1 Introduction

The LIBS is an atomic emission spectroscopy that uses a laser beam at high irradiance beyond 109 W/cm2 as an excitation source. At this high irradiance, the plasma that contains free electrons, excited atoms, and ions is created. The emitted light from the plasma provides characteristic spectra of each element, and its chemical composition can be rapidly determined by identifying different spectra for the analyzed samples. The LIBS, as an elemental analyzer, has great advantages such as standoff analysis and high sensitivity. The LIBS analysis can also be performed in real time without any sample preparation.

As a step toward quantitative analysis, many researchers are studying the LIBS analysis in the context of generating calibration curves which indicate the relation between signal intensity and concentration. One way to build up the calibration curve is to use either standard reference materials (SRMs) that have the certified concentration [1–3] or non-certified materials with relatively well-known concentration [4, 5]. Another way is to compare the LIBS data with the result of comparative analysis such as ICP-OES (ICP-AES) [6, 7] and X-ray fluorescence [8]. The accuracy of calibration curves can be affected by the matrix effect which is caused by difference in the chemical compositions of samples. Although samples may contain the same concentration of a certain element, their signal intensities are not always identical. Hence, correcting the matrix effect has been an important issue in quantitative LIBS analyses.

One way of correcting the matrix effect is by normalization of the spectrum. Gornushkin et al. [9] reported that the surface density normalization method combined with analysis of the mechanical effect of the ablated weight provides a simple solution to deal with the matrix effect. Huang et al. [10] also suggested that normalization of the LIB emission by the current correlated analysis is a convenient way of suppressing the signal fluctuation and improving the LOD determination.

Also, plasma temperature-related correction method is proposed. Dettman et al. [11] and Bulajic et al. [12] described that a simple partial local thermodynamic equilibrium model could reduce the matrix effect to handle changes in sensitivity driven by the plasma temperature. Zhang et al. [13] utilized the calibration method with fixed plasma temperature in order to minimize the matrix effect.

The chemometrics (principal component analysis, partial least squares, or principal component regression) is also commonly applied in quantitative LIBS analysis to compensate for this matrix effect. Anderson et al. [14] used partial least squares regression to improve the accuracy of quantitative chemical analysis of LIBS. Doucet et al. [15] presented the use of chemometrics as a multivariate regression tool to compensate for matrix effects. They used multilinear regression, principal component regression, and partial least square regression and claimed that chemometrics coupled with LIBS was a suitable combination for the quantitative analysis of aluminum alloys. A good application of PCR and PLS models to pharmaceutical ingredients can be found in [16].

In this study, we carried out quantitative analysis of the LIBS signals from SRM samples. In order to minimize errors due to the matrix effect, we used 21 SRMs that belong to different categories of food, clay, sludge, steelmaking alloy, and geochemical and agricultural materials. The large number of SRM samples will make sure that various matrix effects be present in the present analysis. It is expected that the calibration curve of each category and/or material will show characteristic linear trend according to its chemical and physical property. Furthermore, principal component analysis (PCA) was used for a rapid identification and discrimination of the samples. The PCA result was compared with the calibration curve to establish quantitative LIBS procedure for the analysis of various SRM samples.

2 Experimental setup

A LIBS system (RT250-Ec, Applied Spectra Inc.) was used to carry out the experiment with a Nd:YAG laser operating at 1064 nm, pulsed at 10 Hz with a pulse energy of 70 mJ/pulse. The laser beam was focused onto the sample surface by a lens of 50 mm focal length. A high-resolution 6 channel-CCD spectrometer covers the spectrum ranging from 196.466 to 970.528 nm. Time delay of the spectrometer was 1 μs, and the gate width was 1.05 ms. To collect plasma, a lens of 50 mm focal length was used. Samples were placed in the chamber at room pressure and temperature on a XYZ stage. The laser beam was focused on the sample surface and fired on 6 locations with 10 shots for each location.

The 21 powdered SRM samples from NIST (National Institute of Standards and Technology) and USGS (United States Geological Survey) were selected as standard materials shown in Table 1. Those samples were chosen from 6 categories of interests, which are agricultural materials, foods, clays, soils and sediments, steelmaking alloys, and geochemical reference materials. Each of the samples was mixed with paraffin binder at a proportion of 10–100 % concentration by the difference of 10 % and was pelletized with 10 tons of pressure, 2.5 min of dwell time, and 1.5 min of release time (Spex model 3635). The paraffin binder contains only hydrogen and carbon (CnH2n+2), so that it can adjust the concentration without any effect on the result as well as bonding the powder sample.

Table 1 List of 21 SRM samples of varying constituents
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Nine elements (Al, Ca, Mg, Ti, Si, Fe, K, Na, and Mn) in each sample were analyzed. We based our selection of the specific emission lines on the peak intensity, interference with other emission lines, and spectrometer saturation. The selected peaks are as follows: Al (396.152 nm), Ca (422.6727 nm), Mg (285.213 nm), Ti (334.941 nm), Si (288.158 nm), Fe (373.4864 nm), K (766.490 nm), Na (588.995 nm), and Mn (403.076 nm).

3 Results and discussion

3.1 LIBS spectra

Figure 1 shows the LIBS spectra of several SRM samples. It is possible to classify the sample into groups based on their composition from the LIBS spectra. For example, food and agricultural samples such as NIST1515, NIST1573a, NIST1566b, and NIST1567a (first four graphs in Fig. 1) are seen distinct from the signals of the other SRM samples of clays, soils, and steelmaking alloys. Also, the same samples of food and agricultural materials can be subdivided into two minor groups (NIST1515, NIST1573a/NIST1566b, and NIST1567a) according to the existence of CN band at 388 nm. However, in the cases of NIST1515 and NIST1573a, they are indistinguishable through LIBS spectra since both samples have similar chemical components. Thus, we make use of the chemometrics to address the need for a refined discrimination.

