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Double spiking species-specific isotope dilution result calculations simplified


Isotope dilution mass spectrometry (IDMS) is without doubt on of the most valuable tool in modern analytical chemistry. It is avoiding external calibration prone to interferences by matrix effects and is immune against analyte losses during non-quantitative sample preparation steps such as extraction or derivatization if proper analysis protocols are followed. In its extension to multiple species-specific spikes it offers not only the possibility to observe species interconversion but allows for its quantitation and therefore for accurate species  quantitation even in the presence of such interconversions. The species-specific isotope dilution analysis (SIDMS) therefore is a widely applicable method that has been certified in 1998 by the U.S. Environmental Protection Agency (see method 6800) and hailed as the "only available means to make accurate and legally defensible speciated measurements."

One of the main obstacles for its wider application is the cumbersome calculation that need to be performed to obtain the analytical results consisting of more than 270 operations. Due to this complexity of calculations, USEPA recommends solving the system of equations iteratively. Usually, about 6-8 iteratiions are needed to obtain allo unknowns. 

The new approach:
A group of researchers from the Institute for National Measurements Standards, Canada and the University of Cincinnati now has shown that these cumbersome calculations can be greatly simplified by using a matrix notation based deconvolution approach. At the end the calculation essentialy boils down to a multiple regression analysis that can be performed within an Microsoft EXCEL® spreadsheet. The results obtained are in exact agreement with the USEPA iterative two-isotope ratio approach and with the analytical (non-iterative) solution of the same fundamental isotope dilution equations.

The original publication

Juris Meija, Lu Yang, Joseph A. Caruso, Zoltan Mester, Calculations of double spike isotope dilution results revisited, J. Anal. At. Spectrom., 21/11 (2006) 1294.1297. DOI: 10.1039/b607823k

Microsoft Excel spreadsheet for calculating Cr(III) and Cr(VI) concentrations from the double spiking experiment

Related studies and reports

N.A.I.M. Boelrik, A general formula for 'double` spike isotope dilution analysis, Chem. Geol., 3/4 (1968) 323-325. DOI: 10.1016/0009-2541(68)90037-5
 W. Compston, V.M. Oversby, Lead isotopic analysis using a double spike, [Iterative method], J. Geophys. Res., 74 (1969) 4338-4348. DOI: 10.1029/JB074i017p04338

 N.H. Gale, A solution in closed form for lead isotopic analysis using a double spike, Chem. Geol., 6 (1970) 305-310. DOI: 10.1016/0009-2541(70)90031-8

 M.H. Dodson, Simplified equations for double-spiked isotopic analyses, Geochim. Cosmochim. Acta, 34 (1970) 1241-1244. DOI: 10.1016/0016-7037(70)90060-8

 R.D. Russell, The systematics of double spiking, J. Geophys. Res., 76 (1971) 4949-4955. DOI: 10.1029/JB076i020p04949

H.M. "Skip" Kingston, Method of speciated isotope dilution mass spectrometry, U.S. Patent 5,414,259, May 9, 1995

 H.M. "Skip" Kingston, Speciated isotope dilution mass spectrometry of reactive species and related methods, WO Patent 9939198 A1, Aug. 5, 1999

 N.N. Mel'nikov, Error Analysis of the Double-Spike Isotope Dilution Method, Geochem. Int., 41/7 (2003) 694

 H.M. "Skip" Kingston, Speciated Isotope Dilution Mass Spectrometry of reactive Species and Related Methods, US Patent 6,790,673 B1, Sep. 14, 2004.

 N.N. Mel'nikov, Errors of the Double Spiking Technique in the Isotopic Analysis of Common Lead, Geochem. Int., 43/12 (2005) 1228.

Related information:

MetroData: Example a7: Determination of the amount of lead in water using double isotope dilution and inductively coupled plasma mass spectrometry

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last time modified: June 22, 2020


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