The diffusion of helium was characterized in natural sphene (titanite) and synthetic rutile. Polished slabs of sphene and rutile were implanted with 100keV 3He to a dose of 5 x 1015 3He/cm2 and annealed (1atm, furnace). The 3He distributions were measured via nuclear reaction analysis, using the reaction, 3He(d,p)4He. For diffusion in rutile:

D||a (m2/s) = 2.26 x 10-10exp[-126(kJ/mol)/RT]

D||c (m2/s) = 1.75 x 10-8exp[-120(kJ/mol)/RT]

Although activation energies for diffusion parallel to the c- and a-axes were comparable, there was marked diffusional anisotropy, with diffusion parallel to the c-axis about 2 orders of magnitude faster than transport parallel to the a-axis. These diffusivities bracketed the values determined for He diffusion in rutile in bulk release experiments, although the role of anisotropy could not be directly evaluated in those measurements. In titanite, an Arrhenius relationship was obtained at 252 to 550C for diffusion parallel to the a-axis:

D (m2/s) = 2.14 x 10-6exp[-148(kJ/mol)/RT]

In contrast to rutile, titanite exhibited little evidence of anisotropy, as the diffusivities parallel to the a- and c-axes were similar, and the diffusivities for titanites from two different localities were similar. The He diffusion coefficients obtained here were similar to those measured using the bulk release of He by step heating. Over the investigated temperature range, diffusion of He in titanite was similar to that of He diffusion in rutile parallel to the c-axis, but much faster than diffusion parallel to the a-axis. Since the diffusion of He in rutile exhibited such pronounced anisotropy, diffusional loss of He was modelled with a finite-element code, created to simulate diffusion in a cylindrical geometry with differing radial and axial diffusion coefficients. Examples were used to evaluate helium losses from rutile grains as a function of grain size and length-to-diameter ratio in order to understand the occurrence of pronounced anisotropy for He diffusion in some crystals (rutile, zircon) but not in others (apatite, titanite). The density and distribution of interstitial apertures in the crystal structure that might permit He migration was considered. This extension of the concept of ionic porosity was consistent with observations of relative diffusivities and the existence or absence of significant anisotropy for rutile, zircon, apatite and titanite.

Helium Diffusion in Rutile and Titanite, and Consideration of the Origin and Implications of Diffusional Anisotropy. Cherniak, D.J., Watson, E.B.: Chemical Geology, 2011, 288[3-4], 149-61