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Investigation of matrix effects in laser-induced breakdown spectroscopy plasmas of high-alloy steel for matrix and minor elements
Spectrochimica Acta Part B 60 (2005) 1083 – 1091 www.elsevier.com/locate/sab
Investigation of matrix effects in laser-induced breakdown spectroscopy plasmas of high-alloy steel for matrix and minor elementsB Jens Vrenegor*, Reinhard Noll, Volker Sturm Fraunhofer-Institut fu¨r Lasertechnik (ILT), Steinbachstrasse 15, 52074 Aachen, Germany Received 9 December 2004; accepted 12 May 2005 Available online 22 June 2005
Abstract High-alloy steel samples are analysed using laser-induced breakdown spectroscopy (LIBS). A quantitative analysis is carried out for nine elements (Ni, Cr, Cu, Mo, Si, Ti, Mn, Al, C) comparing the influence of single and double pulse excitation and for two different laser burst energies. The laser-induced plasmas are generated with a Nd:YAG laser operating at the fundamental wavelength. Calibrations are carried out with a set of 21 certified high-alloy steel samples including both matrix (concentrations of non-ferrous elements up to 35 wt.%) and minor elements (concentrations up to 6 wt.%). Calibration results are compared by the mean residual deviation. In contrast to papers published so far on LIBS analysis of high-alloy steel, the plasma is generated in a sample stand flushed with argon. The plasma emission is detected timeresolved with a Paschen – Runge spectrometer and with an echelle spectrometer. Electron temperatures are determined using up to 21 atomic lines of iron within a spectral range of 273 – 522 nm. Matrix effects cause mean residual deviations of the calibration curves of 0.02 – 1 wt.% depending on the analyte, single or double pulse excitation and the irradiated laser burst energy. By use of iterative interelement corrections the mean residual deviations are reduced on average by a factor of about two for matrix and minor elements. For the element Cu this value can be improved by a factor of up to four. D 2005 Elsevier B.V. All rights reserved. Keywords: Laser-induced breakdown spectroscopy (LIBS); High-alloy steel; Interelement correction
1. Introduction High-alloy steel grades offer a wide range of material properties with respect to e.g. mechanical strength, corrosion resistance or thermal and electric conductivity tailored to the needs of usage. The constituents of high-alloy steel are mainly the elements Fe, Cr and Ni with a total content of about 95 wt.%. For process control during steelmaking and for identification purposes the chemical composition has to be analysed. The motivation of this work is the economic and technical importance of high-alloy steel in a wide field of industrial applications, home appliances and medical techB This paper was presented at the 3rd International Conference on Laser Induced Plasma Spectroscopy and Applications (LIBS 2004), held in Torremolinos (Ma´laga, Spain), 28 September – 1 October 2004, and is published in the special issue of Spectrochimica Acta Part B, dedicated to that conference. * Corresponding author. Tel.: +49 241 8906 308; fax: +49 241 8906 121. E-mail address: [email protected] (J. Vrenegor).
0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.05.027
nology. The influence of the composition of high-alloy steel grades on the material property is illustrated by the following example. There are nickel alloys, which consist of nickel and iron and have melting temperatures of about 900 -C, whereas the melting temperature of iron and nickel alone is about 1500 -C. For production control of high-alloy steel making processes it is important to analyse the composition of the steel melt, e.g. by taking samples. Laser-induced breakdown spectroscopy (LIBS) is a suitable tool to determine the composition of high-alloy steel samples. Examples for LIBS to analyse steel are given in Refs. [1– 13]. LIBS investigations of high-alloy steel grades were carried out by several groups. For example the influence of different laser wavelengths on the accuracy and precision of analysis has been studied in air at atmospheric pressure for the elements Si, Ti, Nb and Mo [7]. Palanco and Laserna have developed an instrument for a fast quality assessment in the steel industry with sample handling, surface preparation and
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quantitative analysis [1]. The appearance of so-called matrix effects could be reduced by a multivariate calibration. Noll et al. developed a system identifying high-alloy steel grades of pipe fittings in routine industrial operation [6]. LIBS is able to analyse stainless steel samples at high temperatures in air at atmospheric pressure [8]. In a remote LIBS approach stainless steel has been analysed at distances between the plasma and the detection system of more than 10 m [12]. Bassiotis et al. obtained calibration curves for the elements Cr, Ni and Mn in stainless steel samples at atmospheric conditions using internal standardization [16]. Experimental parameters have been optimized to improve the linearities of the calibration curves over a broad range of concentrations. In our study we used a different experimental set-up consisting of an Ar-flushed sample stand and a Paschen – Runge spectrometer having a high spectral resolution in a greater spectral range. We investigated the influence of single and double pulse excitation and different laser burst energies on the mean residual deviation for the quantitative determination of concentrations. Interelement corrections are studied to reduce the influence of matrix effects on the calibration curves.
2. Experimental The experimental set-up is shown in Fig. 1. The laser beam generated by a Q-switched Nd:YAG laser (Continuum, model Surelite I-10, 10 Hz, with double pulse option) working at the fundamental wavelength is guided via a Glan-laser prism and a mirror to a lens focussing the laser beam into an Ar-flushed sample stand onto high-alloy steel samples. The Glan-laser prism is used to attenuate the laser energy while keeping the operational conditions of the laser source constant. The samples are moved during the measurement so that the laser beam propagates over the
sample surface along a circle with a diameter of 3 mm. Thereby the rotating frequency of the sample is about 1 Hz. Hence about 10 laser pulses are irradiated onto the sample during one sample rotation. This leads to reproducible crater geometries over the whole measuring process. The sample rotation approach was compared to the stationary case with no relative movement between laser beam and sample surface, i.e. all laser pulses are irradiated at the same sample location. In the case of sample rotation the progression of the element intensities with increasing laser pulse number is more uniform with a slope of about zero for all laser pulses. The plasma light is detected over a direct light channel with a vacuum Paschen-Runge spectrometer (Model RS 1000 from OBLF, Witten, Germany) without further optical imaging and with a fiber optics and an echelle spectrometer (ESA 3000, LLA, Berlin, Germany). In the Paschen – Runge spectrometer the plasma light is dispersed spectrally covering a spectral range from 178 to 406 nm (grating, 2700 l/ mm) with a spectral resolution of ¨20 pm. The distance of the sample surface to the entrance slit of the spectrometer is ¨300 mm. The plasma signals are detected under the detection angle of a = 10- between the optical axis of the spectrometer and the sample surface. Twenty photomultipliers are located on the Rowland circle (diameter 0.5 m) to detect 19 element lines and the zeroth order signal. The spectral lines installed are listed in Table 1. A signal electronics (multi-channel-integrator electronics MCI, developed at ILT) integrates the signals in programable time windows for each generated plasma. The parameters kept constant for the calibrations and the determination of the plasma parameters are as follows: number of pre-pulses N pp = 50, number of measuring pulses N mp = 300, flow rate of argon through the sample stand 20 l/ min. Both pre-pulses and measuring pulses are focused on the circle during the movement of the sample. Subsequent laser pulses are guided to different sample positions. The
Fig. 1. Schematic view of the experimental set-up. VS = vacuum spectrometer, SE = signal electronics, L= laser, LB = laser beam, PR = Glan-laser prism, M = mirror, FL= focussing lens, ST = argon-flushed sample stand, Ar = inlet, W1 = window of ST, P= laser-induced plasma, FO = fiber optics, ES= echelle spectrometer, Ar OL= outlet, a = plasma detection angle, SM = sample movement, OA= optical axis of VS, W2 = window of VS, E = entrance slit of VS.
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091 Table 1 Spectral lines installed in the Paschen – Runge spectrometer for the analysis of high-alloy steel grades Element
k[nm]
E n [eV]
log(gf)
Al C Cr Cr Cu Fe Fe Mn Mo Ni Si Ti
396.152 193.091 267.715 286.257 324.754 271.441 187.747 293.306 281.615 225.385 251.611 337.280
3.143 7.685 6.179 5.856 3.817 5.553 9.126 5.401 6.071 6.822 4.954 3.687
0.323 0.211 0.36 0.21 0.062 0.44 0.148 0.12 0.51 0.043 0.24 0.18
k emission wavelength, E n excitation energy of upper level, log(gf) logarithm of the absorption oscillator strength [17].
focal length of the plano-convex lens amounts to f = 200 mm and the focal position is Ds = 5 mm within the sample to avoid a gas breakdown in front of the sample surface. The calibrations are carried out with the Paschen – Runge spectrometer in the single (SP) and double pulse (DP) mode each with the laser burst energies E b = 100 and 160 mJ, i.e. E b = 2 50 mJ and 2 80 mJ for the double pulses (with pulse widths at FWHM of s = 6 ns for SP and s = 10 ns for DP). In the double pulse mode the interpulse separation is set to Dt = 30 As. The signals are integrated with a time delay of t delay = 2 As and an integration width of t int = 10 As. Three repetitions on different sample locations are carried out on each sample. For determination of the plasma parameters the echelle spectrometer is used in combination with the Ar-flushed
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sample stand having an optical fiber port. The echelle spectrometer can detect quasi-continuous spectra in the range from 200 to 780 nm with a resolution of about 20 pm. The distance of the plasma to the optical fiber is about 60 mm. The following parameters are taken: SP with a burst energy of E b = 160 mJ, t delay = 6, 10, 20, 30 As and t int = 400 ns. Four samples with a high matrix variation in terms of the elements Fe, Cr and Ni are measured, see Section 4.3. Two repetitions on different sample locations are evaluated for each sample.
