## 4 Results and Discussion  
Selecting the delay time during an LIBS analysis is an important part of measuring elements. The intensity of the signal is greatly affected by the delay time. Generally, the delay times for detecting the emission signal of an ablated sample is under 100 ns for continuum emission, 500 ns-20 \(\upmu\)s for atomic emission, and 100 ns-5 \(\upmu\)s for ionic emission. At the continuum emission, the time for excited atoms to come back to the ground state is too short to be detected. Since the spectral emission lines are eventually extinguished, the time for capturing the signals is important to improve the measurement accuracy. The appropriate delay times are known to vary with the transformation of the ion and the elemental composition of the sample [8; 9; 10]. The appropriate delay time for a quantitative analysis of a target sample is determined by the coefficient of determination, \(R^{2}\). In Figure 4, coefficients of determination, \(R^{2}\) with various delay times are presented to determine the appropriate delay time for the quantitative analysis of coal samples. The spectrometer delay time varied from 0.2 to 2.0 \(\upmu\)s by a 0.2 \(\upmu\)s interval. The 100 spectra samples were consecutively captured at each delay time. The calibration curves for the 100 spectra were obtained using the CA, PLS, and SNR methods. From the calibration curves, the \(R^{2}\) were calculated for delay times from 0.2 to 2.0 \(\upmu\)s. The \(R^{2}\) with the CA showed a relatively high value compared to those of the other analysis methods. The highest \(R^{2}\) for a 1.4 \(\upmu\)s delay time for the CA and PLS methods were 0.97 and 0.91, respectively. However, the highest \(R^{2}\) of the signal-to-noise ratio method for a 1.0 \(\upmu\)s delay time was 0.77. Figure 5 shows the seven emission spectra for seven coal samples at 247.7 nm for C, 656.2 nm for H, 844.6 nm for O, and 544.65 nm for S. All four emission lines were clearly identified from adjacent emission lines, and they were obtained with a delay time of 1.4 \(\upmu\)s. The wavelengths of 247.7, 656.2, 844.6, and 544.65 nm are known to be characteristic wavelengths for identifying the existence of carbon, hydrogen, oxygen, and sulfur, respectively, in coal samples. In Figure 5a, the carbon emission spectrum for Gunvor presented the maximum intensity due to the highest C concentration (74.4%) among the seven coal samples, as shown in Table 2. In Figure 5b, the highest hydrogen emission spectrum appears to occur in the Gunvor sample. However, the base signal line for the Gunvor sample is shifted a little bit. Considering this, the magnitude of the hydrogen spectra for the seven samples is almost identical. Compared to other components such as hydrogen and sulfur, the maximum intensity of the carbon spectrum was much higher than those of the other components. In Figure 5e, the average value of 100 spectra from the seven different coal samples is shown as a full spectrum obtained from the spectrometer. Figure 4: The coefficients of determination, \(R^{2}\) with various delay times for the CA, PLS, and SNR methods. Figure 5: Sample emission spectra for (**a**) carbon, (**b**) hydrogen, (**c**) oxygen, (**d**) sulfur, and (**e**) full spectrum plot for seven coal samples.