Laser-induced breakdown spectroscopy (LIBS) of LPBF-fabricated alloy steel: effect of surface roughness and the laser–material interaction mechanism

Abstract

Laser-induced breakdown spectroscopy (LIBS) is an ideal method for the online elemental analysis of Laser Powder Bed Fusion (LPBF) components due to its in situ and rapid characteristics. However, the inherent surface roughness of LPBF-fabricated parts causes fluctuations in LIBS spectral signals, consequently affecting the accuracy and stability of quantitative analysis. The underlying physical mechanism by which roughness influences spectral signals remains unclear, which restricts the development of relevant spectral correction algorithms. To address this, we prepared alloy steel samples with surface roughness (S_a) ranging from 4.52 to 12.82 µm by adjusting LPBF process parameters and performed LIBS analysis. By analyzing spectral intensity, signal-to-noise ratio (SNR), and relative standard deviation (RSD), we found that the characteristic spectral line intensities of Fe, Cr, Mn, and Ni initially increased and then decreased with increasing roughness, reaching a peak at S_a = 5.61 µm. This peak intensity was 46.4% higher than that of the roughest sample (S_a = 12.82 µm). Plasma temperature and electron density also reached their maximum values at S_a = 5.61 µm (15 790 K and 1.84 × 10¹⁷ cm⁻³ respectively). The observation results of the volume morphology of the ablation plume and the ablation pit both indicate that roughness affects the LIBS signal through a triple coupling effect: low roughness (S_a = 4.52 µm) leads to energy loss due to high reflectivity, while high roughness (S_a ≥ 7.15 µm) weakens ablation efficiency due to an increased ablation threshold and non-uniform energy distribution caused by microstructures. The sample with S_a = 5.61 µm represents an optimal balance between reflectivity and ablation threshold, exhibiting the largest integral of plume area and time (IPAT) and largest volume of ablation pits uniform ablation, which generates stable plasma and, consequently, high-quality spectral signals. This study elucidates the physical mechanism by which roughness influences LIBS spectral signals through a chained pathway of “laser ablation-plasma evolution-spectral response,” laying a theoretical foundation for the development of spectral correction algorithms tailored for complex LPBF surfaces.

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1 Introduction

Laser Powder Bed Fusion (LPBF) technology, which utilizes a high-energy laser beam to selectively melt metal powders layer by layer, enables the rapid fabrication of complex metallic components. This technology holds irreplaceable advantages in fields such as aerospace and nuclear industries. However, the non-equilibrium thermodynamic conditions inherent to the LPBF process can easily lead to elemental segregation and non-uniform distribution of precipitated phases, directly impacting the mechanical properties and service life of the components.^1–3 Therefore, achieving high-precision online elemental analysis for LPBF has become a core requirement to ensure part quality.

Conventional methods for elemental and compositional analysis rely on post-process sampling and preparation, which are often time-consuming and cumbersome, failing to meet the demands of online LPBF monitoring. Laser-induced breakdown spectroscopy (LIBS) technology, which uses a pulsed laser to excite plasma on the sample surface and analyzes the characteristic atomic emission spectra for qualitative and quantitative analysis, is considered an ideal tool for online LPBF monitoring due to its non-contact nature, minimal sample preparation, minor sample damage, multi-elemental simultaneous analysis, and millisecond-level response characteristics.^4–8 However, a key challenge in practical applications is that LPBF-fabricated parts possess an intrinsic and unavoidable surface roughness, this surface roughness is one of the key factors that introduce matrix effects and cause fluctuations in spectral signals and deviations in quantitative analysis.

In fact, the influence of sample physical properties such as roughness on LIBS analysis has received extensive attention. A large number of studies have shown that the mechanical properties and microstructure of the sample, such as hardness and grain size,^9,10 significantly affect plasma characteristics and spectral reproducibility. For powder or pressed samples, their bulk density and compression degree have also been confirmed to be important reasons for spectral line fluctuations.^11,12 Particularly in the analysis involving rough surfaces, Rapin et al.¹³ explicitly revealed the significant impact of sample roughness on hydrogen emission signals. In the LIBS analysis of steel, researchers have developed various qualitative and quantitative analysis methods for different types of steel (such as low alloy steel and high alloy stainless steel),^14–18 aiming to overcome matrix interference and improve analysis accuracy.

