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Spectrochimica Acta Part B 65 (2010) 671–679

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Spectrochimica Acta Part B j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s a b

Calibration free laser-induced breakdown spectroscopy of oxide materials☆ B. Praher a,⁎, V. Palleschi b, R. Viskup a, J. Heitz a, J.D. Pedarnig a,⁎ a b

Christian Doppler Laboratory for Laser-Assisted Diagnostics, Institute of Applied Physics, Johannes Kepler University Linz, A-4040 Linz, Austria Institute for Chemical-Physical Processes of the National Research Council, Via G. Moruzzi, I-56124 Pisa, Italy

a r t i c l e

i n f o

Article history: Received 24 November 2009 Accepted 13 March 2010 Available online 20 May 2010 Keywords: Calibration free laser-induced breakdown spectroscopy (CF-LIBS) Multi-element analysis Oxides

a b s t r a c t The quantitative determination of oxide concentration by laser-induced breakdown spectroscopy is relevant in various fields of applications (e.g.: analysis of ores, concrete, slag). Calibration free laser-induced breakdown spectroscopy and the multivariate calibration are among the methods employed for quantitative concentration analysis of complex materials. We measured the intensity of neutral and ionized atomic emission lines of oxide materials by laser-induced breakdown spectroscopy and we modified the calibration free laser-induced breakdown spectroscopy method to increase the accuracy. The concentration of oxides was obtained by using stoichiometric relations. Sample materials were prepared from oxide powder (Fe2O3, MgO, CaO) by mixing and pressing. The concentration was 9.8–33.3 wt.% Fe2O3, 7.6–33.3 wt.% MgO and 33.3–81.2 wt.% CaO for different samples. Nd:YAG laser (wavelength 1064 nm, pulse duration ≈ 6 ns) ablation was performed in air. The laser-induced plasma emission was measured by an Echelle spectrometer equipped with a sensitivity calibrated ICCD camera. The numerical calibration free laser-induced breakdown spectroscopy algorithm included the fast deconvolution of instrumental function, and the correction of selfabsorption effects. The oxide concentration CCF calculated from calibration free laser-induced breakdown spectroscopy results and the nominal concentration CN were very close for all samples investigated. The relative error in concentration, |CCF–CN|/CN, was b 10%, b 20%, and b 5% for Fe2O3, MgO, and CaO, respectively. The results indicate that this method can be employed for the analysis of major elements in multicomponent technical materials. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Laser-induced breakdown spectroscopy (LIBS) is a versatile method for fast and accurate multi-element analysis of gaseous, liquid and solid samples [1,2]. Commonly, univariate or multivariate regression models are employed for quantitative analysis using calibration samples and standards [3–5]. Drawbacks of this approach are the need of calibration samples and/or standards with same matrices as the samples under investigations and the necessity of constant experimental parameters (e.g. laser energy, spot diameter). An alternative method for quantitative analysis without the need of calibration samples is calibration-free LIBS (CF-LIBS) [6]. The CF-LIBS method (or variants of it) have been used for calibration free analysis of various materials such as copper alloys [7–9], aluminium alloys [10], gallstones [11], coral skeleton [12], Martian rock analogues [13,14], meteorites [15], brass, and soil samples [16]. With complex ☆ This paper was presented at the 5th Euro-Mediterranean Symposium on Laser Induced Breakdown Spectroscopy, held in Tivoli Terme (Rome), Italy, 28 September–1 October 2009, and is published in the Special Issue of Spectrochimica Acta Part B, dedicated to that Symposium. ⁎ Corresponding authors. Tel.: +43 732 2468 9246. E-mail addresses: [email protected] (B. Praher), [email protected] (J.D. Pedarnig). URL: http://www.cdlabor-lad.jku.at/ (B. Praher). 0584-8547/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2010.03.010

