16O fractionation

Geochimica et Cosmochimica Acta 71 (2007) 1115–1129 www.elsevier.com/locate/gca

Oxygen isotopes in synthetic goethite and a model for the apparent pH dependence of goethite–water 18O/16O fractionation Crayton J. Yapp

*

Department of Geological Sciences, Southern Methodist University, Dallas, TX 75275-0395, USA Received 12 May 2006; accepted in revised form 20 November 2006

Abstract Goethite synthesis experiments indicate that, in addition to temperature, pH can affect the measured value of the 18O/16O fractionation factor between goethite and water (aG–W). A simple model was developed which expresses aG–W in terms of kinetic parameters associated with the growth of goethite from aqueous solution. The model predicts that, at a particular temperature, the range of pH over which aG–W changes as pH changes is expected to be comparatively small (3 pH ‘‘units’’) relative to the range of pH values over which goethite can crystallize (pH from 1 to 14). Outside the range of sensitivity to pH, aG–W is predicted to be effectively constant (for constant temperature) at either a low-pH aG–W value or a high-pH aG–W value. It also indicates that the values of aG–W at high pH will be disequilibrium values. Values of aG–W for goethite crystallized at low pH may approach, but probably do not attain, equilibrium values. For goethite synthesized at values of pH from 1 to 2, data from two different laboratories define the following equation for the temperature dependence of 1000 ln aG–W (T in degrees Kelvin) 1000 ln aG–W ¼

1:66  106  12:6 T2

ðIVÞ

Over the range of temperatures from 0 to 120C, values of 1000 ln aG–W from Eq. (IV) differ by 60.1&from those of a published equation [Yapp C.J., 1990. Oxygen isotopes in iron (III) oxides. 1. Mineral–water fractionation factors. Chem. Geol. 85, 329–335]. Therefore, interpretations of data from natural goethites using the older equation are not changed by use of Eq. (IV). Data from a synthetic goethite suggest that the temperature dependence of 1000 ln aG–W at low pH as expressed in Eq. (IV) may be valid for values of pH up to at least 6. This result and the model prediction of an insensitivity of aG–W to pH over a larger range of pH values could explain the observation that Eq. (IV) yields values of aG–W which mimic most 18O/16O fractionations measured to date in natural goethites.  2006 Elsevier Inc. All rights reserved.

1. Introduction Natural variations of 18O/16O ratios in the common low temperature Fe(III) oxyhydroxide, goethite (a-FeOOH), have been used to study surface and near-surface environments with ages ranging from modern up to 108 years (e.g., Yapp, 1987, 1993, 1997, 1998, 2000, 2001; Bird et al., 1992, 1993; Hein et al., 1994; Girard et al., 1997, 2000, 2002; Bao et al., 2000; Pack et al., 2000; Poage et al., 2000;

*

Fax: +1 214 768 2701. E-mail address: [email protected]

0016-7037/$ - see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.gca.2006.11.029

Sjostrom et al., 2004; Tabor et al., 2004; Tabor and Yapp, 2005; Hren et al., 2006). Valid interpretations of the goethite 18 O/16O data in these studies depend upon knowledge of the temperature-dependent, goethite–water fractionation factor (aG–W) that is applicable to natural systems. At the low temperatures characteristic of sedimentary and diagenetic environments, determinations of equilibrium values of aG–W by mineral–water isotopic exchange experiments are precluded by an absence of measurable oxygen isotope exchange (Yapp, 1991). Therefore, the value of aG–W has been determined by mineral synthesis experiments (Yapp, 1987, 1990; Mu¨ller, 1995; Bao and Koch, 1999; Xu et al., 2002) and theoretical calculations (Zheng,

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C.J. Yapp 71 (2007) 1115–1129

1998). In these experiments, goethite was precipitated at various temperatures from aqueous solutions which contained dissolved Fe(III) salts. Even though there were some differences among the experiments in choice of Fe(III) salts, initial concentrations, etc., the results of Yapp (1987, 1990) and Xu et al. (2002) yielded curves for the variation of 1000 ln aG–W with temperature that were analytically indistinguishable. Moreover, the theoretical curve of Zheng (1998) is very similar to the experimental curves of Yapp (1987, 1990) and Xu et al. (2002). These three curves, however, differ significantly from the other published experimental curves. The goethite synthesis experiments fall into two groups based on the pH of the systems: (1) low pH—those with final pH values of 1 to 2; and (2) high pH—those with final pH values of 14. These goethite–water oxygen isotope fractionation curves are shown in Fig. 1. The curve of Yapp (1990) represents syntheses from Fe(III) nitrate solutions at pH values of 2 and has been used with apparent success to interpret data from most natural goethites studied to date. The results of Xu et al. (2002) are for goethite synthesized from solutions of Fe(III) nitrate, Fe(III) sulfate, or Fe(III) ammonium sulfate. Although Xu et al.

14

Goethite-Water 1000ln18α

12

Curves at low pH (~1 to 2) 1. Yapp (1990) 2. Xu, et al. (2002) 3. Müller (1995)

3

Curves at high pH (~14) 4. Yapp (1987) 5. Müller (1995) 6. Müller (1995) 7. Bao and Koch (1999)

10

1, 2

1000lnαG-W

8

6

4

4 5

2 6 0 7 -2

-4 9

10

11

12 6

10 /T

13

2

Fig. 1. Summary of published oxygen isotope curves of 1000 ln aG–W plotted against 106/T2 (in degrees Kelvin) for goethites synthesized from various aqueous Fe(III) solutions. Range of temperatures is from 0 to 60 C. The low pH curves (pH 1 to 2) are (1) Yapp (1990); (2) Xu et al. (2002); and (3) Mu¨ller (1995). The curves of Yapp (1990) and Xu et al. (2002) are analytically indistinguishable and are represented by a single line. The high pH curves (pH 14) are (4) Yapp (1987); (5) and (6) Mu¨ller (1995); and (7) Bao and Koch (1999). See text for discussion.

(2002) do not actually report measured values of pH, they do give the other experimental conditions and state that their experiments were designed to be low pH syntheses. From their stated experimental conditions, the values of pH would have been 1 to 2. Mu¨ller (1995) also produced a low pH (2) experimental curve for nominal goethite synthesized from solutions of Fe(III) nitrate. The curve of Mu¨ller (1995) differs from the other low pH curves (Fig. 1). Bao and Koch (1999) suggested that incomplete removal of residual, initially precipitated ferrihydrite could be an explanation for differences among the published curves extant at that time. If so, some of the differences among the low pH (1 to 2) goethite curves of Fig. 1 might arise from the presence of varying proportions of ferrihydrite. Persistence of such ferrihydrite could be a consequence of long ‘‘half conversion times’’ from ferrihydrite to goethite (via dissolution and re-precipitation) at these low values of pH (Schwertmann and Murad, 1983). Yapp (1987, 1990) used a long-term, aging-rinse method to clean the precipitates, whereas Xu et al. (2002) used a modified acid wash treatment of the type recommended by Bao and Koch (1999) to remove ‘‘ferrihydrite’’. In spite of these different approaches to ‘‘cleaning’’ the final precipitates, the low pH (1 to 2) goethite results of Yapp (1990) and Xu et al. (2002) were the same within experimental error. This suggests a speculation that the low pH results of Mu¨ller (1995) might differ from those of Yapp (1990) and Xu et al. (2002) because of the presence of differing amounts of a ferrihydrite-like material in the precipitates analyzed by Mu¨ller (1995). Yapp (1987), Mu¨ller (1995), and Bao and Koch (1999) published results for high pH (14) syntheses of goethite from, respectively, aqueous Fe(III) nitrate, Fe(III) nitrate, and Fe(III) chloride solutions. These high pH curves differ from one another (Fig. 1). Some of these differences may arise from a ferrihydrite impurity, but at such high values of pH the ‘‘half conversion time’’ of ferrihydrite to goethite is short at 25 C (e.g., <4 days at a pH of 12; Schwertmann and Murad, 1983) and even shorter at higher temperatures. This suggests that there may be other explanations for the differences among the high pH synthetic goethite curves. Nevertheless, at sedimentary temperatures, the high pH curves are generally more similar to one another than they are to the low pH curves (Fig. 1). This apparent, pH-related dichotomy of aG–W values for synthetic goethites seems robust enough to suggest that the explanation may be inherent in the mechanism of goethite crystallization from aqueous solution (with or without a dissolving ferrihydrite precursor). This paper presents a simple model for oxygen isotope fractionation during growth of goethite from aqueous solution. The model indicates some conditions under which pH could be expected to affect the value of aG–W. Published experimental data are discussed in the context of the model. In addition, data from two new syntheses are presented here. One of these new syntheses produced goethite

