Quantitative analysis of the main components in ceramic raw materials based on the desktop LIBS analyzer

1.   Introduction

As a consequence of the continuous large-scale investment in the field of infrastructure construction and improvement in living standards, there is a huge demand for building ceramics in the construction industry in China. Building ceramics production is a process industry with high-energy consumption. The content of key components in ceramic formulas determines both cost factors (e.g. the energy consumption in the firing process) and quality factors (such as the whiteness, transparency and flatness of products). Therefore, the detection and analysis of the concentrations of key elements in the green body before firing will not only realize better quality control, but the reduction of energy consumption and pollution. At present, the daily production of the building ceramics industry lacks rapid detection methods, and usually depends on the experience and judgment of technicians, resulting in high production risk. Traditional chemical analysis by professional institutions is only performed in the case of problems because of the high cost. This lack of analysis prevents the timeous adjustment of the formula and seriously affects production efficiency. Therefore, a fast and simple detection method is needed to provide a basis for the control and adjustment of daily production.

X-ray fluorescence (XRF) and laser-induced breakdown spectroscopy (LIBS) are recognized as spectral analysis technologies suitable for rapid detection [1–3]. The advantage of XRF is nondestructive determination, but the detection ability of light elements is weak; the advantage of LIBS is the quick detection of almost all elements in the periodic table, but part of the sample surface will be ablated by the laser to create plasma during the detection. The building ceramics industry is mainly concerned with the chemical components, being concentrations of the eight oxides (SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃ and TiO₂), together with L.O.I. There are light elements such as Na, Mg and Al, and L.O.I. is also largely determined by light elements such as C, H and O. On the other hand, the unit-price of ceramic raw material is low, and the destruction of samples during detection is not a concern. Therefore, LIBS is more suitable for the analysis of the main components of ceramic raw materials.

There is an abundance of research on the applications of LIBS in energy [4], metallurgy [5, 6], geographical survey [7] and extraterrestrial space exploration [8, 9]. Research on the element content and mineral composition of soil and rock using LIBS is also a hot field [10–14]. LIBS-based analysis of ceramic raw materials (such as clay, feldspar and quartz) is usually qualitative analysis or quantitative analysis of one or several elements in samples from a specific origin or specific raw material types [15–20]. Tang et al analyzed the content of K element in feldspar raw materials and improved the analysis accuracy by Lorentz fitting [18]. Chen et al measured the content of Si, Al, Ca, K, Mg, Mn, Ti and Fe in drilling cutting samples by logging a special laser-induced breakdown spectrometer [20]. Unified modeling and simultaneous quantitative analysis of the eight main oxides and L.O.I. in clay, feldspar, quartz and other types of minerals have rarely been reported in the literature.

In this work, geological samples with wide variations in mineral composition were detected by the fiber-laser-based LIBS analyzer under the same experimental conditions, and the L.O.I. and concentrations of SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃ and TiO₂ in different kind of minerals were analyzed synchronously. The concentrations of these main elements in geological samples for building ceramics were simultaneously detected from the plasma emission induced by the long-pulse-width and low-power fiber laser. The combination of continuous background deduction, FWHM intensity integral and spectral sum normalization was proposed to reduce the differences between sample matrices. Different calibration models were further proposed to improve the analysis performance of different compositions. The desktop LIBS analyzer integrated with the proposed methods provided a solution for daily rapid detection in the ceramics industry.

1.   Introduction

As a consequence of the continuous large-scale investment in the field of infrastructure construction and improvement in living standards, there is a huge demand for building ceramics in the construction industry in China. Building ceramics production is a process industry with high-energy consumption. The content of key components in ceramic formulas determines both cost factors (e.g. the energy consumption in the firing process) and quality factors (such as the whiteness, transparency and flatness of products). Therefore, the detection and analysis of the concentrations of key elements in the green body before firing will not only realize better quality control, but the reduction of energy consumption and pollution. At present, the daily production of the building ceramics industry lacks rapid detection methods, and usually depends on the experience and judgment of technicians, resulting in high production risk. Traditional chemical analysis by professional institutions is only performed in the case of problems because of the high cost. This lack of analysis prevents the timeous adjustment of the formula and seriously affects production efficiency. Therefore, a fast and simple detection method is needed to provide a basis for the control and adjustment of daily production.

X-ray fluorescence (XRF) and laser-induced breakdown spectroscopy (LIBS) are recognized as spectral analysis technologies suitable for rapid detection [1–3]. The advantage of XRF is nondestructive determination, but the detection ability of light elements is weak; the advantage of LIBS is the quick detection of almost all elements in the periodic table, but part of the sample surface will be ablated by the laser to create plasma during the detection. The building ceramics industry is mainly concerned with the chemical components, being concentrations of the eight oxides (SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃ and TiO₂), together with L.O.I. There are light elements such as Na, Mg and Al, and L.O.I. is also largely determined by light elements such as C, H and O. On the other hand, the unit-price of ceramic raw material is low, and the destruction of samples during detection is not a concern. Therefore, LIBS is more suitable for the analysis of the main components of ceramic raw materials.

There is an abundance of research on the applications of LIBS in energy [4], metallurgy [5, 6], geographical survey [7] and extraterrestrial space exploration [8, 9]. Research on the element content and mineral composition of soil and rock using LIBS is also a hot field [10–14]. LIBS-based analysis of ceramic raw materials (such as clay, feldspar and quartz) is usually qualitative analysis or quantitative analysis of one or several elements in samples from a specific origin or specific raw material types [15–20]. Tang et al analyzed the content of K element in feldspar raw materials and improved the analysis accuracy by Lorentz fitting [18]. Chen et al measured the content of Si, Al, Ca, K, Mg, Mn, Ti and Fe in drilling cutting samples by logging a special laser-induced breakdown spectrometer [20]. Unified modeling and simultaneous quantitative analysis of the eight main oxides and L.O.I. in clay, feldspar, quartz and other types of minerals have rarely been reported in the literature.

In this work, geological samples with wide variations in mineral composition were detected by the fiber-laser-based LIBS analyzer under the same experimental conditions, and the L.O.I. and concentrations of SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃ and TiO₂ in different kind of minerals were analyzed synchronously. The concentrations of these main elements in geological samples for building ceramics were simultaneously detected from the plasma emission induced by the long-pulse-width and low-power fiber laser. The combination of continuous background deduction, FWHM intensity integral and spectral sum normalization was proposed to reduce the differences between sample matrices. Different calibration models were further proposed to improve the analysis performance of different compositions. The desktop LIBS analyzer integrated with the proposed methods provided a solution for daily rapid detection in the ceramics industry.

