1. Introduction

The Laser Induced Breakdown Spectroscopy (LIBS) is widely studied due to its greatest advantage and capability for whole element analysis with minimal handling even no sample preparation, which just make the signal generation by ablated laser pulse on material. Moreover, the instrument and operation of a LIBS system is much simpler than some other sensitive element analysis techniques. However, the inevitable problems in LIBS are matrix effect and self-absorption to make spectral signal unsteady which can be partly avoided by utilizing proper confined unit and the signal to noise ratio is also enhanced. The high-repeatability and stable enhancement signal have been proved by proper confined unit, and spark technique, and so on, which can resolve part hindrance in spectral accuracy for quantitative analysis. The relative standard deviation(RSD) decreases from 5.5 ± 0.5% to 2.5 ± 0.5% and Limit of Detection (LOD) increases 15 to 92 times respectively when a microsecond and nanosecond discharge spark was used in LIBS for signal enhancement [1, 2]. Here, a relatively high-voltage power supply is required for discharge firing while it makes the volume of LIBS system large. Besides, pressure confinement with shielding gas at different pressure was also utilized for the destination confinement [3]. Double pulse excitation can enhance the spectral intensity too. The first laser pulse was generated by direction collinear, vertical or angular excites plasma while the second laser pulse re-heats and re-excites the plasma to obtain simultaneously enhanced spectral [4–6]. Among these methods, spatially confined enhancement attracts much more attentions due to an easy way with only a confinement unit on sample surface [7–9]. Shockwave produced by laser pulses is confined in confinement units, thus the shockwave flection has impact on plume known as ‘compressed effect’ [10]. A series of ICCD (Intensified Charge Couple Device) images after various delay time elaborate stable plasma core and higher temperature distribution during restricted-plasma extension. Longer plasma life time gives stronger signal in confinement case. Spatial confinment includes rectangle 1-D confinement [11, 12], pillar and circle 2-D confinement [13, 14], hemisphere 3-D confinement [15].

With the confinement unit installation, rather reliable and enhanced spectral signal form than that by adjusting instruments such as spectrograph, laser, optical route and so forth. As we well known, different material confinement circle with various relative permittivity will induce quite different confinement efficiency, which has not been studied. Confined material selection still remains a challenging topic. Moreover, although the size dependent signal enhancement investigation has been reported but it still exists some problems such as the physical reason of the optimum size of confinement unit. In this paper, the dependences of relative permittivity on spectral signal enhancement were studied by varying materials to confine the plasma, which include PTFE, Nylon/Dacron, Silicagel, and NBR with the relative permittivity 2.2, ~3.3, 3.6, 8~13, 15~22. Higher relative permittivity rings mean stronger enhancement ability to restrict the energy dissipation of plasma better, and the reflected electromagnetic wave indicate the electromagnetic field distribution of plasma become more localized. Spectral signal varies with variation in size of the 2-D PTFE confinement has been studied in detail. This works will make LIBS signal to realize optimized performance to obtain higher accuracy results.

2. Experimental framework

Figure 1 shows the experimental setup of LIBS. The laser is a Q-switched Nd: YAG 1064 nm Laser (Newwave, USA) with pulse duration 5 ns and repetition rate 5 Hz, laser beam was focused on the surface of sample along a certain angle with the focal spot of tens of micrometer in diameter. Then the plasma was produced with 3~5mm height and 1~3 mm diameter. Signal collection section was composed by a fiber with 200 μm diameter installed in fiber holder and two collection lenses with focal length 55 mm and 50 mm (L2, L3) to enhance the NA (numerical aperture) of collected system. After laser ablation, the emission spectra including plasma continuum radiation and elemental atomic lines were acquired by a multichannel spectrometer with the resolution of 0.1 nm which install a charge coupled device (CCD) with 2048 × 2048 pixel (Avantes Avsdesktop USB2, Netherlands). PTFE confinement circles with different sizes were utilized for plasma confinement with the height 1 mm, 2 mm, 3 mm, 4 mm, 5 mm and the diameter 2 mm, 3 mm, 5 mm, respectively. After the confined unit was installed on the sample surface, a laser pulse with 30 mJ focuses on the surface of sample crossing the confinement unit. The incident laser must be injected at a special angle to the collection section due to the emission from the plasma induced by vertical incident laser might be obscured by the opaque confinement unit [17]. The laser output was monitored by energy meter to make sure the fluctuation of injection energy less than 3%. The time delay module controls the gate time of spectrograph and laser pulse to optimize the emission atomic spectrum line of different elements to maximum. Each data was acquired with total 100 laser pulses firing per circle. Focal point and sample movement are controlled by a 3-D mobile station (3-D MS), as shown in Fig. 1.

