Packing thickness dependent plasma emission induced by laser ablating thin-layer microgranular materials

Abstract

An experimental study on the packing thickness (PT) dependent plasma emission caused by laser ablating thin-layer microgranular samples in air was conducted using three sets of size-selected copper grains (median size d₅₀ = 53 μm, 72 μm, and 100 μm, respectively). For each size-selected case, the PT parameter was tuned from 0.15 to 1.00 mm through varying the amount of grains packed into a vessel with a steel bottom wall and the emission spectra of laser-induced plasma were measured at various PT. It is found that there is a striking threshold phenomenon in the measured behavior of PT-dependent plasma emission. Specifically, when PT is less than a threshold PT_th, the emission intensity exhibits an exponential decreasing with incremental thickness; however, when it exceeds PT_th, the emission intensity becomes almost constant. It is also found that the PT_th slightly depends on grain size but the ratio of PT_th to d₅₀ seems to be size independent. Combining the mechanical fundamentals of granular materials, we interpreted the findings by considering a PT-dependent effect of the vessel's bottom on the formation circumstance of a laser-induced plasma. This work has practical significance in assessing a threshold thickness above which laser-induced breakdown spectroscopy, as an analytical technique to quantify elements embedded in microgranular materials, is viable regardless of PT difference.

---

1. Introduction

Powders or discrete micrograins packed into a vessel with a solid bottom wall are a common form of microgranular material which widely exists in various industrial production processes. Appropriate and timely assessment of critical chemical elements embedded in the microgranular materials is sometimes essential for ensuring the consistency and excellence of final products. Laser-induced breakdown spectroscopy (LIBS) is an emerging analytical technique to in situ quantify minor and trace elements embedded in a material by measuring the optical emission of plasma caused by laser ablating the material surface (see, for example ref. 1–4). The advantage of LIBS is that it can be done with no sample preparation, simultaneous multielement detection, in situ remote detection, and spectral data can be real-time collected for many sample phases such as gas, liquid, and solid. Since the 1990s, LIBS has also been widely accepted as a promising technique for analyzing the samples with a granular phase.⁵

In the past decades, much effort has been dedicated to the development of the LIBS-based analysis technique for microgranular samples (see, for example ref. 6–10). Although its attractive features have been demonstrated, from a practical viewpoint, the laser plasma generated from a microgranular sample, in contrast to the case of traditional gas/liquid/solid samples, is usually far from the ideal status as an optical emission source for spectrochemical analysis. This is because that the microgranular sample is a large assemblage of discrete micrograins, belonging to a category of soft matters and having fundamental differences in physical property from those samples with traditional phases. One of the main differences is that microgranular medium is a complex nonlinear mechanical system and its mechanical properties sensitively depend on many specific granular parameters.¹¹ Our recent studies on LIBS of microgranular samples have demonstrated that the plasma emission features can be obviously affected by grain size^12,13 and bulk packing fraction¹⁴ due to the fact that the change of these parameters causes the difference in the mechanical performance (hardness) of the sample surface to produce a repulsion force for the ablated atoms gushing from the surface. In other words, their change makes a considerable difference in the formation environment of a laser-induced plasma.

In terms of the mechanical fundamentals of granular materials,¹¹ for a thin-layer microgranular medium with a given grain size and packing mode (loosely/densely), the packing thickness (PT) is the most important parameter that dominates its mechanical properties due to the existence of the vessel's bottom boundary. Specifically, after a stress, induced by the grains' own weight or by the application of an external pressure to the granular medium, is transmitted to the bottom by the network of force chains, the bottom provides a reaction force for the grains and therefore reversely influences its local mechanical properties. The strength of influence depends on the sample's PT.^15,16 Therefore, an important question arises: does there exist a PT effect on plasma emission in the case of thin-layer microgranular samples? If the answer is affirmative, does there exist a well-defined threshold thickness (PT_th) above which the plasma emission is no longer affected by the PT? In addition, for a microgranular medium with a given PT and packing mode (loosely/densely), the grain size becomes the most important factor influencing its mechanical properties. Along this line, a further question arises: does there exist a grain size-dependent PT effect if the answers to the above-mentioned two questions are all affirmative? Experimentally clarifying these answers is crucial since it is expected to provide useful information on how to constrain the PT so as to achieve optimum performance of direct spectrochemical analysis for thin-layer microgranular materials using LIBS. However, to the best of our knowledge, no experimental work has been done to tackle the issue.