More precisely, the roughness directly affects the fundamental physics of LIBS—the laser ablation process, where the laser interacts with the material to form plasma. The state of this plasma, in turn, critically determines the quality of the spectral signal. Bogarts A. et al.¹⁹ highlighted that the initial temperature and pressure field distribution on the sample surface are crucial “initial conditions” that govern the subsequent expansion and evolution of the plasma plume. Vasantgadkar N. A. et al.²⁰ further emphasized the significant role of the plasma shielding effect during the laser ablation process. Through time-resolved spectral analysis, numerous researchers have found that the internal physicochemical processes of the plasma, such as electron-ion recombination, inter-particle collisions, and potential chemical reactions, directly determine the emission intensity and temporal decay of characteristic spectral lines.^21–25 Gottfried et al.²⁶ demonstrated that analyzing the plasma shockwave can reveal its complex internal chemical kinetics. Elhassan A. et al.²⁷ observed that in femtosecond laser-induced plasma, the early-stage intense continuous background radiation originates from processes like free–free transitions, after which the plasma rapidly expands and cools, leading to a decay in the continuous background and the appearance of atomic characteristic spectral lines. Le Drogoff B. et al.²⁸ reported a similar phenomenon, noting that plasma lifetime and spectral line intensity are closely related to laser energy deposition and subsequent cooling mechanisms. These studies collectively indicate that the evolution dynamics and internal physicochemical state of the laser-induced plasma are the root causes affecting the quality of LIBS spectral signals. Consequently, surface roughness, as a critical interface parameter influencing laser energy absorption and ablation efficiency, interferes with the plasma generation process from the source. This ultimately causes significant spectral signal fluctuations even when all other LIBS parameters are constant. This phenomenon has been widely confirmed; for example, Nicolas et al.²⁹ found that when the surface roughness of 304 stainless steel increased from 0.048 µm to 0.207 µm, the intensity of the Fe I (404.58 nm) spectral line increased by up to a factor of 2. Wang et al.³⁰ observed that for carbon steel with a surface roughness of 0.525 µm, the stability of Fe characteristic spectral lines was higher. Bin Yu et al.³¹ systematically confirmed significant differences in the intensity of Fe, Cr, Mo, and V characteristic spectral lines of ER8 steel at different roughness levels. Xiong et al.³² pointed out that changes in the roughness of 45# steel systematically alter the entire LIBS spectrum signal intensity.

The roughness-induced spectral signal fluctuation severely affects the accuracy and stability of LIBS elemental analysis. The fundamental reason is that even with identical elemental composition, differences in surface roughness alter the efficiency of laser–material interaction, plasma evolution characteristics, and spectral collection efficiency, leading to a nonlinear variation in spectral line intensity and stability.³³ Most existing research is limited to qualitative descriptions of these effects, and a clear understanding of the intrinsic mechanism by which roughness influences LIBS signals through its effect on laser ablation and plasma dynamics is still lacking. This gap in mechanistic understanding poses a significant challenge to the practical application of LIBS elemental analysis. LIBS quantitative analysis models rely on characteristic spectral line intensity information; when applied to LPBF components with varying roughness, spectral feature distortion can lead to systematic deviations in elemental content calculations,^34–36 ultimately impacting the accuracy of online monitoring results and hindering quality control during the printing process. Therefore, a deep investigation into the governing principles and underlying mechanisms of how different roughness levels affect spectral signals is not only a crucial prerequisite for developing subsequent spectral correction algorithms to address systematic deviations in quantitative analysis models, but also a fundamental guarantee for achieving high-precision online LIBS elemental analysis on complex LPBF surfaces.

This study systematically investigates the influence of intrinsic surface roughness levels in Laser Powder Bed Fusion (LPBF)-formed alloy steel samples on the spectral characteristics of laser-induced breakdown spectroscopy (LIBS), with emphasis on signal intensity, stability, and signal-to-noise ratio. The research was conducted through the following approaches: preparing samples with varying roughness through the adjustment of LPBF printing parameters; precisely measuring roughness with a super-depth-of-field microscope; performing LIBS analysis on the alloy steel samples and evaluating the effects of roughness on the overall spectrum and characteristic spectral lines based on line intensity, signal-to-noise ratio (SNR), and relative standard deviation (RSD); using the Boltzmann plot method and Stark broadening method to analyze the influence of roughness on plasma temperature and electron density; and combining high-speed camera observations of LIBS ablation plume evolution with super-depth-of-field microscope characterization of ablation crater morphology to elucidate the mechanism by which different roughness levels affect the LIBS signal.

2 Experimental and methods

2.1 Online LIBS experimental setup applied to LPBF

To apply LIBS technology to the online elemental detection of the LPBF printing process, this study built an experimental setup highly integrated with the LPBF printing equipment. The experimental system primarily consists of a Nd:YAG pulsed laser (wavelength 1064 nm, pulse width 9 ns, maximum single pulse energy 470 mJ), a spectrometer (wavelength range and resolution 0.08 nm @ 237–357 nm, 0.08 nm @ 352–454 nm, 0.15 nm @ 596–817 nm), a digital delay generator, mirrors (reflectance approx. 0.9), a focusing lens (focal length F = 150 mm), a high-speed camera, and a workstation. A schematic diagram of the experimental setup is shown in Fig. 1.

Fig. 1 Schematic diagram of the LIBS experimental setup.