matrices the CF-LIBS method is often only semi-quantitative because of effects like radiation self-absorption and the inaccuracy of parameters like transition probability, electron number density and partition function that are used in the calculation. For correction of self absorption of optically thick lines a curve of growth method has been developed [17] and optically thin lines were used as internal reference [18]. The influence of experimental aberration and inaccuracy of physical parameters on the results of CF-LIBS calculations has been studied for an ideal analytical plasma [19]. Oxide materials are used in many different industrial branches and the analysis of oxide concentration is important for various technical processes therefore. LIBS method has been employed for the analysis of different oxide materials like slag, ore, cement, and concrete. Multivariate and univariate regression have been used for the calculation of oxide concentration in slag originating from secondary metallurgy [20,21] and in ores [22]. Analysis of major oxides in rocks and soils was performed also by using artificial neural networks [23]. The basicity of slag was analyzed by measuring the concentration of oxides like CaO, MgO, and SiO2 [24]. In this study, we measure the laser-induced plasma emission spectra of samples containing Fe2O3, MgO, and CaO, and we examine the CF-LIBS method to determine the oxide concentration with high accuracy directly from collected spectra. The oxidation state of chemical elements is assumed to be known (which is often the case

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B. Praher et al. / Spectrochimica Acta Part B 65 (2010) 671–679

with industrial materials) and oxide concentrations are calculated from element concentration by using the stoichiometric relations. 2. Experimental 2.1. Experimental setup The experimental set-up is shown in Fig. 1. The pulsed radiation of a Nd:YAG laser (Continuum Surelite I-20) with wavelength λ = 1064 nm, pulse duration τL ≈ 6 ns, pulse energy EL ∼ 90 mJ, repetition frequency 5 Hz, and quasi Gaussian beam profile was focused in air atmosphere onto the samples placed on a rotation stage. The target surface was positioned approximately 6 mm above the focal plane to avoid breakdown in air and the resulting laser spot diameter was d ∼ 1 mm. The space integrated emission of laser-induced plasma was collected by using lenses and a pierced mirror. The light was guided by a quartz fiber into an Echelle spectrometer with intensified CCD detector (LTB, Berlin, model Aryelle) employing a delay time of td = 0.8 µs with respect to the laser pulse and a gate time of tg = 0.2 µs. The delay time was sufficient to suppress background signals from continuum plasma radiation. A short gate time was chosen to avoid strong changes in plasma temperature and electron number density during the measurement. The wavelength range of recorded spectra was from 298 to 864 nm with a spectral resolution λ/Δλ ≥ 10,000. LIBS spectra were accumulated for different number of laser shots on the sample. Spectra obtained with single laser pulses allowed for only semi-quantitative analysis. This was probably due to low signal-to-noise ratio of line intensities (especially of Hα line) that introduced large uncertainty in calculations. Quantitative compositional analysis of sample materials was achieved with spectra that were accumulated over 100 laser pulses. A similar observation was reported earlier [14]. The results presented here were obtained by averaging over five spectra for each sample (100 shots per spectrum, 500 shots in total). The noise level of averaged spectra was sufficiently low to avoid significant amplification of noise and deformation of spectra in the numerical deconvolution procedure. All algorithms for numerical CF-LIBS calculations were implemented in the software package MATLAB. 2.2. Investigated materials Three different oxide materials (Fe2O3, MgO and CaO) in powder form were mixed together at different mass ratios. The degree of

purity of the used oxide materials was 99.5% for Fe2O3 (voestalpine Stahl GmbH), 99.5% for MgO (Johnson Matthey) and 99.95% for CaO (Johnson Matthey). The diameter of particles was less than 44 µm for all powder materials. The mixed oxide powders were homogenized for 30 min in a ball mill. Pellets were produced by hydraulic pressing of the powder mixture into discs of 13 mm diameter and 2 mm thickness (pressing for 5 min with 5.000 kg/cm2 at room temperature). The oxide concentration of the five samples used in this study is summarized in Table 1. For all samples, the CaO concentration is higher than or equal to the MgO and Fe2O3 concentration, similar to oxide materials like slag or cement. 3. Signal processing and modeling The CF-LIBS approach is based on the assumption that in an optically thin plasma in local thermal equilibrium (LTE) the integrated spectral line intensity can be described by [1] ð−E = k Te Þ

Iij = FNAij

gi e i Q ðTe Þ

;