Here, we report a study aimed at providing experimental answers to the above-mentioned questions using size-selected copper microgranular samples as an example. To achieve this, we recorded the LIBS spectra of thin-layer copper microgranular samples at various PT ranging from several to tens of grain diameters. Owing to the complexity of a laser-induced plasma formation from a microgranular surface, care was taken to ensure that each LIBS spectrum was recorded without disturbances of grain ejection and granular craters generated by laser-induced shock wave. Detailed analyses of plasma emission variation with PT for three cases of different grain sizes suggest the objective existence of the above-speculated PT effect, well-defined PT_th, and dependence of the PT effect on grain size. Combining the mechanical fundamentals of granular materials, an interpretation for the results will be given by considering an influence of vessel's bottom on the formation of a luminous plasma. In fact, the influence from the bottom wall is very similar to that subtarget effect which was frequently discussed in series of works by Kagawa and co-workers.^17,18 In a breakthrough study on LIBS of thin-layer silicon greases,¹⁸ they put a silicon grease sample with a 100 μm thickness onto a metal plate, demonstrating that the metal plate as a subtarget compensates for the absence of a solid surface in the silicon greases and assists the formation of a luminous plasma with higher temperature and density.

2. Material and methods

2.1 Sample preparation

The copper material with a purity of 99.99% from a commercial source (Qinghe Kangshuo Welding Materials Co., Ltd) was employed in this study. It is composed of polydisperse micrograins with a near-spherical shape and a specific density of 8.9 g cm⁻³. These micrograins were sieved using stainless-steel wire sieves to prepare three sets of size-selected copper grains. Their grain sizes and size distributions were analyzed by a grain size analyzer (Microtrac S3500). The analyzed results are shown in Table 1. The sieved copper microspheres exhibit monomodal size distributions for each size-selected case and have the characteristic diameters of d₅₀ (d₁₀, d₉₀) = 53 (43, 65) μm, 72 (59, 92) μm, and 100 (77, 123) μm, respectively.

Table 1 Characteristic diameters of sieved copper microspheres used in this study. All values are stated in μm. d₁₀ denotes that the portion of microspheres with diameters smaller than this value is 10%; d₅₀ denotes that the portion of microspheres with diameters smaller and larger than this value are 50%, also called as the median diameter; and d₉₀ denotes that the portion of microspheres with diameters below this value is 90%

Sample ID	d 10	d 50	d 90
S1	43	53	65
S2	59	72	92
S3	77	100	123

---

For each set of size-selected copper micrograins, the sample was prepared by packing them into an annular-groove vessel with a steel bottom. The vessel was fixed on a mobile platform with rotating and lifting functions driven by a miniature reduction motor with extremely small vibration and noise. Its dimensions are 23.5 mm in width, 20.0 mm in depth, and 130 mm in outer diameter. The samples' PT parameter was tuned from 0.15 to 1.00 mm with a step length of 50 μm based on a five-step procedure with the help of a 30 mm length and 18 mm width rectangle plastic plate fixed in a position outside the sample platform and inserted vertically the vessel: (i) ensuring that the lower edge of the plastic plate is parallel to and just touches the vessel's bottom, achieving the determination of an initial state of PT equaling to zero; (ii) vertically lowering the vessel to a given distance between the plate's lower edge and the vessel's bottom, achieving the preset of a specific PT value equaling to the given distance; (iii) estimating the volume or amount of the granular material required to fill the vessel to the plate's lower edge using the vessel's bottom area and the preset value of PT; (iv) gently and slowly pouring a certain amount of grains (slightly higher the estimated amount) into the vessel; (v) using the plastic plate to level the surface by rotating the sample platform. All the samples used here are prepared by repeating the five-step procedure without any noticeably shaking or compacting operation, thus possessing a random loose packing mode.

