Not strictly carbonate samples but you might see some tips in our method for ice core CO2 with a MAT 253 and microvolume. The amount of CO2 we can extract from the ice cores is very small so there may be some analogies. I once calculated what the equivalent sample size of CaCO3 would be and it should be about 10ug. Overall, we can get precisions of 0.02 per mil for d13C-CO2 some of is the gas extraction.
My advise would to spend a lot of time tuning the source and don’t overly sacrifice linearity for sensitivity (i.e. there was never any advantage of going above 1.5 mA). Also you have to spend a lot of time optimising the capillary crimps and watch out for flow-regime non-linearity at the lowest end. It’s imperative that the reference and sample signals match throughout the run, particularly as you approach the lowest voltages*. That probably sounds very vague but I guess you just have to do lots of zero-enrichment experiments and then stare plots of the m44 signal versus your raw ratios and delta values until you find your instruments goldilocks zone. Then when it is all said and done you just need to calibrate down in that range and you should be fine.
*I think the Thermo software and the speed of the bellows adjustment is a little inadequate for the very small samples so I had a method were I would do my own “pre-adjustment” based on manometric measurements of the total CO2 in the sample we get offline. Otherwise, if the bellows has to re-adjust, you’ve effectively lost your entire sample. This must be possible with a Kiel Device (or equivalent).
https://www.atmos-meas-tech.net/7/3825/2014/amt-7-3825-2014.pdf
PS. Another tip would be to have Alan Mix on your thesis committee.
Cordially,