3. Samples We analysed 21 certified high-alloy reference steel samples. They are listed in Table 2 giving the reference concentrations of 10 elements. The reference samples are certified reference materials of high-alloy steel from Bureau of Analysed Samples (BAS, Middlesbrough, UK), National Bureau of Standards (NBS, Washington D.C., USA), China National Analysis Center for Iron and Steel (NCS, Beijing, China), Carpenter Technology (Crawley, England), Metimex Reference Material (Pyskowice, Poland), MBH Analytical LTD (Barnet, England), Brammer Standard Company (BSC, Houston, USA) and Research Institute for Ferrous Metallurgy (Budapest, Hungary). Most of these samples represent Cr-/Ni-steel grades. For all samples the iron concentration is greater than 42 wt.%, the chromium concentration is less than 30 wt.% and the nickel concentration is less than 35 wt.%. The concentrations of the minor elements lie below 6 wt.% for Cu and for the other elements below 3 wt.%. The samples were prepared by
Table 2 Composition of the reference samples of high-alloy steel in wt.% Reference sample
Fe
Cr
Ni
C
Si
Mn
Mo
Cu
Al
Ti
CRM S 15 CRM S 19 NBS SRM C 1288 NCS HS 23702-1 NCS HS 23702-2 NCS HS 23702-3 NCS HS 23702-4 NCS HS 23702-5 NCS HS 23702-6 NCS HS 23702-7 ECISS CRM 289-1 Metimex RM MW 27 Metimex RM MW 37 BSC RM B.S. 184A MBH RM PH 1 MBH RM PH 2 MBH RM PH 3 BSC RM B.S. 85D BSC RM B.S. 179A Carpenter RM CT 312 BAS CRM 407/2 Mean
74.0 76.1 42.8 71.6 72.7 71.9 70.7 70.7 71.4 70.3 55.4 45.2 58.9 75.4 73.3 72.8 71.6 67.7 61.1 58.3 93.6 67.9
16.70 7.00 19.55 15.36 12.46 9.32 7.40 17.16 20.76 18.90 14.64 15.57 25.00 12.66 16.10 16.70 15.13 17.09 25.45 29.80 3.03 16.0
3.90 12.80 29.30 10.35 11.52 13.12 16.41 9.05 6.93 7.82 24.68 35.23 12.26 8.34 5.10 3.79 3.16 10.03 5.84 8.93 0.53 11.4
0.043 0.260 0.056 0.061 0.164 0.241 0.184 0.096 0.017 0.101 0.049 0.230 0.250 0.035 0.094 0.070 0.150 0.049 0.017 0.126 0.490 0.1
0.260 2.320 0.410 0.663 0.413 0.960 0.920 0.654 0.171 1.080 0.531 1.950 1.100 0.080 0.180 0.510 1.940 0.550 0.440 0.460 0.660 0.8
0.380 0.320 0.830 0.644 0.981 1.980 1.570 0.730 0.156 0.356 1.016 1.750 1.550 0.060 1.750 0.890 0.440 1.690 1.040 1.600 0.195 0.9
2.460 0.110 2.830 0.620 0.350 0.690 0.500 0.260 0.079 0.170 1.102 n.s. 0.340 2.200 0.160 0.940 0.780 0.590 3.240 0.220 0.830 0.9
1.540 0.190 3.720 0.152 0.363 0.276 0.303 0.126 0.049 0.098 0.000 0.000 0.050 0.041 3.120 4.110 6.280 0.450 1.940 0.150 0.397 1.1
n.s. n.s. 0.003 0.044 0.074 0.038 0.240 0.260 0.034 0.200 0.199 n.s. n.s. 1.000 n.s. n.s. n.s. 0.130 0.009 0.010 0.040 0.2
n.s. 0.048 0.012 0.072 0.210 0.510 1.030 0.570 0.310 0.710 2.010 n.s. n.s. 0.051 n.s. n.s. n.s. 0.480 0.006 0.110 n.s. 0.4
n.s. = concentration value is not specified.
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grinding with Al2O3-grinding paper, grain size 60. The high matrix variation complicates the LIBS analysis as reported in Ref. [1]. Possible reasons can be spectral interferences from the elements nickel, iron and chromium and the wide range of material properties, causing so called matrix effects.
4. Results and discussion 4.1. Analytical figures of merit The calibrations are evaluated both for absolute and standardized intensities. For the latter case the analyte intensities are divided by the intensity of the Fe 271.4 nmline, used as internal standard. The concentration c or concentration ratios cˆ = c analyte / c reference are functions of the corresponding intensities I or intensity ratios Iˆ = I analyte / I reference. For the calibration functions the mean intensity values , averaged over three repetitions and second order regressions are evaluated, see Eqs. (1) and (2): ci ¼ a0;i þ a1;i I < Ii > þ a2;i I < Ii >2
ð1Þ
cˆ i ¼ b0;i þ b1;i I < Iˆ i > þ b2;i I < Iˆ i >2
ð2Þ
where a 0,i , a 1,i , a 2,i , b 0,i , b 1,i and b 2,i are the regression coefficients of the second order regressions of element i and , is the mean intensity value, intensity ratio of element i averaged over three measurements at one sample. A measurement on one sample location comprises N mp = 300 laser bursts. As a figure of merit for the accuracy the mean residual deviations of ten elements R(i) are determined as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP 2 u Ns u ci;reference;s ci;measured;s t s¼1 ð3Þ RðiÞ ¼ Ns where i is the element, s the sample, N s the total number of measured samples; c i measured,s and c i, reference,s are the concentrations of element i and sample s (wt.%) determined with LIBS and the reference concentrations. The precision is defined as the mean relative standard deviations of the intensity ratios of three replicate measurements:
RSD < Iˆ i >
Ns P
¼
s¼1
RSD < Iˆ i > s Ns
ð4Þ
4.2. Calibrations with high-alloy reference samples 4.2.1. Influence of laser burst mode and laser energy Fig. 2 represents four calibration curves for the element Cr. Two burst energies each for single and double pulses are used. Obviously the differences between the double and
Fig. 2. Calibration curve for Chromium for single (squares) and double pulses (triangle).
single pulse calibrations are greater than the differences concerning the different laser burst energies. The calibrations with double pulses show greater saturation effects than the corresponding single pulse calibrations. However, the sensitivity in the low concentration range is higher than the one for single pulses. A similar result was found for lowalloy steel samples, where detection limits can be improved by use of double pulses [6]. The ablation rates are higher for double pulses than for single pulses of the same laser energy [3]. The same behaviour can be seen for the element lines of nickel, copper, manganese, silicon and titanium. These elements are characterized by concentrations higher than 1 wt.%. Fig. 2 shows that for concentration ratios c Cr / c Fe > 0.3, the deviations of the data points from the calibration curve increase. Two of the samples with a high Cr concentration have for example a relatively high Ni concentration, see samples NBS SRM C 1288 and Metimex MW 27 in Table 2. This is an indication that high concentrations of other elements have an influence on the evaporation and excitation processes in the laser-induced plasma. The quantitative influence will be estimated in the Sections 4.2.2– 4.2.4. 4.2.2. Calibration in absolute intensities In this section calibrations are studied using absolute intensities. Fig. 3 shows the copper calibration curve. Copper is an element with a small residual value of R(Cu) = 0.011 wt.% in the single pulse mode and for E b = 160 mJ. Concerning the mean copper concentration of 1.1 wt.% this corresponds to a relative accuracy of 1.0%. Table 3 lists the mean residual deviations R(i) of 10 element lines. The elements are sorted by their concentration range Dc. For chromium two element lines, Cr 267.71 nm and Cr 286.25 nm are evaluated. Because not all of the reference samples have for all elements specified concentration values for all elements the number of regarded samples varies. In the single pulse mode for most of the elements except for Cu there is no significant difference
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091
Fig. 3. Calibration curve for Copper in the single pulse mode (a). RSD(Iˆ ) = 0.9%. R(Cu) = 0.011 wt.%. Absolute difference between the LIBS concentration and the reference concentration vs. the reference concentration (b).
between the calibrations for the two laser burst energies. In spite of that the residuals in the double pulse mode are significantly greater especially for the matrix elements Cr and Ni, but also for the minor elements Cu and Mo. The mean residual values for each element in the single pulse mode are compared with those in the double pulse mode.