2.2 Setup and data acquisition

An overview diagram of the experimental setup is shown in Fig. 1. A Q-switched Nd:YAG laser with a pulse width of 7 ns and a fundamental wavelength of 1064 nm was employed as the ablation source. The pulse energy used to ablate the samples was set at 40 mJ and monitored real-time by an energy meter (MAESTRO 200960). The laser beam was focused using a quartz lens (L1) with a focal length of 75 mm. The samples were exposed to air at atmospheric pressure. The distance of lens to sample surface was set at 65 mm, i.e. the sample surface was positioned off the laser focal plane by a distance of 10 mm closer to L1. The laser spot size on the surface was approximately 500 μm, which is sufficiently large compared with the grain sizes used in this study. Such an arrangement is beneficial for reproducible breakdown and plasma plume for each case of given grain size and PT parameter. A dichroscope (Thorlabs, DMLP 900) was used to transmit the laser beam and reflect the plasma emission light. The reflected light was focused through another quartz lens (L2) with a focal length of 75 mm and collected by a quartz fiber, which was coupled to an Echelle spectrometer (LTB, ARYELLE 200) equipped with an intensified charge-coupled device (ICCD, Andor, DH 334 T). To get a good signal-to-background ratio, LIBS spectra were recorded with a delay time of 1 μs and a gate width of 5 μs.

Fig. 1 Overview diagram of the experimental setup used in this study.

During the LIBS measurements, the sample vessel was rotated for ensuring that each laser pulse ablates a fresh and flat granular surface. Previous publications¹⁹ showed that laser ablating a microgranular sample can initiate an excavation process accompanying the ejection of grains. To avoid the influence of the excavation process on the laser–surface interaction and the spectroscopic measurement of subsequent laser pulses, the laser repetition rate was set at a relatively low-repetition-rate (5 Hz) mode and the vessel was quickly rotated. For each size-selected case, the PT parameter is changed after every 100 single-shot LIBS measurements.

3. Results and discussion

3.1 PT-dependent plasma emission

Using the experimental conditions described above, a series of LIBS spectra for the three size-selected cases were measured at various packing thicknesses. Taking the case of d₅₀ = 53 μm as an example, in Fig. 2 we show the segments of the measured LIBS spectra at PT = 0.15, 0.20, 0.25, 0.30 and 0.35 mm. Each spectrum was generated by the accumulation of 100 single shots. In the following investigation of PT-dependent plasma emission, we chose two Cu I lines at 510.5 nm and 515.3 nm, and one Cu II line at 500.9 nm, which have been used in previous LIBS study,¹⁴ as diagnostic tools. The three lines were chosen because they were present for all these tuned PT cases. Besides, the choice was also because they are non-resonant lines, which can effectively reduce the risk of self-absorption influence on the investigation of PT-dependent plasma emission.

Fig. 2 LIBS spectra in the wavelength range from 500.0 nm to 518.0 nm obtained at the case of d₅₀ = 53 μm. Cu I line at 510.5 nm is enlarged in the insets.

From Fig. 2 one can see that the intensities of the three lines obviously depend on the PT, roughly exhibiting a weakening of plasma emission as PT increases from 0.15 to 0.35 mm, and the weakening rate seems to become slow with incremental PT. For the cases of d₅₀ = 72 μm and 100 μm, the PT-dependent LIBS spectra show similar trends as that of d₅₀ = 53 μm, and therefore are not shown here.

