The (U-Th)/He method

Provided that a state of secular equilibrium has been installed, the fundamental equation for He accumulation due to decay of Uranium and Thorium is:


The isotopic ratio 235U/238U is constant and presently equal to 1/137.88
k235= 9.8485 10-10 a-1
k238= 1.55125 10-10 a-1
k232= 4.9475 10-11 a-1

Emission correction

decay results in spatial separation of the parent and daughter nuclei. Through this mechanism, small U-Th rich crystal grains will "lose" Helium to the surrounding, less enriched rock matrix. Each decay in the U-Th series will have a certain energy. Depending on the mineral, the (= 4He) particle will come to a standstill on a sphere with radius equal to a characteristic stopping distance. If the parent nucleus is located within one stopping distance from the edge of the crystal, then the particle will remain inside the crystal regardless of the path it takes. If the parent nucleus lies within one stopping distance from the edge, there will exist a possibility that it be ejected out of the crystal. The probability of this happening is 50% at the actual crystal edge itself, in the simplified case of a flat crystal surface. On the other hand, decay occuring in a neighbouring crystal can lead to injection of an particle. This effect is often neglected.

The emission effects can be corrected for by dividing the measured age by a parameter FT, which is a function of the surface-to-volume-ratio of the crystal,and the stopping distance. 232Th and 235U have a similar mean energy of decay, which is higher than that of 238U. This can be accounted for by calculating a weighted correction factor:

meanFT = a238238FT + (1-a238)232FT

Where a238 is the fraction of He derived from 238U. Typical values for FT are 0.65 to 0.85

He diffusion

Chemical diffusion can often be described by an Arrhenius-type relationship. It is not different for He:

D/a2=Do/a2e-Ea/RT

where D is the diffusivity (Do being D at a specified temperature), Ea the activation energy, and a the diffusion domain radius. The first two parameters have been extensively studied for apatite in laboratory conditions. Minerals will better be able to retain their Helium at lower temperatures. Experiments on the well known Durango apatite suggest a closing temperature of ~70oC (for crystal radius ~80-90 10-6m). Zircon has a closing temperature of ~180-200oC which is similar to the third of the frequently used mineral, Sphene.