## 2 Materials and Methods
### Semi-Quantitative Analysis of Different Elements in LIB Spectra of Gemstones
#### 3.2.4 Comparative Study of the Elemental Composition of Gemstones  
As in LIBS, the spectral intensity is directly proportional to the concentration of the constituent in the sample and therefore the variation of the spectral intensity represents the variation in the concentration of the constituents in the different samples [38; 39; 40]. Therefore, the intensities of spectral lines have been used to evaluate the relative concentration of the elements present in different gemstones. Instead of calculating the absolute spectral intensity, the signal-to-background (S/B) intensity ratio has been calculated to avoid any experimental parameter variation. A comparative bar graph of (S/B) is shown in Figure 7. The uncertainties shown here are the standard deviations obtained from the spectral lines present in multiple spectra. If one looks for Si intensity, the comparison graph plot shows that the quartz samples (S_1,S_3, and S_5) contains a larger quantity of Si than the other minerals. The quartz is a pure silica mineral with approximately 47% (mineral formula) of Si while the other three gemstones, aquamarine beryl(S_2), diopside (S_4), and enstatite (S_6), have approximately 31%, 26%, and 28%, respectively. If we consider only the three quartz samples, it can be observed that heliotrope (S_3) shows the greatest quantity of Si. SR-XRD analysis of a heliotrope gemstone from Palantine hill, Rome (Italy) reveals that it contains 94% quartz and 1.6 % hematite. PIXE analysis of the same sample shows 46% Si concentration and 0.56% Fe concentration [32]. The LIBS results of the present study are in agreement with mineral formulas. At this point, however, it would be important to know the characteristics of the other samples. Sample S_2 (aquamarine beryl; Be\({}_{3}\)Al\({}_{2}\)Si\({}_{6}\)O\({}_{18}\)) may have approx. 5% Be and 16% Al. In an earlier study, the EPMA technique was used for the quantitative analysis of beryls from Zealand Station, Canada. It suggested that the average Fe concentration ranges from 0.83 to 1.22 wt.%, with a maximum iron content of 1.4 wt.%, whereas the aluminum concentration ranged from 16.98 to 17.78 wt.% Al\({}_{2}\)O\({}_{3}\)[42]. The highest reported concentration of iron in aquamarine beryl is 5.94% from Yukan, Canada, found by [PERSON] et al. [43]. The amounts of Al and Be in the S_2 sample are larger than in the other gemstone samples since they contain these elements only as impurities. Diopside and enstatite are inosilicates and belong to the group of pyroxenes. They represent end members of pyroxene quadrilateral (diopside-hedenbergeite-enstatite-ferrosilite). Diopside is a clinopyroxene while enstatite is an orthopyroxene. The composition of clinopyroxenes ranges between that of diopside and (MgCaSi\({}_{2}\)O\({}_{6}\)) and hedenbergeite (FeCaSi\({}_{2}\)O\({}_{6}\)), whereas orthopyroxenes are a series between enstatite (MgSiO\({}_{3}\)) and ferrosilite (FeSiO\({}_{3}\)). LIB spectral data show that the Mg level in the S/B intensity ratio is higher for diopside and enstatite than for the other gemstones investigated. The LIB spectral analysis for the diopside sample investigated in this work differs significantly from that of the ideal diopside. The level of Al and Fe is high in diopside. Previous studies [34; 35; 44] suggest that in high-temperature and low-pressure conditions, diopside  
Figure 6: [PERSON]–Boltzmann plot for calculating ionization temperature from the data of sample S_1. forms a solid-solution series with the [PERSON]'s molecule (CATS-CaAl2 SiO6). Aluminian-diopside can be considered as an intermediate member of this series. In the aforementioned natural conditions, Al-diopside can form through the reaction of diopside and anorthite (CaAl2 Si2O8). [PERSON] et al. [35] stated that significant ionic substitution is common in pyroxene solid solutions. An investigation of pyroxene crystals from the region of Andranondambo in southern Madagascar was carried out with different techniques [45], and EPMA and Mossbauer data showed a significant amount of Fe.