Back to article

Figures and Tables

The statistical mechanical basis of the triple isotope fractionation
relationship

J.A. Hayles1,

1Department of Earth Science, Rice University, 6100 Main St., Houston, TX 77005, USA

X. Cao2,

2Department of Geology & Geophysics, E235, Howe-Russell Geosciences Complex, Louisiana State University, Baton Rouge, LA 70803, USA

H. Bao2

2Department of Geology & Geophysics, E235, Howe-Russell Geosciences Complex, Louisiana State University, Baton Rouge, LA 70803, USA

Affiliations  |  Corresponding Author  |  Cite as

Hayles, J.A., Cao, X., Bao, H. (2017) The statistical mechanical basis of the triple isotope fractionation relationship. Geochem. Persp. Let. 3, 1-11.

Geochemical Perspectives Letters v3, n1  |  doi: 10.7185/geochemlet.1701
Received 5 March 2016  |  Accepted 20 July 2016  |  Published 17 August 2016
Copyright © 2017 European Association of Geochemistry



Figure 1 (a) β18 vs. κ and (b) Equilibrium α18 vs. θ plots for randomly selected hypothetical diatomic molecules under the harmonic approximation in the 16O-17O-18O system. Temperature is plotted as colour on the same scale for both plots. The model uses 1,000,000 evenly distributed randomly generated values for the secondary mass (0-300 AMU), the bond force constant (0-kUL), and temperature (200-1600 oK). The bond force constant for carbon monoxide (CO) is used as an arbitrary upper limit (UL) for the bond force constant for diatomic oxygen species.
Back to article | Download in Powerpoint


Figure 2 Temperature vs. Δ(Δ17O) plot for equilibrium between randomly selected diatomic molecules under the harmonic approximation in the 16O-17O-18O system. A C value of 0.5305 (HTL) is used for the Δ(Δ17O) definition. 1000 ln α18 is plotted as colour. The range of Δ(Δ17O) values in this plot is expected to be an overestimate for natural samples. The points in this model each correspond to a point in Figure 1a.
Back to article | Download in Powerpoint


Figure 3 Three isotope fractionation parameters for haematite synthesis conducted by Bao and Koch (1999)

Bao, H.M., Koch, P.L. (1999) Oxygen isotope fractionation in ferric oxide-water systems: Low temperature synthesis. Geochimica et Cosmochimica Acta 63, 599-613.

. Values are calculated from newly measured δ18Ohaematite and δ18Owater values, and an assumed Δ17O (C = 0.528) of 0.02 ‰ for the water based on reported Baltimore tap water from Li et al. (2015)

Li, S.N., Levin, N.E., Chesson, L.A. (2015) Continental scale variation in O-17-excess of meteoric waters in the United States. Geochimica et Cosmochimica Acta 164, 110-126.

. Δ(Δ17O) are reported using C = 0.5305. The method for calculating uncertainties can be found in the Supplementary Information. Best fit curves for the ln (α) values are second order polynomials of 1/T. The best fit curves for Δ(Δ17O) and θ are calculated from the fits to ln (α).
Back to article | Download in Powerpoint
Back to article

Supplementary Figures and Tables


Table S-1 Results from both previous δ18O (converted to logarithmic definition) measurements from Bao and Koch (1999) and new δ’18O and Δ17O analysis from this study. δ'17O values for the water are calculated using the δ’18O values for the water measured by Bao and Koch (1999) and published Δ17O values for Baltimore tap water (Li et al., 2015). Values of α are for haematite precipitation with oxygen sourced from water (αhaematite-water). The method for determining uncertainties is described in the text of the Supplementary Information. All uncertainties are 1 σ.
Sample NameT in KPrevious δ'18O (‰)
SMOW
δ'18O (‰) VSMOWδ'17O (‰) VSMOWΔ17O (‰) VSMOW1000 ln (α18)1000 ln (α17)θΔ(Δ17O) (‰) VSMOW
CH-20A303.15-6.9239-6.1482-3.369-0.10741.8828 ± 0.10670.8513 ± 0.06530.4525
(+0.0197; -0.0207)
-0.1475 ± 0.0398
CH-20B303.15-6.9239-6.3531-3.4352-0.06491.6778 ± 0.10670.785 ± 0.06530.468
(+0.0226; -0.0226)
-0.105 ± 0.0398
CH-19A310.15-7.7298-6.8148-3.6828-0.06751.2161 ± 0.10670.5375 ± 0.06530.4428
(+0.0302; -0.033)
-0.1077 ± 0.0398
CG-13A323.15-7.8305-7.1179-3.8504-0.07430.913 ± 0.10670.3699 ± 0.06530.4067
(+0.0409; -0.0462)
-0.1145 ± 0.0398
CG-13B323.15-7.8305-6.9974-3.7403-0.02821.0335 ± 0.10670.4799 ± 0.06530.465
(+0.0361; -0.038)
-0.0683 ± 0.0398
CG-12B343.15-8.5363-8.6214-4.55970.0139-0.5904 ± 0.1067-0.3394 ± 0.06530.5761
(+0.0689; -0.065)
-0.0262 ± 0.0398
CH-15A368.15-9.9493-9.8669-5.2947-0.0603-1.8359 ± 0.1067-1.0744 ± 0.06530.5859
(+0.0212; -0.0225)
-0.1004 ± 0.0398
CH-17A388.15-10.2524-10.0992-5.5437-0.1861-2.0682 ± 0.1067-1.3234 ± 0.06530.6404
(+0.02; -0.0207)
-0.2262 ± 0.0398
CH-16A413.15-10.5555-10.9575-5.8772-0.0643-2.9265 ± 0.1067-1.657 ± 0.06530.5664
(+0.0131; -0.0136)
-0.1044 ± 0.0398
Back to article | Download in Excel