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Fig. 4. Calibration curve for nickel in the single pulse mode (a). Absolute difference between the LIBS concentration and the reference concentration vs. the reference concentration (b).
Considering the four different parameter sets single pulses lead to smaller residuals for the element lines Ni 225.38 nm, Cr 267.71 nm, Cr 286.25 nm, Cu 324.75 nm and Mo 281.61 nm. The ratio / is 2. In spite of that the chosen double pulse parameters show better results for the elements Si, Ti, Mn, Al and C by a factor of about 0.5 – 0.8. Comparing the four calibration parameter sets there is no parameter set that is the best for all elements.
Table 3 Mean residual deviations R(i) of 10 element lines for two different laser burst modes and two different laser burst energies and the ratio of residuals (DP to SP) using absolute intensities Element
Samplesa
Dc [wt.%]
R(i)SP [wt.%]
R(i)DP [wt.%]
/
100 mJ
160 mJ
100 mJ
160 mJ
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
21 21 21 19 20 21 14 21 14 21
34.7 29.7 29.7 6.2 3.2 2.2 2.0 1.9 1.0 0.5
0.39 0.63 0.50 0.038 0.055 0.129 0.042 0.13 0.019 0.020
0.37 0.62 0.57 0.011 0.050 0.101 0.048 0.12 0.029 0.023
0.87 1.45 1.12 0.143 0.086 0.051 0.019 0.07 0.018 0.014
1.59 2.09 1.63 0.127 0.127 0.070 0.031 0.11 0.023 0.018
Dc = concentration range of the reference samples used for the calibration curve, SP= single pulse, DP= double pulses. a For some elements not all of the 21 available reference samples are used, if the concentration is not specified for these elements.
3.2 2.8 2.6 6.0 2.0 0.5 0.6 0.7 0.8 0.7
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4.2.3. Calibration with standardized intensities Besides the evaluation with absolute intensities calibrations are carried out by dividing the absolute analyte intensities to the Fe 271.44 nm-line intensity as an internal standard. By measuring all the elements that can be contained in the steel samples the real content of the elements can be calculated in wt.% [15]. Figs. 4a and 5 show calibration curves for the elements Ni and Si. The coefficient of determinations is close to one which results in good accuracies, see Table 4. Fig. 4a represents the calibration curve for nickel in the single pulse mode and for E b = 160 mJ which is the calibration with the smallest R(Ni)-value and the smallest RSD()-value. The mean residual deviation amounts to 0.13 wt.%. Relating to the mean Nickel concentration value of 11.1 wt.% this means a relative accuracy of 1.2%. The precision of three replicate measurements averaged over all samples is 0.3%. Fig. 4b illustrates the R(Ni)-values in a different plot to visualize the differences of the measured LIBS concentrations to the reference concentrations. Most of the residuals amount to lower than 0.1 wt.%, but all are lower than 0.3 wt.%. In contrast to nickel silicon is an element for which double pulses of 100 mJ burst energy have the smallest R(Si)-values comparing the four parameter sets, see Fig. 5. The residual amounts to R(Si) = 0.041 wt.% with r 2 = 0.997. The precision is RSD() = 1.4%. Table 4 summarizes the results of the calibrations using internal standardization. The ratios / for all regarded elements except for Al exhibit the same tendencies (> 1.0 or <1.0) as for absolute intensities. There is an improvement of R(i) for Ni by a factor of about 3 – 0.13 wt.% for single pulses with E b = 160 mJ. In the double pulse mode the internal standardization leads to a significant reduction of the R(i)-values of Ni, Cr and Mo for both laser burst energies by factors between 1.4 and 4.2. The -values of the elements Si, Ti, Mn and C are in the same order of magnitude. In comparison to the calibrations with absolute intensities the residuals are
Table 4 Mean residual deviations R(i) of 10 element lines for two different laser burst modes and two different laser burst energies using internal standardization Element
R(i)SP [wt.%]
R(i)DP [wt.%]
/
100 mJ
160 mJ
100 mJ
160 mJ
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
0.17 1.04 0.50 0.060 0.040 0.150 0.063 0.144 0.031 0.020
0.13 0.91 0.48 0.042 0.038 0.112 0.065 0.134 0.042 0.025
0.37 1.04 0.61 0.251 0.055 0.041 0.018 0.085 0.031 0.012
0.38 1.64 0.66 0.337 0.038 0.058 0.020 0.050 0.050 0.016
2.5 1.4 1.3 5.7 1.2 0.4 0.3 0.5 1.1 0.6
Same sample set as in Table 3.
improved for six element lines (Ni, Cr 286, Mo, Si, Mn and C) by about 50% comparing the smallest R(i)-values for the four parameter sets studied. Table 5 lists the precision of the intensity ratios of three replicate measurements in terms of RSD() for ten element lines. The precision for the elements Ni, Cr, Cu and Mo is in the range from 0.3% to 1.2%. In contrast to that the RSD-values of the other elements cover a range from 1.1% to 6.2%. Possible reasons for this behaviour are the different properties of the analyte element lines compared to the internal standard line Fe 271.4 nm. The greatest difference between the upper energy levels of the analyte line and the reference line occurs for the element Al with DE n = 2.4 eV. Furthermore the spectral distance is high with Dk = 396.152– 271.441 nm = 124.711 nm. These facts lead probably to the highest RSD-values for Al. Bassiotis et al. determined the RSD values for Mn for eight high-alloy steel samples [16]. Five sample positions each irradiated with 150 laser pulses were measured. With our set-up averaging over the RSD values of 20 samples the mean values amount to 1.6% for single pulses and for
Table 5 Relative standard deviations RSD() in % for nine elements using 10 element lines and internal standardization
Fig. 5. Calibration curve for silicon in the double pulse mode.
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
RSD()SP [%]
RSD()DP [%]
100 mJ
160 mJ
100 mJ
160 mJ
0.3 0.7 0.6 0.7 0.7 3.8 3.5 2.3 5.8 3.3
0.3 0.4 0.5 0.7 0.6 2.5 3.0 1.6 5.3 2.1
0.4 0.7 0.4 1.2 0.8 1.4 2.6 0.8 6.2 4.1
0.4 0.4 0.3 1.1 0.9 1.1 2.1 0.6 2.4 1.9
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091
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line intensities. The multiplicative factors take into account different excitation conditions in the high-alloy plasmas. cˆ i ¼ b0;i þ b1;i I Iˆ i þ b2;i I Iˆ 2i þ
X
kadd;j I cˆ corr;j
ð5Þ
j; ji
cˆ i ¼ b0;i þ b1;i I Iˆ i þ b2;i I Iˆ 2i I Pj;ji 1 þ kmult;j Iˆc corr; j
Fig. 6. Interelement correction of the calibration with the Cr 267.7 nm-line. Single pulses, E b = 160 mJ.
