The geochron is simply the locus of all Pb isotopic compositions for closed systems with different U/Pb ratios today (below).
If aliquots of Pb (like galena) were extracted from reservoirs with different U/Pb at earlier times (and then no subsequent radiogenic Pb grew in, because these are Pb minerals with low U/Pb), they would form an isochron with a steeper slope (below).
minerals with low U/Pb), they would form an isochron with a steeper slope (below).
Fig. 5.29. Pb)Pb isochron diagram showing present‐day composition (P) of galena extracted from a Bulk Earth reservoir 3 Byr ago. After Russell and Farquhar (1960).
If you thought that the Earth’ss mantle had a single Pb isotopic composition that evolved over If you thought that the Earth
mantle had a single Pb isotopic composition that evolved over
time (because it has a single U/Pb ratio), you should be able to see that change in isotopic composition reflected in Pb deposits extracted from the mantle at different times (ages). Below is a plot of many different galenas . You can see that several of them extend to negative (future) ages. And there’s a lot of scatter. This exercise actually works better for a certain restricted class of Pb deposits that form in oceanic environments with little continental contamination.
Fig. 5.30. Pb)Pb isochron diagram showing a compilation of many analysed galenas from different environments. After Stanton and Russell (1959).
Even though that single stage model didn’t work very well, it shows that you could conceivably come up with a “model age” for common Pb.
This is the equation for 207Pb/204Pb of a Pb deposit (no U in it) at time t (when it was extracted from a big homogeneous reservoir like the mantle maybe) that had an initial 7/4 ratio at time T (for single‐stage model /
this is age of Earth) and today has the 235U/204Pb shown below.
(207Pb/204Pb)t‐(207Pb/204Pb)T = (235U/204Pb)(exp(5T)‐exp(5t))
You can write a similar equation for 206Pb/204Pb. Then you combine them, and for a simple single‐stage
single
stage model, T model, T = age of Earth, CD age of Earth, CD = isotopic composition of Canyon Diablo, and t is the isotopic composition of Canyon Diablo, and t is the
model age of the Pb deposit.
(207Pb/204Pb)t‐CD = 1 (exp(5T)‐exp(5t))
(206Pb/204Pb)t‐CD = 137.88 (exp(8T)‐exp(8t))
But like we said, this model doesn’t really work for a LOT of Pb deposits.
So in the mid‐70’s Stacey and Kramers took the Pb isotopic compositions of a whole bunch of galenas and other types of Pb ores, as well as feldspars, and tried to come up with a two‐stage model of the evolution of common Pb on Earth. The model they came up with is shown below.
Fig. 5.32. Pb isotope diagram showing a two‐
stage lead isotope evolution model proposed for the source of galenas ( ! ). After Stacey and Kramers (1975).
This model is similar to the single‐stage one, except at 3.7 Ga there was a big change in the mu of the reservoir from which all Pb is extracted. Most Pb deposits fall on this second stage trend. Stage 1: T = 4.57, ended at t = 3.7 Ga. At this time, 206/204 was 11.152, 207/204 was 12.998, 208/204 was 31.230, mu was 7.192, and omega was 33.208.
Stage 2: started at 3.7 Ga. At present, the Pb iso comp of this reservoir is 206/204 = 18.700, 207/204 = 15.628, and 208/204 =38.630, and mu is 9.735, omega =36.837.
While the S‐K model works sometimes for providing model ages of Pb ores, it also provides a basis for correcting for common (initial) Pb in U/Pb and Th/Pb geochronology. For example, although most 206Pb and 207Pb in an old zircon is radiogenic, if there is ANY 204Pb in it, then there is also some initial (common) 206Pb and 207Pb. This can be corrected for, and subtracted out of the radiogenic fraction by using the S‐K model to provide an estimate of common 206/204 and 207/204 at the apparent age of the zircon, then adjusting the measured 206/204 and 207/204 by an amount appropriate to the measured 204 and the S‐K common Pb estimate for that age. Obviously this is an iterative approach.