL SHERBINI ET AL. 279

Hα line at a wavelength of 656.27 nm can garantee a re-

liable measurement of the electron density, since the line

is optically thin [20].

In this work, we shall adopt a straightforward proce-

dure to calculate the self absorption coefficients of the

plasma to the Mg I, II lines via comparison of the elec-

tron densities evaluated utilizing the Stark broadening of

the magnesium lines to the electron density as deduced

from the optically thin Hα-line [12]. We have calculated

the electron temperatures both before and after correction

to the lines intensities in order to show that the effect of

self absorption may lead to serious errors in temperature

measurements. The use of these lines can open the area

to use of the magnesium lines to measure the electron

temperature in the interstellar plasma.

2. The Effect of the Self Absorption on

Spectral Radiance

The process of re-absorption of the plasma to the light

photons in their path to outside the plasma active volume

is called the self absorption. It is well known that this

process affecting the spectral line shape i.e. the line in-

tensity decreases and its full width at half maximum

(FWHM) increases [22,23].

The self absorption (SA) coefficient at the line center



was defined as the ratio of the spectral radiance

(counts per sec) of a spectral line subjected to self ab-

sorption





to that of the same line in the limit of

negligible self absorption





[19,23-25].



1e o

oo o

SA I































 (1)

Equation (1) indicates that the SA coefficient varies

from unity in case of perfectly optically thin line to the

limit of zero in case of completely self absorbed line [21],

and is the optical depth of the plasma

at the line center.

 

 

o

On the other hand, it was pointed out in Ref’s. [12,13]

that the process of the self absorption indeed affecting

the line intrinsic FWHM o



 through the process of

re-absorption, hence, the line FWHM become





which

is greater than o



. The SA coefficient was then ex-

pressed in terms of the ratio of the Lorentzian (FWHM)

components of the same line as [12].















(2)

where 0.56



 , o



 is the intrinsic FWHM of the

Lorentzian component of the spectral line if the line is

optically thin and



 is the distorted Lorentzian com-

ponent of the same line which resulted from the effect of

the self absorption. An extensive analysis to Equation (2)

was carried out in Ref. [12], and showed that the direct

calculation of the electron density from the measured

Lorentzian component of the extra broadened line





must give an apparent (wrong) larger electron density





line

n values than the expected value calculated from

the same line if the line is optically thin. Therefore,

Equation (2) can be re-written in terms of ratio of the

electron densities as evaluated from the line suffered

from self absorption to that evaluated from the optically

thin Hα-line;





2 linelineline

2line

se e



SA nH



















(3)

In Equation (3) e



can be regarded as a sort of

equivalent density from the line in the limit of zero self

absorption [12], i.e. if the line is optically thin. We have

suggested [12] that e



can be replaced by the electron

density utilizing the optically thin Hα line at 656.27 nm

present in the same emitted spectra under the same ex-

perimental condition. It is worth noting that, the SA co-

efficient of a certain line can be calculated using Equa-

tion (3), then a correction to the spectral line intensity at

the line center can be calculated using Equation (1).

2.1. Stark Broadening of Mg I, II-Lines

The resonance (k and h) lines emitted by the Mg II ion at

wavelengths of 280.27 nm and 279.55 nm are of particu-

lar interest, because fully quantum mechanical calcula-

tions are available for these lines [25]. The measured

widths (FWHM) agree fairly well with semi-classical

calculations. They are usually normalized to a reference

electron density . Neglecting the ion

broadening contribution, the plasma apparent electron

density can be calculated from the Mg II ionic lines by

[19,21,23-25]:

17 3

10 cm

N















N (4)



is the theoretical line full width Stark broadening

parameter, calculated at the same reference electron den-

sity 17 3

10 cm



. A number of experimental and

theoretical studies have been dedicated to measurement/

calculation of the Stark widths and shifts of the men-

tioned Mg II lines. In our work, the parameters



to-

gether with atomic parameters of the Mg II ionic lines

were taken from Ref. [18] and are given at Table 1.

Equation (4) also will be used to estimate the electron

density from the Mg I-line at the wavelength of 285.2 nm

at the reference density of 1016 cm–3.

2.2. Reference Plasma Parameters

Because our experiment was carried in open air, the

A. M. EL SHERBINI ET AL.

280

Table 1. The Stark broadening parameters and the atomic parameters of the Mg I, II lines.

Element Wavelength (nm) Aki

(s–1) Stark parameters (ωs) (pm)/Nr (cm–3) Kind of Transition Ek (eV) Ei (eV)gk

Mg I 285.21 4.91 × 108 0.42/1e16 Resonance 4.34 0 3

Mg II 279.55 2.60 × 108 5.1/1e17 Resonance 4.43 0 4

Mg II 280.27 2.57 × 108 5.1/1e17 Resonance 4.42 0 2

reference electron density can be derived from the opti-

cally thin Hα line appeared in the spectra [12,20,21]. The

presence of this line was attributed to the existence of a

very small concentration of water vapor (humidity) around

the target [12]. This line was critically studied in a pre-

vious publication [20] and was shown to have significant

practical properties; e.g. it exists long time after termina-

tion of the laser pulse, it has a large signal to background

ratio, relatively large Lorentzian (FWHM) component

which ensures a small error in calculating electron den-

sity and finally is optically thin [20].

