Stenström, Kristina; Skog, Göran; Georgiadou, Elisavet; Genberg, Johan; Mellström, Anette

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1 guide to radiocaron units and calculations tenström, Kristina; kog, Göran; Georgiadou, Elisavet; Generg, Johan; Mellström, nette Pulished: Link to pulication Citation for pulished version (P): tenström, K., kog, G., Georgiadou, E., Generg, J., & Mellström,. (011). guide to radiocaron units and calculations. (LUNFD6(NFFR-3111)/1-17/(011)). Lund University, Nuclear Physics. General rights Copyright and moral rights for the pulications made accessile in the pulic portal are retained y the authors and/or other copyright owners and it is a condition of accessing pulications that users recognise and aide y the legal requirements associated with these rights. Users may download and print one copy of any pulication from the pulic portal for the purpose of private study or research. You may not further distriute the material or use it for any profit-making activity or commercial gain You may freely distriute the URL identifying the pulication in the pulic portal? Take down policy If you elieve that this document reaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. L UNDUNI VER I TY PO Box L und

2 guide to radiocaron units and calculations Kristina Eriksson tenström 1, Göran kog, Elisavet Georgiadou 1, Johan Generg 1, nette Johansson 3 1 Lund University, Department of Physics, Division of Nuclear Physics, Box 118, E-1 00 Lund, weden Lund University, Radiocaron Dating Laoratory, Box 118, E-1 00 Lund, weden 3 Lund University, Department of Geology, Box 118, E-1 00 Lund, weden Lund, Octoer 011 Lund University, Department of Physics, Division of Nuclear Physics Internal Report LUNFD6(NFFR-3111)/1-17/(011)

3 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations guide to radiocaron units and calculations Kristina Eriksson tenström 1, Göran kog, Elisavet Georgiadou 1, Johan Generg 1, nette Johansson 3 1 Lund University, Department of Physics, Division of Nuclear Physics, Box 118, E-1 00 Lund, weden Lund University, Radiocaron Dating Laoratory, Box 118, E-1 00 Lund, weden Lund University, Department of Geology, Box 118, E-1 00 Lund, weden LUNFD6(NFFR-3111)/1-17/(011) 1

4 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations Contents 1. Introduction ctivity measurement Isotope fractionation Normalisation tandards Radiocaron quantities and units Per mil depletion or enrichment with regard to standard Per mil depletion or enrichment with regard to standard normalised for isotope fractionation Percent Modern (pm) and percent Modern Caron (pmc) Fraction of modern: F, F m, f M Fraction Modern, F 14 C Fraction contemporary, f c pecific activity and its relation to pmc and F 14 C Relation etween different units Radiocaron age Recommendations References LUNFD6(NFFR-3111)/1-17/(011)

5 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 1. Introduction The first radiocaron dating was performed in 1949 (Liy et al, 1949). t that time, and up until 1977, all radiocaron measurements were performed y measuring the radioactive decay of 14 C. ince then accelerator mass spectrometry (M) has entered the scene. M relies on counting the relative aundance directly in terms of isotope ratios. Even if only working with M, it is difficult to avoid the concept of activity measurement, as most definitions of the jungle of quantities and units that are used in radiocaron measurements stems from the early days of radiocaron dating. In this paper we will review the asic calculations used in radiocaron measurements and we will try to summarize the different quantities and units used. Unfortunately, some quantities have more than one definition, and we will make recommendations of how to use the different expressions.. ctivity measurement The asic information needed in a 14 C measurement performed y decay counting is the measured specific activity of the sample (à ), a standard (à stand ) and a ackground sample (à ). pecific activity equals the numer of decays per time and mass unit, and can e expressed e.g. as counts per minute and gram C (cpm/g C) or as Bq/kg C (I unit). To e representative, the standard and ackground should have undergone the same sample pre-treatment as the sample. The ackground arises oth from a contamination of the sample y caronaceous material (which can e of different specific activity) and from instrumental ackground. The net specific 14 C activity of the sample ( ) is a function of the measured specific 14 C activities of the sample (à ) and of the ackground (à ), and for the standard, stand is a function of à stand and Ã, that is ( ) ( ) = f, (1) 1 = f, () In the simplest case the net specific activities can e written as: = (3) = (4) More information aout ackground corrections when using M can e found e.g. in Donahue et al (1990) and antos (007). Estimation of error The ratio u = = (5) represents the sample activity relative to the standard. ll these quantities involved are affected y errors (counting statistics as well as other, more unspecified). It is important to know how these quantities add up to a total error σ u. For a function u of several variales u(x,y,z,..) the following formula is used (propagation of error): LUNFD6(NFFR-3111)/1-17/(011) 3

