## Pb concentration calculations and TotalPb_ppm

· ☕ 4 min read · ✍️ Bence

This note is to address some questions we’ve recently received about the Pb concentration calculation in iolite, and in particular why when measuring the Pb concentration in zircons you get very different concentrations for each of the Pb channels. That is to say, assuming you’ve measured 204Pb, 206Pb, 207Pb and 208Pb, iolite will calculate a concentration channel for each, along with a “Total Pb” channel, so you’ll have results for 204Pb_ppm, 206Pb_ppm, 207Pb_ppm, 208Pb_ppm and TotalPb_ppm.

For most samples, these values would be within error of one another, with 204Pb_ppm being the least precise (due to low counts) and 208Pb_ppm or TotalPb_ppm being the most precise (due to having the most counts). This is assuming that you have “normal” Pb isotopic abundances in your sample. By normal here, I mean that if you’re using a NIST glass for calibration, your sample also has roughly similar Pb isotopic abundances. In case you’re not familiar with the isotopic make up of modern common Pb, typical isotopic abundances are shown in Table 1.

204Pb 206Pb 207Pb 208Pb
1.4% 24.1% 22.1% 52.4%

#### Table 1: Modern Common Pb Isotopic Abundances e.g. source

If you use, for example, NIST610 to calibrate zircon analyses you may see significantly different values for each of the Pb_ppm channels. Just as an example, below are some concentrations from a randomly selected zircon calibrated with NIST610.

Pb204_ppm Pb206_ppm Pb207_ppm Pb208_ppm TotalPb_ppm
0.70 22.45 1.16 1.88 6.70

#### Table 2: Example Zircon Pb Concentrations (measured relative to NIST610)

Pb concentrations in this example zircon vary from 22 ppm to less than 1 ppm. So, what is going on? Which is the “correct” concentration?

Well, zircons quite regularly have very different Pb isotopic abundances than common Pb. If you’ve measured all four Pb isotopes (or with only very slighly less precision 206Pb, 207Pb and 208Pb), you can calculate the isotopic abundance of each isotope by ratioing the baseline subtracted counts for each channel to the baseline subtracted TotalPb counts. Here are those values for our example zircon (Table 3) along with the calculated isotopic abundances (Table 4).

Pb204_CPS Pb206_CPS Pb207_CPS Pb208_CPS TotalPb_CPS
10.40 5683.54 265.94 1042.94 7004.60

#### Table 3: Baseline Corrected Counts for our example zircon

204Pb 206Pb 207Pb 208Pb TotalPb
0% 81% 4% 15% 100%

#### Table 4: Calculated Isotopic Abundances for our example zircon

This is a rough calculation of isotopic abundance (it does not take into account mass bias), but it is probably sufficiently precise for trace element calculations such as this. You can see that 206Pb in this example comprises over 80% of total Pb, compared to ~24% in normal Pb.

How does our concentration calculation take this into account?

Well, normally we assume that our sample and calibration material have the same isotopic composition, and so we slightly simplify the concentration calculation. Here’s a simplified version of the Longerich et al. equation, where I’ve left out the internal standard part (it’s not important for this discussion):

$$\text{[Pb]} = \frac{CPS_{samp}}{CPS_{RefMat}}[Pb]_{RefMat}$$

Where [Pb] is the concentration of Pb in the sample,
CPSsamp is the baseline subtracted counts per second for the sample,
CPSRefMat is the baseline subtracted counts per second for the Reference Material, and
[Pb]RefMat is the concentration of Pb in the Reference Material.

If we were to include the isotopic composition of the sample and reference material, and use for example 206Pb as our channel of interest, the equation would actually look like this:

$$\text{[Pb]} = \frac{CPS_{samp} / [206Pb]_{samp}} {CPS_{RefMat} / [206Pb]_{RefMat}}[Pb]_{RefMat}$$

Where [206Pb]samp and [206Pb]RefMat is the isotopic abundance of 206Pb in our sample and reference material, respectively. If our sample and reference material have the same isotopic composition, [206Pb]samp and [206Pb]RefMat will be the same value and can be simplified from the equation.

We can see the effect of using the correct isotopic abundance for our example zircon by multiplying the concentrations in Table 2 by the appropriate normal Pb isotope abundance and dividing by the calculated isotope abundance for our sample. For example, the corrected 206Pb concentration would be calculated by:

$$[Pb]_{corr} = \frac {0.24[Pb]} {0.81}$$
$$= \frac {0.24(22.45)} {0.81}$$
$$= 6.7 ppm$$

If we repeat the same process for the other Pb isotopes in our example, using the calculated isotopic abundances from Table 4 and the common Pb isotopic abundances in Table 1, we get the following corrected concentrations:

Pb204_ppm Pb206_ppm Pb207_ppm Pb208_ppm
6.56 6.67 6.75 6.63

#### Table 5: Recalculated Pb concentrations for our example zircon

You can see that they all come out approximately equivalent to the original TotalPb concentration reported in Table 2 (6.7 ppm).

So, to answer the original question: which ppm result is the ‘correct’ one? Well, in this case where our sample does not have the same isotopic composition as our reference material, TotalPb gives us the best estimate of the Pb concentation in our sample.