Haoyu
Dong‡
a,
Xi
Huang‡
a,
Luke
Wadle
b,
Lanh
Trinh
b,
Peizi
Li
a,
Jean-Francois
Silvain
c,
Bai
Cui
b and
Yongfeng
Lu
*a
aDepartment of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA. E-mail: ylu2@unl.edu
bDepartment of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
cCNRS, University of Bordeaux, Bordeaux I.N.P., ICMCB, UMR 5026, F-33608 Pessac, France
First published on 20th March 2025
Laser-Induced Breakdown Spectroscopy (LIBS) has been widely used across industries, medical applications, and environmental monitoring for elemental identification and concentration analysis due to its high accuracy, speed, and efficiency. Beyond elemental identification and concentration analysis, many studies suggest that LIBS signal intensities are influenced by sample surface temperatures, presenting an opportunity for temperature monitoring in processes such as three-dimensional additive manufacturing. In such applications, accurately detecting local temperatures at printing spots of interest is critical, specifically in ceramic printing, where phase transitions require temperatures exceeding one thousand degrees Celsius. Due to the dynamic nature of plasma emissions and experimental variability, there are few reports on the use of LIBS for monitoring sample surface temperatures. The direct use of absolute LIBS intensities is challenging for this purpose. Instead, this study explored the use of intensity ratios for surface temperature estimation. A series of LIBS spectra over wavelengths from 430.96 to 438.99 nm were collected from zirconium carbide (ZrC) at temperatures ranging from 350 to 600 °C. Intensity ratios, including atomic-to-atomic, ionization-to-ionization, and atomic-to-ionization line ratios, were evaluated. These ratios demonstrated significant exponential correlations with surface temperatures. Among the regression models, the highest R-squared (R2) value of 0.976 was observed for the intensity ratio of Zr II 435.974 nm to Zr I 434.789 nm. Additionally, machine learning algorithms were applied for full LIBS spectrum analysis, enabling comprehensive classification and prediction of sample surface temperatures without relying solely on a single intensity ratio. This strategy has demonstrated the potential of machine learning-assisted LIBS for real-time detection of sample surface temperatures in complex and dynamic environments.
In addition to LIBS’ well-established applications in elemental identification and concentration analysis, it is also reported that LIBS signal intensities can be influenced by sample surface temperature variations during laser ablation.17–19 This phenomenon is particularly relevant in scenarios such as real-time temperature monitoring during three-dimensional (3D) additive manufacturing processes. Moreover, remote temperature monitoring/estimation at printing spots of interest is a critical challenge in these complex and dynamic environments, particularly when printing ceramic materials, which requires laser melting or sintering at temperatures exceeding one thousand degrees Celsius due to phase transitions.20,21 Temperature variations at printing points can significantly affect the flow, bonding, and solidification behavior of materials in 3D printing, potentially leading to unexpected defects.22,23 Moreover, physical contact measurement methods, such as thermocouples, are impractical due to their short lifetime at extreme temperatures. Additionally, the dusty environment may affect the performance of infrared thermography. LIBS serves as an active measurement probe directly at the printing point, and with proper laser probe adjustments and appropriate engineering designs, the impact from dusty environments is expected to be minimized.
However, this relationship remains unclear due to the dynamic nature of plasma emissions and variations in actual experimental setups. The quality of LIBS spectra collected using a high-resolution spectrometer is highly dependent on factors such as sample conditions, signal collection efficiency, laser powers, focus conditions, and other related parameters. Even minor changes in an experimental setup can significantly affect the LIBS spectra, particularly the absolute peak intensities. These challenges make it difficult to use LIBS as a direct and reliable tool for temperature estimation.
To address this issue, we explored the use of intensity ratios rather than absolute peak intensities to enhance the understanding of the correlation between LIBS spectra and sample surface temperatures. A series of LIBS spectra over wavelengths from 430.96 to 438.99 nm were collected from zirconium carbide (ZrC) surfaces at temperatures ranging from 350 to 600 °C. The absolute peak intensities, with and without signal-to-noise ratio (SNR) corrections, were analyzed, revealing correlations between sample surface temperatures and peak intensities. For example, surface temperatures showed a positive influence on the C I 437.138 nm peak intensity and a negative influence on the Zr I 434.789 nm peak intensity. However, a reliable mathematical relationship between the surface temperatures and peak intensities could not be established. To further analyze the data, intensity ratios including atomic-to-atomic, ionization-to-ionization, and atomic-to-ionization line ratios were evaluated. These ratios show significant exponential relationships with the surface temperatures. Among all the fit curves, the highest R2 value, 0.976, was observed for the intensity ratio of Zr II 435.974 nm to Zr I 434.789 nm.
