Small Sample Mass Correction

Empirical evidence suggests that constant contamination of samples has an inverse mass relationship which becomes important for small sample sizes. Many laboratories apply an inverse mass correction to normalized background values, but at the CHRONO Centre we apply it to the fractionation corrected C14/C12 ratio of the unnormalized background (BR0 / BR1^2) . The reason is that our standards are produced in large batches and any dependence on mass in the contaminant is in the sample and not the standard. Denoting average R0 ratios with avg and uncertainties with sig, we write

and then use a spectrum of masses to perform a least squares fit to determine the constants a and b and their uncertainties.

Using some results from Bevington, Data Reduction and Error Analysis, if a dataset is modelled as

then the coefficients a and b and their uncertainties can be computed from a least squares minimization:

For the data collected to date for spar calcite we have a=0.195769233e-15 and b=1.68462365e-15. We have carried out a similar analysis for combusted coal backgrounds and do not believe the results to be sufficiently different to warrant maintaining two sets of constants.

In practice we have chosen to implement the small sample correction by shifting the curve vertically so that there is no correction applied to samples of mass equal to our ~1mg background.