 

Fig. 1 Diagrams of Laser induced breakdown spectroscope. (S: Splitter; M: Meter; R: Reflector; L1, L2, L3: Len 1, 2, 3; 3D-MS: 3-dimensional mobile station)

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3. Result and discussion

3.1 Permittivity dependent spectral enhancement

The laser induced breakdown spectrum shows different amplification abilities by varying different material confinement units, including PTFE, Nylon, Dacron, Silicagel (SG), NBR with the relative permittivity 2.2, ~3.3, 3.6, 8~13, 15~22, respectively [18–21]. Due to the silicon is composed of single element and the surface of silicon slice is smooth so that the amplified spectrum is simple and easy to be analyzed, the silicon slice was chosen as the object of study. Figure 2 shows various enhancement factors under different relative permittivity confinement unit being installed. The size of confinement units is 3 mm diameter and 1 mm height (D3H1). The red columns are the amplification ratio of characteristic lines Si I243.5 nm and blue one is the amplification ratio of Si I263.1 nm, respectively. The increase trend of enhancement factor of these two lines was shown as broken line. For the spectral lines of Si I 243.5 nm and Si I 263.1 nm, the enhancement factors increase as 1.12/1.18, 1.17/1.21, 1.37/1.57, 1.46/1.74, 1.74/1.89 gradually by comparison of the intensity in confined case to unconfined case. An obviously increase of the enhancement factor occurs with rising relative permittivity from PTFE 2.2 to NBR ~20. The maximum spectral intensity was amplified 1.74 times for Si I 243.5 nm and 1.89 times for Si I 263.1 nm by using NBR as confinement unit.

 

Fig. 2 Bar chart of various amplification with different confinement rings being used to confine the plasma on the surface of silicon slice. The red and blue columns are a comparison of characteristic lines Si I243.5 nm and Si I263.1nm, respectively. The broken line shows the trend of these two amplification ability with relative permittivity increase.

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Figures 3(a)-3(d) show the signal fluctuation of spectral line Si I 243.1 nm without using confinement unit, and further being compared to the results with PTFE, Nylon, SG, NBR confinement unit using, respectively. The signal fluctuation decreases after different type of confinement unit being installed on the surface of silicon slice to confine plasma. Compared to the results without confinement unit, the RSD reduces by 41.32%, 42.24%, 56.23% and 57.99% corresponding to PTFE, Nylon, SG, NBR confinement unit being used respectively after the spectra are normalized and pretreated for different signal from both confined case and unconfined case. It demonstrates that the more stable signal and uniform plasma formed due to the electromagnetic field of plasma was restricted well by confined unit with various materials. Dacron has similar confinement ability compared with Nylon due to the relative permittivity values is almost same. There exist some abnormal peaks in spectra in the situation without confinement units, which attribute to laser fluctuation or surface uncertainty. However, the intensity fluctuation of abnormal peaks deceased even disappeared because the electromagnetic field of plasma was localized to become more stable and regular when the confined circles are installed.

 

Fig. 3 The comparison of fluctuation from spectral intensity of Si I243.1 nm with unconfined unit and confined unit being used with (a) PTFE (b) Nylon, (c) SG, and (d) NBR, respectively.