The design of this system is closely integrated with the actual LPBF printing environment. The optical path layout strictly adheres to the spatial constraints of the printing chamber. The original forming cylinder in the equipped printing system can move up and down, enabling micrometer-level positioning of the sample. The printing chamber can be purged with high-purity argon or nitrogen to maintain the low-oxygen (<500 ppm) inert atmosphere required for the LPBF process.³⁷ The circulating gas path and purging system realistically reproduce the dynamic airflow during printing, effectively controlling the adhesion of powder and dust to optical windows and sample surfaces, thereby ensuring the stability of the LIBS plasma.^38,39 Compared with common offline LIBS setups, this system is directly embedded in the real LPBF environment (spatial structure, sample temperature, atmospheric composition, and flow state, etc.), providing a reliable technical platform for online elemental detection during the LPBF printing process.

2.2 Experimental samples

Alloy steel samples with dimensions of 8 × 8 × 5 mm were prepared by selecting appropriate LPBF printing parameters. The alloy steel grade is HR-2, and the elemental composition of the printed part is as follows: C ≤ 0.04%, Si ≤ 1%, Mn: 8–10%, P ≤ 0.025%, S ≤ 0.015%, Ni: 5.5–8%, Cr: 19–21.5%, N: 0.2–0.34%, Fe: balance.

After sample preparation, a super-depth-of-field microscope was used to capture magnified images (50×) of the sample surface morphology, and roughness was measured using an optical method. The morphology of the test surfaces is shown in Fig. 2, and the LPBF printing parameters and surface roughness are shown in Table 1. The roughness is defined as the three-dimensional arithmetic mean height (S_a), which can be calculated by eqn (1):^40–43

Where A is the area of the defined region, and z(x,y) is the height deviation of the measured point from the reference plane. This parameter represents the average of the absolute height deviations of all points within the defined area from the arithmetic mean, providing a comprehensive evaluation of the overall surface roughness, which is more suitable for this study's focus on laser ablation. Therefore, all surface roughness results in this paper are expressed as S_a values.⁴⁴

Fig. 2 Morphology of the test surfaces of LPBF-prepared samples with different roughness levels, (a)–(f): samples 1–6.

Table 1 Printing process parameters and corresponding roughness (S_a) for LPBF-prepared samples with different roughness levels

Sample	Laser power (W)	Scanning speed (mm s^−1)	Scan spacing (mm)	S a (µm)
1	420	580	0.1	4.52
2	420	500	0.1	5.61
3	390	420	0.1	7.15
4	360	420	0.1	10.43
5	330	340	0.1	11.96
6	300	260	0.1	12.82

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2.3 Experimental procedure

Before LIBS testing, the LPBF-prepared samples with different roughness levels were placed in the printing area. By adjusting the parameters of the forming cylinder's translation stage, the horizontal distance between the sample's test surface and the focusing lens was set to 145.5 mm (near focus 3%). A power meter (with a measurable energy range of 2 mJ–10 J and a measurable wavelength range of 355–2200 nm, 2940 nm) was used to measure the pulse laser energy focused on the test surface. The laser voltage was adjusted to stabilize the single pulse energy at 90–100 mJ.

During the LIBS test, a digital delay generator was used to trigger the laser. The pulsed laser passed through mirrors R₁, R₂, R₃ and the focusing lens F₁ before being focused onto the sample's test surface, where the laser spot diameter was 1 mm. The focused laser ablated the test surface, generating plasma. The characteristic spectral lines emitted as the plasma cooled were collected by the spectrometer probe, transmitted via optical fiber to the spectrometer. The spectrometer began collecting data with a delay of 2 µs after the laser was triggered to avoid the intense continuous radiation emitted by the plasma in its early stages. The spectral data collected by the spectrometer were processed and analyzed in the workstation. A total of 3 different locations were tested on each sample, with 50 pulse laser ablations and spectral data collections performed at each location. Fig. 3 shows the 3D surface profiles (captured by a super-depth-of-field microscope) and corresponding laser ablation points for the samples.

Fig. 3 3D surface profiles and corresponding laser ablation points on the samples, (a)–(f): samples 1–6.

To evaluate the ablation effect of the pulsed laser on samples with different roughness levels, a high-speed camera (acquisition frequency 20 kHz) was used to observe the evolution of the ablation plume generated by the pulsed laser during the LIBS testing. After testing, a super-depth-of-field microscope was used to capture magnified images (500×) of the laser ablation craters formed on the different roughness samples.

3 Results and discussion

3.1 Influence of surface roughness on spectral signals

To investigate the influence of different surface roughness levels of LPBF-prepared alloy steel samples on spectral signals, spectral data were collected and analyzed for six samples with varying surface roughness under identical experimental conditions. The spectra in the full wavelength range (237–357 nm, 352–454 nm, 596–817 nm) are shown in Fig. 4. As the surface roughness (S_a) increased from 4.52 µm (sample 1) to 12.82 µm (sample 6), the overall spectral intensity exhibited a non-monotonic trend, initially increasing and then decreasing. The highest spectral intensity was observed at a surface roughness of 5.61 µm (sample 2).