2.   Experiment

2.   Experiment

2.1   Experimental instrument

An experiment was performed on the self-developed desktop LIBS analyzer named LIBSeer. The design rendering, front view and system diagram of the instrument are shown in figures 1(a)–(c), respectively. The laser adopts the YDFLP-60-LM1⁺-L1-R (JPT Opto-electronics Co., Ltd) pulse fiber laser, with maximum power of 60 W and single-pulse energy of about 1.5 mJ; the laser focusing lens is a flat convex lens with a focal length of 75 mm; the plasma emission collection lens is a flat convex lens with a focal length of 20 mm, and the collection angle is 30° lateral to the laser incident direction. Two spectrometers (AvaSpec-Mini4096CL, Avantes) are selected to cover the detection spectral wavelength ranges from 240–400 nm and 610–830 nm, respectively.

Figure  1.  (a) Design rendering of LIBSeer, (b) front view of LIBSeer and (c) structure diagram of the system.

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2.1   Experimental instrument

An experiment was performed on the self-developed desktop LIBS analyzer named LIBSeer. The design rendering, front view and system diagram of the instrument are shown in figures 1(a)–(c), respectively. The laser adopts the YDFLP-60-LM1⁺-L1-R (JPT Opto-electronics Co., Ltd) pulse fiber laser, with maximum power of 60 W and single-pulse energy of about 1.5 mJ; the laser focusing lens is a flat convex lens with a focal length of 75 mm; the plasma emission collection lens is a flat convex lens with a focal length of 20 mm, and the collection angle is 30° lateral to the laser incident direction. Two spectrometers (AvaSpec-Mini4096CL, Avantes) are selected to cover the detection spectral wavelength ranges from 240–400 nm and 610–830 nm, respectively.

Figure  1.  (a) Design rendering of LIBSeer, (b) front view of LIBSeer and (c) structure diagram of the system.

DownLoad: Full-Size Img PowerPoint

2.2   Samples and data

There were 16 national reference materials and 14 common ceramic raw materials used in the experiment. The pretreatment procedure of raw materials is: (1) taking a 500 g sample, wet ball milling it for half an hour; (2) drying it and sieving with a 60 mesh sieve; (3) taking about 20 g for chemical analysis, taking the rest of the powder for a LIBS experiment. The content of the oxides of the eight elements and the L.O.I. of each sample are shown in table 1 below.

Table  1.  Reference content of samples (%).

No.	Sample	L.O.I.	SiO2	Al2O3	K2O	Na2O	CaO	MgO	Fe2O3	TiO2
1	GBW03126	5.48	66.84	23.58	0.38	0.34	0.17	0.09	1.94	0.70
2	GBW03127	6.34	70.34	22.20	0.03	0.04	0.07	0.04	0.22	0.18
3	GBW03101a	10.62	49.98	26.27	0.79	0.06	0.13	0.46	10.55	0.70
4	GBW03102a	8.81	53.70	31.32	1.15	2.55	1.80	0.08	0.33	0.03
5	GBW03103	5.10	66.64	13.28	2.50	1.81	3.23	1.84	4.64	0.66
6	GBW03115	8.72	55.90	28.57	1.54	1.74	0.70	0.30	0.86	1.21
7	GBW03104a	4.54	69.34	15.03	3.49	0.16	0.19	0.64	5.65	0.68
8	GBW03124	2.37	60.64	20.05	5.06	8.97	0.52	0.13	1.37	0.12
9	GBW03125	4.75	39.42	29.67	4.72	12.59	5.98	0.92	0.33	0.14
10	GBW03121a	17.31	43.41	34.77	0.78	0.05	0.04	0.07	1.50	0.25
11	GBW03122a	14.81	45.30	37.70	0.04	0.05	0.06	0.02	0.35	0.06
12	GBW03116	0.86	66.26	18.63	9.60	3.69	0.76	0.05	0.19	0.05
13	GBW03134	0.36	67.96	19.62	0.10	11.26	0.48	0.02	0.10	0.05
14	GBW03112a	0.14	98.32	1.10	0.15	0.08	0.04	0.03	0.08	0.02
15	GBW03113a	0.27	94.41	3.20	1.26	0.47	0.09	0.03	0.09	0.02
16	GBW03114	0.53	85.59	5.48	2.07	1.09	0.34	0.16	0.48	0.10
17	RM1	5.73	72.58	17.25	1.51	0.43	0.35	0.41	1.21	0.36
18	RM2	4.05	70.81	15.44	3.62	1.02	1.38	1.25	1.96	0.23
19	RM3	5.44	69.71	13.91	2.93	1.26	2.75	1.97	1.76	0.12
20	RM4	2.57	40.55	47.4	0.28	0.36	0.22	0.79	0.67	0.17
21	RM5	1.26	74.01	13.85	5.29	3.41	0.99	0.18	0.6	0.12
22	RM6	1.26	45.92	46.79	0.62	0.52	0.91	0.54	1.58	1.51
23	RM7	0.27	75.49	13.97	5.47	3.8	0.52	0.03	0.22	0.05
24	RM8	0.45	72.73	14.75	5.04	4.13	1.63	0.29	0.55	0.2
25	RM9	5.82	68.29	15.97	2.16	2.43	1.61	2.38	1.15	0.04
26	RM10	1.15	68.13	18.06	0.33	10.42	0.97	0.52	0.12	0.13
27	RM11	0.44	69.27	17.06	6.95	4.79	0.66	0.14	0.14	0.05
28	RM12	13.38	36.8	44.45	0.32	0.02	0.24	0.13	2.23	2.17
29	RM13	11.13	50.99	34.34	2.02	0.03	0.06	0.2	0.83	0.12
30	RM14	0.32	68.64	18.99	0.35	10.99	0.18	0.06	0.06	0.28

 | Show Table

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The tablet-pressing parameters are: (1) 2 g sample powder for each tablet; (2) with boric acid substrate; (3) 4 and 3.2 cm for the outer diameter and inner diameter of the tablet, respectively; (4) pressing under the pressure of 30 T and keeping the pressure for 30 s.

In order to satisfy the condition of full-power output of the fiber laser and obtain stable excitation and collection results, the laser parameters were optimized as follows: the pulse width of 250 ns, frequency of 40 kHz and duration of 150 μs; the delay and integration time of the spectrometers were optimized to 60 and 100 μs, respectively; and the detection frequency of the instrument is 10 Hz. For each detection, the spectrum collected by the spectrometer corresponded to the whole life cycle of plasma emissions excited by four laser pulses. Finally, there were 300 detections from different positions of each tablet, realized by the automatic rotation and translation of the electric control displacement table. The average spectrum of 300 detections is recorded as the original spectrum of the tablet sample. The pressed tablets of different samples and laser ablation craters after detection are shown in figure 2.