pH and oxygen isotopes in goethite

from a reaction system with a solution pH of 5.9, which is intermediate to the extreme pH values of published results and could provide a test of the model. The results have implications for the interpretation of oxygen isotope data from natural goethites. 2. Experimental methods A long-term goethite synthesis experiment was started on March 20, 1986, and terminated on July 9, 2002 (a total of 5955 days). This long-term synthesis experiment was designated SG-9-1 and was kept at 25 C in a constant temperature bath, except for 1.5 days in transit in 1995 with the author from the University of New Mexico in Albuquerque to Southern Methodist University in Dallas. During the 1.5 days in transit the ambient temperature in the immediate surroundings varied from about 21–27 C. The goethite of SG-9-1 was synthesized using method 2 of Yapp (1987). For this method, 200 ml of 0.5 M NaOH was added to 250 ml of 0.2 M Fe(NO3)3 solution in a thick-walled, high density, 500 ml polyethylene bottle, and sealed. Water level was marked on the bottle. There was no observable change of the water level upon termination of the synthesis experiment, which suggested that the system had remained closed. The final pH of the reaction water was measured with a pH meter [pH = 1.1(±0.1)], and the reaction water was decanted and stored in a closed glass bottle for isotopic analysis. The residual precipitate-water slurry was centrifuged to separate the precipitate from the remaining reaction water. The precipitate was subsequently washed and centrifuged multiple times with de-ionized water until the final pH of an aliquot of rinse water was 5.5 after standing in contact with the precipitate for at least 10 min at room temperature (the original pH of the de-ionized water was 5.5). The thoroughly rinsed SG-9-1 precipitate was dried under vacuum at room temperature. The ‘‘half conversion time’’ (t1/2) of ferrihydrite (initially precipitated) to goethite by dissolution of ferrihydrite and re-precipitation as goethite at low values of pH and a temperature of 25 C is lengthy (t1/2  450 days at a pH of 1, as extrapolated from the data of Schwertmann and Murad, 1983). Therefore, at 25 C and a pH of 1, the synthesis time of 5955 days for SG-9-1 represents 13 half conversion times with, theoretically, about 99.98% of any initial ferrihydrite precipitate converted to goethite—i.e., essentially complete conversion to goethite. In a subsequent section, goethite–water oxygen isotope fractionation for this longer-term synthesis is compared with fractionations measured for low pH syntheses of shorter duration. A second, different type of synthesis experiment (SG-222) was performed in which Fe2+ oxidized to Fe3+ prior to formation of goethite. A well-crystallized sample of natural siderite (FeCO3) was powdered under acetone in a mortar and pestle and sized by passage through a 63 lm brass sieve. Infrared analysis (Yapp and Poths, 1990) had indicated that the siderite contained no discernible iron (III)

1117

oxides. The fine siderite powder (0.6359 mg) was added to a 250 ml glass bottle equipped with a poly-seal screw cap. The bottle was flushed with tank oxygen (purity 99%), followed by addition of 100 ml of 0.005 M H2SO4 solution, and the bottle was then immediately closed and weighed. The closed bottle was placed in an oven with the temperature control set at 46(±1) C. After 396 days the bottle was removed and weighed. There was no measurable loss of weight suggesting that the system had remained closed. A final pH of 5.9(±0.1) was measured for the reaction water, which was then decanted and stored in a separate closed glass bottle for isotopic analysis. The solid reaction product was repeatedly rinsed in de-ionized water until the rinse water attained a pH of 5.5. After rinsing, the solid product of SG-22-2 was dried under vacuum at room temperature. The mineralogy of the synthesis products was determined by X-ray diffraction (XRD) powder analysis with a Rigaku Ultima III diffractometer (for SG-9-1) and a Scintag Pad-V diffractometer (for SG-22-2) using Cu–Ka radiation at 40 kV, 0.5/1.0 mm for the primary slits, 0.2/ 0.3 mm for the receiving slits, and 44 and 30 mA currents for the Rigaku and Scintag instruments, respectively. Oxygen isotope analyses of SG-9-1 were performed using the BrF5 method of Clayton and Mayeda (1963) as modified by Yapp (1987) for goethite. Because SG22-2 was a mixture of fine-grained goethite, hematite and unreacted siderite that could not be physically or chemically separated, the oxygen isotope composition of goethite in SG-22-2 had to be determined by a more indirect method using CO2 evolved from goethite during isothermal incremental vacuum dehydration (Yapp, 2003). This is discussed more fully in a subsequent section. 18 O/16O ratios of the reaction waters were determined by the CO2–H2O equilibration method of Epstein and Mayeda (1953). The 13C/12C ratio of an aliquot of the siderite powder was measured prior to the SG-22-2 goethite synthesis experiment. The analysis was performed by first outgassing a 32.5 mg sample for 60 min at 100 C in vacuum. This was followed by heating in 0.2 bar of pure O2 at 230 C for 120 min. The siderite was then decarbonated by heating for 30 min at 850 C in a pure oxygen atmosphere at 0.2 bars. CO2 and H2O recovered from the SG-22-2 dehydration– decarbonation steps were cryogenically separated (using a dry ice-methanol bath) with collection of the CO2 for measurement of its amount and isotopic composition. Larger amounts of CO2 (> 50 lmol) were measured with a mercury manometer designed for larger samples. The analytical precision for this large manometer was ±0.5 lmol. For smaller amounts, CO2 was measured with a small-sample manometer with a precision of ±0.1 lmol. H2O recovered during dehydration was quantitatively converted to H2 over depleted uranium metal at 760 C with recovery of the H2 by a Toepler pump for measurement of yield with a precision of ±0.5 lmol.

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C.J. Yapp 71 (2007) 1115–1129

Isotope ratios were measured on a dual collector, gassource, isotope ratio mass spectrometer manufactured by Finnigan. The isotopic compositions are reported as d18O or d13C, where   Rsample  dY ¼  1  1000‰ ðIÞ Rstandard = 18O or 13C, and correspondingly, R = 18O/16O or C/12C. The standard is V-SMOW for oxygen and V-PDB for carbon. Analytical precision for measurement of the d18O value of goethite SG-9-1 by the BrF5 method is ±0.2&. The uncertainty in d13C and d18O of CO2 evolved during dehydration-decarbonation of SG-22-2 is ±0.1&for larger CO2 samples (>5 lmol), and ±0.3&for smaller increments of CO2 (<2 lmol). *Y 13

3. Results 3.1. XRD results XRD data for SG-9-1 indicate that the sample is composed only of goethite (Fig. 2a), whereas the XRD spectrum for SG-22-2 indicates the presence of goethite, hematite, and residual, unreacted siderite (Fig. 2b). As mentioned, this siderite could not be physically or chemically removed without affecting the goethite. The presence of the siderite and hematite required that the oxygen isotope composition of the goethite in SG-22-2 be determined by the incremental dehydration–decarbonation method (Yapp, 2003). 3.2. Isotopic results for SG-22-2 The ‘‘pure’’ siderite that was the initial reactant in the SG-22-2 goethite synthesis experiment had a d13C value of 12.2&and its CO2 yield was 99% of the expected amount (Table 1). Moreover, after outgassing at 100 C, the siderite was heated to 850 C and yielded only about 0.2 wt% H2O (yield reported as lmoles of H2 in Table 1), which affirmed the absence of any significant goethite in the siderite prior to the synthesis experiment. It should be noted that only 0.5 lmol of CO2 was recovered from the 32.5 mg sample of siderite at 230 C in O2 (Table 1), and some or all of this CO2 may have derived from oxidation of small amounts of organic matter. Thus, the residual siderite in SG-22-2 should not be a significant contributor to CO2 extracted during stepwise, vacuum decarbonation at T 6 230 C. Results from the stepwise dehydration–decarbonation of SG-22-2 are in Table 1. Table 1 lists the d18O and d13C values of the increments of CO2 evolved during sequential breakdown of SG-22-2 at various temperatures. Note that the increment from step 10 (850 C) had a d13C value of 12.2&, which is the same as that of the precursor siderite (Table 1). This d13C value, plus the thermal behavior of siderite recorded in Table 1, suggests that the CO2 which was evolved from SG-22-2 at 850 C was derived

