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Author Topic:   14C calculations
RAZD
Member (Idle past 98 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 1 of 10 (714576)
12-23-2013 8:07 PM


In doing research for my new version of the age thread I came across this:

http://www.c14dating.com/agecalc.html

quote:
Modern standard

The principal modern radiocarbon standard is N.I.S.T (National Institute of Standards and Technology; Gaithersburg, Maryland, USA) Oxalic Acid I (C2H2O4). Oxalic acid I is N.I.S.T designation SRM 4990 B and is termed HOx1. This is the International Radiocarbon Dating Standard. Ninety-five percent of the activity of Oxalic Acid from the year 1950 is equal to the measured activity of the absolute radiocarbon standard which is 1890 wood. 1890 wood was chosen as the radiocarbon standard because it was growing prior to the fossil fuel effects of the industrial revolution. The activity of 1890 wood is corrected for radioactive decay to 1950. Thus 1950, is year 0 BP by convention in radiocarbon dating and is deemed to be the 'present'. 1950 was chosen for no particular reason other than to honour the publication of the first radiocarbon dates calculated in December 1949 (Taylor, 1987:97).

Conventional radiocarbon ages (BP)

A radiocarbon measurement, termed a conventional radiocarbon age (or CRA) is obtained using a set of parameters outlined by Stuiver and Polach (1977), in the journal Radiocarbon. A time-independent level of C14 activity for the past is assumed in the measurement of a CRA. The activity of this hypothetical level of C14 activity is equal to the activity of the absolute international radiocarbon standard.

The Conventional Radiocarbon Age BP is calculated using the radiocarbon decay equation:

t=-8033 ln(Asn/Aon)

Where -8033 represents the mean lifetime of 14C (Stuiver and Polach, 1977). Aon is the activity in counts per minute of the modern standard, Asn is the equivalent cpm for the sample. 'ln' represents the natural logarithm.

A CRA embraces the following recommended conventions:

  • a half-life of 5568 years;
  • the use of Oxalic acid I or II, or appropriate secondary radiocarbon standards (e.g. ANU sucrose) as the modern radiocarbon standard;
  • correction for sample isotopic fractionation (deltaC13) to a normalized or base value of -25.0 per mille relative to the ratio of C12/C13 in the carbonate standard VPDB (more on fractionation and deltaC13);
  • the use of 1950 AD as 0 BP, ie all C14 ages head back in time from 1950;
  • the assumption that all C14 reservoirs have remained constant through time.

Thus it appears that all the "14C-age" calculations are based on the old half-life value of 5568 years instead of the revised half-life of 5730 years ... and this is so (a) they can be compared to older dates so calculated and (b) to ensure that corrections would not be applied twice.

My interest is to convert graphs of "14C-age" vs calendar age to show ln[14C‰] vs calendar age.

It seems to me that Aon is a constant representing the 14C content in 1950 (although this is complicated by the 1890 wood standard correction for radioactive decay to 1950).

There also has to be a tie to 12C or total carbon .. ie Asn and Aon are counts of 14C/gram carbon (when using ALS) or similar, and this should result in the raw data via reversing the age formula:

Asn = Aon &bul; e^(-t/8033)

Anyone know what a good number for Aon is and what the volume of carbon it represents?


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RAZD
Member (Idle past 98 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 6 of 10 (714624)
12-24-2013 1:49 PM
Reply to: Message 5 by Coyote
12-24-2013 11:44 AM


Re: Examples?
From the site in Message 1:

quote:
Three further terms are sometimes given with reported radiocarbon dates. d14C, D14C and deltaC13.

All are expressed in per mille notation rather than per cent notation (%).
d14C represents the per mille depletion in sample carbon 14 prior to isotopic fractionation correction and is measured by:

d14C=((Asn/Aon) - 1)1000 per mille

D14C represents the 'normalized' value of d14C. 'Normalized' means that the activity is scaled in relation to fractionation of the sample, or its deltaC13 value. All D14C values are normalized to the base value of -25.0 per mille with respect to the standard carbonate (VPDB). D14C is calculated using:

D14C=d14C - 2(dC13 + 25)(1 + d14C/1000) per mille

This value can then be used to calculate the CRA using the equation given above.

Radiocarbon age=-8033 ln(1 + D14C/1000)

This still gives you an age based on the old half-life (-8033*ln(1/2) = 5,568)

If you want to use the modern value of 5730 then the multiplier is -8267, but this still doesn't correct for changes in atmospheric 14C levels over time.

... the conventional age was 5390±40.

And the 5730 age would be 5550 +/- 40 which then needs to be calibrated to atmosphere levels

Using the old values avoids the possibility of making this correction twice.

Enjoy


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This message is a reply to:
 Message 5 by Coyote, posted 12-24-2013 11:44 AM Coyote has responded

Replies to this message:
 Message 8 by Coyote, posted 12-24-2013 2:25 PM RAZD has responded

  
RAZD
Member (Idle past 98 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 7 of 10 (714626)
12-24-2013 2:24 PM
Reply to: Message 3 by Coyote
12-24-2013 12:13 AM


so
so it looks like the best I can do is convert to %Aon ...

t = -8033 ln(Asn/Aon)

-t/8033 = ln(Asn/Aon)

e^-(t/8033) = e^ ln(Asn/Aon) = Asn/Aon

For:

0,0001000.0
1,000883.0
2,000779.6
3,000688.3
4,000607.8
5,000536.6
6,000473.8
7,000418.4
8,000369.4
9,000326.2
10,000288.0
11,000254.3
12,000224.5
13,000198.2
14,000175.0
15,000154.5
16,000136.5
17,000120.5
18,000106.4
19,00093.9
20,00082.9
21,00073.2
22,00064.7
23,00057.1
24,00050.4
25,00044.5
26,00039.3
27,00034.7
28,00030.6
29,00027.0
30,00023.9
31,00021.1
32,00018.6
33,00016.4
34,00014.5
35,00012.8
36,00011.3
37,00010.0
38,0008.8
39,0007.8
40,0006.9
41,0006.1
42,0005.4
43,0004.7
44,0004.2
45,0003.7
46,0003.3
47,0002.9
48,0002.5
49,0002.2
50,0002.0

* compared to 1950 Aon standard

So the second column should represent the actual 14C measured compared to the 1950 Aon standard.

As you can see these amounts are getting quite small, especially when you compare this to the fraction of 14C to 12C at the 1950 standard.

... the conventional age was 5390±40.

This would be 511.2‰ of the 1950 Aon standard

Enjoy

Edited by RAZD, : near 1 half life


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This message is a reply to:
 Message 3 by Coyote, posted 12-24-2013 12:13 AM Coyote has acknowledged this reply

  
RAZD
Member (Idle past 98 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 9 of 10 (714630)
12-24-2013 2:29 PM
Reply to: Message 8 by Coyote
12-24-2013 2:25 PM


Re: Examples?
I have never worried about the difference between the original half-life of 5568 and the modern one of 5730. As noted above, most reporting uses the old figure, and often there is a note saying to multiply by 1.03 if you want to convert to the new one.

Yes, this is what the website in Message 1 says, and it is the convention adopted to ensure that dates aren't double corrected.

Thanks.


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


• • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •

This message is a reply to:
 Message 8 by Coyote, posted 12-24-2013 2:25 PM Coyote has responded

Replies to this message:
 Message 10 by Coyote, posted 12-24-2013 2:58 PM RAZD has acknowledged this reply

  
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