E b = 160 mJ and 0.6% for double pulses and for E b = 160 mJ. Compared to the 3.1% reported in Ref. [16] this is a reduction by a factor of 2 for single pulses and by a factor of 5 for double pulses. As already indicated in Fig. 2 the chromium calibration curve shows increasing residual values for high Cr concentrations. Deviations observed at high concentrations are significant because of the high precision of the measured intensity ratios ( 0.7% cf. Table 5). In previous studies it has been shown that multivariate calibrations can reduce the residual values [1]. In this paper we studied interelement corrections to improve the accuracy of analysis. 4.2.4. Interelement corrections In contrast to multivariate calibrations interelement correction is an iterative method. The residuals R(i) can be corrected additively, see Eq. (5), and multiplicatively, see Eq. (6), considering spectral interferences and matrix effects. The additive factors correct the superposition of
ð6Þ
where c corr,j is the concentration ratio of element j to correct the residuals additively or multiplicatively, k add,j is an additive correction factor for the element j, k mult,j is a multiplicative correction factor for the element j. For example the correction for Cr can be started multiplicatively with nickel. Thereby a regression of the Cr residuals of all calibrated samples is made with the corresponding Ni concentration ratios. The aim is to get a correction factor to calculate the residuals. Then the reduced residuals are taken for making a regression with the measured concentrations of another element considered as a disturbing factor. These corrections are continued with other elements until no further improvement is achieved. Then the absolute Cr concentrations can be calculated with the elemental concentration of the calibration curves of those elements which are contained in the samples [15]. Fig. 6 shows the differences of the measured Cr concentration to the reference concentrations versus the reference concentration, where the bold squares represent uncorrected and open squares the corrected values. The Cr 267.7 nm residual is reduced by a factor of 3 taking into account multiplicative corrections with the elements Ni and Ti for single pulses and 160 mJ. The coefficient of determination can be improved from r 2 = 0.992 to r 2 = 0.999. Table 6 lists all multiplicatively and additively corrected residual values R(i) for all four parameter sets and for 10 element lines. In the column ‘‘disturbing elements‘‘ those elements are listed which have significant influence to reduce the residuals. The sign F*_ means that this element is
Table 6 Additive and multiplicative interelement corrections for ten elements Element
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
Disturbing elements
*Cr, *Mo, *Ti, *C *Ni, *Ti *Ni, *Ti *Si, *Mo + Cr, *Ni, *Cu, *Ti + Cr, *Ti *Si *Ti *Ni, +Mo, *Si *Si
R(i)SP, corr [wt.%]
R(i)DP, corr [wt.%]
Factor of improvementa
100 mJ
100 mJ
SP
0.07 0.31 0.33 0.017 0.021 0.112 0.051 0.085 0.011 0.020
160 mJ
0.08 0.30 0.32 0.010 0.020 0.082 0.051 0.085 0.011 0.024
0.35 0.29 0.34 0.086 0.041 0.043 0.018 0.084 0.011 0.007
160 mJ
0.31 0.81 0.37 0.142 0.026 0.053 0.020 0.042 0.017 0.009 Mean
Corrected R(i) in wt.% and factors of improvement. Same sample set as in Table 4. a Factor of improvement = R(i)uncorr / R(i)corr, where R(i)uncorr are the values from Table 4.
DP
100 mJ
160 mJ
100 mJ
160 mJ
2.7 3.4 1.5 3.5 1.9 1.3 1.2 1.7 2.8 1.0 2.1
1.6 3.0 1.5 4.2 1.9 1.4 1.3 1.6 3.9 1.0 2.1
1.1 3.6 1.8 2.9 1.3 0.9 1.0 1.0 2.8 1.8 1.8
1.2 2.0 1.8 2.4 1.5 1.1 1.0 1.2 2.9 1.8 1.7
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used for a multiplicative correction, whereas the sign F+_ means an additive correction. In the last four columns the factors of improvement are listed. By interelement corrections the mean residual deviations R(i) can be reduced on average for all ten element lines by a factor of 1.7– 2.1. The greatest improvement is achieved for Cu by a factor of about 4 in comparison to the uncorrected residuals (E b = 160 mJ, single pulses). One interesting question is whether the residuals can be explained with differences in the plasma parameters due to the wide range of material properties of the samples. In the next chapter the plasma parameters electron density and electron temperature are determined measuring samples with a high variation of the iron, chromium and nickel content. 4.3. Plasma parameters The plasma parameters are determined for the plasmas of three to four samples with a high difference concerning the iron concentration. The plasmas are detected with an echelle spectrometer. Four time delays t delay = 6, 10, 20 and 30 As are studied. The spectra for the burst energy E b = 160 mJ in the single pulse mode are evaluated. The electron densities are calculated by the Stark-broadening of the Fe I-line 492.05 nm. The line profiles are estimated by a Lorentz fit. Three high-alloy steel samples and one pure iron sample are measured covering iron concentrations in the range between 43 and 99 wt.%. Fig. 7 shows the determined electron density N e as a function of the delay time. The errors of electron densities N e are between 4% and 10%. No significant difference of electron densities between the samples is observed. Besides the electron densities the electron temperatures are determined for atomic lines of Fe. The line intensities are measured assuming that local thermodynamic equilibrium (LTE) conditions are satisfied in the plasma. The echelle
Fig. 7. Electron densities N e for four time delays and four different samples showing a high matrix variation, Fe I-line 492.05 nm. Samples: C 1288 (43 wt.% Fe), MW 37 (59 wt.% Fe), B.S. 184 (75 wt.% Fe), pure iron (99.99 wt.% Fe).
Table 7 Line selection for the Boltzmann-plot No.
k [nm]
log(gf)
E n [eV]
No.
k [nm]
log(gf)
E n [eV]
1 2 3 4 5 6 7 8 9 10 11
273.36 278.81 296.69 299.95 356.54 363.15 364.78 371.99 374.95 404.58 406.36
0.06 0.02 0.404 0.47 0.19 0.036 0.194 0.431 0.161 0.28 0.07
5.39 5.30 4.18 4.99 4.43 4.37 4.31 3.33 4.22 4.55 4.61
12 13 14 15 16 17 18 19 20 21
407.17 411.85 413.47 419.91 421.94 427.18 430.79 432.58 438.35 522.72
0.022 0.28 0.49 0.25 0.12 0.164 0.07 0.01 0.2 0.969
4.65 6.58 5.83 6.00 6.51 4.39 4.43 4.47 4.31 3.93
Twenty-one atomic iron lines from 273 to 522 nm.
offers a wide spectral range for the line selection of the Boltzmann-plot, 21 Fe I-lines are evaluated, see Table 7. For the Boltzmann-plot the line shapes are fitted by Lorentz profiles and from these fits the integrals of the line profiles are determined. Fig. 8(a) shows a typical Boltzmann-plot for the time delay t delay = 20 As and for three different high-alloy steel samples. The transition properties of the lines are taken from the Kurucz data base [17]. Despite the high variation of the iron
Fig. 8. Boltzmann-plot with 21 Fe I-lines (a). Relative error of the slopes about 7%. Electron temperatures Te for three time delays and three highalloy steel samples (b).
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concentration the slopes are similar. The errors of the slopes are taken as the error of the electron temperatures. The significance for the evaluation is enlarged by regarding many lines. These lines are chosen because in the concentration range between 43 and 100 wt.% there is a linear relationship of the intensities versus the concentration. So self-absorption effects can be neglected. The upper energy levels are nearly uniformly distributed from E n = 3.4 eV to about 6.5 eV. The electron temperatures are evaluated at three time delays: t delay = 6, 20 and 30 As. The Fe I electron temperature decays from Te = 10300 K after 6 As to Te = 7600 K after 30 As. The value for t delay = 6 As is comparable with temperatures reported so far [14]. But the values at later times lie about 1000 K higher. The errors of the electron temperatures are about 7%. No significant difference between the samples is observed. So the origin for matrix effects—as, e.g. observed for Cr— does not show up in a significant way looking at the electron densities and electron temperatures. The reason for this might be that the effect of improvement by interelement corrections is in the same order of magnitude as the error of determination of the plasma parameters. For example the Cr 267.71 nm residual can be reduced by 0.6 –0.3 wt.%, see Table 6. Relating the value of the absolute improvement 0.6 wt.% to the mean Cr concentration of 16.0 wt.% of the measured sample set this corresponds to an improvement by about 4%.
5. Conclusions Calibrations were carried out for nine elements with single and double laser bursts and two different laser burst energies. The residuals are dependent on the laser burst mode. Single pulse calibrations have the smallest residuals for the matrix elements Cr and Ni and for the minor elements Cu and Mo, double pulses for the elements Si, Ti, Mn and C. With our set-up precisions of intensity ratios are achieved in terms of RSD values lower than 1.0% for most analytes. Interelement corrections can improve the LIBS analysis on high-alloy steel samples on average by a factor of two for matrix and minor elements. As a trend interelement corrections reduce the residuals stronger for single pulses than for double pulses. Plasma parameters like electron density and electron temperature show no significant difference for a strong variation of the iron concentration in the range of 40 –75 wt.%. Maybe changes of the plasma state exist but cannot be detected experimentally taking into account that the relative errors of determination of the plasma parameters is of the same order of magnitude as the interelement corrections.
