Application of a Spectrum Standardization Method for Carbon Analysis in Coal Using Laser-Induced Breakdown Spectroscopy (LIBS) Xiongwei Li,a Zhe Wang,a,* Yangting Fu,a Zheng Li,a Jianmin Liu,b Weidou Nia a Tsinghua University, State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua-BP Clean Energy Center, Beijing 100084, China b China Guodian Science and Technology Research Institute, Nanjing 100034, China
Measurement of coal carbon content using laser-induced breakdown spectroscopy (LIBS) is limited by its low precision and accuracy. A modified spectrum standardization method was proposed to achieve both reproducible and accurate results for the quantitative analysis of carbon content in coal using LIBS. The proposed method used the molecular emissions of diatomic carbon (C2) and cyanide (CN) to compensate for the diminution of atomic carbon emissions in high volatile content coal samples caused by matrix effect. The compensated carbon line intensities were further converted into an assumed standard state with standard plasma temperature, electron number density, and total number density of carbon, under which the carbon line intensity is proportional to its concentration in the coal samples. To obtain better compensation for fluctuations of total carbon number density, the segmental spectral area was used and an iterative algorithm was applied that is different from our previous spectrum standardization calculations. The modified spectrum standardization model was applied to the measurement of carbon content in 24 bituminous coal samples. The results demonstrate that the proposed method has superior performance over the generally applied normalization methods. The average relative standard deviation was 3.21%, the coefficient of determination was 0.90, the root mean square error of prediction was 2.24%, and the average maximum relative error for the modified model was 12.18%, showing an overall improvement over the corresponding values for the normalization with segmental spectrum area, 6.00%, 0.75, 3.77%, and 15.40%, respectively. Index Headings: Laser-induced breakdown spectroscopy; LIBS; Bituminous coal; Standardization; Quantitative measurement; Precision.
INTRODUCTION The on-line analyses of coal properties are greatly needed by the power industry for coal pricing and combustion optimization.1–3 Carbon content in coal, one of the most important indexes reflecting coal quality, can provide a quick estimation of the calorific value of coal and is very valuable for the operation of coal-fired power plants.4 Laser-induced breakdown spectroscopy (LIBS) is a promising technique for on-line coal measurement because of its rapid analysis, minimal sample preparation, and simultaneous multi-elemental detection.5–7 A number of studies on coal analysis using LIBS have been performed.8–13 The quantitative determination of nonmetallic elements is important for coal analysis because Received 29 October 2013; accepted 14 April 2014. * Author to whom correspondence should be sent. E-mail: zhewang@ tsinghua.edu.cn. DOI: 10.1366/13-07345
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they are the major components of coal and are closely related to coal properties.11–13 The measurement of these elements, however, suffers from both low measurement accuracy and low reproducibility due to multiple factors, such as matrix effects and variations in experimental conditions.14–16 In addition, the low reproducibility of LIBS measurement has become the most serious problem for on-line or at-line measurement of coal properties, including carbon content using LIBS. The most common method used to improve LIBS measurement precision is the internal standard method, which is based on the calculation of the intensity ratio of the analyte and reference element.17,18 To apply this method, a known or constant internal standard concentration is required and the excitation potential of the reference element should be similar to that of the interested element. For the measurement of carbon content in coal, however, an appropriate reference element may not be easily found. Other methods that use background emissions or the spectral area to normalize the signal cannot effectively reduce the measurement uncertainty of carbon content in coal.19–22 Partial least square (PLS) is an effective multivariate analysis method for the analysis of LIBS data because it can use much of the quantitative information from the complex LIBS spectra. Partial least square has been applied to the LIBS quantitative measurement of various samples, including coal samples, in recent years.23–25 Yet, because the composition and structure of coal are so complex that the matrix of the measured coal sample may vary from that of the calibration sample set, the direct application of PLS, which focuses purely on mathematical and statistical data correlation, to coal analysis may have limited accuracy. More important, PLS cannot be applied directly to improve measurement precision. To improve the LIBS measurement precision, we proposed in our previous study a spectrum standardization method by which the recorded characteristic line intensity was converted to the line intensity at a standard plasma state with standard plasma temperature (T0), electron number density (ne0), and total number density of the measured species (ns0).26 A simplified spectrum standardization method was thereafter introduced to further improve the measurement precision and accuracy with much less calculation effort.27 The application of the methods to brass alloy samples showed that both the spectrum standardization method and the simplified spectrum standardization method improved measure-
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ment precision and accuracy, and that the latter method yielded better results. However, the results were not satisfying when the simplified spectrum standardization method was directly applied to the measurement of carbon content in coal, in which complicated and strong matrix effects exist. In this article, the molecular emissions of diatomic carbon (C2) and cyanide (CN) were used to compensate for the diminution of atomic carbon emissions in high volatile content coal samples caused by matrix effect and a special measure was taken to modify the simplified spectrum standardization method for the measurement of carbon content in coal.
Then, from Eq. 1, we obtain: I2 I2 ln C C ¼ a1 Iij þ a2 IT þ a3 ln I1 I1 0 þ a4 ½Dkstark ðDkstark Þ0 C þ a5
where IT is the sum of the multiple line intensities of the measured element, and a1, a2, a3, a4, and a5 are constants calculated using the regression process. Both [ln(I2/I1)]0 and (Dkstark)0 are calculated from all the average of the measured spectra, which can be applied to indicate their standard state values. Rearranging Eq. 3 gives the concentration as
METHOD DESCRIPTION In this section, we first briefly review the simplified spectrum standardization model. We then introduce the modified spectrum standardization method. Brief Introduction of the Simplified Spectrum Standardization Model. In the spectrum standardization model, a standard plasma state is defined by characterizing the plasma with a set of constant parameters (ns0, T0, and ne0) that are calculated in real applications by averaging the corresponding plasma parameters of all the measurements.26 With the assumed existence of the standard plasma state, the deviation of the measured line intensity from the standard state intensity is caused by the fluctuations of the plasma parameters (T, ne, and ns) from the standard state.27 Using Taylor expansion, it is Iij ðns0 ; T0 ; ne0 Þ Iij ðns ; T ; ne Þ ðk1 dns þ k2 C dT þ k3 C dne Þ
ð1Þ
where ns0, T0, and ne0 are the previously defined plasma parameters at the standard state; Iij is the raw measured line intensity; Iij(ns0, T0, ne0) is the calculated standard state line intensity; C is the concentration of the specific element; and k1, k2, and k3 are constants. If we ignore the self-absorption effects and the inter-element interference, Iij(ns0, T0, ne0) is proportional to the measured elemental concentration: Iij ðns0 ; T0 ; ne0 Þ ¼ k0 C
ð2Þ
The deviation of the ns, T, and ne are also correlated with the measured spectral information. On the righthand side of Eq. 1, dns is assumed to be proportional to the fluctuation in the sum of the multiple line intensities of the measured element. Considering that the excited states in plasma follow the Boltzmann distribution under the local thermodynamic equilibrium assumption, dT is associated with the intensity ratio of a pair of lines based on the principle of the Boltzmann distribution.28 The full width half-maximum (FWHM) of the spectral line is assumed to be proportional to electron number density because the characteristic spectral line broadening is mainly caused by the Stark broadening for typical LIBS measurements. The deviation of electron density, dne, may be determined from the FWHM of the Ha spectral line through Stark broadening.28 We can substitute the Iij(ns0, T0, ne0) in Eq. 1 with the concentration in Eq. 2.
