# Current Progress in Femtosecond Laser Ablation/Ionisation Time-of-Flight Mass Spectrometry
## 4 Performance of fs-LIMS Instruments in the Element and Isotope Analysis
### Measurements of Elements and Isotopes
#### 4.4.1 Measurements of Elements  
The much weaker dependence of fs-laser ablation on physical and chemical properties of the material compared with ns-laser ablation allows for the investigation of an increased number of materials, as fractionation effects become significantly reduced [20]. This makes fs-LIMS less matrix-dependent and measurements of standard research materials can be avoided if the semi-quantitative information is sufficient. This is supported by results obtained with both, high and moderate fs-laser ablation by LI-O-TOFMS and LMS, LMS-GT instruments, respectively. The LI-O-TOFMS instrument developed in the groups of [PERSON] and [PERSON] has been used in different types of semi-quantitative analysis of solids [129]. Low discrepancy RSCs for different elements were obtained for a series of artificial samples containing B, C, N, O, F, Si, P, S, Cl, As, Br, Se, I, and Te with He buffer gas pressure of 250 Pa and a laser irradiance of about \(10^{10}\) W cm\({}^{-2}\). In the miniature LMS, the accuracy of the quantitative determination of element abundances is verified against standard reference materials (SRM), typically by either analysing metallic samples such as NIST SRM 661, SRM 664, and SRM 665 [132; 133; 135], or analysing geological standards and natural samples [34; 150]. To quantify the magnitude of fractionation, the relative sensitivity coefficient (RSC) for an element in the sample is introduced. The RSC for a given element is obtained by dividing the measured element concentration, \(X_{m}\), by the expected concentration, \(X\):  
\[\mathbf{RSC_{X}}=\frac{X_{m}}{X} \tag{2}\]  
For well-defined chemical compositions, as is typically the case for NIST SRMs, atomic fractions are stated or can be derived from the provided atomic mass fractions. The mass spectrometric measurements yield atomic intensities and their fractions are calculated by dividing the atomic intensities of a given element with respect to all atomic intensities measured in the sample [135]. By comparing the measured fraction of element \(X\) with the fraction of this element in the given sample, one obtains the RSC of the element. The observed dependence of ion production efficiency on elemental properties (e.g., first ionisation potential, electron affinity, mass number, melting temperature) in these experiments led to the development of chemometrics, which can be used to rationalise the observations [149]. In studies of Cu-Sn-Pb ternary alloys composition, fs-LIMS using an IR fs-laser radiation was employed. The abundances of elements determined from the mass spectrometric analysis were compared with the results obtained by inductively coupled plasma collision/reaction interface mass spectrometry (ICP-CRI-MS) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) reference measurements. The two ICP-MS studies quote smaller errors but these error bars use aliquots of the sample (Table 3) [159]. Performance tests with the fs-LMS instrument investigating the accuracy of the quantitative determination of element abundances were conducted against reference samples [21; 27; 132; 150]. Similar studies were repeated using double-pulse IR fs-LMS [87]. Figure 8 shows the correlations of the measured and certified abundances measured with (a): single pulse (SP) and (b): double pulse (DP), respectively. For truly stoichiometric results, all points would lie on the line with a slope of value 1. Deviation from this slope indicates nonstoichiometric atomic composition measurements which can be caused by various fractionation effects. From these data, the calibrations constants, the RSCs, for LIMS are derived. Figure 8: (**a**) Comparison of the measured and certified atomic abundances by SP IR fs-LMS; (**b**) Comparison of the measured and certified atomic abundances by DP IR fs-LMS. The Fe measurements are low due to the \({}^{56}\)Fe signal saturation effects in the detector channel. Reprinted with permission from [21,87].