Post on 13-Dec-2015
Playing with radioactive decay equations
NND 0
multiply each side by et substitute N=N0-D
teNN 0
teNDN 00
teNND 00
)1(0teND
0NNe t
DNNe t
substitute N0=N-D
NNeD t
)1( teND
U-series Disequilibrium 9/13/10
Lecture outline:
1) Secular equillibrium and disequilibrium
2) U-Th systematics
3) U-excess
4) U-Th disequilbrium dating
5) 232Th “initial” corrections
6) Th excess and sedimentation rates
Geological archives dated by U-series disequilibrium:speleothems (top) and fossil corals (bottom)
Zircon
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 equilibriumAnd 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)
N11 N2
2 N3
dN1dt
1N1dN2dt
1N1 2N2dN3dt
2N2
Decay Chain Systematics:
Consider a 3-member decay chain:
Evolution of this system is governed by the coupled equations:
Note that at secular equil, 2d0
d
N
t
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.
N2 (t)1
2 1N1o e 1t e 2t N2oe 2t
234U Excess
Given: (234U/238U)A of ocean = 1.15Explanation: [you tell me]
The activity of (234U)excess decreases with time: 234234 234 0 tEx ExU U e
And excess 234U corresponds to the 234U not supported by 238U:
234234 238 234 0 238( ) tU U U U e
NOTE: everything in thislecture will be activities (A),unless otherwise noted
And dividing through by 238U activity, we obtain:234
234 0 238234
238 2381 t
A
U UUe
U U
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 barsas you approach secular equilibrium
230Th Deficiency
Given: Many U-rich minerals (such as carbonate) precipitated with virtually no ThExplanation: [you tell me]
So you grow in 230Th due to decay of 238U and excess 234U (in atom number):
1 2 212 1 2
2 1
( ) t t to oN t N e e N e
234 230230 234234
230 234
t toEx ExTh U e e
And converting to activity, substituting formula for 234UEx, dividing by 238UA,and simplifying, we obtain:
230 234 230
234 0230230
238 238230 234
(1 ) 1 ( )t t t
A A
UThe e e
U U
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 measurementsmade today. You then are calculating also 234U/238U initial.
So when/where is the assumption that
initial (234U/238U)A=1.15not a good one?
secularequilibrium
secularequilibrium
230Th-234U activity growth lines
For most samples:
Development of mass spectrometry techniques enable U-Th ages to be measured to ±0.1-5 precisions (Edwards et al., 1987)
Common U-Th series applications:
1. Corals- sea level from fossil terraces- climate reconstruction
2. Cave Stalagmites- climate reconstruction
Cutler et al., 2003
Edwards et al., 1987
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/232Thof contaminant
BUT how do you estimate 230Th/232Th of contaminant?
given: average bulk Earth abundance (230Th/232Th)atom = 4.4e-6at secular equilibrium (Kaufman, 1993)
complication: in most settings this will not apply…
STRATEGY #1: date samples of known age
- especially good for coralsbecause you can absolutelydate them by counting backannual density bands(Cobb et al., 2003a)
-if you can identify a well-datedevent in your sample (volcaniceruption from historic record?), you may be able to do this for older samples
lower error bar = analytical error
upper error bar =analytical error + correctionusing (230Th/232Th)atom of 2.0e-5
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
U/Th isochron plots
- most often used forstalagmites (Partin et al., 2007)
- in these plots, slope α age intercept = (230Th/232Th)act
of contaminant phase
Usually huge range of values uncovered…
translating into huge age errors for “dirty” samplesLESSON: keep it clean (if possible)
Phenomenon: “excess” 230Th present in ocean sedimentsExplanation?
The activity of (230Th)excess decreases with time:
230Th Excess and Deep-Sea sediments
230230 230 0 tEx ExTh Th e
We can define sedimentation rate as:S=distance/time; so t=d/Sand
230 ( / )230 230 0 d SEx ExTh Th e
230 230 0230ln( ) ln( ) ( )Ex Ex
dTh Th
S
and
Depth in sediment core
ln(23
0 Th)
ex
Slope = -/S
If you assume that delivery of 230ThEx is constant through time, can calculateage as a function of depth - or - sedimentation rate
230Th Excess - interpretation
Down-core measurementsin Norwegian core showsedimentation rate changes
But how can you have an increase of 230Thex with depth, given constant 230Thex delivery?
So 230Thex delivery is notconstant.Changes in the rain-rate of particles will lead to increasesand decreases in Th scavenging.
Increased scavengingof 230Th during interglacials in Norway,or sediment focusing.
What could change scavenging rate?