U-Th-Pb Decay Systems 9/9/10

Lecture outline:

1) U-Th-Pb systematics

2) Concordant U-Pb dates

3) Discordant U-Pb dates and opensystem behavior

4) Common Pb-Pb dating

5) The Geochron

Cross-section of a zircon grain from Antarctica, showingU-Th-Pb dates

Zircon

Element Charge Radius (Å)U +4 (+6) oxic 1.05Th +4 1.10Pb +2 1.32

Introduction to U, Th, and Pb

Material U(ppm) Th PbChondrites 0.01 0.04 1.0Troilite .009 <.01 5.9Basalt 0.43 1.6 3.7Galena trace trace HUGEZircon HUGE HUGE traceCarbonates 1.9 1.2 5.6Seawater (surface) 3 ppb 20 fg/g 2.7 pg/gSeawater (deep) 3 ppb 60 fg/g 5 pg/g

Th and U are highly incompatibleand thus are concentrated in crustal materials and depletedin mantle

Why are zircons and galenasthe poster-childrenOf U-Th-Pb dating?

U-Th-Pb decay schemes

238U=99.27%235U=0.72%234U=0.0055%

232Th=100%230Th=<0.0005%

-decays to 206Pb, half-life=4.47 Ga-decays to 207Pb, half-life=0.704 Ga

We can simplify the multi-daughter decay chains to simpleparent-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)

-decays to 208Pb, half-life=14.1 Ga

U-Th-Pb decay chains

206 206 238

204 204 204( 1)t

i

Pb Pb Ue

Pb Pb Pb

U-Th-Pb governing equations

If x=(238U/1204Pb)m

And y=(206Pb/204Pb)m

We have y=b+mx

Where interceptb=(206Pb/204Pb)i

And slope m=(et-1)

207 207 235

204 204 204( 1)t

i

Pb Pb Ue

Pb Pb Pb

208 208 232

204 204 204( 1)t

i

Pb Pb The

Pb Pb Pb

After Smith and Farquhar (1989) * Note that in all three decay schemes,204Pb is used as a reference isotope

You can measure a date with all threesystems, and if those dates agree,then you have concordant dates.

What processes can make U-Th-Pb dates

Discordant?

Wetherill’s concordia

5

8

207 207

204 204

206 206

204 204

1 1

137.88 1

ti

t

i

Pb PbPb Pb e

ePb PbPb Pb

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

5

8

1 1

137.88 1

t

t

em

e

*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

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:

A

If the samples remain closed until present,they will follow a parallel concordia.

Pb loss at 3Ga moves points from A to origin,For complete loss you move to origin, reset system.

The discordia defined by altered samples will intersect The Concordia atthe time of crystallization and the time of metamorphic event.

discordia

U-Pb discordia - open system behavior

Tilton (1960) measured U-Pb isotopes in many minerals from Archaean shieldsacross five continents yield discordant ages, with a discordia that implied aWorld-wide metamorphic event at 600Ma…. But there is no evidence for that….

What would be an alternative explanation?

U-Pb discordia - open system behavior

The data fit a model of continuous diffusional Pb loss from the U-richminerals.

Why might that happen?

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)

What would a U-Pb concordia plot looklike if you incorporated old (4Ga), partially reset zircons into a young (0.5Ga) melt?

So what’s a geochronologist to do??

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

206 206 238

204 204 204( 1)T

i

Pb Pb Ue

Pb Pb Pb

206 206 238 238

204 204 204 204( 1) ( 1)T t

t i

Pb Pb U Ue e

Pb Pb Pb Pb

Bulk Earth evolution:

Pb removed t years ago:

206 206 238

204 204 204( )T t

t i

Pb Pb Ue e

Pb Pb Pb

or

Where:T = age of Eartht = age of formation of low-U mineralC.Diablo = initial Pb isotope values at T

Can construct a similar equationfor 235U-207Pb system…and divide the two equations….

207 207 235

204 204 204( )T t

t i

Pb Pb Ue e

Pb Pb Pb

5 5

8 8

207 207

204 204

206 206

204 204

1 ( )

137.88 ( )

T tt i

T t

t i

Pb PbPb Pb e e

e ePb PbPb Pb

Common (whole-rock) Pb-Pb datingTo get the following equation:

So samples evolve alonggrowth 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

5 8

8 8

1

137.88

T t

T t

e em

e e

* 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

The Holmes-Houtermans Model: Common lead dating

μ = 238U/204Pb

Present-dayμ = 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

“single stage” Pb assumes:1.when Earth formed, U,Th, and P were evenly distributed; Pb isotopic ratios uniform2.Earth solidified and small differences in U/Pb ratios develop3.U/Pb ratio in a region thereafter changed only due to decay4.sometime later, Pb isolated into low-U mineral, remained constant

high µ

low µ

The Geochron: a special Pb-Pb isochron

Isotope ratios of Canyon Diablo Meteorite:206Pb/204Pb 9.3066207Pb/204Pb 10.293208Pb/204Pb 29.475

In a stroke of genius, Pattersontested the following two assumptions by Pb-Pb datingmeteorites and terrestrial sediments

1) Meteorites and Earth formed at the same time

2) Meteorite Pb ratios are representativeof Bulk Earth initial ratios

Fe-S meteoritestony meteoritesterrestrial sediment

Common (whole-rock) Pb-Pb dating

**Remember that this model only applies tosingle 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)

“future”ages?

Implies 2-stage evolution:Bulk Earth was differentiatedinto high-μ and low-μ reservoirsa long time ago (episodic)or continually differentiated

Very radiogenic Pb’s are dueto increasing μ partway throughsource evolution.