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References [1] S. Palanco, J.J. Laserna, Full automation of a laser-induced breakdown spectrometer for quality assessment in the steel industry with sample handling, surface preparation and quantitative analysis capabilities, J. Anal. At. Spectrom. 15 (2000) 1321 – 1327. [2] C. Aragon, J. Aguilera, J. Campus, Improvements in quantitative analysis of steel composition by laser-induced breakdown spectroscopy at atmospheric pressure using an infrared Nd:YAG laser, Appl. Spectrosc. 47 (1993) 606 – 608. [3] R. Sattmann, V. Sturm, R. Noll, Laser-induced breakdown spectroscopy of steel samples using multiple Q-switch Nd:YAG laser pulses, J. Phys., D, Appl. Phys. 28 (1995) 2181 – 2187. [4] V. Sturm, L. Peter, R. Noll, Steel analysis with laser-induced breakdown spectrometry in the vacuum ultraviolet, Appl. Spectrosc. 54 (2000) 1275 – 1278. [5] M. Hemmerlin, R. Meilland, H. Falk, P. Wintjens, L. Paulard, Application of vacuum ultraviolet laser-induced breakdown spectrometry for steel analysis—comparison with spark-optical emission spectrometry figures of merit, Spectrochim. Acta, Part B: Atom. Spectrosc. 56 (2001) 661 – 669. [6] R. Noll, H. Bette, A. Brysch, M. Kraushaar, I. Mo¨nch, L. Peter, V. Sturm, Laser-induced breakdown spectrometry—applications for production control and quality assurance in the steel industry, Spectrochim. Acta, Part B: Atom. Spectrosc. 56 (2001) 637 – 649. [7] L.M. Cabalin, D. Romero, C.C. Garcia, J.M. Baena, J.J. Laserna, Time-resolved laser-induced plasma spectrometry for determination of minor elements in steelmaking process samples, Analyt. Bioanalyt. Chem. 372 (2002) 352 – 359. [8] S. Palanco, L.M. Cabalin, D. Romero, J.J. Laserna, Infrared laser ablation and atomic emission spectrometry of stainless steel at high temperatures, J. Anal. At. Spectrom. 14 (1999) 1883 – 1887. [9] M. Khater, J. Costello, E. Kennedy, Optimization of the emission characteristics of laser-produced steel plasmas in the vacuum ultraviolet: significant improvements in carbon detection limits, Appl. Spectrosc. 56 (2002) 970 – 984. [10] M. Corsi, G. Cristoforetti, M. Hidalgo, D. Iriarte, S. Legnaioli, V. Palleschi, A. Salvetti, E. Tognoni, Temporal and spatial evolution of a laser-induced plasma from a steel target, Appl. Spectrosc. 57 (2003) 715 – 721. [11] L. Peter, V. Sturm, R. Noll, Liquid steel analysis with laser-induced breakdown spectrometry in the vacuum ultraviolet, Appl. Opt. 42 (2003) 6199 – 6204. [12] C. Lopez-Moreno, S. Palanco, J.J. Laserna, Remote laser-induced plasma spectrometry for elemental analysis of samples of environmental interest, J. Anal. At. Spectrom. 19 (2004) 1479 – 1484. [13] V. Sturm, J. Vrenegor, R. Noll, M. Hemmerlin, Bulk analysis of steel samples with surface scale layers by enhanced laser ablation and LIBS analysis of C, P, S, Al, Cr, Cu, Mn and Mo, J. Anal. At. Spectrom. 19 (2004) 451 – 456. [14] J.A. Aguilera, C. Aragon, A comparison of the temperatures and electron densities of laser-produced plasmas obtained in air, argon, and helium at atmospheric pressure, Appl. Phys., A 69 (Suppl.) (1999) S475 – S478. [15] K. Slickers, Automatic Atomic Emission Spectroscopy, 2nd ednR, Bru¨hlsche Universita¨tsdruckerei, Giessen, 1992. [16] I. Bassiotis, A. Diamantopoulou, A. Giannoudakos, F. RoubaniKalantzopoulou, M. Kompitsas, Effects of experimental parameters in quantitative analysis of steel alloy by laser-induced breakdown spectrometry, Spectrochim. Acta, Part B: Atom. Spectrosc. 56 (2001) 671 – 683. [17] Kurucz data base. http://cfa-www.harvard.edu/amdata/ampdata/ kurucz23/sekur.html.
Investigation of matrix effects in laser-induced breakdown spectroscopy plasmas of high-alloy steel for matrix and minor elementsB Jens Vrenegor*, Reinhard Noll, Volker Sturm Fraunhofer-Institut fu¨r Lasertechnik (ILT), Steinbachstrasse 15, 52074 Aachen, Germany Received 9 December 2004; accepted 12 May 2005 Available online 22 June 2005
Abstract High-alloy steel samples are analysed using laser-induced breakdown spectroscopy (LIBS). A quantitative analysis is carried out for nine elements (Ni, Cr, Cu, Mo, Si, Ti, Mn, Al, C) comparing the influence of single and double pulse excitation and for two different laser burst energies. The laser-induced plasmas are generated with a Nd:YAG laser operating at the fundamental wavelength. Calibrations are carried out with a set of 21 certified high-alloy steel samples including both matrix (concentrations of non-ferrous elements up to 35 wt.%) and minor elements (concentrations up to 6 wt.%). Calibration results are compared by the mean residual deviation. In contrast to papers published so far on LIBS analysis of high-alloy steel, the plasma is generated in a sample stand flushed with argon. The plasma emission is detected timeresolved with a Paschen – Runge spectrometer and with an echelle spectrometer. Electron temperatures are determined using up to 21 atomic lines of iron within a spectral range of 273 – 522 nm. Matrix effects cause mean residual deviations of the calibration curves of 0.02 – 1 wt.% depending on the analyte, single or double pulse excitation and the irradiated laser burst energy. By use of iterative interelement corrections the mean residual deviations are reduced on average by a factor of about two for matrix and minor elements. For the element Cu this value can be improved by a factor of up to four. D 2005 Elsevier B.V. All rights reserved. Keywords: Laser-induced breakdown spectroscopy (LIBS); High-alloy steel; Interelement correction
1. Introduction High-alloy steel grades offer a wide range of material properties with respect to e.g. mechanical strength, corrosion resistance or thermal and electric conductivity tailored to the needs of usage. The constituents of high-alloy steel are mainly the elements Fe, Cr and Ni with a total content of about 95 wt.%. For process control during steelmaking and for identification purposes the chemical composition has to be analysed. The motivation of this work is the economic and technical importance of high-alloy steel in a wide field of industrial applications, home appliances and medical techB This paper was presented at the 3rd International Conference on Laser Induced Plasma Spectroscopy and Applications (LIBS 2004), held in Torremolinos (Ma´laga, Spain), 28 September – 1 October 2004, and is published in the special issue of Spectrochimica Acta Part B, dedicated to that conference. * Corresponding author. Tel.: +49 241 8906 308; fax: +49 241 8906 121. E-mail address: [email protected] (J. Vrenegor).
0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.05.027
nology. The influence of the composition of high-alloy steel grades on the material property is illustrated by the following example. There are nickel alloys, which consist of nickel and iron and have melting temperatures of about 900 -C, whereas the melting temperature of iron and nickel alone is about 1500 -C. For production control of high-alloy steel making processes it is important to analyse the composition of the steel melt, e.g. by taking samples. Laser-induced breakdown spectroscopy (LIBS) is a suitable tool to determine the composition of high-alloy steel samples. Examples for LIBS to analyse steel are given in Refs. [1– 13]. LIBS investigations of high-alloy steel grades were carried out by several groups. For example the influence of different laser wavelengths on the accuracy and precision of analysis has been studied in air at atmospheric pressure for the elements Si, Ti, Nb and Mo [7]. Palanco and Laserna have developed an instrument for a fast quality assessment in the steel industry with sample handling, surface preparation and
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quantitative analysis [1]. The appearance of so-called matrix effects could be reduced by a multivariate calibration. Noll et al. developed a system identifying high-alloy steel grades of pipe fittings in routine industrial operation [6]. LIBS is able to analyse stainless steel samples at high temperatures in air at atmospheric pressure [8]. In a remote LIBS approach stainless steel has been analysed at distances between the plasma and the detection system of more than 10 m [12]. Bassiotis et al. obtained calibration curves for the elements Cr, Ni and Mn in stainless steel samples at atmospheric conditions using internal standardization [16]. Experimental parameters have been optimized to improve the linearities of the calibration curves over a broad range of concentrations. In our study we used a different experimental set-up consisting of an Ar-flushed sample stand and a Paschen – Runge spectrometer having a high spectral resolution in a greater spectral range. We investigated the influence of single and double pulse excitation and different laser burst energies on the mean residual deviation for the quantitative determination of concentrations. Interelement corrections are studied to reduce the influence of matrix effects on the calibration curves.