Additionally, multivariate analysis, which has been widely applied in spectroscopy for decades to develop calibration models for classification, pattern recognition, clustering, regression, and other predictive tasks,24–28 was integrated into this work. By leveraging multivariate analysis as a classification and prediction tool, machine learning-assisted LIBS was demonstrated as a potential strategy for surface temperature monitoring.
ZrC powder (CAS: 12070-14-3) with a purity of 99.5% was purchased from Alfa Aesar. The powder was sintered into discs with a diameter of 20 mm and a thickness of approximately 5 mm using a spark plasma sintering (SPS) system (Model 10-4, Thermal Technologies). The sintering process was performed at a maximum temperature of 2000 °C, with an isothermal hold of 10 min under a pressure of 30 MPa in a vacuum of 2 × 10−2 Torr. The heating and cooling rates were both set at 100 °C min−1.21,31 After sintering, the samples were polished using a heavy-duty grinding and polishing machine (UNIPOL-820, MTI) with silicon carbide discs (Electron Microscopy Sciences) of sequential grit sizes: 60, 120, 400, 600, and 800. The polished samples underwent ultrasonic cleaning with ethanol (EX0290-1, Sigma-Aldrich) and were subsequently dried in an oven at 60 °C. A representative sample was analyzed using a ZYGO surface profiler system to assess surface roughness, with an Sa value of 0.176 μm, an Sq value of 0.248 μm, and an Sz value of 8.976 μm.
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Fig. 1 (a) Schematic of the LIBS experimental setup and (b) typical LIBS spectra obtained from the ZrC surface at room temperature and 350 °C. |
The LIBS probe laser pulses ablated polished ZrC surfaces, generating plasma and inevitably creating laser-induced craters, typically on a micrometer scale. To mitigate the impact of crater formation during the LIBS measurements, more than 1000 laser pulses were applied prior to recording the LIBS spectra. Moreover, to mitigate the impact of local grain differences in ceramic samples, an off-focus strategy was applied, utilizing a larger laser spot (an ellipse with a major diameter of ∼1000 μm and a minor diameter of ∼800 μm) to obtain an averaged measurement from the sample surfaces. The wavelength range of the LIBS spectra, ranging from 430.96 to 438.99 nm, was chosen for a balance between the detection of C and Zr peaks, as shown in Fig. 1b. Within this chosen range, four Zr peaks, including two Zr I (434.789 and 436.645 nm) and Zr II peaks (435.974 and 437.978 nm), and four C peaks, including one C I (437.138 nm) and three C II (431.726, 432.310, and 437.428 nm), were used for further analyses. The detailed atomic spectral transitions of these lines can be found in the National Institute of Standards and Technology (NIST) LIBS database.32 During the heating with the CO2 laser, a range of local ZrC surface temperatures were measured using the pyrometer as references, and LIBS measurements were conducted immediately at each temperature. The recorded temperatures included 350, 362, 373, 382, 394, 414, 425, 438, 454, 477, 501, 526, 546, 563, 576, 588, and 600 °C.
The frequency of the LIBS probe laser was set to 30 Hz to enable rapid recording of plasma emissions during the heating process. For each temperature, plasma emissions from over 50 consecutive laser pulses were recorded. To evaluate the correlation between intensity, intensity ratios, and sample temperatures, the LIBS spectra were averaged over every 5 laser pulses, resulting in a total of 10 LIBS spectra obtained at each temperature.
![]() | (1) |
Fig. 2a shows the measured absolute peak intensities of C I 437.138 nm and Zr I 434.789 nm as functions of local sample surface temperatures. The intensity of the C I peak demonstrates an upward trend, increasing from 10844 to 12
208, while the Zr I peak shows a downward trend, decreasing from 6354 to 5231. All these peak intensities were recorded with both a 1 μs gate delay and gate width, showing a temperature-dependent relationship. However, despite the apparent correlation between sample temperatures and peak intensities, it remains challenging to establish a reliable mathematical relationship due to certain unresolved influencing factors. The intensity curve alone is insufficient to serve as a reliable indicator of sample temperature.