from the residual siderite shown to be present by the XRD analysis. The SG-22-2 d18O and d13C data of Table 1 are plotted against XV(H2) in Fig. 3. XV(H2) is the cumulative amount of hydrogen recovered from the sample during stepwise dehydration as a mole fraction of the total hydrogen in the sample. If there were a ferrihydrite-like impurity in SG-22-2, it would break down to hematite at lower temperatures in the early steps (e.g., Hsieh and Yapp, 1999) and thus not interfere with the determination of the goethite d18O value by this dehydration-decarbonation method. The horizontal arrow associated with the carbon data in Fig. 3 indicates four successive increments with ‘‘plateau’’ d13C values for evolved CO2 (steps 5–8; avg. d13C = 9.8&; Table 1). These plateau d13C values characterize CO2 which is presumed to derive from breakdown of the Fe(CO3)OH component in solid solution in goethite (Yapp and Poths, 1991). However, the model of Yapp (2003) for d18O of CO2 evolved from goethite applies only to d18O values of plateau CO2 that is isothermally evolved from the Fe(CO3)OH component. Three of the plateau increments of CO2 (steps 5–7) were evolved at 200 C and exhibit d18O values which range from 14.9&to 16.1&. The amount-weighted average d18O value of these three aliquots of plateau CO2 is 15.4(±0.5)&. The error is one standard deviation of the mean and falls within the uncertainty of the results of Yapp (2003). The apparent first order slope, |m|, for the rate of dehydration of SG-22-2 at 200 C in vacuum is 0.0020(±0.0002) min1 (Table 2), as determined from the data of Table 1. This slope was determined for data exclusive of steps 1 and 2 in Table 1. Relationships between 18 aapp and |m| from the model of Yapp (2003) are shown in Fig. 4. Where,   1000 þ d18 OIPC aapp ¼ ðIIÞ 1000 þ d18 OG d18OIPC = d18O of plateau CO2 isothermally evolved during the breakdown of goethite in vacuum (IPC = Isothermal Plateau CO2). d18OG = d18O of the original goethite (FeOOH). The calculated curves of Fig. 4 incorporate the apparent temperature dependence of a reaction rate constant (Yapp, 2003). An 18aapp value of 1.0248(±0.0003) is predicted for |m| = 0.0020(±0.0002) min1 at an extraction T = 200 C (Fig. 4). For this 18aapp, a measured plateau d18O value of 15.4(±0.5)&corresponds to a d18O value of 9.2(±0.8)&for the synthetic goethite of SG-22-2. Combination of this inferred goethite d18O value of 9.2&with the d18O value of 13.2(±0.1)&for the reaction water (Table 2) yields a value for aG–W of 1.0040(±0.0009) at the synthesis pH of 5.9 and a temperature of 46 C.  aG–W ¼

1000 þ d18 OG 1000 þ d18 OW

 ðIIIÞ

pH and oxygen isotopes in goethite

1119

a

b

35 G (4.18) SG-22-2

(2.45)

S

G

(2.53)

28

(2.80)

G,H (2.69)

21

(4.99)

14

H

G (3.36)

(3.69)

(2.58)

CPS

H

G

G 7

0 10

20

30

40

50

60

Degrees 2θ

Fig. 2. (a) XRD powder spectrum of SG-9-1. The ‘‘d’’ spacings of a few principal goethite peaks are labeled. All peaks in the spectrum correspond to goethite. (b) XRD powder spectrum of SG-22-2. Peaks for the minerals goethite, hematite and siderite were identified in the sample. Some of these peaks ˚ ). are labeled: G = goethite; H = hematite; S = siderite. ‘‘d’’ Spacings are in parentheses (in A

d18OW = d18O of the reaction water. This nominal aG–W value of 1.0040 at 46 C compares with a value of 1.0037 (Table 2) predicted by the equation of Yapp (1990). The XRD pattern (Fig. 2b) is the sole criterion available for stating that the goethite in SG-22-2 is FeOOH (i.e., contains only Fe3+). The possibility that some small

fraction of the iron in this goethite was Fe2+ that escaped oxidation cannot be ruled out. However, no sample remains with which to determine ratios of Fe2+/Fe3+. It is not known if there would be any isotopic consequences even if small amounts of such Fe2+ were present.

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C.J. Yapp 71 (2007) 1115–1129

Table 1 Dehydration–decarbonation data for SG-22-2 (SG-22-2 synthesized at T = 46 C for 396 days) and decarbonation data for an aliquot of the starting siderite material Sample

Step #

T (C)

H2 (lmol)

100 230a 200 200 200 200 200 250 300 850a

214 168 136 55 74 48 79 100 45 60

Aliquot of siderite. Initial sample mass = 32.5 mg Siderite — 60 100 Siderite — 120a 230a a Siderite — 30 850a

3 1 3

SG-22-2 initial SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2 SG-22-2

Time (min.)

sample mass = 169.1 mg 1 60 2 60a 3 60 4 60 5 60 6 60 7 180 8 60 9 60 10 30a

CO2 (lmol) 4.8 9.4 1.9 1.6 2.1 1.25 1.6 1.9 1.9 71.6 0.0 0.5 277

CO2 d13CPDB

CO2 d18OSMOW

XV(H2)

9.0 14.1 11.5 10.2 9.6 9.8 9.9 9.5 18.3 12.2

18.4 17.1 14.9 12.8 14.9 16.1 15.6 15.1 10.7 6.5

0.22 0.39 0.53 0.59 0.66 0.71 0.79 0.89 0.94 1.00

— L 12.2

— — —

— — —

L = sample lost before it could be analyzed. a Indicates closed system in O2. All other increments open system in vacuum (see Yapp, 2003).

3.3. Isotopic results for SG-9-1

Increments of CO2 evolved from SG-22-2 -2

20

-4

18

* 18

16

O

-6

Fe(CO3)OH 10

13

13

OV-SMOW 18

-10

12

*

-14

*

6

4

-12

C

*

8

CV-PDB

-8

14

4. Discussion -16

carbon isotope composition

-20

2 0.2

0.4

0.6

0.8

1.0

XV(H2) 13

18

4.1. Temperature dependence of aG–W for goethite synthesized at low pH

-18

Oxygen isotope composition

0.0

Three analyses of SG-9-1 had an average d18O value of 6.0(±0.2)&, and the reaction water d18O value was 11.9(±0.1)&(Table 2). Combination of these values yields an aG–W of 1.0060(±0.0003) for a synthesis of 5955 days duration at pH = 1.1 and T = 25 C. Within analytical uncertainty, this value of aG–W is the same as published values of 1.0060(±0.0003) for a total synthesis/aging time of 165 days; 1.0063(±0.0003) for 211 days; and 1.0063(±0.0003) for 344 days, all at 25 C and pH 2 (Yapp, 1990). Taken together, these data indicate that the oxygen isotope composition of goethite synthesized at low pH (1 to 2) is not measurably changed by the length of time spent in the synthesis system on time scales up to nearly two decades at 25 C.

Fig. 3. d C and d O of increments of CO2 evolved from SG-22-2 during a stepwise dehydration-decarbonation. Steps marked with an asterisk indicate a closed system extraction in oxygen. All other steps were open system in vacuum (see Table 1). XV(H2) is the cumulative hydrogen evolved as a mole fraction of the total hydrogen in the sample. The horizontal arrow indicates the range of XV(H2) values for which plateau values of d13C are observed for the evolved CO2. This CO2 derives from the Fe(CO3)OH component in the synthetic goethite in the sample (see text). For the 200 C portion of this plateau, the weighted average d18OV-SMOW value of the CO2 is 15.4(±0.5)&, which corresponds to a goethite d18OV-SMOW value of 9.2(±0.8)&(see text and Table 2).

Xu et al. (2002) discussed the agreement of their experimental results with those of Yapp (1987, 1990) and suggested that the similarity of the results to the theoretical curve of Zheng (1998) implied that these experimental fractionations at low pH represent goethite–water oxygen isotope equilibrium. The agreement of the experimental results of Yapp (1990, this work) and the results of Xu et al. (2002) is illustrated by the respective best-fit equations for the temperature dependence of the low pH aG–W values. The low pH goethite and hematite data of Yapp (1990) plus the long-term SG-9-1 data point of Table 2 (all from Fe(NO3)3 solutions) are plotted as 1000 ln aG–W against 106/T2 in Fig. 5 (diamonds). The equation of the linear regression of those data is

pH and oxygen isotopes in goethite

1121

Table 2 Oxygen isotope data of goethite synthesized for this work Sample SG-22-2a SG-9-1 b SG-9-1b SG-9-1b SG-9-1c (Avg.)

Synthesis

Final water 18

Time (days)

T(C)

pH

d O

396 5955

46 25

5.9 1.1

13.2 11.9

5955

25

1.1

11.9

a

d18O of plateau CO2 evolved at 200 C

200 C slope |m| (min1)

d18O of goethite

Measured aG–W

Predicted

15.4 — — — —

0.0020 — — — —

9.2 5.8 5.9 6.3 6.0

1.0040

1.0037

1.0060

1.0061

d

aG-W

18

Estimated uncertainty of the goethite d O value for SG-22-2 as determined by the incremental CO2 method is ±0.8&. Standard error of the slope |m| is ±0.0002. b Analyzed aliquots of SG-9-1. c Average d18O value of SG-9-1 measurements. Standard deviation of mean is ±0.2&. d aG–W predicted with the curve of Yapp (1990).