6 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations u u u u x y z σ... (6) x σ + σ + σ + y z Thus, σ u σ + u σ + u σ u (7) Performing the partial derivates yields 1 1 σ σ + σ + + σ ( ) u ( ) ( ) 1 = σ + σ + ( ) ( σ ) Dividing Eq. 8 with u yields σ u σ + σ σ + (9) u ( ) ( ) ( )( ) Hence the relative error σ u /u can e written as (8) σ u σ = + + σ σ u ( )( ) (10a) For young samples (Ã >> Ã ) this expression is reduced to σ σ σ u = + u (10) 3. Isotope fractionation Isotope fractionation is a process that occurs during chemical reactions as well as during physical processes, and this effect needs to taken into account in most radiocaron measurements. The effect of isotope fractionation is a partial separation of the different isotopes and results in enrichment of one isotope relative to another. In chemical reactions the isotopic fractionation can e a result of slightly different equilirium constants of the different isotopes for a particular chemical reaction. Evaporation, condensation and thermal diffusion may also result in significant fractionation. In the caron cycle isotope fractionation occurs when caron is transferred from one part of the ecosystem to another. s an example, when CO is asored y the leaves of trees and in plants during the process of photosynthesis, relatively more 1 C is asored than C, and C is asored to a higher degree than 14 C. Compared to C, 1 C in cellulose in wood from trees is enriched y a factor of aout % during this process. The fractionation in this case a kinetic effect: the heavier isotope proceeds LUNFD6(NFFR-3111)/1-17/(011) 4

7 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations slower through the photosynthetic process and is therefore depleted. This also means that the specific activity of caron in e.g. a leaf is lower than the specific activity of atmospheric CO that the leaf asored its caron from. Or, if speaking in terms of isotope ratios, the leaf will not have the same isotope ratio as the CO that it grew in. Fractionation can also occur in the laoratory, i.e. in incomplete comustion or reduction. In radiocaron dating this effect needs to e taken into consideration to e ale to compare the 14 C values of different materials, e.g. when comparing atmospheric CO data to tree ring data. To find the age of a sample, the activity of the sample is, asically speaking, compared to the activity of tree rings of known ages and well-determined isotope fractionation. Therefore, the activity of a sample is translated to the activity that the sample would have had if it would have een wood with a particular stale isotope composition. The procedure, called normalisation, is descried elow. First, however, we need to introduce the quantity δ C, which is a measure of isotope fractionation. Instead of stating the C/ 1 C ratios directly, isotope fractionation is more conveniently expressed as δ C, which is the relative deviation of the C/ 1 C ratio of the sample compared to that of a standard material, VPDB (Vienna Pee Dee Belemnite), expressed in per mil: 1 1 ( C/ C) ( C/ C) 1 ( C/ C) C 1000 (11) VPDB VPDB δ = The original standard material was caronate from a marine fossil collected from the Pee Dee Formation in outh Carolina, U. The fossil originated from an extinct squid-resemling organism called a Belemnite. This material, called PDB (Pee Dee Belemnite), had the C/ 1 C ratio of 1.7%. The high value reflects the marine origin of the material. The use of this standard therefore gives most natural materials negative δ C values. The PDB material has een exhausted and replaced y the limestone standard VPDB (NB19), which was manufactured from marle of unknown origin (Friedman et al, 198). ome typical δ C values are shown in Tale 1. The lower the δ C value, the heavier discrimination of C compared to 1 C in the material. Tale 1. Typical δ C values in nature (tuiver and Polach, 1977) Material δ C ( ) Marine caronates 0 (-4 to +4) tmospheric CO -9 (-11 to -6) Grains, seeds, maize, millet -10 (- to -7 Marine organisms -15 (-19 to -11) Bone collagen, wood cellulose -0 (-4 to -18 Grains (wheat, oats, rice, etc) -3 (-7 to -19) Recent wood, charcoal -5 (-30 to -0) Tree leaves, wheat, straw -7 (-3 to -) LUNFD6(NFFR-3111)/1-17/(011) 5

