In exploiting the analytical capabilities of plasma-based spectroscopy method, the evaluation of plasma parameters, particularly the plasma temperature, is a crucial step. In this work, a modified SahaBoltzmann plot, which uses the columnar densities of atomic and ionic ground levels, is utilized to calculate the plasma temperature in a laser-induced plasma from an aluminum alloy target. The columnar densities are here calculated by quantifying the self-absorption of resonance lines. It is demonstrated that this is a promising method for accurate determination of plasma temperature. To validate the capability of this technique, plasma emission is measured at different gate delay times. For each delay, excitation temperature is calculated both by the conventional Saha-Boltzmann plot (by using the excited states) and by exploiting the new Columnar Density Saha–Boltzmann (CD-SB) plot. The results suggest that at later times of the plasma evolution, the CD-SB plot can be more suitable for the determination of plasma temperature than conventional Saha-Boltzmann plot. These findings provide a new approach for physical characterization of plasmas and give access to a wealth of information about the state of plasma.

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Contents lists available at ScienceDirect

Journal of Advanced Research

journal homepage: www.elsevier.com/locate/jare

Original article

Determination of excitation temperature in laser-induced plasmas using

columnar density Saha-Boltzmann plot

Ali Saﬁa, S. Hassan Tavassolia,⇑, Gabriele Cristoforettib, Stefano Legnaiolic, Vincenzo Palleschic,

Fatemeh Rezaeid, Elisabetta Tognonib

a Laser and Plasma Research Institute, Shahid Beheshti University, G. C., Evin, Tehran, Iran

b National Institute of Optics of the National Research Council (INO-CNR), Via G. Moruzzi 1, Pisa, Italy

c Applied and Laser Spectroscopy Laboratory, Institute of Chemistry of Organometallic Compounds, Research Area of National Research Council, Via G. Moruzzi, 1, Pisa, Italy

d Department of Physics, K. N. Toosi University of Technology, 15875-4416 Tehran, Iran

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

Characterization of LIP by the

Columnar Density Saha-Boltzmann

(CD-SB) plot.

Use of strongly self-absorbed lines to

calculate the plasma temperature.

Temporal evolution of the plasma

temperature by CD-SB plot.

CD-SB plot as a promising method to

obtain plasma temperature at later

times.

CD-SB plot does not require the

calibration of the detection system.

a r t i c l e

i n f o

a b s t r a c t

Article history:

In exploiting the analytical capabilities of plasma-based spectroscopy method, the evaluation of plasma

Received 7 October 2018

Revised 17 January 2019

Accepted 18 January 2019

Available online 26 January 2019

parameters, particularly the plasma temperature, is a crucial step. In this work, a modiﬁed Saha-

Boltzmann plot, which uses the columnar densities of atomic and ionic ground levels, is utilized to cal-

culate the plasma temperature in a laser-induced plasma from an aluminum alloy target. The columnar

densities are here calculated by quantifying the self-absorption of resonance lines. It is demonstrated that

Keywords:

Plasma

Spectroscopy

LIBS

Excitation temperature

this is a promising method for accurate determination of plasma temperature. To validate the capability

of this technique, plasma emission is measured at different gate delay times. For each delay, excitation

temperature is calculated both by the conventional Saha-Boltzmann plot (by using the excited states)

and by exploiting the new Columnar Density Saha–Boltzmann (CD-SB) plot. The results suggest that at

later times of the plasma evolution, the CD-SB plot can be more suitable for the determination of plasma

Self-absorption

temperature than conventional Saha-Boltzmann plot. These ﬁndings provide a new approach for physical

Saha-Boltzmann plot

characterization of plasmas and give access to a wealth of information about the state of plasma.

2019 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article

under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction

Over the past decades, laser-induced breakdown spectroscopy

(LIBS) technique has matured into an interesting, simple, sensitive,

Peer review under responsibility of Cairo University.

⇑ Corresponding author.

and rapid tool for the quantitative and qualitative analyses of a

large group of samples [1–5]. It has been used for a wide range

of applications including industrial [6,7], medical [8,9], forensic

2090-1232/ 2019 The Authors. Published by Elsevier B.V. on behalf of Cairo University.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

i

i

¼

e

k T

B

i

i

i

I

n l

T

B

E

i

i

>

I

>

<

I

g

>

3

>

e

:

i

II

3

g

n

e

i

>

>

>

>

>

>

II

k T

B

I

n

3

I

TÞ

U

h

5

n g

k

2

A. Saﬁ et al./Journal of Advanced Research 18 (2019) 1–7

[10,11], and cultural heritage ﬁelds [12,13]. In this technique, a

where superscripts I and II respectively refer to the neutral and sin-

high-power laser pulse is used to create a plasma on the sample

gly ionized species of the element, U is the partition function of the

surface. Spectroscopic analysis of the plasma emission can provide

species (dimensionless), ne (cm3) is the free electron density, Eion

valuable information about sample composition. A more detailed

(eV) is the ﬁrst ionization energy of the element, T (K) represents

description of the LIBS technique has been reported in the litera-

the electron temperature, h (eV s) is the Planck constant, kB (eV K1)

ture [1,14–16].

is the Boltzmann constant, and me (g) is the electron mass.

