You can discuss the Note about Pb concentration calculations here...

3 months later

Bence，Thank you very much for your patience to answer and write a small course，I don't quite understand that In Table 3, the count value of total Pb is 7004, and the count value of Pb206 is 5683. If you look at the count value alone, the total Pb content should also be higher than Pb206, but why the Pb206 calculated in Table 2 is 22.45ppm ,higher than total Pb 6.7ppm，This is an uncorrected value. Do I have any concepts that I don’t understand?

    chenhongjun Yes, if you look at the counts, it's obvious that there is more total Pb than just 206Pb. However, that is not how the concentration equation works (unless you use total Pb). The reason that the 206Pb concentration in Table 2 is higher (ignoring the result for Total Pb for just a second) is that the concentration equation assumes when you use NIST612 as your calibrant that 206Pb makes up about 24% of your Pb. When this is incorrect, and 206Pb makes up significantly more of your Pb (80% in our example), the concentration equation gets the wrong result.

    You can actually see this if you calculate the different isotopic abundances and look at their ratio. For example, in the Note, the zircon has 0.8 206Pb (proportion of Total Pb). The NIST612 calibrant has 0.24 206Pb (proportion of Total Pb). And we know from our calculations in the Note that the actual concentration of Pb in the zircon is about 6.7 ppm. When you ratio the Pb proportions, and multiply it by the actual concentration, you get the offset we see in Table 2. That is:

    0.8 ÷ 0.24 × 6.7 = 22.3 or roughly what we got for Pb concentration based on 206Pb in Table 2.

    If our isotopic compositions were the same, we'd get:

    0.24 ÷ 0.24 × 6.7 = 6.7 i.e. the correct value.

    The little equations above have just stripped out the parts of the concentration equation that deal with converting a CPS value to a ppm value, and just look at the isotopic composition part.

    I hope that helps to clarify. If you have more questions, please just let me know.

      Bence,I probably understand the principle of your concentration calculation equation. At the end of the Note，You calculated the corrected concentrations，As shown in Table 5，But as we said, totalPb=204+206+207+208，So the correct total lead content should be 26.61ppm，Instead of 6.7 in Table 2.Unless these four values are all wrong. But you said in the last sentence“TotalPb gives us the best estimate of the Pb concentation in our sample”.So which value is correct? each corrected isotope value or the total lead value？ I am quite confused.

      I think the confusing part is that Table 2 does not show the concentration of each isotope. Rather, it shows the concentration of Pb in our sample calculated from each isotope.

      If we look at the concentrations calculated from each isotope, we can see that Total Pb gives us the best estimate, because it is unaffected by the isotopic composition issues described in the Note (because it is 100% of Pb by default).

      Table 5 was included just to show that if you correct for isotopic composition, the concentration of Pb calculated from each of the four isotopes is all approximately the same, and that this value is the same as that calculated from Total Pb.
      All good questions! 😃

      Bence，I understand what you mean！That is to say, what we actually calculate is the total lead content, even if it is expressed by different daughter isotopes, if I want to calculate the content of each isotope, such as 206, directly multiply the abundance of this isotope in zircon , You can get its content

        Bence Haha, thank you very much. In addition, I used iolite to process an apatite age with McClure as the standard sample, but the upper intersection point of 207Pb/206Pb in the TW graph is relatively low (0.18-0.2), I don’t know where to ask such questions.

          Feel free to post such questions here on the forum, but I would recommend starting a new discussion so that we can focus on the U-Pb side of things.

          The good thing about posting these sorts of questions is that I'm sure others have (or will have) the same questions, and the answers can help everyone.

          Please provide as much detail as you can. If we can't work it out with the detail you provide, we might ask that you send us your experiment, and we can help from there.

          • Bence

          Thank you very much, I am creating a new discussion to better solve my apatite dating problem