ð1Þ

with F an experimental factor, N the number density of neutral or ionized atoms, Aij the transition probability, gi the degeneracy factor of state i, Ei the energy of the upper level of transition, k the Boltzmann constant, Te the electron temperature, and Q(Te) the partition function. The measured LIBS signal depends on the measurement system and on various processes within the laser-induced plasma. The measured signal therefore deviates from the “true” signal. For quantitative CF-LIBS analysis, the background continuum radiation, noise, the spectral response of the spectrometer, the convolution of signal function with spectrometer function, and self absorption effects have to be taken into account. 3.1. Background and noise The additive background in LIBS measurements is mainly caused by Bremsstrahlung radiation (free-free transitions) and radiative recombination (free-bound transitions) [2]. These effects are relevant mainly in the early stage of plasma as the background intensity from continuum radiation decays faster than the emission intensity of spectral lines. The background can be reduced by selecting a proper delay time with acceptable signal-to-background ratio or by using background correction algorithms (as described, e.g., in [25,26]). In this work, the background signal was sufficiently small for a delay time of td = 0.8 µs and further background correction was not necessary therefore. The noise of an ICCD camera is composed of read out noise, photon noise and noise from the micro-channel plate, dark current noise and the photo-cathode dark noise [27]. The dominant part of the total noise of an ICCD camera is the photon noise which can be described as a Poisson process. The data reported here were obtained by accumulating over 500 laser shots for each averaged spectrum. This accumulation increased the signal-to-noise ratio sufficiently and no further signal processing (i.e., by filtering) was necessary therefore. Table 1 Nominal composition of five different samples produced from Fe2O3, MgO and CaO powders. Sample Nr.

Fig. 1. Schematic of experimental setup for LIBS measurement of pressed oxide materials.

1 2 3 4 5

Fe2O3

MgO

CaO

[wt.%]

[wt.%]

[wt.%]

33.333 38.526 16.711 24.978 9.759

33.333 7.616 24.991 8.328 9.036

33.333 53.858 58.299 66.694 81.205


3.2. Spectral response of spectrometer For the determination of plasma temperature and number densities via Saha–Boltzmann plots the measurement of the spectrometer sensitivity (spectral response) is essential. The spectral response function of the used Echelle spectrometer was determined by measuring the emission of a calibrated Tungsten lamp. Fig. 2 displays the measured spectral response showing a non-linear and oscillatory behaviour. The observed oscillation of sensitivity is due to the diffraction efficiency of Echelle reflection gratings [28] (efficiency changes with direction of reflected beam or diffracted wavelength for each diffraction order) and to the different orders of diffraction used for computation of spectra. In order to avoid significant changes of spectral response due to temperature variations, the response function and the LIBS spectra of samples were measured in the same run. All LIBS spectra were normalized using the measured response function. 3.3. Deconvolution of instrumental function The signal function measured by an optical spectrometer sm(λ) is given by the convolution of the “true” signal function of the light source to be analyzed s(λ) and the transmission function of the spectrometer h(λ) and by an additive noise term n(λ) ′ ′ ′ sm ðλÞ = ∫s λ h λ−λ dλ + nðλÞ: ∞

emission lines where the lower level of transition is equal or close to the ground state [2]. Self-absorption is higher at the maximum of the emission line and lower at the tails. Therefore, the effect of selfabsorption is apparently reducing the line peak intensity and, consequently, increasing the full width at half maximum (FWHM) of the emission lines. When self-absorbed lines are used in CF-LIBS the calculated concentration of corresponding elements is usually underestimated. This problem can be overcome by rejection of strongly selfabsorbed spectral lines and by a correction procedure for spectral lines with only moderate self-absorption. The optical properties of plasma in LTE can be described by the emission coefficient ε(λ) and the absorption coefficient κ(λ). The emission coefficient is described by [31]

εðλÞ =

hc g e−Ei = k Te NP ðλÞ Aij i 4πλ0 Q ðTe Þ

−∞

The true signal can be derived by deconvolution. Numerous algorithms addressing the noise of measured data in a deconvolution process have been developed. An overview of different methods applied in spectroscopy can be found in [29]. We used an algorithm based on the Richardson–Lucy method, adapted for spectra processing [30]. The Richardson–Lucy algorithm estimates the most probable true signal function s(λ) assuming that the transmission function of the spectrometer h(λ) is known and the noise n(λ) is Poisson distributed. The spectrometer transmission function was measured by using a Mercury lamp and h(λ) showed a Gaussian distribution of 0.025 nm width (FWHM) at 300 nm wavelength. This value was in good agreement with the nominal resolution of the spectrometer. 3.4. Self absorption The absorption of photons within the laser-induced plasma is called self-absorption. This phenomenon is observed mainly for

