Oxygen isotope fractionation factors involving cassiterite (SnO2): I. Calculation of reduced partition function ratios from heat capacity and X-ray resonant studies

Abstract Oxygen isotope equilibrium fractionation constants (β 18 O-factors) of cassiterite were evaluated on the basis of heat capacity and X-ray resonant (Mossbauer spectroscopy and X-ray inelastic scattering) data. The low-temperature heat capacity of cassiterite was measured in the range from 13 to 340 K using an adiabatic calorimeter. Results of measurements of two samples agree very closely but deviate more than 5% from previous heat capacity data used for calculation of thermodynamic functions. The temperature dependence of heat capacity was treated using the modern version of the Thirring expansion, and the appropriate temperature dependence of the vibrational kinetic energy was found. Measurements of temperature-dependent Mossbauer parameters of cassiterite were conducted in the range from 300 to 900 K. The attempt to describe Mossbauer fraction and the second order Doppler (SOD) shift on the basis of the Debye model failed. The first term of the Thirring expansion of the Mossbauer SOD shift agrees with that calculated from the Sn sublattice vibration density of states (VDOS) obtained via synchrotron X-ray scattering. Based on this agreement we calculated the kinetic energy of the cassiterite Sn sublattice from VDOS. From the kinetic energy of the total cassiterite crystalline lattice and its Sn sublattice, β 18 O-factors of cassiterite were computed in the temperature range 300–1500 K by the method of Polyakov and Mineev (2000) . Appropriate polynomials, which are valid at temperatures above 400 K, are the following: 1 0 3 ln ⁡ β SnO 2 = ( 7.176 ± 0.252 ) x − ( 0.07369 ± 0.00089 ) x 2 + ( 0.0008026 ± 0.0001022 ) x 3 , x = 10 6 / T 2 ; 10 3 ln ⁡ α CaCO 3 − S nO 2 = 4.607 x − 0.3463 x 2 + 0.01500 x 3 , x = 10 6 / T 2 ; 10 3 ln ⁡ α SiO 2 − S nO 2 = 4.942 x − 0.2963 x 2 + 0.01150 x 3 , x = 10 6 / T 2 . The evaluated cassiterite isotope fractionation factors are significantly different from those obtained by synthesis, increment and empirical methods. To resolve the differences, laboratory direct exchange experiments are needed.