Articles
Evaporation of single crystal forsterite: evaporation kinetics, magnesium isotope fractionation, and implications of mass-dependent isotopic fractionation of a diffusion-controlled reservoir

https://doi.org/10.1016/S0016-7037(98)00286-5Get rights and content

Abstract

Single crystals of forsterite were evaporated in a vacuum furnace at temperatures of 1500–1800°C to study evaporation kinetics, magnesium isotopic fractionation, and magnesium diffusion in forsterite. The evaporation of single crystal forsterite revealed that the evaporation process is kinetically hindered, in agreement with the results of Hashimoto (1990) on polycrystalline forsterite. The activation energy of forsterite evaporation obtained from this study is 628 kJ/mole. Forsterite can thus be much more refractory at low temperatures than expected from thermodynamic predictions.

The evaporation of solid forsterite supports a model of isotopic fractionation under diffusion-controlled conditions such that isotopic fractionation during the evaporation process is restricted to the vicinity of the evaporating surface. The measured solid-gas fractionation factor of 26Mg/24Mg is smaller than the theoretical prediction, suggesting more complicated gas speciation than a monatomic Mg gas. Diffusion coefficients of forsterite at high temperature (1500–1800°C) were obtained based on measurement of isotopic profiles in the evaporation residues. Mg diffusion in forsterite along its crystallographic a-axis has a very high activation energy (608 kJ/mole).

Introduction

Calcium-, aluminum-rich inclusions (CAIs) in meteorites carry important information on the physical and chemical conditions of the solar nebula. The process of evaporation has been shown to play an important role in the formation of CAIs (Kurat 1970, Tanaka and Masuda 1973, Chou et al 1976, Notsu et al 1978, Nagasawa and Onuma 1979; Hashimoto et al., 1979; Lee et al 1979, Hashimoto 1983, Niederer and Papanastassiou 1984, Clayton et al 1988, Davis et al 1990, Ireland et al 1992). Among the metallic rock-forming elements with more than one stable isotope (magnesium, silicon, calcium, titanium, chromium, iron, and nickel), isotopic fractionation is small to immeasurable in ordinary chondrites, achondrites, and lunar and terrestrial rocks (except that silicon varies by about 3‰/amu in terrestrial materials, Tilles, 1961). Large isotopic fractionation of these elements has been found in some CAIs, and has been attributed to evaporation in the solar nebula.

Hashimoto (1983) emphasized the kinetic aspects of evaporation in order to characterize the rate-determining processes for each of the major elements he studied (magnesium, silicon, aluminum, calcium, and iron). He found that use of the chemical composition of the major elements alone did not allow discrimination between evaporation and condensation evolution paths for the origin of CAIs. During equilibrium condensation or evaporation processes, isotopic fractionation is very small for silicon, magnesium, and calcium, because the difference in isotopic partition function ratios for these elements between gas and condensed phase is extremely small at high temperatures. However, heavy-isotope enrichment (up to a few percent per amu) is found in magnesium, silicon, oxygen, titanium, and calcium in CAIs (Clayton et al., 1988). This enrichment results from the kinetic isotope effect between vapor and liquids or solids due to nonequilibrium evaporation of the precursor material (Davis et al., 1990). Thus, stable isotope fractionation effects can be used to distinguish between evaporation and condensation processes.

Evaporation from a crystalline surface produces a kinetic isotope effect in which light isotopes of each evaporating species evaporate at a greater rate than heavy isotopes. The resulting heavy-isotope enrichment at the surface of the solid then propagates into the crystal by diffusion. Thus, measurements of evaporation rates and of the isotopic diffusion profile in the residual crystal can yield both the magnitude of the fractionation effect and the diffusion coefficient for each element. This paper describes the application of this method to magnesium isotopes in the evaporation of single-crystal forsterite (Mg2SiO4).

Molini-Velsko et al. (1987) reported silicon isotopic analyses of evaporation residues produced by heating basalt and two carbonaceous chondrites in a solar furnace. They found that the residues were enriched in the heavy isotopes of silicon by about +1.1 to +1.8‰ per amu after 80% evaporation of the original sample. Davis et al. (1990) studied residues from melts of forsterite composition evaporated under vacuum and showed that the isotopic compositions of the residues follow a Rayleigh law with fractionation factors close to the inverse square-root of molecular masses. Davis et al. also showed that forsterite evaporated from the solid state showed no measurable bulk isotopic fractionation effects. Wang et al 1991, Wang et al 1993 examined magnesium isotope profiles in forsterite residues evaporated from the solid state and found that isotopic fractionation is a diffusion-controlled process during the evaporation of solid forsterite (solid forsterite is a poorly mixed reservoir). Uyeda et al. (1991) used a Rayleigh law to explain isotopic fractionation in both residue and condensates by evaporating forsterite in the solid state under vacuum. Using coarse-grained forsterite (>200 μm) as the evaporation source, they found that δ26Mg in the residues was enriched by <3‰ even after two-thirds of the initial mass had been evaporated.