1.034

7

αApp vs

1.032

|m|

1000lnαG-W at low pH (~ 1 to 2)

(CO from Fe(CO )OH vs. FeOOH)

6

1.030

data of Yapp (1990 + this work) data of Xu, et al. (2002)

Predicted α for SG-22-2 at 200˚C = 1.0248

1.028

αApp

1.026

5

4

1.024 1.022

200˚C 215˚C 230˚C

1.018 1.016

1000lnαG-W

3

170˚C

1.020

2

1 1.014 0.000

0.005

0.010

0.015

0.020

0

|m| (min-1)

Fig. 4. Curves for aapp plotted against |m|. See text for definitions. The labeled curves are vacuum dehydration isotherms which were calculated from the model of Yapp (2003) for d18O in CO2 evolved from the Fe(CO3)OH component in goethite. For dehydration of SG-22-2 at 200 C, the value of |m| was 0.0020(±0.0002) min1 (Table 2). As seen in the figure (square), this corresponds to a value for aapp of 1.0248(±0.0003).

regression of Yapp data y = 1.66(±0.05)x - 12.6(±0.5)

-1

r 2 = 0.99 regression of Xu, et al. data y = 1.66(±0.03)x - 12.6(±0.2)

-2

r2 = 0.98

-3

1000 ln aG–W

1:66  106 ¼  12:6 T2

6

ðIVÞ

r2 = 0.99, and T is in degrees Kelvin. For the range of temperatures from 0 to 120 C, the values of 1000 ln aG–W represented by Eq. (IV) differ by 60.1&from those of the equation of Yapp (1990). Values of 1000 ln aG–W from Xu et al. (2002) for all three types of starting solutions, Fe(NO3)3, FeNH4(SO4)2, and Fe2(SO4)3, are also plotted in Fig. 5 (triangles). Linear regression of those data yields an equation that is identical (within analytical uncertainty) to Eq. (IV) (see Fig. 5). 4.2. pH dependence of aG–W 4.2.1. Data Fig. 6 is a histogram of values of 1000 ln aG–W determined for 25 C. The low pH values (1 to 2) of

7

8

9

10

11

12

106/T2 Fig. 5. Values of 1000 ln aG–W plotted against 106/T2 (in degrees Kelvin) for low pH goethite synthesis data of Yapp (1990, this work): shown as diamonds; and Xu et al. (2002): shown as triangles. The equations of the linear regressions of the respective data sets are shown in the figure together with standard errors of the slopes and intercepts. Within analytical error, the two equations are indistinguishable (see text for discussion).

1000 ln aG–W in Fig. 6 were obtained from the two low pH equations shown in Fig. 5 and the low pH results of Mu¨ller (1995). The high pH values (14) in Fig. 6 are from the results (see Fig. 1) of Yapp (1987), Mu¨ller (1995), and Bao and Koch (1999). The distribution of the oxygen isotope data in Fig. 6 appears to be approximately bimodal and related to pH. The pH dependence of aG–W indicated

1122

C.J. Yapp 71 (2007) 1115–1129 7

1000ln G-W at 25°C (from published results at different pH)

Published low pH synthetic akaganeite-water 1000lnα

6

akaganeite data of Xu, et al. (2002) akaganeite data of Bao and Koch (1999)

5

2

low pH goethite curve of Fig. 5

4

Frequency

1000lnα

3 y = 1.52(±0.04)x - 11.6(±0.3) r 2 = 0.98

2 1

1 0 y = 0.66(±0.05)x - 6.3(±0.4)

-1

pH ~ 14

pH ~ 1 to 2

r 2 = 0.97

-2 -3 6

0

7

8

9 6

10

11

12

2

10 /T -2

-1

0

1

2

3

1000ln

4

5

6

7

8

G-W

Fig. 6. Histogram of 1000 ln aG–W for T = 25 C. The values are from Yapp (1990, this work), Mu¨ller (1995), Bao and Koch (1999), and Xu et al. (2002). There is an apparent pH-related bimodality in the values of 1000 ln aG–W. A model explaining this apparent oxygen isotope bimodality is presented in the text.

by this bimodality is modeled here in terms of the mechanism of growth of goethite crystals. 4.2.2. A model for aG–W An understanding of the mechanism of growth of goethite crystals is made difficult by the complexity of the speciation of Fe(III) in aqueous solution (e.g., Schneider, 1984; Schneider and Schwyn, 1987; Grundl and Delwiche, 1993; Pham et al., 2006). However, within analytical error, there is overall agreement (Fig. 5) of measured values of aG–W among the various low pH experiments performed by Yapp (1987, 1990) and Xu et al. (2002) using starting solutions of either Fe(III) nitrate, Fe(III) sulfate, or ammonium Fe(III) sulfate (ranges of anion concentrations = 0.07–0.85 M for NO3  or 0.01–0.09 M for SO4 2 ). This observation supports a tentative assumption that these anions have no significant effects on values of aG–W during goethite synthesis. As a corollary to this observation, the corresponding concentrations of initial iron (ranging from 0.005 to 0.2 M) also had no analytically significant effect on aG–W in these low pH experiments. The situation is more problematic for chloride ions. Mineral–water oxygen isotope fractionation factors deter-

Fig. 7. Oxygen isotope data (from Bao and Koch, 1999, squares; and Xu et al., 2002, diamonds) and curves representing linear regressions of 1000 ln a against 106/T2 (in degrees Kelvin) for akaganeite synthesized from aqueous Fe(III) chloride solutions at low pH (1 to 2). Equations of the regressions with standard errors of the slopes and intercepts are also presented. The low pH goethite–water curve of Fig. 5 is shown for comparison. See text for discussion.

mined by Xu et al. (2002) for akaganeite (b-FeOOH) and goethite (a-FeOOH) synthesized at a variety of temperatures and at low pH (1 to 2) are shown in Fig. 7. The temperature dependence of the mineral–water fractionation factors for the two different minerals is similar, but for T P25 C, the curves are offset by 60.7&(with akaganeite having the lower values of amin-water at lower temperatures). The akaganeite of Xu et al. (2002) was synthesized from Fe(III) chloride solutions with Cl concentrations ranging from 0.031 to 1.5 M. Thus, the relatively small oxygen isotope difference between their goethite and akaganeite curves might reflect a small effect due to differences in crystal structure and/or a small effect arising from differences in chloride complexation with aqueous Fe(III) hydroxides relative to nitrate or sulfate complexation. Uncertainties about the oxygen isotopic effects of chloride are even greater in the context of the results of Bao and Koch (1999). For synthesis of akaganeite from Fe(III) chloride solutions at low pH (1 to 2) and with initial Cl concentrations from 0.3 to 0.6 M, the akaganeite-water oxygen isotope fractionation factors of Bao and Koch (1999) are systematically lower than those of Xu et al. (2002) and also exhibit a very different dependence of

pH and oxygen isotopes in goethite

1000 ln a on temperature (see Fig. 7). The reasons for these differences in akaganeite results from the two laboratories are not known and more study is needed. Notwithstanding the dichotomy in the low pH akaganeite results, it is assumed, based on cited evidence from low pH goethite syntheses, that the effects of anion chemistry and concentration on mineral–water oxygen isotope fractionation factors during crystallization of goethite are small enough to ignore. This assumption may be particularly reasonable for the freshwater environments in which natural goethites commonly form. A possible explanation for the apparent lack of a direct effect of iron concentration on values of aG–W is presented in a subsequent section. Both mononuclear and polynuclear Fe(III) hydroxide species are part of the aqueous chemistry of iron (e.g., Schneider and Schwyn, 1987), but it may be reasonable to represent 18O/16O fractionation during goethite crystal growth in terms of aqueous mononuclear Fe(III) hydroxide complexes only. This allows development of a relatively simple kinetic model for the mineral–water oxygen isotope fractionation during growth of goethite. The simplification is rooted in the kinetic results of Grundl and Delwiche (1993) and Pham et al. (2006) at 25 C over the range of pH from about 2.5–3.1 and 6.0–9.5, respectively. These results indicate that solid ferric hydroxide grows by addition of the neutral aqueous species 0 FeðOHÞ3 . In a discussion of the implications of their measured goethite–water oxygen isotope fractionation factors, Bao and Koch (1999) outlined the sequence of mononuclear Fe(III) hydroxide deprotonation reactions—including among these reactions the addition of FeðOHÞ03 to the growing solid. For the current paper, it is assumed that 0 chemisorption of FeðOHÞ3 to the crystal surface is the predominant mechanism of addition of iron during growth of goethite crystals at all relevant values of pH. The validity of this assumption may be tested by the ability of the model to account for the oxygen isotope data from the goethite synthesis experiments. For simplicity, H2O molecules directly coordinated (inner coordination sphere) to the various mononuclear Fe(III) species are not shown in the following development of the isotopic model. These inner coordination sphere H2O molecules exchange very rapidly (time constants of 104 s) with bulk ambient water (e.g., Casey and Swaddle, 2003). Consequently, the oxygen isotopic composition of inner sphere H2O molecules may approximate equilibrium fractionation with respect to the bulk water. If so, the oxygen isotopic effects of inner sphere H2O molecules are implicitly included in representations of mineral–bulk water isotopic fractionation for relatively dilute solutions. Reactions illustrating the sequential deprotonation of H2O molecules to form various aqueous mononuclear Fe(III) hydroxide complexes are depicted below. An isotopic material balance equation and a reaction illustrating the formation of goethite, FeOOH(S), are also given.

