Spectral line selection
In this paper, the spectra in the range of 300-600nm were collected, and the Cr and Cu elements in the samples used in the experiment were analyzed. The characteristic spectral lines of Cr and Cu elements were identified by combining the information from the National Institute of Standards and Technology (NIST) database, the collected spectral information and the spectral line recognition software. And atomic lines Cr I 425.44nm, Cr I 427.48nm, Cr I 428.97, Cr I 520.84nm, Cu I 4.75nm, and ionic lines Cr II 405.41nm, Cu II 368.65nm were analyzed, respectively. At the same time, in order to reduce the influence of environmental fluctuation and system error on the detection results, 20 sample points were collected for each sample, and the average value of 5 spectra was taken as the final result for each sample point. One spectrum in the experimental acquisition spectrum is shown in Fig. 2.
Effect Of Surface Hardness On Plasma Temperature
Under the assumption of local thermodynamic equilibrium (LTE)[14], the Cr element was used as the analysis element to calculate the change of plasma temperature of samples with different surface hardness[15, 16, 17]. The spectral parameters of the characteristic spectral lines used are shown in Table 2.
Table 2
Spectral parameters of Cr atomic lines
Wavelength(nm) | Aki(s− 1) | Ek(eV) | gk |
425.44 | 3.15e + 7 | 2.91 | 9 |
427.48 | 3.07e + 7 | 2.90 | 7 |
428.97 | 3.16e + 7 | 2.89 | 5 |
520.84 | 5.06e + 7 | 3.32 | 7 |
The calculation of plasma temperature was carried out for samples numbered S4, S9 and S14 with the same concentration of Cr elements and different surface hardness. And the plasma temperature was obtained using Boltzmann equation:
$$ln\frac{I\lambda }{{{g}_{k}A}_{ki}}=\frac{-{E}_{k}}{kT}+ln\frac{4\pi Z}{hc{N}_{0}}$$
1
where \(I\) is the intensity of the characteristic spectral line, \(\lambda\) is the wavelength of the characteristic spectral line, \({g}_{k}\) is the statistical weight of the upper state, \(k\) is the Boltzmann constant, \(T\) is the plasma temperature, \(Z\) is the partition function, which is usually regarded as the statistical weight of the ground state, \(h\) stands for the Planck constant, \(c\) is the speed of light, and \({N}_{0}\) represents the population density[18]. In Eq. (1), \({E}_{k}\) is defined as the x-axis, and \(ln\frac{I\lambda }{{{g}_{k}A}_{ki}}\) is defined as the y-axis. The slope \(-\frac{1}{kT}\) can be obtained through the known \(ln\frac{I\lambda }{{{g}_{k}A}_{ki}}\) and \({E}_{k}\), and then the plasma temperature can be calculated. The corresponding relationship between plasma temperature and sample surface hardness is shown in Fig. 3. At the same time, the ablation craters profiles of samples with different surface hardness were photographed to research the influence mechanism of surface hardness on plasma, as shown in Fig. 4.
As can be seen from Fig. 3, with the increase of sample surface hardness, the excitation temperature of plasma also increases. This may be because the ablated mass of the sample surface decreases with the increase of the sample surface hardness, which increases the absorption of laser energy by the plasma and intensifies the particles collision inside the plasma. Figure 4 proves this view. From the profile of the ablation craters in Fig. 4, it can be roughly judged that with the increase of sample surface hardness, the volume of the ablation craters decreases, and the ablated mass of the sample decreases. At the same time, the correlation coefficient (R2) between sample surface hardness and plasma temperature can reach 0.853, which has a good linear relationship. Thus plasma temperature can be used as an evaluation index to predict sample surface hardness.
Effect Of Surface Hardness On The Ratio Of Ionic Lines To Atomic Lines
In order to study the effect of surface hardness on the atoms and ions in plasma, the trend of the ratio of ionic lines to atomic lines of Cr and Cu with surface hardness was studied with S4, S9 and S14 samples[19, 20]. The maximum and minimum values of 20 spectra of each sample were removed, and the average values of the remaining 18 spectra were taken. In this paper, the values of Cr II 405.41nm/Cr I 425.44nm and Cu II 368.65nm/Cu I 324.75nm were used as the y-axis, respectively, and the surface hardness was used as the x-axis to establish the relationship between surface hardness and the ratio of ionic to atomic lines, as shown in Fig. 5.
