Fe-Mg order-disorder in orthopyroxene: equilibrium fractionation between the octahedral sites and thermodynamic analysis

The equilibrium intracrystalline distribution coecient, k D, of Fe (i.e. Fe +Mn) and Mg between the M1 and M2 sites of three natural nearly binary Fe-Mg orthopyroxene crystals (Fs14, Fs15 and Fs49) were determined by annealing experiments at several temperatures between 550 and 1000 °C and single crystal X-ray structure re®nements. In addition, the X-ray data of an orthopyroxene crystal (Fs23), which were collected earlier by Molin et al. (1991) between 700 and 1000 °C, were re-re®ned. The data were processed through two di€erent re®nement programs (SHELXL93 and RFINE90) using both unit and individual weights and also both ionic and atomic scattering factors. The calculated site occupancies were found to agree within their estimated standard errors. However, the use of ionic scattering factors led to signi®cantly better goodness of ®t and agreement index, and smaller standard deviations of the site occupancies than those obtained from the use of atomic scattering factors. Furthermore, the weighted re®nements yielded signi®cantly smaller standard deviations of the site occupancies than the unweighted re®nements even when the same set of re ̄ections was used in the two procedures. The site occupancy data from this study were combined with selected published data to develop expressions of k D as a function of temperature and composition. Calculation of the excess con®gurational entropy, DS, suggests that orthopyroxene should be treated as a two parameter symmetric solution instead of as a ``simple mixture''. The calculated DS values and the excess Gibbs free energy of mixing suggested by available cation exchange data lead to a slightly negative enthalpy of mixing in the orthopyroxene solid solution. Introduction In orthopyroxenes, Fe and Mg fractionate between two nonequivalent octahedral sites, M1 and M2, with Fe preferring the larger of the two sites (Ghose 1965). The principal geological interest in this problem stems from its potential application to the determination of cooling rates of terrestrial and extraterrestrial rocks (Ganguly 1982; Anovitz et al. 1988; Skogby 1992; Ganguly et al. 1994; Molin et al. 1994a,b; Artioli and Davoli 1995; Ganguly and Domeneghetti 1996; Zema et al. 1997; Ganguly et al. 1997; Kroll et al. 1997). However, the determination of cooling rate from the observed Fe-Mg ordering state requires accurate data on the equilibrium site fractionation and the kinetics of the fractionation process of these cations. It is also very sensitive to small errors in the site occupancy data, especially for low Fe concentration (Ganguly et al. 1989; Kroll et al. 1997). We report in this paper the results of experimental study on the equilibrium site fractionation in three natural orthopyroxene crystals (Fs14, Fs15 and Fs49) as a function of temperature, as determined by annealing experiments and single crystal X-ray structure re®nements. In addition, we have re-determined the chemical composition and re-re®ned the X-ray data of Molin et al. (1991) of an orthopyroxene crystal (Fs23) from the Johnstown meteorite, which was annealed at several temperatures between 700 and 1000 °C, using di€erent strategies. The need for the type of experimental data presented in this work is highlighted by the recent critical analysis of Kroll et al. (1997), who concluded that ``the large range of reported results is disconcerting'', and emphasized the need for ``new, accurate and consistent site occupancies, the more so if thermodynamic properties of orthopyroxene solid solution are to be derived from the coecients of statistically ®tted thermodynamic models to the data''. Finally we also discuss the implications of the site partitioning data for the thermodynamic mixing properties of the orthopyroxene solid solution. Contrib Mineral Petrol (1999) 136: 297±309 Ó Springer-Verlag 1999 M. Stimp ̄ (&) á J. Ganguly Department of Geosciences, University of Arizona, Tucson, AZ 85721, USA G. Molin Dipartimento di Petrogra®a e Mineralogia, Universita' di Padova, I-35137 Padova, Italy The closure temperature (TC) of cation ordering, obtained by comparing its quenched ordering state with a calibration of equilibrium ordering state versus temperature, plays a critical role in the retrieval of its cooling rate (Ganguly 1982). However, since di€erent structure re®nement programs use di€erent strategies, Ganguly et al. (1994) recommended that the site occupancy determination of an unknown sample should be carried out in the same way as that used in the calibration of equilibrium site occupancy as a function of temperature. It was hoped that in this approach, any inherent error in the site occupancy determination arising from a particular structure re®nement strategy would be self compensating between the unknown and the calibrated samples. Kirfel (1996) carried out an interlaboratory