1123 k1

Fe3þ þ H2 O $ FeðOHÞ k 1

2þ

FeðOHÞ

2þ

þ Hþ

k2

þ

þ H2 O $ FeðOHÞ2 þ Hþ k 2

k3

0 þ FeðOHÞþ 2 þ H2 O $ FeðOHÞ3 þ H k 3

k4

FeðOHÞ03 $ FeðOHÞA 3 k5

FeðOHÞA 3 ! FeOOHðSÞ þ H2 ODHW 0



FeðOHÞ3 þ H2 O $ FeðOHÞ4 þ Hþ k 6

ð2Þ ð3Þ ð4Þ

k 4

k6

ð1Þ

ð5Þ ð6Þ

nðOÞtot ¼ nðOÞFeOOH þ nðOÞDHW ð7aÞ 2 1 ð7bÞ Rtot ¼ ðRFeOOH Þ þ ðRDHW Þ 3 3   H2 ODHW RDHW ¼ ½H2 ODHW  18  O and so forth for other values of R ¼ 16 O DHW where k1 is the rate constant for the forward direction of reaction 1. k1 is the rate constant for the reverse direction of reaction 1, and so forth for the other reactions. An asterisk indicates the heavy oxygen isotopic molecule of a substance. DHW is dehydration water of reaction 5. DHW is distinct from ambient bulk environmental water. n(O) is the moles of oxygen atoms in the indicated substance. A bracket refers to concentration of the indicated species. A It is emphasized that FeðOHÞ3 of reactions 4 and 5 is not an indicator of ferrihydrite. Instead, it is envisioned that a molecule of FeðOHÞ03 chemisorbs from aqueous solution to the surface of a growing goethite crystal to form the A FeðOHÞ3 . It is presumed that this is followed by loss of A H2O (the DHW of reaction 5) from the FeðOHÞ3 as its iron and some of its oxygen and hydrogen are added to the goethite structure. This scenario seems to be generally consistent with the conclusion of Schwertmann and Murad (1983) that goethite grows from solution after precursor ferrihydrite first dissolves. The material balance of Eq. (7b) represents the assumption that there is no local oxygen isotope exchange between DHW and ambient bulk water during the molecular-scale A transition in which DHW is evolved from FeðOHÞ3 to produce FeOOH. It is not known if reactions 3–5 are reasonable representations of the actual detailed reaction mechanisms operative in the growth of goethite crystals. However, for this first attempt to model a possible pH dependence of the goethite–water oxygen isotope fractionation factor, reactions 3–5 are treated as elementary reactions. For reactions 1–3 and 6, the forward and reverse reactions are presumed to be fast—i.e., the second order rate constants appear to be P 1010 M1 s1 at 25 C (Schneider and Schwyn, 1987). M = molarity. Therefore, during crystal growth the aqueous mononuclear Fe(III) hydroxide

1124

C.J. Yapp 71 (2007) 1115–1129

complexes may approximate a kind of moment-to-moment steady state distribution (e.g., Grundl and Delwiche, 1993). 0 Thus, except for FeðOHÞ3 which is the complex presumably added to the growing solid, the fractionations of 18O/16O with respect to water exhibited by the other Fe(III) hydroxide complexes do not appear explicitly in the model. Reaction 5 is depicted as an irreversible reaction, because the growth of a crystal from an oversaturated solution must represent, at some point and to some degree, an irreversible process (i.e., disequilibrium). Possible relative magnitudes of the rate constants k4, k4, and k5 are considered in subsequent discussion. 0 The flux balance equation for FeðOHÞ3 is d½FeðOHÞ03  þ 0 ¼ k 3 ½FeðOHÞ2 ½H2 O  k 3 ½FeðOHÞ3  dt 0 A  ½Hþ   k 4 ½FeðOHÞ3  þ k 4 ½FeðOHÞ3  ½FeðOHÞA 3

ð8Þ

FeðOHÞA 3

is the concentration of on the surface of a growing goethite crystal. Terms derived from reaction 6 do not appear in Eq. (8). This arises from the hypothesis that FeðOHÞ4  is the terminal aqueous mononuclear Fe(III) hydroxide complex in the deprotonation sequence and from an assumption of a quasi-equilibrium distribu0 tion of the FeðOHÞ4  complex relative to FeðOHÞ3 . For addition of 18O from H218O in reaction 3, the reaction would be k 3

 FeðOHÞþ FeðOH Þ03 þ Hþ 2 þ H2 O $  k 3

ð9Þ

Note that combination of reactions 3 and 9 represents sin0 gle-atom exchange of 18O between FeðOHÞ3 and ambient bulk H2O. The asterisks on rate constants (k*) represent the values of those constants for reactions involving the heavy isotopic molecules. 0 The flux balance equation for FeðOH Þ3 is 0

d½FeðOH Þ3  k 3 k 3 þ ¼ ½FeðOHÞ2 ½H2 O   dt a3 a3 k4 0 0  ½FeðOH Þ3 ½Hþ   ½FeðOH Þ3  a4 k 4 A þ ½FeðOH Þ3  a4

dt

A

ð10Þ

Now, for the heavy isotopic molecule with singly substituted 18O dnðO Þtot ¼ k 5 ½FeðOH ÞA 3 dt

ð13bÞ

Note, nðO Þtot ¼ Rtot nðOÞtot Then, Rtot

dnðOÞtot dRtot k 5 A þ nðOÞtot ¼ ½FeðOH Þ3  dt dt a5

ð14Þ

Eq. (14) is expressed in terms of isotope ratios as well as n(O)tot to illustrate the approach. Substitutions to express the flux balance equations for heavy isotopic molecules in terms of isotope ratios can be performed for all such expressions, but the length of the resulting equations precluded their representation in that form for Eqs. (10) and (12). Now, let X = 16O as a fraction of the total moles of oxyA gen in FeðOHÞ3 and Y = 18O as a fraction of the total moA les of oxygen in FeðOHÞ3 . Then, RFeðOHÞA ¼ Y =X. Also, let 3 [fxa] = the total concentration of light and heavy isotopic A molecules of FeðOHÞ3 , where it is assumed that at natural abundance levels on Earth the isotopically heavy oxygen isotopic molecules are overwhelmingly singly substituted by 18O—i.e., Fe18 O16 O16 OHA 3 . If the distribution of oxygen A isotopic atoms among hydroxyl sites in an FeðOHÞ3 moleA cule is stochastic, then [FeðOHÞ3  ¼ X 3 [fxa] and A ½FeðOH Þ3  ¼ 3X 2 Y [fxa]. The factor of 3 arises from the three possible hydroxyl positions that the single 18O atom can occupy in a molecule of ½FeðOH ÞA 3 ], and therefore, 3 ½FeðOH ÞA  ¼ 3X ½fxaR A. 3 FeðOHÞ Then, for Eq. (13a), dt tot ¼ 3k 5 X 3 ½fxa and substituting into Eq. (14) with the assumption of isotopic steady state 3k 5 X 3 ½fxaRtot ¼ 3

k5 3 X ½fxaRFeðOHÞA 3 a5

ð15aÞ

And, ð11Þ

The corresponding expression for the heavy isotopic moleA cule FeðOH Þ3 is: A

d½FeðOH Þ3  k 4 k 4 0 A ¼ ½FeðOH Þ3   ½FeðOH Þ3  dt a4 a4 k5  ½FeðOH ÞA 3 a5

ð13aÞ

3

¼ k 4 ½FeðOHÞ03   k 4 ½FeðOHÞA 3  k 5 ½FeðOHÞ3 

dnðOÞtot A ¼ 3k 5 ½FeðOHÞ3  dt

dnðOÞ

For FeðOHÞA 3 the flux balance is expressed as A d½FeðOHÞ3 

k4 k 4 By definition, a3 ¼ kk3 ; a3 ¼ kk3  ; a4 ¼  ; a4 ¼  ; k4 k 4 3 3 k5 a5 ¼ k . These a values represent kinetic oxygen isotope 5 fractionations for the indicated reaction directions. In general, k > k* (e.g., O’Neil, 1986). The expression for rates of change in n(O)tot is

