Playing with radioactive decay equations

1. - l = t N N e 0 Playing with radioactive decay equations multiply each side by elt substitute N=N0-D substitute N0=N-D

2. U-series Disequilibrium 9/13/10 • Lecture outline: • Secular equillibrium and • disequilibrium • 2) U-Th systematics • 3) U-excess • U-Th disequilbrium dating • 232Th “initial” corrections • 6) Th excess and sedimentation rates Zircon Geological archives dated by U-series disequilibrium: speleothems (top) and fossil corals (bottom)

3. Secular equilibrium and disequilibrium Secular equilibrium: all radioactive species in a decay chain have the same activity Disequilibrium: system is perturbed (removal/enrichment of daughter/parent), and system decays back to secular equilibrium And if you know how (disequilibrium)initial, can calculate t since disequilibrium For U-series decay chain, what are some examples of processes that cause disequilibrium ? There are two types of disequilibria: 1) Daughter excess (i.e. activity of daughter > activity of parent) 2) Daughter deficit (Ad < Ap)

4. Decay Chain Systematics: Consider a 3-member decay chain: Evolution of this system is governed by the coupled equations: Note that at secular equil, As you can see, the solution of these differential equations is quite complicated (except for N1), so we will derive some equations from the disequilibria of 234U and 230Th.

5. NOTE: everything in this lecture will be activities (A), unless otherwise noted 234U Excess Given: (234U/238U)A of ocean = 1.15 Explanation: [you tell me] The activity of (234U)excess decreases with time: And excess 234U corresponds to the 234U not supported by 238U: And dividing through by 238U activity, we obtain: So if you measure 234U/238U, and know (234U/238U)initial can calculate age Note that fixed analytical error (±0.5%) yields larger and larger age error bars as you approach secular equilibrium

6. 230Th Deficiency Given: Many U-rich minerals (such as carbonate) precipitated with virtually no Th Explanation: [you tell me] So you grow in 230Th due to decay of 238U and excess 234U (in atom number): And converting to activity, substituting formula for 234UEx, dividing by 238UA, and simplifying, we obtain: So if you measure (230Th/238U), and assume initial (234U/238U)A=1.15, then you can calculate a sample’s age. *Or, more realistically, you measure (230Th/238U) and 234U/238U, and iteratively find an age that satisfies both the measurements made today. You then are calculating also 234U/238U initial. So when/where is the assumption that initial (234U/238U)A=1.15 not a good one?

7. 230Th-234U activity growth lines Development of mass spectrometry techniques enable U-Th ages to be measured to ±0.1-5 precisions (Edwards et al., 1987) secular equilibrium For most samples: secular equilibrium

8. Common U-Th series applications: Cutler et al., 2003 1. Corals - sea level from fossil terraces - climate reconstruction Edwards et al., 1987 2. Cave Stalagmites - climate reconstruction

9. but what happens when good samples get “dirty”? FACT: most geological samples contain some “initial” or “detrital” or “nonradiogenic” thorium PROBLEM: mass specs cannot distinguish between “detrital” 230Th and radiogenic 230Th SAVING GRACE: “detrital” thorium mostly 232Th (quasi-”stable” on U/Th disequilibrium timescale) STRATEGY: measure 232Th in samples, correct for detrital 230Th using 230Th/232Th of contaminant BUT how do you estimate 230Th/232Th of contaminant? given: average bulk Earth abundance (230Th/232Th)atom = 4.4e-6 at secular equilibrium (Kaufman, 1993) complication: in most settings this will not apply…

10. STRATEGY #1: date samples of known age upper error bar = analytical error + correction using (230Th/232Th)atom of 2.0e-5 lower error bar = analytical error • - especially good for corals • because you can absolutely • date them by counting back • annual density bands • (Cobb et al., 2003a) • if you can identify a well-dated • event in your sample (volcanic • eruption from historic record?), • you may be able to do this for • older samples

11. STRATEGY #2: generate isochrons from samples IDEA: sample multiple samples of the same age but different 232Th concentrations, then you know that they all contain the same 230Thrad, and that 230Thnr will scale with 232Th “dirty” edges “clean” middle “dirty” edges

12. U/Th isochron plots • most often used for • stalagmites (Partin et al., 2007) • in these plots, • slope α age • intercept = (230Th/232Th)act • of contaminant phase

13. Usually huge range of values uncovered… translating into huge age errors for “dirty” samples LESSON: keep it clean (if possible)

14. Slope = -l/S ln(230Th)ex Depth in sediment core 230Th Excess and Deep-Sea sediments Phenomenon: “excess” 230Th present in ocean sediments Explanation? The activity of (230Th)excess decreases with time: If you assume that delivery of 230ThEx is constant through time, can calculate age as a function of depth - or - sedimentation rate We can define sedimentation rate as: S=distance/time; so t=d/S and and

15. 230Th Excess and sedimentation rate changes

16. 230Th Excess - interpretation But how can you have an increase of 230Thex with depth, given constant 230Thex delivery? Down-core measurements in Norwegian core show sedimentation rate changes Increased scavenging of 230Th during interglacials in Norway, or sediment focusing. So 230Thex delivery is not constant. Changes in the rain-rate of particles will lead to increases and decreases in Th scavenging. What could change scavenging rate?