To present the behavior of PT-dependent plasma emission more clearly and globally, the relationship between the intensity of the three lines and the PT parameter for all these tuned PT and size-selected cases needs to be quantified. Each line intensity was obtained by integrating the corresponding peak area in each accumulated spectrum. For comparison convenience, all these intensities of the three lines at each size-selected case were normalized to the corresponding line intensity value at PT = 0.15 mm. Fig. 3 showed the normalized intensities of the three lines versus the PT for the three size-selected cases. Note that each point corresponds to an average of 5 spectra generated by 20 single-shot LIBS accumulations, and error bars correspond to the standard deviations obtained from the 5 spectra.

Fig. 3 Normalized line intensities of Cu I lines at 510.5 nm and 515.3 nm and Cu II line at 500.9 nm versus the packing thickness for the three size-selected cases. (a) d₅₀ = 53 μm; (b) d₅₀ = 72 μm; (c) d₅₀ = 100 μm.

One can see from Fig. 3 that the evolution of the normalized intensities of the three lines with incremental PT exhibits a trend of first decreasing significantly and then becoming almost constant, seeming to obey an exponential decay rule. This provides direct evidence that there is an obvious dependence of plasma emission on the PT (hereinafter called PT effect) at least when PT is less than a certain value, and the dependence may be expressed using an exponential equation parameterized by

where I(PT) is the normalized line intensity at a given PT; α is a value of I(PT) appearing at the cases of large enough PT, and therefore (1 − α) denotes the maximal variation of the normalized line intensity caused by the PT effect which can be served as an indicator to qualitatively describe the strength of PT effect; β is a characteristic length scale associated with the PT effect on the plasma emission. The existence of such a length scale indicates that there should be a well-defined threshold thickness below (above) which the PT effect can be regarded as presence (absence).

Taking Cu I line at 510.5 nm as an example, we fitted the relationships between the normalized line intensity and the PT for the three size-selected cases using eqn (1). The fitted curves are displayed in Fig. 4(a) and the values of the parameters α and β extracted from the fits are summarized in Table 2. One can see that the data can be quite well simulated using the exponential law of eqn (1). Both α and β show a monotonous increase with incremental grain size. The former implies that at least within the grain size range investigated here, the strength of the PT effect becomes weaker with incremental grain size because larger α leads to smaller maximal variation of the normalized line intensity caused by the effect. The later implies that larger grain size should be related to a larger threshold thickness PT_th at which a transition from presence to absence of the PT effect occurs.

Fig. 4 (a) Normalized line intensities of Cu I 510.5 nm versus packing thickness for the three size-selected cases. Solid lines are exponential fittings, R² > 0.97. (b) Black squares (left scale): threshold thickness versus median diameter; red triangles (right scale): ratio of threshold thickness to median diameter versus median diameter; error bars represent the fitting uncertainties.

Table 2 Exponential fitting parameters for the three size-selected cases

Parameter	d 50 = 53 μm	d 50 = 72 μm	d 50 = 100 μm
α	0.42 ± 0.01	0.51 ± 0.01	0.67 ± 0.01
β	0.09 ± 0.02	0.13 ± 0.02	0.18 ± 0.02

---

Here we defined PT_th = 3β + 0.15 as the specific transition point, corresponding to the strength of PT effect being decreased to 1/e³ (approximately equal to 5%) with incremental PT. Such a definition is based on the fact that with incremental PT from this point, it starts to become difficult to identify the presence or absence of the signal enhancement due to the experimental uncertainties. Following this line, the PT_th values at d₅₀ = 53 μm, 72 μm and 100 μm are determined to be around 0.42 mm, 0.54 mm and 0.69 mm, respectively, and shown in Fig. 4(b). It should be stressed that, although the PT_th value slightly depends on the grain size, the ratio of PT_th to d₅₀ (PT_th/d₅₀) seems to be size independent. The average value of PT_th/d₅₀ and its maximum value considering the error upper bound are equal approximately to 7.5 and 9 times the median diameter, respectively [see Fig. 4(b)]. This may imply that there is a common rule in LIBS of thin-layer microgranular materials: when PT is larger than 9 times the grain diameter, the PT effect is absent.

