A Numerical Method for Determining Diffusivity from Annealing Experiments

Astronomy and Astrophysics – Astronomy

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Terrestrial analogs of lunar ilmenite (FeTiO3) have been implanted with solar-wind energy 4He at 4 keV and 3He at 3 keV using Plasma Source Ion Implantation (PSII). Isochronal annealing of the samples revealed thermally induced 4He evolution similar to the helium release of the Apollo 11 regoliths reported by Pepin, et. al., [1970]. These annealing experiments are analyzed with a three dimensional numerical method based on Fick's law for diffusion. An iterative method is used to calculate the diffusivity. The code uses an assumed diffusivity to calculate the amount of gas released during a temperature step. The initial depth profile of the implanted species is generated using the TRIM electronic stopping code [Ziegler, 1996]. The calculated value is compared to the measured value and a linear regression is used to calculate a new diffusivity until there is convergence within a specified tolerance level. The diffusivity as a function of temperature is then fitted to an Arrhenius equation. Analysis of results for 4 keV 4He on ilmenite shows two distinct regions of Arrehnius behavior with activation energies of 0.5 +/- 0.1 eV at emperatures below 800 deg C and 1.5 +/- 0.2 eV at temperatures from 800 deg C to 1100 deg C. Pepin, R. O., L. E. Nyquist, D. Phinney, and D. C. Black (1970) "Rare Gases in Apollo 11 Lunar Material," Proceedings of the Apollo 11 Lunar Science Conference, 2, pp. 1435-1454. Ziegler, J. P. (1996) SRIM Instruction Manual: The Stopping and Range of Ions in Matter, (Yorktown, New York: IBM - Research); based on Ziegler, J. P., J. P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids, (New York: Pergamon Press, 1985).

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