Moreover, because the interaction was carried with the

surface of aluminum target in open air, the reference

electron temperature was derived from the optically thin

Al II ionic lines at 281.6, 358.6 and the 466.2 nm ap-

peared in the same spectra of the plasma under the same

experimental conditions. Constructing the Boltzmann

plot including the spectral intensity of such aluminum

lines leads to precise measurement to the reference

plasma electron temperature.

Figure 1. Experimental setup.

μm diameter quartz fiber cable positioned at distance of

12.5 mm normal to the laser axis and arranged to observe

a circle of cross section of only 2 mm in front of the tar-

get. The wavelength scale was calibrated using a low

pressure Hg-lamp (type Ocean optics). The instrumental

bandwidth was measured from the FWHM of the Hg

lines and was found to be 0.12 ± 0.02 nm. Identification

of the different lines in the LIBS spectrum was carried

out using Spectrum Analyzer Software version 1.6. The

relative response of the detection system was measured

using a standard Deuterium Tungsten-Halogen calibra-

tion light source (type DH-2000-CAL). Over the entire

experiment the gate time was kept at 1 μs and the delay

time was varied in equal steps from 1 - 5 μs.

3. Experimental Setup and Measurement

Procedures

The used experimental setup is shown in Figure 1. A

Q-switched Nd-YAG laser (Quantel, model Brilliant B)

was used at the emission wavelength of 1.06 μm. The

energy per pulse at the target surface was fixed at a level

of 670 mJ. An absolutely calibrated power-meter (Ophier,

model 1z02165) was used, measuring the 4% fraction of

the laser light reflected from a quartz beam splitter to

monitor the incident laser energy, which might changes

from one shot to another. The laser was focused on the

target by a quartz lens of focal length of 10 cm. The tar-

get was a certified aluminum based alloy with traces of

Mg (1.16%) polished and mounted on a xyz-stage to

present a fresh polished surface at each laser shot. The

acquired data was averaged over three shots under the

same conditions for estimating the reproducibility mar-

gins at each data point. The emitted light from the plasma

was analyzed using an echelle type spectrograph (type

Catalina, model SE 200) with a resolving power of 2400

and equipped with a time gated ICCD camera (1064 ×

1064 pix with 13 μm × 13 μm pixel size at a binning

mode of 1 × 1 (type Andor, model iStar DH734-18F). The

emitted light from the plasma was collected using a 25

4. Results and Discussions

The recorded spectra at different delay times ranging

from 1 - 5 μs at a gate time of 1 μs are shown in Figure 2.

We can notice the existence of Hα-line and the Mg I, II

emission lines as well as the Al II ionic lines in the short

wavelength region. The line spectra are superimposed on

a continuum component which decreases with the ad-

vance of acquisition delay time. This continuum is mainly

results from the free-free (Bremesstrahlung process) and

the free-bound transitions. This continuum should be

removed before proceeding in the spectral line shape

analysis.

A Voigt fitting and hence the extraction of the Lor-

entzian FWHM from the Mg II ionic lines at wavelengths

of 280.27, 279.55 nm and the Mg I line at 285.2 nm as

well as to that of the Hα-line was carefully done using

home made software running in MATLAB package. The

A. M. EL SHERBINI ET AL. 281

Figure 2. A sample of the emission spectra from plasma at different delay times showing the different lines appeared Hα, Mg I,

and Mg II as well as Al II ionic line at 281.6 nm (a); at arbitrary delay time of 5 μs (b); and the resolved lines at the short

wavelength region (c).

results of the best fittings to the different lines at an arbi-

trary delay times of 1, 3, 5 μs and at a fixed gate time of

1 μs are shown in Figure 3.

According to Equation (3), the deviation of the meas-

ured electron density calculated from the Mg I, II lines

with respect to that evaluated from the optically thin Hα

line indicates the existence of self absorption. A plot of

the apparent electron density calculated from the Lor-

entzian (FWHM) component from the three Mg I, II lines,

in comparison to that evaluated from the Hα are shown in

Figure 4. This figure confirmed that the Mg I, II lines are

influenced by the effect of the self absorption and hence

the higher the observed electron densities from the mag-

nesium lines.

