12 14 C C/

3.9 Carbon Contamination & Fractionation

Because the ratio ¹⁴C/¹²C in a sample decreases with increasing age - due to the continuous decay of ¹⁴C - a small added impurity of modern natural

carbon causes a disproportionately large shift in age.

) (

12 0 14 12

14

)

( )

( t e

C t C

C

C

⋅

=

1.000E-15 1.000E-14 1.000E-13 1.000E-12 1.000E-11

0 5000 10000 20000 30000 40000 50000

time [^y]

14 C/12 C

+1% modern carbon

e.g. a 50,000 year old sample will

appear as only

~35,000 year old!

Mathematical Exercise

A fraction x of ¹⁴C contamination, that occurred at time t_cont, changes the real age t_real to an apparent observed age t_obs.

( )

) (

) ) (

1 ) (

(

0 0

0

real cont

real obs

real cont

real obs

t t

t t

t t

t t

cont real

obs

e e

e x e

e x e

x e

e

N t x N

N t x N

N t N

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

−

= −

⋅

−

⋅ +

=

⋅ +

⋅

−

=

λ λ

λ λ

λ λ

λ λ

For modern contamination t_cont=0

real

real obs

t

t t

e

e

x e

⋅

−

⋅

−

−

=

−

1

Contamination in the Shroud

real cont

real obs

t t

t t

e e

e

x e _{− ⋅ − ⋅}

⋅

−

⋅

−

−

= _λ ^λ − ^λ _λ

Crucification 36 AD ⇒ t_real = 1952 y;

Measured age: t_obs = 690 y T_1/2=5730 y; λ=1.21·10^-4

For contamination in fire at 1532 AD ⇒ t_cont = 456 y

x = 0.83

For modern day contamination ⇒ t_cont = 0

x = 0.62

Amount of modern carbon must be nearly doubled!

Deviation in Age Determination

 

 



 ⋅ + −

⋅

=

−

=

∆

− +

⋅

=

− +

⋅

=

=

⋅

− +

⋅

=

⋅

−

⋅

−

−

⋅

−

⋅

−

⋅

− −

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

⋅

−

e x x e t

t t

x e

x e x

x e e e

e

e x

e x e

real cont

real cont

real cont real

obs real

obs

real cont

obs

t t obs

real

t t

t t t

t t

t

t t

t

1 1 ln

1 1

) 1

(

) (

) (

λ λ

λ λ

λ λ λ

λ

λ λ

λ

λ

(

)

t t

t = _real − _obs = ⋅ ⋅ ^treal + −

∆ 1 ln _λ^⋅ 1

λ

For modern contamination t_cont=0

Determine the deviation in time ∆t, if at time t_cont a fraction x contamination of ¹⁴C occurred!

Deviation from real Age by Contamination

( )

t obs

real t t x e x t

t = ∆ + = 1 ⋅ln ⋅ _λ^{⋅ real} +1− + λ

Observed age 690 years

Recent contamination Turin fire contamination

500 750 1000 1250 1500 1750 2000 2250 2500

0.001 0.01 0.1 1

Modern Impurity x [%]

Real Age [years]

Considerable contamination necessary to reach “desired” age

long term deviation from real age

( ^{x e x} )

t t

t =

−

= ⋅ ⋅

+ −

∆ 1 ln

1

λ

with 1% contamination real age: 7000 y deviation: ~100 y apparent age: 6900 y real age: 34000 y deviation: ~4000 y apparent age: 30000y real age: 50000 y deviation: ~15000 y apparent age: 35000 y

treal

e^−λ⋅

0 2000 4000 6000 8000 10000 12000 14000

0 10000 20000 30000 40000 50000

age [y]

deviation [y]

1% modern carbon 0.1% modern carbon

a 16000 y old sample contaminated with 3% of modern material will appear ~1400 y too young.

To be original, the shroud needs a >50% contamination with modern material.

t_sample

% of contamination

correction in years

50 % 50 %

Approximation Graph

Contamination with old Material

Can be expressed in terms of ∆t versus the time difference between the age of the sample t_real and the age t_cont of the contaminant ¹⁴C, t_real-t_cont.