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Besides, the temperature of plasma has a vital role in plasma stability and can be estimated by Boltzmann plot [16]:

Plasma induced by focused laser pulse is a collective of high temperature (T) and highly dense charged particles. At the beginning of plasma expansion, simultaneous blast of shockwave is produced in several nanoseconds with the velocity increasing gradually and eventually exceeds the speed of plasma expansion [12]. Subsequently, the shockwave was struck and reflected by the wall of confined unit, besides, electromagnetic (EM) wave had escaped from plasma and then the EM wave struck and was reflected by the wall of confined unit also in an earlier time (approximately 10⁻¹²~10⁻¹¹ s), the interaction between shockwave and plasma is considered to undergo a mechanical action or external force. But differently, the interaction between EM wave and plasma is regarded as an interaction based on the electromagnetic field. The material with higher relative permittivity can reflect more electromagnetic energy, which means the EM field of plasma is localized to a certain area. The enhancement effect of signal intensity is not only originating from the external mechanical force of shockwave but also should be ascribed to the restricted electromagnetic field of plasma. The electromagnetic dominate the process of the “dielectric effect”. Theoretically, when the EM wave struck the surface of the confinement circle at a right angle, the reflection ability of EM wave is determined by the formula of $\text{R}={\left|(\sqrt{{\epsilon }_r}-1)/(\sqrt{{\epsilon }_r}+1)\right|}^2$, where ${\epsilon }_r$ is the relative permittivity of the confinement ring. For the different material, the corresponding R was calculated to be 0.036, 0.084, 0.096, 0.23~0.325, and 0.348~0.423 respectively. The increase of the reflectance ability indicates that more energy of plasma is restricted to make the plasma intensity stronger. The corresponding fluctuation also becomes even and decreases due to the strong spectral intensity. Moreover, the polarized laser pulses also make plasma induce more charged particle scattered with high speed to generate more charged carriers in higher relative permittivity material [22, 23].

3.2 Size dependent spectral enhancement

The details of size dependent signal enhancement was checked, as shown in Fig. 4. The PTFE was chosen as the confinement unit in different sizes due to the low adsorbability to the plasma cooling ashes. The spectral lines of Si I243.5 nm and Si I263.1 nm were selected for spectral analysis. The spectral enhancement factor with using confinement ring to that without using one, shows the same tendency. For the diameter of the circle at 5mm, the ratio gradually increases with changing height of the ring from 1mm to 3 mm and then decrease for 4 mm and 5 mm. While for smaller dimeter rings, the maximum enhancement factor is achieved at 2 mm height ring and 1mm height ring in sequence. For both line Si I243.5 nm and Si I263.1 nm, the peak enhancement factors are 1.62/1.69,1.74/1.73,1.93/2.06 with the size of confinement unit at D2H1/D3H2/D5H3 in sequence, for which the height at 50% /67%/60% of diameter, respectively. Enhancement factor increases to the maximum when the optimum height and diameter determined, as shown in Fig. 4. The maximum peak enhancement factor of 2.06 is observed in the size of the ring with D5H3. The signal enhancement is attributed to the ‘compressed effect’ of shockwave generated by the laser pulse [10].

 

Fig. 4 The spectral amplification factors for spectral lines of (a) Si I243.51 nm and (b) Si I263.1 nm under different-size PTFE confinement circles. The height is 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm with the diameter D = 2 mm, 3 mm, 5 mm, respectively.

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The size of confinement ring is important for the plasma enhancement due to the plasma compressed effect is not dominant in case of unit height smaller than plasma size [17]. In proper-sized confinement circle, most of shockwave reflected by the wall of confined cavity and oscillates in it for multi-times while the shockwave in the vertical direction escapes from the cavity easily. The bremsstrahlung, recombination and characteristic radiation both represent the origin of continues and line spectra which are time-determined. The height of the confinement unit makes a great influence on the interaction frequency between plasma and shockwave, moreover, the diameter has a crucial role in terms of interaction time. Reflected shockwave enhance plasma radiation and interaction between shockwave and plasma increases with proper diameter and height of confinement unit. However, the optimum enhancement factor is limited by the duration of characteristic radiation which requires the shockwave to reflect to plasma during atomic radiation. The shockwave always propagates with supersonic speed [10] and can be decomposed into vertical and horizontal component, as shown in Fig. 5(b), shockwave is produced by a pulse laser and propagates in 3-D space, ${\tau }_1$ and ${\tau }_2$ are the speed in vertical and horizontal directions.

