The role of dislocations and surface morphology in calcite dissolution

The role of dislocations and surface morphology in calcite dissolution IAN N. MACINNISand SUSANL. BRANTLEY &partment of Geosciences, The Pennsylvania State University, University Park, PA 16802, USA (Received March 5, 199 1; accepted in revised form December 1I, I99 1) Abstract-We have measured the dissolution rate for undeformed (p - 10 3 dislocations * cm-* ) calcite ’ in free-drift rotating disk experiments at 1160 t-pm, 25’C and pH 8.6 to be 3.1 X lo-i0 mol.cm-*.sin 0.7 M KC1 solution far from ~uilib~um. The rate increased by a factor of -2.3 for a strained sample (p = 6 X IO* *cmp2). Dissolution rates of calcite far from equilib~um were observed to depend on surface preparation and surface morphology resulting from defects outcropping at the crystal surface, but large rate increases due to surface roughness were not observed. The high dissolution rate for mechanically polished surfaces is attributed to enhanced dissolution at cracks and dislocation loops produced in the grinding process. The initial dissolution rate for cleaved surfaces depends on the surface morphology, but reaches a reproducible steady state value when a constant bimodal size di~~bution of inte~ing pits with time-independent wall slope (B - 3” ) is achieved ( t > 3 h). Steady state is also characterized by a constant ratio of sloped to relatively flat surface. The two populations of etch pits consist of abundant, short-lived, small etch pits (attributed to nucleation at impurity or point defect clusters) and long-lived, larger point-bottomed pits (attributed to dislocations). Consistent with this interpretation, significant di~lu~on at an abundance of nondisl~ation nucleation sites in undefo~~ calcite explains the relatively small increase in dissolution rate for strained samples. Simulation of bulk crystal dissolution based on etch pit growth rates is in reasonable agreement with observed dissolution rates and surface morphology and indicates that discontinuous dissolution at dislocations is necessary to explain the observed steady state surface morphology. Activation energies for pit deepening and widening were measured between 5 and 50°C as 27 f 5 and 37 t 3 kJ * mol-' , respectively. These values are lower than the measured activation energy for bulk di~olution (59 f 12 kJ - mol-’ ).

LIST OF VARIABLES activity of species i in bulk solution unit surface area area which is flat or covered with G2 pits area of inclined regions of surface total geometric surface area critical concentration for spontaneous pit nucleation at dislocations and perfect surface concentrations at the crystal surface, in the bulk solution, and at equilibrium. long-lived, large etch pits (> 100 pm) short-lived, small etch pits ( < 100 pm) overall rate constant constants for dependence of calcite dissolution rate on H+, PCQ, and hydrolysis

% vz x, z, ZF

AG,,

rate constant for calcite precipitation surface and transport rate constants number of moles apparent activation energies for pit opening, deepening, and overall dissolution rate of surface reaction and transport through the boundary layer dissolution rate for inclined and Sat (G2) regions of surface net rate of calcite dissolution net rate of calcite dissolution as surface retreat rate dissolution rate from flat and pointed pits

volume of a pit with basal area Ainc,ind molar volume volume of pointed pit surface retreat rate in areas covered with G2 pits etch pit opening, deepening rate half-width of pit, depth of pointed pit, depth of llat pit free energy of formation of a cylindrical etch pit at a dislocation, and on a perfect crystal surface strain free energy free energy change for creating new surface area in pit free energy change for dissolving a volume of calcite roughness factor relative saturation initial and steady state pit wall dope density of dislocations and point defect clusters initial densities of pointed and flat pits fraction of surface which is inclined INTRODUCI’ION

SURFACEAREAIS A CENTRALvariable to heterogeneous kinetics, but is difficult to quantify when applying experimental di~olution rates to natural systems. For example, modelling weathering mineral grains with irregular St&ace morphology 1113

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Macinnis and S. L. Brantley

or roughness as smooth geometric solids may result in significant errors ( HELGESONet al., 1984; WHITE and PETERSON, 1990). Highly localized dissolution (e.g., etch pits) observed on naturally weathered minerals also suggests that an efiectivesurface area, which accounts for reactive sites, would be more appropriate ( BERNERand HOLDREN,1979; BERNER and SCHOTT,1982); however, quantification of such an effective surface area remains difficult. Thus, it has been proposed that increased densities of reactive sites, such as dislocations, would measurably increase mineral dissolution rates (BERNER, 1978; LASAGA,1983; HELCXSONet al., 1984). Experimentally measured dissolution rates of high and low dislocation density samples have been compared for calcite ( BIANCHETTI and REEDER, 1985; SCHOTT et al., 1989). quartz ( BLUM et al., 1990), feldspar (CYGAN et al., 1989; MURPHY, 1989), chalcopyrite (MURR and HISKEY, 1981). and rutile (CASEY et al., 1988). In each case the rate was unaffected or increased by a small factor (
- k4au+ aHco,_

