Based on statistical analysis of repetitive measurements, definitions of concentration at the detection limit from the literature were specified as four types: (a) peak separation (PKSEP), (b) qualitative detection limit (QUAL), (c) quantitative detection limit (QUANT), and (d) the minimum amount of an element guaranteed detectable (MAGD). As a new approach, for a given mean value of accumulated counts on the background, a reverse calculation yields the mean value of the accumulated counts on the peak fulfilling criteria (a) to (d). Based on the reverse calculation, a diagram was constructed that allows to use the averages of accumulated raw counts of peak and background to decide whether the analysed concentration can be used as quantitative result. The method is valid for any analytical condition and does not need a matrix correction.

The maximum concentrations of La, Nd, Sm, Gd, Ho and Yb in olivine, orthopyroxene, clinopyroxene and garnet (sub-solidus model garnet lherzolite assemblage) were investigated experimentally in the system CaO - MgO - Al2O3 - SiO2. REE-Lα lines were measured at 20 kV / 60 nA on PET (La, Nd, Sm. Gd) and on LIF (Ho, Yb) monochromator crystals with counting times of 80 s (La) to 190 s (Yb) on the peak and total analysis times of ca. 5 min. The maximum concentrations of REE in synthetic garnet and clinopyroxene, partially also in orthopyroxene, make these phases suitable for starting materials of quasi-reversal experiments.

The calculated concentrations at the quantitative detection limit for olivine, orthopyroxene, clinopyroxene and garnet range from 175 ppm [μg/g] for La to 275 ppm for Gd on PET, and from 180 ppm for Ho to 200 ppm for Yb on LIF. In case of La and Nd, compared to the used linear relationship, a full PAP correction yields values higher by about 15%. The background count rates on the REE-Lα peak positions for orthopyroxene, clinopyroxene and garnet in the system CaO - MgO - Al2O3 - SiO2, compared to those measured on pure enstatite, diopside and pyrope standards, are mainly higher due to solid solution effects. REE concentrations less than ca. 4000 ppm did not result in a higher count rate of the background for olivine and orthopyroxene. For clinopyroxene and garnet the effect is larger due to higher solubility of REE.

Concentrations at the quantitative detection limit were calculated for samples with similar count rates as the synthetic standards. On REEAIO3 (La, Nd, Sm, Gd, Ho) and REE3Al5O12 (Yb, Lu) at 20 kV / 20 nA they range from 450 ppm (La) to 900 ppm (Yb), and on REEPO4 at 20 kV / 50 nA and 20 kV / 60 nA they range from 350 ppm (La) to 500 ppm (Gd), and from 350 ppm (Ho) to 400 ppm (Yb). The calculated concentrations are influenced by the sensitivity and the stability of the individual spectrometers. Pre-requisite is a careful selection of the background positions.

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