( )

( ^{x e x} )

t t

t

x e

x e

e x

e x

e

cont real

real cont

real obs

real cont

obs

t t

obs real

t t

t t

t t

t

− +

⋅

⋅

=

−

=

∆

− +

⋅

=

⋅

− +

⋅

=

−

⋅

−

⋅

−

−

⋅

−

⋅

−

⋅

−

⋅

−

1 1 ln

1 )

1 (

) (

) (

λ λ

λ

λ λ

λ

λ

dead carbon impurities

t_cont-t_sample

% of contamination

correction in years

e.g. 5000 y old sample contaminated with 20%

of 16000 y old material will yield a date which is ~1300 y too old.

contamination of sample with “dead carbon” (fossil fuel etc) will cause an increase in the apparent age of sample material

(see dead rabbit example) because the sample shows less

14C/¹²C as it should, simulating an older age for the sample.

Fractionation

Natural chemical or physical processes can fractionate the carbon isotopes during the up-take and alter the ¹³C/¹²C

and ¹⁴C/¹²C isotopic ratios. This requires correction.

e.g. photosynthesis enriches lighter isotopes → carbon in plant has relatively higher ¹²C/¹⁴C ratio than atmosphere.

Fractionation is expressed in terms of δ¹³C which is a measure (in parts of a thousand ppm) of the deviation of the isotopic ratio

13C/¹²C from a standard material (PDB belemnitella americana).

Typical δ¹³C vary between +2‰ to -27‰ and need to be determined for the material to be dated. Additional fractionation

may occur during the chemical preparation of the sample.

Fractionation effects

fractionation term δ¹³C is defined from ¹³C/¹²C isotopic ratios for the sample (sm) and the standard (st) as:

st

st sm

C C

C C C

C C

12 13

12 13 12

13

13

1000  





 



 −

⋅ δ ≡

A negative value δ¹³C means that the sample is isotopically lighter than the standard probe (appears older). A positive

value means that the sample is enriched in the heavier isotope components (appears younger).

For these corrections is assumed that the

14

C/

C ratio scales with the

C/

C ratio!

Excursion: fractionation and eating habits and its impact on dating bones

sample number

C₄-photosynthesis

C₃-photosynthesis

There are two different processes of photochemical assimilation of

CO₂ in plants (photosynthesis cycles) . This leads to quite different carbon fractionation

values δ¹³C ranging from δ¹³C =-26.5‰ to δ¹³C= -12.5 ‰.

C₃ plants dominate the northern cooler regions of Europe and North America. The habitat of C₄

plants are the warmer regions in South- and Central America,

Africa, and Australia.

Fractionation in food chain processes

bicarbonate in ocean water and in ground

CO₂in air

plants

plants plant eater

or animals

bones of plant- eaters

bones of meat- eaters

human bones

pure C₄ eaters

pure C₃ eaters enrichment

in δ¹³C in

bone collage

North American Values

North American plants are predominantly C3 plants

⇒ fractionation values of δ¹³C = -21.4 ‰ are observed in bone collages of plant and meat eating animals.

If additional C₄ plants - like corn – are consumed than will the δ¹³C value increase accordingly.

e.g. ≈10% corn ⇒ δ¹³C ≈ -20 ‰.

Is sea food consumed drastic changes occur since the ocean food chain is characterized by different fractionation processes leading to δ¹³C ≈ -18 ‰.

Ancient eating habits

The fractionation analysis of bone material with parallel

14C dating can help to identify changing eating habits.

fraction of C 4plant consumption in %

BC time [y] AD

Example: increase of corn consumption (C₄ plant) by population due to the corn migration into North America.

The values result from bone analysis of human skeletons.

At 1500 AD: ~75% corn consumption.

Sea food chains

bicarbonate in ocean water and in ground

CO₂in air

plankton similar C₃ (-17.8)

mammals fish, crabs, and coastal fauna

land fauna animal meat birds, fresh water fish

bone material of coastal residents ocean proteins

bone material of inland residents C₃consumer

100%

from sea

100%

from land (C₃) nutrition

Observations

Analysis of skeletons of early population of coastal British Columbia:

δ

C=-13.4±0.9‰ ⇒

100% seafood based nutrition Analysis of skeletons of early population of

Ottawa region:

δ

C=-19.6±0.9‰ ⇒ ≈ 100% C

originated nutrition.

