The dissolution kinetics of major sedimentary carbonate minerals

Earth-Science Reviews 58 (2002) 51 – 84 www.elsevier.com/locate/earscirev

The dissolution kinetics of major sedimentary carbonate minerals John W. Morse a,*, Rolf S. Arvidson b b

a Department of Oceanography, Texas A&M University, College Station, TX, 77843-3146, USA Department of Earth Science, MS-126, Rice University, P.O. Box 1892, Houston, TX, 77251-1892, USA

Abstract Among the most important set of chemical reactions occurring under near Earth surface conditions are those involved in the dissolution of sedimentary carbonate minerals. These minerals comprise about 20% of Phanerozoic sedimentary rocks. Calcite and, to a significantly lesser extent, dolomite are the major carbonate minerals in sedimentary rocks. In modern sediments, aragonite and high-magnesian calcites dominate in shallow water environments. However, calcite is by far the most abundant carbonate mineral in deep sea sediments. An understanding of the factors that control their dissolution rates is important for modeling of geochemical cycles and the impact of fossil fuel CO2 on climate, diagenesis of sediments and sedimentary rocks. It also has practical application for areas such as the behavior of carbonates in petroleum and natural gas reservoirs, and the preservation of buildings and monuments constructed from limestone and marble. In this paper, we summarize important findings from the hundreds of papers constituting the large literature on this topic that has steadily evolved over the last half century. Our primary focus is the chemical kinetics controlling the rates of reaction between sedimentary carbonate minerals and solutions. We will not attempt to address the many applications of these results to such topics as mass transport of carbonate components in the subsurface or the accumulation of calcium carbonate in deep sea sediments. Such complex topics are clearly worthy of review papers on their own merits. Calcite has been by far the most studied mineral over a wide range of conditions and solution compositions. In recent years, there has been a substantial shift in emphasis from measuring changes in solution composition, to determine ‘‘batch’’ reaction rates, to the direct observation of processes occurring on mineral surfaces using techniques such as atomic force microscopy (AFM). However, there remain major challenges in integrating these two very different approaches. A general theory of surface dissolution mechanisms, currently lacking (although see Lasaga and Luttge [Science 291 (2001) 2400]), is required to satisfactorily relate observations of mineral surfaces and the concentration of dissolved components. Studies of aragonite, high-magnesian calcites, magnesite, and dolomite dissolution kinetics are much more limited in number and scope than those for calcite, and provide, at best, a rather rudimentary understanding of how these minerals are likely to behave in natural systems. Although the influences of a limited number of reaction inhibitors have been studied, probably the greatest weakness in application of experimental results to natural systems is understanding the often profound influences of ‘‘foreign’’ ions and organic matter on the near-equilibrium dissolution kinetics of carbonate minerals. D 2002 Elsevier Science B.V. All rights reserved. Keywords: calcite; aragonite; dolomite; magnesite; dissolution; kinetics

*

Corresponding author. Tel.: +1-409-845-9630; fax: +1-409-845-9631. E-mail address: [email protected] (J.W. Morse).

0012-8252/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 5 2 ( 0 1 ) 0 0 0 8 3 - 6

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1. Introduction and background 1.1. Overview and general considerations One of the more basic pieces of knowledge, as anyone who takes an introductory geology course learns, is that if you put a drop of dilute HCl on a rock and it fizzes, the rock is limestone. Thus, starts the learning process about the seemingly simple subject of carbonate mineral dissolution kinetics; a topic on which hundreds of research papers have been written and basic aspects of which still remain highly controversial. Why all this interest in carbonate mineral dissolution kinetics? The answer to the question is simple. These phases are plentiful in sedimentary rocks and modern sediments, and the dissolution process impacts a vast range of important topics. Examples include the fate of fossil fuel CO2, carbonate accumulation in marine sediments, global geochemical cycles, the preservation of monuments and buildings, and petroleum reservoir characteristics. In the early 1980s, Morse (1983) wrote a review article on the more general topic of calcium carbonate dissolution and precipitation kinetics and again, more briefly, visited the topic with Fred Mackenzie (Morse and Mackenzie, 1990) in the late 1980s. For this paper, we have chosen to cover the dissolution kinetics of primarily abiotic aragonite, calcite, high magnesian calcite, magnesite, and dolomite. These minerals comprise the vast majority of carbonate minerals found in sediments and sedimentary rocks. Our primary objective is to distill from a large number of diverse papers into a concise summary of carbonate mineral dissolution kinetics. As such, this paper is primarily limited to laboratory studies of mineral dissolution kinetics and does not cover the extensive literature dealing with dissolution in generally complex natural systems. In addition to our personal collections of papers on this topic, a search was made for papers in the Geo Ref and Chem Abstracts data bases, and then of the references in these papers. Although we hope this represents a reasonably complete literature search, there always remains the possibility that, lurking in some private company’s confidential documents or in a government agency’s internal ‘‘gray literature’’ report, there may be important data that have been missed. No attempt will be made to cite all references on a given topic, as this

would render, in some cases, the paper virtually unreadable. Citations will be made using examples as to what are, in our opinion, the most important, clearly stated, and representative papers on the topic. 1.2. A brief pre-1970 historical perspective The importance of carbonate mineral dissolution in sediments (e.g., Murray and Renard, 1891), during diagenesis and lithification (e.g., Friedman, 1964; Gross, 1964; Land, 1967), and during the evolution of sedimentary rocks (see extensive discussions in Bathurst, 1975; Moore, 1989; Morse and Mackenzie, 1990) has long been recognized. These observations inevitably demanded an understanding of the factors that controlled reaction rates between carbonate minerals and natural waters. However, it was not until about the 1960s that a significant effort was begun to determine experimentally the rates at which carbonate mineral dissolution occurs as a function of solution composition (e.g., Weyl, 1958, 1965; Terjesen et al., 1961; Akin and Lagerwerff, 1965; Berner, 1967; Schmalz, 1967; Nestaas and Terjesen, 1969). As these lines of investigation began to evolve, it also became apparent that major improvements were necessary in the ability to predict carbonate mineral solubility in natural waters (Garrels et al., 1961). There was concurrently a growing appreciation of the complexities of biogenic carbonates, such as aragonite and magnesian calcite, and their behavior during dissolution (Friedman, 1964; Land, 1966, 1967; Schroeder and Siegel, 1969), as well as the relationship of these phases to sedimentary dolomite and dolomitization reaction pathways (Kinsman, 1965; Friedman and Sanders, 1967; Land and Epstein, 1970). Much attention was also focused on processes controlling carbonate deposition in deep sea sediments. Special attention was given as to how dissolution kinetics influence the calcium carbonate compensation depth (CCD, where calcium carbonate ceases to be a major sediment component). The experiments of Peterson (1966) and Berger (1967), in which calcite spheres and assemblages of foraminifera were hung at different depths in the Pacific Ocean, were extremely important. They revealed that the extent of calcite dissolution in seawater was not simply proportional to saturation state and, therefore, the dissolution rate was not diffusion controlled at modest degrees of undersaturation.

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

Their findings, and the large amount of subsequent supporting research discussed in this paper, have been a source of considerable discomfort to those who wish carbonate mineral dissolution rates to simply be directly proportional to the extent of undersaturation (i.e., kinetically first order and thus easily adapted for modeling purposes). Attempts have been made to explain away or to simply ignore the complexities of near-equilibrium carbonate mineral reaction kinetics (e.g., Edmond, 1971; Hales and Emerson, 1997). However, none of these arguments have been based on direct experimental observations and, consequently, must be viewed with skepticism in light of the very substantial body of experimental work carried out in both the basic chemical and geochemical communities.

2. Theoretical considerations 2.1. Rate equations The reaction between a solid and solution is observable by a change in the mass of solid and a change in solution composition. Because these represent ‘‘net’’ changes, it is not usually possible to obtain ‘‘absolute’’ rates of dissolution and precipitation, but only to observe the difference between the opposing reactions. The concept of kinetic equilibrium rests on the idea that at equilibrium the rates of the opposing reactions are equal so that no change is observable with time even though dissolution and precipitation are continually occurring. Lasaga (1998, pp. 82– 93) has cogently discussed this concept, the ‘‘principle of detailed balancing’’, and here his more relevant points for calcite dissolution are summarized following his mode of notation. For the simple reversible first order reaction, at equilibrium the concentrations of a reactant ([A]) and product ([P]) are such that the equilibrium constant Keq is equal to the ratio of the forward (k + ) and reverse (k
) rate constants. kþ

AX P

ð1Þ

½Pe kþ ¼ ¼ Keq k
½Ae

ð2Þ

k


53

Except at conditions very close to equilibrium, generally either the forward or reverse rate is much greater than the opposing reaction so that the net rate is an excellent approximation of the dominant unidirectional rate (R). The reaction rate will increase with increasing degree of disequilibrium until the reaction mechanism changes to transport-controlled kinetics. Here the saturation state will be given as X, which is the ratio of the ion activity product (IAP) to the solubility product (Ksp) for the solid (X = IAP/Ksp). [Note that various representations of the saturation state are given. A common one is the ‘‘saturation index’’, SI, which is generally logX.] The extent of disequilibrium is then simply the difference between X and 1. Thus, for undersaturation it must range from 0 to 1, but for supersaturation it can range from 0 up to numbers substantially > 1. The most commonly used equation in geosciences to describe the rate of carbonate mineral dissolution (e.g., Morse and Berner, 1972) is
 dmcalcite A R¼
k ð1
XÞn ¼ ð3Þ V dt where R is the rate in Amol m
2 h
1 and m is moles of calcite, t is time, A is the total surface area of the solid, V is the volume of solution, k is the rate constant (note that A, V, and k are often combined into a single constant k*) and n is a positive constant known as the ‘‘order’’ of the reaction. This simple empirical equation has the advantage that in a plot of logR vs. log(1
X) the intercept will be k* and the slope n. logR ¼ nlogð1
XÞ þ k*

ð4Þ

Lasaga (1998) found that by detailed balancing (see previous definition), he could obtain Eq. (5), which was used by Sjo¨berg (1976), who found n = 1/2 for calcite.
 dmcalcite A n R¼
k Ksp ¼ ð1
X n Þ ð5Þ V dt Eq. (5) is similar to Eq. (3). However, they are not simply related. Since the observed rate for each equation (R3 and R5), at a given saturation state, must be equal, Eq. (6) gives the relationship between equations. (Note that for n3 = n5 = 1, k3/k5 = Ksp.) n5 ð1
X n5 Þ k3 ð1
XÞn3 ¼ k5 Ksp

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

or
k3

Ksp
IAP Ksp

n3

In the case of linear reactions, i.e., unit order, the functional dependence of DG has the simple form n5 ¼ k5 ðKsp
IAPn5 Þ

ð6Þ

The growth rate law can be modified to apply to dissolution as well and provides a bridge between thermodynamics and kinetics. (The following treatment is generally after that of Lasaga, 1998, modified as appropriate to the purposes of this paper.) The general form of this equation is R ¼ k0 ðAe
Ea =RT Þ

Y

ani i f ðDGÞ

ð7Þ

i

where A is now reactive surface area (cf. Eq. (5)), Ea is the apparent activation energy, T is absolute temperature, R is the ideal gas constant, and ai incorporates ions that may contribute inhibitory or catalytic effects. It should be noted that implicit in this treatment is that inhibitory and catalytic ions influence the apparent overall rate constant but not the reaction order. This is not always true as inhibitors such as phosphate can strongly influence reaction order in addition to the rate constant (Morse, 1973, 1974). (It also assumes that their influence can be simply described by their solution phase activity raised to some power.) Since their influence often is on the surface of the solid, in many cases explicit adsorption isotherm equations would be more appropriate. f (DG) is a function of the Gibbs free energy of disequilibrium ( = 0 at equilibrium). Let us consider Eq. (7) in a simplified form. First, assume a simple solution where no inhibitory or catalytic ions are present and that T is constant. Since DG ¼ RT lnX