κðλÞ =

gj e j e2 λ20 f Q ðTe Þ 4ε0 me c2

− E −E = k T 1−e ð i j Þ e NP ðλÞ

ð4Þ

where e is the elementary charge, gj is the degeneracy factor of state j, ε0 is the dielectric constant, Ej is the energy of the lower level of transition, me is the electron mass, and f is the oscillator strength of the transition. In Fig. 3, the surface of an irradiated target (at position z = 0) and the laser-induced plasma above the surface are shown schematically. The plasma is assumed to be homogeneous and of cylinder symmetry and to extend from z = 0 to z = L along the symmetry axis. The change of intensity I(z,λ) in the plasma is described by the radiation transport equation dI ðz; λÞ = εðλÞdz−κðλÞIðz; λÞdz:

ð5Þ

For optically thin plasma the absorption can be neglected and integration from z = 0 to z = L yields the emitted intensity Ithin(λ) = ε(λ) × L. For optically thick plasma self-absorption is relevant and the solution of transport equation yields an emitted intensity

Ithick ðλÞ = Ithin ðλÞ

Fig. 2. Spectral response of Echelle spectrometer measured with calibrated Tungsten lamp in the range from 298 nm to 864 nm.

ð3Þ

where h is the Planck's constant, c is speed of light in vacuum, λ0 is the central wavelength corresponding to the transition, and P(λ) is the normalized spectral line profile. The absorption coefficient can be expressed by [32] −E = k Te

ð2Þ

673

−τðλÞ 1−e τðλÞ

:

ð6Þ

Fig. 3. Schematic of laser-induced plasma above the surface of ablated target. Surface is at z = 0 and plasma extends from z = 0 to z = L. For self-absorption correction the plasma temperature Te and electron number density Ne are assumed to be homogeneous. The intensity of light emitted by the plasma along the z direction I(z, λ) is calculated by radiation transport equation. The direction of corresponding light emission is indicated by white-coloured arrow symbol.

674


The optical depth is given by τ(λ) = κ(λ) × L and it can be reformulated as τ(λ) = κt × N × P(λ) × L by introducing the factor κt κt =

gj e−Ej = k Te e2 λ20 − E −E = k T 1−e ð i j Þ e : f 2 Q ð T Þ 4ε0 me c e

ð7Þ

This factor can be calculated from spectroscopic parameters of the line and the plasma temperature. A threshold value κth t can be used for preselecting emission lines of low self-absorption, κt ≤ κth t [33]. The optical depth also depends on the width FWHM of (optically thin) spectral line, the number density N related to the element concentration, and the optical path length L. It is not possible to use a single threshold value for all elements and their atomic and ionic emission lines. Therefore, we used separate threshold values for the selection of appropriate lines of Fe, Ca, and Mg. In the case of Fe and Ca, we used the same threshold value for Fe I and Fe II lines, and another value for Ca I and Ca II lines, respectively. For Mg, only Mg I lines are detected in the measured wavelength range. The used threshold th values at temperature of 8500 K were κth t (Fe) = 1.7, κt (Mg) = 14.5, − 30 and κth m3]. Table 2 summarizes the t (Ca) = 5.7, in units of [10 selected spectral lines obeying the threshold criterion. For selfabsorption correction the expression (6) can be rewritten as Ithick ðλÞ = Ithin ðλ0 Þ

1−e−τðλ0 ÞP ðλÞ = Pðλ0 Þ

ð8Þ

τðλ0 Þ

with Ithin(λ0) the intensity at the central wavelength λ0 of transition extrapolated to the case of an optically thin line for the same number density of emitters [31]. The optical depth τ(λ0) is maximum at the central wavelength. The line profile P(λ) is dominated by Stark broadening in LIBS plasma, typically, and is described by a Lorentz function P ðλÞ =

Δλthin 4ðλ−λ0 Þ2 + Δλ2thin

ð9Þ

where Δλthin is the FWHM line width of the optically thin line. From Eqs. (8) and (9) the profile of an optically thick line Ithick(λ) can be calculated for different optical thickness τ(λ0). Following the procedure outlined in reference [34], the ratio of spectral width

Table 2 Spectroscopic parameters λ0, Aij, Ei, and gi of neutral (I) and singly ionized (II) atomic lines of Fe, Mg, and Ca used in the CF-LIBS calculation (data from [40]). The parameter κt is calculated for a temperature of 8500 K.