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ð3Þ
C¼
a1 I þ a2 IT þ a5 h ij i 1 a3 ln II21 ln II21 a4 ½Dkstark ðDkstark Þ0 0
ð4Þ The line intensity at the standard state is proportional to the measured elemental concentration: Iij ðns0 ; T0 ; ne0 Þ ¼ k1 C ¼ k1
a1 I þ a2 IT þ a5 h ij i I2 1 a3 ln I1 ln II21 a4 ½Dkstark ðDkstark Þ0 0
ð5Þ The coefficients a1, a2, a3, a4, and a5 are calculated in two steps. First, the starting values are calculated from the linear regression analysis of Eq. (3), in which the independent variable is a matrix composed of all measured values of Iij, IT, (ln(l2/I1) [ln(l2/I1)]0)C, and [Dkstark ([Dkstark)0]C and the dependent variable is a vector composed of the contents of the element of interest. In the second step, these coefficients are optimized near the starting values using the target of minimum relative standard deviation (RSD) of the calculated elemental contents. As described in Eq. 3, we substitute the standard state line intensity in the standardization equation with the concentration based on linear correlation, which avoids the direct calculation of the standard state line intensity. This substitution requires a good linearity between the standardized line intensity and the concentration of the interested element. However, the linear relationship between the atomic carbon intensity and the carbon content may suffer from the strong matrix effect in coal. Therefore, the substitution of the standard state line intensity by the concentration may not be accurate enough for the estimation, and the optimization with the target of minimum RSD near the regression values may not obtain the accurate coefficients of the standardization equation. Moreover, for coal applications, there are only two eligible atomic carbon lines, and using the sum of the two line intensities to compensate for the fluctuation of total number density of carbon may not be good enough, making the estimation of the starting value even worse and decreasing the applicability of the simplified standard spectrum method for coal samples. That is, the simplified spectrum standardization method needs to be modified for coal applications.
Model Modification for Coal Applications. In the LIBS spectrum of coal, there are molecular emissions from C2 and CN. Diatomic carbon can be formed either by the recombination of the atomic carbon or by the direct ablation of the coal samples; CN can be produced by the reaction between carbon and nitrogen when the measurement of coal is performed in air. The formation of both indicates that part of the carbon has disappeared in generating the atomic line intensity. The modified model uses the molecular emissions from C2 and CN to compensate for the emission intensity of atomic carbon for the following reasons: (1) the formation of molecular C2 causes the reduction of atomic carbon emissions, (2) the increased amount of the ablated molecular C2 due to matrix effects reduces the amount of the ablated atomic carbon, and (3) the production of CN from the reaction between carbon and nitrogen causes the reduction of atomic carbon emissions.29 Then, the compensated intensity of carbon is Iij ¼ IC þ mIC2 þnICN
ð8Þ
Then, the coefficient m can be obtained from m¼
n2 n1
n3 n1
Iij ðns0 ; T0 ; ne0 Þ ¼ Iij þ
ð10Þ
Because the compensated carbon intensity is still affected by the fluctuations of the plasma parameters (ns, T, and ne), the deviations of the plasma parameters from their values at the standard plasma state are used to improve the precision of the compensated carbon intensity. That is, the compensated carbon intensity composed of the measured intensities of the atomic and molecular carbon is converted to the compensated carbon intensity at the standard plasma state. In the previous spectrum standardization model, the sum of multiple atomic and ionic line intensities of the measured element is used to compensate for the fluctuations of its total number density. Because there are only two available atomic lines of carbon (193.029 and 247.856 nm), the total number density of carbon may not be well represented by the sum of its emission line intensities. Because the spectral areas may have some linear relationship with the ablated mass of emitters in
ð11Þ
k X
b1i ITi C þ b2 C i¼1 I2 I2 þ b3 ln ln C I1 I1 0 þ b4 ½Dkstark ðDkstark Þ0 C
ð12Þ
where Iij is the compensated carbon intensity, and b1, b2, b3, b4, and b5 are the coefficients calculated from the regression process (discussed later). If the self-absorption effect can be neglected, the linear function is chosen as the calibration function C ¼ kIij ðns0 ; T0 ; ne0 Þ þ b
ð13Þ
where k and b are constants calculated from the regression process and Iij(ns0, T0, ne0) is the standard state line intensity of the interested element obtained from Eq. 12. From Eqs. 6, 12, and 13, the concentration is
1k
k X
kIC þ kmIC2 þ knICN þ b h i b1i ITi þ b2 þ b3 ln II21 ln II21 0
i¼1
þb4 ½Dkstark ðDkstark Þ0
The coefficient n can be obtained from n¼
k1i ITi C þ k2 C
where ITi is a segmental spectral area, and k1i and k2 are coefficients. Then the standardization equation becomes,
C¼ ð9Þ
k X i¼1
ð7Þ
where n1, n2, n3, and n4 are the coefficients calculated from the regression process using PLS. The relationship between the compensated carbon intensity and the carbon content should be C ¼ n1 Iij þ n4
dns ¼ ns ns0 ¼
ð6Þ
where IC is the emission intensity of the atomic carbon, IC2 is the emission intensity of the molecular carbon, and ICN is the emission intensity of CN; m and n are coefficients calculated from the calibration of the carbon content using IC, IC2, and ICN. That is, C ¼ n1 IC þ n2 IC2 þ n3 ICN þ n4
the plasma, in the proposed model we use the linear combination of several segmental spectral areas to better compensate for the fluctuations of total carbon number density. If we assume stoichiometric ablation, the total number density of carbon is proportional to the product of the segmental spectral areas and the carbon concentration. Then, the deviation of the ns is
ð14Þ
To perform the linear regression of Eq. 12, we require knowledge of the standard state line intensity. The standard state line intensity is initially estimated as the average value of repeatedly measured line intensities to obtain the coefficients in the standardization equation. The more accurately the standard state line intensity is estimated, the more accurately coefficients in the standardization equation can be calculated, and vice versa. Therefore, a new iterative procedure is applied to the standardization equation to obtain a more accurate measure of the standard state line intensity. The accuracy of the standard state line intensity is judged by the linear relationship between the standard state line intensity and the concentration. As shown in Fig. 1, the iterative procedure for establishing the spectrum standardization model is performed as follows: (1) For each sample, the average of the compensated carbon intensities obtained from the repeatedly measurements is regarded as the initial value of the standard state line intensity; (2) the
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FIG. 1. Flow diagram of the proposed iterative algorithm for the modified spectrum standardization method.
coefficients in Eq. 12 are calculated from the regression process using the values of the standard state line intensities; (3) the converted line intensity for each measurement is obtained from the right-hand side of Eq. 12 using the obtained coefficients, and the average of the converted line intensities for the repeated measurements is regarded as the new value of the standard state line intensity; (4) the coefficient of determination (R2) of the calibration curve between the standard state line intensities and the concentrations is calculated; (5) steps 2–4 are repeated until the R2 of the calibration curve achieves the maximum, and then the coefficients in Eq. 12 calculated in step 2 are determined as the final values. In this study, the analyte is carbon in bituminous coal. On the right-hand side of Eq. 12, Iij is the combination of the integrated intensity of an atomic carbon line (193.029 or 247.856 nm), the integrated intensity of C2 in the range of 470–473.7 nm, and the integrated intensity of CN in the range of 385.6–390 nm. The integrated intensity is defined as the integration of channel readings of the spectral line above the background continuum. On the right-hand side of Eq. 12, ITi (i = 1, 2, 3) are the segmental spectral areas in the range 190–310, 310–560, and 560–770 nm, respectively. The intensity ratio of two silicon atomic lines (212.412 and 250.689 nm) is used to monitor the plasma temperature variations. The Stark broadening terms are determined by the FWHM of the Ha spectral line after the Lorentz curve fitting. Experimental Setup. The LIBS system Spectrolaser 4000 (XRF Scientific, Australia) was used in this experiment. The experimental arrangement is similar to the one described previously.27 Briefly, a Q-switched Nd : YAG laser emitting at 532 nm with a pulse duration of 5 ns was used as the ablation source. The laser energy was adjusted to be 120 mJ/pulse. The laser beam was focused onto the sample surface to create a plasma using a plano-convex quartz lens with a 150 mm focal length. The plasma emission was collected using four fiber optics, each directed to a Czerny–Turner spectro-
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graph and detected by a charge-coupled device (CCD, Avantes, The Netherlands). The four spectrometers and CCD detectors covered an overall range 190–310, 310– 560, 560–770, and 770–950 nm, with a nominal resolution of 0.09 nm. The gate delay time was adjusted to 2 ls, and the integration time was fixed at 1 ms. The samples were 24 standard bituminous coals, which were certified by the China Coal Research Institute. Carbon was the element of interest, and its concentration ranged from 42 to 82% (Table I). Table I also gives the content of volatile matter in each coal sample on the air-dry basis. The powder of each coal sample was placed into a small aluminum pellet die (u = 30 mm; h = 3 mm), which was pressed using a hydraulic jack under a pressure of 20 tons. The samples were mounted on an auto-controlled x,y translation stage and exposed to air at atmospheric pressure. Similar to our previous study, the samples were divided into calibration and validation sets. The calibration set provided the spectral data for modeling, and the validation data set was used to verify the accuracy of the model. To ensure a wide range and even concentration distribution in both sets, all samples were first arranged in order of their carbon concentrations, and then one of every three samples was chosen for validation. Twenty-five locations were probed for each pellet. Each location was fired twice; the first shot of 150 mJ was to remove any contaminant, and the second shot of 120 mJ was for analysis. A fan was used to blow off the aerosol particles after each laser shot to prevent signal change caused by aerosol production. All spectra were background-subtracted to reduce the systematic signal fluctuation. The intensity was defined as the integration of channel readings of an emission line above the background continuum. The system was warmed up for at least 1 h to ensure the thermal stability of the instruments.
