3.9 Carbon Contamination & FractionationBecause 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.

)(012

14

12

140)()( ttet

CCt

CC −⋅−⋅= λ

1.000E-15

1.000E-14

1.000E-13

1.000E-12

1.000E-11

0 5000 10000 20000 30000 40000 50000

time [y]

14C

/12C

+1% modern carbon

e.g. a 50,000 yearold sample willappear as only~35,000 year old!

Mathematical ExerciseA fraction x of 14C contamination, that occurred at time tcont,changes the real age treal to an apparent observed age tobs.

( )

)()()1()(

000

realcont

realobs

realcontrealobs

tt

tt

tttt

contrealobs

eeeex

exexee

NtNx

NtNx

NtN

⋅−⋅−

⋅−⋅−

⋅−⋅−⋅−⋅−

−−

=

⋅−⋅+=

⋅+⋅−=

λλ

λλ

λλλλ

For modern contamination tcont=0

real

realobs

t

tt

eeex ⋅−

⋅−⋅−

−−

= λ

λλ

1

Contamination in the Shroud

realcont

realobs

tt

tt

eeeex ⋅−⋅−

⋅−⋅−

−−

= λλ

λλ

Crucification 36 AD ⇒ treal = 1952 y;Measured age: tobs = 690 y

T1/2=5730 y; λ=1.21·10-4

For contamination in fire at 1532 AD ⇒ tcont = 456 yx = 0.83

For modern day contamination ⇒ tcont = 0x = 0.62

Amount of modern carbon must be nearly doubled!

Deviation in Age Determination

−+⋅⋅=−=∆

−+⋅=−+⋅==

⋅−+⋅=

⋅−

⋅−

−⋅−⋅−

⋅−−⋅−

⋅−

⋅−

⋅−⋅−⋅−

xeexttt

xexxeexe

ee

exexe

real

cont

realcont

real

contrealobs

real

obs

realcontobs

t

t

obsreal

ttt

ttt

t

t

ttt

1ln1

11

)1(

)()(

λ

λ

λλ

λλ

λ

λ

λλλ

λ

( )xexttt realtobsreal −+⋅⋅=−=∆ ⋅ 1ln1 λ

λ

For modern contamination tcont=0

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

Deviation from real Age by Contamination

( ) obst

obsreal txexttt real +−+⋅⋅=+∆= ⋅ 1ln1 λ

λ

Observed age 690 years

Recent contaminationTurin fire contamination

500750

1000125015001750200022502500

0.001 0.01 0.1 1

Modern Impurity x [%]

Rea

l Age

[y

ears

]

Considerable contamination necessary to reach “desired” age

long term deviation from real age

( )xexttt realtobsreal −+⋅⋅=−=∆ ⋅ 1ln1 λ

λwith 1% contaminationreal age: 7000 y deviation: ~100 yapparent age: 6900 y

real age: 34000 y deviation: ~4000 yapparent age: 30000y

real age: 50000 y deviation: ~15000 yapparent age: 35000 y

realte ⋅−λ

0

2000

4000

6000

8000

10000

12000

14000

0 10000 20000 30000 40000 50000

age [y]

devi

atio

n [

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.

tsample

% of contamination

corr

ectio

n in

yea

rs50 %50 %

Approximation Graph

Contamination with old MaterialCan be expressed in terms of ∆t versus the time difference between the age of the sample treal and the age tcont of the contaminant 14C, treal-tcont.

( )( )xexttt

xexeexexe

contreal

realcontrealobs

realcontobs

ttobsreal

tttt

ttt

−+⋅⋅=−=∆

−+⋅=

⋅−+⋅=

−⋅

−⋅−−⋅−

⋅−⋅−⋅−

1ln11

)1()()(

λ

λλ

λλλ

λ

dead carbon impurities

tcont-tsample

% of contamination

corr

ectio

n in

yea

rs

e.g. 5000 y old sample contaminated with 20% of 16000 y old materialwill 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.

FractionationNatural chemical or physical processes can fractionate

the carbon isotopes during the up-take and alter the 13C/12Cand 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 ratio13C/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 effectsfractionation term δ13C is defined from 13C/12C isotopic

ratios for the sample (sm) and the standard (st) as:

st

stsm

CC

CC

CC

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 14C/13C ratio scales with the 13C/12C 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 C4plants are the warmer regions in

South- and Central America, Africa, and Australia.