Fig. 4 Spectra of samples with different surface roughness levels in the full wavelength range (237–357 nm, 352–454 nm, 596–817 nm).

To further evaluate the influence of surface roughness on the spectral signals of key elements, the wavelength range of 360–445 nm, which is rich in major alloy steel elements (Fe, Cr, Mn, Ni), was selected for analysis. The spectra of the six samples with different surface roughness levels in the 360–445 nm range are shown in Fig. 5. The figure reveals numerous spectral lines, most of which originate from iron atoms. By consulting the NIST database, four atomic emission characteristic spectral lines with high signal-to-noise ratios (background intensity below 1000) were identified for these elements: Fe I 404.55 nm, Cr I 428.92 nm, Mn I 403.02 nm, and Ni I 361.89 nm. Their positions are marked in Fig. 5. A comparative analysis of the spectra from samples with different roughness levels within this wavelength range revealed that the intensity variation trends of the four characteristic spectral lines were consistent with the overall spectral trend mentioned above: the intensity was the highest when S_a was 5.61 µm, and the lowest when S_a was 12.82 µm.

Fig. 5 Spectra of samples with different surface roughness levels in the 360–445 nm wavelength range, (a)–(f): samples 1–6.

To more intuitively reveal the influence of surface roughness on the intensity of the characteristic spectral peaks, Lorentzian fitting was performed on the spectral data of the four aforementioned atomic spectral lines (Fe I 404.55 nm, Cr I 428.92 nm, Mn I 403.02 nm, and Ni I 361.89 nm). The fitting results are shown in Fig. 6. The fitting results clearly reveal the degree of influence of roughness: compared with the best roughness sample 2 (S_a = 5.61 µm), the spectral line intensity of the roughest sample 6 (S_a = 12.82 µm) decreased significantly by 43.55% to 49.19% (among them, Fe I 404.55 nm decreased by 46.36%, Cr I 428.92 nm decreased by 49.19%) Mn I 403.02 nm decreased by 48.33%, Ni I 361.89 nm decreased by 47.27%. This result confirms that surface roughness has a significant and nonlinear modulation effect on the intensity of LIBS characteristic spectral lines.

Fig. 6 Fe, Cr, Mn, and Ni characteristic peaks obtained after Lorentzian fitting.

Spectral signal intensity, signal-to-noise ratio (SNR), and stability are the core indicators for evaluating LIBS signal quality. SNR refers to the ratio of the characteristic peak intensity to the background noise; a higher value indicates a clearer signal and less noise interference. It can be calculated by eqn (2):⁴⁵

Where I is the characteristic peak intensity and σ is the standard deviation of the background signal intensity.

Spectral line stability is evaluated using the relative standard deviation (RSD); a lower value indicates higher stability among multiple test values (characteristic peak intensities). It can be calculated by eqn (3):⁴⁶

Where n is the number of tests, I_i is the characteristic peak intensity obtained from the i-th test, and Ī is the arithmetic mean of the characteristic peak intensities over all tests.

To this end, 150 spectra (50 per location) collected from three different excitation points for each roughness sample group were processed to generate a comparative plot of the intensity, SNR, and RSD of the four atomic spectral lines as a function of roughness (Fig. 7). The intensity variation trend of the four atomic spectral lines was consistent with the previous observations. SNR is used to measure spectral signal quality. As shown in Fig. 7, the SNR of the Fe I 404.55 nm, Cr I 428.92 nm, and Mn I 403.02 nm lines initially increased and then stabilized as roughness increased, reaching their maximum values at 5.61 µm (sample 2). However, the SNR of Ni I 361.89 nm showed a distinct lack of regularity. Notably, under any given roughness condition, the line intensity and SNR of Ni I 361.89 nm were the lowest among the four spectral lines. The fundamental reason is that when the background noise level is comparable, spectral line intensity and SNR are positively correlated. However, the background noise corresponding to different roughness samples is not entirely consistent. Spectral lines with lower intensity are more susceptible to background noise disturbances, causing the variation trend of Ni I 361.89 nm's SNR to deviate from the other three spectral lines. RSD is used to evaluate spectral signal stability, and a lower value indicates higher line stability. As shown in Fig. 7, the RSD of all four spectral lines reached its maximum value at a roughness of 4.52 µm (sample 1). As the roughness continues to increase, the RSD of the spectral line generally shows an unstable trend of first decreasing and then continuously fluctuating. Although the RSD variation patterns of the four spectral lines are not completely consistent, for the Cr, Mn, and Ni spectral lines, the RSD reaches the minimum value when the roughness is 5.61 µm, while for the Fe spectral line, the RSD reaches the minimum value when the roughness is 7.15 µm (sample 3). However, in general, 5.61 µm (sample 2) does have a certain enhancing effect on the stability of spectral lines.