RESULTS AND DISCUSSION We evaluated the performance of the modified spectrum standardization model by comparing it with the univariate calibration model using segmental normalization.25 We chose four parameters to evaluate the performance of the modified spectrum standardization model. These parameters included the RSD of the spectral line intensity, the R2 of calibration curve, the root mean square error of prediction (RMSEP) of the mass concentration, and the maximum relative error (MRE) of the predicted mass concentrations. The RSD can evaluate the precision of a measurement. The smaller the RSD is, the more precise the LIBS measurements will be. The R2 can assess the quality of the data points that are used to establish the calibration model. The RMSEP and MRE can indicate the accuracy of predictions made by the models. Emission Intensity of Atomic and Molecular Carbon. As shown in Fig. 2a, the calibration between the spectral intensity of C(I) 247 nm and the carbon concentration for the 24 bituminous coal samples is poor, and the R2 is 0.46. If only the coal samples whose volatile content is less than 23% are chosen for calibration, the R2 will increase to 0.90, as shown in
TABLE I. Carbon concentrations of 24 coal samples. Calibration set
Sample number C (%) Volatile matter (%) Sample number
Validation set
1 47.12 11.31 9
C (%) Volatile matter (%)
70.45 14.41
Sample number
17
C (%) Volatile matter (%)
53.42 25.58
2 52.61 23.23 10 74.7 33.4 18 55.67 19.11
3
4
5
6
7
8
53.77 14.03
54.72 13.1
58.12 30.43
59.84 28.65
67.18 18.21
67.77 34.46
11
12
13
14
15
16
76.69 33.41
77.28 32.22
78.64 33.9
79.02 11.42
79.98 31.92
81.54 12.43
19
20
21
22
23
24
59.91 28.9
72.71 30.91
75.96 32.94
78.58 32.41
79.7 15.3
81.45 11
Fig. 2b. The volatile in coal is a mixture of short- and long-chain hydrocarbons, aromatic hydrocarbons, and some sulfur, and it will be liberated at high temperatures. This means that if the carbon contents in two coal samples are almost the same, the emission intensity of the atomic carbon in the high volatile content coal sample will be obviously lower than that in the low-volatile-content coal sample (e.g., samples 7 and 8).
Figure 3a shows the calibration plot between the emission intensity of C2 in the range 470–473.7 nm and the carbon concentration for the 24 bituminous coals; the R2 is 0.61. As shown in Fig. 3b, if only the coal samples whose volatile content is less than 23% are chosen for the calibration, the R2 is 0.64; if only the coal samples whose volatile content is larger than 23% are chosen for the calibration, the R2 is 0.74. It shows a contrary tendency for the emission intensity of C2 compared with
FIG. 2. Calibration plots of the C(I) 247 nm line. (a) For all 24 samples. (b) For samples with volatile content less than 23%.
FIG. 3. Calibration plots of the molecular emission of C2. (a) For all 24 samples. (b) For samples with volatile content less than 23%.
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FIG. 4. The RSD values of the C(I) 247 nm line intensity for 24 coal samples using different spectral processing methods.
the spectral intensity of C(I), 247 nm. That is, if the carbon contents of two coal samples are almost the same, the emission intensity of C2 in the high volatile content sample will be obviously larger than that in the lowvolatile-content sample (e.g., samples 7 and 8). Because of the opposite tendencies of the spectral intensity of C(I) 247 nm and the emission intensity of C2, the molecular emission from C2 was used to compensate for the diminution of the emission intensity of atomic carbon in the high volatile coal samples. In addition, because CN was also produced from the reaction between carbon and nitrogen in air, the molecular emission from CN was also used to compensate for the emission intensity of atomic carbon. The compensated carbon intensity can be obtained using Eqs. 6–10. Uncertainty Reduction. The integrated intensity of C(I) 247 nm after segmental normalization was selected to establish the univariate calibration model. The integrated intensity of C(I) 247 nm, the integrated intensity of C2 in the range 470–473.7 nm, and the integrated intensity of CN in the range 385.6–390 nm were used to obtain the compensated carbon intensity, which was then used to establish the spectrum standardization model. The average RSD of the raw C(I) 247 nm line intensity is 3.79%, and the value of C(I) 247 nm after segmental normalization is 6.00%. This indicates that the segmental normalization method cannot effectively reduce the signal uncertainty. Figure 4 shows the comparison of the RSD values of the C(I) 247 nm line intensity using different dataprocessing methods for all 24 bituminous coal samples. The average RSD of the compensated carbon intensity is 4.56%, and the value of the compensated carbon intensity using the modified spectrum standardization is 3.21%. The modified spectrum standardization method shows the best reproducibility because it not only compensates for the diminution of the atomic carbon intensities caused by matrix effect but also effectively compensates for the pulse-to-pulse signal fluctuations caused by the variations of plasma parameters (T, ne, and ns). Accuracy Improvement. The predicted carbon concentration of a sample is defined as the average value calculated from the 25 repeated measurements. The
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FIG. 5. Calibration plots of the C(I) 247 nm line after segmental spectral area normalization.
matrix effects of coal are so strong that the C(I) 247 nm line intensity does not have a good linearity with the carbon concentration (see Fig. 2a). The R2 value of the calibration curve between the C(I) 247 nm line intensities and the carbon concentration is only 0.46. When the C(I) 247 nm line intensity was normalized using the segmental spectral area, the R2 value of the calibration curve increased to 0.75 (Fig. 5). Given that the segmental spectrum area may be linearly related to the ablation mass, the segmental normalization method can partly compensate for the variation in the ablation mass. Therefore, the segmental normalization method can improve the R2 value of the calibration curve. Figure 6 shows the calibration plots of the compensated carbon intensity and the carbon content. The R2 value of the calibration curve is 0.85. The performance of the model in prediction accuracy can be justified using the RMSEP. The RMSEP of the univariate model that uses the compensated carbon intensity is 3.38%, whereas the corresponding value for the univariate model using the segmental normalization is 3.77%. Compared with the segmental spectral area normalization, the improvement in R2 and the reduction in RMSEP indicate that the emission intensities of C2 and CN can better compensate for the diminution of atomic carbon
FIG. 6. Calibration plots of the compensated carbon intensity.
FIG. 7. Calibration and validation plots for the spectrum standardization model.