(11

where ai is the activity of species i in the bulk solution, HICOt is CO1( aq) + J$C03, and k,, kz, k,, and k, are rate constants. The dissolution rate at 25°C is described by the k, term for pH < -4 (Region I ) and is limited primarily by H+ transport through the diffusions boundary layer adjacent to the calcite surface. In Region 2 (4 < pH < 5.5) the rate is also dependent on PCs and is described by the k, and k2 terms. The rate above pH -5.5 is described by kz, k3, and the precipitation rate, k4 (dependent on P,o,), and is independent of pH for CO*-free solutions far from calcite equilibrium. SjSberg and Rickard separated the surface reaction and transport components of the rate based on hydrodynamically constrained dissolution experiments using the rotating disk technique ( WBERG, 1978; RICKARDand SJOBERG,1983; SJOESERG and RICKARD, 1983, 1984). The disk rotation rate determines the boundary layer thickness and hence the degree of transport control ( PLESKOVand ~LINOVSK1, 1976). The rate in regions 2 and 3 is limited by both the transport rate of reaction products across the boundary layer (R7) and the rate

of surface chemical reactions (Kc.) according to RICKARDand SJOBERG (1983): TRANSPORT: CHEMICAL:

RT = kT(Cs - C’h)

(2)

R<. = kc(Co - c;).

(31

Herekr and kc are the transport (diffusion) and chemical rate constants and C,, C,, and C0 are the respective concentrations at the crystal surface, in the bulk solution, and at equilibrium. The net di~olution rate under mixed kinetic control reduces to a form including the relative saturation (Q -= C’JC,), consistent with empirical observations: R = k,( 1 - it”‘)

(4)

where k. is the overall rate constant ( RICKARDand SJOBERG,1983). Equation (4) is empirically equivalent to the combined ks and k4 terms of Eqn. ( I ) for pH above 7 and Pco, c 0.03 atm ( PLUMMER et al.. 1979; RICKARDand SJ~BERG, 1983). Compton and co-workers have recently measured species concentrations at the calcite surface more directly by mounting a strip pH detector immediately adjacent to the calcite crystal in the wall of a flow cell (COMPTON and UNWIN, 1990; COMPTON and PRITCHARD, 1990). COMPTONand UNWIN ( 1990) have determined the reaction at the calcite surface to be first order in H+ at pH < 4. At pH > 7 in COz-free solutions, COMPTONand PRITCHARD( 1990) found the Plummer model to be applicable for the surface reaction, but with rate constants (i.e., k, and k4) dependent on concentrations at the calcite surface. The apparent rate measured in solution depends on the hydrodynamic conditions.

THEORY OF ETCH PIT NUCLEATION AND GROWTH it is convenient to think of mineral dissolution as a series of steps: ( 1) detachment of species from kink sites on ledges, (2) diffusion along and desorption from ledges,(3) diffusion acrossthe flat terraces between ledges,(4) desorption from terraces,and finally (5) diffusion through the hydrodynamic boundary layer to reach the bulk solution ( HIRTHand POUND,1957;ZHANG and NANCOLLAS, 1990). It follows that the dissolution rate should increase with the density of ledges on the surface. One way to increase the ledge density is simply to form pits on the surface, which is limited by the energetics of pit nucleation (CABRERAand LEWNE,1956: HIRTH and POUND, 1957: BENNEMA gnd VAN ENCKEVORT. 1979; BRANTLEY et al., 1986; LASAGA and BLUM, 1986; SCHOTT et al., 1989; SCHOTT, 1990; ZHANG and NANCOLL.AS, 1990). The free energy of formation of a cylindrical etch pit on a fiat, undefo~~ (“perfect”) crystal surface, AC,,, is comprised of two competing terms (see BRANTLEY et al., 1986; SCIHOTTet al., 1989, for details). Pit formation is favored by the driving force for dissolution of the volume of crystal lattice (AC”<,{ac In (fl)), but impeded by the increased surface energy associated with the new surface area of the pit walls ( AG,,,, ) : AG,,‘,,,= AG,,,, + AG,,,fi A

(6)

pit must grow past a critical radius to overcome a free energy barrier, beyond which the volume term dominates the surface term, and the pit grows spontaneously. Far from chemical equiiib~um the free energy barrier should be relatively insignificant ( /In (Q)] very large) compared to available thermal energy, and etch pits will form spontaneously. It follows that closer to equilibrium, past a cnitical concentration (C,,,), the energy barrier would be large enough to prevent spontaneous etch pit nucleation. It must be emphasized also that etch pits on the order of atoms in depth would be expected to nucleate randomly over the entire perfect surface, not to nucleate repeatedly at the same location. Therefore, etch pits deep enough to be observed with the optical microscope would not be expected to form by nucleation on a perfect surface. High energy sites, such as outcropping dislocations, are present on real crystal surfaces. The elastic strain energy stored in the deformed

1115

Kinetics of calcite dissolution lattice around a dislocation core plus the energy of the core will lower the free energy of pit formation at a dislocation outcrop ( AGdrs)by AG,,: AGdrs= AG,,-

AG,,.

