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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)