Fig. 7 Comparison of (a) intensity, (b) SNR, and (c) RSD for Fe, Cr, Mn, and Ni atomic spectral lines of samples with different roughness levels.

In summary, the roughness of 5.61 µm (sample 2) achieved the best performance on all three key indicators—line intensity, SNR, and RSD—simultaneously: it provided the highest line intensity, a high SNR, and a low RSD.

3.2 Influence of surface roughness on plasma characteristics

In LIBS analysis, plasma temperature T and electron density n_e are two crucial parameters describing plasma characteristics, and a sample's surface roughness can influence plasma generation, formation, and distribution.⁴⁷ Therefore, to better understand the influence of surface roughness on plasma characteristics, we analyzed the plasma temperature T of the six samples with different roughness levels. Assuming that the plasma is in a state of local thermodynamic equilibrium (LTE), the energy level distribution of each species in the plasma follows the Boltzmann distribution, and the self-absorption effect of spectral lines is not considered. When the plasma is regarded as a point light source, the spectral intensity I_ki of the transition from energy level k to i can be expressed as eqn (4):⁴⁸Where h is Planck's constant, c is the speed of light, A_ki is the transition probability, λ_ki is the wavelength, n_s is the number density of atoms or ions, g_k is the statistical weight, U^s(T) is the partition function, E_k is the energy of the upper energy level, k_B is the Boltzmann constant, and T is the plasma temperature. Taking the natural logarithm of both sides of the equation yields eqn (5):⁴⁹In the above equation, by setting , , X = E_k, , the equation can be simplified to eqn (6):

Y = kX + b (6)

in this equation, the slope k can be obtained from the data for Y and X, and the specific value of k is then used to calculate the plasma temperature T. The data related to Y and X can be looked up in the NIST database. The relevant data for the Fe characteristic spectral lines used to calculate the plasma temperature T are shown in Table 2.

Table 2 Characteristic spectral line parameters for Fe

Spectral	A (nm)	A ki (10^8 s^−1)	E k (eV)	g k
Fe I	385.99	0.097	3.211	9
Fe I	404.58	0.862	4.549	9
Fe I	411.85	0.496	6.583	13
Fe I	438.35	0.5	4.312	11
Fe I	440.47	0.275	4.371	9

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The Boltzmann plots for Fe characteristic spectral lines at different roughness levels are shown in Fig. 8(a). By further calculating the slopes of the fitted lines for different roughness levels, the variation of plasma temperature T for different roughness samples was determined, as shown in Fig. 8(c). The plasma temperature T shows an unstable trend of first increasing, then decreasing and continuously fluctuating with the increase of the surface roughness of the sample, reaching its maximum value of 15 790 K at a roughness of 5.61 µm (sample 2). When the roughness is greater than 5.61 µm, the fluctuation of plasma temperature T increases, and the stability significantly decreases, indicating that its thermodynamic equilibrium state is disrupted due to the change in surface roughness.

Fig. 8 (a) Boltzmann plots of Fe I lines for different roughness samples, with straight lines representing linear fits of the data; (b) Lorentzian fit of the H line at 656.28 nm; (c) variation of plasma temperature and electron density for different roughness samples.

The calculation of electron density n_e is commonly performed using the Stark broadening method of the Hα spectral line. Generally, the spectral line broadening in LIBS emission spectra consists of instrumental broadening (Δλ_i), which follows a Gaussian profile, and Stark broadening (Δλ_Stark), which follows a Lorentzian profile. Due to their combined effect, the resulting LIBS spectral line exhibits a Voigt profile, with its width denoted as Δλ_m. The Stark broadening component can be extracted through the deconvolution of the measured spectral linewidth (Δλ_m) and the instrumental broadening (Δλ_i). Alternatively, the instrumental broadening (Δλ_i) can be estimated using the emission spectrum of a standard low-pressure mercury lamp. In this study, this value was determined to be approximately 0.114 nm.⁵⁰ The final resulting Stark broadening (Δλ_Stark) exhibited slight variations depending on the sample's surface roughness, with values ranging from approximately 0.732–0.834 nm. After obtaining Δλ_Stark, it is substituted into eqn (7):⁵¹

In this equation, n_e is the electron density, Δλ_Hα is the FWHM of the Hα line at 656.28 nm (this refers to the net broadening value after subtracting the instrumental broadening Δλ_i from the measured linewidth Δλ_m, i.e., Δλ_Stark), and α_1/2 is the reduced Stark broadening coefficient. According to the research by Kepple and Griem, the specific value of α_1/2 is dependent on plasma conditions (plasma temperature T, electron density n_e), and their relationship is shown in Table 3.⁵²

Table 3 Correspondence between plasma temperature T, electron density n_e, and α_1/2

T (K)	n e (cm^−3)	α 1/2
5 × 10^3	10^15	0.00969
	10^16	0.0149
	10^17	0.0189
1 × 10^4	10^15	0.00777
	10^16	0.0134
	10^17	0.0186
	10^18	0.0215
2 × 10^4	10^15	0.00601
	10^16	0.0114
	10^17	0.0175
	10^18	0.0226

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In air, a typical electron density is on the order of 10¹⁷ cm⁻³.⁵³ Combined with the plasma temperatures calculated in this study (14 585–15 790 K), interpolation of the data in Table 3 suggests that a value of 0.0181 for α_1/2 is appropriate for calculating n_e using eqn (7).