(7)

In contrast to pit nucleation on the perfect crystal, in highly undersaturated solutions there is no free energy barrier to pit formation at a dislocation. An energy barrier will appear closer to mineral saturation ( C,,,d > C,,,J , beyond which the nucleation of dislocation etch pits will no longer be spontaneous. The critical concentration below which dislocation etch pits will spontaneously nucleate can be calculated by maximizing AG,, with respect to pit radius (see BRANTLEY et al., 1986). We have calculated Cenr.d= 0.7. Co for calcite at 2S’C using data from f!iCHOlTetal.(1989) and 85 mJ - m-’ interfacial energy (MORSE, 1986). Etch pit nucleation on calcite should be significantly reduced in solutions above 0.7 - C,: all of our experiments were run such that C e Cc,. EXPERIMENTAL Samples for these experiments were prepared from rhombs of clear Shtall calcite ( SEGNITet al., 1962). The natural samples are optical grade and will be referred to as unstrained. Dislocation densities of unstrained samples were measured by counting pits on freshly cleaved faces etched in gently stirred concentrated formic acid for 30 set at room temperature (after KEITH and GILMAN, 1960). One calcite plate was heated at 45O’C for 1 week before etching in formic acid. X-ray topography (TANNER, 1976), well suited for characterizing low dislocation densities (p < 106- cme2), was also applied to the undeformed calcite. Plates 1 mm thick were cut parallel to the (lOi4) cleavage plane (X-ray hexagonal Miller indices; WINCHELL,1956) and washed for a few seconds with 0.1 M HCI to remove surface damage. Lang projection topographs using MO Kol X-rays on ( lOi4) reflections were used. One rhomb, called the strained sample, was cored normal to the cleavage plane and deformed in a Brace-type rig (greatestprinciple stress normal to cleavage, 2 X low3 s-’ steady state strain rate, >lO% strain, 380 MPa peak stress, 23°C) at MIT by Brian Evans. Strained and unstrained samples were also observed under transmission electron microscopy by Rich Reeder (Dept. of Earth and Space Sciences, SUNY at Stony Brook). Two sample preparation methods were used. The first series of experiments used rough calcite surfaces. Calcite plates (~5 mm thick) were cut parallel to the faces of the rhombs and mounted with EPOFIX epoxy in ring molds (5 mm X 25 mm diam.). The exposed surface of the plate was polished with 600-g& (22 pm) alumina grinding powder followed by a 10 set treatment with 0.1 M HCI to remove polishing damage. For one experiment, in order to remove any deeper polishing damage, the ground surface was pre-etched in lo-’ M HCl as a rotating disk (see below) at 1160 rpm for 20 min. The second preparation method consisted of mounting cleaved plates in ring molds without polishing or acid treatment. Samples were. precleaned with Optima grade acetone in a sonic bath. The surface of the mount was then coated with a thin layer of acrylic paint such that only a circle of calcite was exposed at the center of the mount, preventing dissolution at the edges of the sample and providing a measurable surface area (similar to the technique of CoMproN and DALY, 1984). Up to ten locations on the surface of the mounted calcite sample were photographed under the reflected-light microscope before each experiment. Photographs ofthese locations were taken at subsequent stages in the experiment in order to record surface morphology changes during dissolution. Etch pit dimensions were measured from reflected-light photomicrographs taken with differential interference contrast (DIC) (for width), and Mirau double-beam interference (for depth) objectives. The Mirau photos were taken with monochromatic light (wavelength = 540 nm) , where adjacent fringes correspond to changes in surface elevation of 270 nm (% wavelength, ROCHOWand ROCHOW,1979), allowing surface slopes up to 15” to be measured. Total pit depths relative to the original acrylic-painted surface were measured with the mechanical microscope stage. All experiments were carried out in 0.7 M KC1 solutions prepared from Puratronic and Ultrapure grade KC1 crystals and degassed

deionized distilled water adjusted to pH 8.6 f 0.05 with KOH solution. A Cot-free atmosphere was maintained by bubbling prepurified N2 through 0.3 M NaOH and deionized water. This gas was bubbled through the KC1 solution before the experiment and while the experiment was stopped for photography. During the experiment the gas was simply passed above the solution so as not to disturb the RD hydrodynamics. The prepared calcite disk was placed in a Teflon holder attached to the Teflon-coated shaft of a variable speed stirrer motor. The dissolution experiments were carried out with 300 mL of starting solution in a 500 mL 3-neck flask held in a constant temperature bath ( 20.1 “C) . Runs were carried out in the temperature range 5-50°C. The solution was kept stirred with a submersible magnetic stirrer until the start of each experiment. At the beginning of each run the rotating disk assembly was lowered into the solution and rotated at 1160 + 20 rpm. This fast rotation speed was chosen to lie within a regime of minimized transport control in the dissolution rate. Runs longer than -20 h were achieved in a series of shorter experiments, each starting with fresh solution, such that dissolution rates were measured far from equilibrium. The amount of calcite dissolution was determined from pH changes measured with an Orion Ross combination pH electrode. The electrode was standardized with pH 7 and 10 buffets (0.05 M) in the same water bath before and after each experiment. Liquid junction potential corrections were made by also standardizing electrodes in strong base solutions made up to 0.7 M KCl. Typical electrode drift was less than 0.03 pH units over the course of an experiment, which lasted up to 1 day including photography stops. Readings were taken every 2 min and all drift error was corrected. Recorded pH values were converted to concentrations of released Ca2+ using the freedrift equations and 0.7 M ionic strength values for pK, and pK2 of SJ~BERG( 1978). Calculated final Ca concentrations were within 15% of DCP analyses of the final solutions. Instantaneous dissolution rates were calculated by least squares linear regression of [ Ca2+] vs. time over 10 to 20 min intervals. Reported dissolution rates are normalized to the surface area of calcite exposed to the solution, as determined by digitizing on a photograph of the disk. RESULTS The formic acid etching revealed deep, point-bottomed etch pits (type GI described later) irregularly distributed