8 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 4. Normalisation Now let s look at the normalisation procedure, i.e. the translation of the measured activity to the activity that the sample would have had if it would have een wood with δ C = -5. For this purpose we introduce the C fractionation factor (Frac /1 ): C 1 C δ C= 5 Frac /1 = (1) C 1 C The 14 C fractionation factor (Frac 14/1 ) is approximately given y the square of the C fractionation factor (tuiver and Roinson, 1974): ( ) Frac Frac Frac Frac () 14 /1 /1 14 / /1 ccording to tuiver and Roinson (1974) an exponent of 1.9 may e more correct. The normalised specific activity of the sample, N, is thus given y C 1 C δ C= 5 N = Frac14 /1 ( Frac/1 ) = (14) C 1 C Using the definition of δ C (eq. 11), equation (14) aove can e rewritten as 5 C C VPDB N = = = δ C C δ C δ C C VPDB ( +δ ) 5 C (15) The last step is (eq. 11) is approximation which renders an error of maximum 1 for δ C-values etween -35 and +3. LUNFD6(NFFR-3111)/1-17/(011) 6

9 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 5. tandards Radiocaron measurements are performed relative to a standard of known activity (eq. 5). Due to the radioactive decay of 14 C the specific activity of any 14 C standard material decreases with time. Therefore the asolute radiocaron standard has een estalished. The specific activity of this asolute radiocaron standard ( as ) has een defined as (see e.g. Mook and van der Plicht, 1999): as =6 Bq/kg C. (16) as is intended to correspond to the hypothetical specific activity of atmospheric caron of year 1950, measured in 1950, making the assumption that this hypothetical atmosphere is free from human perturations and normalised to δ C = -5. as can e written as: λc (y 1950) as = 1950[ 5] e (17) where 1950[-5] means the specific activity of the hypothetical 1950 atmosphere, normalised to δ C=- 5, and decayed to the present. Please note that 1950[-5] corresponds to an activity measured at the present, while as refers to the value if measured in In the exponential λ C is ased on the Camridge half-life 1 of (T 1/ ) C =5730±40 years and y corresponds to the year of measurement: thus the exponential translates 1950[-5] to the value that it would have had in The real-world atmospheric 14 C level in 1950 was lower than as due to human influence. ince it was desirale that the hypothetical atmosphere should e free from the fossil fuel effects of the industrial revolution, wood from year 1890 (corrected for radioactive decay to 1950) was chosen to correspond to the asolute radiocaron standard. The principal radiocaron standard is NIT oxalic acid 3 I, also referred to as OxI, NB 4 or RM 4990 B (δ C value close to -19 ). The OxI standard was made from a crop of 1955 sugar eet. t that time the 14 C specific activity of the atmosphere had egun to rise due to the atmospheric testing of thermonuclear weapons 5. Therefore as is defined as 95% the specific activity, in D 1950, of OxI (normalised to δ C = -19 with respect to VPDB). In other words, the specific activity of OxI ( OxI ) is first measured and normalised to δ C = -19 giving the normalised sample activity ON : ( 19 +δ C) ON = 0.95OxI 0.95 OxI 1 (18) δ C This value is then corrected for decay since 1950 to otain asolute international standard specific activity, as : λc (y 1950) 1 1 as = ONe where λ C = yr and y is the year of measurement. (19) 867 The OxI standard is no longer commercially availale. ome other standards that are now availale are listed in Tale. 1 For further information aout half-lives, see section 9. National Institute of tandards and Technology; Gaithersurg, Maryland, U 3 C H O 4 4 From the former name of NIT: National Bureau of tandards 5 These detonations resulted in the om effect, which peaked in 1963 when the atmospheric 14 C level was aout twice the natural level. LUNFD6(NFFR-3111)/1-17/(011) 7