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Fig. 2 Absolute peak intensities of C I 437.138 nm and Zr I 434.789 nm (a) with and (b) without SNR corrections. |
Fig. 2b shows the measured peak intensities of C I 437.138 nm and Zr I 434.789 nm after SNR corrections. The SNR of C I 437.138 nm decreases from 143.93 to 123.24, while the SNR of Zr I 434.789 nm decreases from 84.31 to 52.79. The SNR here is defined as the ratio of peak intensities to the continuum backgrounds. Interestingly, the intensity trends of C I 437.138 nm with and without SNR corrections show opposite behaviours. Several factors influence the SNRs, including continuum background emission and the ionization states of the plasma. Therefore, it is possible that the trends could be read oppositely due to different continuum background emission levels caused by different surface temperatures. Sample surface temperature could impact the ionization states of the plasma generated during LIBS. At higher sample temperatures, the laser-induced plasma tends to have more atoms in ionized states, indicating a warmer plasma.17,18,33 As a result, the proportion of neutral atoms decreases in the plasma, leading to a decrease in the intensity of atomic lines. Therefore, it is reasonable that the peak intensities of C I 437.138 nm and Zr I 434.789 nm after SNR corrections show the same downward trends as functions of surface temperatures. This observation suggests the potential of using the intensity ratios, rather than the absolute peak intensities, as more reliable indicators for sample surface temperature estimation.
![]() | (2) |
For atomic-to-atomic and ionization-to-ionization ratios (at the same energy levels), the partition function Z(T) is identical and canceled out. For ionization-to-atomic ratios, the variation in sample temperatures within a range of 250 °C could be considered to cause only minor changes in plasma temperatures, since typical plasma temperatures33,34 reach thousands of degrees Celsius. As a result, the partition functions are nearly identical, and the ratio of the two partition functions can be treated as a constant. Since plasma temperature tends to increase with sample temperature,17,18,33 a simple linear mathematical relationship is assumed to link sample surface temperature to the plasma temperature. Based on this assumption, the regression expression for the data can be formulated as follows:
![]() | (3) |
Fig. 3a shows the change in the intensity ratio of C II 432.310 nm to C II 431.726 nm as the surface temperature increases. When the sample temperature increases from 350 to 600 °C, the intensity ratio decreases from 0.53 to 0.49, with a faster decline observed between 350 °C and 400 °C compared to the range from 400 to 600 °C. The excitation energy Ei of the 432.310 nm peak is 209552.39 cm−1, which is slightly lower than the Ei of the 431.726 nm peak (209622.32 cm−1). Therefore, the intensity ratio of both peaks decreases following an exponential trend. Fig. 3b presents the intensity ratio of Zr I 436.645 nm to Zr I 434.789 nm, which exhibits an upward trend as the surface temperature increases, increasing from 0.59 to 0.68.
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Fig. 3 Atomic-to-atomic and ionization-to-ionization ratios of the same element. Peak intensity ratio of (a) C II 432.310 nm/C II 431.726 nm and (b) Zr I 436.645 nm/Zr I 434.789 nm. |
Fig. 4 shows the ionization-to-atomic ratios and their corresponding fitting curves. The intensity ratio of C II 431.726 nm to C I 437.138 nm is shown in Fig. 4a, indicating an upward trend as the sample temperature increases, increasing from 0.59 to 0.68. The excitation energy Ei of C II 431.726 nm is 209632.22 cm−1, while that of C I 437.138 nm is 84
851.47 cm−1. Since the excitation energy for ionization is significantly higher than that for atomic transitions, the ionization-to-atomic intensity ratio consistently exhibits an upward trend. These observations align with our previous discussion that surface temperatures can influence the ionization states of the plasma generated during LIBS. As the surface temperature increases, the proportion of neutral atoms in the plasma decreases, leading to a decrease in the intensity of atomic lines. Simultaneously, the number of ionized atoms in the plasma increases, resulting in a corresponding increase in the intensity of ionization lines. Similarly, upward trends were observed in the ratios of Zr II 435.974 nm to Zr I 434.789 nm and Zr II 437.978 nm to Zr I 434.789 nm, as shown in Fig. 4b and c, respectively.
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Fig. 4 Ionization-to-atomic ratios of the same element. Peak intensity ratios of (a) C II 431.726 nm/C I 437.138 nm, (b) Zr II 435.974 nm/Zr I 434.789 nm, and (c) Zr II 437.978 nm/Zr I 434.789 nm. |
The regression parameters for the peak intensity ratios are summarized in Table 1. The R2 value for the fit of the C II 437.138 nm to C II 432.310 nm ratio is 0.889, which is significantly higher than that for the fit of the C II 437.138 nm to C I 431.726 nm ratio (0.688). This difference suggests that as the gap in excitation energy between peaks increases, the parameter b in the regression equation becomes larger, thereby minimizing the impact of temperature fluctuations on the intensity ratios.
