ESS 109C Isotope Geochemistry Notes

April 25, 2007

High-precision Geochronology

1. Class notes & homeworks are available online –
   http://www2.ess.ucla.edu/~schauble/Isotope_geochemistry/
   
   
2. High-precision Geochronology: U, Th/Pb
1. With ⁴⁰Ar*/³⁹Ar, most precise system for age determination.
2. Special property à multiple decay chains with different, long half-lives ending at different isotopes of lead

1. ²³⁸U à ²⁰⁶Pb (t_1/2 = 4.5 Gyr)

2. ²³⁵U à ²⁰⁶Pb (t_1/2 = 0.7 Gyr)

3. ²³²Th à ²⁰⁸Pb (t_1/2 = 14 Gyr)

ii. Able to probe, even date episodes of open-system behavior (esp. loss of daughter), because each decay chain will respond slightly differently depending on the timing and severity of the event.

iii. Able to determine age from lead-isotope composition alone.

3. Half lives in U-Pb system known to very high precision (ideally ~0.1-0.2‰)

i. Improved by interest in and availability of U-isotope separates, pure U-materials.

ii. Most accurately known geochronometry half-lives

1. U-Pb ages used to calibrate/check decay constants of other systems.

3. Isochron forms of decay equations:
1. I.e., ²⁰⁶Pb/²⁰⁴Pb = ²³⁸U/²⁰⁴Pb(e^l(238)t – 1) + (²⁰⁶Pb/²⁰⁴Pb)_initial
2. ²⁰⁷Pb/²⁰⁴Pb = ²³⁵U/²⁰⁴Pb(e^l(235)t – 1) + (²⁰⁷Pb/²⁰⁴Pb)_initial
3. ²⁰⁸Pb/²⁰⁴Pb = ²³²Th/²⁰⁴Pb(e^lt(232) – 1) + (²⁰⁸Pb/²⁰⁴Pb)_initial
4. Thus two or three ages can be determined for a set of samples.

i. Concordance: agreement of ages on a sample as determined by different methods, especially ²³⁸U/²⁰⁶Pb and ²³⁵U/²⁰⁷Pb

ii. Many geological samples are Discordant to some extent – not surprising because Pb²⁺ is mobile in fluids, as is U⁶⁺ (in oxidizing conditions).

5. U and Th don’t substitute easily for major cations in minerals (i.e., they disperse rather poorly in the common minerals).

i. U,Th/Pb ages typically determined in U, Th-rich accessory minerals, esp. ZrSiO₄-zircon, ZrO₂-baddeleyite, (Ce,LREE)PO₄ monazite, (Yb,HREE)PO₄ xenotime, Ca₅(PO₄)₃(OH,F,Cl) apatite, CaTiSiO₅ sphene

4. Pb/Pb dating
1. Start from ratio of two U/Pb isochron equations:
   
   
   

²⁰⁷Pb/²⁰⁴Pb = ²³⁵U/²⁰⁴Pb(e^l(235)t – 1) + (²⁰⁷Pb/²⁰⁴Pb)_initial
²⁰⁶Pb/²⁰⁴Pb ²³⁸U/²⁰⁴Pb(e^l(238)t – 1) + (²⁰⁶Pb/²⁰⁴Pb)_initial

²⁰⁷Pb/²⁰⁴Pb – (²⁰⁷Pb/²⁰⁴Pb)_initial = ²³⁵U/²⁰⁴Pb(e^l(235)t – 1)
²⁰⁶Pb/²⁰⁴Pb – (²⁰⁶Pb/²⁰⁴Pb)_initial ²³⁸U/²⁰⁴Pb(e^l(238)t – 1)

(²⁰⁷Pb/²⁰⁴Pb)* = (²⁰⁷Pb/²⁰⁶Pb)* = ²³⁵U(e^l(235)t – 1)
(²⁰⁶Pb/²⁰⁴Pb)* ²³⁸U(e^l(238)t – 1)

2. ²³⁵U/²³⁸U is nearly constant (assumed = 1/137.88), so an age can be determined only by measuring Pb isotope composition!
   
   (²⁰⁷Pb/²⁰⁶Pb)* = (e^l(235)t – 1)
   137.88(e^l(238)t – 1)
   
   

i. As with ⁴⁰Ar*/³⁹Ar – enables maximal precision in mass-spectrometry.

ii. Particularly effective where initial U/Pb is high and sample is ancient, then (²⁰⁷Pb/²⁰⁶Pb)* ≈ ²⁰⁷Pb/²⁰⁶Pb

iii. Also facilitates ion-probe age dating.

5. Dealing with discordant ages (Pb-loss)
1. Samples with concordant ²³⁸U/²⁰⁶Pb, ²³⁵U/²⁰⁷Pb, and ²⁰⁷Pb/²⁰⁶Pb ages have a particular U-Pb isotope relationship, that can be depicted with various functions called “Concordia”
2. Most common forms are Wetherill’s Concordia and Tera-Wasserburg Concordia

i. Wetherill: Plot ²⁰⁶Pb*/²³⁸U vs. ²⁰⁷Pb*/²³⁵U (=137.88x²⁰⁷Pb*/²³⁸U)

At Concordia, ²⁰⁶Pb*/²³⁸U = e^l(238)t – 1
²⁰⁷Pb*/²³⁵U = e^l(235)t – 1

ii. Tera-Wasserbug: Plot (²⁰⁷Pb/²⁰⁶Pb)* vs. ²³⁸U/²⁰⁶Pb*

At Concordia, ²³⁸U/²⁰⁶Pb* = 1/(e^l(238)t – 1)

3. Any sample which has seen partial lead or uranium addition/loss since crystallization will not fall on the Concordia.
4. Typically, samples from the same rock (i.e., different zircon grains from a large chunk of a granite) will form a ~linear array.

i. Upper (old age) projection of this array through the Concordia curve is taken as a crystallization or cooling age

ii. Low (young age) projection is taken as lead-loss age – for ancient (Precambrian) samples this often corresponds to a metamorphic and/or heating event.

iii. Zircon batches or “splits” from a rock to form the linear array may be distinguished by magnetic or color properties, or by sequential leaching/abrasion to remove radiation damage or alteration material.

6. U,Th/He geochronology
1. Same decay scheme as U,Th/Pb, but obtained by measuring 4He abundance rather than Pb.
2. Advantage: many ⁴He produced by each decay. ⁴He easy to liberate from a sample by heating
3. Disadvantage: ⁴He diffuses very fast, almost always partially lost
4. It’s not a bug, it’s a feature!

i. Age is not of crystallization, but of cooling below a temperature where ⁴He ceases to diffuse out of the crystal – the Closure Temperature.

1. Depends on mineral, grain size, rate of cooling, possibly other properties like crystal defects.

2. Must have pure, well-characterized samples to get useful results.

ii. Apatite closure temperature ~70ºC, corresponds to a typical depth of 3 km for continental geotherm.

iii. Apatite U,Th/He age gives time since exhumation above ~3 km, useful for determining rates of fault motion, ages of mountains & other large topographic features.

7. Systems like U,Th/He, ⁴⁰Ar*/³⁹Ar where the daughter diffuses out of crystals at moderate temperatures are used in Thermochronology – the measurement of temperature-time paths of rocks.