ISOTOPIC FRACTIONATONS ASSOCIATED WITH PHOSPHORIC ACID DIGESTION OF CARBONATE MINERALS
4. R ESULTS AND D ISCUSSION
4.2 Model results for the oxygen-isotope and clumped-isotope fractionations associated with carbonic acid dissociation
Table 3-3 summarizes the vibration frequencies we calculate for the various isotopologues of H2CO3. The negative frequencies, ϖ, correspond to the decomposition frequencies νL† in section 3.1. Following procedures outlined in section 3, these frequencies are used in our transition-state-based predictions of the proportions of different CO2 isotopologues that are produced by dissociation of the H2CO3 intermediate, and the temperature dependence of those proportions. Unless stated otherwise, all of our calculations assume that reactant carbonate has a δ13CVPDB value of 0‰, a δ18OVSMOW value of 0‰ and a stochastic distribution of multiply-substituted isotopologues (Table 1), and that the H2CO3 intermediate is identical in isotopic composition to reactant carbonate.
Table 3-3 Scaled vibration frequencies (unit: cm-1 ) for different transition state (TS) isotopologues during phosphoric acid digestion of carbonate minerals (H2CO3 model, DFT-B3LYP/6-31G* with a frequency scaling factor of 0.9614). The underlined atoms denote the ones to be abstracted during acid digestion. Isotopologue ϖ1ϖ2ϖ3ϖ4ϖ5ϖ6ϖ7ϖ8ϖ9ϖ10ϖ11ϖ12 H212C16O16O16O-1650.22381.74489.85588.65720.73760.00927.16 1246.501267.181903.522102.573573.50 H213 C16 O16 O16 O-1643.59380.77488.29577.55710.57754.21920.93 1234.691266.941881.482069.333573.50 H212C17O16O16O-1649.47381.07489.52587.30716.91750.19925.95 1230.071266.521901.172101.663573.50 H212C16O17O16O-1650.10378.19488.88587.13719.09755.13926.78 1237.111266.921896.672094.473573.50 H212C16O16O17O-1649.38377.05487.91587.36713.34757.87924.34 1246.341265.391902.992102.513567.31 H212C18O16O16O-1648.80380.42489.21586.08713.11741.52924.84 1215.381265.981899.152100.893573.50 H212C16O18O16O-1649.99374.93488.00585.78717.47750.72926.43 1228.351266.801890.272087.853573.50 H212C16O16O18O-1648.64372.65486.21586.06706.41756.43921.86 1246.191263.811902.532102.453561.83 H213C17O16O16O-1642.83380.13488.01576.12707.41744.04919.75 1217.631266.311878.832068.743573.50 H213C16O17O16O-1643.46377.27487.23576.01708.42750.10920.55 1225.281266.721872.202063.053573.50 H213C16O16O17O-1642.75376.08486.35576.41704.07751.04918.05 1234.521265.141881.012069.223567.30 H212C17O17O16O-1649.35377.52488.56585.76715.41745.12925.59 1220.741266.331894.082093.593573.50 H212 C17 O16 O17 O-1648.63376.41487.58585.96709.09748.37923.15 1229.931264.711900.642101.593567.31 H212C16O17O17O-1649.26373.46486.96585.84711.98752.68923.96 1236.951265.121896.152094.393567.31 H213C18O16O16O-1642.14379.51487.73574.82704.33734.92918.66 1202.371265.781876.562068.243573.50 H213C16O18O16O-1643.34374.05486.27574.66706.31746.40920.21 1216.511266.591863.662058.043573.50 H213C16O16O18O-1642.00371.68484.64575.27697.76748.85915.50 