Previous investigations showed that forsterite evaporates congruently (the chemical composition of the residue remains the same) both from the solid and the liquid state under either equilibrium or kinetic conditions Mysen and Kushiro 1988, Nagahara et al 1988, Hashimoto 1990, Nagahara and Ozawa 1996. Mysen and Kushiro (1988) measured the equilibrium vapor pressure of forsterite under different oxygen fugacities by the Knudsen method. They found that the evaporation rate of forsterite is independent of oxygen fugacity within experimental error. Nagahara et al. (1994) remeasured the vapor pressure of forsterite using the same experimental setup as Mysen and Kushiro (1988) and obtained the enthalpy and entropy of evaporation of forsterite. Using their equilibrium phase relations, they explained that the difference in the origin of type IA (Fe-poor) and type II (Fe-rich) chondrules was due to their formation at different olivine gas pressures. Hashimoto (1990) examined evaporation kinetics of polycrystalline forsterite under close to free evaporation conditions using a high temperature vacuum furnace, and found that Mg, SiO2 and O (or O2) are the rate-determining gas species during forsterite evaporation. He also pointed out that at 1700°C, Mg2SiO4 evaporates about one-tenth as fast as predicted from equilibrium thermodynamics with no kinetic barriers impeding the process. As the result of this kinetic effect, Mg2SiO4 may evaporate at the same rate as an intrinsically more refractory material. Wang et al. (1993) reported the evaporation kinetics of single crystal forsterite instead of polycrystalline forsterite as Hashimoto 1990, Davis et al 1990 and Wang et al. (1991) had used. As the effective surface area of the polycrystalline forsterite is very difficult to determine accurately, the single crystal study provides a more accurate measurement of the forsterite evaporation kinetics.

Both Rees (1969) and Eberhardt et al. (1964) measured isotope ratios as a function of time in a thermal ionization mass spectrometer. These data show an initial increase in the ratio of the heavy to light isotopes, followed by a relatively long flat period and another increase as the sample on the filament diminishes. Eberhardt et al. (1964) pointed out that the initial enrichment of isotope ratios was not understood. Rees (1969) derived the following equation to describe this isotopic fractionation: Δ(x)=(1−α)(1−e−x/D), where Δ(x) is the isotopic composition of the mixed layer extending from depth x to depth x + D, α is the isotopic fractionation factor between the vapor phase and the residual phase, and D is the thickness of the mixed layer near the evaporating surface. With the thickness of the mixed layer D unconstrained, it is very difficult to use this formula quantitatively. A treatment of this problem, including diffusion control, is given in Appendix A.

Diffusion plays an important role in controlling magnesium isotopic fractionation during the evaporation of solid forsterite Wang et al 1991, Wang et al 1993. There are four major mechanisms related to volume diffusion in a crystal (see Manning, 1974 for details): (1) interchange of two neighboring atoms in the crystal lattice (exchange mechanism); (2) moving of interstitial atoms from one interstitial site to another (interstitial mechanism); (3) movement of vacancies in the crystal structure (vacancy mechanism); and (4) pushing a normal lattice atom into an interstitial site by replacing it with an interstitial atom (interstitialcy mechanism). Different mechanisms usually have different activation energies and may control diffusion rates over different temperature ranges. Buening and Buseck (1973) showed that iron-magnesium interdiffusion in olivine changes at 1125°C to a higher activation energy process, indicating more than one diffusion mechanism. Another complication for the study of diffusion is anisotropy of the crystal, such as Clark and Long (1971) observed for nickel diffusion in olivine (Fo94). The chemical diffusion coefficient of nickel in olivine is an order of magnitude greater along the c-axis than along the a- and b-axes over the temperature range 1149–1234°C. They found that this anisotropy in diffusion coefficients decreases with increasing temperature. Anisotropy in diffusion was also detected for iron-magnesium interdiffusion in olivine (Buening and Buseck, 1973). Morioka (1980) observed similar anisotropy of cobalt-magnesium interdiffusion in olivine. Chakraborty et al. (1994) measured the self-diffusion of Mg in synthetic single crystal forsterite from 1000 to 1300°C and found that at 1100°C, diffusion along the c-axis is four times faster than along the a-axis and six times faster than along the b-axis. They also found the diffusion coefficient to be only a weak function of oxygen fugacity at 1100°C. The anisotropy of oxygen diffusion in forsterite is very small to almost undetectable, within experimental resolution (Jaoul et al., 1983). Our knowledge of magnesium diffusion in forsterite is rather limited and spans a relatively narrow temperature range Hallwig et al 1980, Morioka 1981, Chakraborty et al 1994.

In this study, we present measurements of magnesium isotope fractionation occurring in the irreversible evaporation of single-crystal forsterite. The experimental results obtained are: (1) the evaporation rate as a function of temperature, (2) the self-diffusion coefficient of magnesium in forsterite as a function of temperature, and (3) the isotopic fractionation factor of the evaporation process. These data permit determination of the molecular speciation of the vapor in the rate-controlling step. The diffusion coefficients apply at higher temperatures than those measured previously, and are important for terrestrial mantle processes.