Analysis of skeletons of early population of central British Columbia:

δ

C=-15.4±0.3‰ ⇒ ≈65% seafood (salmon)

& ≈35% C

originated nutrition.

The Norsemen and Vikings

BC calibrated ¹⁴C age AD

Iron-age fish mammals

drastic change of nutrition

sea food

vegetables & meat

sea food

Immigration of Indo-Europeans? Viking migrations!

Fractionation standard

Fractionation of ¹⁴C is defined in terms of the one for ¹³C:

C C

C C

C C C

C C

st

st sm

13 14

12 13

12 13 12

13

13

2 1000

δ δ

δ

⋅

=

 





 



 −

⋅

≡

often calculated relative to a standard value δ¹³C_wood=-25‰

Fractionation corrections

Corrections can be made for fractionation effects by first assessing the specific ¹³C content of the sample because the ¹⁴C fractionation is known to be twice that of ¹³C. This yields correction formula:

14 14 13

12 12

2 (25 )

1 1000

corr uncorr

C C C

C C

δ

 ⋅ + 

= ⋅ −  

 

example: material has δ¹³C = -12 ‰

(since isotopically heavier than wood standard δ13C_wood = -25 ‰, it appears older than it is.)

14C/¹²C|_uncorr=5.00·10^-13 this gives:

14C/¹²C|_corr=4.87·10^-13

Age correction

sample has δ¹³C = -12 ‰ and appears older:

C y C

C t C

C y C

C t C

corr org corr

uncorr org uncorr

64 . 10 8116

87 . 4

10 3 . ln 1

64 . ) 8266

(

) ln (

1

86 . 10 7898

0 . 5

10 3 . ln 1 64 . ) 8266

(

) ln (

1

13 12 12

14

12 14

13 12 12

14

12 14

 =



 





⋅

⋅ ⋅

 =











⋅ 

=

 =



 





⋅

⋅ ⋅

 =











⋅ 

=

−

−

−

−

λ λ

y

= 218

−

corr

t

t

Approximate formula

The age correction can be approximated by a simple empirically derived formula for material with a certain fractionation of δ¹³C in units ‰.

[y]

25 16 (

C ) t

t

−

≈ ⋅ δ +

Previous example δ¹³C=-12 ‰

y 208 25

12

16 − + =

≈

− t ( )

t

agreement within statistical uncertainties!

Fractionation in the Shroud

14 14 13

12 12

2 (25 )

1 1000

corr uncorr

C C C

C C

δ

 ⋅ + 

= ⋅ − 

 

C ; C C

C

real obs

12 12

12 14 12

14

10 021 .

1

; 10 194

.

1 ⋅ ⁻ ≡ ⋅ ⁻

≡

The observed ¹⁴C/¹²C ratio corresponds to an age of 690 years Believing the shroud originated in 36 AD forces to expect a “real”

14C/¹²C ratio of 1.021·10^-12, because much more should have

decayed. Enrichment in heavy isotopes (¹³C,¹⁴C) by fractionation would make the shroud apparently younger. What would be the fractionation δ¹³C and the corresponding enrichment in ¹³C?

Required Change in ¹³ C Abundance

4 . 47 25

1 500

25 1

500

12 14 12 14

12 14 12 14

13

− =

 

 







 

 







−

⋅

=

−

 

 







 

 







−

⋅

=

obs real

uncorr corr

C C C C

C C C C δ C

Far higher than observed in natural material (typically +2 to -27) Possible enrichment at combustion conditions is still under debate!

Summary

Carbon Contamination and Fractionation are natural processes which have to be taken into account in the final analysis of the data. They can cause significant systematic errors if not considered

properly. In fact these systematic errors resemble the main source of uncertainty in all radioactive

dating results and is typically much larger than standard statistical uncertainties which are

determined by sample size and counting conditions.