 

Fig. 5 (a)Image of interaction between shockwave and plasma and (b)the diagram of shockwave reflected by confined unit.

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The life time of plasma is 2.5~3.5 μs approximately, the shockwave expanding speed decays from 20000 m/s to 2500 m/s within 200 nanoseconds and then remains a supersonic speed below 1500 m/s for a long time, which means the the process of shockwave is reflected by unit wall and then impacts on plasma will consume 0.85~1.45 μs, 1.25~2.15 μs, 2.85~3.05 μs by using D2 mm, D3 mm, D5 mm confined unit in terms of direction ${\tau }_1$. So, the plasma emission gradually become strong during the time of 0.6 μs ~1 μs, and more intensified signal emission occurs during 1.5 μs ~2.9 μs. Then it weakens, even disappeared after 3.2 μs. Therefore, the enhancement factor should be D5>D3>D2 when the height of unit is 3 mm as shown in Fig. 4. Another speed direction ${\tau }_2$ decides the escaping-time of shockwave, but the consuming time reaches a maximum of 3.2 μs and the propagation distance reaches ~3 mm along the direction ${\tau }_2$. The enhancement factor decreases when increase height larger than 3 mm, the main reason is that the characteristic radiation decreases again when it exceeds the optimum height. The shockwave carried energy interact on the plasma continues but the optimum times has missed which means that the reflected shockwave interact on the relative weaken plasma.

4. Application

According to experimental study on the optimum condition of relative permittivity and size dependent enhancement, the application on the quantitative analysis of coal was performed. Firstly, the pretreatment of the spectra is necessary to reduce analysis error. The abnormal peaks, due to the errors from spectrometer and matrix difference of samples, make a great influence on the accuracy. Firstly, to locate the abnormal peaks X (including $x_{11},x_{12}\dots x_{ij}$, $\text{i}$ represents number of pulses and $j$ is the dimensions of spectra, maximum is 8192 in this work) from the data after eliminated the back continues bremsstrahlung radiation. Secondly, the lost peaks marked by P (such as $p_{iv}$ and the maximum of $\text{ν}$ is 8192 also) are filled by Partial Least-Squares (PLS) regression. Finding the intensity of peaks $p_{uv}$ is not equal to 0 in ${\nu }^{th}$ dimension, thus PLS is applied to obtain the coefficient as follows:

There are $(\text{i}-1)$ sets of data that the intensity in location $\text{ν}$ is not absence which means there be $(\text{i}-1)$ sets of coefficients ($a_1,a_2,a_3\dots a_k\dots$) produced by PLS regression. Finally, the intensity of the lost peaks is calculated by

Which the $a_k^{\text{'}}$ is the mean of $(\text{i}-1)$ sets of coefficients $a_k$ while assuming the number of lost peak is 1 in some dimension. Obviously, the lost peaks might be not only one in the same dimension, the data treatment is similar to mentioned above steps but it was processed one by one, which mean that the PLS regress data extracted from whole data with ${\nu }^{th}$ dimension is not absence.

However, the number of lost peaks must be controlled below 1% of the number of all peaks to define data as valid and should not be eliminated in terms of the same measurement. On the other hand, the lost peaks in the same dimension must be controlled below 5%~7% of training number of sample, and if the peaks lost exceed 95% of training size in this dimension will be defined as accidental peaks and assigning the intensity value to 0. Moreover, the peak shift beyond 0.1 nm in spectra was defined as abnormal peak and must be corrected by statistic methods. PCA (Principle Component Analysis) is used to confirm the key parameters from spectral information. Figure 6(a) is the scores of data treatment and original data by PCA which demonstrates the component 1 possession increase from 49.4% to 67.7%, indicating the explanation of data increase for the component 1. But the component 2 possession decreases from 33.6% to 11% which indicates the explanation of data dominate by component 1 after spectral treatment. There exists ~4% of data loss of the component 1 and component 2 might be the continuous radiation and the abnormal data.