2. Experimental The experimental set-up is shown in Fig. 1. The laser beam generated by a Q-switched Nd:YAG laser (Continuum, model Surelite I-10, 10 Hz, with double pulse option) working at the fundamental wavelength is guided via a Glan-laser prism and a mirror to a lens focussing the laser beam into an Ar-flushed sample stand onto high-alloy steel samples. The Glan-laser prism is used to attenuate the laser energy while keeping the operational conditions of the laser source constant. The samples are moved during the measurement so that the laser beam propagates over the
sample surface along a circle with a diameter of 3 mm. Thereby the rotating frequency of the sample is about 1 Hz. Hence about 10 laser pulses are irradiated onto the sample during one sample rotation. This leads to reproducible crater geometries over the whole measuring process. The sample rotation approach was compared to the stationary case with no relative movement between laser beam and sample surface, i.e. all laser pulses are irradiated at the same sample location. In the case of sample rotation the progression of the element intensities with increasing laser pulse number is more uniform with a slope of about zero for all laser pulses. The plasma light is detected over a direct light channel with a vacuum Paschen-Runge spectrometer (Model RS 1000 from OBLF, Witten, Germany) without further optical imaging and with a fiber optics and an echelle spectrometer (ESA 3000, LLA, Berlin, Germany). In the Paschen – Runge spectrometer the plasma light is dispersed spectrally covering a spectral range from 178 to 406 nm (grating, 2700 l/ mm) with a spectral resolution of ¨20 pm. The distance of the sample surface to the entrance slit of the spectrometer is ¨300 mm. The plasma signals are detected under the detection angle of a = 10- between the optical axis of the spectrometer and the sample surface. Twenty photomultipliers are located on the Rowland circle (diameter 0.5 m) to detect 19 element lines and the zeroth order signal. The spectral lines installed are listed in Table 1. A signal electronics (multi-channel-integrator electronics MCI, developed at ILT) integrates the signals in programable time windows for each generated plasma. The parameters kept constant for the calibrations and the determination of the plasma parameters are as follows: number of pre-pulses N pp = 50, number of measuring pulses N mp = 300, flow rate of argon through the sample stand 20 l/ min. Both pre-pulses and measuring pulses are focused on the circle during the movement of the sample. Subsequent laser pulses are guided to different sample positions. The
Fig. 1. Schematic view of the experimental set-up. VS = vacuum spectrometer, SE = signal electronics, L= laser, LB = laser beam, PR = Glan-laser prism, M = mirror, FL= focussing lens, ST = argon-flushed sample stand, Ar = inlet, W1 = window of ST, P= laser-induced plasma, FO = fiber optics, ES= echelle spectrometer, Ar OL= outlet, a = plasma detection angle, SM = sample movement, OA= optical axis of VS, W2 = window of VS, E = entrance slit of VS.
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091 Table 1 Spectral lines installed in the Paschen – Runge spectrometer for the analysis of high-alloy steel grades Element
k[nm]
E n [eV]
log(gf)
Al C Cr Cr Cu Fe Fe Mn Mo Ni Si Ti
396.152 193.091 267.715 286.257 324.754 271.441 187.747 293.306 281.615 225.385 251.611 337.280
3.143 7.685 6.179 5.856 3.817 5.553 9.126 5.401 6.071 6.822 4.954 3.687
0.323 0.211 0.36 0.21 0.062 0.44 0.148 0.12 0.51 0.043 0.24 0.18
k emission wavelength, E n excitation energy of upper level, log(gf) logarithm of the absorption oscillator strength [17].
focal length of the plano-convex lens amounts to f = 200 mm and the focal position is Ds = 5 mm within the sample to avoid a gas breakdown in front of the sample surface. The calibrations are carried out with the Paschen – Runge spectrometer in the single (SP) and double pulse (DP) mode each with the laser burst energies E b = 100 and 160 mJ, i.e. E b = 2 50 mJ and 2 80 mJ for the double pulses (with pulse widths at FWHM of s = 6 ns for SP and s = 10 ns for DP). In the double pulse mode the interpulse separation is set to Dt = 30 As. The signals are integrated with a time delay of t delay = 2 As and an integration width of t int = 10 As. Three repetitions on different sample locations are carried out on each sample. For determination of the plasma parameters the echelle spectrometer is used in combination with the Ar-flushed
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sample stand having an optical fiber port. The echelle spectrometer can detect quasi-continuous spectra in the range from 200 to 780 nm with a resolution of about 20 pm. The distance of the plasma to the optical fiber is about 60 mm. The following parameters are taken: SP with a burst energy of E b = 160 mJ, t delay = 6, 10, 20, 30 As and t int = 400 ns. Four samples with a high matrix variation in terms of the elements Fe, Cr and Ni are measured, see Section 4.3. Two repetitions on different sample locations are evaluated for each sample.
3. Samples We analysed 21 certified high-alloy reference steel samples. They are listed in Table 2 giving the reference concentrations of 10 elements. The reference samples are certified reference materials of high-alloy steel from Bureau of Analysed Samples (BAS, Middlesbrough, UK), National Bureau of Standards (NBS, Washington D.C., USA), China National Analysis Center for Iron and Steel (NCS, Beijing, China), Carpenter Technology (Crawley, England), Metimex Reference Material (Pyskowice, Poland), MBH Analytical LTD (Barnet, England), Brammer Standard Company (BSC, Houston, USA) and Research Institute for Ferrous Metallurgy (Budapest, Hungary). Most of these samples represent Cr-/Ni-steel grades. For all samples the iron concentration is greater than 42 wt.%, the chromium concentration is less than 30 wt.% and the nickel concentration is less than 35 wt.%. The concentrations of the minor elements lie below 6 wt.% for Cu and for the other elements below 3 wt.%. The samples were prepared by
Table 2 Composition of the reference samples of high-alloy steel in wt.% Reference sample
Fe
Cr
Ni
C
Si
Mn
Mo
Cu
Al
Ti
CRM S 15 CRM S 19 NBS SRM C 1288 NCS HS 23702-1 NCS HS 23702-2 NCS HS 23702-3 NCS HS 23702-4 NCS HS 23702-5 NCS HS 23702-6 NCS HS 23702-7 ECISS CRM 289-1 Metimex RM MW 27 Metimex RM MW 37 BSC RM B.S. 184A MBH RM PH 1 MBH RM PH 2 MBH RM PH 3 BSC RM B.S. 85D BSC RM B.S. 179A Carpenter RM CT 312 BAS CRM 407/2 Mean
74.0 76.1 42.8 71.6 72.7 71.9 70.7 70.7 71.4 70.3 55.4 45.2 58.9 75.4 73.3 72.8 71.6 67.7 61.1 58.3 93.6 67.9
16.70 7.00 19.55 15.36 12.46 9.32 7.40 17.16 20.76 18.90 14.64 15.57 25.00 12.66 16.10 16.70 15.13 17.09 25.45 29.80 3.03 16.0
3.90 12.80 29.30 10.35 11.52 13.12 16.41 9.05 6.93 7.82 24.68 35.23 12.26 8.34 5.10 3.79 3.16 10.03 5.84 8.93 0.53 11.4
0.043 0.260 0.056 0.061 0.164 0.241 0.184 0.096 0.017 0.101 0.049 0.230 0.250 0.035 0.094 0.070 0.150 0.049 0.017 0.126 0.490 0.1
0.260 2.320 0.410 0.663 0.413 0.960 0.920 0.654 0.171 1.080 0.531 1.950 1.100 0.080 0.180 0.510 1.940 0.550 0.440 0.460 0.660 0.8
0.380 0.320 0.830 0.644 0.981 1.980 1.570 0.730 0.156 0.356 1.016 1.750 1.550 0.060 1.750 0.890 0.440 1.690 1.040 1.600 0.195 0.9
2.460 0.110 2.830 0.620 0.350 0.690 0.500 0.260 0.079 0.170 1.102 n.s. 0.340 2.200 0.160 0.940 0.780 0.590 3.240 0.220 0.830 0.9
1.540 0.190 3.720 0.152 0.363 0.276 0.303 0.126 0.049 0.098 0.000 0.000 0.050 0.041 3.120 4.110 6.280 0.450 1.940 0.150 0.397 1.1
n.s. n.s. 0.003 0.044 0.074 0.038 0.240 0.260 0.034 0.200 0.199 n.s. n.s. 1.000 n.s. n.s. n.s. 0.130 0.009 0.010 0.040 0.2
n.s. 0.048 0.012 0.072 0.210 0.510 1.030 0.570 0.310 0.710 2.010 n.s. n.s. 0.051 n.s. n.s. n.s. 0.480 0.006 0.110 n.s. 0.4
n.s. = concentration value is not specified.
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grinding with Al2O3-grinding paper, grain size 60. The high matrix variation complicates the LIBS analysis as reported in Ref. [1]. Possible reasons can be spectral interferences from the elements nickel, iron and chromium and the wide range of material properties, causing so called matrix effects.