ð12Þ

Rtot ¼

1 R A a5 FeðOHÞ3

ð15bÞ

Assumptions of moment-to-moment steady states for isotopic ratios and concentrations of aqueous species and A surface-bound FeðOHÞ3 during crystal growth are expressed as d½ ¼ 0 and dt

dR ¼0 dt

pH and oxygen isotopes in goethite

With these assumptions, combination of Eqs. (7b), (8), (10), (11), (12), and (15b) yields the following expression for aG–W:

 a3eq AC  ð16Þ aG–W ¼ 2 1 1 B a4 3 þ 3 aG–DHW where,      k4 k4 1 þ  k 4 A ¼ ½H  þ k 3 k 3 fk 4 þ k 5 g 0  1 a3 k4   B C a k k a k 3 4 4 3 C B4  B ¼ ½Hþ  þ  a4 k 3 a4 @ k 4 k 5 A þ a4 a5 ðk 4 þ k 5 Þ  C¼  k 4 k 5 þ a5 a4 a5 RFeðOHÞ0 a3 RFeOOH 3 ; a3eq ¼ ¼ ; RW RW a3 RG aGDHW ¼ RDHW

aG–W ¼

The subscript ‘‘eq’’ refers to equilibrium oxygen isotope fractionation —in this case for reaction 3. The magnitude, at the site of the reaction, of the oxygen isotope fractionation (aG-DHW) between locally produced goethite and DHW (as DHW egresses the reaction site) is not known. It is speculated that it would be a disequilibrium value (and >1) because of the presumed irreversibility of the process. For the following discussions, it is worth noting that values of a for oxygen isotopes (kinetic or equilibrium) commonly differ from unity by only a few percent or less (e.g., O’Neil, 1986). The complexity of Eq. (16) discourages an appreciation of the physical processes represented. Therefore, it is instructive to consider some limiting conditions. 4.2.3. aG–W for reversibility in reaction 4 If reaction 4 were reversible and if k4  k5, Eq. (16) would simplify to

a4eq ¼

3a3eq a4eq a5 ð2 þ 1=aG–DHW Þ a4 a4

and a3eq a4eq ¼

ð17Þ RFeðOHÞ0 RFeðOHÞA 3

RW

3

RFeðOHÞ0 3

¼

RFeðOHÞA 3

RW

unless aG–DHW = a5/(3  2a5), Eq. (17) indicates that aG–W itself would not be an equilibrium value. More importantly, the data of Fig. 6 indicate that there is an effect of pH on the value of aG–W, and this contradicts the prediction of Eq. (17). Therefore, for growth of goethite crystals, it is likely that the relationship of k4 to k5 is very different from that implicit in Eq. (17). 4.2.4. aG–W for irreversibility in reaction 4 If reaction 4 were actually irreversible (e.g., Grundl and Delwiche, 1993), it would imply that k4 = 0. Setting k4 = 0 in Eq. (16) leads to the following result:  3a3eq ½Hþ  þ kk34  aG–W ¼ ð18Þ a4 ð2 þ 1=aG–DHW Þ ½Hþ  þ aa34 kk34

and,

aG–W ¼

1125

¼ aðA–WÞeq

aðA–WÞeq is the equilibrium oxygen isotope fractionation facA tor between FeðOHÞ3 and ambient bulk water. Eq. (17) predicts no dependence of aG–W on pH, because k4  k5 implies effective oxygen isotopic equilibrium beA tween the intermediate species, FeðOHÞ3 , and the ambient bulk water during growth of goethite. Approximate equilibrium in the intermediate step represented by reaction 4 would preclude an influence of pH on the value of aG–W through the deprotonation process of reaction 3. However,

It should be noted that a5 does not appear in Eq. (18), because the assumption of oxygen isotopic steady state requires that the isotope ratio of the unidirectional flux into A the FeðOHÞ3 portion of the system equals the isotope ratio of the flux out. Thus, the isotope ratio of the flux out of the A FeðOHÞ3 ‘‘reservoir’’ is determined in previous steps, and a5 does not appear in Eq. (18). This is an internally consistent consequence of the mathematical derivation when both reactions 4 and 5 are irreversible. Eq. (18) predicts that the value of aG–W depends upon the pH of the ambient bulk solution. Eq. (18) also indicates that the particular characteristics of the pH dependence are determined by the value of the ratio k4/k3. As noted, the rate constant for reaction 3 is large (P 1010 M1 s1). If reaction 4 were not only irreversible during crystal growth, but also relatively slow (e.g., Grundl and Delwiche, 1993), it would imply that the ratio k4/k3 is a very small number. For a solution with a comparatively low initial Fe(III) concentration of 0.0005 M, Grundl and Delwiche (1993) give a half-time (t1/2) of 5 min for the first order decrease of the 0 concentration of FeðOHÞ3 during crystal growth at 25 C. This implies a value for k4 of 0.0023 s1 and a value for k4/k3 of 2.3 · 1013 M. However, as discussed by Grundl and Delwiche (1993), Fe3+ ions have an inhibitory effect on the rate of crystal growth (i.e., on k4). This effect (proportional to the initial concentration of Fe3+ in solution) could manifest itself in the dependence of aG–W on pH by changing the ratio of k4/k3 and thereby shifting the specific values of pH that define the high and low ends of the pH-sensitive range. This possibility may be testable by experiment. Grundl and Delwiche (1993) also found that excess Cl in solution did not modify t1/2 (i.e., k4). However, if different anions modified k4 to different degrees, this would further complicate assessment of k4/k3 values. These possible influences are not directly considered, but are implicit in subsequent discussion of variations of k4/k3. The concentration of iron in aqueous solution does not appear explicitly in Eq. (16) (nor, consequently, in Eq. (18)). This may be explained by considering an important

1126

C.J. Yapp 71 (2007) 1115–1129

subset of the various reactions in the model—in particular the competing reactions represented by the reverse direction in reaction 3 and the forward direction of the presumably irreversible reaction 4. The rate ðr3 Þ of the reverse direction of reaction 3 for the heavy isotopic molecule is ex0 pressed as r3 ¼ k 3 ½FeðOH Þ3 ½Hþ , whereas the forward rate ðr4 Þ of reaction 4 is expressed as r4 ¼ k 4 ½FeðOH Þ03 . The ratio of these rates is r3 =r4 ¼ fk 3 =k 4 g½Hþ . Thus, [H+] is expected to affect the relative rates, but the concentration of iron in solution cancels out of the ratio. Eq. (16) is derived from the ratios of the flux balance equations, and such cancellation accounts for the absence of a predicted direct effect of iron concentration on the value of aG–W. This prediction is consistent with experimental results for goethites crystallized at low pH from Fe(III) nitrate and sulfate solutions of varying concentrations (Xu et al., 2002). Given that values of a are near unity, very small values of k4/k3 would suggest that the summations involving [H+] in Eq. (18) should each be dominated by the value of [H+] at relatively low pH. Thus, for ½Hþ   k 4 =k 3 or pH <  logðk 4 =k 3 Þ aG–W 

3a3eq low pH equation a4 ð2 þ 1=aG–DHW Þ

ð19Þ

Eq. (19) predicts that aG–W is an equilibrium value only if aG–DHW = a4/(3  2a4). If this condition were realized, the model predicts that aG–W at low pH would have the same value as the equilibrium oxygen isotope fractionation 0 factor (a3eq ) between aqueous FeðOHÞ3 and ambient H2O. The prospects for realization of this condition are unknown. Therefore, it is suggested that aG–W at low pH may approach, but probably not equal, an equilibrium value. If ½Hþ  k 4 =k 3 , Eq. (18) becomes aG–W 