1234.381263.551880.602069.113561.83 H212C18O17O16O-1648.68376.86488.26584.53711.79736.22924.50 1206.141265.811891.852092.853573.50 H212C18O16O17O-1647.96375.78487.27584.69704.84740.04922.07 1215.251264.171898.622100.823567.30 H212C17O18O16O-1649.24374.25487.71584.41713.89740.56925.26 1212.101266.211887.462087.003573.50 H212C17O16O18O-1647.89372.02485.88584.61701.79747.20920.69 1229.811263.121900.182101.543561.83 H212C16O18O17O-1649.15370.15486.11584.50710.69747.92923.62 1228.191265.001889.762087.763567.31 H212C16O17O18O-1648.51369.01485.28584.55705.19751.07921.48 1236.821263.531895.702094.333561.83 H213C17O17O16O-1642.70376.62486.96574.56705.29739.84919.39 1208.331266.131869.282062.503573.50 H213C17O16O17O-1641.99375.46486.07574.94700.60741.04916.89 1217.481264.511878.362068.623567.30 H213C16O17O17O-1642.62372.53485.31574.88702.27746.55917.68 1225.121264.921871.742062.913567.30
Table 3-3 (Continued) Isotopologue ϖ1ϖ2ϖ3ϖ4ϖ5ϖ6ϖ7ϖ8ϖ9ϖ10ϖ11ϖ12 H212C17O17O17O-1648.51372.80486.65584.43707.89742.97922.80 1220.601264.521893.562093.513567.30 H212C18O18O16O-1648.57373.59487.42583.16710.40731.48924.19 1197.601265.701885.042086.303573.50 H212C18O16O18O-1647.21371.41485.56583.28697.20739.13919.62 1215.141262.561898.162100.763561.82 H212 C16 O18 O18 O-1648.40365.67484.44583.22704.07746.11921.15 1228.051263.401889.312087.693561.83 H213C18O17O16O-1642.01375.99486.70573.25702.27730.63918.33 1193.181265.621866.792062.043573.50 H213C18O16O17O-1641.30374.86485.79573.61697.17732.16915.83 1202.231263.981876.092068.123567.30 H213C17O18O16O-1642.58373.39486.01573.20703.17736.12919.08 1199.681266.011860.502057.533573.50 H213C17O16O18O-1641.23371.07484.35573.76693.95739.07914.36 1217.361262.911877.952068.523561.82 H213C16O18O17O-1642.50369.27484.37573.53700.54742.45917.34 1216.331264.791863.212057.903567.30 H213C16O17O18O-1641.87368.09483.62573.74696.18744.09915.14 1224.971263.331871.342062.803561.82 H212C18O17O17O-1647.84372.17486.35583.15703.81734.43921.73 1206.011264.001891.332092.773567.30 H212 C17 O18 O17 O-1648.40369.49485.81583.08706.73738.01922.48 1211.961264.411886.952086.923567.30 H212C17O17O18O-1647.76368.38484.96583.09700.72741.63920.33 1220.481262.931893.112093.453561.83 H213C17O17O17O-1641.85371.91485.04573.39698.92736.38916.54 1208.181264.331868.832062.363567.30 H213C18O18O16O-1641.90372.76485.76571.88700.13726.89918.04 1184.641265.501857.792057.103573.50 H213C18O16O18O-1640.55370.49484.08572.38690.16730.46913.32 1202.121262.381875.682068.023561.82 H213 C16 O18 O18 O-1641.75364.78482.70572.40694.69739.72914.81 1216.181263.201862.822057.773561.82 H212C18O18O17O-1647.73368.85485.53581.79702.81729.25921.42 1197.471263.891884.522086.213567.30 H212C18O17O18O-1647.09367.76484.66581.75696.27733.38919.28 1205.901262.401890.882092.703561.82 H212C17O18O18O-1647.65365.03484.14581.75699.73736.48920.02 1211.831262.811886.502086.843561.82 H213C18O17O17O-1641.17371.29484.78572.05695.63727.32915.50 