10 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations Tale. ome common radiocaron secondary standards tandard Material δ C ( ) pmc 6 OxII (RM 4990 C) Oxalic acid IE-C6 (NU) ucrose IE-C7 Oxalic acid IE-C8 Oxalic acid If using OxII, the equation of ON aove (eq. 18) ecomes (Donahue et al, 1990): ON = 1950[ 5] = 0.95OxI = OxII (0) δ COxI COxII 1 δ In M isotope ratios ( 14 C/ 1 C and/or 14 C/ C) are measured instead of specific activities. The specific 14 C activity of a natural sample is proportional to N( C) N( C) N( C) N( C) N( C) N( C) + + N( C) + N( C) N( C) (1) where N( 1 C), N( C) and N( 14 C) is the numer of nuclides of the different isotopes in the sample. ccording to Donahue et al (1990) the last approximation in (eq. 1) introduces an error of aout 0.1 equivalent to approximately 1 14 C year. Using the approximation in (eq. 1), (eq. 0) can e rewritten in terms of the isotopic ration 14 C/ 1 C (Donahue et al, 1990): C C 1000 C () 1 = 1 = 1 C C C 1950[ 5] OxI OxI C C δ δ OxII OxII That is, for 14 C/ 1 C measurements the term ( 14 C/ 1 C) has simply sustituted the specific activity. For 14 C/ C ratios the situation is somewhat different, as shown in Donahue et al (1990): C C C (3) = = C C C 1950[ 5] OxI OxI C C δ δ OxII OxII ee definition elow, (eq. 31) LUNFD6(NFFR-3111)/1-17/(011) 8

11 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 6. Radiocaron quantities and units There exist a numer of different quantities and units in the field of radiocaron measurements, and the suitale quantity to use is related to the particular type of measurement. In general there are three modes of reporting 14 C activities: 1) asolute activity (i.e. the specific activity of 14 C equal to the activity per kg of caron, usually expressed as Bq/g C or dpm/g C) ) activity ratio (the ratio etween the asolute activities of a sample and the standard 3) relative activity (the difference etween the asolute activities of a sample and the standard relative to the asolute standard activity) ccording to Mook and van der Plicht (1999) the asic definitions originate from decisions made at international radiocaron conferences. tuiver and Polach (1977) have tried to summarize what was used until 1977, and this paper is still frequently cited in the literature today. However, as also pointed out y Mook and van der Plicht (1999), some of these definitions can e confused and misinterpreted. n example is of percent modern, which in the tuiver and Polach paper has two definitions (and an incorrect sign in Tale 1 of the paper; it should e %). Therefore even more quantities, symols and units have een introduced over the years, and it can e discussed if this has improved the situation or made it even harder to sort out what different symols and units actually mean. Donahue et al (1990) introduced the quantity fraction of modern, using the symol F (which later has een denoted F m ) as descried in paragraph 6.5. lso this quantity has een widely used in the literature with another definition than the original. The aerosol community also use the term fraction modern, ut use the symol f M, and unfortunately two slightly different definitions of f M are in use. The aerosol field has also introduced the term fraction contemporary f c (Currie et al, 1989), which can e found in some 14 C source apportionment pulications. Mook and van der Plicht (1999) made an attempt clean up the mess y introducing new symols and definitions. These have however not een widely adapted, perhaps due to the reluctance to adapt a new nomenclature that is not very transparent at a first glance (the symols do not provide information that caron is involved). Reimer et al (004) have introduced a new symol for fraction modern, F 14 C, which is very useful for post-om calirations. mong the most frequently quantities used, which are descried elow, are 14 C, pmc, F m, f M, F 14 C and specific activity. LUNFD6(NFFR-3111)/1-17/(011) 9

