Mimicking Biological Carbon Isotope Signatures in Fe-C-O-H Systems under Equilibrium Conditions

JelteHarnmeijer*

Submitted to Geochimica et Cosmochimica Acta

15 July2007

Center for Astrobiology and Early Earth Evolution, Box 351310, University of Washington, Seattle, WA, 98195-1310, USA

*E-mail: . Phone: +01-706-202-3321.

Keywords: carbon isotopes, COH fluids, metamorphism, graphite, decarbonation

Abstract

With metamorphism, the interpretation of 13C systematics in rocks can be hampered by a variety of processes. As is amply evidenced by a plethora of ongoing controversies, biological 13C signatures (‘biosignatures’) are particularly prone to such obfuscation. Processes imparting an isotopic fractionation not mediated by enzymatic metabolism(a.k.a. ‘life’) includeisotopic re-equilibration with carbon in metasomatic C-O-H fluids and/or carbonate, precipitation of remobilized carbon, devolatilization of organic matter, and post-diagenetic carbon production resulting from decarbonation reactions of carbonates. Under the assumption of equilibrium, however, the isotopic behaviour and evolution of carbon under the sway of these processes is largely quantifiable.

In this theoretical study, a Modified Redlich-Kwong (MRK) equation of state built on recent thermodynamic fluid species data is coupled with recent advances in our understanding of equilibrium isotope fractionation to arrive at a flexible model for the isotopic behaviour and evolution of carbon in Fe-C-O-H systems under geologically relevant conditions of P, T and fO2. Calculations are performed within the thermodynamic space: 1000 > P > 10000 bar, 400 < T < 1200 C and log(fO2QFM)-6< log(fO2) < log(fO2QFM)+8.

Implications of the model are discussed with a view to its application in differentiating between carbon of biological and non-biological origin. The production of isotopically depleted ‘life-like’ reduced carbon from an unfractionated carbon pool at isotopic and thermodynamic equilibrium is possible only under geologically irrelevant conditions (P < 100 bar, log(fO2) log(fO2QFM)– 6). Isotopically depleted reduced carbon can theoretically be produced through extensive open-system Rayleigh-style degassing of abundant precursor graphite-like hydrocarbon material, although the paucity of such material in high concentrations strongly contests the operation of such a mechanism. Only under exceptional circumstances can commonly invoked processes, such as graphite precipitation from C-O-H fluids and the decarbonation of carbonates, give rise to carbon fractionation of the magnitude incurred during enzymatically-mediated metabolic processes (13C -15‰).

The non-biological fractionation of carbon capable of mimicking a biological isotopic fingerprint, therefore, necessitates conditions of severe disequilibrium. In the absence of a deeper understanding into non-biological disequilibrium processes, carbon isotopes remain an unsuitable indicator of primitive biology in highly metamorphosed rocks.

SYMBOLS

Ppressure (in bars)

Ttemperature (in degrees Kelvin)

ximole fraction of fluid component i in the fluid phase

ichemical potential of fluid component i in a real fluid

i*chemical potential of pure fluid component i

iochemical potential of pure fluid component i in the standard state

fifugacity of fluid component i

fi*fugacity of pure fluid componenti

fiofugacity of pure fluid componenti in the standard state

ifugacity coefficient of fluid component i in a real fluid

i*fugacity coefficient of pure fluid component i

aiactivity of fluid component i

iactivity coefficient of fluid component i

Rmolar gas constant (8.3143 J K-1 mol-1)

Xcarbmolar proportion of carbon in the form of carbonate

XredCmolar proportion of carbon in the form of reduced carbon

Rxmolar ratio of carbonate carbon to reduced carbon, Xcarb/XredC

δ13Cisotopic ratio of carbon, versus PDB standard (in permil, ‰)

1.INTRODUCTION

Over the last half a century, isotopes of carbon have proven an invaluable and versatile tool in extending our understanding of Earth’s lithosphere, atmosphere and biosphere into the geological past. Of all the stable isotope systems, fractionations of carbon are amongst the best understood.