1193.041263.821866.332061.903567.30 H213C17O18O17O-1641.74368.63484.12572.03697.26732.17916.23 1199.521264.211860.052057.393567.30 H213C17O17O18O-1641.10367.48483.35572.22692.51734.13914.02 1208.051262.731868.422062.243561.82 H212C18O18O18O-1646.98364.40483.85580.40695.42728.04918.98 1197.361262.301884.072086.133561.82 H213C18O18O17O-1641.05368.01483.87570.68694.07722.97915.21 1184.491263.701857.342056.963567.30 H213C18O17O18O-1640.42366.88483.09570.83688.88725.32913.00 1192.921262.221865.932061.783561.82 H213C17O18O18O-1640.99364.17482.44570.86691.14729.60913.71 1199.391262.621859.662057.263561.82 H213C18O18O18O-1640.31363.56482.19569.46687.64720.61912.71 1184.371262.101856.952056.823561.82
We define the fractionations of oxygen isotope (1000lnα*) and multiply substituted species (Δ47*, Δ48*, Δ49*) during acid digestion as the differences between δ18O, Δ47, Δ48, Δ49 in the product CO2 and δ18O, Δ63, Δ64, Δ65 in the reactant carbonates, respectively:
2 3
18
*
47 47 63 48 48 64 49 49 65
18
/1000 1
1000ln 1000 ln , , ,
/1000 1
CO XCO
O O α δ
δ
∗ ∗ ∗
= + Δ = Δ − Δ Δ = Δ − Δ Δ = Δ − Δ
+
where Δ48, Δ49, Δ63, Δ64 and Δ65 are defined, similar to Δ47, following the same principle as in Eiler and Schauble (2004):
12 18 18 13 18 17
48 12 16 16
48 48 12 18 18 13 18 17
12 16 16
13 18 18
49 12 16 16
49 49 13 18 1
[ ] [ ]
[ ]
- 1 1000 - 1 1000
[ ] [ ]
[ ]
[ ]
[ ]
- 1 1000 [ actual
s s
stochastic
s
actual stochastic
C O O C O O
R C O O
C O O C O O
R
C O O C O O
R C O O
C O R
+
Δ = × = ×
+
Δ = × =
⎛ ⎞
⎜ ⎟
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎝ ⎠ ⎜⎜⎝ ⎟⎟⎠
⎛ ⎞
⎜ ⎟
⎝ ⎠ 8
12 16 16
13 18 16 16 12 18 17 16 13 17 17 16 12 17 17 17
63 12 16 16 16
63 63 13 18 16 16 12 18 17 16 13 17 17 16 12
- 1 1000 ]
[ ]
[ ] [ ] [ ] [ ]
[ ]
- 1 1000
[ ] [ ] [ ] [
s s
actual
s s s
stochastic
O C O O
C O O O C O O O C O O O C O O O
R C O O O
C O O O C O O O C O O O C
R
×
+ + +
Δ = × =
+ + +
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎛ ⎞
⎜ ⎟
⎝ ⎠ 17 17 17
12 16 16 16
12 18 18 16 13 18 17 16 12 18 18 17 13 17 17 17
64 12 16 16 16
64 64 12 18 18 16 13 18 17 16 12 18 18
- 1 1000 ]
[ ]
[ ] [ ] [ ] [ ]
[ ]
- 1 1000
[ ] [ ] [
s s
actual
s s
stochastic
O O O C O O O
C O O O C O O O C O O O C O O O
R C O O O
C O O O C O O O C O O
R
×
+ + +
Δ = × =
+ +
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎛ ⎞
⎜ ⎟
⎝ ⎠ 17 13 17 17 17
12 16 16 16
12 18 18 17 13 18 18 16 13 18 17 17
65 12 16 16 16
65 65 12 18 18 17 13 18 18 16 13 18 17 17
- 1 1000
] [ ]
[ ]
[ ] [ ] [ ]
[ ]
- 1 1000
[ ] [ ] [ ]
s s
s
actual
s s s
stochastic
O C O O O
C O O O
C O O O C O O O C O O O
R C O O O
C O O O C O O O C O O O
R
× +
+ +
Δ = × =
+ +
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎛ ⎞
⎜ ⎟
⎝ ⎠
12 16 16 16
- 1 1000
[ C O O O]s
×
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
,
where ‘s’ in the subscript denotes the abundance of an isotopologue when all the isotopes are stochastically distributed.