12 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 6.1. Per mil depletion or enrichment with regard to standard These quantities and units do not take isotope fractionation into account (tuvier and Polach, 1977): 14 d C = (4) ON The term δ 14 C is used oth with and without age correction (y=year of measurement; x=year of formation or year of growth, λ C =(1/867) years -1 ): C (without age correction) (5) 14 δ = as (Eq. 5) corresponds to the 14 C content of the sample at the time of measurement. (Eq. 6) elow instead corresponds to the 14 C content of the sample at the time of growth: λc(y x) λc(1950 x) 14 e e δ C = = (with age correction) (6) as ON Here it is ovious that it is very important to state if δ 14 C is with or without age correction! 6.. Per mil depletion or enrichment with regard to standard normalised for isotope fractionation When taking isotope fractionation into account the d 14 C and δ 14 C aove (eq. 4-6) ecome (tuiver and Polach, 1977): 14 N D C = (7) ON C (without age correction) (8) 14 N = as λc(y x) λc(1950 x) Ne Ne = = (with age correction) (9) as ON (y=year of measurement; x=year of formation or growth, λ C =(1/867) years -1 ) Here is a source of misinterpretations. s Reimer et al (004) points out, there is a risk of confusion for and 14 C. equals 14 C only when the year of growth is the same as the year of measurement. Today, some authors actually mean (age corrected) ut use the term 14 C (called age corrected 14 C or 14 C corrected for decay ). s Reimer et al (004) point out, 14 C decreases with time and depends on the year of measurement. This means that a sample grown/formed e.g. in 1977 will give different 14 C if measured today versus if it was measured in and D 14 C do not change with time, since oth the standard and the sample decay at the same rate. LUNFD6(NFFR-3111)/1-17/(011) 10

13 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 6.3. Percent Modern (pm) and percent Modern Caron (pmc) pmc is frequently used for environmental samples and for post-om applications. Unfortunately, there are at least two definitions of percent Modern or percent Modern Caron. In tuiver and Polach (1977) it is stated: The 8 th International Conference on Radiocaron Dating (Proceedings, 197) accepted the replacement of D 14 C per mil y percent Modern, equated to the activity ratio N / ON x100%. Then these authors introduced a new term, asolute percent Modern (pm) as: N pm = 100% (30) as This ratio decreases with time and depends on the year of measurement, just like 14 C. In the ac program from NEC the following definition is used (the same as at the 8 th International Conference on Radiocaron Dating): N pmc = 100% (31) ON This ratio is constant over time, and thus the values of the standards in Tale are according to this definition. It would have een convenient if pm was only used for ( N / as ) 100%, and pmc was reserved for ( N / ON ) 100%. This is however not the case: some authors use pmc as ( N / as ) 100%. lthough the difference etween the two is rather small today ( as / ON is in 011), it will ecome more important with time. Thus, we should always state what definition we use! Below we use the definition ( N / ON ) 100% (eq. 31) Fraction of modern: F, F m, f M Donahue et al (1990) introduce the term fraction of modern, F, as 14 C C = C C [ 5] F (3) [ 5] ccording to the equations in the section tandards (eq. 0,, 3) aove this equals C C C C F = = = (33) [ 5] [ 5] N C C ON C C 1950[ 5] OxI[ 19] Thus, using equations (7) and (31) 14 N D C pmc N F = = + 1 = = (34) (1950 y) /867 ON % ase In Donahue et al (1990) there is a discussion aout ackground corrections, and the authors introduce the term F m as the measured fraction modern, which should e sujected to ackground correction to LUNFD6(NFFR-3111)/1-17/(011) 11