Fig. 1
figure 1

LIBS spectra of several SRM samples. First four graphs (NIST 1515, 1573a, 1566b, and 1567a) are clearly distinguishable from the rest

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3.2 Principal component analysis (PCA)

Figure 2 shows the PCA result from 21 SRM samples where 90 % concentration samples are composed of the SRM and the binder in the proportion of 9:1. Some samples were hard to pelletize without the use of a binder as such to mix with the paraffin binder at 90 % concentration was needed. The SRM samples that were indistinguishable from LIBS spectra were discriminated using the PCA procedure, as one could see from the results for NIST1515 (red square) and NIST1573a (yellow triangle). Four distinct groups of food and agricultural, clay and soil, steelmaking alloy, and sludge are shown in Fig. 2.

Fig. 2
figure 2

PCA result from 21 SRM sample of 90 % concentration

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The PCA results show clear separation of each group especially in the case of steelmaking alloy where all are comprised of different elements. Some scatterings are present in the PCA plot due to a possible incomplete mixing of SRM and paraffin binder due to their large particle size (for example, NIST68c, NIST2782, NIST59a, SCo-1, NIST2780). The PCA results seem to be clustered altogether in some cases of NIST1567a, NIST1568a, NIST1577c, NIST1566b, and NIST1575a. One can assume that they all have similar major elemental composition.

As mentioned in the experimental setup, each sample was mixed with the paraffin binder at a proportion of 10–100 % concentration at an increment of 10 %. Therefore, the dispersion of PCA results of all samples converges at the origin according to the decrease in the concentration as shown in Fig. 3, which suggests that the samples at low concentration have similar characteristics.

Fig. 3
figure 3

PCA results according to the concentration

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3.3 Calibration curve

Building a database of elemental calibration curve is needed before carrying out the quantitative analysis of an unknown sample. Background subtraction was applied in order to deal with the continuum of each spectra. The area of emission peak with subtraction of the background adjacent to emission line was used as the signal intensity. The concentration of the element is shown in Table 2 with the tested SRM samples. The combination of chemometrics and calibration curves of pure SRM samples with respect to the known sample intensities was performed as a solution to the matrix effect [1–8]. Similar groups emerged from the PCA data (Fig. 3). We categorized 3–7 groups of elements with the analyzed calibration curves of the whole samples, since the characteristics of each element were not considered in the PCA results in Fig. 3.

Figure 4 shows 5 groups (b–f) separated from the combined calibration curve of Fe (Fig. 4a). The concentration in all of the calibration curves is the total concentration of element in the sample. Figure 4 is consistent with Table 1 and PCA results in Fig. 3, as classified into (b) food and agricultural material, (c) clay, (d) clay and sludge, (e) granite type, and (f) steelmaking alloy. Figure 5a, a combined calibration for Ca, was not categorized as well, while food, clay, and steelmaking alloy groups were mixed with (b)–(h) groups altogether. Table 3 shows complete classification of SRM samples with respect to elements from calibration curve. It can be inferred from Table 3 that the effect of particular elements must be taken into account when performing quantitative LIBS analysis, in order to build accurate calibration curves. This is because the PCA results were not applicable to some of the elements such as K, Mg, and Ca.

Table 2 Concentration of SRMs [14]
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Fig. 4
figure 4

Categorization of Fe by calibration curves of all SRM samples. 5 distinct groups (b–f) emerged from the combined graph (a)

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Fig. 5
figure 5

Categorization of Ca by calibration curve of all SRM samples. 7 distinct groups (b–h) emerged from the combined graph (a)

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Table 3 Groups for each element from calibration curve
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Figure 6 shows linear fittings of Ca whose characteristics are randomly grouped. It is not categorized with specific materials, rather the result is verified to be accurate having a high correlation coefficient, R 2.

Fig. 6
figure 6

Calibration curves of Ca showing 7 groups from Table 3

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Figure 7 is a calibration curve of Fe. It shows high correlation coefficient amongst all the groups except for group 5 that is comprised of food and agricultural materials. The experimental error of group 5 seems to be higher than other groups since it has lower concentration of Fe. This suggests raising the sensitivity by considering the low pressure circumstances and the optimized layout of the experimental setup to detect minor elements.

Fig. 7
figure 7

Calibration curves of Fe showing 5 groups from Table 3

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Figure 8 corresponds to the calibration curves of Si and Ti. We applied polynomial fittings because Si and Ti tend to have nonlinear curves. The result was successful as they were well categorized with the expected groups of Table 3. Although polynomial fitting can achieve high correlation coefficient, it makes it more difficult to estimate concentrations beyond the range of calibration curves than linear fitting. Therefore, linear fitting is a preferred method if the error is not so critical.

Fig. 8
figure 8

Calibration curves of a Si of 3 groups and b Ti of 3 groups from Table 3

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4 Conclusion

In this research, a quantitative LIBS analysis was applied to handle the matrix effect. The 21 powdered SRM samples from NIST and USGS were chosen from agricultural materials, foods, clays, soils and sediments, steelmaking alloys, and geochemical reference materials based on the samples’ basic constituents. The PCA method was applied to categorize the samples with similar characteristics. The obtained calibration curves exhibit significant improvement to their curve accuracy through the PCA procedure as well as the quantitative analysis of characteristics of groups by elements. Samples of various SRMs were successfully grouped through the accurate calibration curves of K, Mg, and Ca, without any correlation to the results of PCA data. The present result illustrated a novel quantitative LIBS analysis with significantly diminishing matrix effect.