against a background of more abundant, shallow, indistinct pits (type G2). Only the GI pits showed a one-to-one correspondence across opposing cleavage faces. The background G2 pits were absent on the sample heated at 450°C. The dislocation density ( pd) of the unstrained calcite is estimated at 103*0,’ . cmm2basedon the deep, point-bottomed pits; higher densities of pits near cleavage steps were excluded (see Dis-

cussion section). The X-ray topography also revealed a low pd (600 - cmm2) and growth banding up to mm in scale in the undeformed sample (Fig. 1a). The dislocations in the unstrained sample were straight or slightly curved over distances up to at least 1 mm, but examples of direction changes, or bends, and multiple dislocations diverging, or branching, from a single point were also observed with X-ray topography. The dislocation density of the unstrained sample was below the limit for determination by TEM, 10 6 - cmV2 (Fig. 1b) . TEM analysis of the strained sample (Fig. lc) revealed a uniformly distributed dislocation density of 6 X 10’ *cmm2, and a high density of dislocation loops (2 X 10 I5- cme3), characteristic of deformation by dislocation glide (Rich Reeder, pets. commun.) . For all samples except the cleaved strained crystal, the dissolution rate for initially rough calcite samples is initially transient and then approaches a steady value (Fig. 2). Table 1 lists dissolution rates averaged over the steady state period,

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1. N. Maclnnis and S. L. Brantley

FIG. 1. X-ray topography and TEM images. (a) The X-ray topograph for the unstrained sample shows growth bands, but the dislocations are not clearly shown at this scale. (b) The TEM image of the unstrained sample shows no dislocations. The dark lines are Bragg contours and the dark spots are an artifact of the carbon coating procedure. (c) The TEM image of the strained sample shows a uniform distribution of dislocations (6 X lOa. cm-*) and a high density of dislocation loops (2 X 10 I5 *cm-‘). TEM images courtesy of Rich Reeder.

+ 1 standard deviation, and the saturation state at the end of the run. There is no statistical difference between the average steady state rate of the unstrained and strained samples with rough surfaces (9.5 + 2.3. lo-” and 9.8 + 2.0. lo-” mol.cm-*.s-‘, respectively). The rate for the unstrained rough sample pretreated for 20 min in 10e3 M HCl (Fig. 2) was significantly slower (2.9 + 0.2 - lo-” mole cm-’ - SC’). This is similar to the steady state dissolution rate of 3.1 + 0.4 X lo-” mol -cm-’ - SC’ for the cleaved unstrained sample (Fig. 3 ) . Early transient rates for cleaved, unstrained samples were always low (-1.2 * 0.2 X lo-” mol.cm-*es-‘) in runs without photography stops. The initial rate for the cleaved, strained sample was -7.1 X lo-” mol. cm-*. SC’, but increased throughout the run. The dissolution rate for the cleaved strained sample is comparable to the rough strained samples. Note that in a small number of experiments, including both 50°C runs, an unidentified amorphous precipitate appeared on the dissolving surface. Dissolution of the calcite samples produced a circular area covered with etch pits (Fig. 4). A steep step, marked (a) on Fig. 4, separates the dissolved region from the original surface, exposed by removing the acrylic coating. Large steps within

t /h Flc. 2. Trends in instantaneous dissolution rates with time at 25°C for initially rough surfaces of strained and unstrained calcite, prepared by 6OO-gritgrinding. Run names are indicated in the legend (0, A, UR = unstrained rough; 0, A, SR = strained rough). A run for a rough surface prepared by pre-etching a cleaved surface for 20 min in lo-’ M HCl (X, URE25- 1) is included for comparison. Horizontal lines show the region over which the steady state rate was calculated. Steady state rates, including two shorter runs, are given in Table 1.