ð8Þ

we can combine terms to let k V¼ k0 ðe
Ea =RT Þ

ð9Þ

and then letting k W= 2.303RT R ¼ Ak Vf ðk WlogXÞ

ð10Þ

For a constant reactive surface area, and if f is such that k VVcan be combined with k Vyielding k, the following simple equation results. R ¼ k f ðSIÞ

ð11Þ

f ðDGÞ ¼
ð1
expðDG=RT ÞÞ

ð12Þ

from which the following relationship can be derived: ceq
c ¼ ceq ð1
expðDG=RT ÞÞ

ð13Þ

At high undersaturations the rate becomes independent of DG and a ‘‘dissolution plateau ’’ is reached, whereas close to equilibrium (small DG ) the approximation given in Eq. (14) is valid and produces the ‘‘linear region’’. f ðDGÞ ¼ DG=RT

ð14Þ

A more general form of Eq. (13) that is often used, where n p 1, is Eq. (15) (Lasaga, 1998). f ðDGÞ ¼
ð1
expðnDG=RT ÞÞ

ð15Þ

The three major rate equations will be called here the general (Eq. (3)), detailed balancing (Eq. (5)) and thermodynamic rate equations (Eqs. (7) and (15)). Because their forms are quite different, mathematical relationships among them are not simple (e.g., Eq. (6)). In order to demonstrate how they differ functionally, Fig. 1 has been constructed. This was done using different values of n. It should be kept in mind that in Eq. (3), n is a ‘‘true’’ or ‘‘classical’’ reaction order, but that the n’s in Eqs. (5) and (15) are not. A range in saturation from equilibrium to 0.1 was used. In order to make results comparable, rates were normalized to the rate at X = 0.1. This results in a rate ranging from 0 at equilibrium to 1 at X = 0.1; the equations produce a straight line for n = 1. For the general rate equation the shape of the plot becomes increasingly non-linear and concave with increasing n. At high values of n this can result in an apparent change of solubility. For the detailed balancing equation, values of n < 1 produce concave curves and for values of n > 1 convex curves. For the thermodynamic rate equation, curves of increasing convexity are produced with increasing n. It should be kept in mind that normalization to X = 0.1 rates hides differences in absolute rates for a set of values of n in a given equation. It should also be noted that in cases where reaction rate is linear with respect to X, all equations

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

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with n = 1 (first order reaction) will describe the relationship equally well. Before leaving the topic of rate equations we note that the ‘‘darling’’ of rate equations for many investigators studying dissolution processes in natural systems (particularly seawater) is 2
R ¼ kð½CO2
3 eq 
½CO3 bulk

water Þ

ð16Þ

This equation assumes that the reaction is first order and that because the concentration of Ca2 + is much greater than CO32
that it can be approximated as constant. Then variations in carbonate ion activity control saturation state. Perhaps, because this makes interpretation of data and modeling relatively easy, many of our colleagues have held tenaciously to its use in spite of what we view as overwhelming data indicating that it is incorrect in many situations where reactions are not first order. 2.2. Rate controlling mechanisms A basic concept in chemical kinetics is that reactions consist of a series of different physical and chemical processes that can be broken down into different ‘‘steps’’. For dissolution, these steps generally include at a minimum: 1. 2. 3. 4.

5. 6. 7.

Fig. 1. Plots of the normalized dissolution rate vs. saturation state for (A) the general rate equation (Eq. (3)), (B) the detailed balancing equation (Eq. (5)) and (C) the thermodynamic rate equation (Eqs. (7) and (15)).

diffusion of reactants through solution to the solid surface, adsorption of the reactants on the solid surface, migration of the reactants on the surface to an ‘‘active’’ site (e.g., a dislocation), the chemical reaction between the adsorbed reactant and solid which may involve several intermediate steps where bonds are broken and formed, and hydration of ions occurs, migration of products away from the reaction site, desorption of the products to the solution, diffusion of products away from the surface to the ‘‘bulk’’ solution.

A central concept in reaction kinetics is that one of these steps will be the slowest and that the reaction can, therefore, not proceed faster than this rate limiting step. Steps 1 and 7 involve the diffusive transport of reactants and products through the solution to and

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

from the surface. When this process is rate-limiting, the reaction is said to be diffusion controlled. Steps 2 – 6 occur on the surface of the solid and when one of them is rate controlling the reaction is said to be surface controlled. As Berner (1978) pointed out, very soluble minerals tend to undergo reactions that are diffusion-controlled, whereas relatively insoluble minerals have surface controlled reaction rates until very high degrees of disequilibrium are obtained. Carbonate minerals fall into the latter category. Surface controlled reactions tend to be non-linear with respect to saturation state while diffusion controlled reactions are linear with respect to saturation state. Although most literature on the topic is concerned with crystal growth rather than dissolution, many of the same basic concepts are applicable to both processes (e.g., Nielson, 1964; Lasaga, 1998). A solution can either be close to stationary (‘‘stagnant’’) or moving (laminar or turbulent flow) with respect to the solid surface. In moving solutions, advective transport is substantially faster than molecular diffusion. Therefore, the thickness of a stagnant boundary layer, where water movement is slow relative to diffusive transport, between the solid surface and bulk turbulent solution can control the rate of reaction. Mathematically this can be demonstrated from Fick’s first law c
c  eq bulk J ¼
D x

ð17Þ

where J is the flux per unit area, D is the molecular diffusion coefficient and x is the thickness of the stagnant boundary layer. If we multiply by surface area (A), the total rate of dissolution is obtained from Eq. (17). Eq. (16) is produced by letting k = AD/x, and if ceq and cbulk are divided by ceq and n set equal to 1, then Eq. (3) results. Because, for a diffusion controlled reaction, the dissolution rate is dependent on the thickness of the stagnant boundary layer, the undersaturation at which diffusion starts to become rate controlling can be determined by manipulating the thickness of the stagnant boundary layer by physical means. These include changing the stirring rate of the solution and mounting the solid on a disk that can be rotated at different speeds. The undersaturation at which these physical changes start to cause changes in the reaction rate

represents the critical undersaturation for a change from surface to diffusion controlled reaction rates. Much of the theoretical work on surface controlled reaction rates rests on the concept that surfaces are energetically highly heterogeneous. Because reaction rates at sites of different energy on the surface can be expected to vary exponentially with site energy, the relative abundance of high-energy sites exerts a major influence on reaction rate. Two general classes of surface sites exist. The first is dislocations, with screw dislocations being probably the most important. The second class of sites is those associated with steps, ledges and ‘‘kinks’’. These lead to models of surface reactions such as those proposed by Burton et al. (1951) (see Lasaga, 1998, for extensive discussion; see also Fig. 2). These high-energy sites are also favorable adsorption sites for reaction inhibitors. Their interaction with these sites can cause large changes in reaction rates even at relatively low percentages of surface coverage. Unfortunately there is currently no sound theoretical framework for relating directly the form of reaction rate – saturation state equations to surface mechanisms. It is even more unfortunate that there has been what at best might be considered highly speculative efforts to do so by some researchers studying carbonate mineral dissolution kinetics, as will be discussed later in this paper. Also to be discussed later are relatively recent approaches that are being used to observe directly surfaces on a near

Fig. 2. The BCF model for surfaces with adsorbed ions shown in black. Step, kink, hole and nucleus refer to the different types of surface sites and the numbers refer to the number of likely chemical bonds.

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

atomic scale. These approaches show promise for better understanding of processes occurring on carbonate mineral surfaces. 2.3. New approaches to studying surface processes Regardless of their working differences, the various rate equations described above all involve the notion that the distance from equilibrium, as described by X DGr ð¼ e RT Þ, is a driving force in controlling the rate of the overall reaction, and explicitly or implicitly emphasize the role of dissolved components in terms of the overall rate mechanism. As will be discussed in more detail shortly, in the study of the surface controlled reaction, there has been increasing interest in understanding how the macroscopically observed rate is explicitly controlled by processes on the mineral surface. This interest has come about to a large extent because of the advent of the atomic force microscope (AFM, Binnig et al., 1986; Marti et al., 1987). AFM permits direct, atomic scale in aquo observation of individual mineral faces. It can provide angstrom-level vertical resolution; lateral resolutions range from the micron- to subnanometer-scale, but with increasing resolution coming at the expense of a smaller field of view. The instrument is ideally suited to resolving relatively flat surfaces whose overall relief is less than 0.5 Am. Since its introduction, AFM has seen broad application in the study of mineral – water interaction involving quartz (Gratz et al., 1991), feldspars (Hochella et al., 1990; Drake and Hellmann, 1991), zeolites (Weisenhorn et al., 1990), clays (Lindgreen et al., 1991), and oxides (Johnsson et al., 1991), and AFM techniques are now well established. Application to carbonate minerals thus far has focused entirely on calcite (Hillner et al., 1992a,b; Gratz et al., 1993; Dove and Platt, 1996; Liang et al., 1996a,b; Davis et al., 2000; Lea et al., 2001). Despite the capabilities of AFM, application to mineral reaction rates must satisfy certain criteria (Dove and Platt, 1996). Because of the limited durability of its cantilever tip, AFM cannot approach the time scales of extended experiments conducted with relative simplicity in batch or even flow-through reactors, imposing a limit with respect to the measurement of extremely slow reactions. Conversely, rates must also be sufficiently slow to be resolvable through comparison of raster images acquired at a fixed scan-

57

ning frequency. Dove and Platt (1996) have estimated an overall range of 10
6 to 10
10 mol m
2 s
1. More importantly, they point to discrepancies between AFM rates computed from migrating step velocities and those measured by conventional powder methods, and to long-standing problems regarding the treatment of reactive surface area in these calculations. Liang et al. (1996b) and Lea et al. (2001) have also measured individual step velocities of etch pits. Despite the detail in these measurements, the overall relationship among etch pit step velocities and the phenomenological rate laws described above is unclear. These issues are discussed in more detail below. A more recent development is the application of optical interferometry to the study of mineral surface kinetics (MacInnis and Brantley, 1992; Lu¨ttge et al., 1999). The interferometer is essentially an optical microscope equipped with a Mirau objective that produces a series of interference fringes. The interaction of these fringes with the mineral surface is used to produce a topographic map of the surface. Dissolution rates are measured through time-lapse scans of a reacted (oriented) mineral surface: Dh ¼ vðhklÞ Dt
1

r ¼ vðhklÞ V

ð18Þ ð19Þ

Here, Dh is the difference in surface height at a given point on the mineral surface after elapsed time Dt, v(hkl ) is the (surface-normal) velocity, V is the molar volume, and r is the computed rate. Interferometry simultaneously combines high vertical resolution (]0.5 nm), large vertical scan range, and a large field of view, and thus allows imaging of near-macroscopic surface features. Rates determined by surface-normal retreat of relatively large areas of the mineral surface can also be compared directly (in units of moles per unit area per unit time) to those of conventional powder experiments. 2.4. Complexities introduced by the carbonic acid system The dissolution of most salts simply results in the release of their constituent cations and anions (e.g., NaCl ! Na + + Cl
) to solution. However, the disso-

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

lution of carbonate minerals necessarily involves the carbonic acid system. Therefore, parameters that control carbonate ion activity such as pH, PCO2, and alkalinity also must be considered. For example, the relationship between aCO23
and PCO2 and pH is given by Eq. (20), where it can be observed that PCO2 and pH can co-vary over a range of values and still yield the same carbonate ion activity. ¼ logK** þ log PCO2 þ 2pH logaCO2
3

ð20Þ

K** is the product of the Henry’s law constant for CO2 and the first and second dissociation constants of carbonic acid (e.g., see Morse and Mackenzie, 1990). These relationships introduce several practical and theoretical difficulties to the study of carbonate mineral dissolution kinetics. In the region where the dissolution rate is controlled by diffusive transport in solution, the equilibrium concentration of ions near the mineral surface must be determined. However, parameters such as PCO2 and pH will not be the same as in the bulk solution. While it may be possible to make a reasonably good estimate of the equilibrium carbonate ion activity, in solutions where the calcium ion activity is much greater than carbonate ion activity (Eq. (21)), the activities of other aCO 2
¼ 3

Ksp aCa2þ

ð21Þ

species such as bicarbonate ions, carbonic acid and CO2(aq) will be dependent on near-surface PCO2 and pH. Each of these species will, therefore, have a different chemical potential gradient between the near surface region and the bulk solution. Further complications (e.g., Weyl, 1958; Berner and Morse, 1974; Sjo¨berg, 1976; Sjo¨berg and Rickard, 1983; Rickard and Sjo¨berg, 1983; Dreybrodt and Buhmann, 1991; Dreybrodt et al., 1996; Liu and Dreybrodt, 1997; Zhang and Grattoni, 1998) include: 1.