Fig. 3-4 and Table 3-4 present the oxygen isotope fractionations that accompany phosphoric acid digestion over a range of relevant temperatures, as predicted by our transition-state theory model. The predicted oxygen isotope fractionation and its temperature dependence are broadly similar to those determined for different carbonate minerals in previous laboratory studies. At 25°C, our model predicted oxygen isotope fractionation of 10.72‰, is in the middle of the range of observed fractionations among different carbonate minerals (from 10.06‰ for MnCO3 to 11.92‰ for MgCO3), and is very close to the experimental determined fractionation for calcite (10.20‰). The temperature sensitivity of our predicted oxygen isotope fractionation during phosphoric acid digestion (-0.055‰/°C at 25°C) is also only slightly above the range of temperature sensitivities experimentally determined for different carbonate minerals (MnCO3 appears to possess the highest temperature sensitivity of oxygen isotope aid digestion fractionation, -0.052‰/°C at 25°C).
Figure 3-4: Oxygen isotope fractionations (1000lnα*, where α* is the 18O/16O ratio of product CO2 divided by that for reactant carbonate) plotted vs. 105T-2 in K (the upper horizontal edge indicates T in ˚C, for reference).
The dashed line is the predicted
temperature dependent fractionation based on our model
of H2CO3 dissociation. Labled solid lines are measured experimental values for various metal carbonates (Table 4). The structurally simple transition-state structure model we propose captures the first-order magnitude and temperature dependence of observed fractionations, and mostly closely approaches the best-determined value for calcite
Table 3-4 Comparison of model predicted and experimentally observed phosphoric acid digestion fractionations. Carbonate Mineralsδ18 OSMOW‡ (‰,XCO3)Temperature range (°C) 1000lnα* (‰, 25°C§ )Δ47* (‰, 25°C¥ ) 1000lnα* (‰§ ) 1000lnα* Reference Dolomite(CaMg(CO3)2)11.53 2511.03 0.214N/AN/A Sharma and Clayton, 1965 Magnesite(MgCO3) 18.23 50-100 11.92 0.1980.2134.23+6.84×105 /T2 Das Sharma et al., 2002 Simthsonite(ZnCO3) 26.01 25-72 11.49 0.2050.1873.96+6.69×105 /T2 Gilg et al., 2003 Siderite(FeCO3) 4.22 25-150 11.54 0.2040.1553.85+6.84×105 /T2 Rosenbaum and Sheppard, 1986 Rhodochrosite(MnCO3)18.15 20-90 10.06 0.2340.1232.29+6.91×105 /T2 Bottcher, 1996
Calcite Calcite(CaCO3) 6.43 25-9510.20 0.2310.2323.89+5.61×105 /T2 Das Sharma et al., 2002 Aragonite(CaCO3) 10.57 25-75 10.36 0.2290.2324.24+5.44×105 /T2 Recal. from Kim et al., 2007 Strontianite(SrCO3) 14.57 25-62 10.46 0.2250.2385.30+4.59×105 /T2 Sharma and Sharma, 1969a Cerussite(PbCO3) 15.97 25-72 10.52 0.2240.1905.13+4.79×105 /T2 Gilg et al., 2003Aragonite Witherite(BaCO3) 6.20 20-9010.91 0.2160.2495.76+4.58×105 /T2 Bottcher, 1996 1000lnα* 0 10.72 2.58+7.25×105 /T2 This work Δ47* 0.220 0.0186+0.179×105 /T2 This work Δ48* 0.137 -0.0787+0.192×105 /T2 This work H2CO3 Model£ Δ49* 0.593 -0.0386+0.561×105 /T2 This work ‡ Oxygen isotope compositions of the reactant carbonate minerals. § Equations for experimentally determined temperature dependence from Gilg et al., 2003, where T is in the unit of Kelvin. Isotope fractionations during phosphoric acid fractionation at 25°C are estimated from these equations. ¥ PredictedΔ47* for different carbonate minerals at 25°C, based on the inverse correlation between 1000lnα* and Δ47* (first column) or the absolute Δ47* value (second column) predicted by our cluster model. See section 4.4.3 for details. £ Calculations here assumes δ13 CVPDB=0‰, δ18 OVSMOW=0‰ and stochastic distribution of multiply-substituted isotopologues for the reactant carbonate.
