Geochronology II: U-Th-Pb

Chapter 3

U-Th-Pb Three radionuclides decaying to 3 isotopes of Pb at different rates:

232Th decays to 208Pb with a half-life of 14 Ga. 238U decays to 206Pb with a half-life of 4.47 Ga. 235U decays to 207Pb with a half-life of 707 Ma. The remaining isotope, 204Pb, is used for ‘normalization’.

Decay is a combination of alphas and betas: 238U: 8 alphas 235U: 7 alphas 232Th: 6 alphas Energy emitted accounts for ~80% of radioactive energy production in

the Earth (most of the rest is 40K)

The particular geochronological ‘power’ comes from from two isotopes of U, with identical chemical behavior (or nearly so), decaying to 2 Pb isotopes at very different rates.

Chemistry of U, Th, and Pb U and Th are actinide series REE. Both U and Th generally have a valence of

+4, but under oxidizing conditions, such as at the surface of the Earth, U has a valence

of +6. In six-fold coordination, U4+ has an ionic radius of 89 pm and 100 pm in 8 fold (100

pico meters = 1 Å). U6+ has an ionic radius of 73 pm in 6-fold and 86 pm in 8-fold coordination

Th4+ has an ionic radius of 94 pm in 6-fold and 1.05Å in 8-fold coordination.

The combination of somewhat large size and high charge makes them highly incompatible. Th slightly more incompatible than U.

Both Th and U are refractory, insoluble, and immobile, with the exception of U6+

(favored at the Earth’s surface), which forms the UO42- oxyanion, which is quite

soluble and mobile.

Pb is moderately volatile, chalcophile, and somewhat siderophile. Essentially always in the 2+ state in nature. Ionic radius of Pb2+ is 119 pm in 6-fold coordination and 129 pm in 8-fold coordination. As a result, Pb is moderately incompatible. Although not particularly soluble, it does seem to form some soluble complexes and is somewhat mobile.

235U/238U The U-Pb system is generally regarded as the most precise, most

valuable dating system.

The power is a consequence of two U isotopes decaying at different rates to two Pb isotopes.

Since 235U and 238U are isotopes of the same element, we can expect the to behave identically – almost. The canonical 235U/238U ratio is 1/137.88, but recent work suggests a

value of 1/137.82. Furthermore, small ( a few per mil) variations in the ratio have now been demonstrated (resulting from small difference in chemical behavior).

Mostly, these variation of negligible, but as precision improves, it will become necessary to actually measure this ratio in each sample precisely.

Bear in mind that the ratio of 1/137.82 is the ratio today: it changes continually with time as 235U decays more rapidly.

Typo in book

Pb-Pb DatingWe can write two decay equations:

Divide one by the other:

Assuming 235U/238U is constant:

Ratio of radiogenic 207Pb to 206Pb is proportional to time (don’t need to know U/Pb ratio).

Pb-Pb Isochrons Jargon: geochronologists long ago named the

238U/204Pb ratio ‘µ’.

Our ‘isochron’ equation for the 238U-206Pb system is:

For the 235U–207Pb decay, it is:

Suppose we plot 207Pb/204Pb vs. 206Pb/204Pb. The slope on such a plot is:

Figure 3.1

Pb-Pb Isochrons On a plot of 207Pb/204Pb

vs. 206Pb/204Pb, the slope is proportional to time and is therefore an isochron.

Parent/daughter ratio not needed.

Intercept does not give the initial ratios.

Our equation:

cannot be solved directly for t. Need to use indirect

method.

Total Pb Isochrons The U-Pb system achieves its greatest power when we use the

238U-206Pb, 235U-207Pb, and 207Pb-206Pb methods in combination. Ideally, all ages should agree. If so, they are said to be

‘concordant’. Often, age information can still be extracted from non-

concordant systems.

One approach to testing for concordancy is to plot 238U/206Pb against 207Pb/206Pb - the “Tera-Wasserburg” diagram. Purely radiogenic Pb will have unique 207Pb*/206Pb* and 238U/206Pb* ratios at any given time and hence define a ‘concordia’ curve on such a diagram:

Error in book

Figure 3.2

Tera-Wasserburg Diagram “Concordant” data

containing variable amounts of “common” (i.e., initial) Pb will define a lines with slope:

The intercept with the concordia curve gives the age. Y-intercept gives initial 207Pb/206Pb.

Th/U ratiosWe can, of course calculate ages using the

conventional isochron method based on 232Th/208Pb ratios.