Furthermore, another effective method for estimating electron density n_e comes from the work of Gigosos and Cardenoso.⁵⁴ This method is based on computer simulations that include ion dynamics effects, establishing a quantitative relationship between the Stark broadening of hydrogen lines and plasma parameters through numerical calculations. First, based on the calculated Stark broadening (Δλ_Stark) of the Hα line at 656.28 nm and the plasma temperature (T), the reduced mass µ is determined by considering the plasma composition (for alloy samples ablated in air, µ = 1.0 is used). Subsequently, by performing a two-dimensional interpolation in the corresponding data table from the literature based on the specific values of T and Δλ_Stark, the corresponding log (n_e) can be obtained. Finally, n_e is derived after unit conversion. For the experimental conditions of this study (T = 14 585–15 790 K, Δλ_Stark = 0.732–0.834 nm), the electron density n_e obtained by this method ranges from 8.96 × 10¹⁶ – 1.12 × 10¹⁷ cm⁻³. This is within an acceptable margin of error compared to the n_e results calculated using the Stark broadening formula (1.46 × 10¹⁷ – 1.84 × 10¹⁷ cm⁻³), which, to some extent, confirms the reliability of the electron density diagnosis.

The Hα 656.28 nm characteristic peaks and their Lorentzian fitting curves for different roughness samples are shown in Fig. 8 (b). The electron densities for samples with varying roughness were calculated using the Stark broadening method, and their variation is depicted in Fig. 8(c). The variation trend is similar to that of the plasma temperature. The electron density n_e also reached its maximum value of 1.84 × 10¹⁷ cm⁻³ at a roughness of 5.61 µm (sample 2). As the roughness further increases, the electron density decreases and then stabilizes.

At the same time, because the Boltzmann plot method for calculating plasma temperature T is only valid under local thermodynamic equilibrium (LTE) conditions, it is necessary to confirm whether the current plasma conditions satisfy the McWhirter criterion.⁵⁵ This criterion states that the minimum electron density required to achieve LTE is given by eqn (8):

n_e ≥ 1.6 × 10¹²T^1/2(ΔE_k)³ (8)

In this equation, n_e is the electron density, T is the plasma temperature, and ΔE_k is the maximum energy difference between the upper and lower levels of the spectral lines used to calculate the plasma temperature.

When calculating the plasma temperature, the maximum energy difference between the upper and lower levels of the selected spectral lines was 3.372 eV, and the maximum plasma temperature was 15 790 K. The calculated critical value for the electron density to achieve LTE was 7.709 × 10¹⁵ cm⁻³. The electron densities calculated for the different roughness samples were all greater than this critical value, indicating that the plasma reached LTE conditions under all the different roughness experimental conditions, and thus the calculated plasma temperatures are reliable.

3.3 Laser ablation behavior and influencing mechanism of samples with different surface roughness levels

The preceding sections (3.1 and 3.2) revealed that the sample surface roughness has a significant impact on spectral signal intensity, stability, SNR, plasma temperature T, and electron density n_e, with all indicators performing optimally at a roughness of 5.61 µm (sample 2). To gain a deeper understanding of the physical mechanism behind this phenomenon, this subsection systematically investigates the influence of roughness on laser ablation behavior by combining high-speed camera plume observations, ablation threshold analysis, and ablation crater morphological characterization.

The evolution of the ablation plume during the LIBS process, captured by a high-speed camera (Fig. 9), shows that for all samples with different roughness levels, a small and regular initial plume formed during the early stage of laser ablation (50 µs). As time progressed (to 100 µs), the plume rapidly expanded to its maximum area. Notably, for the sample with a roughness of 5.61 µm (sample 2), the maximum value of plume area (MVP) was 30.49 mm², which was significantly larger than that of the other samples, and its plume duration was also relatively longer. According to the research by Mahmood et al., the expansion dynamics of a laser-ablated plume are closely correlated with the ablated mass. Within the framework of the “snow plow model”, the relationship between the plume's front position and time can be used to estimate the ablated mass.⁵⁶ Therefore, for the samples compared in this study, if their plume expansion dynamics exhibit similar behavior—that is, if their velocity decay patterns are comparable—then the integral of plume area and time (IPAT) can be considered an indirect indicator for the relative comparison of the effective ablated mass. Among the samples compared in this experiment, if the expansion dynamics of the plumes are similar, that is, their velocity decay modes are close, then the IPAT can be regarded as an indirect indicator for relatively comparing the effective ablation amount.