Despite this deep knowledge, there has been continued uncertainty about the origin of carbon isotope fractionations in rocks that are extremely ancient, highly metamorphosed and/or extraterrestrial. Examples of such unresolved controversies include: (i) the ambiguous biogenicity of 3.8 Ga graphite in Isua, southwest Greenland (e.g. Mojzsis et al., 1996; Mojzsis and Harrison, 2000; Rosing, 1999; Schidlowski, 1988; Schidlowski, 1993; Schidlowski, 2001; van Zuilen et al., 2002; van Zuilen et al., 2003); (ii) the purported F[JH1]ischer-Tropsch-type synthesis of 3.5 Ga kerogen in the Pilbara, northwest Australia (e.g. Brasier et al., 2002; Brasier et al., 2005; Schopf et al., 2002; Schopf and Packer, 1987; Ueno et al., 2004); and (iii) the origin of carbonaceous phases in meteorites (e.g. McKay et al., 1996; McSween, 1997; McSween and Harvey, 1998). These problems are not trivial, as they affect our understanding of how, when and where life began. As our foremost biosignature, the ability to differentiate between carbon of non-biological and biological origin is indubitably of widespread importance.

Several studies indicate that water-column and postburial diagenesis [RB2]are not accompanied by significant isotopic changes (Meyers and Eadie, 1993; Schelske and Hodell, 1995). Other studies suggest that the selective loss of specific fractions of total organic carbon can and does lead to diagenetic isotope shifts (Benner et al., 1987; Lehmann et al., 2002). Even if diagenetic isotope shifts occur, their effect is only on the order of 0 to -2 ‰, depending on concentrations of porewater sulphate and oxygen (Lehmann et al., 2002).[RB3]

At and above greenschist facies metamorphic conditions, carbonaceous material becomes increasingly graphitic in nature. Kerogen, defined as ‘insoluble non-crystalline organic material’, is a common constituent of low-grade sedimentary rocks spanning the rock-record as far back as 3.5 Ga. Although disagreement exists in the application of the term ‘graphitic kerogen’ (e.g. Marshall et al., 2007), kerogen exhibits similar petrological behaviour (colour, reflectivity, etc.) to graphite. At temperatures considered in this study (T > 400 C), kerogen is known to transform to graphite. In the absence of contradictory evidence, kerogen is here assumed to share the same isotopic and thermodynamic properties as graphite. To avoid confusion, the term ‘reduced carbon’ is applied to both kerogen and graphite.

As indicated by carbon analyses of primitive igneous rocks such as carbonatites and diamondiferous kimberlites, the partial melting of average mantle rocks gives rise to carbon with a fairly narrow isotopic range of –5 ± 2 ‰(Deines, 2002; Deines and Gold, 1973).[RB4] Occurrences of reduced carbon with this unfractionated, non-biological isotopic signature (Javoy et al., 1978) on the order of a few weight percent[RB5] are not uncommon in, for instance, kimberlites and other classes of ultramafic rocks[RB6](Pasteris, 1981). Clearly, a significant amount of our planet’s re[JH7][RB8]duced carbon reservoir is derived from non-biological sources.

In many geological settings, simple carbon-bearing molecules such as CO, CO2, CH4, other light hydrocarbons and organic acids represent the most abundant and geochemically reactive components of fluids (Horita, 2001). Consequently, many geological fluids can comfortably[RB9] be described within the C-O-H system. C-O-H fluids derived from magmatic –that is, from strictly non-biological- sources have long been implicated with vein-type graphite deposition in a diversity of locales[RB10](Douthitt, 1982; Duke and Rumble, 1986; Frost et al., 1989).

It hasalso long been known that the δ13C values of remobilized carbon hosted in granitic, mafic and certain ultramafic rocks, on the other hand, are generally lighter and more variable than primitive mantle carbon, ranging between –15 and –30 ‰ (e.g. Fuex and Baker, 1973, see also Figure 1). Isotopic fractionations of carbon in this range are also imparted during autotrophic metabolism by living organisms (Figure 2). Consequently, some workers have ascribed a partly or wholly biological origin to such isotopically depleted and remobilized graphite(for a discussion see Duke and Rumble, 1986; Mancuso and Seavoy, 1981; Mancuso and Seavoy, 1982; Rumble et al., 1986; Rumble and Hoering, 1986).