Figure  2.  (a) Tablets of different materials, (b) side view of the tablet, (c) vertical view of the tablet and (d) the ablation craters under an electron microscope.

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The typical spectra collected are shown in figure 3. In the range of 240–400 nm and 610–830 nm, the characteristic spectral lines of Si, Al, K, Na, Ca, Mg, Fe and Ti are all included, and the characteristic spectral lines of other elements, such as H and O, which are related to L.O.I., are also included.

Figure  3.  Characteristic spectral lines of different elements in the range of (a) 240–400 nm and (b) 610–830 nm.

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2.2   Samples and data

There were 16 national reference materials and 14 common ceramic raw materials used in the experiment. The pretreatment procedure of raw materials is: (1) taking a 500 g sample, wet ball milling it for half an hour; (2) drying it and sieving with a 60 mesh sieve; (3) taking about 20 g for chemical analysis, taking the rest of the powder for a LIBS experiment. The content of the oxides of the eight elements and the L.O.I. of each sample are shown in table 1 below.

Table  1.  Reference content of samples (%).

No.	Sample	L.O.I.	SiO2	Al2O3	K2O	Na2O	CaO	MgO	Fe2O3	TiO2
1	GBW03126	5.48	66.84	23.58	0.38	0.34	0.17	0.09	1.94	0.70
2	GBW03127	6.34	70.34	22.20	0.03	0.04	0.07	0.04	0.22	0.18
3	GBW03101a	10.62	49.98	26.27	0.79	0.06	0.13	0.46	10.55	0.70
4	GBW03102a	8.81	53.70	31.32	1.15	2.55	1.80	0.08	0.33	0.03
5	GBW03103	5.10	66.64	13.28	2.50	1.81	3.23	1.84	4.64	0.66
6	GBW03115	8.72	55.90	28.57	1.54	1.74	0.70	0.30	0.86	1.21
7	GBW03104a	4.54	69.34	15.03	3.49	0.16	0.19	0.64	5.65	0.68
8	GBW03124	2.37	60.64	20.05	5.06	8.97	0.52	0.13	1.37	0.12
9	GBW03125	4.75	39.42	29.67	4.72	12.59	5.98	0.92	0.33	0.14
10	GBW03121a	17.31	43.41	34.77	0.78	0.05	0.04	0.07	1.50	0.25
11	GBW03122a	14.81	45.30	37.70	0.04	0.05	0.06	0.02	0.35	0.06
12	GBW03116	0.86	66.26	18.63	9.60	3.69	0.76	0.05	0.19	0.05
13	GBW03134	0.36	67.96	19.62	0.10	11.26	0.48	0.02	0.10	0.05
14	GBW03112a	0.14	98.32	1.10	0.15	0.08	0.04	0.03	0.08	0.02
15	GBW03113a	0.27	94.41	3.20	1.26	0.47	0.09	0.03	0.09	0.02
16	GBW03114	0.53	85.59	5.48	2.07	1.09	0.34	0.16	0.48	0.10
17	RM1	5.73	72.58	17.25	1.51	0.43	0.35	0.41	1.21	0.36
18	RM2	4.05	70.81	15.44	3.62	1.02	1.38	1.25	1.96	0.23
19	RM3	5.44	69.71	13.91	2.93	1.26	2.75	1.97	1.76	0.12
20	RM4	2.57	40.55	47.4	0.28	0.36	0.22	0.79	0.67	0.17
21	RM5	1.26	74.01	13.85	5.29	3.41	0.99	0.18	0.6	0.12
22	RM6	1.26	45.92	46.79	0.62	0.52	0.91	0.54	1.58	1.51
23	RM7	0.27	75.49	13.97	5.47	3.8	0.52	0.03	0.22	0.05
24	RM8	0.45	72.73	14.75	5.04	4.13	1.63	0.29	0.55	0.2
25	RM9	5.82	68.29	15.97	2.16	2.43	1.61	2.38	1.15	0.04
26	RM10	1.15	68.13	18.06	0.33	10.42	0.97	0.52	0.12	0.13
27	RM11	0.44	69.27	17.06	6.95	4.79	0.66	0.14	0.14	0.05
28	RM12	13.38	36.8	44.45	0.32	0.02	0.24	0.13	2.23	2.17
29	RM13	11.13	50.99	34.34	2.02	0.03	0.06	0.2	0.83	0.12
30	RM14	0.32	68.64	18.99	0.35	10.99	0.18	0.06	0.06	0.28

 | Show Table

DownLoad: CSV

The tablet-pressing parameters are: (1) 2 g sample powder for each tablet; (2) with boric acid substrate; (3) 4 and 3.2 cm for the outer diameter and inner diameter of the tablet, respectively; (4) pressing under the pressure of 30 T and keeping the pressure for 30 s.

In order to satisfy the condition of full-power output of the fiber laser and obtain stable excitation and collection results, the laser parameters were optimized as follows: the pulse width of 250 ns, frequency of 40 kHz and duration of 150 μs; the delay and integration time of the spectrometers were optimized to 60 and 100 μs, respectively; and the detection frequency of the instrument is 10 Hz. For each detection, the spectrum collected by the spectrometer corresponded to the whole life cycle of plasma emissions excited by four laser pulses. Finally, there were 300 detections from different positions of each tablet, realized by the automatic rotation and translation of the electric control displacement table. The average spectrum of 300 detections is recorded as the original spectrum of the tablet sample. The pressed tablets of different samples and laser ablation craters after detection are shown in figure 2.

Figure  2.  (a) Tablets of different materials, (b) side view of the tablet, (c) vertical view of the tablet and (d) the ablation craters under an electron microscope.

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The typical spectra collected are shown in figure 3. In the range of 240–400 nm and 610–830 nm, the characteristic spectral lines of Si, Al, K, Na, Ca, Mg, Fe and Ti are all included, and the characteristic spectral lines of other elements, such as H and O, which are related to L.O.I., are also included.

Figure  3.  Characteristic spectral lines of different elements in the range of (a) 240–400 nm and (b) 610–830 nm.