14 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations otain the true fraction modern of the sample, F. omehow, other authors have picked up F m (or f M ) instead of F as the term for true fraction modern of the sample. s stated y Reimer et al (004) the term fraction modern has een used with and without δ C-normalization of the sample activity, which is unfortunate. Furthermore, in e.g. aerosol science the term fraction modern is associated to the symol f M and is if often unclear if the definition N / ON or N / as has een used. E.g. in Currie et al (1989) it is stated (in the glossary at page 461): modern caron 0.95 times the 14 C specific activity of RM 4990B, normalized to δ C=-19 (PDB). ample caron is normalized to C=-5 (PDB); the per mil difference of the normalized sample / modern-caron ratio from unity is denoted 14 C. This statement is confusing. The first sentence must refer to ON (eq. 0), otherwise it should have een added that it refers to the activity as if measured in Then the second statement does not agree with the tuiver & Polach definition of 14 C (eq. 8) (in this there is as and not ON ). Either modern caron should e the specific activity of RM 4990B (OxI) as if measured in 1950, or it should e instead of 14 C Fraction Modern, F 14 C Reimer et al (004) highlight the prolems with the different terms and symols in radiocaron measurements for post-om samples and propose = 14 N F C (35) ON F 14 C, like pmc (eq. 31), D 14 C (eq. 7) and (eq. 9), do not change with time (does not depend on the year of measurement). F 14 C has to our knowledge not een sujected to misinterpretations in the literature, and we recommend the use of this unit for post-om samples Fraction contemporary, f c In some papers using 14 C for source apportionment of organic aerosols the term fraction contemporary f c is used (e.g. Currie et al, 1989, zidat et al. 004), and is defined as the ratio etween fraction modern in the sample and fraction modern in contemporary caron in the year of sampling. The f c this method render is however only correct if all modern caron in the sample has the same fraction modern as the atmosphere the year of sampling. tmospheric organic aerosol may however originate from iomass which has accumulated 14 C over decades with varying atmospheric F 14 C values. Lewis et al (004) has comined the atmospheric 14 C values with a growth function of a tree to calculate how the 14C concentration varies with the age of the tree. In their paper the calculation is done for trees harvested in They used the equation: t F 14 C = F 14 C (t) t1 t w(t)dt w(t)dt t1 where F 14 C is the fraction modern caron in the atmospheric CO at time t. w is a weighting function to determine the incorporation of caron into the iomass as a function to time. LUNFD6(NFFR-3111)/1-17/(011) 1

15 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations w is calculated y deriving the Chapman-Richards growth model presented in Lewis et al. (004): V = (1 e (t t 0) τ ) m In the equation V is the volume of the tree or the iomass of a community. t is the year of measurement and t 0 is year when the tree starts to grow., τ and m are selected to fit the growth of the iomass. Lewis et al. (004) used τ = 50 and m = 3. The value of is irrelevant once the function has een derived. Using the same equation and parameters to calculate F 14 C - using values from atmospheric measurements y Levin et al. (008 and personal communication) and tuiver and Quay (1981) - the F 14 C value depends on age of the tree and when it was harvested. For trees harvested in 007 the effect is most important for trees which are etween 60 and 70 years old where the values range etween 1.1 and 1.3. For a 30 year old tree the F 14 C value is, according to the model, standard tree has to e assumed in order to derive the F 14 C content in iomass urning. The value to derive f c is ecause of different sources of the particles hard to do. We therefore recommend that f c is only used then there is one source of modern caron or the sources have the same 14 C concentration. s always it must e stated whether f c was calculated using normalised 14 C data and if asolute or relative standard is eing used. In the paper y zidate et al. (004) neither is to e found. 7. pecific activity and its relation to pmc and F 14 C In measurements of enhanced 14 C radioactivity (nuclear industry, iomedical research) the specific activity of the sample is required: = 6 Bq/kg C (36) as From the M measurements we get (pmc according to eq. 31): N N pmc = 100% = 100% (37) C (1950 y) ON ase λ Thus we need to de-normalise the sample activity N (eq. 15) to achieve : N = (38) δ C Now pmc can e written as: pmc = 100% (39) λc (1950 y) ase δ C Therefore the ratio of / as that we need to calculate the specific activity is given y: LUNFD6(NFFR-3111)/1-17/(011)

16 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations δ C = as 100% Finally, we can now write specific activity as: pmc λc (1950 y) e (40) δ C 1+ pmc 1000 = 100% δ C = 100% λc (1950 y) e 6 Bq/kg C pmc (1950 y) /867 e 6 Bq/kg C δ C = F C e (1950 y) /867 6 Bq/kg C (41) 8. Relation etween different units Tale summarizes some of the definitions of the different quantities used to express the 14 C content of a sample. Tale. ome common expressions of 14 C content Expression Comment (y 1950) /867 = e (eq. 19) as ON = ON 14 N D C C as 14 N = λc(y x) λc(1950 x) Ne Ne = = as ON N pmc = 100% ON (eq. 7) Without age correction (eq. 8) With age correction (eq. 9) (eq. 31) LUNFD6(NFFR-3111)/1-17/(011) 14