[JH11][RB12]Geological processes imparting an isotopic fractionation not mediated by biological enzymatic metabolism [JH13]include isotopic re-equilibration with carbon in metasomatic C-O-H fluids and/or carbonate, precipitation of remobilized carbon, devolatilization of organic matter, and fresh carbon production resulting from decarbonation reactions of carbonates. Under the assumption of equilibrium, however, the isotopic behaviour and evolution of carbon under the sway of these processes is largely quantifiable, such that careful consideration of their geological history can hopefully refute or establish a biogenic origin. Hence, some of the controversies over the origin of reduced carbon in ancient, metamorphosed and extraterrestrial rocks may be resolvable.

[JH14][RB15]In this paper, a Modified Redlich-Kwong (MRK) equation of state built onrecent thermodynamic fluid species data is coupled withrecent advances in our understanding of equilibrium isotope fractionation to arrive at a versatilemodel for the isotopic behavior and evolution of reduced carbon– including graphitic kerogen –interacting with C-O-H fluids and Fe-C-O-H systems under geologically relevant conditions of P, T and fO2. An attempt is made to constrain the conditions under which it becomes possible for purely geological processes to mimic biological δ13C fractionation, and concurrently to shed light on the conditionsunder which a non-biological origin can be refuted.

2.THE MODIFIED REDLICH-KWONG (MRK) EQUATION OF STATE

2.1.Calculation of Species Activities

The modeling of fluids consisting of sub- or super- critical fluid mixtures of multiple components requires an understanding of how their chemical potentials respond to changes in state variables such as P, T and changes in composition, xi. The derivation of an expression for the chemical potential of a fluid componenti, i, in a ‘real’ or ‘non-ideal’ multi-component fluid mixture (x1, ..., xn) at specified conditions of P, T, xibegins with consideration of its chemical potentialin a pure (single-component, xi=1) fluid, amended through introduction of the activity, ai:

i =i* + RT ln ai(1)

=i* + RT lnxi + RT lni (2)

Here, for the species i, xi is its proportion in the fluid mixture, i is its activity coefficient in the fluid mixture, ai(=ixi) is its activity in the fluid mixture, and i* is the chemical potential of pure (xi = 1; ai = 1) species i.

The above equations signify a ‘dilution correction’ for a multi-species fluid applied to the chemical potential of a pure species, i*, at a specified P, T. This connotes an improvement over the assumption of ideal mixing. This pure-species chemical potential i* at a given pressure P mustitself be explicitly evaluated by extrapolating from a ‘standard’- or ‘reference’- state, at which P = PR. If io denotes the chemical potential of pure (xi = 1; ai = 1) componenti in the standard state, then:

i* = io + (3)

For fluids, this equation is more conveniently expressed in terms of the so-called ‘fugacity’ of a species:

i* = io + RT ln(4)

Here,fio is the standard state fugacity and fi* is the fugacity at the specified P, both for a pure species i. The above equation is effectively a ‘pressure correction’ for a pure species, but still requires correction for impure fluids. The chemical potential of a species in an impure fluid at specified P, that is, a non-ideal mixture of non-ideal fluids, is now given by:

i = io + RT ln (5)

i = io + RT ln (6)

i = io + RT ln (7)

Here,fi(=γi xii* P = xii P since i = γii*) is the fugacity of species i at the specified conditions in the fluid mixture. By combining equations (2), (4) and (5) above we arrive at a convenient expression for the species activity:

ai = fi / fi*(8)

Equations of state are equations that attempt to capture the relationship between the state variablesP, T and V, and subsequently allow for the calculation of chemical potentials. The Redlich-Kwong equation of state (Redlich and Kwong, 1949), which incorporates parameters relevant to molecular dynamics of C-O-H fluids of interest here, takes the form:

P = (9)

Here, constant b accounts for repulsive forces by parameterizing molecular size and constant a accounts for intermolecular attraction. For fluids bearing molecules exhibiting a large dipole moment, such as H2O and CO2, a modified Redlich-Kwong (‘MRK’) equation was proposed (de Santis et al., 1974),whose parameters were later improved(Holloway, 1977). The latter contained errors subsequently corrected (Flowers, 1979).

