Introduction In the first commercial inductively coupled pla

Introduction In 1984, the first commercial inductively coupled plasma mass spectrometry (ICP-MS) appeared, soon after that, Gray (1985) analyzed the elemental and Pb isotopic compositions of granites by combining ICP-MS and laser ablation (LA), thereby initiating the application of LA-ICP-MS in the micro-analysis. Jackson et al. (1992) and Fryer et al. (1993) fully demonstrated the significant potential of LA-ICP-MS in the micro-analysis of trace-elemental compositions and U–Pb isotopic ages of geological samples. Walder et al. (1993) applied LA-Multi-Collector-ICP-MS (LA-MC-ICP-MS) to analyze Pb isotope of solid samples and demonstrated that LA-MC-ICP-MS has a potential to become a significant tool to micro-analyze different isotopic ratios in solid samples. The micro-analysis of element content and isotopic ratios in solid samples by LA-ICP-MS and LA-MC-ICP-MS has become an attractive frontier in the analytical sciences. Compared to solution nebulization (SN)-(MC)-ICP-MS, LA-(MC)-ICP-MS can provide in situ and high-resolution (>5 μm for profile analysis and n × 10 nm ∼ n × 100 nm for depth analysis) elemental/isotopic compositions of solid samples with lower sample consumption and more efficiency (less than 3 min for a single-point analysis) (Günther et al., 1998; Jarvis and Williams, 1993; Perkins et al., 1993). Additionally, the application of LA-(MC)-ICP-MS can avoid the sample-digestion-related problems e.g., incomplete digestion of some minerals (Cotta and Enzweiler, 2012; Hu et al., 2010; Hu and Qi, 2014; Zhang et al., 2012, 2015), poor stability/memory effect of some elements in dilute KU-57788 solutions (Hu et al., 2008d; Liu et al., 2003; Münker, 1998) as well as the strong interferences from oxides (Košler et al., 2005; Oeser et al., 2014) and hydrides (Czas et al., 2012; Regnery et al., 2010). In recent years, the analytical technique has quickly developed and been widely used in numerous fields including geology, metallurgy, environmental science, biology, chemistry, materials science and archeology (Durrant and Ward, 2005). Even though LA-(MC)-ICP-MS is fast, sensitive, and able to probe microscale features, it is still held back by the interferences (Jiang et al., 1988; Konter and Storm, 2014; Moens et al., 2001; Tanner et al., 2002), sensitivity drift (Liu et al., 2013; Luo et al., 2007) and elemental/isotopic fractionation (Günther and Koch, 2008; Horn, 2008). Thus, rigorous and suitable calibration methods must provide the means to obtain quantitative data. Over the last few decades, different methods have been developed and successfully used for the determination of element content and isotopic ratios (Miliszkiewicz et al., 2015).
Basic knowledge of (MC-)ICP-MS and mass selection The sample aerosol obtained by solution nebulization or laser ablation is introduced into the high-temperature ICP, where the aerosol is evaporated, dissociated, atomized and ionized to generate ions. The positively charged ions are extracted from the argon plasma into the high vacuum of the mass spectrometry via the interface of sampler and skimmer cones (Becker, 2008; Wieser et al., 2012). The mass to charge ratio of elements is then measured to evaluate the element content or isotopic ratio of the analyzed elements. However, the observed or measured isotopic ratio is commonly deviated from the true or theoretical value as a function of the mass difference, which is defined as mass fractionation or discrimination (Jarvis and Williams, 1993). Although the causes of the mass fractionation are not entirely understood, space-charge effects within the plasma region and supersonic gaseous expansion between the sample and skimmer cones are mainly responsible (Andrén et al., 2004; Ponzevera et al., 2006), and both processes favor the transmission of the heavier isotopes into the mass spectrometry. For the mass fractionation in element content analysis (i.e., elemental fractionation), it is not only affected by isotope mass difference and instrumental conditions, but also affected by element characters (e.g., condensation temperature, first ionization potential and evaporation enthalpy). The elemental fractionation can be evaluated by the fractionation index, which is defined as the ratio of the integrated signal obtained for the second half time of the continuous ablation to the signal for the first half time, normalized to the internal standard (e.g., Ca) (Fryer et al., 1995) (Equation (1)).