4. Results and discussion 4.1. Analytical figures of merit The calibrations are evaluated both for absolute and standardized intensities. For the latter case the analyte intensities are divided by the intensity of the Fe 271.4 nmline, used as internal standard. The concentration c or concentration ratios cˆ = c analyte / c reference are functions of the corresponding intensities I or intensity ratios Iˆ = I analyte / I reference. For the calibration functions the mean intensity values ,
ð1Þ
cˆ i ¼ b0;i þ b1;i I < Iˆ i > þ b2;i I < Iˆ i >2
ð2Þ
where a 0,i , a 1,i , a 2,i , b 0,i , b 1,i and b 2,i are the regression coefficients of the second order regressions of element i and ,
RSD < Iˆ i >
Ns P
¼
s¼1
RSD < Iˆ i > s Ns
ð4Þ
4.2. Calibrations with high-alloy reference samples 4.2.1. Influence of laser burst mode and laser energy Fig. 2 represents four calibration curves for the element Cr. Two burst energies each for single and double pulses are used. Obviously the differences between the double and
Fig. 2. Calibration curve for Chromium for single (squares) and double pulses (triangle).
single pulse calibrations are greater than the differences concerning the different laser burst energies. The calibrations with double pulses show greater saturation effects than the corresponding single pulse calibrations. However, the sensitivity in the low concentration range is higher than the one for single pulses. A similar result was found for lowalloy steel samples, where detection limits can be improved by use of double pulses [6]. The ablation rates are higher for double pulses than for single pulses of the same laser energy [3]. The same behaviour can be seen for the element lines of nickel, copper, manganese, silicon and titanium. These elements are characterized by concentrations higher than 1 wt.%. Fig. 2 shows that for concentration ratios c Cr / c Fe > 0.3, the deviations of the data points from the calibration curve increase. Two of the samples with a high Cr concentration have for example a relatively high Ni concentration, see samples NBS SRM C 1288 and Metimex MW 27 in Table 2. This is an indication that high concentrations of other elements have an influence on the evaporation and excitation processes in the laser-induced plasma. The quantitative influence will be estimated in the Sections 4.2.2– 4.2.4. 4.2.2. Calibration in absolute intensities In this section calibrations are studied using absolute intensities. Fig. 3 shows the copper calibration curve. Copper is an element with a small residual value of R(Cu) = 0.011 wt.% in the single pulse mode and for E b = 160 mJ. Concerning the mean copper concentration of 1.1 wt.% this corresponds to a relative accuracy of 1.0%. Table 3 lists the mean residual deviations R(i) of 10 element lines. The elements are sorted by their concentration range Dc. For chromium two element lines, Cr 267.71 nm and Cr 286.25 nm are evaluated. Because not all of the reference samples have for all elements specified concentration values for all elements the number of regarded samples varies. In the single pulse mode for most of the elements except for Cu there is no significant difference
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Fig. 3. Calibration curve for Copper in the single pulse mode (a). RSD(Iˆ ) = 0.9%. R(Cu) = 0.011 wt.%. Absolute difference between the LIBS concentration and the reference concentration vs. the reference concentration (b).
between the calibrations for the two laser burst energies. In spite of that the residuals in the double pulse mode are significantly greater especially for the matrix elements Cr and Ni, but also for the minor elements Cu and Mo. The mean residual values for each element in the single pulse mode are compared with those in the double pulse mode.
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Fig. 4. Calibration curve for nickel in the single pulse mode (a). Absolute difference between the LIBS concentration and the reference concentration vs. the reference concentration (b).
Considering the four different parameter sets single pulses lead to smaller residuals for the element lines Ni 225.38 nm, Cr 267.71 nm, Cr 286.25 nm, Cu 324.75 nm and Mo 281.61 nm. The ratio
Table 3 Mean residual deviations R(i) of 10 element lines for two different laser burst modes and two different laser burst energies and the ratio of residuals (DP to SP) using absolute intensities Element
Samplesa
Dc [wt.%]
R(i)SP [wt.%]
R(i)DP [wt.%]
100 mJ
160 mJ
100 mJ
160 mJ
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
21 21 21 19 20 21 14 21 14 21
34.7 29.7 29.7 6.2 3.2 2.2 2.0 1.9 1.0 0.5
0.39 0.63 0.50 0.038 0.055 0.129 0.042 0.13 0.019 0.020
0.37 0.62 0.57 0.011 0.050 0.101 0.048 0.12 0.029 0.023
0.87 1.45 1.12 0.143 0.086 0.051 0.019 0.07 0.018 0.014
1.59 2.09 1.63 0.127 0.127 0.070 0.031 0.11 0.023 0.018
Dc = concentration range of the reference samples used for the calibration curve, SP= single pulse, DP= double pulses. a For some elements not all of the 21 available reference samples are used, if the concentration is not specified for these elements.
3.2 2.8 2.6 6.0 2.0 0.5 0.6 0.7 0.8 0.7
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4.2.3. Calibration with standardized intensities Besides the evaluation with absolute intensities calibrations are carried out by dividing the absolute analyte intensities to the Fe 271.44 nm-line intensity as an internal standard. By measuring all the elements that can be contained in the steel samples the real content of the elements can be calculated in wt.% [15]. Figs. 4a and 5 show calibration curves for the elements Ni and Si. The coefficient of determinations is close to one which results in good accuracies, see Table 4. Fig. 4a represents the calibration curve for nickel in the single pulse mode and for E b = 160 mJ which is the calibration with the smallest R(Ni)-value and the smallest RSD(
Table 4 Mean residual deviations R(i) of 10 element lines for two different laser burst modes and two different laser burst energies using internal standardization Element
R(i)SP [wt.%]
R(i)DP [wt.%]
100 mJ
160 mJ
100 mJ
160 mJ
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
0.17 1.04 0.50 0.060 0.040 0.150 0.063 0.144 0.031 0.020
0.13 0.91 0.48 0.042 0.038 0.112 0.065 0.134 0.042 0.025
0.37 1.04 0.61 0.251 0.055 0.041 0.018 0.085 0.031 0.012
0.38 1.64 0.66 0.337 0.038 0.058 0.020 0.050 0.050 0.016
2.5 1.4 1.3 5.7 1.2 0.4 0.3 0.5 1.1 0.6
Same sample set as in Table 3.
improved for six element lines (Ni, Cr 286, Mo, Si, Mn and C) by about 50% comparing the smallest R(i)-values for the four parameter sets studied. Table 5 lists the precision of the intensity ratios of three replicate measurements in terms of RSD(
Table 5 Relative standard deviations RSD(
Fig. 5. Calibration curve for silicon in the double pulse mode.
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
RSD(
RSD(
100 mJ
160 mJ
100 mJ
160 mJ
0.3 0.7 0.6 0.7 0.7 3.8 3.5 2.3 5.8 3.3
0.3 0.4 0.5 0.7 0.6 2.5 3.0 1.6 5.3 2.1
0.4 0.7 0.4 1.2 0.8 1.4 2.6 0.8 6.2 4.1
0.4 0.4 0.3 1.1 0.9 1.1 2.1 0.6 2.4 1.9
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091
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line intensities. The multiplicative factors take into account different excitation conditions in the high-alloy plasmas. cˆ i ¼ b0;i þ b1;i I Iˆ i þ b2;i I Iˆ 2i þ
X
kadd;j I cˆ corr;j
ð5Þ
j; ji
cˆ i ¼ b0;i þ b1;i I Iˆ i þ b2;i I Iˆ 2i I Pj;ji 1 þ kmult;j Iˆc corr; j
Fig. 6. Interelement correction of the calibration with the Cr 267.7 nm-line. Single pulses, E b = 160 mJ.
