I apologize in advance for this long-winded explanation of a DRS I am posting!
I have posted a DRS with an alternative approach to reducing LA Hf data. The DRS is really only a small modification of an approach that has been used before (I am afraid I do not know all the references). The approach is to apply a scaled Hf mass bias factor (BetaHf) for the Yb and Lu interference removals. In low-Yb zircons, an internal (i.e., determined internally for each measurement) Yb mass bias factor (typically based on 173Yb/171Yb) cannot be precisely determined, leading to large measurement (“internal”) uncertainties in the 176Hf/177Hf. Scaling the much-more-precisely determined BetaHf to apply to Yb and Lu results in much more precise final 176Hf/177Hf ratios. I am certain that I have seen this approach in other Iolite Hf DRS before (again, sorry I do not know all the references), which have allowed the user to enter a single factor to scale BetaHf.
The small modification in the DRS I have posted allows this scaling factor (“XBeta” = BetaYb/BetaHf) to be determined using a high Yb/Hf reference zircon. There are two small advantages of this approach over the user-chosen scaling factor: 1) A spline can be fit to the high Yb/Hf reference zircon selections, which is useful if “XBeta” changes throughout an analysis sequence. 2) The high Yb/Hf reference zircon can be used to determine this factor, instead of iteratively guessing at it in the DRS settings to find the scalar that most accurately reproduces the 176Hf/177Hf of the secondary reference zircons. If no high Yb/Hf reference zircon was measured, this option can be unchecked, and the single user-chosen scaling factor can be used instead.
One or more high Yb/Hf reference zircons should be used regardless to ensure that the 176Yb correction is done accurately in samples which commonly have Yb/Hf that exceed most of the widely used natural reference zircons (e.g., Mud Tank, Plešovice, 91500, GJ-1, etc.). See Fisher et al. (2011; Chemical Geology) for a thorough discussion of this. By default, the DRS uses MUNZirc4 (if the selection group exists) synthesized and characterized in that study, but other high Yb/Hf reference zircons (e.g., R33) could be used instead. You could even use an in-house zircon sample with high Yb/Hf, even if the 176Hf/177Hf is not well characterized. The calculation simply constrains BetaYb/BetaHfit does not rely on a reference Hf isotope ratio.

I should also note that I have seen the “Hf Isotopes” DRS, which I think comes standard with recent versions of Iolite 4. It seems to me (please, anyone, correct me if I am wrong) that DRS uses a Hf mass bias factor for all ratios but calculates an "optimal" 176Yb/173Yb (different from the canonical ratio) that most accurately subtracts the 176Yb interference. It also seems to do some sort of muti-standard optimization, which presumable finds the optimal 176Yb/173Yb that minimized bias in the final 176Hf/177Hf for the multiple standards. Again, I am not certain my understanding of this DRS is correct (there doesn’t seem to be any documentation). If my understanding is correct, this indeed seems like a good alternative approach to scaling the Hf mass bias factor for Yb. Perhaps someone could compare the results from the two approaches…

A few things to note if you decide to use this DRS:

1) The final normalized 176Hf/177Hf (normalized to 176Hf/177Hf of a reference zircon; we typically use Plešovice; magnitude of final normalization is usually very small in our lab) result calculated with “XBeta” is called “StdCorr_Hf176_177x”.

2) If the “Use reference material for XBeta?” toggle is unchecked, the “StdCorr_Hf176_177x” result will instead be calculated with the single user-chosen scaling factor entered below (“Scale Hf Beta for BetaYb”), which is 1 as default.

3) The 176Lu correction is pretty small, so it probably does not make a big difference, but the scaled Hf mass bias factor (scaled by “XBeta”) is also used for Lu.

4) It is a good idea to take a look at the “XBeta” spline for the “Yb Beta Reference material”. If it is overfit or if there is one wonky measurement, this can have a big effect on the StdCorr_Hf176_177x of high Yb/Hf standards and samples. In fact, a mean spline often works best (sort of defeats the purpose of using the spline instead of a single scaling factor, but oh well).

5) The “Reference material for XBeta” is not self-normalized in any way, so it can still be treated as a “secondary” or quality-control standard. It simply is used to calibrate “XBeta” (BetaYb/BetaHf).

6) You may notice that the “XBeta” for other standards and samples can be quite different than those determined for the “Reference material for XBeta”. They probably also have very large measurement uncertainties due to low Yb signals. The BetaHf is scaled using the XBeta spline calibrated by the “Reference material for XBeta”, not these results, so don’t worry about it. However, if the XBeta for a standard or sample with high Yb/Hf is very different than the “Reference material for XBeta”, then you might consider whether this approach is best for that sample!

7) The final normalized 176Hf/177Hf calculated using the internal BetaYb (that determined internally for each measurement) is also calculated and is called “StdCorr_Hf176_177”. Again, you will probably notice that the uncertainties on this are quite large for low-Yb zircon.

8) Scrutinize your results! In almost all cases in our lab, the “XBeta” approach accurately (and precisely) reproduces the 176Hf/177Hf of a range of standards with a wide range of Yb/Hf. However, in a few cases, I have noticed that the internally determined Yb mass bias factor (described in point 7 above) yielded more accurate results. I typically apply some criteria (Yb/Hf of the measurement and magnitude of the discrepancy between the two results) offline after exporting the data from Iolite to decide which result to report. My approach with these criteria (described in the methods appendix of Granseth et al. (2021; Gondwana Research)) may be a bit overcomplicated and should not necessarily be adopted. The point is that the “XBeta” approach doesn’t guarantee (obviously) the most accurate results, so it is necessary to scrutinize the data as you normally would.

Finally, a couple notes about references: I used the “Hf Isotopes Example” from the iolite4-python-examples drs folder on GitHub. I was informed by Bence that the basic calculations there probably originated from Woodhead et al. (2004; Chemical Geology), including the direct determination of BetaYb instead of assuming BetaHf for Yb and Lu (as apparently was done before). As I mentioned, the approach of scaling BetaHf for a more precise 176Hf/177Hf instead of using the internal BetaYb has certainly been implemented before me, but I don’t have an overview of appropriate references. If you use the implementation in this DRS (and want to be generous), you can cite Granseth et al. (2021; Gondwana Research) and find a description of the main DRS steps in the methods appendix there. It was an Iolite 3 DRS used there, but the calculations are nearly the same. Steps 17 are all that is relevant; you can ignore the bit about the offline result selection based on various criteria.

Good luck!