The MRK equation of state offers excellent correlation with experimental data, except at extreme metamorphic grades (P > 15000 bars, T > 1100 C) (Belonoshko and Saxena, 1991; Frost and Wood, 1995; Kerrick and Jacobs, 1981)[RB16]. These mantle-like conditions are not germane to the crustal rocks considered here.

In equation (7) above, the temperature-dependent constant,a,can be expanded into temperature –independent and –dependent terms:

a = a(T) = a(0) + a(1)(T)(10)

Here,a(0) reflects intermolecular attraction due to dispersive London forces anda(1)(T) accounts for temperature-dependent hydrogen bonding, permanent dipoles, and quadrupoles. For non-polar species ([RB17]e.g. CO, CH4 and H2), therefore,a(1) = 0. The mixing parameters and thermodynamic constants used(after a compilation in Frost and Wood, 1995), are tabulated in Table 1 below.

Using this MRK equation of state, an expression for the fugacity co-efficient, (i, see equation 5, above) can be derived(Prausnitz, 1969):

(11)

Here, a = and b =. The values taken on by ai,j are tabulated in Table 2.

2.2.Calculation of Reduced Carbon Saturation Surface

In a supersaturated C-O-H fluid, total pressure, P, is given by the sum of partial pressures of 6 dominant fluid species:

PTOTAL = ∑pi = P(12)

P = pCO + pCO2 + pCH4 + pH2O + pH2 + pO2(13)

Likewise, relationships between the molar compositions can be expressed:

∑xi = xCO + xCO2 + xCH4 + xH2O + xH2 + xO2 = 1(14)

For geological systems, the partial pressure of O2 is negligible, and we assume xO2, pO20. Rewriting the above in terms of fugacities and activity coefficients:

fi = γi xiiP(15)

Now, applying the assumption of ideal mixing (i=1) leads to the simplification:

pixiP(16)

fi xii P(17)

And hence, from equations (11) and (12):

(18)

In the presence of reduced carbon, the activity of carbon, aC, is fixed at unity. Pairs of the species’ fugacities can now be related to one another through P-,T- and fO2- dependent equilibrium constants, k(i,,j):

C + 0.5 O2 = CO:k(O2,CO) = fCO/(fO2)0.5

= =(19)

C + O2 = CO2:k(O2,CO2) = fCO2/fO2

= =(20)

C + 2 H2 = CH4:k(H2,CH4) = fCH4/(fH2)2 = =(21)

H2 + 0.5 O2 = H2O:k(H2,H2O) = fH2O/(fO2)0.5 = =(22)

[JH18]Substituting these into equation (12) allows for the calculation of xiunder the assumption of fluid ideality from the roots of quadratic equations (e.g. Ohmoto and Kerrick, 1977) or through the use of thermodynamic data tables (Chase, 1998). An iterative calculation[JH19](e.g. Hall and Bodnar, 1990) now allows for the evaluation of i(and hence xi) of all fluid components in a non-ideal fluid as a function of P, T and any single compositional variable xi. Importantly, the stability of reduced carbonin P – T space must first be constrained for equations (16-19) to meet their intended utility. To this end, we next examine the thermodynamic behaviour of C-O-H fluids in the context of graphite stability after introducing a useful proxy for the influence of the geological environment on the equilibrating fluid composition – the oxygen fugacity, fO2.

3.THE THERMODYNAMIC BEHAVIOUR OF C-O-H FLUIDS

The behaviour of C-O-H fluids,at conditions relevant to geological systems on Earth, is well understood. Several techniques are commonly used to visualize the compositional behaviour of such systems in composition space(Connolly, 1995; Holloway, 1984; Huizenga, 2001). The ternary C-O-H diagram (Figure 3) lends itself naturally to this purpose.

3.1.Oxygen Buffers

In addition to pressure and temperature, the geological environment usually lends further constraints on the composition of C-O-H fluids by virtue of the mineral assemblage with which the fluid equilibrates. To this end, the oxygen fugacity, fO2, provides a useful proxy.