FIG. 8. Maximum relative error of the predicted C concentration for the different methods.
emissions in high volatile coal samples, caused by matrix effects. Figure 7 demonstrates the calibration and validation results of the modified spectrum standardization model. The R2 of the present model is 0.90, and RMSEP is 2.24%. Compared with the univariate model that uses the compensated carbon intensity, the increased R2 indicates that the matrix effect is further corrected by compensating for the spectroscopic signal fluctuations attributed to the variation of the plasma parameters (T, ne, and ns). The lowered RMSEP of the present model implies that plasma-parameter correction terms in the present model contribute to the improvement in the prediction accuracy. The performance of the model in prediction accuracy can also be justified by the MRE, which is defined as Cpre Cnom ð15Þ MRE ¼ max 3 100% Cnom
coal. In the modified spectrum standardization model, we first compensated for the diminution of atomic carbon emissions in high volatile coal samples, caused by matrix effects, using the emission intensities of C2 and CN, and then converted the compensated carbon line intensities to the carbon line intensities at the standard state to further compensate for the fluctuations in the line intensities caused by the variations in the plasma parameters. The modified spectrum standardization method uses the segmental spectral area to correct the fluctuations of the total carbon number density and also applies a new iterative algorithm to the standardization calculations to obtain more accurate standard state line intensities. The assays of the carbon concentration of 24 bituminous coal samples using the proposed model show an improvement in both the measurement precision and accuracy compared to the traditional single-variable method using segmental spectrum area normalization.
where Cpre is the predicted concentration for each measurement, and Cnom is the nominal elemental concentration for the sample. The MRE indicates the largest deviation of a single measurement and can evaluate the prediction accuracy of the model, especially for conditions in which only a single-shot assay is allowed. The average MRE of the present model is 12.18%, whereas the value of the univariate calibration model with segmental spectral area normalization is 15.40% (Fig. 8). These results further demonstrated the advantage of the present model in improving measurement accuracy.
The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 51276100) and National Basic Research Program (973 Program) (No. 2013CB228501).
CONCLUSION The previously reported simplified spectrum standardization model can obviously reduce the signal uncertainty and improve the measurement accuracy by converting the line intensity to the intensity at the standard plasma state. However, the strong matrix effects of coal lead to an unsatisfactory linear relationship between the emission intensity and the concentration. Consequently, the simplified spectrum standardization method cannot be directly applied to the measurement of carbon content in
ACKNOWLEDGMENTS
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8. F.J. Wallis, B.L. Chadwick, R.J.S. Morrison. ‘‘Analysis of Lignite Using Laser-Induced Breakdown Spectroscopy’’. Appl. Spectrosc. 2000. 54(8): 1231-1235. ˜ 9. T. Ctvrtnickova, M.P. Mateo, A. Yanez, G. Nicolas. ‘‘Characterization of Coal Fly Ash Components by Laser-Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2009. 64(10): 1093-1097. 10. L.G. Blevins, C.R. Shaddix, S.M. Sickafoose, P.M. Walsh. ‘‘LaserInduced Breakdown Spectroscopy at High Temperatures in Industrial Boilers and Furnaces’’. Appl. Optics. 2003. 42(30): 61076118. 11. Z. Wang, T. Yuan, S. Lui, Z. Hou, X. Li, Z. Li, W. Ni. ‘‘Major Elements Analysis in Bituminous Coals Under Different Ambient Gases by Laser-Induced Breakdown Spectroscopy with PLS Modeling’’. Front. Phys. 2012. 7(6): 708-713. 12. S. Yao, J. Lu, J. Zheng, M. Dong. ‘‘Analyzing Unburned Carbon in Fly Ash Using Laser-Induced Breakdown Spectroscopy with Multivariate Calibration Method’’. J. Anal. Atom. Spectrom. 2012. 27(3): 473-478. 13. Z. Wang, Y. Deguchi, M. Kuwahara, T. Taira, X. Zhang, J. Yan, J. Liu, H. Watanabe, R. Kurose. ‘‘Quantitative Elemental Detection of Size-Segregated Particles Using Laser-Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2013. 87: 130-138. 14. J. Li, J. Lu, Z. Lin, S. Gong, C. Xie, L. Chang, L. Yang, P. Li. ‘‘Effects of Experimental Parameters on Elemental Analysis of Coal by Laser-Induced Breakdown Spectroscopy’’. Opt. Laser Technol. 2009. 41(8): 907-913. 15. J. Yu, Q.L. Ma, V. Motto-Ros, W.Q. Lei, X.C. Wang, X.S. Bai. ‘‘LaserInduced Plasma and Laser-Induced Breakdown Spectroscopy (LIBS) in China: The Challenge and the Opportunity’’. Front. Phys. 2012. 7(6): 649-669. 16. X. Li, W. Zhou, Z. Cui. ‘‘Temperature and Electron Density of Soil Plasma Generated by LA-FPDPS’’. Front. Phys. 2012. 7(6): 721-727. 17. J.H. Kwak, C. Lenth, C. Salb, E.J. Ko, K.W. Kim, K. Park. ‘‘Quantitative Analysis of Arsenic in Mine Tailing Soils Using Double Pulse-Laser Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2009. 64(10): 1105-1110. 18. D. Mukherjee, A. Rai, M.R. Zachariah. ‘‘Quantitative Laser-Induced Breakdown Spectroscopy for Aerosols via Internal Calibration: Application to the Oxidative Coating of Aluminum Nanoparticles’’. J. Aerosol Sci. 2006. 37(6): 677-695.
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19. L. Xu, V. Bulatov, V.V. Gridin, I. Schechter. ‘‘Absolute Analysis of Particulate Materials by Laser-Induced Breakdown Spectroscopy’’. Anal. Chem. 1997. 69(11): 2103-2108. 20. F.J. Fortes, M. Corte´s, M.D. Simo´n, L.M. Cabalı´ n, J.J. Laserna. ‘‘Chronocultural Sorting of Archaeological Bronze Objects Using Laser-Induced Breakdown Spectrometry’’. Anal. Chim. Acta. 2005. 554(1-2): 136-143. 21. D. Body, B.L. Chadwick. ‘‘Optimization of the Spectral Data Processing in a LIBS Simultaneous Elemental Analysis System’’. Spectrochim. Acta B. 2001. 56(6): 725-736. 22. J.A. Bolger. ‘‘Semi-Quantitative Laser-Induced Breakdown Spectroscopy for Analysis of Mineral Drill Core’’. Appl. Spectrosc. 2000. 54(2): 181-189. 23. M.M. Tripathi, K.E. Eseller, F.Y. Yueh, J.P. Singh. ‘‘Multivariate Calibration of Spectra Obtained by Laser Induced Breakdown Spectroscopy of Plutonium Oxide Surrogate Residues’’. Spectrochim. Acta B. 2009. 64(11-12): 1212-1218. 24. S. Yao, J. Lu, M. Dong, K. Chen, J. Li, J. Li. ‘‘Extracting Coal Ash Content from Laser-Induced Breakdown Spectroscopy (LIBS) Spectra by Multivariate Analysis’’. Appl. Spectrosc. 2011. 65(10): 1197-1201. 25. J. Feng, Z. Wang, L. West, Z. Li, W. Ni. ‘‘A PLS Model Based on Dominant Factor for Coal Analysis Using Laser-Induced Breakdown Spectroscopy’’. Anal. Bioanal. Chem. 2011. 400(10): 3261-3271. 26. Z. Wang, L. Li, L. West, Z. Li, W. Ni. ‘‘A Spectrum Standardization Approach for Laser-Induced Breakdown Spectroscopy Measurements’’. Spectrochim. Acta B. 2012. 68: 58-64. 27. L. Li, Z. Wang, T. Yuan, Z. Hou, Z. Li, W. Ni. ‘‘A Simplified Spectrum Standardization Method for Laser-Induced Breakdown Spectroscopy Measurements’’. J. Anal. Atom. Spectrom. 2011. 26(11): 22742280. 28. E. Tognoni, V. Palleschi, M. Corsi, G. Cristoforetti, N. Omenetto, I. Gornushkin, B.W. Smith, J.D. Winefordner. ‘‘From Sample to Signal in Laser-Induced Breakdown Spectroscopy: A Complex Route to Quantitative Analysis’’. In: A.W. Miziolek, V. Palleschi, I. Schechter, editors. Laser-Induced Breakdown Spectroscopy (LIBS): Fundamentals and Applications. Cambridge, UK: Cambridge University Press, 2006. Pp. 127-136. 29. M. Dong, X. Mao, J.J. Gonzalez, J. Lu, R.E. Russo. ‘‘Carbon Isotope Separation and Molecular Formation in Laser-Induced Plasmas by Laser Ablation Molecular Isotopic Spectrometry’’. Anal. Chem. 2013. 85(5): 2899-2906.
