More developments on the closure temperature concept

To calculate the closure temperature of any point in a mineral without carrying out the full forward numerical calculations, Dodson (1986) analyzed the problems for different effective shapes systematically and modified his closure temperature equation for the whole minerals slightly to apply to individual points. His formulation is by adding a correction term to Equation 5-75b. This correction term will be referred to as gi in this book and another correction term by Ganguly and Tirone (1999, 2001) will be referred to as g2- The formulation of Dodson (1986) for the calculation of closure temperature at every point of a profile is 

Example 5.70 Treat hornblende grains as isotropic spheres of radius 0.5 mm. Diffusivity is given by D = exp(-12.94-32,257/T) m /s. Calculate Tc of the whole mineral grains and Tc at the center of the grains for cooling rate of 30 K/Myr. 

Obtained from Dodson (1986) by subtracting the volume average value from the position-dependent G(x) value. 

The value of 2 depends onM=Doxla (Equation 5-108) and the position xja in the mineral. Because M depends on the initial temperature Tq. 

As M- 00, 2- 0. The relation between g2 and M is shown in Table 5-5 for various positions inside a crystal. Equation 5-109 reduces to Equation 5-75b (that is, gi 0.01) when M 0.3 for a sphere, 0.6 for a cylinder, and 1.2 for a plane sheet. Example 5-11 shows how to evaluate the effect of low initial temperature on the closure temperature. 

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