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.