VPDB-VSMOW

Introduction

This page is an effort to document the proper calculations required to convert from the VPDB scale to the VSMOW scale. Such a page might seem ridiculous given that the conversion is generally viewed as a straightforward calculation:

δ¹⁸O_VPDB = 0.97001 × δ¹⁸O_VSMOW − 29.99 ‰

δ¹⁸O_VSMOW = 1.03092 × δ¹⁸O_VPDB + 30.92 ‰

These conversions are wonderfully easy and appropriate to use when one is interested in converting among VPDB Mineral and VSMOW Mineral or among VPDB CO2 and VSMOW CO2. That is, if your project is about calcite and your δ¹⁸O are relative to an accepted value that is also calcite in the VPDB scale, then you can use the above equations to convert your calcite δ¹⁸O to a VSMOW value; or if your project is about CO2 and your δ¹⁸O are relative to an accepted value that is also CO2 in the VPDB scale, then you can use the above equations to convert your calcite δ¹⁸O to a VSMOW value. In IsoLab, we measure the isotope composition of CO₂, not calcite. If your project is ever going to consider the δ¹⁸O of the CO₂ itself, then you must account for the phosphoric acid digestion temperature and associated fractionation before or after applying the above equations. Below, we describe the details of converting from VPDB_mineral to VPDB_CO2 to VSMOW_CO2 to VSMOW_mineral. Everything in this page has already been described elsewhere and those citations are included below. This page was written after matlab code 'vpdb-vsmow.m'.

Isotope Ratios

Isotope ratios used in the current page. Material also encompasses virtual materials. See Literature Cited section below for full citation.
Material	Ratio	Value	Source
SMOW	R18	0.0020052	Baertschi, 1976
NBS19	R13	0.011202	Zhang and Li, 1990
VSMOW	R17	0.0003799	Li et al., 1988
VSMOW	R18	0.0020052	Baertschi, 1976

VPDB	R13	0.0111802	isodat software, R13_NBS19 / ((δ¹³C_NBS19,VPDB / 1000) + 1)
VPDB	R18	0.0020672	isodat software, R18_SMOW * α_{VPDB,VSMOWSLAP}

Alphas (α)

Using the same nomenclature as Kim et al. (2015), this section outlines the employed α values. A δ value can be recast as an α value by (δ/1000)+1. For example the δ¹⁸O_SLAP,VSMOW = -55.5 ‰. The α_SLAP,VSMOW, then, is 0.9445. Th nomenclature SLAP,VSMOW reads the δ or α of SLAP relative to VSMOW. Below the same nomenclature of X relative to Y (X,Y) for a variety of materials or virtual scales is shown.

Alpha values for various relationships where X relative to Y is noted by X,Y.
Relationship	Alpha	Comment	Source
NBS19,VPDB	0.9978	consensus d18Ovpdb value for NBS19 -2.2 permil	Kim et al., 2015
VSMOW_CO2,VSMOW	1.04120	oxygen isotope fractionation between CO2 equilibrated with VSMOW water and liquid VSMOW	Kim et al., 2015 → O'Neil et al., 1975 and Friedman and O'Neil 1977
NBS19,PDB	0.99781	d18O of NBS19 relative to PDB	Kim et al. 2015 → Coplen et al., 1983
PDB_CO2,PDB	1.01025	oxygen isotope fractionation between CO2 and solid calcite (100 % phosphoric acid at 25 °C)	Kim et al. 2015 →, Sharma and Clayton, 1965; Friedman and O'Neil, 1977
VSMOW_CO2,PDB_CO2	0.999737	oxygen isotope fractionation between CO2 equilibrated with VSMOW and CO2 evolved from pdb	Kim et al. 2015 → Craig, 1957; Coplen et al., 1983

VPDB,VSMOWSLAP	1.03092	Equation 2 in Kim et al. (2015) illustrates the above five α values to calculate this very well known α	Kim et al. 2015

Other α values based on calculations of above:

α_{VPDB_CO2,VSMOW} = α_{VSMOW_CO2,VSMOW} * (1 / α_{VSMOW_CO2,PDB_CO2})

α_{NBS19_CO2,VSMOW} = α_{VSMOW_CO2,VSMOW} * (1 / α_{VSMOW_CO2,PDB_CO2}) * (1 / α_NBS19,VPDB)

α_NBS19,VSMOW = α_{VSMOW_CO2,VSMOW} * (1 / α_{VSMOW_CO2,PDB_CO2}) * (1 / α_NBS19,VPDB) * (1 / α_{PDB_CO2,PDB})

deltas (δ)


Material	δ	scale	value (‰)	source
NBS19	δ¹³C	VPDB	+1.95	ciaaw.org
NBS19	δ¹⁸O	VPDB	-2.2	Friedman et al., 1982, Gonfiantini, 1984
NBS19	δ¹⁸O	VSMOW	+28.65	ciaaw.org
LSVEC	δ¹³C	VPDB	-46.6	ciaaw.org
NBS18	δ¹³C	VPDB	-5.01	ciaaw.org
NBS18	δ¹⁸O	VSMOW	+7.20	ciaaw.org

Carbonate Phosphoric Acid Fractionation

Equation 6 from Kim et al. (2015):