E b = 160 mJ and 0.6% for double pulses and for E b = 160 mJ. Compared to the 3.1% reported in Ref. [16] this is a reduction by a factor of 2 for single pulses and by a factor of 5 for double pulses. As already indicated in Fig. 2 the chromium calibration curve shows increasing residual values for high Cr concentrations. Deviations observed at high concentrations are significant because of the high precision of the measured intensity ratios ( 0.7% cf. Table 5). In previous studies it has been shown that multivariate calibrations can reduce the residual values [1]. In this paper we studied interelement corrections to improve the accuracy of analysis. 4.2.4. Interelement corrections In contrast to multivariate calibrations interelement correction is an iterative method. The residuals R(i) can be corrected additively, see Eq. (5), and multiplicatively, see Eq. (6), considering spectral interferences and matrix effects. The additive factors correct the superposition of
ð6Þ
where c corr,j is the concentration ratio of element j to correct the residuals additively or multiplicatively, k add,j is an additive correction factor for the element j, k mult,j is a multiplicative correction factor for the element j. For example the correction for Cr can be started multiplicatively with nickel. Thereby a regression of the Cr residuals of all calibrated samples is made with the corresponding Ni concentration ratios. The aim is to get a correction factor to calculate the residuals. Then the reduced residuals are taken for making a regression with the measured concentrations of another element considered as a disturbing factor. These corrections are continued with other elements until no further improvement is achieved. Then the absolute Cr concentrations can be calculated with the elemental concentration of the calibration curves of those elements which are contained in the samples [15]. Fig. 6 shows the differences of the measured Cr concentration to the reference concentrations versus the reference concentration, where the bold squares represent uncorrected and open squares the corrected values. The Cr 267.7 nm residual is reduced by a factor of 3 taking into account multiplicative corrections with the elements Ni and Ti for single pulses and 160 mJ. The coefficient of determination can be improved from r 2 = 0.992 to r 2 = 0.999. Table 6 lists all multiplicatively and additively corrected residual values R(i) for all four parameter sets and for 10 element lines. In the column ‘‘disturbing elements‘‘ those elements are listed which have significant influence to reduce the residuals. The sign F*_ means that this element is
Table 6 Additive and multiplicative interelement corrections for ten elements Element
Ni Cr 267 Cr 286 Cu Mo Si Ti Mn Al C
Disturbing elements
*Cr, *Mo, *Ti, *C *Ni, *Ti *Ni, *Ti *Si, *Mo + Cr, *Ni, *Cu, *Ti + Cr, *Ti *Si *Ti *Ni, +Mo, *Si *Si
R(i)SP, corr [wt.%]
R(i)DP, corr [wt.%]
Factor of improvementa
100 mJ
100 mJ
SP
0.07 0.31 0.33 0.017 0.021 0.112 0.051 0.085 0.011 0.020
160 mJ
0.08 0.30 0.32 0.010 0.020 0.082 0.051 0.085 0.011 0.024
0.35 0.29 0.34 0.086 0.041 0.043 0.018 0.084 0.011 0.007
160 mJ
0.31 0.81 0.37 0.142 0.026 0.053 0.020 0.042 0.017 0.009 Mean
Corrected R(i) in wt.% and factors of improvement. Same sample set as in Table 4. a Factor of improvement = R(i)uncorr / R(i)corr, where R(i)uncorr are the values from Table 4.
DP
100 mJ
160 mJ
100 mJ
160 mJ
2.7 3.4 1.5 3.5 1.9 1.3 1.2 1.7 2.8 1.0 2.1
1.6 3.0 1.5 4.2 1.9 1.4 1.3 1.6 3.9 1.0 2.1
1.1 3.6 1.8 2.9 1.3 0.9 1.0 1.0 2.8 1.8 1.8
1.2 2.0 1.8 2.4 1.5 1.1 1.0 1.2 2.9 1.8 1.7
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used for a multiplicative correction, whereas the sign F+_ means an additive correction. In the last four columns the factors of improvement are listed. By interelement corrections the mean residual deviations R(i) can be reduced on average for all ten element lines by a factor of 1.7– 2.1. The greatest improvement is achieved for Cu by a factor of about 4 in comparison to the uncorrected residuals (E b = 160 mJ, single pulses). One interesting question is whether the residuals can be explained with differences in the plasma parameters due to the wide range of material properties of the samples. In the next chapter the plasma parameters electron density and electron temperature are determined measuring samples with a high variation of the iron, chromium and nickel content. 4.3. Plasma parameters The plasma parameters are determined for the plasmas of three to four samples with a high difference concerning the iron concentration. The plasmas are detected with an echelle spectrometer. Four time delays t delay = 6, 10, 20 and 30 As are studied. The spectra for the burst energy E b = 160 mJ in the single pulse mode are evaluated. The electron densities are calculated by the Stark-broadening of the Fe I-line 492.05 nm. The line profiles are estimated by a Lorentz fit. Three high-alloy steel samples and one pure iron sample are measured covering iron concentrations in the range between 43 and 99 wt.%. Fig. 7 shows the determined electron density N e as a function of the delay time. The errors of electron densities N e are between 4% and 10%. No significant difference of electron densities between the samples is observed. Besides the electron densities the electron temperatures are determined for atomic lines of Fe. The line intensities are measured assuming that local thermodynamic equilibrium (LTE) conditions are satisfied in the plasma. The echelle
Fig. 7. Electron densities N e for four time delays and four different samples showing a high matrix variation, Fe I-line 492.05 nm. Samples: C 1288 (43 wt.% Fe), MW 37 (59 wt.% Fe), B.S. 184 (75 wt.% Fe), pure iron (99.99 wt.% Fe).
Table 7 Line selection for the Boltzmann-plot No.
k [nm]
log(gf)
E n [eV]
No.
k [nm]
log(gf)
E n [eV]
1 2 3 4 5 6 7 8 9 10 11
273.36 278.81 296.69 299.95 356.54 363.15 364.78 371.99 374.95 404.58 406.36
0.06 0.02 0.404 0.47 0.19 0.036 0.194 0.431 0.161 0.28 0.07
5.39 5.30 4.18 4.99 4.43 4.37 4.31 3.33 4.22 4.55 4.61
12 13 14 15 16 17 18 19 20 21
407.17 411.85 413.47 419.91 421.94 427.18 430.79 432.58 438.35 522.72
0.022 0.28 0.49 0.25 0.12 0.164 0.07 0.01 0.2 0.969
4.65 6.58 5.83 6.00 6.51 4.39 4.43 4.47 4.31 3.93
Twenty-one atomic iron lines from 273 to 522 nm.
offers a wide spectral range for the line selection of the Boltzmann-plot, 21 Fe I-lines are evaluated, see Table 7. For the Boltzmann-plot the line shapes are fitted by Lorentz profiles and from these fits the integrals of the line profiles are determined. Fig. 8(a) shows a typical Boltzmann-plot for the time delay t delay = 20 As and for three different high-alloy steel samples. The transition properties of the lines are taken from the Kurucz data base [17]. Despite the high variation of the iron
Fig. 8. Boltzmann-plot with 21 Fe I-lines (a). Relative error of the slopes about 7%. Electron temperatures Te for three time delays and three highalloy steel samples (b).
J. Vrenegor et al. / Spectrochimica Acta Part B 60 (2005) 1083 – 1091
concentration the slopes are similar. The errors of the slopes are taken as the error of the electron temperatures. The significance for the evaluation is enlarged by regarding many lines. These lines are chosen because in the concentration range between 43 and 100 wt.% there is a linear relationship of the intensities versus the concentration. So self-absorption effects can be neglected. The upper energy levels are nearly uniformly distributed from E n = 3.4 eV to about 6.5 eV. The electron temperatures are evaluated at three time delays: t delay = 6, 20 and 30 As. The Fe I electron temperature decays from Te = 10300 K after 6 As to Te = 7600 K after 30 As. The value for t delay = 6 As is comparable with temperatures reported so far [14]. But the values at later times lie about 1000 K higher. The errors of the electron temperatures are about 7%. No significant difference between the samples is observed. So the origin for matrix effects—as, e.g. observed for Cr— does not show up in a significant way looking at the electron densities and electron temperatures. The reason for this might be that the effect of improvement by interelement corrections is in the same order of magnitude as the error of determination of the plasma parameters. For example the Cr 267.71 nm residual can be reduced by 0.6 –0.3 wt.%, see Table 6. Relating the value of the absolute improvement 0.6 wt.% to the mean Cr concentration of 16.0 wt.% of the measured sample set this corresponds to an improvement by about 4%.
5. Conclusions Calibrations were carried out for nine elements with single and double laser bursts and two different laser burst energies. The residuals are dependent on the laser burst mode. Single pulse calibrations have the smallest residuals for the matrix elements Cr and Ni and for the minor elements Cu and Mo, double pulses for the elements Si, Ti, Mn and C. With our set-up precisions of intensity ratios are achieved in terms of RSD values lower than 1.0% for most analytes. Interelement corrections can improve the LIBS analysis on high-alloy steel samples on average by a factor of two for matrix and minor elements. As a trend interelement corrections reduce the residuals stronger for single pulses than for double pulses. Plasma parameters like electron density and electron temperature show no significant difference for a strong variation of the iron concentration in the range of 40 –75 wt.%. Maybe changes of the plasma state exist but cannot be detected experimentally taking into account that the relative errors of determination of the plasma parameters is of the same order of magnitude as the interelement corrections.
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