Kinetics of calcite dissolution

1117

TABLE 1

the dissolved area, marked (c) on Fig. 4, correspond to cleavage steps on the original surface. The orientation of the rhombohedral etch pits reflects the calcite structure. The pits are clearly eccentric, with tips skewed relative to the geometric center of their outlines (Fig. 4). Pit walls have a shallow slope with respect to the original surface ( < 10” ) , with 2 shallow and 2 steep walls (steep/shallow slope ratio < 2.5), reflecting the eccentricity. The pits divide into two groups: long-lived, large pits which are visible to the naked eye (GI pits, (d) and (e) on Fig. 4), and short-lived, smaller pits (G2, < - 100 pm on Fig. 4). Within these groups some pits are pointed, with the shape of inverted rhombohedral pyramids, reflecting the symmetry of calcite. The tips of some Gl pointed pits consist of several closely spaced, intersecting pits. Other pits are flat-bottomed, truncated pyramids. Terraced pits are flat Gl pits with G2, or even GI, pits inside ((e) on Fig. 4). Our photographs reveal individual GI terraced pits which have developed from earlier GI pointed pits. Some GI terraced pits also resulted

FIG. 3. Trends in instantaneous dissolution rates with time at 25°C for cleaved surfaces of strained (A, SC) and unstrained (0, A, UC) calcite. The pre-etched ( IO-’ M HCI) cleaved run (X, URE) is included for comparison. Horizontal lines show the region over which the steady state rate was calculated. Steady state rates are given in Table 1.

FIG. 4. Large-scale DIC photomicrograph showing representative morphological features on a cleaved unstrained calcite surface after 23 h dissolution at 5°C. (a) Step between dissolved and undissolved surface after removal of the acrylic coating; (b) cleavage step on original surface and (c) corresponding step after dissolution; (d) eccentric GI (large) pointed pit; (e) GI terraced pit containing small G2 pits; (f) twin boundary. The inset shows the definition of x.

when the tips of pointed pits were accidentally filled with acrylic when the coating was re-applied between stages of longer runs. A schematic profile showing the pit morphologies is summarized in Fig. Sa. Surfaces of cleaved-unstrained samples, rough-unstrained (600~grit, 10 set acid wash), and cleaved-strained samples after 0 and 3 h dissolution at 25°C are compared in Fig. 6. The cleaved-unstrained surface ( Fig. 6a), marked initially by only a few cleavage steps, is covered by etch pits after 3 h. Arrays of pits also follow larger cleavage steps on the initial surface. The rough surface (Fig. 6b) has also been replaced with etch pits after only 3 h, with higher densities of deep pits at the sites of scratches or cracks on the initial surface. Pits are smaller, less regularly shaped and more densely distributed on this sample as compared to the cleaved-unstrained sample. The pits on the strained sample (Fig. 6c) are smaller than the unstrained samples and have not intersected after 3 h. These pits are asymmetric ( 2 .straight walls and 2 curved walls); flat and terraced pits are absent. Linear arrays of pits follow cleavage cracks observed on the initial surface, and grow to cover most of the surface by 10 h. Areas between these arrays have pit densities of at least lo6 *cm-‘. The surface between these pits appears to be very finely pitted (at the resolving limit of our photos), unlike the flat areas between pits on the unstrained samples. The remainder of this section deals with the unstrained calcite in more detail. Pit growth and the evolution of surface morphology is shown on photomicrographs of an area of the same cleaved surface taken at intervals in run UC25-1 (Fig. 7). Some cleavage steps are present on the starting surface. Etch pits,

I. N. Maclnnis and S. L. Brantley

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FIG. 5. (a) Schematic profile of representative morphology features. I, original crystal surface; 2, acrylic coating; 3, Cl pointed pit; 4, GI terraced pit; 5, G2 pointed pit; 6, G2 flat pit; 7. lip between original surface and current surface in areas free of Cl pits, resulting from intersecting G2 pits, used to calculate the background dissolution rate, ub. Postulated origins for Cl pit types are shown: pointed pits follow straight dislocations; deeper terraced pits follow bent or branching dislocations; shallower GI terraced pits result from dislocation loops, possibly related to cleaving damage. (b) Protiles at the same location on a cleaved unstrained surface after 0,0.5, 1.5, 3, 11. and 17.5 h dissolution time at 25°C (absolute depth between profiles is unknown), with calculated roughness factors R annotated. (c-e) Etch pit simulation of profiles after 0.5, I .5, 3, 11, 17.5, and 40 h dissolution for the unstrained sample, V, = 54 X IO-‘” m -SC’, u, = 2.7 X lo-” m.s-‘: (c) continuous dissolution at dislocations only, Ed = 103.cm-2, and oh = 5 X lo-” m es-‘; (d) point defect clusters included, pc = 10’ *cm-‘; (e) dissolution at dislocations is discontinuous. ( f) Calculated dissolution rates from the simulations.

mostly flat bottomed, are present after only 30 min. Linear arrays of closely intergrown pointed pits which appear to originate at cleavage steps on the starting surface contrast with the random distribution of pits on the flat areas between steps. At 3 h the early pits have all intersected and a new generation of smaller G2 pits has nucleated, beginning the development of a bimodal pit size distribution. After 3 h the surface is fully covered with pits, with little flat surface remaining. At 11 h, the bimodal pit size distribution (Gl vs.