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3.   Results and discussion

3.   Results and discussion

3.1   Spectral data preprocessing

There were two tablets for each kind of sample listed in table 1. For each tablet, the experiment was repeated twice on different days with the same experimental parameters. Finally, there were four groups (two tablets, two experiments) of original spectral data for each kind of sample. Four plasma emissions were collected by the spectrometers in each detection to obtain sufficient spectral intensity, but due to the lack of time resolution, there was also strong continuous background radiation in the original spectrum. Therefore, the first data preprocessing was continuous background deduction. Furthermore, due to the self-absorption effect and the limited resolution of the module spectrometer, it may not be able to effectively capture the ideal peak intensity of the characteristic spectral line. Therefore, another data preprocessing method used was calculating the full width at half maximum (FWHM) to represent the characteristic spectral line intensity.

3.1   Spectral data preprocessing

There were two tablets for each kind of sample listed in table 1. For each tablet, the experiment was repeated twice on different days with the same experimental parameters. Finally, there were four groups (two tablets, two experiments) of original spectral data for each kind of sample. Four plasma emissions were collected by the spectrometers in each detection to obtain sufficient spectral intensity, but due to the lack of time resolution, there was also strong continuous background radiation in the original spectrum. Therefore, the first data preprocessing was continuous background deduction. Furthermore, due to the self-absorption effect and the limited resolution of the module spectrometer, it may not be able to effectively capture the ideal peak intensity of the characteristic spectral line. Therefore, another data preprocessing method used was calculating the full width at half maximum (FWHM) to represent the characteristic spectral line intensity.

3.2   Univariate calibration

Figure 4 shows the correlation between the content and the intensity of the characteristic spectral line of each element. The error bar reflects the standard deviation of spectral intensity between the four experiments for each sample. Due to the different mineral compositions of ceramic raw materials, the spectral line intensity of each element was affected by the matrix effect and could not reflect the element content directly.

Figure  4.  Relationship between the spectral line intensity in the original spectrum and the content of the corresponding element.

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In order to reduce the influence of the matrix effect on the spectrum, it is necessary to select an appropriate reference value to normalize the original spectral line intensity. The content of each element in different ceramic raw materials varies widely. There is no suitable element to select the reference line for an internal standard. Spectral sum normalization is a feasible method, calculating the sum of the full spectrum detected by the spectrometer as the reference value. The average and relative standard deviation (RSD) values of the spectral sum of each sample in the four experiments are shown in table 2. It can be seen that either the spectral sums or the RSDs of different samples were quite different, due to differences in the plasma emission caused by different matrix compositions.

Table  2.  Spectral sums and RSDs of different kinds of samples.

No.	Spectral sum (106)	RSD (%)	No.	Spectral sum (106)	RSD (%)	No.	Spectral sum (106)	RSD (%)
1	1.13	4.27	11	1.86	3.25	21	1.17	2.41
2	1.43	0.91	12	1.25	3.10	22	1.54	1.82
3	2.59	2.30	13	1.21	0.69	23	1.30	3.36
4	1.77	2.48	14	0.91	3.15	24	1.23	1.17
5	1.91	1.68	15	0.93	2.32	25	2.43	3.38
6	1.58	3.39	16	0.99	0.46	26	1.26	2.33
7	2.04	2.48	17	1.84	3.24	27	1.25	1.60
8	1.12	0.76	18	2.41	2.36	28	2.16	3.19
9	1.64	2.06	19	2.51	2.47	29	1.87	3.24
10	1.91	2.91	20	1.92	0.93	30	1.26	2.77

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The calibration results of the content of each component listed in table 1 using normalized spectral intensity are shown in figure 5. It can be seen that, for most of the components, the correlation between the spectral line intensity and the content was significantly improved after spectral sum normalization.

Figure  5.  Relationship between the spectral line intensity after the spectral sum normalization and the content of the corresponding element.

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The characteristic spectral lines and corresponding correlation coefficients (R) selected for each component in figures 4 and 5 are shown in table 3. After spectral sum normalization, the correlation coefficients between all characteristic spectral lines and corresponding content are improved. Further analysis of the spectral lines after spectral sum normalization shows that: (1) L.O.I. includes the structural water discharged during 1000 ℃ ignition, CO₂ decomposed by carbonate, SO₂ decomposed by sulfate, and the loss of material after the thermal decomposition of organic matter. The characteristic spectral line of H can only represent the water content in the sample to some extent, but cannot represent the total L.O.I. Therefore, there was some correlation between L.O.I. and H line at 656.5 nm, but the desired calibration result could not be obtained. (2) As a major element in geological samples, Si exists in most pedogenic minerals in different forms. In a common building ceramics body formula, quartz is usually used as a ridge material, clay as ductile material and feldspar as flux. All these kinds of minerals contain Si. The characteristic line of Si is seriously affected by the matrix effect. Therefore, the correlation between SiO₂ content and Si line at 288.2 nm was weak. (3) As a major element in clay and feldspar, Al mainly exists in each sample in the form of aluminosilicate. Only part of Al in sample Nos. 20, 22 and 28 may exist in the form of alumina or hydrated alumina. Therefore, for different kinds of samples, the influence of the matrix effect on Al was more consistent than on Si. The correlation coefficient between the Al₂O₃ content and Al line at 309.2 nm reached 0.96 after spectral sum normalization. (4) For K, Na, Ca and Mg, the main form that exists is aluminosilicate in ceramic raw materials, and the correlation coefficient between oxide content and spectral line is more than 0.97 after spectral sum normalization. (5) Most of the Fe and Ti directly exist in the form of oxides in the samples, so the influence of the matrix effect is relatively weak. The correlation coefficients reached 0.99 after spectral sum normalization.

Table  3.  Correlation coefficients (R) between characteristic spectral line intensity and concentration.

Component	Element	Characteristic spectral line	Rorga	Rnrmb
L.O.I.	H	656.5 nm	0.81	0.86
SiO2	Si	288.2 nm	-0.27	0.39
Al2O3	Al	309.2 nm	0.85	0.96
K2O	K	769.9 nm	0.79	0.97
Na2O	Na	819.5 nm	0.96	0.97
CaO	Ca	317.9 nm	0.91	0.98
MgO	Mg	280.3 nm	0.96	0.97
Fe2O3	Fe	259.9 nm	0.99	0.99
TiO2	Ti	334.9 nm	0.94	0.99
a The correlation coefficient between original spectral line intensity and concentration. b The correlation coefficient between spectral sum normalized intensity and concentration.

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For comparison between the different calibration methods, the mean absolute errors (MAEs) of direct calibration of L.O.I. and the oxides are shown in table 4. For L.O.I. and most of the oxide content, calibration with the spectral sum normalized intensity can obtain better MAEs.

Table  4.  MAEs of 30 kinds of samples with different calibration methods.