Fig. 9 Ablation plume evolution during the LIBS process for samples with different roughness level.

As shown in Fig. 10(a) and (b), the IPAT value for sample 2 was the highest, suggesting that it had the highest effective ablation amount under these experimental conditions. In contrast, the MVP and IPAT values for the roughest samples (samples 3–6, S_a = 7.15–12.82 µm) and the lowest roughness sample (sample 1, S_a = 4.52 µm) were all lower. To further evaluate the amount of ablated material, we measured the volume of the ablation craters using a a super-depth-of-field microscope, as depicted in Fig. 10(c). We discovered a significant positive correlation between the trend of the ablated crater volume as a function of roughness and the corresponding IPAT values. Specifically, sample 2, with a roughness of 5.61 µm, exhibited the largest crater volume. As the roughness increased further, the crater volume decreased and showed subsequent fluctuations. This finding strongly supports the validity of using IPAT as an indirect indicator for the effective ablated mass.

Fig. 10 (a) Fitted curves of ablation plume variation over time for different roughness samples; (b) the maximum value of the plume area and the integral of the plume area with time vary with the roughness; (c) the variation of ablation pit volume with roughness.

The differences in the plume behavior described above stem from the fundamental influence of roughness on the efficiency of “laser–material” interaction. The ablation threshold of a material is a key parameter for measuring the difficulty of resisting laser ablation and can be calculated by eqn 9:⁵⁷

Where D is the ablation crater diameter, W₀ is a parameter related to the laser, which can be considered a constant here, F₀ is the laser fluence, and F_th is the x-intercept, which is the ablation threshold of the material.

By analyzing the ablation threshold fitting results for different roughness samples (Fig. 11), we observed that the material's ablation threshold F_th systematically increased with the increase in surface roughness. This means that, under the same incident laser fluence, a material with a higher roughness surface is more difficult to ablate effectively.

Fig. 11 Ablation threshold fitting results for different roughness samples.

The morphology of the ablation craters observed with a super-depth-of-field microscope (Fig. 12) provides direct evidence for the above phenomenon and reveals the specific mechanism by which roughness affects ablation behavior. Sample 1 (low roughness, S_a = 4.52 µm): the ablation crater appears relatively circular with minimal ablation traces in the central area (no significant dramatic fluctuations). This indicates that although its ablation threshold is relatively low, the high reflectivity of the smooth surface causes a large amount of the incident laser energy to be reflected rather than used for material ablation. This ultimately leads to insufficient effective ablation, poor plasma generation efficiency (consistent with the low IPAT value in Fig. 10), and substandard spectral signal quality (Fig. 7). Sample 2 (moderate roughness, S_a = 5.61 µm): the ablation crater has clear edges, and the central area shows significant ablation traces. At this roughness, the moderate increase in surface roughness effectively reduces laser reflectivity and enhances laser energy absorption. At the same time, its ablation threshold, while higher than that of sample 1, is still at a relatively favorable level. This combination of “low reflectivity” and a “tolerable ablation threshold” allows laser energy to be efficiently converted into ablation energy, producing a strong and stable plasma (T, n_e, IPAT and volume of ablation pits are all at their maximum), which ultimately results in the best spectral signal quality. Samples 3–6 (high roughness, S_a = 7.15–12.82 µm): the ablation craters tend to be irregular (with blurred edges), and as the roughness increases, the uniformity of the structures within the crater decreases.

Fig. 12 Ablation crater morphology of different roughness samples, (a)–(f): samples 1–6.

Although the high-roughness surfaces further reduce reflectivity, the significantly increased ablation threshold becomes the dominant factor, making the material more difficult to ablate. More importantly, the complex microstructures (peaks and valleys) of the rough surface lead to an extremely non-uniform distribution of laser energy: some areas may be over-ablated due to multiple reflections or scattering, while shaded areas or deep valleys may receive insufficient energy. This non-uniform energy distribution and fluctuation in effective ablation volume not only reduce overall ablation efficiency (low IPAT and volume of ablation pits, Fig. 10) but also severely disrupt the stability of plasma generation. In addition, the microstructures themselves may physically obstruct or scatter plasma radiation, reducing spectral collection efficiency. These factors combine to weaken spectral signal intensity, decrease stability (high RSD), and worsen the signal-to-noise ratio (Fig. 7), while also degrading plasma characteristics (T, n_e) (Fig. 8(c)).