G2) is evident. Many of the terraced Gi pits follow the cleavage steps on the original surface. The GI pits have almost intersected by 17.5 h; therefore, at this time the G2 pits are mainly located within GI terraced pits. However, intersection ofthe GI pointed pits did not occur even after 43 h dissolution at 25°C. The total etch pit density at 30 min (exclusive of pits at cleavage steps and twins) and the G2 pit density at 17.5 h are similar, on the order of lo5 -cm-‘, but significantly higher

Kinetics of calcite dissolution

1119

FIG. 6. DIC photomicrographs after 0 and 3 h dissolution at 25°C for (a) cleaved unstrained, (b) rough unstrained (arrow points to deeper etching at the site of a scratch on the original surface), and (c) cleaved strained surfaces.

than the estimated dislocation density, - 10 3 - cm-*. Only about 10% of the pits are pointed at 30 min. GI pit densities at 43 h are at least 250.cm-*, a very qualitative estimate considering that the pits are intersecting. Changes in surface morphology with time are further illustrated by profiles constructed from pairs of interference and reflected-light photos (Fig. 5b). Features of the original cleavage surface, such as small steps, dissolved away in 3 h. After this time the surface appears relatively smooth (but not flat). G2 pits are not clearly seen at the scale of Fig. Sb, reflecting the bimodal size distribution. The series of profiles also shows a pair of early pointed pits at a cleavage step developing into a GI terraced pit. Steep and shallow GI pit wall slopes were determined from interlerograms and show similar trends with time (Fig. 8). Higher initial slopes decrease to a steady value after only a few hours of dissolution (shallow -2.2” + 0.4, steep -4.7” f 0.6). Cleavage steps, which were initially near vertical, also become incised with steep and shallow segments after dissolution to give a slope of -3’, similar to the average of steep and shallow pit walls (see Fig. 4). Pit width and depth measured from photos of a 25°C cleaved, unstrained run (UC251 ) are plotted against time in Fig. 9. The average size of G2 pits remains relatively constant, while GI depth (terraced pits excluded) and width show

a linear increase with time, reflecting the bimodal size distribution. DISCUSSION Defect Densities and Etch Pit Growth The correlation between individual etch pits and dislocations has been shown for many materials ( SANGWAL,1987), including calcite (KEITH and GILMAN, 1960; PATEL and GOSWAMI, 1962; THOMASand RENSHAW,1965). However, these studies have not demonstrated that all etch pits are associated with dislocations or that all dislocations will produce etch pits. The correspondence of the pointed GI pits on opposing cleavage faces of the unstrained calcite etched in formic acid is expected for dislocations passing through the crystal. Growth of the pointed GI pits in our rotating disk dissolution experiments required repeated nucleation at the same location on the surface over long time periods, also suggesting growth at dislocations. The higher density of Gl pits at large cleavage steps suggests that some dislocation loops near the surface result from cleaving damage (HARI BABU and BANSIGIR, 1969; LEFAUCHEUXand ROBERT, 1977): for this reason, these pits were not included in the pd estimate ( lo3 - cm-*) for the bulk unstrained crystal. The low ( 103. cmm2) dislo-

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1120

FIG. 7. DIC photomicrographs showing successive dissolution of the same area of a cleaved surface of unstrained calcite at 25°C (run UC25-I): (a) 0; (b) 0.5; (c) 1.5; (d) 3; (e) 1 I: and (f) 17.5 h total dissolution time.

cation density estimated from etching is in agreement with the direct imaging by X-ray topography. Other studies of undeformed calcites report pd of - 10’ -cm-’ derived from etching (THOMAS and RENSHAW, 1965; COMPTON and UNWIN, 1990), and lo-103. cm-’ from X-ray topography ( ZARKA, 1972). Although dislocation estimates by these methods may be too low, more definitive methods for low dislocation densities are not available. The TEM observations only indicate that &j < lo6 - cm-’ for the unstrained calcite.

t

/h

FIG. 8. Slopes for the walls of GZ pits plotted with respect to dissolution time for cleaved unstrained samples at 25°C. Eccentricity of the pits results in 2 steep (A) and 2 shallow (0) sides.

The differential interference contrast photos give the impression that the pits in our dissolution experiments are very steep walled, but wall slopes measured from interference fringes are below - lo”, comparable with surveys of pits in calcite and a variety of materials (IVES and MCAUSLAND, 1968). The pit wall slopes of calcite do not correspond to low-index facets, possibly due to the rapid dissolution rate. The similar slopes of dissolved cleavage steps and the etch pits suggests that pit wall slopes away from the dislocation core are not directly controlled by the dislocations. The eccentricity in calcite etch pit profiles has been attributed to the angle of intersection of dislocations with the surface ( MEHTA and THUMAR, 1986). In our case, it is more reasonable that eccentricity results from the variation in dissolution rates with direction on the surface since dissolved cleavage steps were also eccentric. This is supported by studies of calcite growth hillocks ( PAQUETTE and REEDER, 1990), and the effect of carboxylic acids on pit walls ( COMPTON et al., 1989; BARWISE et al., 1990). The size and wall slope of the terraced and flat GI pits suggest that they result from pointed pits which have ceased dissolving normal to the crystal surface but have continued to dissolve laterally (Fig. 5). This was illustrated by changes in one pointed pit in which acrylic coated the tip: the uncoated walls continued to grow outward while growth normal to the surface ceased. Growth of new pits on the flat base of this pit

