…using the following parameters:
(1.a) Compute abundance ratios of 13C/12C, 17O/16O and 18O/16O
(1.b) Compute abundances of 12C, 13C, 16O, 17O and 18O
(1.c) Compute abundances of isotopologues with masses 44 to 49
…by making the assumption that your reference gas is stochastic (this is usually not true, but we correct for that later in the process).
(1.d) Compute binned abundances of isotopologues grouped by mass
(2.a) Measure the abundance ratios of your sample gas for masses 45 to 49 (R45-Sample, etc.)
…based on peak height measurements from your dual-inlet spectrometer:
Ideally, these voltages reflect abundance ratios, so that:
And, using the conventional δ notation (relative to your reference gas):
(2.b) Compute the bulk composition of your sample gas
One way to do that is to define:
You can then compute <fc red>R18-Sample</fc> by numerically solving the following equation:
R17-Sample and R13-Sample may then be directly calculated:
(3.a) “Scramble” your sample gas
This means computing the abundance of each isotopologue of a gas with the same bulk composition as your sample, but in a stochastic state. This is done by following the steps (1.b) to (1.d) above:
Then (note the asterisk, here used to denote the stochastic state):
Ending up with the following “stochastic abundance ratios”:
(3.b) Compute raw Δ values
These Δ values are called “raw” because they have not yet been corrected for a number of analytical artifacts. Most importantly, we have assumed that your reference gas is in a stochastic state, which is unlikely. This is why raw Δ47 values are typically underestimated by roughly the actual Δ47 value of your reference gas.
…using equilibrated CO2 standards prepared using various recipes.
(to be continued soon)