The self absorption coefficients were calculated utiliz-

ing Equation (3) to the three Mg I, II lines at different

delay times with the results shown in Figure 5. A loga-

rithmic decrease in the SA values with delay time can be

observed, indicating an increase of the optical depth of

the lines with delay time. This means that as the plasma

become cooler with the delay time (as a result of expan-

sion) the population of the atoms in the lower state be-

comes higher and hence the more the absorption.

Moreover, the calculated SA values for the resonance

doublets (h and k) Mg II lines shows nearly an equal de-

creasing rates, which is in agreement with the known

A. M. EL SHERBINI ET AL.

282

Figure 3. The quality of the Voigt fitting to the different spectral Mg I , II-lines used in the investigation as well as the Hα-line

at delay times of 1, 3 and 5 μs.

absorption oscillator strengths of the lines (0.61 and 0.31

respectively).

A correction to the Mg I, II lines spectral radiances

was carried out according to Equation (1). Saha-Boltz-

mann plots were constructed [26,27] with the result as

shown in Figure 6, utilizing the Mg I, II lines intensities

both before and after correction against effect of self ab-

sorption. We can notice the scattering of the points cor-

responding to emission wavelengths of 280.27 and

279.55 nm before correction against this effect. After the

application of correction procedures and re-construction

of the plot, the points are tending to coincide with one

another forming a straight line. This figure primarily in-

dicates the effectiveness of the correction process.

In order to evaluate the reference electron temperature

we have utilizing the spectral radiances from the Al II

ionic lines at 281.6, 358.6 and the 466.2 nm to con-

structed the Boltzmann line with the result as shown in

Figure 7. One basic advantage of utilizing such alumi-

num lines is that they are optically thin [12]. One can

A. M. EL SHERBINI ET AL. 283

Figure 4. The temporal variation of the measured electron

densities utilizing the Hα line (lower solid squares), from the

Mg I line at 285.2 nm (solid inverted triangles), from the

Mg II ionic line at 279.2 nm (solid circles) and from the

ionic Mg II line at 280.2 nm (solid triangles).

Figure 5. A demonstration to the variation of the coeffi-

cients of self absorption for from the Mg I line at 285.2 nm

(solid inverted triangles), from the Mg II ionic line at 279.2

nm (solid circles) and from the ionic Mg II line at 280.2 nm

(solid triangles).

Figure 6. The Saha-Boltzmann plot utilizing spectral line

intensities from the Mg I, II lines before correction (lower

open figures) and after correction against self absorption

(upper solid figure). The slope of the upper line indicates a

temperature of 1.12 eV, while the lower dashed line 1.92 eV.

(Squares = Mg I line at 285.2 nm, inverted triangles at Mg

II 279.55 nm and the circle at Mg II 280.27 nm).

Figure 7. The Boltzmann plot utilizing the Al II ionic lines

(281.6 nm (square), 466.2 nm (inverted triangle) and 358.6

nm (solid circle) taken at an arbitrary delay and gate times

of 1 μs. The slope of the best fit straight line indicated tem-

perature of 1.14 eV.

notice the existence of the points on the straight line with

slope indicating the reference electron temperature.

Figure 8 shows the overall temperatures variation with

delay time as evaluated from the Mg I, II lines both be-

fore and after correction in comparison with the refer-

ence temperature as deduced from the Al II ionic lines.

We can notice that, the calculated electron temperatures

from the Mg II lines without correction against self ab-

sorption effects are larger than after correction. This

large deviation of the evaluated temperatures shows that

the Mg I, II lines, should be corrected against effect of

self absorption before used in plasma diagnostics.

5. Conclusion

We have measured the plasma electron temperature and

density utilizing three lines emerging from magnesium in

LIBS experiment. The effect of the self absorption on

three Mg II lines at 280.27, 279.55 and Mg I resonance

line at 285.2 nm were quantified utilizing simple formu-

las based on the measurement of the ratio of the apparent

electron density from the lines of interest to that derived

from the optically thin Hα line. The spectral line intensi-

ties were then corrected. The electron temperatures were

re-evaluated and compared to reference temperatures

utilizing the Al II ionic lines. This comparison shows an

excellent agreement between the reference temperatures

and the measured utilizing the magnesium emission lines.

The results shows that the Mg I, II lines appeared at the

short wavelength region of the LIBS spectrum are good

candidates for measuring the temperature of the plasma

in LIBS experiments, but after correction against self

absorption.

6. Acknowledgements

The experimental part of this work was conducted at the

A. M. EL SHERBINI ET AL.

284

Figure 8. Presentation to the variation of the measured

electron temperature with delay time utilizing Mg I, II lines

after correcting spectral intensities against effect of self

absorption (lower open circles), without correction (upper

solid circles) and from the Al II ionic spectral line intensi-

ties (red solid triangles).

Laboratory of Lasers and New Materials (LLNM), Phys-

ics Dep., Cairo Univ., Egypt. The authors express their

gratitude to the valuable discussions with Prof. S. H. Al-

lam and Dr. H. Hegazy.

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