Kinetics of calcite dissolution

FIG. 9. Pit (a) width and (b) depth with respect to dissolution time for cleaved unstrained calcite at 25°C. Gl pits = 0, G2 pits = A. Symbol without error bar indicates that only one pit was measured.

resulted in a terraced GI pit. Acrylic paint does not explain why other GI pointed pits stopped growing deeper and became flat bottomed. It is possible that the high-energy site (dislocation) which caused the GI pit to grow deeper has changed. It has been proposed that terraced pits result from jogs or branchings ( JOSHI et al., 1978) or discontinuous impurity segregations ( GILMAN, 1960) along dislocations. Bent and branching dislocations or some effect of the growth banding are the most probable sources for terraced Cl pits in view of our X-ray topography observations. In addition, dislocation loops or microcracks induced by cleaving are possible causes for arrays of GI terraced pits following cleavage steps (Fig. 7d). The linear increase in GI pointed pit depth, and GI pointed and terraced pit width (Fig. 9) indicates a constant growth rate. This is actually an apparent growth rate since the tops of the pits are being removed due to intersection with other pits. Assuming that this intersection rate is also constant with time, the pit deepening rate (u,) has been determined from the total pit depth relative to the undissolved surface at any time. The actual pit opening rate (u,, from half-width) has been calculated from the width/depth ratio measured on interferograms and the total pit depth. The agreement between deepening rates from experiments of differing duration at the same temperature support the intersection rate assumption (Table 2). The large error bars for V, reflect the uncertainty in extrapolating pit wall slopes back to the original surface. The small size and high density of the G2 pits might suggest formation by spontaneous nucleation of unit-depth pits on perfect calcite surface. in the highly undersaturated solutions (see Introduction section). Such pits would not be expected to continue growing to resolvable depths, however, and could not explain the growth of G2 pits to microscopically visible

1121

sizes. Prolonged heating of a cleaved surface at 450°C also appears to eliminate the sites for G2 pit growth in formic acid. THOMAS and RENSHAW( 1965) attributed the disappearance of background pits in heated samples to the annihilation of point defect clusters (cation and anion vacancies) at the surface and in the bulk crystal, since the density of small pits decreased even for surfaces cleaved from a crystal after heating. The growth of G2 etch pits to 1 pm in depth suggests defect clusters rather than atomic-scale point defects. A cluster density of > lo6 - cm-* was estimated for undeformed calcite samples by THOMASand RENSHAW( 1965), an order of magnitude higher than our estimate of G2 pit density. A variable density of defect or impurity clusters was probably incorporated into the unstrained calcite during growth; the strain field around these sites would locally alter the diffraction condition in X-ray topography (ZARKA, 1972)) explaining the growth bands (Fig. 1a). Nucleation at defect clusters explains the high density, small size, and development of flat-bottomed G2 pits. Annihilation of individual G2 flat pits by intersection with other etch pits results in constant average G2 pit dimensions (Fig. 9). The background dissolution rate due to growth and intersection of G2 pits (ub, reported in Table 2) was calculated based on the height of the step between the dissolved and original surface in areas free of large (Cl)pits (Fig. 5a). The dislocation density of the strained sample (6 X lo8 - cm-*) is orders of magnitude higher than the unstrained calcite, but is not unusually high compared to naturally deformed samples (e.g., 40 X 10’ - cm-* in BRIEGEL and GOETZE, 1978). The lo6 -cm-* pit density suggests that all dislocations in the strained sample do not produce etch pits. However, the maximum width for pits with a uniform distribution of 6 X 10’ -cm-* would be 0.4 pm, the lower resolution limit of our photomicrographs. The finely pitted surface between the etch pits on the cleaved strained sample possibly reflects this dislocation density, or the high density of dislocation loops. Dissolution Rates Initial transient rates were found to be higher than steady state rates in cleaved runs where the sample was removed for photography at frequent intervals due to introduction of atmospheric COz. Similar problems at the beginning of rotating disk experiments were reported by RKKARD and SJ~BERG( 1983 ) . In runs without photography stops the rate started at a low value and gradually increased to reach steady state. The cleaved strained run was terminated before reaching