Peak 1 | Peak 2 | a | b | c | R 2 |
---|---|---|---|---|---|
C II 432.310 nm | C II 431.726 nm | 0.498 | 1.082 | −334.307 | 0.698 |
C II 437.138 nm | C I 431.726 nm | 0.576 | −29.908 | −161.779 | 0.889 |
Zr II 435.974 nm | Zr I 434.789 nm | 4.910 | −456.195 | 293.350 | 0.976 |
Zr I 436.645 nm | Zr I 434.789 nm | 35.715 | −26116.506 | 6001.716 | 0.929 |
Zr II 437.978 nm | Zr I 434.789 nm | 5.730 | −656.087 | 443.246 | 0.968 |
Notably, the R2 value for the fit of the Zr II 435.974 nm to Zr I 434.789 nm ratio is 0.976 and that for the fit of the Zr II 437.978 nm to Zr I 434.789 nm is 0.968, both indicating a reliable fitting correlation. However, despite the high R2, these ratio curves are still difficult to use directly for surface temperature estimation based on the fitting curves.
Principal component and discriminant function analysis (PC-DFA) was applied. PC-DFA has been proven to be efficient for spectroscopy analyses to establish classification models in our previous studies.35–37 In this study, LIBS spectra obtained at different sample temperatures were classified by PC-DFA to establish a classification model via cross-validation approach. LIBS spectra in the wavelength range of 430.96 to 438.99 nm were used for the PC-DFA analyses.
In PC-DFA, principal component analysis (PCA) was first performed on the LIBS spectra to reduce the original data dimensions (wavelengths in a spectrum) into a smaller number of principal components (PCs), which were then used as inputs for discriminant function analysis (DFA). The raw LIBS spectra, initially consisting of 1024 data dimensions, were reduced to 5 PCs through PCA, capturing 71.9% of the dataset's most significant information. This dimensionality reduction simplified the analysis by condensing the spectral information into 5 PCs while retaining the majority of the dataset's variance. Fig. 5 shows a PCA plot of the dataset as a function of PC1, PC2, and PC3, with data points color-coded to represent temperatures ranging from 350 °C to 600 °C. In this model, PC1 explains the largest portion of the dataset's variance, accounting for 48.46%, while PC2 and PC3 contribute 13.02% and 6.15%, respectively. Through PCA, the dimensionality of the LIBS spectra was effectively reduced from 1024 variables to 5 PCs.
PC scores for each PC represent the transformed values of the original data after applying PCA. Therefore, the PC scores of the 5 PCs were input into DFA using two approaches, Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA), for cross-validation classification. Fig. 6 shows the classification results by LDA and QDA, respectively. The direct classification accuracy of the LDA and QDA methods was 62.2% and 72.3%, respectively. Notably, most of the misclassified spectra fell into neighbouring groups, approximately ±15 °C from the correct temperature. This is attributed to variations in the LIBS spectra during the measurement process. Therefore, by allowing for a reasonable tolerance—for instance, considering linked neighbouring groups as correct—the modified classification accuracies for LDA and QDA improve to 94.6% and 95.0%, respectively. These results highlight a strong correlation between the LIBS spectra and sample surface temperatures, demonstrating the potential of this classification approach for reliable surface temperature estimation.
To further evaluate the prediction capability of the machine learning models, the dataset was randomly divided into two groups: a training group and a testing group. The training group comprised 90% of the dataset and was used to build the classification model, while the remaining 10% served as the testing group, containing spectra unknown to the model, for external validation in the PC-DFA process. The training group was used for the classification model and the testing group was used as testing spectra (unknown to the model) for external validation in PC-DFA. This cycle was repeated for 30 rounds to ensure reliability and robustness. The direct prediction accuracies are summarized in Fig. 7, which demonstrate the robustness of the PC-DFA method in achieving consistent direct prediction accuracies across multiple iterations of random dataset grouping. Moreover, we also tested two additional machine learning approaches, Support Vector Machines (SVMs) and Artificial Neural Networks (ANNs), as alternative prediction tools to evaluate their performance in comparison to PC-DFA. QDA, LDA, SVMs, and ANNs demonstrated varying levels of performance, achieving average direct prediction accuracies of 60.2% ± 6.4%, 58.9% ± 6.0%, 53.3% ± 5.8%, and 51.3% ± 6.7%, respectively.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ja00437j |
‡ Haoyu Dong and Xi Huang contributed equally to this work. |
This journal is © The Royal Society of Chemistry 2025 |