Method	L.O.I.	SiO2	Al2O3	K2O	Na2O	CaO	MgO	Fe2O3	TiO2
Lnra	2.03	12.06	4.84	1.10	0.69	0.31	0.11	0.20	0.10
Lnr&Nrmb	1.80	10.38	2.66	0.44	0.62	0.15	0.11	0.24	0.06
Sqr&Nrmc	1.82	9.48	2.12	0.36	0.58	0.11	0.08	0.19	0.05
a Linear calibration. b Spectral sum normalization. c Square function calibration.

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In the building ceramic structure of SiO₂-Al₂O₃-K₂O(Na₂O) the following applies: the production will not be affected if the absolute errors of CaO, MgO, Fe₂O₃ and TiO₂ are less than 0.2%; the absolute error of K₂O and Na₂O should not exceed 0.5% for firing temperature control; the absolute errors of L.O.I., SiO₂ and Al₂O₃ should not exceed 2% for structure and shrinkage control. Therefore, (1) the direct calibration of CaO, MgO, Fe₂O₃ and TiO₂ can meet the requirements of production control; (2) the direct calibration of K₂O can meet the requirement of production control, but direct calibration of Na₂O should be further improved; (3) it is not feasible to directly calibrate the L.O.I., SiO₂ and Al₂O₃ with spectral lines of H, Si and Al, respectively. Other methods should be used to further improve the prediction accuracy.

3.2   Univariate calibration

Figure 4 shows the correlation between the content and the intensity of the characteristic spectral line of each element. The error bar reflects the standard deviation of spectral intensity between the four experiments for each sample. Due to the different mineral compositions of ceramic raw materials, the spectral line intensity of each element was affected by the matrix effect and could not reflect the element content directly.

Figure  4.  Relationship between the spectral line intensity in the original spectrum and the content of the corresponding element.

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In order to reduce the influence of the matrix effect on the spectrum, it is necessary to select an appropriate reference value to normalize the original spectral line intensity. The content of each element in different ceramic raw materials varies widely. There is no suitable element to select the reference line for an internal standard. Spectral sum normalization is a feasible method, calculating the sum of the full spectrum detected by the spectrometer as the reference value. The average and relative standard deviation (RSD) values of the spectral sum of each sample in the four experiments are shown in table 2. It can be seen that either the spectral sums or the RSDs of different samples were quite different, due to differences in the plasma emission caused by different matrix compositions.

Table  2.  Spectral sums and RSDs of different kinds of samples.

No.	Spectral sum (106)	RSD (%)	No.	Spectral sum (106)	RSD (%)	No.	Spectral sum (106)	RSD (%)
1	1.13	4.27	11	1.86	3.25	21	1.17	2.41
2	1.43	0.91	12	1.25	3.10	22	1.54	1.82
3	2.59	2.30	13	1.21	0.69	23	1.30	3.36
4	1.77	2.48	14	0.91	3.15	24	1.23	1.17
5	1.91	1.68	15	0.93	2.32	25	2.43	3.38
6	1.58	3.39	16	0.99	0.46	26	1.26	2.33
7	2.04	2.48	17	1.84	3.24	27	1.25	1.60
8	1.12	0.76	18	2.41	2.36	28	2.16	3.19
9	1.64	2.06	19	2.51	2.47	29	1.87	3.24
10	1.91	2.91	20	1.92	0.93	30	1.26	2.77

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The calibration results of the content of each component listed in table 1 using normalized spectral intensity are shown in figure 5. It can be seen that, for most of the components, the correlation between the spectral line intensity and the content was significantly improved after spectral sum normalization.

Figure  5.  Relationship between the spectral line intensity after the spectral sum normalization and the content of the corresponding element.

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The characteristic spectral lines and corresponding correlation coefficients (R) selected for each component in figures 4 and 5 are shown in table 3. After spectral sum normalization, the correlation coefficients between all characteristic spectral lines and corresponding content are improved. Further analysis of the spectral lines after spectral sum normalization shows that: (1) L.O.I. includes the structural water discharged during 1000 ℃ ignition, CO₂ decomposed by carbonate, SO₂ decomposed by sulfate, and the loss of material after the thermal decomposition of organic matter. The characteristic spectral line of H can only represent the water content in the sample to some extent, but cannot represent the total L.O.I. Therefore, there was some correlation between L.O.I. and H line at 656.5 nm, but the desired calibration result could not be obtained. (2) As a major element in geological samples, Si exists in most pedogenic minerals in different forms. In a common building ceramics body formula, quartz is usually used as a ridge material, clay as ductile material and feldspar as flux. All these kinds of minerals contain Si. The characteristic line of Si is seriously affected by the matrix effect. Therefore, the correlation between SiO₂ content and Si line at 288.2 nm was weak. (3) As a major element in clay and feldspar, Al mainly exists in each sample in the form of aluminosilicate. Only part of Al in sample Nos. 20, 22 and 28 may exist in the form of alumina or hydrated alumina. Therefore, for different kinds of samples, the influence of the matrix effect on Al was more consistent than on Si. The correlation coefficient between the Al₂O₃ content and Al line at 309.2 nm reached 0.96 after spectral sum normalization. (4) For K, Na, Ca and Mg, the main form that exists is aluminosilicate in ceramic raw materials, and the correlation coefficient between oxide content and spectral line is more than 0.97 after spectral sum normalization. (5) Most of the Fe and Ti directly exist in the form of oxides in the samples, so the influence of the matrix effect is relatively weak. The correlation coefficients reached 0.99 after spectral sum normalization.

Table  3.  Correlation coefficients (R) between characteristic spectral line intensity and concentration.

Component	Element	Characteristic spectral line	Rorga	Rnrmb
L.O.I.	H	656.5 nm	0.81	0.86
SiO2	Si	288.2 nm	-0.27	0.39
Al2O3	Al	309.2 nm	0.85	0.96
K2O	K	769.9 nm	0.79	0.97
Na2O	Na	819.5 nm	0.96	0.97
CaO	Ca	317.9 nm	0.91	0.98
MgO	Mg	280.3 nm	0.96	0.97
Fe2O3	Fe	259.9 nm	0.99	0.99
TiO2	Ti	334.9 nm	0.94	0.99
a The correlation coefficient between original spectral line intensity and concentration. b The correlation coefficient between spectral sum normalized intensity and concentration.

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For comparison between the different calibration methods, the mean absolute errors (MAEs) of direct calibration of L.O.I. and the oxides are shown in table 4. For L.O.I. and most of the oxide content, calibration with the spectral sum normalized intensity can obtain better MAEs.

Table  4.  MAEs of 30 kinds of samples with different calibration methods.