Section snippets

Vacuum furnace

The evaporation experiments were conducted in a vacuum furnace designed and built by Akihiko Hashimoto at the Harvard-Smithsonian Astrophysical Observatory (Hashimoto, 1990) and now located at the University of Chicago. The furnace chamber is cylindrical, with a height of 46 cm and a diameter of 36 cm. In the center is a pair of vertically mounted hemicylindrical tungsten mesh resistance heaters (about 15 cm high and 2.5 cm in diameter). Outside the heaters is a seven-layer, tungsten-molybdenum

Forsterite evaporation kinetics

The average evaporation rate of synthetic forsterite at each temperature is listed in Table 3. The error is estimated either from the standard deviation of repeated runs at the same temperature or from the combination of errors in the weighing and the surface area determination. The actual uncertainty is probably larger due to crystal surface defects that we are unable to assess. For future experiments on kinetic evaporation of solid materials, it is important to anneal the sample to remove

Conclusions

The evaporation of solid forsterite supports our model of isotopic fractionation under diffusion-controlled conditions (Appendix A), such that isotopic fractionation during the evaporation process is restricted to the vicinity of the evaporating surface. Evaporation does not necessarily result in measurable, mass-dependent kinetic isotopic fractionation in the whole evaporation residue. The limit of our ability to detect isotopic fractionation in meteoritic materials should not be used as

Acknowledgements

This research was supported by the National Aeronautics and Space Administration, through grants NAGW-3345 and NAGW-3069 (to RNC), NAGW-3384 (to AMD), and NAG9-28 (to J. A. Wood), and the Smithsonian Institution Scholarly Studies Program, through grant SS72-3-86 (to J. A. Wood). We are grateful to Dr. Robert C. Morris of Allied-Signal, Inc. for providing us with the single crystal forsterite used in our experiments. The first author would like to thank Zhenwei Qin for his advice in finding the

References (63)

  • H. Nagahara et al.

    Evaporation of forsterite in H2 gas

    Geochim. Cosmochim. Acta

    (1996)
  • F.R. Niederer et al.

    Ca isotopes in refractory inclusions

    Geochim. Cosmochim. Acta

    (1984)
  • K. Notsu et al.

    High temperature heating of the Allende meteorite

    Geochim. Cosmochim. Acta

    (1978)
  • C.E. Rees

    Fractionation effects in the measurement of molybdenum isotope abundance ratios

    Int. J. Mass Spectrom. Ion Phys.

    (1969)
  • T. Tanaka et al.

    Rare-earth elements in matrix, inclusions, and chondrules of the Allende meteorite

    Icarus

    (1973)
  • W.A. Tiller et al.

    The redistribution of solute atoms during the solidification of metals

    Acta Metall.

    (1953)
  • A. Tsuchiyama et al.

    Isotopic effects on diffusion in MgO melt simulated by the molecular dynamics (MD) method and implications for isotopic mass fractionation in magmatic systems

    Geochim. Cosmochim. Acta

    (1994)
  • C. Uyeda et al.

    Magnesium isotopic fractionation of silicates produced in condensation experiments

    Earth Planet. Sci. Lett.

    (1991)
  • R.J. Bearman et al.

    Mass dependence of the self diffusion coefficients in two equimolar binary liquid Lennard-Jones systems determined through molecular dynamics simulation

    Molec. Phys.

    (1981)
  • J. Bigeleisen

    Isotopic exchange reactions and chemical kinetics

    B.N.L. U.S. Rep.

    (1948)
  • J. Bigeleisen

    The relative reaction velocities of isotopic molecules

    J. Chem. Phys.

    (1949)
  • J. Bigeleisen et al.

    Calculation of equilibrium constants for isotopic exchange reactions

    J. Chem. Phys.

    (1947)
  • D.K. Buening et al.

    Fe-Mg lattice diffusion in olivine

    J. Geophys. Res.

    (1973)
  • H.S. Carslaw et al.

    Conduction of Heat in Solids

    (1959)
  • S. Chakraborty et al.

    Mg tracer diffusion in synthetic forsterite and San Carlos olivine as a function of P, T and fO2

    Phys. Chem. Minerals

    (1994)
  • M.W. Chase et al.

    JANAF thermodynamical tables, 3rd ed

    J. Phys. Chem. Ref. Data

    (1985)
  • C.-L. Chou et al.

    Allende inclusionsVolatile-element distribution and evidence for incomplete volatilization of precursor solids

    Geochim. Cosmochim. Acta

    (1976)
  • A.M. Clark et al.

    The anisotropic diffusion of nickel in olivine

  • Clayton R. N., Hinton R. W., and Davis A. M. (1988) Isotopic variations in the rock-forming elements in meteorites....
  • J. Crank

    Free and Moving Boundary Problems

    (1984)
  • A.M. Davis et al.

    Isotope mass fractionation during evaporation of Mg2SiO4

    Nature

    (1990)
  • Cited by (0)

    Present address: Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015.

    Present address: Department of the Earth and Planetary Sciences, Hokkaido University, Kita-ku, Sapporo 060, Japan.

    View full text