Measurement of coal carbon content using laser-induced breakdown spectroscopy (LIBS) is limited by its low precision and accuracy. A modified spectrum standardization method was proposed to achieve both reproducible and accurate results for the quantitative analysis of carbon content in coal using LIBS. The proposed method used the molecular emissions of diatomic carbon (C2) and cyanide (CN) to compensate for the diminution of atomic carbon emissions in high volatile content coal samples caused by matrix effect. The compensated carbon line intensities were further converted into an assumed standard state with standard plasma temperature, electron number density, and total number density of carbon, under which the carbon line intensity is proportional to its concentration in the coal samples. To obtain better compensation for fluctuations of total carbon number density, the segmental spectral area was used and an iterative algorithm was applied that is different from our previous spectrum standardization calculations. The modified spectrum standardization model was applied to the measurement of carbon content in 24 bituminous coal samples. The results demonstrate that the proposed method has superior performance over the generally applied normalization methods. The average relative standard deviation was 3.21%, the coefficient of determination was 0.90, the root mean square error of prediction was 2.24%, and the average maximum relative error for the modified model was 12.18%, showing an overall improvement over the corresponding values for the normalization with segmental spectrum area, 6.00%, 0.75, 3.77%, and 15.40%, respectively. Index Headings: Laser-induced breakdown spectroscopy; LIBS; Bituminous coal; Standardization; Quantitative measurement; Precision.
INTRODUCTION The on-line analyses of coal properties are greatly needed by the power industry for coal pricing and combustion optimization.1–3 Carbon content in coal, one of the most important indexes reflecting coal quality, can provide a quick estimation of the calorific value of coal and is very valuable for the operation of coal-fired power plants.4 Laser-induced breakdown spectroscopy (LIBS) is a promising technique for on-line coal measurement because of its rapid analysis, minimal sample preparation, and simultaneous multi-elemental detection.5–7 A number of studies on coal analysis using LIBS have been performed.8–13 The quantitative determination of nonmetallic elements is important for coal analysis because Received 29 October 2013; accepted 14 April 2014. * Author to whom correspondence should be sent. E-mail: zhewang@ tsinghua.edu.cn. DOI: 10.1366/13-07345
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they are the major components of coal and are closely related to coal properties.11–13 The measurement of these elements, however, suffers from both low measurement accuracy and low reproducibility due to multiple factors, such as matrix effects and variations in experimental conditions.14–16 In addition, the low reproducibility of LIBS measurement has become the most serious problem for on-line or at-line measurement of coal properties, including carbon content using LIBS. The most common method used to improve LIBS measurement precision is the internal standard method, which is based on the calculation of the intensity ratio of the analyte and reference element.17,18 To apply this method, a known or constant internal standard concentration is required and the excitation potential of the reference element should be similar to that of the interested element. For the measurement of carbon content in coal, however, an appropriate reference element may not be easily found. Other methods that use background emissions or the spectral area to normalize the signal cannot effectively reduce the measurement uncertainty of carbon content in coal.19–22 Partial least square (PLS) is an effective multivariate analysis method for the analysis of LIBS data because it can use much of the quantitative information from the complex LIBS spectra. Partial least square has been applied to the LIBS quantitative measurement of various samples, including coal samples, in recent years.23–25 Yet, because the composition and structure of coal are so complex that the matrix of the measured coal sample may vary from that of the calibration sample set, the direct application of PLS, which focuses purely on mathematical and statistical data correlation, to coal analysis may have limited accuracy. More important, PLS cannot be applied directly to improve measurement precision. To improve the LIBS measurement precision, we proposed in our previous study a spectrum standardization method by which the recorded characteristic line intensity was converted to the line intensity at a standard plasma state with standard plasma temperature (T0), electron number density (ne0), and total number density of the measured species (ns0).26 A simplified spectrum standardization method was thereafter introduced to further improve the measurement precision and accuracy with much less calculation effort.27 The application of the methods to brass alloy samples showed that both the spectrum standardization method and the simplified spectrum standardization method improved measure-
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ment precision and accuracy, and that the latter method yielded better results. However, the results were not satisfying when the simplified spectrum standardization method was directly applied to the measurement of carbon content in coal, in which complicated and strong matrix effects exist. In this article, the molecular emissions of diatomic carbon (C2) and cyanide (CN) were used to compensate for the diminution of atomic carbon emissions in high volatile content coal samples caused by matrix effect and a special measure was taken to modify the simplified spectrum standardization method for the measurement of carbon content in coal.
Then, from Eq. 1, we obtain: I2 I2 ln C C ¼ a1 Iij þ a2 IT þ a3 ln I1 I1 0 þ a4 ½Dkstark ðDkstark Þ0 C þ a5
where IT is the sum of the multiple line intensities of the measured element, and a1, a2, a3, a4, and a5 are constants calculated using the regression process. Both [ln(I2/I1)]0 and (Dkstark)0 are calculated from all the average of the measured spectra, which can be applied to indicate their standard state values. Rearranging Eq. 3 gives the concentration as
METHOD DESCRIPTION In this section, we first briefly review the simplified spectrum standardization model. We then introduce the modified spectrum standardization method. Brief Introduction of the Simplified Spectrum Standardization Model. In the spectrum standardization model, a standard plasma state is defined by characterizing the plasma with a set of constant parameters (ns0, T0, and ne0) that are calculated in real applications by averaging the corresponding plasma parameters of all the measurements.26 With the assumed existence of the standard plasma state, the deviation of the measured line intensity from the standard state intensity is caused by the fluctuations of the plasma parameters (T, ne, and ns) from the standard state.27 Using Taylor expansion, it is Iij ðns0 ; T0 ; ne0 Þ Iij ðns ; T ; ne Þ ðk1 dns þ k2 C dT þ k3 C dne Þ
ð1Þ
where ns0, T0, and ne0 are the previously defined plasma parameters at the standard state; Iij is the raw measured line intensity; Iij(ns0, T0, ne0) is the calculated standard state line intensity; C is the concentration of the specific element; and k1, k2, and k3 are constants. If we ignore the self-absorption effects and the inter-element interference, Iij(ns0, T0, ne0) is proportional to the measured elemental concentration: Iij ðns0 ; T0 ; ne0 Þ ¼ k0 C
ð2Þ
The deviation of the ns, T, and ne are also correlated with the measured spectral information. On the righthand side of Eq. 1, dns is assumed to be proportional to the fluctuation in the sum of the multiple line intensities of the measured element. Considering that the excited states in plasma follow the Boltzmann distribution under the local thermodynamic equilibrium assumption, dT is associated with the intensity ratio of a pair of lines based on the principle of the Boltzmann distribution.28 The full width half-maximum (FWHM) of the spectral line is assumed to be proportional to electron number density because the characteristic spectral line broadening is mainly caused by the Stark broadening for typical LIBS measurements. The deviation of electron density, dne, may be determined from the FWHM of the Ha spectral line through Stark broadening.28 We can substitute the Iij(ns0, T0, ne0) in Eq. 1 with the concentration in Eq. 2.
