The thermochronometric systems discussed in this volume broadly share three features: parent isotopes, daughter products, and one or more time-dependent, temperature-sensitive processes by which daughter products are altered or lost. If these processes can be measured in the laboratory, and their behavior confidently extrapolated to geological time scales, it becomes possible to construct a forward model of the system that predicts how a given instance of it will evolve assuming a particular starting arrangement and subsequent time-temperature history.

Two abiding issues impact the reliability of apatite fission-track analysis and thermal history inversion in particular: reproducibility of track-length measurements and variability of annealing kinetics. In the companion to this paper, we addressed the first by demonstrating that using c-axis projection to normalize track lengths for crystallographic angle improves reproducibility among measurements acquired by Barbarand et al. (2003a, 2003b). We continue here by looking at the effect of c-axis projection on extrapolation of laboratory measurements to geological time scales. We find that c-axis projection improves agreement between predictions of empirical annealing models fit to measurements by Barbarand et al. (2003b) analysts 1 and 3, further corroborating its effectiveness in ameliorating observer bias. Furthermore, these annealing models closely match predictions from the Carlson et al. (1999) annealing data set, which was obtained by a different analyst using a different etching protocol. Normalizing for angle thus allows us to create a single annealing model that encompasses both data sets and etching techniques. By combining the different compositional varieties of apatite in the two data sets, the resulting model provides an improved basis for estimating apatite kinetic properties in unknowns using proxies such as composition, etch-figure dimension, and unit-cell parameters. Predictions from a fanning curvilinear model form accord with conventional expectations of annealing at high and low temperatures, and its use for thermal history inversion will not introduce spurious late cooling events.

Accurate thermochronologic interpretation of zircon (U-Th)/He dates requires a realistic and practically useful understanding of He diffusion kinetics in natural zircon, ideally across the range of variation that characterize typically dated specimens. Here we present a series of date and diffusion measurements that document the importance of alpha dose, which we interpret to be correlated with accumulated radiation damage, on He diffusivity. This effect is manifest in both date-effective uranium (eU) correlations among zircon grains from single hand samples and in diffusion experiments on pairs of crystallographically oriented slabs of zircon with alpha doses ranging from ∼10¹⁶ to 10¹⁹ α/g. We interpret these results as due to two contrasting effects of radiation damage in zircon, both of which have much larger effects on He diffusivity and thermal sensitivity of the zircon (U-Th)/He system than crystallographic anisotropy. Between 1.2 × 10¹⁶ α/g and 1.4 × 10¹⁸ α/g, the frequency factor, D₀, measured in the c-axis parallel direction decreases by roughly four orders of magnitude, causing He diffusivity to decrease dramatically (for example by three orders of magnitude at temperatures between 140 and 220 °C). Above ∼2 × 10¹⁸ α/g, however, activation energy decreases by a factor of roughly two, and diffusivity increases by about nine orders of magnitude by 8.2 × 10¹⁸ α/g. We interpret these two trends with a model that describes the increasing tortuosity of diffusion pathways with progressive damage accumulation, which in turn causes decreases in He diffusivity at low damage. At high damage, increasing diffusivity results from damage zone interconnection and consequential shrinking of the effective diffusion domain size. Our model predicts that the bulk zircon (U-Th)/He closure temperature (T_c) increases from about 140 to 220 °C between alpha doses of 10¹⁶ to 10¹⁸ α/g, followed by a dramatic decrease in T_c above this dose. Linking this parameterization to one describing damage annealing as a function of time and temperature, we can model the coevolution of damage, He diffusivity, and (U-Th)/He date of zircon. This model generates positive or negative date-eU correlations depending on the extent of damage in each grain and the date-eU sample's time-temperature history.

A new model for examining fission-track data from natural specimens has been developed on the basis of new laboratory data describing fission-track annealing in a wide variety of apatites and the empirical correction for fission-track length anisotropy presented in earlier papers. Using revised and simplified statistical methods, we examine how well various empirical equations are able to fit the laboratory data and reproduce expected behavior on geological time scales. Based on the latter criterion, we find that so-called "fanning Arrhenius" models of mean track length are not the best-suited for our data. Instead, we find that fitting c-axis projected lengths with a model that incorporates some curvature on an Arrhenius plot produces results that are in better agreement with the available geological benchmarks. In examining the relative annealing behavior of apatites with different resistance to annealing, we find that the laboratory-time-scale behavior of any two apatites can be reproduced well by a simple one- or two-parameter equation. This function is used to convert the reduced fission-track length of one apatite that has undergone a certain time-temperature history into the length that would be measured in a second, less-resistant apatite that has undergone the same history. Using this conversion, we create a single model that encompasses the annealing behavior of all of the apatites we studied. The predictions made by this model match closely those made by fits to data for individual apatites. We therefore infer that, although the conversion equation is imperfect, it presents an excellent practical solution to characterizing the range of kinetic variability for annealing of fission tracks in apatite.