# Research Methods - Thermochronology

## Apatite (U-Th-Sm)/He - dating

During the last 10 years the understanding of the diffusion behavior of He in apatite has been increased (Lippolt et al., 1994; Wolf et al., 1996, 1998, Farley, 2000).

The closure temperature of mineral grains that accumulate radiogenic He during the α-disintegration of 238U, 235U, 232Th and daughter products is dependent on: activation energy (E), a geometric factor for the crystal form (A), thermal diffusivity (D0), the length of the average diffusion pathway from the interior to the surface of the grain (a) and the cooling rate at closure temperature (dT/dt; Dodson, 1973).

The concept of He-diffusion in apatite assumes that the diffusion path (a) is the grain size. Therefore, the geometry (A) of the mineral grain is very important (Meesters and Dunai, 2002a, b).

A correction has to be applied for the loss of radiogenic He generated within an outer rim of the mineral grain by the α-stopping distances (apatite: 25µm). The most important requirements for (U-Th-Sm)/He thermochronology are 1.) minerals free from inclusion and cracks, 2.) idiomorphic crystals, 3.) a homogeneous distribution of U and Th.

The apatite closure temperature is in the range of 75 ±7 °C for a simple monotonic cooling rate of 10 °C/m.y., a subgrain domain size < 60 µm, an activation energy (Ea) of about 36 kcal/mol and a log(D0) of 7.7 ±0.6 cm²/s (Wolf et al., 1996).

Farley proposed Ea = 33 ±0.5 kcal/mol with log(D0) = 1.5 ±0.6 cm2/s for Durango apatite. The implied He closure temperature for a grain of 100 µm radius is 68°C assuming a 10°C/Ma cooling rate. The closure temperature concept is only appropriate for uniform and moderate to rapid cooling from temperatures corresponding to complete He diffusive loss to complete He retention.

For such thermal histories, the calculated (U-Th-Sm)/He ages are estimates of the time elapsed since cooling through a relatively narrow temperature range, where the crystal size and chemistry does not influence the (U-Th-Sm)/He ages of apatite (Warnock et al., 1997; Wolf et al., 1998; Reiners and Farley, 2001, Farley, 2002; Ehlers and Farley, 2003).

If the cooling rate is slow relative to the He production or if He was only partially retained in the crystal for long periods of time, the He content and therefore the calculated (U-Th)/He ages of a crystal can be strongly dependent on variations in fractional He loss caused by crystal size variations. Wolf et al. (1998) describe solutions for the full radiogenic ingrowth-diffusion equation for different geological situations.

The He production and diffusion model assumes a homogenous distribution of U and Th in secular equilibrium and that He is lost only by volume diffusion. Spherical diffusion geometry is assumed (Wolf et al., 1996).

Basically the results of such simulations are (Reiners and Wolf, 2001): 1.) The differences in age between small and large crystal size are greatest in the temperature range between ~30 to 75 °C, 2.) The difference in age with crystal size increases with time at a given depth. 3.) The depth (and temperature) of the maximum age difference decreases with time. Furthermore, nowadays a He partial retention zone between 40 and 90 °C is assumed (Wolf et al., 1998).

Meesters and Dunai (2002a, b) generalized the production-diffusion equations to diffusion domains of various shapes and arbitrary cooling histories. Their set of equations allows calculating the α-ejection corrected ages and accounts for non-homogeneous distribution of uranium and thorium. The equations presented by Meesters and Dunai (2002a, b) and Dunai (2005) can be applied to all radiogenic He-bearing minerals.