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ð3Þ
C¼
a1 I þ a2 IT þ a5 h ij i 1 a3 ln II21 ln II21 a4 ½Dkstark ðDkstark Þ0 0
ð4Þ The line intensity at the standard state is proportional to the measured elemental concentration: Iij ðns0 ; T0 ; ne0 Þ ¼ k1 C ¼ k1
a1 I þ a2 IT þ a5 h ij i I2 1 a3 ln I1 ln II21 a4 ½Dkstark ðDkstark Þ0 0
ð5Þ The coefficients a1, a2, a3, a4, and a5 are calculated in two steps. First, the starting values are calculated from the linear regression analysis of Eq. (3), in which the independent variable is a matrix composed of all measured values of Iij, IT, (ln(l2/I1) [ln(l2/I1)]0)C, and [Dkstark ([Dkstark)0]C and the dependent variable is a vector composed of the contents of the element of interest. In the second step, these coefficients are optimized near the starting values using the target of minimum relative standard deviation (RSD) of the calculated elemental contents. As described in Eq. 3, we substitute the standard state line intensity in the standardization equation with the concentration based on linear correlation, which avoids the direct calculation of the standard state line intensity. This substitution requires a good linearity between the standardized line intensity and the concentration of the interested element. However, the linear relationship between the atomic carbon intensity and the carbon content may suffer from the strong matrix effect in coal. Therefore, the substitution of the standard state line intensity by the concentration may not be accurate enough for the estimation, and the optimization with the target of minimum RSD near the regression values may not obtain the accurate coefficients of the standardization equation. Moreover, for coal applications, there are only two eligible atomic carbon lines, and using the sum of the two line intensities to compensate for the fluctuation of total number density of carbon may not be good enough, making the estimation of the starting value even worse and decreasing the applicability of the simplified standard spectrum method for coal samples. That is, the simplified spectrum standardization method needs to be modified for coal applications.
Model Modification for Coal Applications. In the LIBS spectrum of coal, there are molecular emissions from C2 and CN. Diatomic carbon can be formed either by the recombination of the atomic carbon or by the direct ablation of the coal samples; CN can be produced by the reaction between carbon and nitrogen when the measurement of coal is performed in air. The formation of both indicates that part of the carbon has disappeared in generating the atomic line intensity. The modified model uses the molecular emissions from C2 and CN to compensate for the emission intensity of atomic carbon for the following reasons: (1) the formation of molecular C2 causes the reduction of atomic carbon emissions, (2) the increased amount of the ablated molecular C2 due to matrix effects reduces the amount of the ablated atomic carbon, and (3) the production of CN from the reaction between carbon and nitrogen causes the reduction of atomic carbon emissions.29 Then, the compensated intensity of carbon is Iij ¼ IC þ mIC2 þnICN
ð8Þ
Then, the coefficient m can be obtained from m¼
n2 n1
n3 n1
Iij ðns0 ; T0 ; ne0 Þ ¼ Iij þ
ð10Þ
Because the compensated carbon intensity is still affected by the fluctuations of the plasma parameters (ns, T, and ne), the deviations of the plasma parameters from their values at the standard plasma state are used to improve the precision of the compensated carbon intensity. That is, the compensated carbon intensity composed of the measured intensities of the atomic and molecular carbon is converted to the compensated carbon intensity at the standard plasma state. In the previous spectrum standardization model, the sum of multiple atomic and ionic line intensities of the measured element is used to compensate for the fluctuations of its total number density. Because there are only two available atomic lines of carbon (193.029 and 247.856 nm), the total number density of carbon may not be well represented by the sum of its emission line intensities. Because the spectral areas may have some linear relationship with the ablated mass of emitters in
ð11Þ
k X
b1i ITi C þ b2 C i¼1 I2 I2 þ b3 ln ln C I1 I1 0 þ b4 ½Dkstark ðDkstark Þ0 C
ð12Þ
where Iij is the compensated carbon intensity, and b1, b2, b3, b4, and b5 are the coefficients calculated from the regression process (discussed later). If the self-absorption effect can be neglected, the linear function is chosen as the calibration function C ¼ kIij ðns0 ; T0 ; ne0 Þ þ b
ð13Þ
where k and b are constants calculated from the regression process and Iij(ns0, T0, ne0) is the standard state line intensity of the interested element obtained from Eq. 12. From Eqs. 6, 12, and 13, the concentration is
1k
k X
kIC þ kmIC2 þ knICN þ b h i b1i ITi þ b2 þ b3 ln II21 ln II21 0
i¼1
þb4 ½Dkstark ðDkstark Þ0
The coefficient n can be obtained from n¼
k1i ITi C þ k2 C
where ITi is a segmental spectral area, and k1i and k2 are coefficients. Then the standardization equation becomes,
C¼ ð9Þ
k X i¼1
ð7Þ
where n1, n2, n3, and n4 are the coefficients calculated from the regression process using PLS. The relationship between the compensated carbon intensity and the carbon content should be C ¼ n1 Iij þ n4
dns ¼ ns ns0 ¼
ð6Þ
where IC is the emission intensity of the atomic carbon, IC2 is the emission intensity of the molecular carbon, and ICN is the emission intensity of CN; m and n are coefficients calculated from the calibration of the carbon content using IC, IC2, and ICN. That is, C ¼ n1 IC þ n2 IC2 þ n3 ICN þ n4
the plasma, in the proposed model we use the linear combination of several segmental spectral areas to better compensate for the fluctuations of total carbon number density. If we assume stoichiometric ablation, the total number density of carbon is proportional to the product of the segmental spectral areas and the carbon concentration. Then, the deviation of the ns is
ð14Þ
To perform the linear regression of Eq. 12, we require knowledge of the standard state line intensity. The standard state line intensity is initially estimated as the average value of repeatedly measured line intensities to obtain the coefficients in the standardization equation. The more accurately the standard state line intensity is estimated, the more accurately coefficients in the standardization equation can be calculated, and vice versa. Therefore, a new iterative procedure is applied to the standardization equation to obtain a more accurate measure of the standard state line intensity. The accuracy of the standard state line intensity is judged by the linear relationship between the standard state line intensity and the concentration. As shown in Fig. 1, the iterative procedure for establishing the spectrum standardization model is performed as follows: (1) For each sample, the average of the compensated carbon intensities obtained from the repeatedly measurements is regarded as the initial value of the standard state line intensity; (2) the
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FIG. 1. Flow diagram of the proposed iterative algorithm for the modified spectrum standardization method.
coefficients in Eq. 12 are calculated from the regression process using the values of the standard state line intensities; (3) the converted line intensity for each measurement is obtained from the right-hand side of Eq. 12 using the obtained coefficients, and the average of the converted line intensities for the repeated measurements is regarded as the new value of the standard state line intensity; (4) the coefficient of determination (R2) of the calibration curve between the standard state line intensities and the concentrations is calculated; (5) steps 2–4 are repeated until the R2 of the calibration curve achieves the maximum, and then the coefficients in Eq. 12 calculated in step 2 are determined as the final values. In this study, the analyte is carbon in bituminous coal. On the right-hand side of Eq. 12, Iij is the combination of the integrated intensity of an atomic carbon line (193.029 or 247.856 nm), the integrated intensity of C2 in the range of 470–473.7 nm, and the integrated intensity of CN in the range of 385.6–390 nm. The integrated intensity is defined as the integration of channel readings of the spectral line above the background continuum. On the right-hand side of Eq. 12, ITi (i = 1, 2, 3) are the segmental spectral areas in the range 190–310, 310–560, and 560–770 nm, respectively. The intensity ratio of two silicon atomic lines (212.412 and 250.689 nm) is used to monitor the plasma temperature variations. The Stark broadening terms are determined by the FWHM of the Ha spectral line after the Lorentz curve fitting. Experimental Setup. The LIBS system Spectrolaser 4000 (XRF Scientific, Australia) was used in this experiment. The experimental arrangement is similar to the one described previously.27 Briefly, a Q-switched Nd : YAG laser emitting at 532 nm with a pulse duration of 5 ns was used as the ablation source. The laser energy was adjusted to be 120 mJ/pulse. The laser beam was focused onto the sample surface to create a plasma using a plano-convex quartz lens with a 150 mm focal length. The plasma emission was collected using four fiber optics, each directed to a Czerny–Turner spectro-
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graph and detected by a charge-coupled device (CCD, Avantes, The Netherlands). The four spectrometers and CCD detectors covered an overall range 190–310, 310– 560, 560–770, and 770–950 nm, with a nominal resolution of 0.09 nm. The gate delay time was adjusted to 2 ls, and the integration time was fixed at 1 ms. The samples were 24 standard bituminous coals, which were certified by the China Coal Research Institute. Carbon was the element of interest, and its concentration ranged from 42 to 82% (Table I). Table I also gives the content of volatile matter in each coal sample on the air-dry basis. The powder of each coal sample was placed into a small aluminum pellet die (u = 30 mm; h = 3 mm), which was pressed using a hydraulic jack under a pressure of 20 tons. The samples were mounted on an auto-controlled x,y translation stage and exposed to air at atmospheric pressure. Similar to our previous study, the samples were divided into calibration and validation sets. The calibration set provided the spectral data for modeling, and the validation data set was used to verify the accuracy of the model. To ensure a wide range and even concentration distribution in both sets, all samples were first arranged in order of their carbon concentrations, and then one of every three samples was chosen for validation. Twenty-five locations were probed for each pellet. Each location was fired twice; the first shot of 150 mJ was to remove any contaminant, and the second shot of 120 mJ was for analysis. A fan was used to blow off the aerosol particles after each laser shot to prevent signal change caused by aerosol production. All spectra were background-subtracted to reduce the systematic signal fluctuation. The intensity was defined as the integration of channel readings of an emission line above the background continuum. The system was warmed up for at least 1 h to ensure the thermal stability of the instruments.