2. 3. 4.

pH involves the hydrogen ion whose diffusion coefficient is about three times, faster than that of the other diffusing species, demands of electro-neutrality at any point along the transport region, reactions between the diffusing species, and the fact that these reactions involve their kinetic rates.

These difficulties have been the focus of much discussion and controversy over the years. In fact, some research groups such as Plummer et al. (e.g., Plummer and Wigley, 1976; Plummer et al., 1978, 1979; Busenberg and Plummer, 1986) have largely based their interpretations and models for calcite dissolution on a very non-traditional framework focused on carbonic acid system parameters rather than saturation state. These complications resulting from the carbonic acid system also carry over to the calcite surface and the relative abundances of surfacespecies. This will subsequently be discussed in more detail.

3. Calcite dissolution kinetics 3.1. Dissolution kinetics in simple solutions at STP 3.1.1. General considerations Natural waters have a huge range in composition over which carbonate minerals will react with them. In this section, we address the kinetics of calcite dissolution in relatively dilute waters of simple composition. These waters can have a very wide range of pH values, PCO2s and saturation states. The major parameter of interest is saturation state and how it is related to carbonic acid system species and calcium. Numerous studies have demonstrated that at extreme undersaturations diffusion controlled dissolution kinetics prevail. As equilibrium is approached, there is a transition region to surface-controlled dissolution kinetics, and then a region of changing surface-controlled reaction mechanisms until equilibrium is reached (Fig. 3). Older studies tended to largely focus on greater distances from equilibrium where changes in bulk solution composition could be readily monitored and manipulated. Many more recent studies, utilizing advanced techniques such as atomic force microscopy (AFM), have been concerned with developing a better understanding of reaction mechanisms on mineral surfaces. Although studies that measure bulk solution chemistry can provide good information on the relationships between solution composition and reaction rates, they remain largely non-mechanistic in their interpretation. Surface studies provide interesting insights into the types of reactions that are occurring,

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

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Fig. 3. Schematic representation of rate controlling mechanisms for calcite dissolution as a function of pH and temperature. (Based on Sjo¨berg and Rickard, 1983.)

but are hard to extrapolate to net reaction rates. A major challenge is to find better ways to integrate these approaches into meaningful and practically useful models.

The slope of the linear fit to the data (
0.95) can be assumed within the uncertainty of the data to be unity, indicating a first order reaction with respect to aH +. This relationship appears to hold up over about 5

3.1.2. Diffusion controlled dissolution Many natural waters are highly undersaturated with respect to carbonate minerals and in these waters the rate of carbonate mineral dissolution may be primarily controlled by the hydrodynamic conditions that influence the thickness of the stagnant boundary layer. Examples of such waters include acid mine waters, acidic waters in peat bogs, acid rain and acidic lakes. When carbonate minerals and waters encounter one another under these conditions, typically either the solid or solution will dominate mass action. If the solid dominates (a high A/V ratio), the solution’s composition will rapidly evolve to less undersaturated conditions where diffusion control of the reaction will pass to surface controlled processes (e.g., a drop of acid rain falling into a crack in a limestone rock). If the solution dominates (a very low A/V ratio), then little change will occur in the solution composition and the solid will be relatively quickly and totally dissolved (e.g., a small grain of calcite gets blown into an acid lake). Fig. 4 shows results from a number of investigations on calcite dissolution kinetics in the diffusion controlled region below a pH of approximately 4 – 5.

Fig. 4. Log of the calcite dissolution rate vs. pH far from equilibrium where the dissolution rate is close to first order with respect to aH + . (After Plummer et al. (1979) — see their paper for key to symbols and lines and discussion.)

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

orders of magnitude in rate. It is therefore possible to represent the rate (R) by the simple equation R ¼ ka nHþ

ð22Þ

At 25 jC, Plummer et al. (1978) gave a value for k of about 50 10
3 cm s
1 and n = 1, whereas, Sjo¨berg and Rickard (1984a) obtained a value for k of about 3 10
3 cm s
1 (for a mid-range diffusion boundary layer (DBL) thickness of 30 Am) and n = 0.9. At a pH of 4, these values produce a difference in predicted rate of close to seven times faster for the results of Plummer et al. (1978) than those of Sjo¨berg and Rickard (1984a). However, the results are close to identical if a lower limiting value of 4 Am is used for the DBL, illustrating the importance of the difficult task of assessing the thickness of the DBL. It is interesting that the rate in this region is independent of PCO2. A possible explanation for this is that as pH decreases, PCO2 must increase (Eq. (20)). Over the diffusion-controlled range of dissolution, PCO2 must be quite high, eventually exceeding 1 atm at very low pH, as evidenced by the ‘‘fizzing’’ of calcite in acidic solutions. For example, using Eq. (20) and setting PCO2 = 1 atm and pH = 4, results in a carbonate ion activity of 10
10.85. This would require a ridiculous equilibrium calcium ion activity of close to 50 for a purely transport-controlled system! Since this very simple calculation leads to unsatisfactory implications, a better explanation must be found. Sjo¨berg and Rickard (1984a), using the rotating disk method and mixed kinetic theory, were able to show that the transition to H + dependence occurs when H + penetrates the DBL and first reaches the surface. Reactions in the surface boundary layer result in a surface H + concentration value several orders of magnitude less than that in solution. This provides an avenue for avoiding extremely high near-surface PCO2 and calcium ion activity values at equilibrium, which is obviously not the case. Sjo¨berg and Rickard (1985) investigated the issue of the influence of dissolved calcium on dissolution kinetics in the H + -dependent region in an elegant paper. They demonstrated that in this region solution calcium concentrations did not influence dissolution rates. The concentration of calcium did, however, influence the pH at which the transition to H + dependence occurred. As calcium concentration increases so

does the transition pH, from about 4.75 in pure KCl to 6 in KCl containing 10
2 M Ca2 +. Sjo¨berg and Rickard (1985) argue that because flow rates in many natural systems are relatively slow and Ca2 + concentration are often substantial that an end-member transport-controlled dissolution rate for calcite may persist over a substantial pH range. Compton et al. (1989) found that under very acidic (pH < 4) conditions, dissolution control passed from H + diffusion control to a first order heterogeneous reaction of H + at the surface. Their data could be modeled assuming a finite rate of heterogeneous reaction according to Eq. (23), where the rate constant has a value of 0.043 F 0.015 cm s
1 and [H + ]s is the surface H + concentration. R ðmol cm
2 s
1 Þ ¼ k½Hþ s

ð23Þ

Yet, another complication that has received considerable attention is that of reaction kinetics among the components of the carbonic acid system. The hydration/dehydration kinetics of dissolved CO2 are sufficiently slow that under some circumstances they may play an important role in dissolution reactions. This appears most likely to occur in systems with relatively low V/A ratios such as subsurface waters (e.g., see extensive discussions in Dreybrodt and Buhmann, 1991; Dreybrodt et al., 1996; Liu and Dreybrodt, 1997). For small (]10 Am) particles, it has been found that the stagnant boundary layer can be assumed infinitely thick and that hydrodynamic conditions are not of great importance (e.g., Nielson, 1964). In the case of larger particles and large surfaces, this is not true and hydrodynamic conditions can become a factor in controlling the rate of dissolution (see discussion in Morse, 1983). For biogenic carbonates with complex microporous structures, the relationships between ‘‘geometric’’ surface area based on particle size and ‘‘reactive’’ surface area are complex (Walter and Morse, 1984b). 3.1.3. The transition region to surface controlled dissolution Following the general conceptual classification scheme of Van Name and Hill (1916), Sjo¨berg and Rickard divided their studies of carbonate reaction kinetics into the three general categories (see Fig. 3)

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

of transport-controlled kinetics, mixed kinetics, and chemically controlled kinetics (Rickard and Sjo¨berg, 1983; Sjo¨berg and Rickard, 1983, 1984a). Much of their research was focused on the transitional mixed kinetic regime which poses special challenges due to the fact that the reaction rates may show intermediate behavior between a strong dependence and independence of hydrodynamic conditions. This is illustrated in Fig. 5 where the dependence of dissolution rate on the rotating disk spin rate is intermediate between the ideal relationship and total independence of dissolution rate on spin rate. The work of Rickard and Sjo¨berg (1983) was important in showing that the rate constant for calcite dissolution in this transition area could be represented by Eq. (24), k ¼ kC kT =ðkC þ kT Þ

ð24Þ

where kT is the transport controlled rate constant and kC is the chemically controlled rate constant. When kTHkC the rate is chemically controlled and when kCHkT the rate is transport controlled.

61

Fig. 6. The calcite dissolution rate vs. Xn for n = 1 and n = 1/2. (After Rickard and Sjo¨berg, 1983.)

Rickard and Sjo¨berg (1983) also were able to derive important relationships between the different types of equations used to represent calcite dissolution kinetics. For a pH > 7 and PCO2 < 0.03, it was shown that the model-based equation of Plummer et al. (1978) could be recast as
 a þ R ¼ k 1
bH X ð25Þ asHþ where abH + and asH + are the hydrogen ion activities in the bulk solution and near the surface, respectively. As the two hydrogen ion activities approach each other, the general empirical rate equation (Eq. (3)) is obtained for a first order reaction (n = 1). Sjo¨berg (1976) found that dissolution kinetics in this region followed Eq. (5) with n = 1/2 for dilute solutions (influences of solution composition on the parameters of this equation will be discussed in a later section). Fig. 6 shows the differences in results obtained for n = 1 and n = 1/2 in Eq. (5), indicating that the rate is proportional to Xn when n = 1/2. Rickard and Sjo¨berg noted that in the region of 0.4 < X < 1 that  1 1
X 2 c
logX ð26Þ and, therefore, for X > 0.4 rates described by Eqs. (27) and (28) are indistinguishable.

Fig. 5. The dissolution rate of calcite as a function of the square root of the disk rotation rate (x) for runs with Carrera marble (short dashed line) and Iceland spar calcite (long dashed line). The straight line represents a transport controlled reaction. (After Rickard and Sjo¨berg, 1983.)

