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.
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