comparison of cation distribution studies using the same X-ray data sets for olivine and orthopyroxene crystals, and found considerable disagreement among the results. He, thus, reinforced the recommendation of Ganguly et al. (1994). As an alternative, he suggested determination of the site occupancies using ``multiple re®nement approach''. In this work, we also compare results of site occupancy determination obtained by subjecting the same X-ray data for a crystal to di€erent re®nement strategies in order to isolate the di€erences arising from those in the re®nement schemes, and to recommend a good working procedure. Experimental procedure We separated several crystals of orthopyroxene from two samples of stony-iron (type IVA) meteorites, Steinbach and SaÄ o JoaÄ o Nepomuceno (Haack et al. 1996), and from a terrestrial granulite facies sample from the Central Gneiss Complex of British Columbia, Canada (Hollister 1982, sample number TPK 30F). From these crystals, we selected two crystals from SaÄ o JoaÄ o Nepomuceno and one from each of the rest that were best suited for X-ray structure re®nements, and determined their initial ordering states without bulk compositional constraints. The selected crystals from SaÄ o JoaÄ o Nepomuceno (Fs14), Steinbach (Fs15) and granulite (Fs49) were labeled SJN(23 and 25), ST77 and HO28, respectively. Each crystal was disordered successively at several temperatures up to 1000 °C for suciently long duration to achieve a steady state as determined by time series study. After completion of the disordering experiments, the crystals were successively ordered at the same set of temperatures. Thus, the equilibrium ordering state at each temperature was ``reversed'', that is established by approaching it from the states which were initially more ordered and more disordered than the equilibrium state. The annealing experiments were carried out by sealing each crystal, along with a physically separated mixture of wuÈ stite and iron, in a silica tube in the presence of a ̄owing Ar gas. The assembly was then suspended at the ``hot spot'', which was calibrated to be 5 cm long, in a vertical tube furnace, and drop-quenched in water. The furnace was always preheated to the desired temperatures before insertion of the samples. Temperature was monitored by a chromel-alumel or a Pt-Pt10%Rh thermocouple with its junction placed at essentially the same horizontal section of the furnace as that containing the sample. The separation between the thermocouple junction and the sample was £0.5 cm. After each annealing experiment, the crystal was mounted on a single crystal di€ractometer for X-ray data collection, and then subjected to the next experimental cycle. Except for SJN, only one crystal was used for the entire calibration of distribution coecient versus temperature at a ®xed bulk composition. After completion of the annealing experiments and X-ray data collections, each crystal was analyzed in an electron microprobe, and treated according to a projection scheme, as discussed later, to determine its statistically most probable bulk composition. X-ray structure re®nements and site occupancy determinations Single crystal X-ray intensity data were obtained using either a Siemens AED II or a NONIUS CAD-4 fourcircle automated di€ractometer and MoKa radiation (graphite monochromator). The equivalent pairs hkl and h kl were measured using x scan mode in the 2h range 3 to 60° or 70°. After correcting the X-ray intensities for Lorentz, polarization and absorption factors (North et al. 1968), the values for the equivalent pairs were averaged and the site occupancies were re®ned in the space group Pbca, along with a scale factor, extinction coecient and atomic positional and anisotropic thermal parameters. The total number of nonequivalent re ̄ections varied between 900 and 1800. The scattering factors were taken from the International Tables for X-ray Crystallography (1974) and Tokonami (1965). In the re®nements using ionic scattering factors, Fe, Mg, Ca, Cr, Na, Al and Ti were considered to have the respective formal charges, whereas Si and O were considered to be in the partly ionized states of 2.5+ and 1.5), respectively. It was assumed, as is the common practice (e.g., Domeneghetti et al. 1985; Ganguly et al. 1994; Yang and Ghose 1994) that Al, Cr, Fe and Ti were con®ned to the M1 site, Ca and Na to the M2 site, and that Mn partitioned between the two octahedral sites in the same way as Fe (Hawthorne and Ito 1978). Structure and site occupancy re®nements were carried out using di€erent weighting schemes, scattering factors and two di€erent programs, SHELXL-93 and RFINE90. The results are summarized in Tables 1±2 for the crystals ST77, SJN 23 and 25, JS and HO28. The stated uncertainties (1r) of the site occupancies are those due only to the statistical errors of the structural data. The possible e€ects of the errors of the bulk composition are discussed later. 298