R ¼
kAlogX ¼
kAðSIÞ  1 R ¼ kA 1
X 2

ð27Þ ð28Þ

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3.1.4. Near-equilibrium surface controlled dissolution Rickard and Sjo¨berg (1983) made the important observation that chemically controlled rate constants (kC) depend differently on surface areas for different calcites (e.g., Iceland spar and precipitate powders). They argue that this is due to differences in the types and abundances of reactive surface sites on the differing calcites. Compton et al. (1986) also concluded that changes in surface morphology (roughness), arising from differences in sample preparation techniques or the dissolution reaction itself, could cause differences in measured dissolution rate. The distressing result of this is that there can be no general equation that is applicable to all calcites that simply relates surface area and solution composition! It also implies that the influences of inhibitors will differ for different calcites. The detailed study of the surfaces of dissolving calcite offer the potential for better understanding and quantifying these surface site influences. Because the concentration of highly reactive surface sites can be related, at least in part, to crystal defect density, Schott et al. (1989) used strained calcites to investigate the rate dependence of calcite dissolution on defect density. Following the work of

Helgeson et al. (1984), they pointed out that the basic rate equation for dissolution under substantially undersaturated conditions Y n R ¼ k Se ai i ð29Þ i

could be modified (following Blum and Lasaga, 1987) to include the influence of dislocations by setting (
 X
DG þ p kSe ¼ m exp kT perfect surface sites
 ) X
DG þ d exp þ þ ð30Þ kT dislocation surface sites where m is a frequency factor and k is the Boltzman constant. The subscripts p and d refer to perfect site and dislocation site Gibbs free energies, respectively. Schott et al. (1989) pointed out that dislocations can influence dissolution kinetics (Fig. 7) by increasing the potential energy of the solid (acrystal in Eq. (29)) and increasing the number of dislocation surface sites (term 2 in Eq. (30)). They found that even at high dislocation densities (1011 cm
3) only about a 4%

Fig. 7. Schematic illustration of parallel process involved in crystal dissolution. Horizontal length of arrows is relative to rate and thickness represents quantity of material dissolved. (After Schott et al., 1989.)

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increase in activity occurred, so that the second (surface dislocation) influence was strongly dependent on reaction kinetics. Eqs. (29) and (30) were then combined and modified to produce Eq. (31), where Stot is the total surface area and Sd is the area covered by defect sites (Stot can be used since SpHSd), and kp and kd are the dissolution rates at perfect and dislocation sites, respectively. Y n R¼ ai i ðStot kp þ Sd kd Þ ð31Þ

model. They found that the following reactions provided an adequate description of calcite dissolution and precipitation in dilute solutions (> denotes a surface complex): k1

þ þ > CO
3 þ 2H U > Ca þ H2 CO3 k5

k2

> Caþ þ H2 CO3 U > CO3 H0 þ CaHCOþ 3 k6

i

For unstrained calcite, Schott et al. (1989) found good agreement with Busenberg and Plummer (1986) and Sjo¨berg and Rickard (1984a). However, for strained calcite with defect densities greater than about 107 to 108 cm
3, a major (2 – 3 times) increase in near equilibrium dissolution rates was observed. The fact that little influence of defect density on dissolution rates was observed at high undersaturations, where transport control dominates, confirmed that the increase in rates near equilibrium, where reaction rate is surface controlled, was the result of an increase in surface dislocations.

63

ð32Þ

ð33Þ

k3

> CO3 H0 þ CaHCOþ 3 U k7

þ

> Ca þ H2 CO3 þ CaCO03 k4

CaCO3ðsolidÞ U CaCO03 k8

ð34Þ ð35Þ

The overall reaction rate is given by 2 Rate ¼ k1 > CO
3 ðaHþ Þ þ ðk2
k5 Þ

> Caþ aH2 CO* þ k4
ðk6
k3 Þ 3

0

3.1.5. The surface complexation model One of the most interesting advances in understanding calcite dissolution kinetics in simple solutions came from the surface complexation model for carbonate minerals developed and initially applied to calcite dissolution kinetics by Van Cappellen et al. (1993). The basic idea of their work is that the speciation of surface sites is strongly influenced by solution chemistry other than simple saturation state. Just as the ratios of different carbonic acid species vary as a function of PCO2 at a given pH, so can the ratios of various surface complexes. At high PCO2 values, the dissolution rate at a given saturation state, can be increased by the formation of carbonate complexes with surface calcium ions. It was thus possible to correlate the dissolution kinetics of calcite with the relative abundances of surface complexes formed at the mineral – water interface. Subsequently, Arakaki and Mucci (1995) were able to arrive at a general equation for calcite dissolution and precipitation in simple solutions by combining their own experimental data with those of others (Plummer et al., 1978; Chou et al., 1989) and the Van Cappellen et al. (1993) surface complexation

> CO3 H aCaHCOþ3
k7 > Caþ aH2 CO* aCaCO03
k8 aCaCO03

ð36Þ

3

3.1.6. Direct observations of dissolving surfaces In addition to the TEM work by Schott et al. (1989) described above, observations of dissolving calcite surfaces have been made directly (either in situ or ex situ) using a variety of atomic or near-atomic scale techniques, including atomic force microscopy and optical interferometry. This recent work has focused largely on the growth of etch pits, their morphology and distribution. There are significant differences in experimental conditions (e.g., pH, PCO2, ionic strength, Ca2 + concentration) among these various efforts, giving rise to obvious variation in computed dissolution rates; moreover, the resolution of the dissolution rate itself in familiar units can be a complex matter. However, a common observation has been the distinct differences in step velocities of opposed steps that form the etch pit. Two of the neighboring, intersecting steps forming a corner are ‘‘slow’’ while the diagonally opposite pair is ‘‘fast’’ (see Fig. 8). The difference in velocities ranges from 2 to 4 (Park et al., 1996). The relative step velocities obviously determines the over-

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

Fig. 8. Schematic diagram of etch pit on the surface of the 101¯4 cleavage plane of calcite, showing nonequivalent [4¯41] and [481¯] step directions. ‘‘Slow’’ steps are those having an intersection with the cleavage surface of 78j5V(acute), while the fast steps penetrate the surface at an angle of 101j55V(obtuse). Adapted from Britt and Hlady (1997).

all rate of etch pit expansion and deepening. Liang et al. (1996b) have suggested that the migration of single steps is limited by the rate at which (double) kinks appear and are subsequently annihilated. MacInnis and Brantley (1992) performed rotating disk experiments far from equilibrium (0.7 M KCl – KOH, pH f 8.6) using undeformed and strained calcite, measuring etch pit dimensions using reflected light photomicroscopy and a Mirau double beam interference objective (this technique differs from scanning interferometry work, described later). In agreement with Schott et al. (1989), they found dislocation density to be several orders of magnitude higher for strained vs. undeformed samples; however, the large increase in dislocations in strained calcite did not correspond to a simple increase in etch pit development, nor to a correspondingly large increase in dissolution rate. Moreover, they found two etch pit populations to develop that differ in size, distribution, and lifetime, reflecting point defect clusters vs. true dislocations, respectively. The former gives rise to numerous, but smaller, shallow pits; the latter to deeper pits whose wall slope angles vary but whose mean angle is similar to that observed for cleavage steps. Their overall steady state rate (3.1 10
10 mol cm
2 s
1 from reacted fluid chemistry) is more than f 3 times higher than rates achieved in pure

water by Plummer et al. (1978) and Chou et al. (1989). They also calculated rates from the velocities of etch pit step edge migration, etch pit floor deepening, and estimates of areal distribution of etch pit types, that are in good agreement (within 2r) with their initial (bulk) rate measurements. They concluded that the primary contribution to overall dissolution rate is from steeply inclined surfaces, i.e., the (steep) walls of etch pits attributed to true dislocations. Bimodal populations of etch pits are also observed in AFM dissolution experiments conducted at pH 9 in pure NaOH solutions by Liang et al. (1996a): abundant, but short-lived, shallow pits attributed to point defects or impurities ( < 1 Am in lateral dimension, one atomic layer or 0.3 nm in depth), and less abundant, deep (f 40 atomic layers in depth) pits attributed to dislocations. This distribution may also correspond to the shallow vs. deep pits observed by MacInnis and Brantley (1992). Similar population distributions have also been noted by Ertan et al. (unpublished data; see also Fig. 9). Etch pits orient along the [481¯] or [4¯41] step directions. As mentioned above, Liang et al. (1996a) measured two step velocities related to etch pit geometry: fast (3.4 nm s
1) and slow (1.5 nm s
1). However, no recalculation of these velocities is made to afford direct comparison with steady state rates (this would have required an estimate of step density). In recent AFM work, Lea et al. (2001) observed that the step velocity differs depending on the characteristic angle of intersection between step wall and the terrace. Obtuse (+) steps have roughly twice the velocity in undersaturated solutions compared to acute (
) steps. They also observed that the velocity of obtuse steps decreases more than acute steps with increasing carbonate ion concentration. This anisotropy changes the shape of the pit itself, leading to rounded intersections between [481¯] + and [4¯41] + step edges. The anisotropy in step velocities measured by Lea et al. (2001) and Liang et al. (1996a) (see also Liang and Baer 1997) was also observed by Jordan and Rammensee (1998), using scanning force microscopy to measure calcite dissolution rates in pure water at ambient P CO 2 (10
3.5 at 24 jC, corresponding to a pH of f 5.6): 2.5 nm s
1 fast and 0.5 nm s
1 slow. They represented net removal of material from the calcite surface by migrating steps as a function both of the mean velocity and the step density. Etch pits represent

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

65

Fig. 9. Sequence of 3D rendered images of scanning interferometer data from the 101¯4 calcite cleavage surface dissolving at pH f 9, PCO2 10
3.5. Panel (A) is the pristine surface; panels (B), (C) and (D) record development and coalescence of etch pits after 15-, 60-, and 240-min reaction (Ertan et al., unpublished data).

areas of high (or maximum) step density; surrounding terraces (‘‘intersectional’’ regions) are characterized by low step density. By calculating a step density from etch pit wall angles, the authors compute the rate of deep etch pit dissolution to be 1.5 F 0.3 10
10 mol cm
2 s
1 (cf., e.g. Busenberg and Plummer 1986, 2.4 10
10 mol cm
2 s
1 at pH 5.60, PCO2 = 0). The summed velocity of Liang et al. (1996a; 4.9 nm s
1) is comparable to the lateral velocity of etch pit walls observed by MacInnis and Brantley (1992;

5.4 nm s
1), although the description of pit depths is a function of instrumentation: shallow vs. ‘‘deep’’ pits described by Liang et al. (1996a) are 0.3 vs. f 12 nm for MacInnis and Brantley (1992); certainly depths of less than one nm would not have been observable by the optical system of MacInnis and Brantley (1992). Conversely, the 800-nm etch pit depths measured after 30 min of reaction by the latter workers would have been difficult to resolve with (high-resolution) AFM instruments.