3 high pH equation a3 ð2 þ 1=aG–DHW Þ

ð20Þ

a3 is a kinetic fractionation factor, and it is apparent that the value of aG–W at high pH predicted by Eq. (20) does not represent equilibrium between goethite and water. The values of aG–W at high and low pH (at some temperature) should be different, if a3 6¼ a4 (see Eq. (18)). As previously discussed, the data of Fig. 6 indicate a pH dependence for aG–W, and the model represented by Eq. (18) anticipates such a dependence. The low pH and high pH extremes of Eq. (18) (i.e., Eqs. (19) and (20)) indicate that the ratio [aG–W (low pH)]/[aG–W (high pH)] = a3/a4. If log (k4/k3) lies between the extremes of pH in Fig. 6, the aG–W values in Fig. 6 could be used to determine the ratio a3/a4. Such an intermediate value for k4/k3(2.3 · 1013 M at 25 C) is assumed—i.e., log (k4/k3) = 12.6. The agreement of the low pH aG–W values measured by Yapp (1990, this work) and Xu et al. (2002) suggests use of a low pH aG–W value of 1.0061 at 25 C (Fig. 5 and Eq. (IV)). Choice of a high pH aG–W value is more problematic because of the observed range of aG–W values at high pH in

Fig. 6. The high-pH aG–W value of 1.0018 at 25 C (Yapp, 1987) for goethite crystallized from Fe(III) nitrate solutions (Figs. 1 and 6) implies a3/a4 = 1.0043, whereas a3/a4 = 1.0077 for a high-pH aG–W of 0.9984 (from Fe(III) chloride solutions, Bao and Koch, 1999). At present, there is little information that would favor a choice of one value over another. As a basis for discussion, the extremum value of 1.0077 for a3/a4 at 25 C will be used. The magnitude of the ratio a3/a4 can be determined in the same manner at other temperatures. These values may then be used in Eq. (18). As seen in Eq. (18), for a particular temperature, the value of aG–W at low pH determines the value of the ratio, 3a3eq =fa4 ð2 þ 1=aG–DHW Þg, and this ratio may be used at all values of pH in Eq. (18). Therefore, for a known value of k4/k3 at a temperature of interest, Eq. (18) can be used to predict values of aG–W as a function of pH in the range of pH values between the high and low extremes. As mentioned, at a moderately low initial Fe(III) concentration of 0.0005 M, the value of k4/k3 may be 2.3 · 1013 M at 25 C. The values of k4/k3 at other temperatures could be calculated if the difference in the values of the respective Arrhenius activation energies of these rate constants were known. A small difference would imply a small dependence on temperature. However, these activation energies are not known and the aforementioned value for k4/k3 at 25 C will be used as a basis for further discussion. Values of 3a3eq =fa4 ð2 þ 1=aG–DHW Þg were determined for 25, 46, and 62 C using Eq. (IV) These values are 1.0061, 1.0037, and 1.0022, respectively. From these low-pH aG–W results and values of aG–W from the high-pH equation of Bao and Koch (1999), the calculated a3/a4 ratios are 1.0077, 1.0057, and 1.0045 at 25, 46, and 62 C, respectively. The values for a temperature of 46 C were chosen for further discussion because they correspond to a temperature for which a relevant experimental result is available to test the model prediction. To illustrate the implications of the model, values of 1000 ln aG–W were calculated as a function of pH at 46 C using Eq. (18) and are plotted in Fig. 8. The darker, solid curve represents a value of 2.3 · 1013 M for k4/k3. For comparison, two additional curves are shown for k4/k3 values of 1013 and 1012 M. Curves calculated for other temperatures would have similar shapes, but different amplitudes and possibly different k4/k3 values. As seen in Fig. 8, for a particular value of k4/k3, the value of aG–W is predicted to vary with pH over a comparatively narrow range of pH (3 pH ‘‘units’’) relative to the range of pH values (from 1 to 14) over which goethite can crystallize. At values of pH outside this range the value of aG–W is expected to be relatively constant at either the low pH value or the high pH value. In fact, the model curves in Fig. 8 predict that the low-pH aG–W value should be observed for values of pH 6 10. The curves of Fig. 8 also suggest that it is unlikely that the value of k4/k3 was lower than 1013 M at 46 C in the high pH experiments of Bao and Koch (1999), because the predicted value of 1000 ln aG–

pH and oxygen isotopes in goethite

1127

5 4

k4/k-3

1000lnαG-W

3 2 10-13

1 10-12

0 -1

1000lnαG-W vs. pH (at 46˚C)

-2 -3 0

2

4

6

8

10

12

14

pH

Fig. 8. Curves of 1000 ln aG–W vs. pH calculated for 46 C using published data and the model for oxygen isotope fractionation during growth of goethite presented in the text (see text for details). The darker, solid curve was calculated for a k4/k3 ratio of 2.3 · 1013 M. Two bracketing curves are shown for comparison and represent values for k4/k3 of 1013 and 1012 M. The low pH (2) and high pH (14) data points (squares) are, respectively, from Eq. (IV) (this work) and Bao and Koch (1999) and are shown for reference. The data point (diamond) at a pH of 5.9(±0.1) was measured for goethite synthesized at 46(±1) C (experiment SG-22-2, Tables 1 and 2). For SG-22-2, the measured value of 1000 ln aG–W is 4.0(±0.9) and was not used to calculate the model curve at 46 C (see text). Therefore, the correspondence (within analytical error) of this measured result with the model curve suggests that, as predicted, the low pH value of 1000 ln aG–W is constant up to at least a pH of 6.

would not have decreased to the experimental value of 2.0 until model values of pH significantly exceeded the experimental pH value of 14. The data point (diamond) in Fig. 8 for a pH of 5.9(±0.1) is from goethite synthesized at 46(±1) C in experiment SG-22-2 (Table 2), and its 1000 ln aG–W value of 4.0(±0.9) plots, within analytical error, on the 46 C model curve. The value of aG–W measured for SG-22-2 was not used to calculate the model curve at 46 C. Therefore, the correspondence (within analytical error) of the result from SG-22-2 with the model curve suggests that the value of aG–W is constant up to at least a pH of 6. If the value of k4/k3 is 2.3 · 1013 M, it suggests a speculative, model-derived explanation for some of the differences among the high pH curves of Fig. 1 (nominally at pH values of 14). Comparatively small differences (1 to 1.5 pH ‘‘units’’) among the actual pH values of the different high pH experiments are predicted to produce relatively large variations among values of aG–W (with higher values of aG–W for somewhat lower pH values; Fig. 8). Such variations might account, in part, for the differences among the high pH curves of Fig. 1. This sensitivity to pH would not be expected at the low-pH end of the spectrum. The validity of the predicted shape of the model curve and a model-derived value of k4/k3 at a particular temperature could be determined by a series of goethite synthesis experiments in solutions of varying pH, followed by measurement of the values of aG–W. In what appears to be an important range of pH (7–12) for constraining values of k4/k3, hematite commonly co-precipitates with, and can W

even predominate over, goethite (Schwertmann and Murad, 1983). However, this experimental complication might not preclude the determination of values for k4/k3. If goethite in this pH range could be synthesized to include the Fe(CO3)OH component in solid solution, the approach illustrated by Fig. 4 could be employed to estimate the goethite d18O value (e.g., goethite in SG-22-2, Tables 1 and 2). Therefore, goethite synthesis experiments over a range of pH values may be useful for the determination of k4/k3 even if hematite is part of the product. 5. Conclusion Goethite synthesis experiments indicate that pH affects the measured value of aG–W. A simple model predicts a pH dependence for aG–W in terms of kinetic parameters related to the growth of goethite crystals. The model indicates that the range of pH over which aG–W changes as pH changes is expected to be comparatively small (3 pH ‘‘units’’) relative to the range of pH values (1 to 14) over which goethite can crystallize. Outside this range of sensitivity to pH, aG–W is predicted to be relatively constant at either a low pH aG–W value or a high pH aG–W value. Data from synthetic goethite (SG-22-2) suggest that Eq. (IV) for the temperature dependence of 1000 ln aG–W at low pH (1 to 2) is relevant for values of pH up to at least 6. This result and the model prediction of an insensitivity of aG–W to pH over an even larger range of pH values could explain the observation that the equation of Yapp (1990), or its effective equivalent (Eq. (IV) of this work), yields

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values of aG–W which mimic most 18O/16O fractionations measured thus far in natural goethites. New experiments are needed to test the model prediction of shape of the curve of 1000 ln aG–W vs. pH and to determine the ranges of pH values over which aG–W is sensitive to pH at different temperatures. The flux balance approach applied to goethite in this paper might also be used in studies of isotopic fractionations in minerals such as hematite, calcite, and perhaps gibbsite.

