Instrumental isotopic fractionation in mass spectrometer source can be interpreted in terms of Rayleigh (1902) distillation process. The observed changes in measured values of isotopic ratios during spectrometric runs are quantitatively explained in terms of change in mass fraction of the sample (sample consumption), and in terms of vapor/residue distribution coefficients (Ds) which values are different over the mass range of the isotopes of the element. In substance, a D=D(m) function which is not constant over the mass range of the isotopes of the element (Cavazzini 2009, 2012).. In different spectrometric runs of a same sample, in general, the position and the shape of the D=D(m) function is not reproduced. This irreproducibility causes the change in the geometry of distributions of measured values isotopic ratios from run to run. lnx vs. lny distributions (x, y = measured values of isotopic ratios of the element) are linear distributions, theoretically, and, in practice, these distributions can be linearly fitted with a very good success. Parameters of linear best-fit of a distribution (slope S and intercept I) are related to the true values of the isotopic ratios x0, y0, and to ratios and differences between the values of the distribution coefficients of the isotopes that define the two ratios. They change from run to run, due to changes in the D=D(m) function. Due to Rayleigh's assumption in solving the differential equation, from a theoretical point of view, intra-run geometrical parameters S and I are fixed, and pairs (S, I) from distributions obtained in different spectrometric runs of a sample are not, in general, inter-run linearly correlated because of the change in the D=D(m) curve from run to run. However, if the isotopic ratios x, y are characterized by an equivalent mass difference between the mass at the numerator and the mass at the denominator, some quantities can be neglected, and pairs (S, I) from different runs are expected to be linearly correlated. The true values of the isotopic ratios, x0, y0, are expected to be the parameters of the correlation, so that we expect that the true values of the isotopic ratios can be determined by fitting a straight line through a set of pairs (S, I) from different spectrometric runs of a sample (Cavazzini and Roccato 2017). In the case of two isotopic ratios x, y characterized by an equivalent mass difference between the isotope at the numerator and the isotope at the denominator, the change in the value of the ratio y/x is very small during a run, even if the range of isotopic fractionation is large. This means that we know the value of quantity y/x with a certain good precision (note that is impossible for any of the isotopic ratios). This quantity can be used as a useful constraint to calculate the true values of the isotopic ratios. J. W. S. Rayleigh. On the distillation of binary mixtures. Philosophical Magazine, Ser. 6 (4), 521-537 (1902). G. Cavazzini. Rayleigh's distillation law and linear hypothesis of isotope fractionation in thermal ionization mass spectrometry. International Journal of Mass Spectrometry, 288, 84-91 (2009) G. Cavazzini. Distillation law and exponential model of isotope fractionation. International Journal of Mass Spectrometry, 309, 129-132 (2012) G. Cavazzini and D. Roccato. Inter-measurements determination of isotopic composition of Strontium (Abstract) in Geosciences¨a tool in a changing world, Pisa, 4-6 Settembre (2017)
Inter-measurement determination of the isotopic composition of Sr (II)
2019
Abstract
Instrumental isotopic fractionation in mass spectrometer source can be interpreted in terms of Rayleigh (1902) distillation process. The observed changes in measured values of isotopic ratios during spectrometric runs are quantitatively explained in terms of change in mass fraction of the sample (sample consumption), and in terms of vapor/residue distribution coefficients (Ds) which values are different over the mass range of the isotopes of the element. In substance, a D=D(m) function which is not constant over the mass range of the isotopes of the element (Cavazzini 2009, 2012).. In different spectrometric runs of a same sample, in general, the position and the shape of the D=D(m) function is not reproduced. This irreproducibility causes the change in the geometry of distributions of measured values isotopic ratios from run to run. lnx vs. lny distributions (x, y = measured values of isotopic ratios of the element) are linear distributions, theoretically, and, in practice, these distributions can be linearly fitted with a very good success. Parameters of linear best-fit of a distribution (slope S and intercept I) are related to the true values of the isotopic ratios x0, y0, and to ratios and differences between the values of the distribution coefficients of the isotopes that define the two ratios. They change from run to run, due to changes in the D=D(m) function. Due to Rayleigh's assumption in solving the differential equation, from a theoretical point of view, intra-run geometrical parameters S and I are fixed, and pairs (S, I) from distributions obtained in different spectrometric runs of a sample are not, in general, inter-run linearly correlated because of the change in the D=D(m) curve from run to run. However, if the isotopic ratios x, y are characterized by an equivalent mass difference between the mass at the numerator and the mass at the denominator, some quantities can be neglected, and pairs (S, I) from different runs are expected to be linearly correlated. The true values of the isotopic ratios, x0, y0, are expected to be the parameters of the correlation, so that we expect that the true values of the isotopic ratios can be determined by fitting a straight line through a set of pairs (S, I) from different spectrometric runs of a sample (Cavazzini and Roccato 2017). In the case of two isotopic ratios x, y characterized by an equivalent mass difference between the isotope at the numerator and the isotope at the denominator, the change in the value of the ratio y/x is very small during a run, even if the range of isotopic fractionation is large. This means that we know the value of quantity y/x with a certain good precision (note that is impossible for any of the isotopic ratios). This quantity can be used as a useful constraint to calculate the true values of the isotopic ratios. J. W. S. Rayleigh. On the distillation of binary mixtures. Philosophical Magazine, Ser. 6 (4), 521-537 (1902). G. Cavazzini. Rayleigh's distillation law and linear hypothesis of isotope fractionation in thermal ionization mass spectrometry. International Journal of Mass Spectrometry, 288, 84-91 (2009) G. Cavazzini. Distillation law and exponential model of isotope fractionation. International Journal of Mass Spectrometry, 309, 129-132 (2012) G. Cavazzini and D. Roccato. Inter-measurements determination of isotopic composition of Strontium (Abstract) in Geosciences¨a tool in a changing world, Pisa, 4-6 Settembre (2017)I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