3.2 PT-dependent plasma parameter

The plasma emission features strongly depend on various thermodynamic parameters of plasma, in particular the plasma temperature and the electron density. To interpret the observed trends of PT-dependent plasma emission, it is necessary to determine how the plasma parameters affect the plasma emission. Here, following previous studies,^12,13 we selected the line of Cu I 510.5 nm to calculate the electron density by analyzing its Stark-broadening. It is worth mentioning that the observed profiles of this line are all approximately Lorentzian, implying that the other broadening mechanisms contributing to the line width are negligible. Thus, we used the FWHM of the Lorentzian curve obtained by fitting the measured line profile to calculate the electron density.

In addition, it is well known that there is an effect mediated by laser-induced shock wave during the formation of a luminous plasma.^20–22 Namely, when the laser irradiance exceeds the sample's ablation threshold, most of the ablated particles from the surface are still neutral atoms. As the ablated vapor expands, ionization of the ablated atoms occurs directly in the region behind the shock wave front, a higher temperature to a larger ionization rate in the region. This implies that the intensity ratio of ionic to atomic line from the same elemental species can serves as a sensitive temperature indicator. Here, we used the intensity ratio of Cu II 500.9 nm to Cu I 515.3 nm to indirectly estimate the plasma temperature.

For comparison convenience, the line intensity ratio (normalized to the corresponding values at PT = 0.15 mm: 0.26 @ 53 μm, 0.18 @ 72 μm, and 0.31 @ 100 μm) and the calculated electron density (normalized to the corresponding values at PT = 0.15 mm: 1.17 × 10¹⁷ cm⁻³ @ 53 μm, 1.38 × 10¹⁷ cm⁻³ @ 72 μm, and 1.42 × 10¹⁷ cm⁻³ @ 100 μm) versus the packing thickness are presented in Fig. 5. One can clearly see that the evolution of the normalized line intensity ratio (positive correlation with the plasma temperature) with incremental PT, similar to the case of the normalized line intensity, also exhibits a trend of first decreasing significantly and then becoming almost constant. However, the variation of the normalized electron density with PT is very small. All these indicate that compared to the electron density, the plasma temperature may play an important role in influencing the plasma emission features observed here.

Fig. 5 (a) Normalized intensity ratio of Cu II 500.9 nm to Cu I 515.3 nm as a function of the packing thickness. (b) Normalized electron density as a function of the packing thickness.

3.3 Explanation and discussion of the results

Considering that the disturbances to the plasma formation and spectroscopic measurement among laser pulses have been effectively avoided in current experiment. The only implication from the transition of PT effect is that certain distinct changes to the circumstance for plasma formation occur in the two PT regions divided by the PT_th. The complex process of plasma formation induced by high power pulsed laser interacting with a material surface was investigated in detail by Kagawa and co-workers.^20–22 They proved that the evolution of a laser-induced plasma in surrounding gases can be simplified into two distinct stages. In the first stage, the plasma is called a primary plasma, which acts as an initial explosion energy source to generate a shock wave. In the second stage, the plasma expands with time around the primary one and the atoms in the plasma are excited by the shock wave, which emits sharp spectral lines used for elemental analysis. The most important point in the formation of the secondary plasma is that its formation energy is mainly supplied by the kinetic energy of the atoms gushing from the primary plasma. For a soft material, during the secondary plasma formation, certain portions of recoil energy are absorbed by the soft surface and the gushed atoms cannot acquire sufficient speed to form a shock wave. As a result, a good secondary plasma could not be generated. On the other hand, based on the detailed revelation for the plasma evolution, they further demonstrated that the inherent difficulty of obtaining a good secondary plasma for LIBS-based analysis of a soft material can be overcome by setting a solid subtarget on the back of a thin-layer soft sample, so as to produce the repulsion force by which the speed of the gushed atoms is increased sufficiently.^{17,18,23–25}