Method	L.O.I.	SiO2	Al2O3	K2O	Na2O	CaO	MgO	Fe2O3	TiO2
Lnra	2.03	12.06	4.84	1.10	0.69	0.31	0.11	0.20	0.10
Lnr&Nrmb	1.80	10.38	2.66	0.44	0.62	0.15	0.11	0.24	0.06
Sqr&Nrmc	1.82	9.48	2.12	0.36	0.58	0.11	0.08	0.19	0.05
a Linear calibration. b Spectral sum normalization. c Square function calibration.

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In the building ceramic structure of SiO₂-Al₂O₃-K₂O(Na₂O) the following applies: the production will not be affected if the absolute errors of CaO, MgO, Fe₂O₃ and TiO₂ are less than 0.2%; the absolute error of K₂O and Na₂O should not exceed 0.5% for firing temperature control; the absolute errors of L.O.I., SiO₂ and Al₂O₃ should not exceed 2% for structure and shrinkage control. Therefore, (1) the direct calibration of CaO, MgO, Fe₂O₃ and TiO₂ can meet the requirements of production control; (2) the direct calibration of K₂O can meet the requirement of production control, but direct calibration of Na₂O should be further improved; (3) it is not feasible to directly calibrate the L.O.I., SiO₂ and Al₂O₃ with spectral lines of H, Si and Al, respectively. Other methods should be used to further improve the prediction accuracy.

3.3   Multivariate analysis

The concentrations of L.O.I., SiO₂, Al₂O₃, K₂O and Na₂O are in a wide range in different kinds of ceramic raw materials. The direct calibration could not meet the production requirement. Therefore, more variables were added to build a multivariate model for the quantitative analysis of these compositions.

3.3   Multivariate analysis

The concentrations of L.O.I., SiO₂, Al₂O₃, K₂O and Na₂O are in a wide range in different kinds of ceramic raw materials. The direct calibration could not meet the production requirement. Therefore, more variables were added to build a multivariate model for the quantitative analysis of these compositions.

3.3.1   Double-line analysis of K₂O and Na₂O

In order to avoid over-fitting caused by excess variables in multivariate analysis, few variables as possible should be selected. The correlation coefficient between the characteristic line intensity and oxide content reached 0.97 for K and Na, and the univariate calibration model could almost meet the requirement of production control. Therefore, only the characteristic lines of the same element with the oxide were selected for the multivariate analysis of K₂O and Na₂O. Spectral lines at 766.5 and 769.9 nm were selected for K, while spectral lines at 818.3 and 819.5 nm were selected for Na. The calibration model is described as,

where X stands for K or Na, C stands for the content of the oxide, I_X1 and I_X2 stand for the spectral sum normalized intensities of the two selected spectral lines of K or Na, and a₀–a₄ are the fitting coefficients.

The comparison results of the content calibration of K and Na with different calibration models are shown in table 5. The determination coefficient (R²) and MAE values show that the double-line calibration of K and Na can obtain better results than the univariate calibration with either of the spectral lines alone, and the analysis accuracy can meet the requirement of the building ceramic production control.

Table  5.  Comparison results of K₂O and Na₂O with different calibration models.

	R2	MAE (%)
UnCal_K@766.5 nma	0.936	0.45
UnCal_K@769.9 nm	0.957	0.36
DlCal_K@766.5&769.9 nmb	0.958	0.35
UnCal_Na@818.3 nm	0.955	0.56
UnCal_Na@819.5 nm	0.950	0.58
DlCal_Na@818.3&819.5 nm	0.964	0.43
a Univariate calibration. b Double-line calibration.

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3.3.1   Double-line analysis of K₂O and Na₂O

In order to avoid over-fitting caused by excess variables in multivariate analysis, few variables as possible should be selected. The correlation coefficient between the characteristic line intensity and oxide content reached 0.97 for K and Na, and the univariate calibration model could almost meet the requirement of production control. Therefore, only the characteristic lines of the same element with the oxide were selected for the multivariate analysis of K₂O and Na₂O. Spectral lines at 766.5 and 769.9 nm were selected for K, while spectral lines at 818.3 and 819.5 nm were selected for Na. The calibration model is described as,

where X stands for K or Na, C stands for the content of the oxide, I_X1 and I_X2 stand for the spectral sum normalized intensities of the two selected spectral lines of K or Na, and a₀–a₄ are the fitting coefficients.

The comparison results of the content calibration of K and Na with different calibration models are shown in table 5. The determination coefficient (R²) and MAE values show that the double-line calibration of K and Na can obtain better results than the univariate calibration with either of the spectral lines alone, and the analysis accuracy can meet the requirement of the building ceramic production control.

Table  5.  Comparison results of K₂O and Na₂O with different calibration models.

	R2	MAE (%)
UnCal_K@766.5 nma	0.936	0.45
UnCal_K@769.9 nm	0.957	0.36
DlCal_K@766.5&769.9 nmb	0.958	0.35
UnCal_Na@818.3 nm	0.955	0.56
UnCal_Na@819.5 nm	0.950	0.58
DlCal_Na@818.3&819.5 nm	0.964	0.43
a Univariate calibration. b Double-line calibration.

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3.3.2   Multivariate analysis of L.O.I., SiO₂ and Al₂O₃

It can be seen from table 4 that for L.O.I., SiO₂ and Al₂O₃, the accuracy of univariate analysis should be further improved to meet the production control requirement. The multivariate analysis model is described as,

where C stands for the content of SiO₂, Al₂O₃ or L.O.I., I_k stands for the spectral sum normalized intensity of the kth selected spectral line, n is the number of the selected spectral lines, and a₀–a_2n are the fitting coefficients. The R² and MAE of different combinations of spectral lines are shown in table 6. It can be seen that because the interaction among L.O.I., SiO₂ and Al₂O₃ was considered to some extent, the combination of the spectral lines of H, Si, Al and the average of the whole spectrum can obtain the best R² and MAE for SiO₂ and Al₂O₃, and adding the spectral line of O can improve the R² of L.O.I. slightly.

Table  6.  Comparison results of multivariate regression with different spectral line combinations.

