doi:10.1016/j.gca.2004.08.034 Oxygen isotope fractionation factors involving cassiterite (SnO 2 ): I. Calculation of reduced partition function ratios from heat capacity and X-ray resonant studies V. B. POLYAKOV, 1, * S. D. MINEEV, 1 R. N. CLAYTON, 2 G. HU, 3 V. M. GUREVICH, 1 D. A. KHRAMOV, 1 K. S. GAVRICHEV, 4 V. E. GORBUNOV, 4 and L. N. GOLUSHINA 4 1 V. I. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosygin Street 19, Moscow, 119991, Russia 2 Enrico Fermi Institute, Department of Chemistry and Department of the Geophysical Sciences, University of Chicago, Chicago, IL 60637, USA 3 Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA 4 N. S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninsky Prospect, 31, Moscow, 119991, Russia (Received January 6, 2004; accepted in revised form August 30, 2004) Abstract—Oxygen isotope equilibrium fractionation constants ( 18 O-factors) of cassiterite were evaluated on the basis of heat capacity and X-ray resonant (Mössbauer 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 depen- dence 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 Mössbauer parameters of cassiterite were conducted in the range from 300 to 900 K. The attempt to describe Mössbauer 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 Mössbauer 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,  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: 10 3 ln 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 CaCO 3 -SnO 2 = 4.607x - 0.3463x 2 + 0.01500x 3 , x = 10 6 / T 2 ; 10 3 ln SiO 2 -SnO 2 = 4.942x - 0.2963x 2 + 0.01150x 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 experi- ments are needed. Copyright © 2005 Elsevier Ltd 1. INTRODUCTION Naturally occurring cassiterite is the most abundant of the tin minerals and plays a crucial role in the chemistry and geochem- istry of tin. Cassiterite forms associations with different oxy- gen-bearing minerals such as oxides, silicates, etc., and is potentially useful for oxygen isotope geochemistry. However, full utilization of oxygen isotope studies of tin deposits (Kelly and Rye, 1979; Patterson et al., 1981; Sushchevskaya et al., 1985; Sun and Eadington, 1987; Strauch et al., 1994) is limited due to a lack of reliable equilibrium oxygen isotope constants involving cassiterite. There are several possible approaches to obtain data on equilibrium isotope constants of minerals (Clayton, 1981; Chacko, 1993; Chacko et al., 2001): 1. Evaluation of equilibrium isotope fractionation coeffi- cients from experimental data on the isotope exchange reaction conducted under laboratory conditions (laboratory method) (e.g., Northrop and Clayton, 1966; Chiba et al., 1989). 2. Synthesis of a mineral in the laboratory and direct analysis of coexisting mineral and water (synthesis method) (e.g., O’Neil, 1986; Vitali et al., 2001). 3. Evaluation of equilibrium isotope fractionation coeffi- cients on the basis of isotopic fractionation measured in natural samples using independent mineralogical geothermometers for calibration (empirical or natural sample method) (e.g., Wada and Suzuki, 1983; Valley, 1986). 4. Theoretical calculation of equilibrium isotopic constants using spectral models and/or potentials of interatomic interac- tions (theoretical calculation) (e.g., Bigeleisen and Mayer, 1947; Urey, 1947; Kieffer, 1982; Patel et al., 1991). 5. A semiempirical increment method previously established by Galimov (1973) for calculating the reduced isotopic parti- tion function ratio (-factor) of gas molecules and extended by Schütze (1980) to solids (increment method) (see also Richter and Hoernes, 1988; Zheng, 1991). Unfortunately, there is no method that can be recognized as universal. Each of the methods has advantages and limitations. * Author to whom correspondence should be addressed (polyakov@ geokhi.ru). Geochimica et Cosmochimica Acta, Vol. 69, No. 5, pp. 1287–1300, 2005 Copyright © 2005 Elsevier Ltd Printed in the USA. All rights reserved 0016-7037/05 $30.00 + .00 1287