Partially annealed thermal-neutron-induced fission tracks in apatite exhibit mean etch- able lengths that range continuously between a maximum for tracks oriented parallel to the crystallographic c-axis and a minimum for tracks perpendicular to c. A simple empirical model quantifies this crystallographic orientation dependence based on the assumption that the mean etchable fission track length aL ary angle to the c-axis is given by the corresponding radius of an ellipse. The ellipse has semiaxes equal to, respectively, the mean track lengths parallel (lc) and perpendicular (la) to the c-axis.

The elliptical model is tested against 61 isothermal partial annealing experiments per- formed on thermal-neutron-induced fission tracks in Tioga apatite. It is found to adequately characterize etchable fission track length distributions in partially annealed apatites when la. ≥ 8.4 μm. The difference between lc and la increases systematically and continu- ously as both mean lengths decrease, and fission-track lengths are distributed normally about their mean with a standard deviation of ca. 0.75 μm, regardless of crystallographic orientation and relative degree of partial annealing. For la < 8.4 μm, the elliptical model apparently fails because tracks at relatively high angles to the c-axis experience greatly accelerated etchable length reduction.

Experimentally determined values of lc and la in apatite have greater physical significance than does the arithmetic (conventional) mean fission track length. Application of the pro- posed elliptical annealing model to controlled laboratory experiments may provide valuable insight, heretofore unattainable, into the physical process(es) by which fission tracks anneal in apatite.

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