Also if the age is known (for example from a Pb–Pb isochron) we can calculate Th/U ratios for that set of samples, assuming constant Th/U. On a plot of 208Pb/204Pb vs 206Pb/204Pb, the slope will be given by:

where κ=232Th/238U; κBSE ≈ 4

Figure 3.3

Zircon Dating

Zircon DatingZircon (ZrSiO4) readily accepts U4+ in the Zr4+ site but

excludes Pb. To a first approximation, there will be no initial or “common” Pb – making it a very attractive target for dating.

Zircon is also hard (Mohs 7.5) and chemically resistant. It is a common accessory mineral in many (felsic) igneous and metamorphic rocks.

Also preserved in coarse grained sediments.

The approach used for zircon dating can apply to other U-rich minerals such as titanite (aka sphene, CaTiSiO5), monazite ( ThPO4), alanite (Ce2Al3(SiO4)3OH) and apatite (Ca10(PO4)6(OH)2).

Concordia Diagram A concordia diagram is a plot of

206Pb*/238U vs. 207Pb*/235U, i.e., the ratios of the number of atoms of radiogenic daughter produced to the number of atoms of radioactive parent. These are proportional to time, e.g.:

This is, in effect, a plot of the 238U–206Pb age against the 235U–207Pb age.

Because only a small correction for “common Pb” is necessary for most zircons, these ratios are readily calculated, and this diagram is very often used in zircon dating.

If the ages agree, i.e., if they are concordant, they will plot on the concordia curve. If not, we may still be able to

extract age information.

Thinking about the concordia diagram

The best way to think about how the concordia diagram works is to imagine the points staying fixed and the diagram, and curve, growing as time passes.

Imagine a zircon formed at 3.0 Ga. At the time of formation, it would plot at the origin and the diagram would look like this.

Three billion years later If the system

remained closed for the subsequent 3 billion years, our zircon would plot at the 3 Ga point on the concordia diagram.

Suppose, however, it is now heated to the point where Pb can diffuse out and is lost completely. How would our point it move on the diagram?

★

Concordia Curves

Now imagine zircons formed at 4 Ga partially losing Pb at 3 Ga. They move toward the origin at that time (left).

When we come along 3 Ga later, we find them on a chord intersecting the concordia curve at 4 and 3 Ga.

U Loss U gain essentially mimics

Pb loss in moving the point toward the origin.

U loss is less common, but age information can still be retained.

Continuous Pb loss or Pb gain (latter is particularly unlikely) do not take predictable paths and destroy age information.

Issues and SolutionsWhat makes zircon a good clock, namely a high U

content, also tends to destroy that clock through radiation damage. Radiation damaged zircons are referred to a “metamict”. Damaged zones are most likely to richest in U and to have

lost Pb and be discordant.

Various approaches have been taken effectively remove metamict areas and analyze remaining zircon. Abrasion: Krough (1982) Annealing followed by step-wise dissolution (Mattinson,

2005).

Figure 3.18

Step-wise Dissolution

Figure 3.9

Step-wise dissolution

Figure 3.10

In situ Analysis

U-Th Decay Series Dating

Figure 3.11

Radioactive EquilibriumThe abundance of a nuclide that is both radioactive

and radiogenic (e.g., 230Th) will vary with time according to:

The r.h.s. is just the difference between its rate of production and its rate of decay.

This nuclide is radioactive equilibrium if its abundance does not change with time, i.e., dND/dt = 0.

What does this say about its ratio relative to its parent?

Thought Experiment Imagine a hopper with a

spring-loaded door into which marbles fall.

As weight builds up, the door opens and marbles fall out. If weight builds more, the door opens more until marbles fall out faster.

Once marbles are falling out of the hopper as fast as they are falling in, the position of the door remains stationary and the rate of fall of marbles becomes constant.

Non-equilibrium When a system is perturbed and forced out of radioactive

equilibrium, it will return to the equilibrium state at a rate that depends of the initial abundance of parent and daughter and the two decay constants (assuming a closed system).

This predictable rate of return to equilibrium is the basis of decay series dating.

No time information (other than a minimum elapsed time since disturbance) can be obtained from a system at equilibrium. Equilibrium also erases all previous history.

To know how the daughter nuclide abundance varies with time, we integrate the previous equation:

ActivityBecause traditionally decay-series isotopes were

measured by measuring their radioactive decay (counters of sorts), and many still are, we use activity (decays per unit time) in place of abundance. Also turns out this makes the math easier in many cases.

Activity is simply –dN/dt and is related to molar abundance by the decay constant:

We express activity by writing the nuclide or ratio in parentheses, e.g., (234U) or (230Th/238U).

234U–238U dating 234U is the first reasonably long-lived (t1/2 = 245 ka)

daughter of 238U.

At equilibrium (234U)=(238U) but in seawater (234U/238U) = 1.145. Why? Deviations of the (234U/238U) ratio from the equilibrium value (1)

are usually expressed in per mil units and denoted as δ234U. Thus a (234U/238U) value of 1.145 would be expressed as δ234U = 145.