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

This highlights a central problem in using AFM in dissolution studies; namely scale. Although AFM provides high specific detail (permitting the angstrom-scale resolution of lateral step migrations), relating the velocity of step directions to the bulk dissolution rates described above requires several pieces of information: 1.

a geometric model that relates (observable) motion of step traces to the three dimensional removal of surface material at etch pits; 2. an estimate of the statistical distribution (density) of etch pits across the reactive surface; 3. and, most importantly, an understanding of how this process evolves during the approach to a ‘‘steady state’’ rate of removal. Also, removal of material by step migration may also occur at flat terraces, whose specific rate will be far less than that observed at etch pits but whose a real contribution to the total rate may be significant. Since etch pits grow both by widening and deepening, they must ultimately coalesce (as shown by MacInnis and Brantley, 1992; a model for etch pit size distributions was introduced by MacInnis and Brantley, 1993), and the overall rate is thus a reflection of competing processes. These are etch pit deepening; step migration, whose velocity reflects crystallographic control (Liang et al., 1996a,b) and pit depth (thus, the change in pit wall angle with time observed by MacInnis and Brantley, 1992); coalescence of etch pit boundaries. This results in a surface of variable relief containing etch pit floors, step edges, and slowly reacting terraces. The long-term evolution of this process is at present not understood (long-term AFM experiments are currently technically difficult), and requires a quantitative, comprehensive model to relate atomic-scale processes to bulk phenomenological observations. In addition, these problems relate to current questions regarding the relationship between total surface area, as quantified, e.g., by gas absorption techniques (BET, Brunauer et al., 1938) and reactive surface area (White and Peterson, 1990; Rufe and Hochella, 1999). This relationship is an area of active research in the field of mineral – solution kinetics (e.g., Gautier et al., 2001). Direct observation of atomic-scale processes must ultimately relate to ‘‘whole mineral’’ reactivity

(Dove and Platt, 1996). One alternative way of approaching this problem is through application of vertical scanning interferometry, which allows quantification of both the evolution of surface features in three dimensions, and a relatively simple means of computing bulk rates. As an illustration, a sequence of interferometer-derived images is shown in Fig. 9. These depict 3D rendered data collected over the course of calcite dissolution at a pH of f 9 and PCO2 of 10
3.5. These data show the initial development of etch pits on a 101¯4 cleavage surface, whose growth and development ultimately lead to widespread interference and coalescence. Through the use of fixed (unreacted) reference points, absolute differences in surface height data can be computed over each time step, leading to a detailed history of reaction rates in conventional units (mol/unit area/unit time). Interferometry can also establish the statistical distribution of rates (Lu¨ttge et al., 1999), and thus permits quantification of the overall heterogeneity of the dissolution process. Recent dolomite dissolution experiments using scanning interferometry (Lu¨ttge et al., 2002, described below) have also highlighted relationships between geometric and BET surface areas, intrinsic and average dissolution rates. In a series of unique experiments, Shiraki et al. (2000) compared calcite dissolution rates measured by reacted fluid chemistry as well as by AFM step velocities. AFM rates (given in mol cm
2 s
1) are somewhat depressed relative to those determined from solution chemistry; overall, however, there is fair agreement (Fig. 10). Step velocities also differed from those recorded in other AFM studies by a factor of f 3. For example, their average velocity at a pH of 8.9 is 1.6 nm s
1, less than that recorded by MacInnis and Brantley (1992; 5.4 nm s
1) or Liang et al. (1996a; 4.9 nm s
1). Rates measured by Shiraki et al. (2000) are also in good agreement (within error, see Fig. 10) with the measured rates of Plummer et al. (1978). 3.2. Influence of temperature Although the influence of pressure on carbonate reaction kinetics has not been investigated, several studies have focused on how calcite dissolution kinetics vary with temperature. Early work on the topic was summarized by Plummer et al. (1979). This data set was confined to dissolution in acidic solutions

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

67

Fig. 10. Comparison of AFM-derived calcite dissolution rates with those from previous studies using powders. Closed squares with error bars are AFM rates, closed triangles are rates from reacted solution chemistry, both taken from Shiraki et al. (2000); open square is datum from MacInnis and Brantley (1992); open circles and solid line are data from Sjo¨berg (1976); dotted line is from the model of Chou et al. (1989); and dashed line is from model of Plummer et al. (1978).

where transport control is generally rate limiting (see previous discussion). A fairly wide range (about 8 – 60 kJ mol
1) of activation energies was reported. However, probably the most reliable values in dilute solutions were close to the same; 8.4 kJ mol
1 by Plummer et al. (1978) and 10.5 kJ mol
1 by Sjo¨berg (1978). This is a relatively small change in dissolution rate with temperature of about 13% for every 10 jC (e.g., rates of biologic processes typically roughly double for each 10 jC change in temperature). Subsequently, Sjo¨berg and Rickard (1984b) made a much more in depth study of the influences of temperature on carbonate dissolution kinetics under a variety of conditions. Although these conditions were constrained to inhibitor-free solutions far from equilibrium, they still revealed a quite complex impact of temperature on calcite dissolution kinetics. Their

results are summarized in Fig. 3. The boundaries between H + -dependent, transitional and H + -independent regimes were found to move to lower pH values with increasing temperature. Gutjahr et al. (1996a) found a high activation energy (35 kJ mol
1) in the near equilibrium region confirming that the calcite dissolution reaction is surface controlled in this region of saturation. Interestingly, they also found that the reaction order changed from 2 at 20 jC to 1.2 at 70 jC, whereas the rate constant increased from 1 10
10 to 2 10
10 mol cm
2 s
1. Outside of this limited amount of work and that in seawater (see next section), little is known about the influences of temperature on calcite dissolution kinetics in the surface-controlled near equilibrium region that is common in natural systems or how the

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

influence of inhibitors may interact with changing temperature. This imposes a very substantial limitation on our ability to predict calcite dissolution kinetics in the ‘‘real world’’. 3.3. Influences of solution composition and reaction inhibitors 3.3.1. General considerations The previously discussed studies of calcite in compositionally simple and generally dilute solutions provide information that is primarily of interest from a ‘‘pure chemistry’’ standpoint, but of limited utility for most natural waters which are chemically complex and where reactions often proceed relatively close to equilibrium (e.g., the deep ocean). However, just as equilibrium thermodynamics provide a valuable starting point for looking at deviations from equilibrium in natural systems, so also do the results of studies of calcite dissolution in ‘‘pure’’ systems provide a basis for looking at the influences of inhibitors common in natural waters. The very major impact that ‘‘foreign’’ ions can have on calcite dissolution was recognized by early investigators such as Weyl (1958) and Terjesen et al. (1961), who demonstrated that metal ions even at submicromolar concentrations can severely retard calcite dissolution. Table 1 gives a listing of studies of inhibitors of calcite dissolution. Unfortunately, many of these studies have been done under very different saturation states, and in solutions often not containing the same major ions and using differing techniques.

Since, as expected, it has been observed that inhibitory influences often dramatically increase with increasing saturation state and there is site competition among inhibitors and between inhibitors and major ions, results are often contradictory and not readily comparable. Therefore, only relatively few of these studies, which illustrate major points, will be discussed. Because the inhibitory influence of ions occurs dominantly by their interactions with the calcite surfaces, it is necessary to understand how these ions interact with surfaces. This is a very major and complex topic, and calcite surface chemistry will, therefore, only be dealt with to a rather limited degree in this paper. It is worth noting here, however, that basically two approaches are used in discussing surface interactions of ions that inhibit growth or dissolution kinetics (for references and discussion relative to carbonates, see Gutjahr et al., 1996b). The first is the Langmuir – Volmer model that assumes reversible adsorption at specific surface sites according to the Langmuir adsorption isotherm. The second is the Cabrera and Vermilyea model that assumes irreversible adsorption of additives on a terrace whereby the advancing steps get caught by additives while they grow between them (seen also in AFM work; see, e.g., Dove and Hochella, 1993; Gratz et al., 1993). Examples of these two approaches follow later in this section. It is important to note that generally the kinetics of the adsorption reaction are ignored and that only the initial linear part of a Langmuir adsorption isotherm is considered. It has usually not been dem-

Table 1 Studies of calcite dissolution inhibitors Inhibitor

References

Ca2 + Mg2 +

Sjo¨berg (1978), Buhmann and Dreybrodt (1987) Akin and Lagerwerff (1965), Benjamin et al. (1977), Berner (1967, 1975, 1978), Buhmann and Dreybrodt (1987), Gutjahr et al. (1996b), Mo¨ller (1973), Mo¨ller and Rajagopalan (1975), Plath et al. (1980), Plummer and Mackenzie (1974), Reddy and Wang (1980), Sjo¨berg (1978), Walter and Morse (1984a), Weyl (1958, 1965) Gutjahr et al. (1996b) Gutjahr et al. (1996b), Nestaas and Terjesen (1969), Salem et al. (1994), Terjesen et al. (1961)

Sr2 + and Ba2 + Transition and heavy metals Sulfate Phosphate Silica and nitrate Organics

Akin and Lagerwerff (1965), Buhmann and Dreybrodt (1987), Erga and Terjesen (1956), Kushnir (1983), Mucci et al. (1989), Sjo¨berg (1978) Berner and Morse (1974), Morse (1974), Nancollas et al. (1981), Reddy (1977), Sjo¨berg (1978), Svensson and Dreybrodt (1992) Morse (1974) Barwise et al. (1990), Berger (1967), Compton and Sanders (1993), Morse (1974), Suess (1970)

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

onstrated that beyond some inhibitor solution concentration the dissolution rate becomes independent of inhibitor concentration as would be predicted for surface site saturation by the Langmuir– Volmer model. 3.3.2. Inhibitor behavior in relatively dilute solutions In the previous discussion of calcite dissolution kinetics, the primary variables influencing saturation state and reaction kinetics were parameters such as PCO2 and pH in the carbonic acid system, the anion variable. However, it has also been found that the cation, Ca2 +, concentration can also influence reaction rate beyond its simple influence on saturation. Sjo¨berg (1978) found about a 17% increase in the rate constant over a range of initial calcium concentrations from 0 to 10 mM which could be interpreted in terms of a Langmuir-type adsorption isotherm. A similar, but substantially smaller influence, was found for magnesium whose influence increased with increasing magnesium concentration and saturation state. The combined influences of Ca2 + and Mg2 + were investigated and a complex relationship was found leading Sjo¨berg to conclude that it would be impractical to produce a general equation describing the effect of inhibitors on calcite dissolution rates. Sjo¨berg (1978) also found that both phosphate and sulfate could inhibit calcite dissolution and that their influences increased with increasing calcium and magnesium concentrations. This is probably the result of, at least in part, the adsorption of calcium and magnesium that produces a more positive and cationic surface (cation bridging) that increases the adsorption of phosphate and sulfate. Sjo¨berg (1978) also was able to demonstrate that for phosphate-free artificial seawater, rates could be well predicted by simply adjusting the rate constant for the presence of sulfate. His results showed that the other major and minor ions of seawater have little influence on calcite dissolution kinetics. More recently, Buhmann and Dreybrodt (1987) found that for diffusion-controlled calcite dissolution, the inhibitory influences of calcium, magnesium and sulfate could largely be accounted for by the ‘‘common ion effect’’, that results in changes in the differences between surface and bulk solution concentrations of Ca2 +. Svensson and Dreybrodt (1992) found that the difference in behavior between natural calcite samples

69

and pure NBS calcite could largely be explained in terms of the influence of phosphate associated with the natural samples. Following on the early work of Terjesen et al. (1961) and Nestaas and Terjesen (1969) that demonstrated a strong inhibitory effect of trace metals on calcite dissolution, Salem et al. (1994) studied the inhibitory influences of several transition metals on calcite under diffusion controlled conditions in dilute solutions. They observed major reductions in reaction rates even at micromolar concentrations of the metals and found the relative order of inhibitory strength to be Ni > Cu > Mn > Co. They attributed the inhibitory effects of these metals to Langmuir adsorption that caused the blockage of active surface dissolution sites. More recently, Lea et al. (2001) have also documented significant reductions in AFM step velocities with additions of Mn2 + greater than 0.5 AM. There have been surprisingly few studies of the influence of organic compounds on the dissolution of calcite in dilute solutions. Barwise et al. (1990) found by studying etch pit development that the di-anions of maleic and tartaric acids are powerful inhibitors capable of completely stopping proton-induced calcite dissolution. Compton and Sanders (1993) made the interesting observation that in equilibrated acidic solutions, humic acids had no influence on calcite dissolution rates, but that if fresh sodium salts of humic acid were added significant inhibition of dissolution occurred. 3.3.3. Studies of reaction kinetics and inhibitors in seawater Probably the most historically important studies of calcite dissolution were not conducted in the laboratory, but rather in the ocean by Berger (1967) and Peterson (1966), who hung packets containing foraminifera tests and polished calcite spheres, respectively, at different depths in the Pacific Ocean. Their rates of dissolution, based on weight change, were then related to the in situ saturation states of the seawater. The most important finding was that the dissolution rate of calcite in seawater is not directly proportional to the extent of undersaturation and therefore simple first order kinetics cannot be used to describe this process. Similar results were later obtained for the Atlantic Ocean (Milliman, 1977; Honjo and Erez, 1978). Their findings are in general