As can be seen from Fig. 5, with the increase of sample hardness, the ratio of ionic lines and atomic lines of Cr and Cu elements showed an upward trend. This suggests that the increase of surface hardness leads to the increase of the number of ions in the plasma. This may be because samples with higher surface hardness have stronger repulsive force. With the increase of sample surface hardness, the shock wave front speeds increases, which increases the collision probability of particles and the ionization rate of atoms. Abdel-salam et al.[21] also demonstrated that the harder the sample, the faster the shock wave and the greater the ratio of ionic lines to atomic lines. Meanwhile, the linear relationship between the surface hardness of samples and the ratio of ionic lines to atomic lines of elements can be seen that the ratio of ionic lines to atomic lines of elements can also be used as an evaluation index for hardness testing.
Effect Of Surface Hardness On The Calibration Curve
As one of the matrix effects, a change in surface hardness can affect the calibration curve. In this paper, the influence of surface hardness of samples on the calibration curves of Cr and Cu elements in samples was analyzed. Similarly, the maximum and minimum values of 20 spectra of each sample were removed, and the remaining 18 spectra were calculated. The performance of the calibration curve was evaluated using the values of LOD, RMSE, ARE, and RSD. The calculation equation of each parameter is as follows:
$$LOD\left(wt\text{\%}\right)=\frac{3\sigma }{k}$$
2
$$RMSE\left(wt\text{\%}\right)=\sqrt{\frac{{\sum }_{i=1}^{N}(\stackrel{\wedge }{{c}_{i}}-{c}_{i}{)}^{2}}{N}}$$
3
$$ARE\left(\text{\%}\right)=\frac{100}{N}{\sum }_{i=1}^{N}\frac{|\stackrel{\wedge }{{c}_{i}}-{c}_{i}|}{{c}_{i}}$$
4
$$RSD\left(\text{\%}\right)=\frac{\sqrt{\sum _{i=1}^{n}\frac{{(\stackrel{\wedge }{{c}_{i}}-\stackrel{-}{c})}^{2}}{n-1}}}{\stackrel{-}{c}}\times 100$$
5
In Eq. (2), \(\sigma\) is the standard deviation of the spectral background signal, and \(k\) is the slope of the calibration curve. In Eqs. (3), (4), and (5), \(N\) (= 5 in this work) represents the number of samples with the same hardness and different element concentrations, \(n\) (= 18 in this work) is the number of repeated measurements of the same sample under the same conditions. \(\stackrel{\wedge }{{c}_{i}}\), \({c}_{i}\), \(\stackrel{-}{c}\) represent the predicted concentration, the actual concentration, and the average value of repeated measurements, respectively.
Figure 6 shows the calibration curves of Cr and Cu elements with different surface hardness. Among them, the R2 of the calibration curve of Cr and Cu elements in the samples with a surface hardness of 98HA is better than that of the samples with a surface hardness of 43HA and 70HA. The evaluation parameters of the calibration curve in Fig. 6 are calculated, and the results are shown in Table 3.
Table 3
Parameter values of calibration curves of Cr and Cu elements with different surface hardness
Element | Hardness(HA) | R2 | RMSE(wt%) | ARE(%) | RSD(%) | LOD(wt%) |
Cr | 43 | 0.895 | 0.044 | 12.356 | 13.496 | 0.015 |
70 | 0.838 | 0.096 | 26.562 | 16.909 | 0.016 |
98 | 0.962 | 0.027 | 9.763 | 19.383 | 0.017 |
Cu | 43 | 0.874 | 0.054 | 16.010 | 24.220 | 0.034 |
70 | 0.714 | 0.089 | 27.245 | 32.692 | 0.036 |
98 | 0.899 | 0.047 | 15.862 | 34.383 | 0.045 |
As can be seen from Table 3, the RMSE and ARE values of Cr and Cu calibration curves of samples with a surface hardness of 98HA are smaller than those of samples with a hardness of 43HA and 70HA, which indicates that the accuracy of Cr and Cu calibration curves with a surface hardness of 98HA is better. This is attributed to the increase of surface hardness, which reduces the ablated mass of the sample, the plasma can absorb the laser energy more fully, and the detection value is closer to the actual value. However, the RMSE and ARE values of Cr and Cu element calibration curves with a surface hardness of 70HA are relatively large, which may be the fluctuation of laser energy, resulting in a large deviation between the detection value and the actual value. In contrast to the improvement of detection accuracy, the LOD and RSD values of Cr and Cu elements of the sample with a surface hardness of 98HA become larger, indicating that the stability of detection decreases and the repeatability of experimental results decreases. It may be that the shock wave front speeds increase, which intensifies the disordered state of particle collision inside the plasma. And the background signal and noise signal fluctuate greatly, resulting in the large fluctuation of each measurement result.