The U-series Disequilibrium Method of Dating
•Uranium series, or Ionium dating, is based on the radioactive decay of uranium in calcium carbonate and other minerals that precipitate from solution.
•Natural 238U decays into 234Th, while the other isotope of U, 234U, decays into 230Th. Because the U is soluble in water and the Th is not, minerals that precipitate from solution often contain U but very little Th. Through time Th is formed in the mineral as the U decays.
•The Th is itself a radioactive element and it decays into daughter products. The 234Th decays into 234U and the 230Th decays into 226Ra.
•Ra is also radioactive, and it decays into Rn in a very short time. If the mineral is of sufficient age the entire suit of U decay products, from 238U through to 206Pb (238U - 234Th - 234U - 230Th - 226Ra - 222Rn - 218Po - 214Pb - 214 Bi - 214Po - 210Pb - 210Po - 206 Pb = the U series), will be present.
•The critical elements in this series are 238U, 234U and 230Th because of their half lives. For any mineral that initially contained only U, the time since its formation can be calculated from the 238U/ 234U and 234U/ 230 Th ratios.
NdtdN N
dtdN
dtN
dN
CtN ln 0ln NC
0lnln NtN tNN 0lnln
tNN
0ln
teNN
0
teNN 0
NND 0*
teNND 00*
)1(* 0teND
21
0021 T
eNN
2
1)21
ln( T
21)2ln( T
693.02ln
21 T
•The rock or mineral system has neither gained nor lost either parent or daughter atoms so that the ratio of D*/N has changed only as a result of radioactive decay. This condition is often expressed by the statement that the rock or mineral sample must be a “closed system” with respect to the parent and daughter.
•It must be possible to assign a realistic value to D0. This can usually be done reliably, especially when D* is much greater than D0.
•The value of the decay constant () must be known accurately.
•The measurements of D and N must be accurate and representative of the rock or mineral to be dated.
Dating Assumptions
111 N
dt
dN
22112 NN
dt
dN teNN 1011
0101122
2 teNNdt
dN
ttt eNeeNN 221 02
01
12
12 )(
)( 2101
12
12
tt eeNN
0t
If it is a decay series:
If
))(( 1312
0121
1
NC
))(( 2321
0121
2
NC
))(( 3231
0121
3
NC
tn
ttn
neCeCeCN 2121
ttt eCeCeCN 3213213
A series of n:
If n=3
)( 2101
12
12
tt eeNN
teNN 101
12
12
112
12 NN
constant1
12
2
1
NN
21 002 N
U23892
21
212
1
2
2
1
N
N2211 NN
nnNNNN .......332211
nn
NN
11 000.1......
33
22
22
11 NN
NN
UPaThU 234234234238
AXASA UUU 234234234
tAXAX eUU 2340234234
ASAAX UUU 23402340234
234UA=activity of 234U per unit weight of sample at the present time234UAS=activity of 234U in secular equilibrium with 238U234UAX=activity of excess 234U per unit weight of sample
tAAAA eUUUU 234)( 2380234238234
t
A
AAA e
U
UU
U
U234)(1)(
238
2380234
238
234
15.1)( 00
238
234
AU
U
tA e
U
U234)1(1)( 0
0238
234
AAS UU 238234 Since secular equilibrium
230Th/232Th Method
*On the earth surface U becomes uranyl ions UO2
2+ such as (UO2)(CO3)3-4
*Based on the assumption 230Th and 232Th simultaneously removed from sea water.
Assumptions:
• The 230Th/232Th ratio in the water mass adjacent to the sediment in a given ocean basin has remained constant during the last several hundred thousand years.
• 230Th and 232Th have the same chemical speciation in sea water and there is no isotopic fractionation between sea water and the mineral phases with which the Th is associated in the sediment.
• 230Th and 232Th occurring in detrital mineral particles are excluded from the analysis.
• Th isotopes do not migrate in the sediment.
AsAxA ThThTh 230230230
tAxAx eThTh 2300230230
tAx e
Th
Th
Th
ThAx
2300232
230
232
230
)()(
teRR 0
)ln(1 0
RR
t
For Excess:
)( 2101
12
12
tt eeNN
)( 2302340234
234230
234230 tts eeUTh
AUU 238234
0234 230234230 1234 te
If secular equilibrium reaches
)1( 230238230 tAAs eUTh
For Supported:
)1( 230230 2380230230 tA
tAxA eUeThTh
)1()()()( 230230232
2380
232
230
232
230t
At
A eTh
Ue
Th
Th
Th
ThAx
ah
eRR
0ah
RR 0lnln
am
m
a
Sum up excess and supported
Consider supported is negligible
)1( 230238230 tAs eUTh
)( 2302340234
234230
234230 ttxx eeUTh
)( 2302340234
234230
230230
230230 ttAxxAx eeUThTh
U/Th method
*Calcium Carbonate is free of 230Th.*If secular equilibrium reaches:
If excess 234U presents
)()()( 230234238
2340234
234230
230238
230tt
A
AsAAx ee
U
UU
U
Th
ASAAX UUU 23402340234
)()( 2302342340234
234230
230230 ttAsAAx eeUUTh
))(1()1()( 2302342300
234230
230238
230ttt
A eeeU
Th
A
A
U
U238
0234
0 AAs UU 238234 Where
tA e
U
Th2301)( 234
230
If there is no excess
Fortunately it turns out that the presence of excess 234U makes a very small difference.