Combination	R2	MAE (%)
H656.5 nm+O777.4 nm	0.793	1.51
H656.5 nm+O777.4 nm+SpcAvga	0.814	1.35
H656.5 nm+Si288.2 nm+Al308.2 nm	0.829	1.22
H656.5 nm+Si288.2 nm+Al308.2 nm+O777.4 nm	0.856	1.13
H656.5 nm+Si288.2 nm+Al308.2 nm+SpcAvg	0.846	1.12
H656.5 nm+Si288.2 nm+Al308.2 nm+O777.4 nm+SpcAvg	0.860	1.12
Si288.2nm+Si252.8nm	0.362	8.43
Si288.2 nm+Al308.2 nm	0.948	2.70
Si288.2 nm+H656.5 nm	0.535	7.64
Si288.2 nm+SpcAvg	0.670	6.53
Si288.2 nm+Al308.2 nm+SpcAvg	0.962	2.31
Si288.2 nm+Al308.2 nm+H656.5 nm+SpcAvg	0.971	2.07
Al308.2 nm+Al394.4 nm	0.956	1.73
Al308.2 nm+Si288.2 nm	0.968	1.68
Al308.2 nm+H656.5 nm	0.961	1.68
Al308.2 nm+SpcAvg	0.959	1.67
Al308.2 nm+Si288.2 nm+SpcAvg	0.974	1.42
Al308.2 nm+Si288.2 nm+H656.5 nm+SpcAvg	0.977	1.38
a The average of the whole spectrum.

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Partial least squares regression (PLSR) was further introduced to build the multivariate model with more spectral lines. There are 34 lines listed in table 7, which were used as the input of PLSR. Furthermore, the whole spectrum was also used as the input of PLSR as a comparison.

Table  7.  Spectral lines selected for PLSR.

Element	Wavelength of characteristic spectral line (nm)
Si	243.5(Ⅰ), 250.7(Ⅰ), 252.8(Ⅰ), 288.2(Ⅰ)
Al	257.6(Ⅰ), 308.2(Ⅰ), 309.2(Ⅰ), 394.4(Ⅰ), 396.2(Ⅰ), 281.6(Ⅱ)
K	766.5(Ⅰ), 769.9(Ⅰ)
Na	818.3(Ⅰ), 819.5(Ⅰ)
Ca	643.9(Ⅰ), 646.3(Ⅰ), 315.9(Ⅱ), 317.9(Ⅱ), 393.4(Ⅱ), 396.8(Ⅱ)
Mg	285.2(Ⅰ), 279.5(Ⅱ), 280.3(Ⅱ)
Fe	248.3(Ⅰ), 373.5(Ⅰ), 259.9(Ⅱ), 263.2(Ⅱ), 275.6(Ⅱ)
Ti	365.4(Ⅰ), 334.9(Ⅱ), 368.5(Ⅱ)
Else	777.4(O I), 656.5(H I), 670.8(Li I)

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The leave-one-out (LOO) validation results of different methods are shown in table 8. It can be seen that (1) the PLS model with the 35 selected spectral intensities can obtain better R² and MAE than the model with the whole spectrum for SiO₂ and Al₂O₃; (2) the PLS model with either the whole spectrum or the 35 selected spectral intensities cannot obtain better R² and MAE than the multiple regression described above. The specific absolute errors (AEs) of the 30 samples with the PLSR are shown in figure 6, to further analyze the poor performance of PLS in the experiment. It can be seen that there are some samples with AE larger than 5% and even larger than 10%. Analyzing each sample specifically, the main reasons for the large AEs of the samples may be that (1) there are no samples with a similar matrix in the training set of LOO validation (e.g. samples 22 and 28 are calcined bauxite and calcined flint clay, respectively, and there are no other similar calcined bauxite and flint clay samples in the 30 samples); (2) the content of the component cannot be well expressed by the selected lines (e.g. the L.O.I. of sample ten is 17.31%, whereas the concentration of the structural water is only 13.24% and the concentration of SO₃ is 5.51%, but there are no S lines in the whole spectrum in the experiment). In conclusion, under the complex sample matrix and limited sample types of ceramic raw materials, more variable dimensions do not always lead to better analysis results.

Table  8.  LOO validation results of multiple regression and PLSR.

	L.O.I.			SiO2			Al2O3
	R2	MAE		R2	MAE		R2	MAE
Mlt_Ra	0.662	1.83		0.922	3.15		0.956	1.87
PLSR1b	0.514	2.52		0.917	3.42		0.955	2.00
PLSR2c	0.472	2.33		0.859	4.61		0.841	3.41
a Multiple regression with equation (2). b PLSR with 34 spectral lines and the average of the whole spectrum as the input. c PLSR with the whole spectrum as the input.

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Figure  6.  AEs of the 30 samples in the LOO validation of PLSR with (a) the 34 selected spectral lines and the average of the whole spectrum, (b) the whole spectrum.

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3.3.2   Multivariate analysis of L.O.I., SiO₂ and Al₂O₃

It can be seen from table 4 that for L.O.I., SiO₂ and Al₂O₃, the accuracy of univariate analysis should be further improved to meet the production control requirement. The multivariate analysis model is described as,

where C stands for the content of SiO₂, Al₂O₃ or L.O.I., I_k stands for the spectral sum normalized intensity of the kth selected spectral line, n is the number of the selected spectral lines, and a₀–a_2n are the fitting coefficients. The R² and MAE of different combinations of spectral lines are shown in table 6. It can be seen that because the interaction among L.O.I., SiO₂ and Al₂O₃ was considered to some extent, the combination of the spectral lines of H, Si, Al and the average of the whole spectrum can obtain the best R² and MAE for SiO₂ and Al₂O₃, and adding the spectral line of O can improve the R² of L.O.I. slightly.

Table  6.  Comparison results of multivariate regression with different spectral line combinations.

Combination	R2	MAE (%)
H656.5 nm+O777.4 nm	0.793	1.51
H656.5 nm+O777.4 nm+SpcAvga	0.814	1.35
H656.5 nm+Si288.2 nm+Al308.2 nm	0.829	1.22
H656.5 nm+Si288.2 nm+Al308.2 nm+O777.4 nm	0.856	1.13
H656.5 nm+Si288.2 nm+Al308.2 nm+SpcAvg	0.846	1.12
H656.5 nm+Si288.2 nm+Al308.2 nm+O777.4 nm+SpcAvg	0.860	1.12
Si288.2nm+Si252.8nm	0.362	8.43
Si288.2 nm+Al308.2 nm	0.948	2.70
Si288.2 nm+H656.5 nm	0.535	7.64
Si288.2 nm+SpcAvg	0.670	6.53
Si288.2 nm+Al308.2 nm+SpcAvg	0.962	2.31
Si288.2 nm+Al308.2 nm+H656.5 nm+SpcAvg	0.971	2.07
Al308.2 nm+Al394.4 nm	0.956	1.73
Al308.2 nm+Si288.2 nm	0.968	1.68
Al308.2 nm+H656.5 nm	0.961	1.68
Al308.2 nm+SpcAvg	0.959	1.67
Al308.2 nm+Si288.2 nm+SpcAvg	0.974	1.42
Al308.2 nm+Si288.2 nm+H656.5 nm+SpcAvg	0.977	1.38
a The average of the whole spectrum.