 

Fig. 6 (a) The scores of treatment and origin spectra by PCA and (b) The distribution of scores with component 1 and component 2 in terms of treatment and origin data.

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Signal stability and repeatability in LIBS are significant for quantitative analysis. The intensity enhancement can be observed by utilizing different materials with various relative permittivity. Quantitative coal analysis without and with NBR confined unit has been investigated. As shown in Fig. 7(a), the typical spectra from coal slice were amplified with confinement circle installed (dash dot line) compared with that without confinement unit (solid line). The original spectra were obtained from 40 different samples with different known composition in the coal for standard curve establishing and the parameters of other 18 unknown coal samples were predicted to check the model. 48 points marked by laser pulse in the coal slice with around 240 sets of spectra due to per 5 pulses illuminating on the same position, as shown in the inset of Fig. 7(a).

 

Fig. 7 (a) Amplified atomic spectrum with confinement unit compared with original atomic spectrum of coal, and inset shows ablated coal slice. The fitting curves of 18 sets of data with respect to carbon (b), ash(c), and volatile (d) of the coal, respectively.

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Figures 7(b)-7(d) show the calibration curve established from 40 sets of samples with the spectrum collection using the confined unit NBR in same way as that in prediction to predict the carbon content, ash content, and volatile content, respectively. The prediction value of the three parameters including carbon, ash and volatile in the coal were calculated by principal component analysis combining with PLS (Partial Least Squares). The correlation coefficient R² is 0.99 for coal and volatile content while 0.98 for ash. The Root Mean Square Error of Prediction (RMSEP) of carbon, ash and volatile in the coal is 0.68, 0.77, 0.66 and Absolute Relative Error (ARE) is 1.17%, 4.02%, 1.96%, respectively, which indicates the prediction value is very close to actual value. Therefore, the enhancement by high-relative permittivity confinement unit is an effective way to make accuracy improved in LIBS, finally to realize industrial production monitoring.

Conclusion

In this work, size and relative permittivity dependent signal enhancement with different materials have been investigated qualitatively and quantitatively by using silicon and coal sample. Signal fluctuation for Si I 243.1 nm was reduced drastically in different confinement units and the corresponding RSD reduces by 41.32% for PTFE, 42.24% for Nylon, 56.23% for SG and 57.99% for NBR, respectively. Therefore, the higher is the relative permittivity, the better is plasma confinement effect. Enhancement factor 1.89 for Si I263.1 nm and 1.80 for C I193.09 nm were observed by using the NBR to confine plasma. Higher relative permittivity of material means strong ability to confine electromagnetic wave and more plasma energy being reflected back. The size of PTFE confinement unit with different diameters of 2 mm, 3 mm, 5 mm and height 1 mm, 2 mm, 3 mm, 4 mm, 5 mm were separately examined. Optimum spectra were obtained by adjusting gate delay time and data processing including normalization, peak shift, abnormal peak process, which minimize the errors of laser energy fluctuation or instrumental error to uniform the spectrum. The maximum enhancement factor can be realized in the case of D2H1, D3H2, and D5H3. The optimal size of confined unit for signal intensity enhancement is attributed to proper interaction time between shockwave and plasma. Finally, NBR confinement unit were utilized for calibration and predication in quantitative analysis of carbon, ash and volatile in coal. The fitting results show R² is 0.99 both for carbon and volatile and 0.98 for ash. The results suggest a negligible matrix effect and small LIBS signal fluctuation on different materials. Therefore, our method can be realized so as to make the LIBS can be widely used for on-line monitoring during industrial production.