In a previous post I tried to clear up some of the confusion surrounding the fact that the “absolute” isotope ratio in a standard used for AMS measurement of Be-10/Be-9 ratios is defined based on a decay-counting measurement, so what you think this ratio is depends on what you think the half-life of Be-10 is. To review this a bit,

1. The measurement we need to compute an exposure age is the amount of Be-1o in a sample. We determine this by measuring the amount of Be in our sample, determining the Be-10/Be-9 ratio by AMS, and  multiplying.

2. AMS measurement of the 10/9 ratio is done by comparing the 10/9 ratio in the sample to the 10/9 ratio of a standard  whose absolute isotope ratio is already known.

3. The absolute isotope ratio of the standard is usually defined by a decay-counting measurement to determine how much Be-10 is present. This requires knowing the half-life of Be-10. If you use a different value of the half-life,this implies a different absolute isotope ratio for the standard, a different isotope ratio for your sample, and, eventually, a different exposure age. So from this perspective, an exposure age can be said to be “normalized to a particular value of the half-life.” Unfortunately, this description is extremely confusing if you are not completely familiar with the preparation of AMS standards.

The point of the previous post was to make all readers completely familiar with the preparation of AMS isotope ratio standards. In case that failed, the point of this post is to explain how to reduce the confusion caused by the semi-equivalency of the value of the Be-10 half-life and the number of Be-10 atoms in your sample. I summarize a couple of steps that have been taken in the past few years to alleviate this, as well as recommendations for how to keep things simple and reduce confusion as much as possible.

Step 1. Make an AMS standard whose absolute isotope ratio is determined independently of the Be-10 half-life. Kuni Nishiizumi and a number of co-authors accomplished this in a 2007 paper:

K. Nishiizumi, M. Imamura, M. Caffee, J. Southon, R. Finkel, and J. McAnich. Absolute calibration of Be-10 AMS standards. Nuclear Instruments and Methods in Physics Research B, 258:403–413, 2007.

These authors made the observation that the whole point of an accelerator mass spectrometer is to detect and count the number of atoms of Be-10 that enter a detector. If you could hang onto all those atoms, you would have a precisely determined number of Be-1o atoms that could be used to mix up an AMS standard with known 10/9 ratio. And you would not have determined the number of atoms of Be-10 by decay counting, so this would be independent of the Be-10 half-life. They implemented this very smart idea by placing a silicon wafer in the LLNL AMS detector array that would trap Be-10 atoms entering the detector. They then put a Be-10-rich cathode in the accelerator source and injected a large number of Be-10 atoms into the detector. These were detected, counted, and came to rest in the silicon wafer. They then dissolved the wafer and added a gravimetrically determined amount of Be-9. The result: a stock of Be (I will call this the “implantation standard”) whose absolute 10/9 ratio was known independently of the half-life. They then used this stock of Be to prepare several samples for AMS analysis, and used the AMS to compare the 10/9 ratio of this material to that in commonly used AMS standards (whose isotope ratios were previously only known by a decay-counting measurement). The result: absolute measurements of the 10/9 ratios in these standards that were independent of the value of the Be-10 half-life.

This is an enormously valuable contribution because it decoupled the question of “how many atoms of Be-10 are there in my sample” from the question of “what is the Be-10 half-life.” In addition, this paper includes a long list of absolute isotope ratios determined for various commonly used AMS standards, all referenced to the implantation standard. This list is important because it allows interrelation of AMS measurements normalized to different standards. For example, these measurements showed that the “07KNSTD3110” standard  material has an absolute 10/9 ratio of 2.85 x 10^-12. If we want to compare that with measurements made against the “LLNL3000” standard material with an assumed isotope ratio of 3 x 10^-12, the intercomparison measurements in this paper reveal that we have to multiply the latter measurements by 0.8644. Some of these intercomparison measurements existed before, but this paper put a large set of internally consistent intercomparison measurements in one place.

Step 2. Strongly encourage anyone calculating exposure ages and/or erosion rates to determine and specify the Be measurement standard used for their AMS measurements. This is critically important for the usefulness and scientific longevity of AMS results — if there’s no information about what actual AMS standard measurements are linked to, then it’s impossible to determine how many atoms of Be-10 are actually in the samples. If you can’t determine how many atoms of Be-10 were observed in a study, then obviously the study is totally useless to future researchers.