Our transition-state-theory model of phosphoric acid digestion predicts that CO2 produced by dissociation of an H2CO3 intermediate has abundances of 13C-18O bonds, as reflected by the Δ47* value, +0.220‰ higher than the ∆63 value of reactant carbonate at 25°C, with a temperature sensitivity of -0.0010‰/°C over the temperature range of 25°C to 80°C (Fig. 3-5). The predicted fractionation at 25˚C is indistinguishable from this study’s experimentally determined value of 0.232‰ for calcite (Table 3-2), and the
Figure 3-5: Fractionations of multiply-substituted species (Δ47*, Δ48*,Δ49*) during phosphoric acid digestion predicted by our H2CO3 dissociation model, plotted as a function of 105T-2, in K. The solid circle is the average value of Δ47*
experimentally determined during phosphoric acid digestion of calcite at 25°C (Table 3-2; this study). The bar is 1 standard deviation (1σ) of multiple replicate extractions of this calcite (the standard error of the average is approximately the size of the symbol).
temperature dependence is close to the experimentally measured value of ca.
-0.0016‰/°C (Ghosh et al, 2006). There are no experimental data documenting
fractionations of 12C18O2 and 13C18O2 isotopologues during acid digestion of carbonates, but for future reference we note here that our transition state theory model predicts Δ48* to be 0.137‰ at 25°C with a temperature dependence of -0.0011‰/°C, and Δ49* to be 0.593‰ at 25°C with a temperature dependence of -0.0033‰/°C (Fig. 3-5).
The most obvious weakness of our transition state theory model is the need to choose a frequency scaling factor (which presumably reflects the effects of anharmonicity; see section 2.3, above). We tested the potential effects of this assumption by repeating our calculations with no scaling factors. In this case, the predicted acid digestion fractionations at 25°C are 11.32‰ for δ18O*, 0.235‰ for Δ47*, 0.156‰ for Δ48*, and 0.642‰ for Δ49*. These results are sufficiently similar to the results of our preferred model that we do not regard the frequency scaling factors as plausible sources of large systematic error.
Our transition state theory model also predicts the mass dependency of the oxygen isotope fractionation that accompanies phosphoric acid digestion. This is relevant for analyses of the bulk isotopic compositions of reactant carbonates because one must assume the mass dependence of the acid digestion fractionation in order to ion-correct the measured mass spectrum of product CO2. Generally speaking, measurements of the carbon and oxygen isotope compositions of CO2 on a gas source isotope ratio mass spectrometer examine CO2 isotopologue ions having nominal molecular masses of 44, 45 and 46 amu. Because the instruments commonly used for this purpose cannot mass resolve 13C16O2 from 12C17O16O, one must make some assumption to correct for the contribution of 12C17O16O to the mass 45 amu ion beam. This is generally accomplished
by assuming a relationship between 17O and 18O abundance of the form: 1717 A 1818 A
B B
R R
R R
⎛ ⎞λ
= ⎜ ⎟
⎝ ⎠
(Assonov and Brenninkmeijer, 2003; Miller et al., 2007), where the value λ must be assumed or determined by independent experiments (such as fluorination of reactant carbonate and product CO2 followed by isotopic analyses of the resulting O2 gases). To the best of our knowledge, there are no experimental determinations of λ associated with phosphoric acid digestion of carbonate minerals; a value 0.528 has been suggested (Assonov and Brenninkmeijer, 2003; Miller et al., 2007). This value of λ characterizes the isotopic variations of natural waters (Li and Meijer, 1998; Barkan and Luz, 2005), and presumably is inherited by carbonate minerals that form in isotopic equilibrium with natural waters, although there is no reason to suppose it also is characteristic of the acid digestion reaction process by which carbonates are measured. Our transition state theory of phosphoric acid digestion predicts that the value of λ associated with its isotopic fractionations is 0.5281. Thus, our model agrees with and provides an independent theoretical justification for the suggested value of 0.528 for CO2 extracted from carbonate samples (Miller et al., 2007) and standards (e.g., PDB and NBS-19; Assonov and Brenninkmeijer, 2003).
4.3 Dependence of acid digestion fractionations on the isotopic compositions of