Let us now return to the spectroscopic results obtained in this study. For PT ≤ PT_th, smaller PT to stronger plasma emission and higher plasma temperature indicates that the secondary plasma as an emission source of the measured LIBS spectra can be quite well formed in the PT region. It should be attributed to the existence of the vessel's bottom influencing the formation circumstance for the secondary plasma. Specifically, in the region of PT ≤ PT_th, the bottom wall plays a role of subtarget to produce the repulsion force for the atoms gushing from the primary plasma and enhance the speed of atoms. According to common sense, the enhanced efficiency should depend on the PT parameter and obey smaller PT to greater enhanced efficiency. Indeed, an increase of plasma emission and plasma temperature with decreasing PT has been observed in the present experiment. It implies that decreasing PT leads to the bottom having more and more high efficiency to enhance the speed of the gushed atoms. As a result, a secondary plasma with higher temperature is generated with the decrease of PT.

For the observed exponential dependence of plasma emission on PT, it is actually consistent with previous measurements of the penetration force required to push a flat plate approaching a solid bottom boundary of the vessel containing granular media by Stone and co-workers.^26,27 They found that the presence of a bottom boundary has a short-range influence on the plate penetration and the penetration resistance increases exponentially when the distance from the bottom reaches a few grain diameters. It has been demonstrated that such a short-range effect originates from the boundary effect on a local jamming of the granular media induced by the penetrating plate near the bottom. Our result that the maximum value of the PT_th considering the error upper bound is equal to 9 times grain diameters, is just in agreement with the short-range effect and implies that the existence of the vessel's bottom starts to influence the local jamming of the microgranular sample induced by the atoms gushing from primary plasma when decreasing the PT to several grain diameters. Further decreasing the PT, the penetration resistance (repulsion force) of the atoms vertically through the microgranular medium increases exponentially with decreasing PT, which is well reflected by the measured plasma emission and plasma temperature. Following this line, in the region of PT ≥ PT_th, the almost constant plasma emission and plasma temperature clearly suggests that the vessel's bottom has a vanishing influence on a local jamming of the microgranular sample induced by the atoms gushing from primary plasma. In other words, the bottom cannot serve as a role of subtarget to produce the repulsion force for the atoms anymore. In addition, for the result about smaller grain size to larger maximal variation (1 − α) of the normalized line intensity caused by the PT effect, it is understandable when considering smaller grain size to poorer mechanical performances in the microgranular samples, and therefore to higher enhanced efficiency for the speed of the atoms gushing from the primary plasma.

It needs to be emphasized that the transition of PT effect from presence to absence discovered here should be a common phenomenon in LIBS analysis of thin-layer microgranular materials when the following two conditions are met: (i) a luminous plasma is generated by a laser pulse ablating a sufficiently thin microgranular layer which is packed into a solid substrate; (ii) the existence of the substrate influences the formation of the luminous plasma and leads to an enhancement of its emission signal. Knowing and understanding such a phenomenon is essential for developing a modern LIBS technique to quantitatively analyze the elements embedded in a microgranular material. The most difficult problem with the analytical technique is that the expected linear relationship between the measured intensity of the spectral line and the concentration of the corresponding element is often flawed due to the irreproducibility of luminous plasma produced from the microgranular surfaces with different packing thickness. The presence–absence transition of the PT effect tells us that this problem could be well resolved once the PT parameter of microgranular materials to be analyzed is set at the region above a well-defined threshold thickness. In addition, as mentioned above, when PT ≤ PT_th, the relationship between the plasma emission intensity and the PT provides information about the bottom boundary effects on the local jamming of granular media. No work has been reported on the analysis of the local jamming of granular media using LIBS. We believe that this is of considerable interest for future works. On the other hand, considering that the bottom boundary effects on the local jamming of granular media is the decisive factor for the threshold phenomenon, the specific value of threshold thickness should depend on many granular parameters such as roughness and shape and the surface properties of the bottom boundary such as the texture and the friction coefficient. Further works are still needed for a better understanding of the role of each parameter in such a threshold phenomenon.