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agreement with the near equilibrium dissolution kinetics of calcite in simple solutions. These studies were followed by an extensive investigation of the dissolution kinetics of calcite in seawater using the constant composition pH-stat technique by Morse and Berner (Morse and Berner, 1972; Morse, 1973; Berner and Morse, 1974; Morse, 1974). Over a broad range of saturation states (Fig. 11; note the DpH is the difference between the equilibrium and experimental pH values), the general pattern of the relationship between pH and dissolution rate is similar to that subsequently found in dilute solutions by Sjo¨berg and Rickard (1983; see Fig. 3). A major difficulty in understanding the dissolution kinetics of calcite in seawater is that the saturation state of seawater is generally greater than 0.7 with respect to calcite (e.g., see Morse and Mackenzie, 1990, Fig. 4.10) which is approximately a DpH of only 0.2. Thus, an understanding of the dissolution behavior of calcite in the ocean, and influences of factors such as inhibitors and temperature, must be obtained over a pH range of less than 0.2. Morse and Berner (1979) have summarized much of what is known about the dissolution kinetics of calcite in seawater. Over the saturation range of interest in the ocean, the reaction order for phosphate-free seawater is about 3 (Eq. (3)) for calcite powders (Morse and Berner, 1972) and 4.5 for pelagic biogenic calcite tests (Morse, 1978; Kier, 1980). Sjo¨berg (1978) found a reaction order of 2 when the square root of the saturation state was used [R = kA(1
X1/2)2]. One of

Fig. 11. Schematic representation of the dissolution behavior of calcite in seawater over a wide range of undersaturations denoted by DpH. (From Morse, 1973.) The three regions are roughly analogous to those shown in Fig. 3.

Fig. 12. The dissolution rate of different calcites in the water column of the Pacific Ocean and laboratory experiments. For the laboratory experiments, undersaturations were translated into the water depths at which they occurred in the Pacific Ocean. Water column: spheres = long dashed line; forminifera = dashed – dotted line. Experimental: calcite powder = dotted line; sediment = solid line. (After Morse and Berner, 1972.)

the most interesting findings of this work was that calcite spheres, powder, calcitic pelagic foraminifera tests, and calcite-rich deep sea sediments all yielded about the same pattern of reaction rate with respect to seawater saturation state, and that a major increase in reaction rate occurred at the saturation state close to that observed for the foraminiferal lysocline (Morse and Berner, 1972; Fig. 12). Morse (1974) used the approach shown in Fig. 13 to investigate a large number of possible dissolution inhibitors in seawater. Briefly, what he found was that the only inhibitor that had a major influence on calcite dissolution kinetics in seawater was phosphate. Over a reasonable range of phosphate concentrations for seawater, a minor influence was observed on the rate

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

71

Fig. 13. The ‘‘flow diagram’’ for studies of inhibitors of calcite dissolution in seawater. (From Morse, 1974.)

constant, but a very large influence was observed on the reaction order which increased up to about 16 at a phosphate concentration of only 10 AM (Fig. 14). These results were interpreted by Berner and Morse (1974) in terms of the previously discussed Cabrera and Vermilyea model. Berner and Morse (1974) hypothesized that increasing concentrations of phosphate at active sites (kinks) resulted in a closer spacing of phosphate ions that progressively raised the ‘‘critical undersaturation’’ for dissolution on retreating steps. A large number of papers have been written concerning the dissolution of biogenic carbonates and calcium carbonate-rich sediments, speculating on deep sea carbonate dissolution kinetics based on observations of fluxes from sediments and microelectrode measurements in sediments. The topic of carbonate accumulation, in both shallow and deep water sediments, and the role of biologic processes, both in the water column and in sediments, remains a vigorous

and controversial field of inquiry. However, at some point these studies will need to bridge the gap between the carefully controlled laboratory investigations discussed here and the complex natural oceanic environments. At present it is clear that there is a long way to go in doing so. This is exemplified by the recent paper by Hales and Emerson (1997) where simple first order kinetics, with a vastly lower rate constant than observed in experiments, are necessary to model their results for fluxes from deep sea sediments.

4. Dissolution of other sedimentary carbonate minerals 4.1. Aragonite dissolution kinetics Aragonite is by far the dominant carbonate mineral in tropical and subtropical shallow water carbonaterich sediments. It is found in deep sea sediments

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Fig. 14. The variation of the reaction order (n) and log of the rate constant (k) vs. dissolved phosphate concentration in seawater. (From Morse and Berner, 1979.)

primarily along ridge crests, and is the carbonate mineral that precipitates directly from seawater at high supersaturations. The dissolution of aragonite is a fundamental process involved in the conversion of aragonite to calcite during the lithification of carbonate sediments when they are exposed to fresh water. (See Morse and Mackenzie, 1990, for extensive discussion and references.) It is, therefore, rather surprising that relative to calcite only a very modest amount of research has been done on the dissolution kinetics of aragonite. In one of the first, and certainly the most extensive investigations of aragonite dissolution kinetics, Morse et al. (1979) determined the dissolution kinetics of synthetic aragonite and pteropod tests in seawater. Between a saturation state of near-equilibrium to 0.44, they found the empirical reaction order (Eq. (3)) to be 2.93, which is close to that observed for calcite in seawater under similar conditions. At greater undersaturations it increased to 7.27. Subsequently, Kier (1980) found an empirical reaction order for pteropod tests of 4.2, which compared well with the value of 4.5 found for calcitic sediments in his experiments.

Morse et al. (1979) found a rather strange influence of phosphate on aragonite dissolution kinetics. It initially catalyzes dissolution to an extent that is dependent on both saturation state and phosphate concentration. However, after about 4 h of reaction, no influence is apparent. This is suggestive of a complex kinetically controlled interaction of phosphate with the surface of aragonite. Busenberg and Plummer (1986) found the reaction kinetics and rate constants for aragonite to be very similar to those determined for calcite (see their Table 3, p. 149, for constants using their pseudo-mechanistic equation formulation). Gutjahr et al. (1996a,b) also studied aragonite dissolution kinetics in conjunction with their studies of calcite dissolution. They determined a reaction order for aragonite that is close to 3. This is in good agreement with the earlier work of Morse et al. (1979) in seawater. One peculiar observation they made was that, although the aragonite dissolution rates closely corresponded to those for calcite, the influence of stirring rate extended closer to equilibrium for aragonite than calcite. They hypothesized that this may be the result of preferential dissolution of aragonite on a favored crystallographic face. 4.2. High-magnesian calcite dissolution kinetics Because of their importance as both a skeletal and inorganic cement component of marine sediments, considerable energy has been directed at understanding how magnesian calcites behave in natural waters. Together with aragonite, metastable calcites with 10– 20+ mol% MgCO3 form the effective reactant phases in shallow water carbonate sediments, participating in subsequent diagenetic reactions to produce the commonly observed stable low-Mg calcite (and possibly dolomite) mineralogy of sedimentary carbonate rocks. Quantification of the rate and identification of the mechanism by which this transformation is accomplished has thus been a key goal of studies conducted over the past f 30 years. Prior to ca. 1970, experimental work focused on the diagenetic stabiliza‘ tion reaction of metastable marine calcite containing excess magnesium to form stable (low-Mg) calcite ( F dolomite). Results of work by Friedman (1964); Schroeder and Siegel 1969), and Land (1966, 1967) are variable and compare with difficulty, and do not

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contain absolute reaction rates. They are chiefly concerned with relationships between solid phase stoichiometry, bulk solution composition, and the relative rate of magnesium vs. calcium release to solution. Land (1967) observed that short-term (24 h) dissolution of skeletal magnesian calcites yielded congruent release to solution; by comparison, longer term experiments produced incongruent enrichment of dissolved magnesium at 25 jC, with the relative rate of this process proportional to the Mg content of the reactant calcite. Dolomite was not observed to precipitate at 25 jC, but did exsolve under hydrothermal conditions (300 jC), and the relative rate of this process (all other things being equal) was also roughly proportional to solid reactant Mg content (Land, 1967). The problems regarding magnesian calcite that bear on their dissolution kinetics can be organized as three general questions: 1.

2.

3.

What is the appropriate formulation of the relationship between the activity of solution components (calcium, magnesium, carbonate ion, etc.) and saturation state with respect to a calcite of a given magnesium content? How can apparent differences in reactivity be related to the phase’s origin (synthetic or inorganic vs. biogenic)? and How can reactive surface area be quantified in biogenic magnesian calcites?

There have been several review volumes (e.g., Mackenzie et al., 1983; Morse and Mackenzie, 1990) that have covered this ground in extensive detail; what follows here is a brief encapsulation of aspects relevant to dissolution kinetics. 4.2.1. Stoichiometric saturation In the case of magnesian calcites, the practice of relating reaction rates to the distance from equilibrium (X) becomes problematic, and controversy has revolved around just how this equilibrium should be defined. This problem arises partly from uncertainties in free energy values, from the larger question of whether magnesian calcites ever attain a true metastable equilibrium state, and how to represent this relationship in thermodynamic calculations. The issue of how magnesium substitution affects solubility has thus received far more attention than that of the effect

73

on dissolution rate alone. Thorstenson and Plummer (1977) approached this problem by introducing the concept of stoichiometric saturation. For a magnesian calcite having a composition Ca(1
x)MgxCO3, they proposed that the equilibrium constant is given by the product of activities IAPmag

cal

¼ ðCa2þ Þ1
x ðMg2þ Þx ðCO2
3 Þ,

ð37Þ

where x = mole fraction lattice magnesium. Magnesian calcite is thus assumed to react as a one-component phase having a fixed composition. With this assumption, the Gibbs – Duhem equality of chemical potentials of CaCO3 and MgCO3 between solid and aqueous phases can no longer be asserted. However, stoichiometric saturation was offered as a resolution to the problem of magnesian calcites that react so slowly as to preclude thermodynamic equilibrium, giving the appearance of reacting with apparently fixed composition. This concept was controversial at the time of its introduction (see responses by Garrels and Wollast, 1978; Lafon, 1978; Thorstenson and Plummer, 1978) and its usage has not been fully resolved. Plummer and Mackenzie (1974), in earlier free drift experiments dissolving biogenic magnesian calcite at fixed PCO2, derived equilibrium constants pffifor the dissolution rate from reciprocal root time (1/ t) plots of free drift data (see below). Their approach implicitly assumed that only the CaCO3 component attains a true saturation state, represented by IAPCaCO3 ¼ ðCa2þ ÞðCO2
3 Þ:

ð38Þ

However, subsequent solubility determinations have demonstrated the utility of the concept of stoichiometric saturation, and Walter and Morse (1984a) have shown that magnesian calcite reaction orders computed from rate vs. (1
X)stoich-sat relations are not vastly dissimilar to those of pure calcite. In still earlier work, Land (1967) observed that dissolution of biogenic magnesian calcite in pure water proceeded incongruently, which he attributed to a faster dissolution rate of MgCO3 vs. CaCO3 component. Plummer and Mackenzie (1974) argued that the ratio of Mg2 + /Ca2 + in solution reflected initially congruent dissolution, but that the dissolving phase differed in composition (and thus, presumably, solubility) from the bulk solid (initial = 24.7 vs.