RESULTS AND DISCUSSION We evaluated the performance of the modified spectrum standardization model by comparing it with the univariate calibration model using segmental normalization.25 We chose four parameters to evaluate the performance of the modified spectrum standardization model. These parameters included the RSD of the spectral line intensity, the R2 of calibration curve, the root mean square error of prediction (RMSEP) of the mass concentration, and the maximum relative error (MRE) of the predicted mass concentrations. The RSD can evaluate the precision of a measurement. The smaller the RSD is, the more precise the LIBS measurements will be. The R2 can assess the quality of the data points that are used to establish the calibration model. The RMSEP and MRE can indicate the accuracy of predictions made by the models. Emission Intensity of Atomic and Molecular Carbon. As shown in Fig. 2a, the calibration between the spectral intensity of C(I) 247 nm and the carbon concentration for the 24 bituminous coal samples is poor, and the R2 is 0.46. If only the coal samples whose volatile content is less than 23% are chosen for calibration, the R2 will increase to 0.90, as shown in
TABLE I. Carbon concentrations of 24 coal samples. Calibration set
Sample number C (%) Volatile matter (%) Sample number
Validation set
1 47.12 11.31 9
C (%) Volatile matter (%)
70.45 14.41
Sample number
17
C (%) Volatile matter (%)
53.42 25.58
2 52.61 23.23 10 74.7 33.4 18 55.67 19.11
3
4
5
6
7
8
53.77 14.03
54.72 13.1
58.12 30.43
59.84 28.65
67.18 18.21
67.77 34.46
11
12
13
14
15
16
76.69 33.41
77.28 32.22
78.64 33.9
79.02 11.42
79.98 31.92
81.54 12.43
19
20
21
22
23
24
59.91 28.9
72.71 30.91
75.96 32.94
78.58 32.41
79.7 15.3
81.45 11
Fig. 2b. The volatile in coal is a mixture of short- and long-chain hydrocarbons, aromatic hydrocarbons, and some sulfur, and it will be liberated at high temperatures. This means that if the carbon contents in two coal samples are almost the same, the emission intensity of the atomic carbon in the high volatile content coal sample will be obviously lower than that in the low-volatile-content coal sample (e.g., samples 7 and 8).
Figure 3a shows the calibration plot between the emission intensity of C2 in the range 470–473.7 nm and the carbon concentration for the 24 bituminous coals; the R2 is 0.61. As shown in Fig. 3b, if only the coal samples whose volatile content is less than 23% are chosen for the calibration, the R2 is 0.64; if only the coal samples whose volatile content is larger than 23% are chosen for the calibration, the R2 is 0.74. It shows a contrary tendency for the emission intensity of C2 compared with
FIG. 2. Calibration plots of the C(I) 247 nm line. (a) For all 24 samples. (b) For samples with volatile content less than 23%.
FIG. 3. Calibration plots of the molecular emission of C2. (a) For all 24 samples. (b) For samples with volatile content less than 23%.
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FIG. 4. The RSD values of the C(I) 247 nm line intensity for 24 coal samples using different spectral processing methods.
the spectral intensity of C(I), 247 nm. That is, if the carbon contents of two coal samples are almost the same, the emission intensity of C2 in the high volatile content sample will be obviously larger than that in the lowvolatile-content sample (e.g., samples 7 and 8). Because of the opposite tendencies of the spectral intensity of C(I) 247 nm and the emission intensity of C2, the molecular emission from C2 was used to compensate for the diminution of the emission intensity of atomic carbon in the high volatile coal samples. In addition, because CN was also produced from the reaction between carbon and nitrogen in air, the molecular emission from CN was also used to compensate for the emission intensity of atomic carbon. The compensated carbon intensity can be obtained using Eqs. 6–10. Uncertainty Reduction. The integrated intensity of C(I) 247 nm after segmental normalization was selected to establish the univariate calibration model. The integrated intensity of C(I) 247 nm, the integrated intensity of C2 in the range 470–473.7 nm, and the integrated intensity of CN in the range 385.6–390 nm were used to obtain the compensated carbon intensity, which was then used to establish the spectrum standardization model. The average RSD of the raw C(I) 247 nm line intensity is 3.79%, and the value of C(I) 247 nm after segmental normalization is 6.00%. This indicates that the segmental normalization method cannot effectively reduce the signal uncertainty. Figure 4 shows the comparison of the RSD values of the C(I) 247 nm line intensity using different dataprocessing methods for all 24 bituminous coal samples. The average RSD of the compensated carbon intensity is 4.56%, and the value of the compensated carbon intensity using the modified spectrum standardization is 3.21%. The modified spectrum standardization method shows the best reproducibility because it not only compensates for the diminution of the atomic carbon intensities caused by matrix effect but also effectively compensates for the pulse-to-pulse signal fluctuations caused by the variations of plasma parameters (T, ne, and ns). Accuracy Improvement. The predicted carbon concentration of a sample is defined as the average value calculated from the 25 repeated measurements. The
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FIG. 5. Calibration plots of the C(I) 247 nm line after segmental spectral area normalization.
matrix effects of coal are so strong that the C(I) 247 nm line intensity does not have a good linearity with the carbon concentration (see Fig. 2a). The R2 value of the calibration curve between the C(I) 247 nm line intensities and the carbon concentration is only 0.46. When the C(I) 247 nm line intensity was normalized using the segmental spectral area, the R2 value of the calibration curve increased to 0.75 (Fig. 5). Given that the segmental spectrum area may be linearly related to the ablation mass, the segmental normalization method can partly compensate for the variation in the ablation mass. Therefore, the segmental normalization method can improve the R2 value of the calibration curve. Figure 6 shows the calibration plots of the compensated carbon intensity and the carbon content. The R2 value of the calibration curve is 0.85. The performance of the model in prediction accuracy can be justified using the RMSEP. The RMSEP of the univariate model that uses the compensated carbon intensity is 3.38%, whereas the corresponding value for the univariate model using the segmental normalization is 3.77%. Compared with the segmental spectral area normalization, the improvement in R2 and the reduction in RMSEP indicate that the emission intensities of C2 and CN can better compensate for the diminution of atomic carbon
FIG. 6. Calibration plots of the compensated carbon intensity.
FIG. 7. Calibration and validation plots for the spectrum standardization model.
