I’ve recently received a handful of queries as to how to interpret Be AMS results from the SUERC AMS facility so as to make sure they are properly standardized for use with the online exposure age calculators. This question is related to the issue of how the Be-10 half-life is related to the absolute isotope ratio of an AMS standard that I’ve discussed in this previous post and also this one.

Here is a screen grab of the header section of a SUERC results spreadsheet (with sample names blurred to protect the innocent).

After the column for the sample name, this shows the following data.

First, two columns headed “% of standard” and “$\sigma$ (% of standard)”. These columns are the most basic description of the actual AMS measurement: remember, what the AMS measurement actually does is compare the Be-10/Be-9 ratio in a sample to the Be-10/Be-9 ratio in a standard. The first line of the file tells us that a sample called “NIST,” which is presumably the NIST “SRM 4325” Be standard material, has a Be-10/Be-9 ratio that is 100% of the standard, without uncertainty. The NIST standard material, as already discussed, is a stock of Be whose Be-10/Be-9 ratio is independently known. What this means, therefore, is that the NIST standard is the standard to which all the measurements are referenced. Subsequent lines then describe the relationship between the 10/9 ratio in each unknown sample and that in the standard. The 10/9 ratio in the first sample, for example, is 0.465% of the 10/9 ratio in the NIST standard. These lines have uncertainties in this relationship; the size of the uncertainty mostly depends on how many Be-10 atoms were actually counted. So these two columns, once again, are the actual data that was collected by the AMS — the relationship between the 10/9 ratio in  a sample and that in a standard.

The overall goal of this exercise, of course, is to determine the actual Be-10/Be-9 ratio in your sample. So if we define $R_{U}$ to be the 10/9 ratio in an unknown sample, $R_{S}$ to be the 10/9 ratio in the NIST standard, and $R_{M}$ to be the ratio of 10/9 ratios that we have measured, then: i) we want to know $R_{U}$,  ii) $R_{U} = R_{S} R_{M}$, and iii) we have measured $R_{M}$, so iv) to compute the answer we want, we need a value for $R_{S}$.

As discussed in the previous post, the absolute isotope ratio of the NIST Be standard is based on two measurements: a measurement of the total amount of Be present, and a measurement of the activity, that is, the rate of radioactive decay, of the Be-10 present. Thus, a value for the Be-10 decay constant, or equivalently the Be-10 half-life, is required to compute this ratio. If we assume a value for the Be-10 half-life, we can compute the amount of Be-10 present in the standard material, we can then compute the absolute 10/9 ratio of the standard, and we can apply the measurement described above to compute the absolute 10/9 ratio for an unknown sample. This is what happens in the red, blue, and green columns above.

The red columns — columns 4 and 5 if in the screen grab above — have the header line “10Be/9Be t(1/2)=1.53 Ma.” What this means is that a value of 1.53 Ma for the half-life of Be-10 was used to compute the amount of Be-10 present in the NIST standard, and thus its absolute 10/9 ratio. Given the Be-10 activity actually measured and the equations in the previous post, this yields an absolute 10/9 ratio of 3.06 x 10^-11 for the standard. Then to compute the absolute 10/9 ratio in the first sample, we apply the relationship described above: 3.06 x 10^-11 x 0.00465 = 1.42 x 10^-13. Again, if we assume that the NIST standard material has an absolute isotope ratio of 3.06 x 10^-11, which follows from its measured activity and the assumption that the Be-10 half-life is 1.53 Ma, then this sample has a 10/9 ratio of 1.42 x 10^-13. One would describe this measurement as being “normalized to the NIST standard with an assumed isotope ratio of 3.06 x 10^-11.” To use an atoms/g concentration calculated from this measured ratio in the online exposure age calculators, one would refer to the table of standardizations here and use the “NIST_30600” standardization.

The next two columns, colored green, are headed “10Be/9Be t(1/2) = 1.34 Ma.” If we assume that the Be-10 half-life is 1.34 Ma, which was the value originally assumed in preparation of the NIST standard, then the activity measurement implies a true 10/9 ratio for the standard of 2.68 x 10^-11. This is the “certified” ratio for the NIST standard. In this case, we would compute the true 10/9 ratio of the sample by 2.68 x 10^-11 x 0.00465 = 1.25 x 10^-13. So we started with the same AMS measurement, but by assuming a different value for the Be-10 half-life, we obtained a different true isotope ratio for the NIST standard, and thus a different true isotope ratio for the sample. This value for the true 10/9 ratio in the sample would be described as “normalized to the NIST standard with an assumed isotope ratio of 2.68 x 10^-11,” and the standardization code for the online calculators is “NIST_Certified.”

The final two columns, colored blue, are headed “10Be/9Be t(1/2) = 1.36 Ma.” If we assume that the Be-10 half-life is 1.36 Ma, which was a value estimated by Kuni Nishiizumi as a byproduct of creating the implantation standards described in this previous post, then the activity measurement implies a true 10/9 ratio for the standard of 2.79 x 10^-11. In this case, we would compute the true 10/9 ratio of the sample by 2.79x 10^-11 x 0.00465 = 1.30 x 10^-13.  This value for the true 10/9 ratio in the sample would be described as “normalized to the NIST standard with an assumed isotope ratio of 2.79 x 10^-11,” and the standardization code for the online calculators is “NIST_27900.”

To summarize, there is a lot of redundant information in this spreadsheet. The actual measurement that was made — a comparison of the 10/9 ratio in the sample with that of the NIST standard — is presented four different ways. Personally, I find this confusing. The important thing, however, is that these all describe the same measurement. Calculating atoms/g in your sample using the ratio reported in the red columns and, in the online exposure age calculator, identifying it with the “NIST_30600” standardization, will yield the same exposure age as calculating atoms/g using the ratio in the blue columns and identifying it with the “NIST_27900” standardization.