4. Conclusions

In the range of packing thickness (PT) from 0.15 mm to 1.00 mm, we experimentally investigate the PT dependence of the optical emission of plasma induced by nanosecond laser ablating the thin-layer copper microgranular samples in air for three size-selected cases (median size d₅₀ = 53 μm, 72 μm, and 100 μm, respectively). The most important finding is that the measured trend of PT-dependent plasma emission shows a threshold phenomenon. We demonstrate that the specific PT corresponding to the occurrence of such a threshold phenomenon represents a transition point, below (above) which an influence of the bottom of sample vessel on the plasma emission is present (absent). Such a bottom influence is attributed to a boundary effect on a local jamming of microgranular samples induced by the formation process of a laser-induced plasma. This finding not only has a potential use in the assessment of a lower PT limit for performing spectrochemical analysis of thin-layer microgranular materials using LIBS without consideration of PT differences, but also shows that the boundary effects on a local jamming of microgranular media may be probed using LIBS signal.

Data availability

The data supporting the findings of this study are available within the article.

Author contributions

Conceptualization: Kou Zhao, Qiang Zeng, Yaju Li and Dongbin Qian; methodology: Kou Zhao, Qiang Zeng, Yaju Li and Dongbin Qian; software: Yaju Li and Dongbin Qian; validation: Kou Zhao and Xinwei Wang; formal analysis: Kou Zhao and Qiang Zeng; investigation: Kou Zhao and Qiang Zeng; resources, Kou Zhao, Qiang Zeng, Shu Hang Gong, Xiangyu Shi and Yifan Wu; data curation: Jinrui Ye, Xueqi Liu and Liangwen Chen; writing-original draft preparation: Kou Zhao; writing-review and editing: Yaju Li and Dongbin Qian; visualization: Kou Zhao and Xinwei Wang; supervision: Yaju Li, Dongbin Qian, Shaofeng Zhang, Lei Yang and Xinwen Ma; project administration: Dongbin Qian and Xinwen Ma; funding acquisition: Dongbin Qian and Xinwen Ma. All authors have read and agreed to the published version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported, in part, by the National Key Research and Development Program of China (No. 2022YFA1602500) and National Natural Science Foundation of China program (No. U2241288).

