Converting 36Cl ratios to ACE format

Converting ³⁶Cl ratios to ACE format

In ACE, two Chlorine attributes are required to date ³⁶Cl samples; Cl, the Chlorine concentration and clRatio, the ratio of ³⁶Cl to Cl (see ACE Input Variables for further information). However these attributes are not the only ones by which ³⁶Cl nuclide inventories can be quantified, and other types of attributes could similarly be used to describe the cosmogenic inventory of Chlorine. For example Licciardi et al 2008 report values of measured ³⁵Cl/³⁷Cl and ³⁶Cl/³⁷Cl ratios of spiked samples (Table 1 below), which when combined with other information can be used to determine ³⁶Cl inventories:

Click on Table to expand

As the Licciardi et al dataset is included with ACE, the purpose of this post is to outline how the original ³⁵Cl/³⁷Cl and ³⁶Cl/³⁷Cl ratios are converted to ³⁶Cl to Cl ratios for use within ACE.

In a spiked sample, the measured concentration of any Cl nuclide is the sum of rock (original) and carrier (added sample with known ratio) concentrations. For the case of³⁶Cl:

$[^{36}Cl]_{meas} = [^{36}Cl]_{rck} + [^{36}Cl]_{carr}$

Where $[^{36}Cl]_{meas}$ is the measured concentration of ³⁶Cl, $[^{36}Cl]_{rck}$ the concentration in the original (unspiked) rock sample, and $[^{36}Cl]_{carr}$ the concentration in the carrier. Nuclide concentrations in the rock can therefore be calculated as the measured concentrations minus the carrier concentrations:

	³⁵Cl	³⁶Cl	³⁷Cl
Measured	$(\frac{^{35}Cl}{^{37}Cl})_{meas}. [^{37}Cl]_{meas}$	$(\frac{^{36}Cl}{^{37}Cl})_{meas}. [^{37}Cl]_{meas}$	$[^{37}Cl]_{meas}$
Carrier	$\frac{(1-en).w. A_v}{A_w}$	⁰	$\frac{en.w. A_v}{A_w}$
Rock	$(\frac{^{35}Cl}{^{37}Cl})_{meas}.[^{37}Cl]_{meas} \newline - \frac{(1-en).w. A_v}{A_w}$	$(\frac{^{36}Cl}{^{37}Cl})_{meas}.[^{37}Cl]_{meas}$	$[^{37}Cl]_{meas}\newline - \frac{en.w. A_v}{A_w}$

Where $(\frac{^{35}Cl}{^{37}Cl})_{meas}$ and $(\frac{^{36}Cl}{^{37}Cl})_{meas}$ are the measured Cl ratios (given in Table 1 above), $[^{37}Cl]_{meas}$ is the (to be determined) number of measured ³⁷Cl atoms, $en$ is the carrier enrichment factor (0.94 for Licciardi et al 2008, see footnote in Table 1), $w$ the carrier weight, $A_v$ Avogadro’s number and $A_w$ the atomic weight of Cl.

For convenience most of the terms in the table above are expressed in terms of $[^{37}Cl]_{meas}$ , as when this is known we can easily calculate $[^{36}Cl]_{meas}$ and $[^{35}Cl]_{meas}$ from the measured nuclide ratios. To determine $[^{37}Cl]_{meas}$ , we know that in the original sample $(\frac{^{35}Cl}{^{37}Cl})_{rock}$ = 3.127 by the natural abundances of these nuclides. By subsituting terms in the above table for $[^{35}Cl]_{rock}$ and $[^{37}Cl]_{rock}$ , we can rearrange the expression to get:

$[^{37}Cl]_{meas} = \frac{w.A_v}{A_w}\frac{en(1+\frac{^{35}Cl}{^{37}Cl})_{rock}-1}{(\frac{^{35}Cl}{^{37}Cl})_{rock}-(\frac{^{35}Cl}{^{37}Cl})_{meas}}$

After calculating $[^{37}Cl]_{meas}$ , all other terms in the table above can be computed, and from these clRatio, the ratio of ³⁶Cl to total Cl in the rock, which is used as an ACE input. Results are listed for each sample listed in Table 2 are given below:

Sample	[³⁷Cl]_meas	[³⁷Cl]_rock	[³⁶Cl]_rock	[³⁵Cl]_rock	clRatio

IC02-16	2.34E+19	4.35E+18	943695	1.36E+19	52.61
IC02-17	2.34E+19	4.29E+18	1030479	1.34E+19	58.28
IC02-19	2.30E+19	3.85E+18	853429	1.20E+19	53.75
IC02-20	2.01E+19	4.08E+18	852535	1.27E+19	50.74
IC02-17	2.01E+19	4.01E+18	1070024	1.25E+19	64.67
LEIT-1	2.29E+19	3.83E+18	982401	1.20E+19	62.17
LEIT-2A	1.98E+19	3.68E+18	935814	1.15E+19	61.73
LEIT-2B	1.98E+19	3.69E+18	1048548	1.15E+19	68.93
LEIT-3	2.06E+19	4.44E+18	1086694	1.39E+19	59.35
LEIT-4	2.02E+19	4.08E+18	942088	1.27E+19	56.02
LEIT-5	2.03E+19	4.27E+18	1001751	1.33E+19	56.95
BUR-1	2.31E+19	3.99E+18	1357844	1.25E+19	82.53
BUR-2	2.02E+19	4.34E+18	1049643	1.35E+19	58.71
BUR-3	2.08E+19	4.75E+18	1393224	1.48E+19	71.09
BUR-4	2.08E+19	4.68E+18	1135448	1.46E+19	58.91
BUR-5	2.02E+19	4.11E+18	933476	1.28E+19	55.11
BUR-6	2.09E+19	4.87E+18	1402267	1.52E+19	69.93
IC02-1A	1.87E+19	2.58E+18	2260624	8.07E+18	212.27
IC02-1B	1.82E+19	2.52E+18	1987581	7.88E+18	191.24
IC02-7	1.93E+19	3.21E+18	1404660	1.00E+19	106.18
IC02-10	2.14E+19	2.34E+18	1682564	7.30E+18	174.5
IC02-11	2.15E+19	2.37E+18	1681085	7.41E+18	171.99
IC03-9	1.85E+19	2.41E+18	1862454	7.51E+18	187.81

It is the values in the far right column of this table that are used clRatio, the ratio of ³⁶Cl to total Cl for the Licciardi dataset. The dataset can be downloaded here.

This entry was posted on Monday, March 23rd, 2009 at 4:48 pm and is filed under Software News. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.