The fO2 - T curves associated with the most-commonly used oxygen buffers (Table 1) are shown in Figure 4(a). Taken together, the curves connote the buffering capabilities of a broad range of geological environments. It is rare, however, for an assemblage to correspond exactly to the oxygen buffer equilibrium. Although the oxygen fugacity of the various buffers typically varies by ~50 orders of magnitude over the range of geological temperatures, they exhibit similar slopes infO2 - T space. In consequence, oxygen fugacities in geological systems typically fall within +6 log units and -8 log units of the FMQ buffer, which inhabits a median position amongst the commonly used buffers (Figure 4(b)). This corresponds to the fO2range used in this study.

3.2.Graphite Stability

Phase-equilibrium experiments and other thermodynamic studies involving graphite have proven to be difficult to interpret, and have led to somewhat conflicting results. These problems stem largely from variability in the crystalline nature, ordering and thermodynamic properties of graphite (Koziol, 2004).

In the presence of graphite under specified P, T conditions, the fluid composition will lie on the appropriate graphite saturation isotherm. This reasonably assumes an activity of graphite, aC, of unity in the fluid, implying that the fluid is saturated with respect to graphite. Fluids plotting within the stability field of graphite, but above the graphite saturation isotherm, are not graphite-saturated, implying aC < 1. Fluids plotting below the graphite saturation isotherm are prohibitively oxidizing or reducing. Here, graphite is unstable with respect to [JH20]CO/CO2 or CH4, respectively. In practice, because of equilibria with H2, graphite remains stable with respect to CH4 under all geologically reasonablefO2 conditions. Under a broad range of geological conditions, the degree of dissociation of graphite into CO and CO2 is also small. This is because the conversion of all available graphite to CO-CO2 requires activities of O2 that are unlikely at sub-solidus temperatures (compare Figure 4 5). From a thermodynamic perspective, then, the abundance of graphite in diverse rocks with a variety of histories is not surprising. [JH21][RB22]

At a specified P, T, the upper of graphite stability in fO2-spaceoccurs when the equilibrating fluid is characterized by xCO2 + xCO = 1 (Figure 5).[JH23] The graphite stability field expands with increased pressure. With increasing temperatures, graphite-fluid equilibria are increasingly in favour of the fluid phase (‘degassing’), causing amounts of graphite to decrease. On the C-O-H diagram, this enrichment in fluid C is indicated by a shift in the graphite saturation isotherm towards the graphite ternary endmember.

C =

The continued ability of the system to provide graphite buffering capacity depends on the amount of carbon present in the rock.

3.3.Supercritical Behaviour

3.3.1.Behaviour on the Fluid Binaries

As pointed out by Holloway(1984), in the presence of graphite and at temperatures below T400C(but above the unmixing temperature – see below) and pressures aboveP 300 bars, supercritical C-O-H fluids will consist of either CO-CO2-H2O mixtures or H2-CH4-H2O mixtures. Regarded schematically, this occurs when the composition of the C-O-H fluid falls on, respectively, the CO2-H2O join or the CH4-H2O join in the C-O-H composition diagram.[JH24] This situation arises when the graphite saturation isotherm overlaps with the binary joins. Fluid equilibria dictate that CO/CO2 or H2/CH4 ratios are exceedingly low under these conditions[JH25]. CO/CO2/H2O or H2/CH4/H2O ratios are entirely fixed through specification of a single internal variable, such as fO2.

3.3.2.General Supercritical Behaviour

The coincidence of the C-O-H composition with the graphite saturation isotherm denotes a special case. More generally, the molar fractions of CO2, H2O, O2, CO, H2 and CH4 are variably fixed in a C-O-H fluid, depending on constraints placed on the system due to the geological environment. In the case of a single supercritical fluid, three different scenarioscan be envisaged under specified P, T conditions (Figure 3): (i) a fluid whose composition falls outside the stability field of graphite, and is not externally buffered – in which case the relative proportions of species are set by fluid equilibria; (ii) a fluid whose composition falls outside the stability field of graphite, but is externally buffered; and (iii) a buffered fluid whose composition falls within the stability field of graphite. Each will be treated in turn.