To exploit the analytical capabilities of the LIBS technique, the

Eq. (1) can be written in terms of the number density of the

characterization of the LIBS plasma, i.e. the evaluation of plasma

lower level of an ionic transition:

parameters, is a crucial step. The physical characterization of

plasma and diagnostic approaches for the evaluation of plasma

parameters have been the focus of several publications. It is well

nII ð2pmekBTÞ3=2 2nI ðEIIþEionÞ

gII neh3 UIðTÞ

ð2Þ

known that among the plasma parameters, plasma temperature

plays an important role [17–24]. The knowledge of plasma temper-

ature has a great signiﬁcance in describing other plasma character-

istics such as the relative populations of energy levels and the

velocity distribution of particles [16]. In particular, in applying

the CF-LIBS procedure introduced by Ciucci et al. in Ref. [25] for

where EII (eV) is the lower level energy of the ionic transition and gII

is the degeneracy of the i level. Multiplying both sides of Eq. (2) by

the optical path length l and taking the natural logarithm, the coor-

dinates of the spectral lines in the columnar density Saha–Boltz-

mann plane are given:

the quantitative analysis of plasma composition, the accurate

determination of the plasma electron temperature is crucial.

Although several spectroscopic methods exist for determining

the excitation temperature in LIBS, Boltzmann plot and Saha-

Boltzmann plot methods [26] are by far the most used. However,

y ¼ mx þb

where b ¼ ln

!

UIðTÞ and m ¼ k1

ð3Þ

ð4Þ

it must be emphasized that both of these methods have important

limitations, particularly at long delay times when the plasma

becomes cooler and the population of atoms in the lower state

increases. In these conditions, the emission originates mainly from

( I

x ¼ EII þEion

for

for

)

neutral lines

ionic lines

ð5Þ

resonance transitions or from low-lying energy levels which are

more prone to self-absorption, resulting in an inaccurate estima-

tion of the plasma temperature. Furthermore, at long delay times,

ionic lines tend to disappear because of ion recombination, making

the Saha-Boltzmann method hardly exploitable. It should also be

8

>ln nil

y ¼ i

>ln nIIl ln 2ð2pmhkBTÞ2

for

for

9

neutral lines=

ionic lines ;

ð6Þ

kept in mind that both Boltzmann and Saha-Boltzmann plot meth-

ods have an additional intrinsic limitation. Both methods, in fact,

make use of the population of excited states and usually rely on

the hypothesis that plasma is in Local Thermodynamic Equilibrium

(LTE), which extends the validity of temperature calculation to all

the energy levels. Actually, this approach may be inaccurate since

ground levels are largely the most populated levels, slight devia-

tions from LTE or small uncertainties in determining the popula-

tion of excited levels can lead to signiﬁcant errors in the

description of excitation and ionization equilibrium.

In the following section, it is shown that the above-mentioned

limitation is overcome by using a columnar density Saha-

Boltzmann plot approach since columnar densities of ground levels

can be directly calculated. Moreover, the presence of strong self-

absorption in resonance lines guarantees the LTE of the atomic sys-

tem. Therefore, this approach, originally introduced by Cristoforetti

and Tognoni [27], opens up a new way to calculate plasma temper-

ature accurately.

This modiﬁed Saha–Boltzmann expression is similar to the clas-

sical Saha–Boltzmann plot, the slope of the linear plot being

related to the plasma temperature. Comparing it with the conven-

tional Saha-Boltzmann plot, however, it is evident that some differ-

ences exist between them in the calculation of plasma

temperature. In particular, variable y is determined by using the

columnar density (nil) rather than line intensity for both atomic

and ionic lines of the desired elements. In addition, coordinate x

represents the lower (rather than the upper) level energy values.

For the construction of the CD-SB plot, electron density and also

spectroscopic data for both atomic and ionic lines should be avail-

able. In principle, the plasma electron temperature should be

determined iteratively, because of the explicit dependence of y

on T in Eq. (6). However, the iteration of the calculation procedure

is not needed in practice since the dependence of y on T is weak

and involves only a logarithmic term.

As seen in Eq. (6), the columnar density (nil) must be known for

both atomic and ionic lines of the elements of interest. A simple

Methodology

method is presented below to calculate columnar density which

is based on measuring the self-absorption coefﬁcient of optically

In this section, the basic theoretical framework for calculating

the ground-level temperature of an element through a modiﬁed

Saha-Boltzmann plot called ‘Columnar Density Saha-Boltzmann

(CD-SB)’ plot is outlined. A more detailed description of this

method is available in Ref. [27].

Similar to other LIBS methodologies, in the CD-SB plot method

it is assumed that plasma is spatially homogenous in the measure-

ment time interval. In order to obtain ground level temperature,

the ratios of number densities between successive ionization

stages can be expressed by the Saha–Eggert equation [28]:

ne nII ¼ ð2pmekBTÞ3=2 2UððTÞeEion ð1Þ

thick lines. The equation of radiative transfer is considered as fol-

lows [29]

IðkÞ ¼ 8phc2 nj gi 1 ekðkÞl ð7Þ

0 i j

where i and j respectively refer to the lower and upper levels of the

transition, IðkÞis the spectral line intensity (erg s1 cm3), k0 is the

central wavelength (cm) of the transition, c is the speed of light

(cm s1), ni, nj, gi, and gj are the number densities (cm3) and degen-

eracies (dimensionless) of the levels, k(k) is the absorption coefﬁ-

cient (cm1), and l is the absorption path length (cm).

In Eq. (7), the value of k(k)l (the optical depth) is crucial in

determining the self-absorption degree of the emission line and

can be expressed as