Acknowledgments I wish to thank David Cole, Huiming Bao, and Derek Sjostrom for helpful reviews, and Weimin Feng for translation of the paper by Xu et al. This research was supported by NSF Grant EAR-0106257. Associate editor: David R. Cole

References Bao, H., Koch, P.L., 1999. Oxygen isotope fractionation in ferric oxide– water systems: low temperature synthesis. Geochim. Cosmochim. Acta 63, 599–613. Bao, H., Koch, P.L., Thiemens, M.H., 2000. Oxygen isotope composition of ferric oxides from recent soil, hydrologic, and marine environments. Geochim. Cosmochim. Acta 64, 2221–2231. Bird, M.I., Longstaffe, F.J., Fyfe, W.S., Bildgen, P., 1992. Oxygen isotope systematics in a multi-phase weathering system in Haiti. Geochim. Cosmochim. Acta 56, 2831–2838. Bird, M.I., Longstaffe, F.J., Fyfe, W.S., Kronber, B.I., Kishida, A., 1993. An oxygen-isotope study of weathering in the eastern Amazon Basin, Brazil. Climate Change in Continental Isotopic Records, Geophys. Monograph 78, 295–307. Casey, W.H., Swaddle, T.W., 2003. Why small? The use of small inorganic clusters to understand mineral surface and dissolution reactions in geochemistry. Rev. Geophys. 41. doi:10.1029/2002RG000118, 2/1008, 4-1 to 4-20. Clayton, R.N., Mayeda, T.K., 1963. The use of bromine pentafluoride in the extraction of oxygen from oxides and silicates for isotopic analysis. Geochim. Cosmochim. Acta 27, 43–52. Epstein, S., Mayeda, T., 1953. Variation of O18 content of waters from natural sources. Geochim. Cosmochim. Acta 4, 213–224. Girard, J.P., Razanadranorosa, D., Freyssinet, P., 1997. Laser oxygen isotope analysis of weathering goethite from the lateritic profile of Yaou, French Guiana: paleoweathering and paleoclimatic implications. Appl. Geochem. 12, 163–174. Girard, J.P., Freyssinet, P., Gilles, C., 2000. Unraveling climatic change from intra-profile variation in oxygen and hydrogen isotopic composition of goethite and kaolinite in laterites: an integrated study from Yaou, French Guiana. Geochim. Cosmochim. Acta 64, 4467– 4477. Girard, J.-P., Freyssinet, P., Morillon, A.-C., 2002. Oxygen isotope study of Cayenne duricrust paleosurfaces: implications for past climate and laterization processes over French Guiana. Chem. Geol. 191, 329–343. Grundl, T., Delwiche, J., 1993. Kinetics of ferric oxyhydroxide precipitation. , J. Contam. Hydrol. 14, 71–97. Hein, J.R., Yeh, H.W., Gunn, S.H., Gibbs, A.E., Wang, C.H., 1994. Composition and origin of hydrothermal ironstones from central Pacific seamounts. Geochim. Cosmochim. Acta 58, 179–189. Hren, M.T., Lowe, D.R., Tice, M.M., Byerly, G., Chamberlain, C.P., 2006. Stable isotope and rare earth element evidence for recent

ironstone pods within Archean Barberton greenstone belt, South Africa. Geochim. Cosmochim. Acta 70, 1457–1470. Hsieh, J.C.C., Yapp, C.J., 1999. Stable carbon isotope budget of CO2 in a wet, modern soil as inferred from Fe(CO3)OH in pedogenic goethite: possible role of calcite dissolution. Geochim. Cosmochim. Acta 63, 767– 783. Mu¨ller, J., 1995. Oxygen isotopes in iron (III) oxides: a new preparation line; mineral–water fractionation factors and paleoenvironmental considerations. Isotopes Environ. Health Stud. 31, 301–302. O’Neil, J.R., 1986. Theoretical and experimental aspects of isotopic fractionation. In: Valley, J.W., Taylor, H.P., Jr, O’Neil, J.R. (Eds.), Stable Isotopes in High Temperature Geological Processes. Rev. Mineral. 16. Mineralogical Society of America, Washington, DC, pp. 1–40. Pack, A., Gutzmer, J., Beukes, N.J., Van Niekerk, H.S., 2000. Supergene ferromanganese wad deposits derived from Permian Karoo strata along the Late Cretaceous-Mid-Tertiary African land surface, Ryedale, South Africa. Econ. Geol. 95, 203–220. Pham, A.N., Rose, A.L., Feitz, A.J., Waite, T.D., 2006. Kinetics of Fe(III) precipitation in aqueous solutions at pH 6.0–9.5 and 25 C. Geochim. Cosmochim. Acta 70, 640–650. Poage, M.A., Sjostrom, D.J., Goldberg, J., Chamberlain, C.P., Furniss, G., 2000. Isotopic evidence for Holocene climate change in the northern Rockies from a goethite-rich ferricrete chronosequence. Chem. Geol. 166, 327–340. Schneider, W., 1984. Hydrolysis of iron(III)–Chaotic olation versus nucleation. Comments Inorg. Chem. 3, 205–223. Schneider, W., Schwyn, B., 1987. The hydrolysis of iron in synthetic, biological, and aquatic media. In: Stumm, W. (Ed.), Aquatic Chemistry: Chemical Processes at the Particle-Water Interface. Wiley, New York, pp. 167–196. Schwertmann, U., Murad, E., 1983. Effect of pH on the formation of goethite and hematite from ferrihydrite. Clays Clay Mineral. 31, 277– 284. Sjostrom, D.J., Hren, M.T., Chamberlain, C.P., 2004. Oxygen isotope records of goethite from ferricrete deposits indicate regionally varying Holocene climate change in the Rocky Mountain region, USA. Quat. Res. 61, 64–71. Tabor, N.J., Yapp, C.J., 2005. Juxtaposed Permian and Pleistocene isotopic archives: surficial environments recorded in calcite and goethite from the Wichita Mountains, Oklahoma. In: Mora, G., Surge, D. (Eds.), Isotopic and elemental tracers of Cenozoic climate change. GSA Spec. Pap 395, pp. 55–70. Tabor, N.J., Montan˜ez, I.P., Zierenberg, R., Currie, B.S., 2004. Mineralogical and geochemical evolution of a basalt-hosted fossil soil (Late Triassic, Ischigualasto Formation, northwest Argentina): potential for paleoenvironmental reconstruction. GSA Bull. 116, 1280–1293. Xu, B-L., Zhou, G-T., Zheng, Y-F., 2002. An experimental study of oxygen isotope fractionations in goethite-akaganeite-water systems at low temperature (in Chinese). Geochimica 31, 366–374. Yapp, C.J., 1987. Oxygen and hydrogen isotope variations among goethites (a-FeOOH) and the determination of paleotemperatures. Geochim. Cosmochim. Acta 51, 355–364. Yapp, C.J., 1990. Oxygen isotopes in iron (III) oxides. 1. Mineral–water fractionation factors. Chem. Geol. 85, 329–335. Yapp, C.J., 1991. Oxygen isotopes in an oolitic ironstone and the determination of goethite d18O values by selective dissolution of impurities: the 5 M NaOH method. Geochim. Cosmochim. Acta 55, 2627–2634. Yapp, C.J., 1993. Paleoenvironment and the oxygen isotope geochemistry of ironstone of the Upper Ordovician Neda Formation, Wisconsin, USA. Geochim. Cosmochim. Acta 57, 2319–2327. Yapp, C.J., 1997. An assessment of isotopic equilibrium in goethites from a bog iron deposit and a lateritic regolith. Chem. Geol. 135, 159–171. Yapp, C.J., 1998. Paleoenvironmental interpretations of oxygen isotope ratios in oolitic ironstones. Geochim. Cosmochim Acta 62, 2409–2420.

pH and oxygen isotopes in goethite Yapp, C.J., 2000. Climatic implications of surface domains in arrays of dD and d18O from hydroxyl minerals: goethite as an example. Geochim. Cosmochim. Acta 64, 2009–2025. Yapp, C.J., 2001. Rusty relics of Earth history: iron (III) oxides, isotopes and surficial environments. Ann. Rev. Earth Planet. Sci. 29, 165–199. Yapp, C.J., 2003. A model for 18O/16O variations in CO2 evolved from goethite during the solid state a-FeOOH to a-Fe2O3 phase transition. Geochim. Cosmochim. Acta 67, 1991–2004.

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Yapp, C.J., Poths, H., 1990. Infrared spectral evidence for a minor Fe(III) carbonate-bearing component in natural goethite. Clays Clay Mineral. 38, 442–444. Yapp, C.J., Poths, H., 1991. 13C/12C ratios of the Fe(III) carbonate component in natural goethites. Taylor, H.P., Jr. et al. (Ed.), Stable Isotope Geochemistry: A Tribute to Samuel Epstein, Geochem. Soc. Spec. Publ. 3, pp. 257–270. Zheng, Y.-F., 1998. Oxygen isotope fractionation between hydroxide minerals and water. Phys. Chem. Mineral. 25, 213–221.