Closure temperature

The age that is obtained by the methods described previously is the time elapsed since the mineral(s) stopped equilibrating with each other and the rest of the outside world. This represents the moment when diffusion rates for the isotopes 

Parent Daughter X (year ) Half life Normalizing Mass bias correction Other isotopes Other isotopes Ref CHUR  

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The critical value c of the diffusion coefficient is the value of which makes this relationship an equality and is related to the closure temperature Tc through the Arrhenius equation (8.4.4). Therefore... 

At a given F, we can therefore ascribe a temperature to the maximum relative rate of loss for a system to be closed and a temperature to the minimum relative rate of loss for a system to be open. This interval may be thought of as the closure temperature interval. 

Figure 8.22 Closure temperature Tc as a function of the rate of loss for a spherical geometry [equation (8.7.6)]. The numbers on the curves are for different fractions lost by the mineral. Amphibole data from Harrison (1981), orthoclase data from Foland (1974). Points A, A, B, B see text.

Dodson, M. H. (1973). Closure temperature in cooling geochronological and petrological systems. Contrib. Mineral. Petrol., 40, 259-74. 

The concept of closure temperature is particularly important in geochronology. According to Dodson (1973), closure temperature f can be defined as the temperature of the system at the time corresponding to its apparent age. ... 

The analytical representation of closure temperature for a geochronological system (Dodson, 1973) is... 

Ganguly and Ruitz (1986) investigated the significance of closure temperature in terms of simple equilibrium thermodynamics. Assuming Rb-Sr exchanges between phases a and jS to be representable in terms of the equilibrium... 

Table 11.5 Some estimates of closure temperature, related to dilfusion of daughter isotope. Large discrepancies and wide ranges can be ascribed to differences in cooling rates of system and grain size dimensions.

Discrete values of closure temperatures in various minerals and mineral couples for the " °Ar- Ar and Rb-Sr geochronological systems are reported in table 11.5. 

Several models for diffusive transport in and among minerals have been discussed in the literature one is the fast grain boundary (FGB) model of Eiler et al. (1992, 1993). The FGB model considers the effects of diffusion between non-adjacent grains and shows that, when mass balance terms are included, closure temperatures become a strong function of both the modal abundances of constituent minerals and the differences in diffusion coefficients among all coexisting minerals. 

Diffusive loss of Ar from a mineral, affecting age determination (closure temperature)... 

Note. The closure temperature (see later discussion) depends on grain size and cooling rate here it is calculated for a radius of 0.1 mm and a cooling rate of 5 K/Myr (Brady, 1995). Cylinder shape model means that the grains are treated as infinitely long cylinders with diffusion along the cross section (in the plane Ic). 

Figure 1-20 Explanation of closure time, closure age, and closure temperature (Tc). (a) The cooling history, (b) " Ar accumulation history. The long dashed line shows the accumulation of " °Ar if there were no Ar loss since formation. The thin solid curve shows a real accumulation history. The short dashed line shows how the age is obtained from the present-day " °Ar/" °K ratio. For a mineral grain cooling down from 1200 K, when the temperature is between 1200 and 1037 K (at 5 Myr), all °Ar is lost once produced. Then from 1037 to 571K (at 30 Myr), there is partial loss, and the loss becomes smaller and smaller. Below 571 K, essentially all newly produced " Ar is retained. When °Ar/ °K ratio is determined, one calculates the age based on the present-day °Ar/" °K ratio and the age corresponds to the time of closure ta about 20 Myr). That is, the age is 130 Ma, although the mineral formed at 150 Ma. The temperature at t— 20 Myr is the closure temperature ( 704 K). Adapted from Dodson (1973).

The closure temperature defined above is related to the diffusion property, the grain size of the mineral, and the "shape" of the crystals as follows (Dodson, 1973) ... 

In summary, when using an isotopic system to determine the age, the meaning of the age is the closure age, as defined in Figure 1-20. The temperature at the time of closure is referred to as the closure temperature (Tc), which varies from one mineral to another. Tc decreases as diffusivity in the mineral increases, or activation energy decreases, or grain size decreases. Tc of some isotopic systems (such as U-Pb in zircon) is high and the isotopic systems hence record an older age that... 

Because the closure temperature depends on the diffusion properties of a mineral and on the isotopic systems, by determining the closure ages of several minerals (sometimes using different isotopic systems), the closure temperature can be found to be a function of closure age. Figure 1-21 shows an example. That is, with the concept of closure temperature and closure age, it is possible to reveal the full temperature-time history of a rock (thermochronology), more than simply the formation age. 

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