Imagine a coral growing from seawater incorporating U into calcite. We can divide the 234U into part that is supported by 238U and part that is not: the excess above the 238U activity:

(234U) = (234U)s + (234U)u = (238U) + (234U)u

234U–238U datingThe unsupported 234U will decay according to:

(234U)uo is just the initial excess of (234U) over (238U)

and because the activity of 238U does not change measurably on the timescales of interest (238U) = (238U)0 and:

and

Total (234U) is:

234U–238U dating Dividing through by the 238U activity, we have:

Thus we can date a sample provided we know the initial 234U/238U ratio. The application of 234U/238U has been largely restricted to corals where we can assume the initial ratio is that of seawater. It is not generally useful for freshwater carbonates because of uncertainty in the initial activity ratio.

Mollusk shells and pelagic biogenic carbonate (e.g., foraminiferal ooze) often take up U after initial deposition of the carbonate and death of the organism, thus violating our closed system assumption. The technique is typically useful up to 4 half-lives.

230Th-238U Dating The 234U-238U technique does not have high temperature applications,

because at high temperature, radiation damage, which is the reason 234U is removed in weathering more easily than 238U, anneals quite rapidly.

Disequilibrium between 230Th (the daughter of 234U) and its U parents provides useful geochronological information in both high- and low-temperature systems.

We start with:

Divide by normalizing isotope:

In this case again we need to know the initial 230Th/232Th ratio

Figure 3.12

230Th Dating an Mn Nodule Consider an Mn nodule

growing outward and excess 230Th decaying inward. We assume the nodule grows at a constant rate such that

z = st.

Substituting z/s for t and a full expression for (230Th)u, we have:

z/s = 0 at surface, so we know initial ratio and can solve for z/s – the growth rate.

Th/U Carbonate DatingCarbonates concentrate U and exclude Th. This

leads to (230Th/238U) ratios much smaller than 1 (the equilibrium value); indeed, (230Th/238U) in many modern carbonates approaches 0.

The problem is complicated by the disequilibrium that will generally exist between 234U and 238U. The relevant equation is:

Hence we must also measure (234U/238U).

A W G Pike et al. Science 2012;336:1409-1413

Published by AAAS

Oldest European Cave Paintings

Pike et al. (2012) used th-U dating to determine the age of flowstone coatings over cave painting in northern Europe.

The oldest, a simple red disk, has a minimum age of 40,800 years.

Modern humans or Neanderthals?

Fig. 5 The Panel de las Manos, El Castillo Cave, showing the location of samples O-82 overlaying a negative hand stencil, and O-83 overlaying a large red stippled disk.

A W G Pike et al. Science 2012;336:1409-1413

Published by AAAS

Th–U Dating at High Temperature

Now consider the case of high-temperature systems (e.g., magmas) where it is reasonable to assume 234U and 238U are in equilibrium (allowing us to treat 230Th as the direct daughter). Th and U have different partition coefficients, so melting disturbs the radioactive equilibrium.

We can derive the following:

The tricks to this derivation are to make the approximations λ230 – λ238 = λ230 and e-λ238t = 1; i.e., assume λ238 ≈ 0; this is the mathematical equivalent of assuming the activity of 238U does not change with time.

The first term on the right describes the decay of unsupported 230Th while the second term describes the growth of supported 230Th.

Th-U Dating

Note that this equation has the form of a straight line in (230Th/232Th) — (238U/232Th) space, where the first term is the intercept and (1 – e–λ230t) is the slope; both are function of t. The intercept changes with

time.

The plot rotates around the point where

After infinite time, the slope = 1 because Figure 3.13

Figure 3.14

Th-U Example This is 230Th–238U mineral isochron obtained on a

peralkaline lava from the African Rift Valley in Kenya (Black et al., 1997) yields an age of 36,200±2600 yrs.

However, the eruption of age of this lava is constrained by stratigraphy and 14C dating to be less than 9,000 yrs. Other lavas in the area yielded similarly precise, but anomalously old, U-Th ages.

Black et al. interpreted the ages to reflect the time of crystallization of the phenocrysts, which in this case predates eruption by >25,000 yrs.

In most cases concentrations of Th and U are so low that accurate measurement of Th-U disequilibria on mineral separates remains challenging.

Some minerals, however, such as zircon, allanite ((Ca,Ce,Y,La)2(Al,Fe+3)3 (SiO4)3(OH)), pyrochlore

(Na,Ca)2Nb2O6(OH,F)), and baddeleyite (ZrO2),

concentrate uranium and/or thorium sufficiently that they can be analyzed with the ion microprobe and U-Th ages determined not only on individual grains, but also of individual zones of mineral grains.

