1. U-Th-Pb Decay Systems 9/9/10
Lecture outline:
U-Th-Pb systematics
2) Concordant U-Pb dates
3) Discordant U-Pb dates and open
system behavior
4) Common Pb-Pb dating
5) The Geochron
Zircon
Cross-section of a zircon grain from Antarctica, showing
U-Th-Pb dates

2. Why are zircons and galenas
Introduction to U, Th, and Pb
Element Charge Radius (Å)
U +4 (+6) oxic 1.05 Th Pb
Th and U are highly incompatible
and thus are concentrated
in crustal materials and depleted
in mantle
Material U(ppm) Th Pb
Chondrites
Troilite <
Basalt
Galena trace trace HUGE
Zircon HUGE HUGE trace
Carbonates
Seawater (surface) 3 ppb 20 fg/g 2.7 pg/g
Seawater (deep) 3 ppb 60 fg/g 5 pg/g
Why are zircons and galenas
the poster-children
Of U-Th-Pb dating?

3. U-Th-Pb decay schemes -decays to 206Pb, half-life=4.47 Ga
We can simplify the multi-daughter decay chains to simple
parent-daughter systems if and only if the system is in
secular equilibrium (~5 half-lives of the longest-lived daughter):
238U --> 206Pb (234U = 248,000y)
235U--> 207Pb (228Ra = 5.75y)
232Th-->208Pb (231Pa = 32,500y)

4. U-Th-Pb decay chains

5. U-Th-Pb governing equations
* Note that in all three decay schemes,
204Pb is used as a reference isotope
After Smith and Farquhar (1989)
You can measure a date with all three
systems, and if those dates agree,
then you have concordant dates.
If x=(238U/1204Pb)m
And y=(206Pb/204Pb)m
We have y=b+mx
Where intercept b=(206Pb/204Pb)i
And slope m=(eλt-1)
What processes can
make U-Th-Pb dates
Discordant?

6. Wetherill’s concordia
If x=(206Pb/204Pb)m
And y=(207Pb/204Pb)m
We have y=mx+(y0+x0)
Where (y0,x0)=primordial Pb isotopic composition
And slope
*cannot be solved algebraically, must use
iterative solving or Tables (like 10.3 in book)
The U-Pb concordia: line of concordant
206Pb/238U and 207Pb/235U ages
Physical Interpretation:
- at t=0 (crystallization), both ratios = 0
- system evolves along concordia,
growing radiogenic Pb, as long as
it remains a closed system
- you can use either ratio to calculate age

7. U-Pb discordia - open system behavior
So what if you lose Pb during metamorphosis (very common – why?)
For a zircon that formed at 4.0Ga experienced metamorphic event at 3.0Ga:
Pb loss at 3Ga moves points from A to origin,
For complete loss you move to origin, reset system.
If the samples remain closed until present,
they will follow a parallel concordia. A
discordia
The discordia defined by altered samples will intersect The Concordia at
the time of crystallization and the time of metamorphic event.

8. U-Pb discordia - open system behavior
Tilton (1960) measured U-Pb isotopes in many minerals from Archaean shields
across five continents yield discordant ages, with a discordia that implied a
World-wide metamorphic event at 600Ma…. But there is no evidence for that….
What would be an alternative explanation?

9. U-Pb discordia - open system behavior
Indeed, Pb loss does not often occur in a single metamorphic event - it can be quite
complicated (i.e. multiple events or even continous Pb loss)
The data fit a model of continuous
diffusional Pb loss from the U-rich
minerals.
Why might that happen?
What would a U-Pb concordia plot look
like if you incorporated old (4Ga), partially
reset zircons into a young (0.5Ga) melt?
So what’s a geochronologist to do??

10. Common (whole-rock) Pb-Pb dating
- for minerals with virtually no U or Th
- single stage history: mantle contains mixture of radiogenic and common Pb,
which is then “tapped” to form low-U galena
Bulk Earth evolution:
Where:
T = age of Earth
t = age of formation of low-U mineral
C.Diablo = initial Pb isotope values at T
Pb removed t years ago: or
Can construct a similar equation
for 235U-207Pb system…
and divide the two equations….

11. Common (whole-rock) Pb-Pb dating
To get the following equation:
* In this equation,
‘t’ is time since
galena crystallation,
T is the age of the Earth
co-genetic common lead samples
will define an isochron
So samples evolve along
growth curve, which depends on:
1) The U/Pb ratio in the source (μ)
2) The time since Earth’s formation
If x=(206Pb/204Pb)m
And y=(207Pb/204Pb)m
We have y=mx+(y0+x0)
Where (y0,x0)=primordial Pb isotopic composition
And slope

12. The Holmes-Houtermans Model: Common lead dating
“single stage” Pb assumes:
when Earth formed, U,Th, and P were evenly distributed; Pb isotopic ratios uniform
Earth solidified and small differences in U/Pb ratios develop
U/Pb ratio in a region thereafter changed only due to decay
sometime later, Pb isolated into low-U mineral, remained constant
high µ
low µ
μ = 238U/204Pb
Present-day
μ = 6-14
high-μ materials will yield more radiogenic Pb isotope values during time T
while low- μ yield lower radiogenic values over time T

13. The Geochron: a special Pb-Pb isochron
In a stroke of genius, Patterson
tested the following two
assumptions by Pb-Pb dating
meteorites and terrestrial sediments
1) Meteorites and Earth formed at the
same time
2) Meteorite Pb ratios are representative
of Bulk Earth initial ratios
Fe-S meteorite
stony meteorites
terrestrial sediment
Isotope ratios of
Canyon Diablo Meteorite:
206Pb/204Pb
207Pb/204Pb
208Pb/204Pb

14. Common (whole-rock) Pb-Pb dating
**Remember that this model only applies to
single stage leads (that’s one special lead!)
What geological circumstances would favor single-stage evolution?
Or where might you find these special leads?
What if you encounter a set of samples that indicate “future ages?”
with a single-stage Pb model? (see below plot)
Implies 2-stage evolution:
Bulk Earth was differentiated
into high-μ and low-μ reservoirs
a long time ago (episodic)
or continually differentiated
Very radiogenic Pb’s are due
to increasing μ partway through
source evolution.
“future”
ages?