Fe I

Fe II Mg I

Ca I

Ca II

λ0

Aij

Ei

[nm]

[108 s− 1]

[eV]

367.9913 368.7456 370.9246 372.7619 374.3362 376.554 382.4444 387.2501 389.9707 298.482 298.554 333.2146 333.6674 382.9355 516.7322 558.197 560.129 560.285 318.128 373.69

0.0138 0.0801 0.156 0.225 0.26 0.98 0.0283 0.105 0.0258 0.36 0.18 0.102 0.17 0.899 0.113 0.06 0.086 0.14 0.58 1.7

3.3683 4.2204 4.2562 4.2833 4.3013 6.5284 3.441 4.1909 3.2657 5.8232 5.8756 6.4314 6.4314 5.9459 5.1078 4.7435 4.7386 4.7353 7.0472 6.4679

gi

κt [10− 30 m3]

9 9 7 5 3 15 7 5 5 6 4 3 3 3 3 7 5 3 4 2

0.6365 1.1529 1.6568 1.64 1.1068 0.994 1.1821 0.8517 0.7379 0.4158 0.129 0.9398 1.564 14.4119 5.8495 5.4302 5.6132 5.5087 1.3842 3.8391

Rwidth is obtained from calculated FWHM line widths of optically thick lines (Δλthick) and thin lines (Δλthin) Rwidth ðτðλ0 ÞÞ =

Δλthick ≥1: Δλthin

ð10Þ

Numerical integration of intensities Ithick(λ) and Ithin(λ) over the relevant spectral range yields the ratio of intensities Rarea Rarea ðτðλ0 ÞÞ =

Ithick ≤1: Ithin

ð11Þ

In Fig. 4a and b, the calculated spectral line profiles and the ratio of integrated line intensities Rarea and of spectral line widths Rwidth are shown for different optical depth. The calculated values of ratios are in good agreement to the results presented in [31,34]. The correlation of Rarea and Rwidth is shown in Fig. 4c. The dashed line represents the data shown in Fig. 4b and the solid line is a power law approximation according to Ithin ≈ Ithick

Δλthick 0:819 : Δλthin

ð12Þ

This approximation introduces a relative error less than 2.2% and allows for a fast and simple correction of the intensity of optically thick lines. The obtained value for the exponent (0.819) is similar to the value of 0.852 that can be derived from results presented in an earlier publication [34]. The integrated line intensity Ithick and the line width Δλthick are obtained from measured spectra. The line width Δλthin can be calculated by Ne Δλthin ≈ ΔλStark ≈ 2w 1016

ð13Þ

if Stark broadening dominates over Doppler broadening and the Stark broadening parameter w is known [1]. The electron number density is determined from the Hα line profile (Section 3.5). In the case of an unknown Stark broadening parameter, the line width Δλthin can be calculated in an iterative process as described in the next section. 3.5. CF LIBS algorithm The developed algorithm for calibration-free quantitative analysis of LIBS spectra consists of four major parts as shown in the flow diagram in Fig. 5. First, time-resolved measurements of the LIBS spectra and of the plasma plume expansion are recorded. Measured spectra are deconvolved and the length of visible plasma plume is determined [35]. The optical path length in plasma L is assumed to be equal to the length of the visible plume. In the second part, the measured spectra are evaluated and the electron number density Ne, the plasma temperature Te and the relative number densities of species are determined. The absolute number densities of species are calculated assuming that the sum of all ionized atoms is equal to the number density of electrons (quasi-neutrality of plasma). The electron number density is calculated from broadening of the Hα line by FWHA = 0:549nm ×

Ne 10 m−3 23

0:67965

ð14Þ

with FWHA denoting the full width at half area of this hydrogen emission line [36]. The numerical pre-factor (0.549) is assumed to be independent of temperature and electron number density [37]. The Hα emission originated from a contamination of samples by atmospheric humidity. This line was not self-absorbed. The Ne values as calculated from Hα line and from other element lines with known Stark broadening parameter were comparable. For temperature


675

Fig. 5. Flow diagram of developed CF-LIBS algorithm including iterative Saha– Boltzmann analysis of measured LIBS spectra and self-absorption correction, and the calculation of number density of analyzed species.

The left side of Eq. (15) reads 8 > > > > > > >