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bulk = f 18 mol% MgCO3). Thus, the phase governing the initial dissolution rate in a multimodal assemblage of magnesian calcite mineralogies is the most soluble. Plummer and Mackenzie (1974) argued that incongruent dissolution follows a so-called parabolic rate law, which casts time (but not concentration) as the independent variable, and derived rate constants based on the following relationship, Ci ¼ 2ð1
ni Þk t 1=2

ð39Þ

In this equation, Ci is the dissolved concentration of the ith component in bulk solution, k is the rate constant, t is time, and the term (1
ni) is a correction factor to accommodate the stoichiometry of the incongruent reaction (ni = the ratio of stoichiometric coefficients of component i in mineral product over mineral reactant). In similar free drift experiments, Wollast and Reinhard-Derie (1977) confirmed these results, as well as subsequent reprecipitation of a calcite poorer in Mg than the initial reactant. Bertram et al. (1991) explored the effect of temperature on dissolution of synthetic magnesian calcites (f 2 to 19 mol% MgCO3), finding solubility to decrease with temperature in a manner similar to pure calcite. Using pH-stat techniques, Walter and Morse (1985) measured dissolution rates of carefully treated biogenic magnesian calcites (11– 18 mol% MgCO3), computing rate constants and reaction orders fit to Eq. (3), calculating saturation state from stoichiometric activity products and stoichiometric constants (Walter and Morse, 1984a). Rates were reported on a per unit mass (Amol g
1 h
1) vs. per unit area basis because of large differences in reactive vs. BET surface area (see below). They observed no systematic variation in rate parameters with MgCO3 content, although reaction orders are somewhat higher (n = 3.2– 3.5) compared to low-Mg calcite. 4.2.2. Biogenic vs. abiogenic phases In comparing calcites of similar Mg content, biogenic calcites exhibit greater structural and chemical heterogeneity and accommodate higher concentrations of nonstoichiometric components such as water and hydroxyl (Mackenzie et al., 1983; Gaffey, 1988), sodium, and bicarbonate. As is discussed below, a key observation made in these papers is

that microstructural differences in biogenic magnesian calcites exert a far stronger influence on their dissolution kinetics than their relative thermodynamic stabilities. Walter and Hanor (1979) found orthophosphate to inhibit the dissolution rate of biogenic magnesian calcite in a manner similar to that observed for pure calcite, i.e., the inhibition increased with increasing phosphate concentration and as calcite saturation was approached. Biogenic magnesian calcites also show larger unit cell volumes, and do not show smooth variation in c/a axial ratios with magnesium substitution compared to synthetic phases (Bischoff et al., 1983). This difference has been attributed to greater carbonate ion positional disorder (Bischoff et al., 1985; Paquette and Reeder, 1990). Bischoff et al. (1987) concluded that biogenic phases, when compared to synthetic magnesian calcites of similar Mg content, are more soluble, and moreover do not show the smooth variation in stability vs. composition characteristic of the latter. They proposed that the use of a single IAP vs. solid composition curve was inappropriate, and that subsequent work should consider the use of three curves that reflect the inherent heterogeneity of the total dataset: synthetic materials, carefully treated biogenic materials, and untreated biogenic materials. 4.2.3. The role of reactive surface area In comparing the dissolution rates of pure calcite and biogenic magnesian calcites having a range of Mg content, Walter and Morse (1984b, 1985) observed that the primary differences were most strongly controlled not by magnesium composition but by relationships between total (BET) surface area, grain size and microstructure. They observed that although dissolution rates in general increased with BET surface area, these increases did not show a simple proportionality. By assuming a unit ratio of reactive to total surface area in synthetic calcite (f 5-Am grain diameter), they were able to show that the complex microstructures characteristic of biogenic Mg calcites result in their having reactive surface areas that constitute as little as 1% or less of the total area. This must in part result from the large differences in transport efficiency of gases vs. dissolved solutes, and from the high tortuosity of complex networks of small pore spaces characteristic of skeletal pore systems. Thus, in these cases,

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BET area measurements are virtually useless as a measure of reactive area. In summary, magnesian calcites exhibit unique properties that complicate their reaction kinetics, and the actual dissolution mechanisms are to a large extent still unresolved. In synthetic phases, the addition of lattice magnesium below about 6 mol% MgCO3 has a relatively minor effect on thermodynamic stability, and may actually decrease solubility at f 3 mol%; from 6 mol% up to f 15 mol%, there is a well-documented overall increase in solubility (Mucci and Morse, 1984; Bischoff et al., 1987; Navrotsky and Capobianco, 1987; Bischoff, 1998). Because of the accessibility and importance of biogenic magnesian calcite in natural marine environments, dissolution work has focused predominantly on these materials. However, correct comparison of dissolution rates of biogenic magnesian calcites depends strongly on evaluation of reactive surface area, and differences in dissolution rate as a function of Mg content alone may be minor by comparison. As a practical device, the use of stoichiometric saturation to estimate distances from equilibrium allows satisfactory comparison of phases of varying composition, but is not free of uncertainty on a theoretical basis. Lastly, it is unclear what ‘‘net’’ effect these various physical properties (initial Mg content, distribution, and heterogeneity, grain size and microstructure, defect density, solution composition) have on the reaction path (congruent or incongruent) of magnesian calcites during stabilization in natural environments (Bischoff et al., 1993). 4.3. Dolomite dissolution kinetics

sedimentary dolomites of Recent age that have not undergone extensive recrystallization. Although it is difficult to separate the independent contributions of disordering and excess calcium, Chai et al. (1995) have shown that even small amounts of calcium substitution generate positive heats of formation for dolomite, and thus are strongly destabilizing. Inorganic calcite, in contrast, can accommodate a comparatively large extent of magnesium substitution, with only minor changes in enthalpy (Navrotsky and Capobianco, 1987). This limited understanding of dolomite solubility thus handicaps the description of near-equilibrium kinetics, whose expressions typically include an explicit free energy term. To be complete, a model of the kinetics of dolomite dissolution (and growth) must ultimately address the large difference in reactivity compared to calcite as well as magnesite, and the role played by crystal structure and composition. Busenberg and Plummer (1982) undertook the first significant laboratory measurement of dolomite dissolution rates at pH > 2 and at temperatures typical of sedimentary environments. Actual dissolution rates were measured by the weight loss of cleavage fragments, and conditions included large variations in fixed PCO2 (0 to f 1 bar), pH ( < 1 to f 10), solution composition (added calcium and magnesium), and temperature (5 –65 jC). Because this paper has become the de facto point of comparison in all subsequent work, and because of the limited literature on dolomite dissolution, the work is described below in some detail. Following the earlier approach to calcite of Plummer et al. (1978); Busenberg and Plummer (1982) proposed that their rate data could be fit to the expression, 1

In contrast to calcite, the attention devoted to laboratory determination of dolomite dissolution kinetics has been quite limited, and noteworthy results reside in only a handful of key papers. The limited data available reflect both the general difficulty in experiments involving dolomite, slow reaction rates, and the large uncertainty regarding the relationship between its reactivity, structure, and composition. The uncertainty in the thermodynamic solubility of ordered, stoichiometric (alternating equimolar lattice layers of calcium and magnesium) dolomite spans almost an order of magnitude (e.g., cf. pKa 19.71, Garrels et al., 1960; 17.33, Robie et al., 1979; 18.14, Johnson et al., 1992). Substitution of calcium for magnesium is typical in

75

1

R ¼ k1 aH2 þ þ k2 a 2

H2 CO*3

1

þ k3 aH2 2 O
k4 aHCO
3

ð40Þ

representing three parallel, forward dissolution reactions, each having a common order n = 1/2 at 25 jC. Each term thus describes a contribution to the overall reaction rate that becomes significant over a range of pH. At pH less than 6 and PCO2 close to zero, the rate is proportional to H + activity and only the first term is important. As PCO2 is increased, this linear relationship persists over a decreasing span in pH, and in a pure CO2 atmosphere the first term is adequate only below a pH of 1.6. A second term is thus added to accommodate this apparent dependence on CO2 (H2CO*3 = H2CO3 + CO2). Above pH 8

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

(and PCO2 f 0), a third term describes the dissolution rate’s approach to a constant value. Because maintaining moderate pH values (]4.5) at a high PCO2 requires the addition of carbonate alkalinity, the reduction in observed vs. predicted rates was interpreted to be the influence of HCO3
ion, described by the addition of a fourth ‘‘backward’’ (precipitation) rate term in Eq. (40). Rate constants at 25 jC for k1 through k4 are 1.7 10
8, 4.3 10
10, 2.5 10
13, and 2.8 10
8 (mol cm
2 s
1), respectively. Busenberg and Plummer (1982) also observed a complex pattern of incongruent dissolution behavior. In dissolution runs using pure water, the initial ratio of Ca to Mg released to solution was less than unity (leaving the solid calcium-rich). This pattern then reversed itself, with the solid yielding greater calcium than magnesium (leaving a magnesium-rich surface), but with sufficient reaction the yield approached congruence. Busenberg and Plummer (1982) used this evidence of incongruent surface reactions to construct a rather elaborate reaction scheme consistent with Eq. (40). The parallel reactions associated with k1, k2, and k3 are k10

CaMgðCO3 Þ2 þ Hþ ! MgCO3 þ Ca2þ þ HCO
3 CaMgðCO3 Þ2 þ H2 CO03 k20

! MgCO3 þ Ca2þ þ 2HCO
3

ð41Þ

ð42Þ

CaMgðCO3 Þ2 þ H2 O k30


! MgCO3 þ Ca2þ þ HCO
3 þ OH

ð43Þ

in which ‘‘MgCO3’’ is the Mg-enriched surface. In order to accommodate the evidence for incongruent reactions, they argue that the subsequent reactions (listed also respectively) involving ‘‘MgCO3’’ are slower and rate-limiting: k 1W

MgCO3 þ Hþ ! Mg2þ þ HCO
3 k 2W

MgCO3 þ H2 CO03 ! Mg2þ þ 2HCO
3 k 3W


MgCO3 þ H2 O ! Mg2þ þ HCO
3 þ OH

ð44Þ ð45Þ ð46Þ

Because these reactions consume only one half of the molar equivalent of dolomite per mole reactant (H +, H2CO03, H2O), they concluded this was the origin of the observed reaction order n = 1/2. (This conclusion does not, however, explain the initial observed incongruent step, in which magnesium is released prior to calcium). Busenberg and Plummer (1982) observed the order with respect to hydrogen ion to increase with temperature above 45 jC, giving values of 0.6 at 55 jC and 0.7 at 65 jC. In earlier rotating disk experiments (pH < 2), Lund et al. (1973) described a similar variation of reaction order with respect to HCl concentration and temperature (n = 0.44 at 25 jC, 0.61 at 50 jC, and 0.85 at 100 jC). In experiments using a fluidized bed reactor, steady state rates measured by Chou et al. (1989) are similar to those of Busenberg and Plummer (1982) in the region of high pH (8 – 9). However, increasingly higher rates were measured at lower pH, resulting in an overall disagreement of slightly less than an order of magnitude at pH 3. Chou et al. (1989) did not fix the PCO2 prevailing within the reactor as did Busenberg and Plummer (1982), but computed PCO2 from the alkalinity and pH of the reacted solution. In addition to the disagreement at low pH, Chou et al. (1989) also calculated a reaction order using Eq. (40) of n = 3/4. Rate constants at 25 jC for k1 through k3 are 2.6 10
7, 1.0 10
8, and 2.2 10
12. Chou et al. (1989) argued that the scheme of successive reactions described by Busenberg and Plummer (1982) would not produce fractional orders less than unity, and instead attributed their observed order to the degree of surface protonation and the availability of surface complexes. Relatively recent dissolution work at pH < 5 was presented by Gautelier et al. (1999). In these rotating disk experiments, log rates were found to be linear with respect to pH over the range of 1 – 5, giving k1 = 9.8 10
8, 5.1 10
7, and 1.8 10
6 mol cm
2 s
1 and orders n = 0.63, 0.73, and 0.80 at 25, 50, and 80 jC, both respectively. Below a pH of f 1, the dissolution rate approached a plateau and became independent of pH. Gautelier et al. (1999) used their measured pH and dissolution rate data to estimate the diffusional boundary layer thickness and surface hydrogen ion activity. They argued that a decrease in the ratio of surface to bulk hydrogen ion activities (aH + surf /aH + bulk) with increasing bulk pH

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

indicates the increasing role of solute transport on measured reaction rates (Gautelier et al., 1999, their Fig. 9, p. 23). They concluded that the fractional order of the reaction with respect to hydrogen ion is responsible for this behavior. Fig. 15 compares the data from Busenberg and Plummer (1982), Chou et al. (1989), and Gautelier et al. (1999) at 25 jC. Talman and Gunter (1992) found the order of hydrogen ion dependence to increase with temperature, but with increasing evidence of stirring rate dependence at temperatures over 100 jC. By comparison, Lund et al. (1973) found no stirring rate (and thus no solute transport) dependence of dolomite dissolution at temperatures below 50 jC (in 1M HCl). Busenberg and Plummer (1982) also found no dissolution rate dependence on stirring rate at 45 jC, pH 3 – 4.4. However, the conclusions of Gautelier et al.