17 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations Below follows some useful conversions etween units (y=year of measurement; x=year of growth, =specific activity in Bq/kg C). F 14 C can e written as F C D C 1 pmc = C 1 e N N (y-1950)/867 = = + = = (1950 y) /867 + ON % ase Bq/kg C δ C (x-1950)/867 (y 1950) /867 = 1 e = e (4) Not normalized to C fractionation should e written with minuscules (small letters) to differentiate them from units using normalized 14 C concentrations which should e written with majuscules (capital letters), e.g.: d14 = ON δ14 = as LUNFD6(NFFR-3111)/1-17/(011) 15

18 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 9. Radiocaron age The radioactive decay law states: λt N(t) = N0e (43) where N(t) is the numer of nuclides at time t and N(t=0)=N 0. This is equivalent to λt N = ONe (44) and we have = = 14 N λt F C e (45) ON By convention 1950 D equals 0 BP (Before Present) is set to t=0. By another convention the decay constant, called the Liy decay constant (λ L ), is set to λ L =1/8033 yr -1. Please note that this value is not the same as the Camrige decay constant (λ C =1/867 yr -1 ). The conventional radiocaron age is given y 1 N N 14 T14 = ln = 8033ln = 8033ln F = 8033ln F C (46) C-years λl ON ON The Liy half-life 7 is then given y 1 T1/ = 8033ln = 5568 yr (47) L ( ) Then a sample with N = ON / has the radiocaron age 5568 BP. Equations (46) and (6) give the error t: ( ) t = F C (48) F C relative error of 1% thus gives t= radiocaron years =80 radiocaron years. useful expression for (or age corrected 14 C ) is given y comining (eq. 9) and (eq. 46). λl T14 ( C years λ C (1950 x) ) λc (1950 x) Ne = = e e ON T14 C years T cal years = e e (49) 7 This half-life was estimated y Liy. Later on (1960ies) an improved value of the half-life came into use, the Camridge half-life, (T 1/ ) C =5730±40 years. Even though the Liy half-life is not correct, it is still used to otain radiocaron age (which is further converted to calendar years: this process is called caliration). Moreover, neither the Camridge half-life may e entirely correct (Chiu et al, 007). LUNFD6(NFFR-3111)/1-17/(011) 16

19 Eriksson tenström, kog, Georgiadou, Generg & Johansson: guide to radiocaron units and calculations 10. Recommendations In your papers use a proper reference in for quantities, units and symols, and make sure that the definition cannot e sujected to misinterpretations (in particular pmc, 14 C and fraction modern) For post-om samples use F 14 C with (Reimer et al, 004) as reference. References rnold JR, Liy WF cience 3(110), Chiu T-C, Fairanks RG, Cao L, Mortlock R Quaternary cience Reviews 6, Currie L, tafford TW, heffield E, Klouda G, Wise, Fletcher R Radiocaron 31(3), Donahue DJ, Linick TW, Jull JT Radiocaron 3(), Friedman I, O Neil J, Ceula G Geostandards Newsletter 6, Mook WG, van der Plicht J Radiocaron 41(3), Reimer PJ, Brown T, Reimer RW Radiocaron 46(3), antos GM, outhon JR, Griffin, Beaupre R, Druffel ERM Nucl Instr Meth B49, tuiver M, Roinson W Earth and Planetary cience Letters 3, tuiver M, Polach H Radiocaron 19(3), zidat,., Jenk, T. M., Gäggeler, H. W., ynal, H.., Fisseha, R., Baltensperger, U., Kalerer, M., amurova, V., Wacker, L., aurer, M., chwikowski, M., and Hajdas, I Radiocaron 46(1), LUNFD6(NFFR-3111)/1-17/(011) 17