This is easy for some measurements — because the AMS lab that made the measurements places this information at the top of all of their results spreadsheets supplied to users. Some labs (i.e., LLNL) clearly state the standard material that they used along with the absolute isotope ratio assumed for that material. This is the simplest and easiest-to-understand approach. Other labs  (i.e., SUERC) state the standard material used and the half-life of Be-10 that they used to define its absolute isotope ratio. This approach provides the information in a somewhat less accessible form: the user must obtain more information (i.e. the activity of the standard) to determine what absolute isotope ratio was assumed for the standard. As discussed in the last post, stating the half-life assumed in interpreting the activity of the standard material does fully define the standardization, but experience shows that it is much more confusing for users who are not familiar with how AMS standards are produced. Other labs (e.g., PRIME) do not by default supply standardization information with their results, so users must look on a lab website (e.g., here for PRIME) or fish around in the AMS literature. This approach is the least optimal.

In 2009, I decided that the best way to address this situation was not simply to hector scientists about proper data reporting (although this is also a popular strategy, as documented in this post) but to give them an incentive to do it properly. The online exposure age calculator provided this opportunity. The calculator had started to become very commonly used by Earth scientists who wished to use cosmogenic-nuclide exposure ages and erosion rates in their research, but were not specialists in the method and were not completely familiar with all details of Be-10 measurement and production rate estimation. I modified the online calculators to require as input a description of the Be-1o AMS standard used for the measurements. Basically, I trolled through the tables in the Nishiizumi et al. (2007) paper as well as some other published intercomparisons, and defined a number of possible combinations of actual standard material and assumed isotope ratio. These possible standardizations are tabulated here. This meant that users had to figure out which of these standardizations applied to their measurements, and enter it. Because the online calculator was supplying users a valuable and time-saving service — computing exposure ages according to commonly accepted practice without requiring the user to understand all details — users were willing to incur a small amount of extra work, that is, figuring out the AMS standard used for their measurements, to gain this benefit. The way this happened in practice was that users would ask their AMS lab which standardization applied — the AMS folks would either tell them (if the relevant standard was tabulated) or contact me to add their particular standard/ratio comparison to the approved list. Basically, this worked — by providing users a benefit for properly assembling the information, they became motivated to obtain this information from those responsible for their AMS measurements. In addition, the fact that all users of the online calculator knew that this information was required, motivated them to demand it from others in the course of paper or proposal review. Essentially, adding a standardization requirement to the online calculator harnessed worthwhile incentives and peer pressure to improve data reporting. At present, nearly all publications about cosmogenic-nuclide exposure dating properly describe the standardization of their Be-10 measurements. This is a huge improvement over the past situation.

Recommendations. Finally, I have some recommendations for the best way to make Be-10 measurement standardization as clear as possible for all users.

The first is to reduce confusion about the link between the half-life of Be-10 and the assumed isotope ratio of a standard by not describing AMS standards in terms of a half-life. This means saying “the NIST SRM 4325 standard with an assumed 10/9 ratio of 2.68 x 10^-11” and not saying “the NIST SRM 4325 standard with a Be-10 half-life of 1.34 Ma.” It also means not making statements such as “these Be-10 measurements are normalized to a Be-10 half-life of 1.5 Myr.” The reasoning here is as follows: what we are really trying to do is determine the number of atoms of Be-10 in a sample. Thus, we should describe how these measurements are standardized by likewise stating how many atoms of Be-10 are in the standard. In addition, all AMS standards must by definition have an absolute 10/9 ratio, but this is not always determined by decay counting. Thus, the absolute isotope ratio is a common descriptor that can be applied to any AMS standard. Yes, it is true that stating a standard material and an assumed half-life does fully and correctly describe an AMS standard — but it’s a lot less confusing to keep separate the question of “how many atoms of Be-10 are in my sample” from “what is the half-life of Be-10.” IT IS LESS CONFUSING to describe standards in terms of an assumed 10/9 ratio. Keep things simple — first, determine how many atoms of Be-10 there are in your sample. Then, after you’ve figured that out, decide what value of the Be-10 half-life should be used to interpret your results (see this post).

The second is to use AMS standards whose absolute isotope ratios are linked to the Nishiizumi implantation experiment, not to a decay-counting measurement. This is why the online exposure age calculator renormalizes all data to the “07KNSTD” standardization, which is derived from the implantation experiment. Again, this keeps the question of “how many atoms” separate from “what is the half-life.” This issue is alleviated somewhat now that accurate measurements of the Be-10 half-life exist — and in principle, using the new half-life measurement with existing activity measurements for AMS standards most likely yields more precise absolute isotope ratios for many AMS standards than does referencing them to the Nishiizumi implantation standards — but converting this half-life measurement into new absolute isotope ratios for decay-counting-based standards has not really made it into published form yet. So I may take back this recommendation in future.