Mantle evolution curve¶
We first need the mantle evolution curve to draw the evolution of Osimium. The curve is obtained from Allègre and Luck (1980): Ignore this curve
$$(^{187}Os/^{186}Os) = (^{187}Os/^{186}Os)_0 + (^{187}Re/^{186}Os)_{mantle}(e^{\lambda t}-1)$$The coefficients are as follow:
$(^{187}Os/^{186}Os)_0 = 0.805$ (the intercept of the curve)
$(^{187}Re/^{186}Os)_{mantle} = 3.15$ (the slope of the curve)
$\lambda = 1.61e-11 yr^{-1}$
Another curve is for $^{187}Os/^{188}Os$ is as follows: We used this curve
$$(^{187}Os/^{188}Os) = (^{187}Os/^{186}Os)_0 + (^{187}Re/^{188}Os)_{mantle}(e^{\lambda t}-1)$$The coefficients are as follow:
$(^{187}Os/^{188}Os)_0 = 0.1296$ (the intercept of the curve)
$(^{187}Re/^{188}Os)_{mantle} = 0.4345$ (the slope of the curve)
$\lambda = 1.61e-11 yr^{-1}$
Allègre, C.J. and Luck, J.M., 1980. Osmium isotopes as petrogenetic and geological tracers. Earth and Planetary Science Letters, 48(1), pp.148-154.
We examined the $\gamma$ and $T_{RD}$ calculation¶
The model age of a sample is the time at which its Os isotopic composition is the same as that of the mantle, i.e. $(^{187}Os/^{188}Os)_{sample} = (^{187}Os/^{188}Os)_{Mantle}$
$\gamma$¶
$T_{RD}$¶
$$T_{RD} = \frac{1}{\lambda} \left[ln\left[\frac{(^{187}Os/^{188}Os)_{Mantle}-^{187}Os/^{188}Os)_{Sample}}{(^{187}Re/^{188}Os)_{Mantle}} \right]+1\right]$$The coefficients are as follow:
$(^{187}Os/^{188}Os)_{Mantle} = 0.1296$
$(^{187}Re/^{188}Os)_{Mantle} = 0.4345$
