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Table 6 Quantity descriptions of the model equation for the GUM workbench. Equation is taken from Bièvre De and Peiser (1997)

From: Expanded uncertainty modeling of the uranium isotope dilution standards

Symbols Unit Definition
CUSample mol U/g Mol U/g of solution in the unknown sample (taken from the certificate value of NBL and D&G)
R58mix at/at 235U/238U ratio in the mixture (spiked sample) (calculated from the assigned masses)
R58spike at/at Certified value of 235U/238U ratio in the spike
R58Sample at/at Certified value of 235U/238U in the sample
Mspike g Mass of spike (assigned proportions as described in Tables 1 and 2)
Msample g Mass of sample (assigned proportions as described in Tables 1 and 2)
C238spike mol/g 238U in spike calculated from uranium content in U-metal and atom fraction of 238U in the spike, the latter value is from the certificate
AF238USample mol/g Atom fraction of 238U in the unknown sample and calculated from the assigned masses and certificate values
δCF58comparator   Delta value for the correction factor of the comparator 235U/238U
(RSE% 7.810995 × 10−5, Hasozbek et al. 2013)
Cspike mol/g Concentration of spike molU/g (taken from the certificate value and diluted estimations are given in Table 3)
AF238spike mol/g Atom fraction of 238U in spike from the certified value
Cspikeg mol/g Spike aliquant concentration (taken from the certificate value and diluted estimations are given in Table 3)
Atwtspike   Atomic weight of spike (CRM 112A)
WtSolution g Weight of the metal and powder solution (for the dilution and equilibration purposes, 20 ml of vials are taken into account and the mixtures do not exceed over 10 ml.)
Purity gU/g Uranium content from the certificate
R48Sample at/at Certified value of 234U/238U in sample
R68Sample at/at Certified value of 236U/238U in sample
δ R58comparator   Delta factor representing the relative uncertainty on the comparator used for the mass fractionation correction (expanded uncertainty is 0.00065 (k = 2), Hasozbek et al. 2013)
  1. {Calculation of concentration of target element in sample using IDMS equation based on assigned amount ratios}-CUSample = ((R58mixR58spike)/(R58SampleR58mix)) × (Mspike/Msample) × (C238spike/AF238USample) × δCF58comparator
  2. {Calculation of the concentration of the 238U in spike}-C238spike = Cspike × AF238spike
  3. {Calculation of the U concentration of the spike}-Cspike = Cspikeg/Atwtspike
  4. {Calculation of the concentration of the spike solution}-Cspikeg = Wtpiece/WtSolution × Purity
  5. {Calculation of the atom fractions of 235U and 238U in the sample}-AF238USample = 1/((R48Sample + R58Sample + R68Sample) × δ R58comparator + 1)