FIG. 8. Maximum relative error of the predicted C concentration for the different methods.
emissions in high volatile coal samples, caused by matrix effects. Figure 7 demonstrates the calibration and validation results of the modified spectrum standardization model. The R2 of the present model is 0.90, and RMSEP is 2.24%. Compared with the univariate model that uses the compensated carbon intensity, the increased R2 indicates that the matrix effect is further corrected by compensating for the spectroscopic signal fluctuations attributed to the variation of the plasma parameters (T, ne, and ns). The lowered RMSEP of the present model implies that plasma-parameter correction terms in the present model contribute to the improvement in the prediction accuracy. The performance of the model in prediction accuracy can also be justified by the MRE, which is defined as Cpre Cnom ð15Þ MRE ¼ max 3 100% Cnom
coal. In the modified spectrum standardization model, we first compensated for the diminution of atomic carbon emissions in high volatile coal samples, caused by matrix effects, using the emission intensities of C2 and CN, and then converted the compensated carbon line intensities to the carbon line intensities at the standard state to further compensate for the fluctuations in the line intensities caused by the variations in the plasma parameters. The modified spectrum standardization method uses the segmental spectral area to correct the fluctuations of the total carbon number density and also applies a new iterative algorithm to the standardization calculations to obtain more accurate standard state line intensities. The assays of the carbon concentration of 24 bituminous coal samples using the proposed model show an improvement in both the measurement precision and accuracy compared to the traditional single-variable method using segmental spectrum area normalization.
where Cpre is the predicted concentration for each measurement, and Cnom is the nominal elemental concentration for the sample. The MRE indicates the largest deviation of a single measurement and can evaluate the prediction accuracy of the model, especially for conditions in which only a single-shot assay is allowed. The average MRE of the present model is 12.18%, whereas the value of the univariate calibration model with segmental spectral area normalization is 15.40% (Fig. 8). These results further demonstrated the advantage of the present model in improving measurement accuracy.
The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 51276100) and National Basic Research Program (973 Program) (No. 2013CB228501).
CONCLUSION The previously reported simplified spectrum standardization model can obviously reduce the signal uncertainty and improve the measurement accuracy by converting the line intensity to the intensity at the standard plasma state. However, the strong matrix effects of coal lead to an unsatisfactory linear relationship between the emission intensity and the concentration. Consequently, the simplified spectrum standardization method cannot be directly applied to the measurement of carbon content in
ACKNOWLEDGMENTS
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8. F.J. Wallis, B.L. Chadwick, R.J.S. Morrison. ‘‘Analysis of Lignite Using Laser-Induced Breakdown Spectroscopy’’. Appl. Spectrosc. 2000. 54(8): 1231-1235. ˜ 9. T. Ctvrtnickova, M.P. Mateo, A. Yanez, G. Nicolas. ‘‘Characterization of Coal Fly Ash Components by Laser-Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2009. 64(10): 1093-1097. 10. L.G. Blevins, C.R. Shaddix, S.M. Sickafoose, P.M. Walsh. ‘‘LaserInduced Breakdown Spectroscopy at High Temperatures in Industrial Boilers and Furnaces’’. Appl. Optics. 2003. 42(30): 61076118. 11. Z. Wang, T. Yuan, S. Lui, Z. Hou, X. Li, Z. Li, W. Ni. ‘‘Major Elements Analysis in Bituminous Coals Under Different Ambient Gases by Laser-Induced Breakdown Spectroscopy with PLS Modeling’’. Front. Phys. 2012. 7(6): 708-713. 12. S. Yao, J. Lu, J. Zheng, M. Dong. ‘‘Analyzing Unburned Carbon in Fly Ash Using Laser-Induced Breakdown Spectroscopy with Multivariate Calibration Method’’. J. Anal. Atom. Spectrom. 2012. 27(3): 473-478. 13. Z. Wang, Y. Deguchi, M. Kuwahara, T. Taira, X. Zhang, J. Yan, J. Liu, H. Watanabe, R. Kurose. ‘‘Quantitative Elemental Detection of Size-Segregated Particles Using Laser-Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2013. 87: 130-138. 14. J. Li, J. Lu, Z. Lin, S. Gong, C. Xie, L. Chang, L. Yang, P. Li. ‘‘Effects of Experimental Parameters on Elemental Analysis of Coal by Laser-Induced Breakdown Spectroscopy’’. Opt. Laser Technol. 2009. 41(8): 907-913. 15. J. Yu, Q.L. Ma, V. Motto-Ros, W.Q. Lei, X.C. Wang, X.S. Bai. ‘‘LaserInduced Plasma and Laser-Induced Breakdown Spectroscopy (LIBS) in China: The Challenge and the Opportunity’’. Front. Phys. 2012. 7(6): 649-669. 16. X. Li, W. Zhou, Z. Cui. ‘‘Temperature and Electron Density of Soil Plasma Generated by LA-FPDPS’’. Front. Phys. 2012. 7(6): 721-727. 17. J.H. Kwak, C. Lenth, C. Salb, E.J. Ko, K.W. Kim, K. Park. ‘‘Quantitative Analysis of Arsenic in Mine Tailing Soils Using Double Pulse-Laser Induced Breakdown Spectroscopy’’. Spectrochim. Acta B. 2009. 64(10): 1105-1110. 18. D. Mukherjee, A. Rai, M.R. Zachariah. ‘‘Quantitative Laser-Induced Breakdown Spectroscopy for Aerosols via Internal Calibration: Application to the Oxidative Coating of Aluminum Nanoparticles’’. J. Aerosol Sci. 2006. 37(6): 677-695.
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19. L. Xu, V. Bulatov, V.V. Gridin, I. Schechter. ‘‘Absolute Analysis of Particulate Materials by Laser-Induced Breakdown Spectroscopy’’. Anal. Chem. 1997. 69(11): 2103-2108. 20. F.J. Fortes, M. Corte´s, M.D. Simo´n, L.M. Cabalı´ n, J.J. Laserna. ‘‘Chronocultural Sorting of Archaeological Bronze Objects Using Laser-Induced Breakdown Spectrometry’’. Anal. Chim. Acta. 2005. 554(1-2): 136-143. 21. D. Body, B.L. Chadwick. ‘‘Optimization of the Spectral Data Processing in a LIBS Simultaneous Elemental Analysis System’’. Spectrochim. Acta B. 2001. 56(6): 725-736. 22. J.A. Bolger. ‘‘Semi-Quantitative Laser-Induced Breakdown Spectroscopy for Analysis of Mineral Drill Core’’. Appl. Spectrosc. 2000. 54(2): 181-189. 23. M.M. Tripathi, K.E. Eseller, F.Y. Yueh, J.P. Singh. ‘‘Multivariate Calibration of Spectra Obtained by Laser Induced Breakdown Spectroscopy of Plutonium Oxide Surrogate Residues’’. Spectrochim. Acta B. 2009. 64(11-12): 1212-1218. 24. S. Yao, J. Lu, M. Dong, K. Chen, J. Li, J. Li. ‘‘Extracting Coal Ash Content from Laser-Induced Breakdown Spectroscopy (LIBS) Spectra by Multivariate Analysis’’. Appl. Spectrosc. 2011. 65(10): 1197-1201. 25. J. Feng, Z. Wang, L. West, Z. Li, W. Ni. ‘‘A PLS Model Based on Dominant Factor for Coal Analysis Using Laser-Induced Breakdown Spectroscopy’’. Anal. Bioanal. Chem. 2011. 400(10): 3261-3271. 26. Z. Wang, L. Li, L. West, Z. Li, W. Ni. ‘‘A Spectrum Standardization Approach for Laser-Induced Breakdown Spectroscopy Measurements’’. Spectrochim. Acta B. 2012. 68: 58-64. 27. L. Li, Z. Wang, T. Yuan, Z. Hou, Z. Li, W. Ni. ‘‘A Simplified Spectrum Standardization Method for Laser-Induced Breakdown Spectroscopy Measurements’’. J. Anal. Atom. Spectrom. 2011. 26(11): 22742280. 28. E. Tognoni, V. Palleschi, M. Corsi, G. Cristoforetti, N. Omenetto, I. Gornushkin, B.W. Smith, J.D. Winefordner. ‘‘From Sample to Signal in Laser-Induced Breakdown Spectroscopy: A Complex Route to Quantitative Analysis’’. In: A.W. Miziolek, V. Palleschi, I. Schechter, editors. Laser-Induced Breakdown Spectroscopy (LIBS): Fundamentals and Applications. Cambridge, UK: Cambridge University Press, 2006. Pp. 127-136. 29. M. Dong, X. Mao, J.J. Gonzalez, J. Lu, R.E. Russo. ‘‘Carbon Isotope Separation and Molecular Formation in Laser-Induced Plasmas by Laser Ablation Molecular Isotopic Spectrometry’’. Anal. Chem. 2013. 85(5): 2899-2906.