By integrating high-speed camera plume observations, ablation threshold calculations, and ablation crater morphological and volume analysis, it is clear that roughness severely affects laser ablation efficiency and the stability of plasma generation by controlling laser reflectivity, material ablation threshold, and the uniformity of laser energy distribution at the microscopic scale. A roughness of 5.61 µm (sample 2) represents the optimal balance between the gain from reduced reflectivity and the loss from an increased ablation threshold. This balance leads to the most efficient and stable ablation and plasma generation, which is the fundamental physical mechanism behind its comprehensive optimal spectral signal and plasma parameters. Roughness that is either too low (dominated by reflection loss) or too high (dominated by ablation difficulty and non-uniform energy distribution) will lead to a decrease in ablation efficiency and a degradation of plasma characteristics, thereby reducing LIBS analysis performance. A schematic diagram of the mechanism by which the reflectivity and ablation threshold of samples with different roughness levels influence plasma and spectral signals is shown in Fig. 13.

Fig. 13 Schematic diagram of the mechanism by which reflectivity and ablation threshold of different roughness samples influence plasma and spectral signals.

4 Conclusions

This study elucidates the nonlinear influence mechanism of LPBF alloy steel roughness on LIBS signals, which is mainly controlled by the coupling of laser reflectivity, ablation threshold, and micro energy distribution. The optimal balance is achieved at S_a = 5.61 µm. The specific conclusion is as follows.

(1)As the surface roughness (S_a) increased from 4.52 µm (sample 1) to 12.82 µm (sample 6), the LIBS spectral signal showed a nonlinear evolution. The full-band spectral line intensity and the characteristic spectral line intensities of Fe, Cr, Mn, and Ni (Fe I 404.55 nm, Cr I 428.92 nm, Mn I 403.02 nm, and Ni I 361.89 nm) all exhibited a trend of “initial enhancement followed by a decrease”, peaking at 5.61 µm (sample 2). Compared to the roughest sample, sample 6 (S_a = 12.82 µm), the characteristic spectral line intensity of sample 2 was 43.55%∼49.19% higher. The SNR of the Fe, Cr, and Mn spectral lines was optimal at 5.61 µm, while the Ni line, due to its lowest intensity, was significantly disturbed by background noise, showing weaker regularity in its SNR. The relative standard deviation (RSD) of the spectral lines was highest at 4.52 µm (sample 1) and showed a trend of “decreasing, then increasing, then decreasing again” with increasing roughness. Although the RSD variation trends for the four characteristic spectral lines were not perfectly consistent, the minimum RSD of the Cr, Mn, and Ni spectral lines all occurred at 5.61 µm (sample 2).

(2)Roughness systematically influences the core parameters of the plasma by altering the plasma formation environment. Both plasma temperature (T) and electron density (n_e) showed a trend of “initial increase followed by a decrease” with increasing roughness, reaching maximum values at 5.61 µm (T = 15 790 K, n_e = 1.84 × 10¹⁷ cm⁻³). At the highest roughness (S_a = 12.82 µm), T and n_e decreased by 8.26% and 21.9%, respectively, from their peak values. The change in plasma characteristics is directly related to the quality of the spectral signal, which is essentially the influence of roughness on the “laser–material” energy transfer efficiency and the plasma evolution process.

(3)High-speed camera plume observations, ablation threshold calculations, and ablation crater volume morphological analysis demonstrate that roughness governs ablation efficiency and plasma generation through a triple-effect mechanism. Energy coupling efficiency: the ablation threshold (F_th) systematically increased with roughness, making it more difficult to ablate a rougher surface. Reflectivity and energy distribution: the high reflectivity of the low-roughness (4.52 µm) sample 1 led to laser energy loss (the ablation crater was regular but the center was lightly ablated), resulting in insufficient effective ablation (low IPAT and volume of ablation pits) and poor plasma generation. The moderate-roughness (5.61 µm) sample 2 had reduced reflectivity and a moderate ablation threshold, leading to efficient energy absorption (clear crater edges, significant central ablation). The plume area was maximal (MVP = 30.49 mm²), the duration was longest (highest IPAT), and plasma generation was optimal. The high-roughness (7.15–12.82 µm) samples 3–6 had higher ablation thresholds, and their surface microstructures caused non-uniform laser energy distribution (irregular and non-uniform craters). This led to a reduced effective ablation volume (low IPAT and volume of ablation pits) and severely disrupted the stability of plasma generation. Additionally, microstructures themselves may physically obstruct or scatter plasma radiation, reducing spectral collection efficiency.

Author contributions

Tian Huang: investigation, writing – review & editing, writing – original draft, methodology. Xinzhou Zhang, Liwen Cao and Tao Zhu: conceptualization, formal analysis, project administration, validation, supervision. Changqiu Chen, Qian Liu and Jing Zhao: visualization, data curation, software. Shuke Huang, Ming Huang, Xianfeng Shen and Zhihui Xia: investigation, funding acquisition, resources.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data supporting the findings of this study are included in the manuscript. Relevant data can be made available from the corresponding author upon reasonable request.

Acknowledgements

This work is supported by the National Key Research and Development Program of China (grant no. 2023YFB4603300 and no. 2023YFB4603302).

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