Fractionation in food chain processesbicarbonate in ocean water and in ground

CO2 in air

plants

plants

plant eateror

animals

bonesof

plant-eaters

bonesof

meat-eaters

human

bones

pure C4 eaters

pure C3 eaters

enrichment in δ13C inbone 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 sincethe ocean food chain is characterized by differentfractionation processes leading to δ13C ≈ -18 ‰.

Ancient eating habitsThe fractionation analysis of bone material with parallel 14C dating can help to identify changing eating habits.

frac

tion

of C

4pl

ant c

onsu

mpt

ion

in %

BC time [y] AD

Example: increase of corn consumption (C4 plant) bypopulation due to the corn migration into North America. The values result from bone analysis of human skeletons.At 1500 AD: ~75% cornconsumption.

Sea food chainsbicarbonate in ocean water and in ground

CO2 in airplanktonsimilar C3(-17.8)

mammalsfish, crabs, and coastal fauna

land faunaanimal meatbirds, freshwater fish

bone materialof coastalresidents ocean proteins

bone materialof inlandresidents C3 consumer

100%from sea

100%from land (C3)

nutrition

ObservationsAnalysis of skeletons of early population of coastal British Columbia:δ13C=-13.4±0.9‰ ⇒ ≈ 100% seafood based nutrition

Analysis of skeletons of early population of Ottawa region:δ13C=-19.6±0.9‰ ⇒ ≈ 100% C3 originated nutrition.

Analysis of skeletons of early population of central British Columbia:δ13C=-15.4±0.3‰ ⇒ ≈65% seafood (salmon)

& ≈35% C3 originated nutrition.

The Norsemen and Vikings

BC calibrated 14C age AD

Iron-age mam

mal

s

fish

drastic change of nutritionsea food

vegetables & meat

sea food

Immigration of Indo-Europeans? Viking migrations!

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

CC

CC

CC

CC

C

st

stsm

1314

12

13

12

13

12

13

13

2

1000

δδ

δ

⋅=

−

⋅≡

often calculated relative to a standard value δ13Cwood=-25‰

Fractionation correctionsCorrections 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 )11000corr uncorr

C C CC C

δ ⋅ += ⋅ −

example: material has δ13C = -12 ‰

(since isotopically heavier than wood standardδ13Cwood = -25 ‰, it appears older than it is.)

14C/12C|uncorr=5.00·10-13

this gives:14C/12C|corr=4.87·10-13

Age correctionsample has δ13C = -12 ‰ and appears older:

yCCCC

t

yCCCC

t

corr

orgcorr

uncorr

orguncorr

64.81161087.4

103.1ln64.8266)()(

ln1

86.7898100.5103.1ln64.8266

)()(

ln1

13

12

1214

1214

13

12

1214

1214

=

⋅⋅

⋅=

⋅=

=

⋅⋅

⋅=

⋅=

−

−

−

−

λ

λ

y218=− uncorrcorr tt

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

[y]2516 13 )C(tt uncorrcorr +⋅≈− δ

Previous example δ13C=-12 ‰

y208251216 =+−≈− )(tt uncorrcorr

agreement within statistical uncertainties!

Fractionation in the Shroud14 14 13

12 12

2 (25 )11000corr uncorr

C C CC C

δ ⋅ += ⋅ −

;CC

CC

realobs

1212

1412

12

14

10021.1;10194.1 −− ⋅≡⋅≡

The observed 14C/12C ratio corresponds to an age of 690 yearsBelieving the shroud originated in 36 AD forces to expect a “real”14C/12C ratio of 1.021·10-12, because much more should havedecayed. Enrichment in heavy isotopes (13C,14C) by fractionationwould make the shroud apparently younger. What would be the fractionation δ13C and the corresponding enrichment in 13C?

Required Change in 13C Abundance

4.47251500251500

12

14

12

14

12

14

12

14

13 =−

−⋅=−

−⋅=

obs

real

uncorr

corr

CCCC

CCCC

Cδ

Far higher than observed in natural material (typically +2 to -27)

Possible enrichment at combustion conditions is still under debate!

SummaryCarbon 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.