77

(1999) are not independent of assumptions regarding DBL, and it is thus difficult to reconcile the extent to which they reflect uncertainty in these assumptions as well as measured values. Moreover, the use of surface to bulk activity ratios in this case can be somewhat deceptive, as the observed relationship may result from a small but constant offset (error?) between estimated surface and bulk activities. It is also difficult to evaluate to what degree either concentration or transport of CO2 away from the reacting surface may have influenced measured rates, given Busenberg and Plummer’s (1982) observation of the rate’s dependence on CO2. Gautelier et al. (1999) also noted a decrease in apparent activation energy with increasing pH (46 kJ mol
1 at pH = 0 vs. 15 kJ mol
1 at pH 5). An activation energy of 15 kJ mol
1 is characteristic of diffusion-controlled reactions, but although this

Fig. 15. Dolomite dissolution rate data as a function of pH, taken from the following sources: open circles, Busenberg and Plummer (1982) (weight loss); open squares, Gautelier et al. (1999) (rotating disk, solution chemistry); solid curve, equation of Chou et al. (1989) (column reactor, solution chemistry); filled circle, Lu¨ttge et al. (2000) (fluid cell, vertical scanning interferometer).

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J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

pattern is compatible with the authors’ assertion of increasing transport control with increasing pH, it may also reflect the role of CO2 and its corresponding temperature-dependent solubility. In a recent series of papers, Pokrovsky and coworkers (Pokrovsky and Schott, 1999; Pokrovsky et al., 1999a,b) have championed the surface complexation model (see above discussion of Van Cappellen et al., 1993) as a means of resolving the reactivity and reaction rates of dolomite and magnesite. Surface complexation constants in these papers are recovered by a variety of methods (surface potentiometric titration, streaming potential and electrophoresis) that in turn involve a large number of assumptions and empirical parameters that may defy simple comparisons to existing data. At first appearance, the dissolution rate data for dolomite of Pokrovsky et al. (1999a), most of which are recovered under relatively high pH (5.4 – 11), cannot be easily related to the overall trends in log rate vs. pH in either Busenberg and Plummer (1982) or Chou et al. (1989), and differ in apparent order. For example, rates measured by Pokrovsky et al. (1999a) in solutions of pH of less than f 8 (and total carbon < 0.001 M) show little change (judging by the apparent experimental uncertainty) with respect to pH. Above pH 8, the large concentrations in total carbon (0.001 – 0.08 M) also complicate comparisons of their rates with earlier studies. In spite of the difficulties in comparing earlier data, Pokrovsky et al. (1999a) argue that their observed rates can be correlated with surface speciation predicted from the complexation model. Three primary hydration sites are invoked for dolomite: > CO3H0, > MgOH0, and > CaOH0. Depending on pH, these sites may also play host to the additional surface spe+ cies > CO 3 Mg + , > CO 3 Ca + , > CO
3 , > MgOH 2 ,
0
+ > MgHCO3, > MgCO3 , > MgO , > CaOH2, CaHCO3,
> CaCO
3 , and > CaO . Pokrovsky et al. (1999a) ascribe the four terms in Busenberg and Plummer’s (1982) rate equation to reactions involving surface species. For example, Pokrovsky et al. (1999a) argue that the increase in dissolution rate at pH < 6 reflects the increasing protonation of > CO
3 surface sites, such that the first term in Eq. (40) becomes

RHþ ¼ kCO3 f> CO3 H0 gn

ð47Þ

Following Van Cappellen et al. (1993), they use the above equation and data from Busenberg and Plummer (1982) and Chou et al. (1989) to compute a second order dependence on > CO3H0 (n = 2), and conclude that this is evidence for protonation of the two surface carbonates adjacent to hydrated Ca and Mg sites prior to cation release. In like manner, they argue that under neutral to high pH conditions, the decrease in the overall rate (attributed to the action of the third term in Eq. (40)) can be understood as the replacement of > CaOH2+ and >MgOH 2+ by less protonated > CaOH0 and > MgOH0 sites (see also Van Cappellen et al., 1993): þ n RH2 O ¼ kMe ðf>CaOHþ 2 and >MgOH2 gÞ

ð48Þ

with order n = 2. They also suggest that the systematic variation of this reaction order in the carbonate minerals (n = 1, 2, and 4, for calcite, dolomite, and magnesite, respectively) indicates the increase in the number of metals adjacent to a carbonate group that require hydration. In addition, Pokrovsky et al. (1999a) sug2
gest that dissolved HCO
will also titrate 3 or CO3 protonated metal sites to produce MeHCO30 and MeCO
3 , and thus act to inhibit dissolution (Busenberg and Plummer’s ‘‘backward’’ reaction). Despite the insight provided by the above models in terms of possible surface reaction mechanisms, a fundamental issue remains in the relationship between the observed reaction rate and the extent to which the total surface participates in this process. In dissolution experiments at pH 3, Lu¨ttge et al. (2002) used vertical scanning interferometry (see above) to measure the development of etch pits on three different cleavage surfaces. They were able to compare the rates of etch pit growth with the dissolution rate of the surrounding (flat) surface. Etch pit rates vary with the cleavage surface on which they develop, with two surfaces both giving rates of 1 10
10 mol cm
2 s
1, and the third producing etch pits that grew at rates up to 10
9 mol cm
2 s
1. However, the rates with respect to etch pits are significantly faster than those measured using the ‘‘whole’’ surface, which gave a mean of 1.08 10
11 mol cm
2 s
1 (see Fig. 15). These rates are also significantly lower than the rate measured by Busenberg and Plummer (1982) at pH 3.0 ( PCO2 f 0) of 2.95 10
10 mol cm
2 s
1 (cf. also

J.W. Morse, R.S. Arvidson / Earth-Science Reviews 58 (2002) 51–84

f 1.5 10 – 10 mol cm
2 s
1 from Chou et al., 1989). These differences are not as yet understood, but point to significant discrepancies between rates normalized to simple estimates of reactive surface area and those measured directly from topographic changes in the mineral surface. 4.4. Magnesite dissolution kinetics Magnesite dissolution rate data are available from Chou et al. (1989) and Pokrovsky and Schott (1999), and show a pattern with respect to pH that is similar to calcite and dolomite. Although the rates for magnesite are exceedingly slow, the two studies compare reasonably well within the pH range of 4– 8. They diverge at pH less than 4, where the data of Pokrovsky and Schott (1999) become invariant with pH. In a manner very similar to the treatment of dolomite described above, Pokrovsky and Schott (1999) construct a general rate equation for magnesite representing contribution of H + - and H2O-promoted dissolution in acid and neutral to alkaline conditions by > CO3H0 and > MgOH2+, respectively: n þ þ Rþ ¼ kCO f> CO3 H0 gm þ kMg f> MgOHþ 2g 3

ð49Þ

They use the overall pattern of rate vs. pH to define four mechanistically distinct regions: an acid region (pH < 2.5) in which rates are invariant with pH; a region between pH 3 and 5 in which rates are proportional to H + activity; a second pH-invariant region between 5 and 8; and an alkaline region (pH > 8) in which rates decline with pH as well as bicarbonate and carbonate concentrations. They further argue that the combination of transition state theory and the surface complexation model permit the calculation of surface precursor complex concentrations in these regions. Under acid conditions, this complex arises through the protonation of four > CO3
sites; as pH increases, this precursor complex is formed through the hydra0 0 tion of four > MgCO
3 , > MgHCO3, or > MgOH + yielding four > MgOH 2 . Pokrovsky and Schott (1999) conclude that the dissolution reaction is thus limited by the rate of cleavage of MgUO bonds, involving either the complete (fourfold) protonation of surface carbonate (at low pH) or complete hydration of surface metal ions at high pH.

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5. Summary and discussion The direct, atomic-scale observations of reacting mineral surfaces made possible by the AFM have brought about a large divergence in focus from previous, solution-oriented work. These observations show etch pit growth and step movements to be highly directional, complex processes. Ultimately, these data must be incorporated within a general understanding of: 1. 2.

3.

how a mineral component detaches from the surface, how this process is mediated by the distribution of surface energy and by species available from bulk solution and how this process affects the surface area available for subsequent reactions, and how the properties of this reacting surface phase differ from those of the bulk solid.

For example, a model recently introduced by Lasaga and Luttge (2001) focuses on the functional relationship between the velocity of migrating steps and the extent of disequilibrium. This model also implies that although local material is clearly lost during etch pit development, the primary role of etch pits in the dissolution process is to serve as a generating source of new steps, whose migration ultimately controls the rate of removal of bulk material. In addition, there is a critical need to link detailed observations made at angstrom to micron scales to the overall dissolution rates measured in the more ‘‘classical’’ experiments reviewed here (e.g., Dove and Platt, 1996; Shiraki et al., 2000), and to the ‘‘natural’’ rates observed in watershed and water column studies. Early work on magnesian calcite focused on its thermodynamic stability as a function of magnesium content. This pattern is complicated by increased solubility and strong surface area control for magnesian calcites of biogenic origin, although there is clear evidence of a general increase in solubility attending an increase in magnesium content for both biogenic and inorganic phases. In addition to increased reactivity, the heterogeneity in microarchitecture and uncertainties in reactive surface area of biogenic magnesian calcites tend to obscure differences in dissolution rate solely as a function of solid composition. These factors make construction of a generalized

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kinetic scheme difficult. Lastly, despite its utility, the representation of magnesian calcite as a phase of fixed stoichiometry results in a rate law in which thermodynamic and kinetic terms are poorly separated. As current work on surface mechanism has been dominated by pure calcite, magnesian calcites have also yet to see any scrutiny from these newer approaches. In contrast to calcite, work on dolomite and magnesite dissolution kinetics is still in its infancy. Most of the experimental work published thus far has been cast in the formalism of Plummer and coworkers, and requires much more attention to the near-equilibrium region. The mechanistic meaning of the observed variation in fractional order with respect to hydrogen ion activity remains unresolved, as do observations concerning the apparent reaction of MgCO3 and CaCO3 as independent components. Approaches that incorporate the surface complexation model of Van Cappellen et al. (1993) appear promising, but the extensive parameterization will require substantially more verification.

Acknowledgements This research was supported in part by a grant from the Department of Energy (DE-FG03-00ER15033; Morse) and the Louis and Elizabeth Scherck Chair endowment (Morse). We would like to dedicate this paper to the memory of Dr. Lennart Sjo¨berg who died in 1996. His outstanding work, in collaboration with Dr. David Rickard, was a major and lasting contribution to our understanding of carbonate dissolution kinetics. We are grateful for the many helpful comments and suggestions on the manuscript by Drs. Gerald M. Friedman, Fred T. Mackenzie and Alfonso Mucci.

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