References

1. A. W. Miziolek, V. Palleschi and I. Schechter, Laser-Induced Breakdown Spectroscopy Fundamentals and Applications, Cambridge University Press, 2006.
2. S. Musazzi and U. Perini, Laser-Induced Breakdown Spectroscopy: Theory and Applications, Springer Series in Optical Sciences, 2014.
3. Z. Wang, M. S. Afgan, W. Gu, Y. Song, Y. Wang, Z. Hou, W. Song and Z. Li, TrAC, Trends Anal. Chem., 2021, 143, 116385.
4. S. K. H. Shah, J. Iqbal, P. Ahmad, M. U. Khandaker, S. Haq and M. Naeem, Radiat. Phys. Chem., 2020, 170, 108666.
5. R. Wisbrun, I. Schechter, R. Niessner, H. Schroder and K. L. Kompa, Anal. Chem., 1994, 66, 2964–2975.
6. E. J. Judge, J. E. Barefield, J. M. Berg, S. M. Clegg, G. J. Havrilla, V. M. Montoya, L. A. Le and L. N. Lopez, Spectrochim. Acta, Part B, 2013, 83–84, 28–36.
7. R. Viskup, B. Praher, T. Stehrer, J. Jasik, H. Wolfmeir, E. Arenholz, J. D. Pedarnig and J. Heitz, Appl. Surf. Sci., 2009, 255, 5215–5219.
8. T. Stehrer, B. Praher, R. Viskup, J. Jasik, H. Wolfmeir, E. Arenholz, J. Heitz and J. D. Pedarnig, J. Anal. At. Spectrom., 2009, 24, 973–978.
9. S. J. Pandey, R. Locke, R. M. Gaume and M. Baudelet, Spectrochim. Acta, Part B, 2018, 148, 99–104.
10. M. E. Essington, G. V. Melnichenko, M. A. Stewart and R. A. Hull, Soil Sci. Soc. Am. J., 2009, 73, 1469–1478.
11. J. Duran, Sands, Powders, and Grains: An Introduction to the Physics of Granular, Springer, New York, 2000.
12. X. Li, Y. Li, S. Li, M. Zhou, L. Chen, J. Meng, D. Qian, J. Yang, S. f. Zhang, Y. Wu and X. Ma, Phys. Rev. Appl., 2021, 16, 024017.
13. Y. Li, X. Li, S. Li, M. Zhou, D. Qian, L. Chen, J. Yang, S. Zhang and X. Ma, J. Anal. At. Spectrom., 2021, 36, 1969–1976.
14. X. Li, X. Liu, S. Gong, Y. Li, L. Chen, D. Qian, S. Zhang and X. Ma, J. Anal. At. Spectrom., 2023, 38, 902–910.
15. L. Vanel and E. Clément, Eur. Phys. J. B, 1999, 11, 525–533.
16. M. Sperl, Granul. Matter, 2005, 8, 59–65.
17. K. Kagawa, T. J. Lie, R. Hedwig, S. N. Abdulmajid, M. M. Suliyanti and H. Kurniawan, Jpn. J. Appl. Phys., 2000, 39, 2643–2646.
18. M. M. Suliyanti, R. Hedwig, H. Kurniawan and K. Kagawa, Jpn. J. Appl. Phys., 1998, 37, 6628.
19. J. O. Marston and F. Pacheco-Vazquez, Phys. Rev. E, 2019, 99, 030901.
20. K. Kagawa, K. Kawai, M. Tani and T. Kobayashi, Appl. Spectrosc., 1994, 48, 198–205.
21. K. Kagawa, S. Yokoi and S. Nakajima, Opt. Commun., 1983, 45, 261–265.
22. A. M. Marpaung, R. Hedwig, M. Pardede, T. J. Lie, M. O. Tjia, K. Kagawa and H. Kurniawan, Spectrochim. Acta, Part B, 2000, 55, 1591–1599.
23. H. Suyanto, T. J. Lie, K. H. Kurniawan, K. Kagawa and M. O. Tjia, Spectrochim. Acta, Part B, 2017, 137, 59–63.
24. J. Iqbal, M. Pardede, E. Jobiliong, R. Hedwig, M. Ramli, A. Khumaeni, W. S. Budi, N. Idris, S. N. Abdulmadjid, K. Lahna, M. A. Marpaung, I. Karnadi, Z. S. Lie, H. Suyanto, D. P. Kurniawan, T. J. Lie, K. H. Kurniawan, K. Kagawa and M. O. Tjia, Microchem. J., 2018, 142, 108–116.
25. Z. S. Lie, M. Pardede, R. Hedwig, M. M. Suliyanti, K. H. Kurniawan, Munadi, Y. I. Lee, K. Kagawa, I. Hattori and M. O. Tjia, Anal. Bioanal. Chem., 2008, 390, 1781–1787.
26. M. B. Stone, D. P. Bernstein, R. Barry, M. D. Pelc, Y. K. Tsui and P. Schiffer, Nature, 2004, 427, 503–504.
27. M. B. Stone, R. Barry, D. P. Bernstein, M. D. Pelc, Y. K. Tsui and P. Schiffer, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, 70, 041301.

---

Footnote

† These authors contributed equally to this work.

---