Rayleigh's distillation law and linear hypothesis of isotope fractionation in thermal ionization mass spectrometry

The relationship which exists between Rayleigh's distillation law and linear models of instrumental isotopic fractionation in thermal ionization mass spectrometry is shown. If the process of isotope fractionation in the mass spectrometer source occurs in terms of a Rayleigh's distillation, and, within the range of mass of isotopes of the element, the vapor/residue distribution coefficient is a linear function of mass with a slope which is sufficiently small in absolute value, then the linear hypothesis of isotope fractionation is fulfilled. The model shows that the fractionation factor per amu, defined as the instantaneous difference between the measured and true values of the isotope ratio, per unit of measured/true value and per unit of mass difference between the two isotopes which define the ratio, can be interpreted as a function of two parameters: the residual mass fraction of the sample on the filament, and the rate of change of the distribution coefficient with mass. These two parameters can be calculated and, in particular, the value of the residual mass fraction of the sample when the measured values of the isotopic ratios coincide with the actual values can be calculated as a function of the rate of change with mass of the distribution coefficient. A linear model of instrumental isotopic fractionation can be derived from the exponential hypothesis of fractionation, which can be also interpreted in terms of a Rayleigh's distillation process, but where mass is an exponential function of the distribution coefficient. Experimental results of instrumental isotopic fractionation (up to 1%amu-1) of strontium in NIST standard reference material 987, loaded as a nitrate on a single tungsten filament, can be interpreted in terms of the linear models of isotope fractionation (and therefore of Rayleigh's distillation law) within experimental error. They show: (i) changes in the vapor/residue distribution coefficient with mass in the range -0.006 to -0.004amu-1; (ii) approximately constant rates of sample consumption in the range of residual mass fraction from ~1 to ~0.3-0.25, which are between 0.05 and 0.13% min-1; (iii) values of the residual mass fraction of the sample, when the measured values of the isotopic ratios coincide with the true ones, between 0.3668 and 0.3671, which correspond to sample consumption of 63.3%. Since the linear hypothesis of fractionation is fulfilled, the values of isotopic ratios of strontium in the standard material can be determined. The global weighted averages of the weighted averages of the results obtained in eleven runs in which 86Sr, 87Sr and 88Sr peaks were sampled are as follows: 86Sr/88Sr = 0.119445±0.000053, 87Sr/86Sr = 0.71016±0.00019, and 87Sr/88Sr = 0.084826±0.000040.