207207Pb Pb (5)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

Concordia- Discordia

(

Pb/

Pb)

= (

Pb/

Pb)

+ (

U/

Pb) (e

-1 ) (

Pb)

= (

Pb)

+ (

U) (e

-1 )

(

Pb)

- (

Pb)

=

U (e

-1 )

206

Pb* =

U (e

-1 )

206

Pb*/

U = (e

-1 )

207

Pb*/

U = (e

-1 )

Instead of finding the age (t), we can reverse the procedure and

use the two eq to calculate compatible sets of (

Pb*/

U)

and (

Pb*/

U) for specified values of t

206

Pb

238

U = e

- 1

207

Pb

235

U = e

- 1

The U-Pb-Th System The U-Pb-Th System

Concordia

Concordia = = Simultaneous co- Simultaneous co- evolution of

evolution of

Pb and Pb and

Pb via: Pb via:

238238

U U  

U U  

Pb Pb

235235

U U  

Pb Pb

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)

Age

Pb-loss event

Upper intercept = age

Lower intercept = any Pb-loss event

Concordia/Discordia

Plot

Pb*/

U vs.

Pb*/

U

All points with the same age form a curve = Concordia;

If the data fall along a line instead = Discordia Use zircons; exclude Pb, all Pb is radiogenic

Discordia beneath Concordia = Pb loss (usually) or U gain Discordia above Concordia = U loss

Most rocks are discordant and can be explained by Pb loss

Intersection of Discordia line with Concordia curve gives age of formation

and age of Pb loss

Concordia discordia

• The concordia curve is the locus of points for which the 206Pb/238U age equals the 207Pb/

235U.

• It is curved due to different half-lives of 238U

and 235U.

Evolution of Pb isotopes with time

• Growth of daughter isotopes

• Because there are so many variables in Pb isotopic system (three diff decay const), it is convenient to display the data as concordia diagram.

• On this diagram, families of concordia (growth) curves can be calibrated for different

238U/204Pb ratios (called µ). Each curve can be

calibrated for time and equal time points can be

joined to give isochrons.

The Geochron

•Plot data from several meteorites, which define a line

•Initial ratio determined by the Canyon Diablo troilite

(FeS, incorporates Pb,but not U; initial Pb isotope ratios are preserved)

If U/Pb, sample is right of geochron If U/Pb, sample is left of geochron The Geochron is the Pb-Pb isochron

with a slope corresponding to T=4.56 Ga that passes through the composition of primordial Pb - reflects closed system evolution of lead in solar system

Uranium-Thorium-Lead

238U ²⁰⁶Pb, t_½ = 4.47 Gyr

235U ²⁰⁷Pb, t_½ = 0.70 Gyr

232Th²⁰⁸Pb, t_½ = 14.0 Gyr

No longer in pseudolinear decay regime

Plot

Pb/

Pb vs.

206

Pb/

Pb

Line = isochron if it passes through initial ratios

Steeper slope = older age Evolution lines depend on 

238U/²³⁵U = 137.88

everywhere (today)

= ²³⁸U/²⁰⁴Pb

 = ²³²Th/²³⁵U ~ 4.0

(chondrites)

Can derive equations relating the Pb isotopes – useful because don’t need to measure parents