1000 * ln * alpha_{CO2(acid)-calcite} = 3.48 * (10^3/T) - 1.47
where T is in Kelvin
acid.alpha25 = exp((3.48 * (10^3/(25+273.15)) - 1.47)/1000); % 1.01025419478517
acid.alpha70 = exp((3.48 * (10^3/(70+273.15)) - 1.47)/1000); % 1.00870904256074
acid.alpha90 = exp((3.48 * (10^3/(90+273.15)) - 1.47)/1000); % 1.00814581509316

Derived values

vpdb.R18_calc = smow.R18*vpdb_vsmowslap

vpdb.d18O_isodat_vs_calc = (vpdb.R18isodat/vpdb.R18_calc-1)*1000

nbs19.d18Ovpdb_CO2_25 = nbs19.d18Ovpdb*acid.alpha25 + (acid.alpha25-1)*1000

nbs19.d18Ovpdb_CO2_90 = nbs19.d18Ovpdb*acid.alpha90 + (acid.alpha90-1)*1000

nbs19.d18Ovsmow_CO2_90 = nbs19.d18Ovpdb_CO2_90 * 1.03092 + 30.92

Polly Working Reference Gas (pollywg)

All NBS19 measurements made on polly were reevaluated on 171206 using file NBS19_all_csv_files_combined.csv and matlab script polly_reverse_SamRef.m created on 171206. This script reverses the reference and sample data allowing one to use the "sample" as the reference. In this case, the samples are all NBS19 preps. I also used some SIRFER CO2 equilibrated with VSMOW, GISP, and SLAP to make sure I was getting something reasonable. The result of this effort is currently centering in on a d18Ovpdb value for the polly reference gas of 1.7515 permil. The delta difference between NBS19 and pollywg is -4.1517. Assuming the CO2 of NBS19 has a values of nbs19.d18Ovpdb_CO2_90 = 5.92789, then the d18O vs VPDB of pollywg is +1.7515. The same script provides a d13C value.

pollywg.d13Cvpdb = -10.2527; % existing value of -10.3 is within error of this value

pollywg.d18Ovpdb = 1.7515;

pollywg.d18Ovsmow = 32.726;

Psi example

We have been using D47crunch, written by Mathieu Daëron (Daëron 2021), to process our carbonate isotope data gathered from our Nu Perspective / NuCarb named Psi. One of the carbonate standards we use, ETH-3, has an accepted δ¹⁸O_VPDB value of -1.78 ‰, according to Bernasconi et al. 2018 Table 4 Average column. A typical output from D47crunch in the Replicate Summary Table shows a δ¹⁸O_VSMOW value of +37.89 ‰. Using the VPDB to VSMOW equation from the top of this page (-1.78 * 1.03092 + 30.92) yields 29.08 ‰. This is our first clue that the D47crunch output is a δ¹⁸O value of the CO₂ derived from carbonate, not of the carbonate itself. Psi digests carbonate at 70 °C. To convert the D47crunch δ¹⁸O_VSMOW CO2 value to a δ¹⁸O_VSMOW carbonate value, we need to use the above α value associated with 70 °C, 1.008709.

δ¹⁸O_{VSMOW-Carbonate} = (δ¹⁸O_VSMOW-CO2 - 8.709) / 1.008709

δ¹⁸O_{VSMOW-Carbonate} = (+37.89 - 8.709) / 1.008709

δ¹⁸O_{VSMOW-Carbonate} = 28.93 ‰; very near to 29.08 value in the above paragraph.

Literature Cited

Baertschi P. (1976). Absolute 18O content of standard mean ocean water. Earth and Planetary Science Letters 31, no. 3: 341-44. doi: 10.1016/0012-821X(76)90115-1.
Bernasconi et al. (2018). Reducing Uncertainties in Carbonate Clumped Isotope Analysis Through Consistent Carbonate-Based Standardization. Geochemistry, Geophysics, Geosystems doi: 10.1029/2017GC007385.
Brand WA, Coplen TB, Vogl J, Rosner M, Prohaska T. (2014). Assessment of International Reference Materials for Isotope-Ratio Analysis (IUPAC Technical Report). Pure and Applied Chemistry 86, no. 3. doi: 10.1515/pac-2013-1023.
Daëron M. (2021). Full Propagation of Analytical Uncertainties in Δ ₄₇ Measurements. Geochemistry, Geophysics, Geosystems. 22, 5. doi: 10.1029/2020GC009592.
Friedman I, O'Neil J, Cebula G. (1982). Two New Carbonate Stable-Isotope Standards. Geostandards Newsletter 6, no. 1: 11?12. doi: 10.1111/j.1751-908X.1982.tb00340.x
Gonfiantini R. (1984). Advisory Group Meeting on Stable Isotope Reference Samples for Geochemical and Hydrological Investigations. IAEA
Kim S-T, Coplen TB, Horita J. (2015). Normalization of Stable Isotope Data for Carbonate Minerals: Implementation of IUPAC Guidelines. Geochimica et Cosmochimica Acta 158: 276?89. doi: 10.1016/j.gca.2015.02.011.
Zhang Q-L, Li W-J. (1990). A Calibrated Measurement of the Atomic Weight of Carbon. Chinese Science Bulletin 35 no. 4: 290?96.

Last modified: 2025-02-25 21:22:44