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Partial least squares regression (PLSR) was further introduced to build the multivariate model with more spectral lines. There are 34 lines listed in table 7, which were used as the input of PLSR. Furthermore, the whole spectrum was also used as the input of PLSR as a comparison.

Table  7.  Spectral lines selected for PLSR.

Element	Wavelength of characteristic spectral line (nm)
Si	243.5(Ⅰ), 250.7(Ⅰ), 252.8(Ⅰ), 288.2(Ⅰ)
Al	257.6(Ⅰ), 308.2(Ⅰ), 309.2(Ⅰ), 394.4(Ⅰ), 396.2(Ⅰ), 281.6(Ⅱ)
K	766.5(Ⅰ), 769.9(Ⅰ)
Na	818.3(Ⅰ), 819.5(Ⅰ)
Ca	643.9(Ⅰ), 646.3(Ⅰ), 315.9(Ⅱ), 317.9(Ⅱ), 393.4(Ⅱ), 396.8(Ⅱ)
Mg	285.2(Ⅰ), 279.5(Ⅱ), 280.3(Ⅱ)
Fe	248.3(Ⅰ), 373.5(Ⅰ), 259.9(Ⅱ), 263.2(Ⅱ), 275.6(Ⅱ)
Ti	365.4(Ⅰ), 334.9(Ⅱ), 368.5(Ⅱ)
Else	777.4(O I), 656.5(H I), 670.8(Li I)

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DownLoad: CSV

The leave-one-out (LOO) validation results of different methods are shown in table 8. It can be seen that (1) the PLS model with the 35 selected spectral intensities can obtain better R² and MAE than the model with the whole spectrum for SiO₂ and Al₂O₃; (2) the PLS model with either the whole spectrum or the 35 selected spectral intensities cannot obtain better R² and MAE than the multiple regression described above. The specific absolute errors (AEs) of the 30 samples with the PLSR are shown in figure 6, to further analyze the poor performance of PLS in the experiment. It can be seen that there are some samples with AE larger than 5% and even larger than 10%. Analyzing each sample specifically, the main reasons for the large AEs of the samples may be that (1) there are no samples with a similar matrix in the training set of LOO validation (e.g. samples 22 and 28 are calcined bauxite and calcined flint clay, respectively, and there are no other similar calcined bauxite and flint clay samples in the 30 samples); (2) the content of the component cannot be well expressed by the selected lines (e.g. the L.O.I. of sample ten is 17.31%, whereas the concentration of the structural water is only 13.24% and the concentration of SO₃ is 5.51%, but there are no S lines in the whole spectrum in the experiment). In conclusion, under the complex sample matrix and limited sample types of ceramic raw materials, more variable dimensions do not always lead to better analysis results.

Table  8.  LOO validation results of multiple regression and PLSR.

	L.O.I.			SiO2			Al2O3
	R2	MAE		R2	MAE		R2	MAE
Mlt_Ra	0.662	1.83		0.922	3.15		0.956	1.87
PLSR1b	0.514	2.52		0.917	3.42		0.955	2.00
PLSR2c	0.472	2.33		0.859	4.61		0.841	3.41
a Multiple regression with equation (2). b PLSR with 34 spectral lines and the average of the whole spectrum as the input. c PLSR with the whole spectrum as the input.

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Figure  6.  AEs of the 30 samples in the LOO validation of PLSR with (a) the 34 selected spectral lines and the average of the whole spectrum, (b) the whole spectrum.

DownLoad: Full-Size Img PowerPoint

4.   Conclusion

In this paper, we introduced the quantitative analysis of SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃, TiO₂ and L.O.I. with the atomic emission spectrum induced by a fiber-laser-based LIBS analyzer. Different data processing and analysis methods were discussed to meet the production control requirement. With the combination of continuous background deduction, FWHM intensity integral and spectral sum normalization, the MAEs of univariate calibration were reduced to below 0.2% for CaO, MgO, Fe₂O₃ and TiO₂, which can meet the production control requirement. Furthermore, using the double-line analysis model of K and Na, the MAEs of K₂O and Na₂O were reduced to below 0.5%, meeting the production control requirement. Multiple regression and PLSR were further introduced for the analysis of SiO₂, Al₂O₃ and L.O.I. The optimized analysis model reduced the MAEs of SiO₂, Al₂O₃ and L.O.I. to 2.07%, 1.38% and 1.12%, respectively. It is proved that the use of the fiber-laser-based desktop LIBS analyzer is feasible for the quantitative analysis of the main inorganic elements in geological samples. However, due to the complex sample matrix effect and the limited kinds of experimental samples, complex multivariate analysis did not effectively improve the prediction accuracy. In future work, with the increase in the number of modeling samples, it is expected that there will be further improvement in the analysis accuracy of the instrument through the use of complex multivariable analysis algorithms. This will lead to an expansion of application fields.

4.   Conclusion

In this paper, we introduced the quantitative analysis of SiO₂, Al₂O₃, K₂O, Na₂O, CaO, MgO, Fe₂O₃, TiO₂ and L.O.I. with the atomic emission spectrum induced by a fiber-laser-based LIBS analyzer. Different data processing and analysis methods were discussed to meet the production control requirement. With the combination of continuous background deduction, FWHM intensity integral and spectral sum normalization, the MAEs of univariate calibration were reduced to below 0.2% for CaO, MgO, Fe₂O₃ and TiO₂, which can meet the production control requirement. Furthermore, using the double-line analysis model of K and Na, the MAEs of K₂O and Na₂O were reduced to below 0.5%, meeting the production control requirement. Multiple regression and PLSR were further introduced for the analysis of SiO₂, Al₂O₃ and L.O.I. The optimized analysis model reduced the MAEs of SiO₂, Al₂O₃ and L.O.I. to 2.07%, 1.38% and 1.12%, respectively. It is proved that the use of the fiber-laser-based desktop LIBS analyzer is feasible for the quantitative analysis of the main inorganic elements in geological samples. However, due to the complex sample matrix effect and the limited kinds of experimental samples, complex multivariate analysis did not effectively improve the prediction accuracy. In future work, with the increase in the number of modeling samples, it is expected that there will be further improvement in the analysis accuracy of the instrument through the use of complex multivariable analysis algorithms. This will lead to an expansion of application fields.