Using ion probe 230Th–238U dating of allanite from in the pyroclastic products of the 73 Ka Toba eruption, Vazquez and Reid (2004) found that allanite cores had crystallized between 100 and 225 thousand years ago, whereas most rims had ages identical with error of the eruption age.

231Pa–235U Dating 231Pa (t1/2 = 32.67 ka) is the granddaughter of 235U, but the

intervening nuclide 231Th has a sufficiently short half-life that we can always ignore it. Pa is typically in the 5+ valance state with ionic radii of 92 pm and partitions readily into the same igneous and metamorphic accessory minerals that concentrate U and Th, but like Th, it is excluded from carbonates. like Th and unlike U, Pa is generally immobile.

Precisely the same principles apply to 231Pa-235U dating as to 238U decay series dating:

And since we can assume λ235 to be 0:

231Pa–235U Dating Advantages

No long-lived intermediate comparable to 234U

the half-life of 235U is less than a sixth of that of 238U and thus it decays more rapidly

231Pa decays more rapidly 230Th.

Disadvantages Abundance of 235U is less

than 1% of that of 238U 231Pa is less abundant

than 230Th 231Pa decay constant is

less well known than that of 234U or 230Th

Short half-life means it is useful over a smaller range of time.

The value of the 231Pa-235U system, like that of the 207Pb–235U one comes in using it in combination with the 238U decay

Figure 3.15

231Pa*/235U–230Th*/234U Concordia

Concordia diagram analogous to the Pb one, defining concordant ages.

Black line is for (234U/238U)=1; red line is for (234U/238U)=1.145

Ages of corals from Araki Island shown (Chiu et al., 2006)

Figure 3.16

226Ra dating 226Ra t1/2 = 1600 yrs

No long-lived daughter isotope to ratio it to, so ratioed to Ba instead.

226Ra/Ba–230Th/Ba diagram is an isochron diagram analogous to the 230Th/232Th–238U/232Th one

Figure shows 226Ra-230Th whole rock isochron on obtained on a sequence of trachytic lavas from Longonot volcano in the Gregory Rift of Kenya. The samples represent roughly 5 km3 of lava. The degree of igneous fractionation increases upward in the sequence, resulting in a range of whole rock compositions and Th/Ba ratios. The age of 4274 years dates this igneous differentiation and falls within the range of eruption ages, 5650 to 3280 years BP, inferred from 14C dating.

210Pb Datingt1/2 22 yrs.

6th great granddaughter of 226Ra. One of these intermediates is 222Rn (t1/2 ≈ 3 days), a noble gas, which can diffuse into the atmosphere before decaying.

Essentially, this means 210Pb can take a different path into the hydrologic system than stable Pb isotopes.

That leads to excess, or unsupported, 210Pb in young sediments.

CompactionFor detrital sedimentation (as opposed to an Mn

nodule), we need to consider compaction.

To correct for compaction, we replace depth, z, with a function called mass-depth, which has units of depth per unit area. We define ∆mi as the mass of sediment in the core in depth interval ∆zi and the mass-depth, mi, at depth zi as the total mass (per cross-sectional area of the core) above zi.

Models of 210Pb accumulation Constant Flux or Constant Rate of Supply Model

Rate of fallout of 210Pb constant and independent of sedimentation rate.

Constant Initial Concentration or Constant Activity Model. 210Pb enters sediment absorbed onto particles – accumulation

proportional to sedimentation rate; initial concentration is constant.

Constant Sedimentation Model Sedimentation rate is constant, but 210Pb accumulation rate is not

Constant Flux–Constant Sedimentation Model Both sedimentation and Pb accumulation rate is constant. Simplest assumption.

210Pb DatingConstant Activity Model

Constant Flux ModelA(i) is the integrated 210Pb activity in the sediment

column beneath mass-depth i, A(0) is total integrated activity in column.

Constant Flux–Constant Sedimentation Model

and

Figure 3.17

Example of constant flux-constant sedimentation model

Tehuantepec River (Mexico) estuary

Changes at 1930 and 1972 due to land use and demographic changes and channelization

0.66 g/cm2-yr

0.22 g/cm2-yr

0.1 g/cm2-yr

Figure 3.18

210Po Dating 210Pb decays (via 210Bi) to 210Po; t1/2

= 138 days

Po is volatile and is lost quantitatively (or nearly so) from lava upon eruption. It then returns to equilibrium activity through:

Assume (210Po/210Pb)0 is zero (this gives maximum age).

Rubin used this to date EPR lavas collected after evidence of eruption. Concluded eruption occurred only months before eruption