TABLE 2

1122

I. N. Maclnnis and S. L. Brantley

steady state in order to prevent the disintegration of the sample by the localized dissolution at microcracks and twin boundaries (Fig. 6). We used the initial rate in this run since the subsequent rate increase probably reflects the increased surface area, rather than the bulk strained sample. The measured rates listed in Table 1 correspond to k3 in Eqn. ( 1) since the system remained far from equilibrium (0 < 0.05 ) , COz-free, and in pH region 3. The starting solutions were totally undersaturated, and in the runs the dissolution rate showed no dependence on the saturation state according to relations such as Eqn. (4). The dissolution rates indicate that the system was under mainly surface reaction control; the rate limit calculated for pure transport control in a similar system was -16 X lo-” mol.cm-‘-s-l (see Fig. 3 Of SJOBERG and RICKARD, 1983). Our average rough surface rates are within error of the values for rough surfaces from SJOBERGand RICKARD( 1984; 7 X lo-” mol.cm-**s-l at 1160 rpm, 0.7 M KCl). The scatter in our rates suggests that our grinding technique was less reproducible, possibly due to deviations from the cleavage plane. Steady state rates for our cleaved, unstrained runs are slightly higher than literature values for dissolution far from equilibrium. The range in solutions and experimental techniques used by other researchers in part explains the discrepancy. PLUMMER et al. ( 1978) measured a rate of 1.2 X lo-” mol. cm-2 - s-’ for stirred calcite powder suspensions in deionized water, while a rate constant of 0.65 X IO-” was measured for powders in fluidized bed mol-cm-2.s-’ experiments by CHOU et al. ( 1989 ). COMPTONet al. ( 1986 ) extrapolated the trend in rates for samples polished with successively finer grits, as measured in rotating disk experiments, to estimate the initial rate for a perfectly polished calcite surface in 0.3 M KC1 at 1.4 X lO-‘o mol. cm-2 - SC’. COMPTON et al. ( 1986) found that the rate increased as the surface dissolved and roughened. Using the flow cell technique, COMPTON and PRITCHARD( 1990) determined the rate constant for dissolution at the crystal surface in 0.5 M KC1 to be a maximum of 0.95 X lo-” mol-cm~2*s-‘. Our observed rate increase of -2.3 times for strained over undeformed cleaved samples, although not well constrained, is comparable to observations by SCHOTTet al. ( 1989) in rotating cylinder experiments using strained samples free of microcracks (J. Schott, pers. commun.). Effect of temperature Dissolution rates for experiments between -5 and 50°C are displayed as surface retreat rates (&,,) in Arrhenius plots in Fig. 10. The plot is linear up to 40°C with an apparent activation energy of 59 -t 12 kJ - mol-’ , comparable to 53 k.I. mol- ’ calculated for data measured under similar conditions by SJ~BERG and RICKARD ( 1984). These high Arrhenius activation energies also suggest considerable surface control of the dissolution. Anomalously low rates were measured at 5O”C, and are probably related to the unidentified amorphous precipitates found on the surface after these runs. Surface coatings in occasional dissolution runs have also been observed by some other workers (D. Rickard, pers. commun.).

Temperature

3.1

/“C

3.2 3.3 3.4 3.5 1000 T-’ /K-l

3.6

FIG. 10. Arrhenius plots with apparent activation energies for pit opening ( 0, (2) and deepening (A, a). The plot for overall dissolution rate (mms-‘) is included for comparison, but the 50°C rates are excluded from the calculated Qd,$(0) due to the formation of a precipitate on the surface (arrow indicates that the rate is probably higher).

The Arrhenius plots for pit opening and deepening rates are linear even though the Arrhenius plot for bulk dissolution is non-linear above 40°C (Fig. 10). This suggests that the precipitates observed at 50°C do not interfere with pit growth. The apparent activation energy is larger for pit opening (a = 36.5 + 3.1 kJ - mol-’ ) than pit deepening ( Qz = 27.2 + 4.5 kJ - mol -’ ) , as expected since deepening an etch pit at a dislocation releases strain energy. SHAH and PANDYA ( 1985) report the apparent activation energy for pit deepening in calcite to depend on the etching solution, varying from 2 kJ - mol-’ in 2.5 X 10e2 M HCI, to 66.5 kJ - mol-’ in >4.8 M NaOH solution, possibly reflecting the diffusion and surface controlled regimes. Surface complexation reactions might explain the QI = 95 kJ - mol-’ in lactic acid solutions (co.1 11 M and <4O”C). More detailed measurements in this area are needed. Lower Qx and QZ values than Qdis suggest that etch pit deepening and opening are not the rate-limiting steps in calcite dissolution under our experiment conditions. The steady state dissolution rate is significantly lower than the pit deepening rate (v,) below 40°C. The total dissolution rate includes growth of GI etch pits and the background dissolution rate (Us) due to growth and intersection of G2 pits. Difficulty in measuring the background retreat rate as a function of temperature prevented the calculation of the overall activation energy of the dissolution reaction. Effect of surface preparation The enhanced dissolution rate for the 600-g& rough surfaces compared to cleaved surfaces must be due to ( 1) surface irregularity (roughness ) and/or ( 2 ) surface damage.

1123

Kinetics of calcite dissolution A quantitative measure of surface roughness is the factor h ( HELGESONet al., 1984; WHITE and PETERSON,1990): X=

real surface area ; ( geometric surface area 1

(8)

or for the case of our linear profiles in Fig. 5: x =

length of profile tracing * profile width I I

(9)

Any surface has a real surface area = X X geometric surface area, where X - 1 for a cleaved surface and X > 1 for a rough surface. In our experiments, the rough surface should dissolve X times faster than the cleaved surface since our rates are normalized to geometric surface area. However, the observed rate remained high even though the rough surface is dissolved away in only 3 h (Fig. 6b). In the case of the cleaved surface, we might expect the roughness to increase with the growth of etch pits. The calculated h for the profiles in Fig. 5b (annotated on the plot, includes G2 pits) increases early in the run but returns to the initial value after 3 h. The maximum value for the roughness factor is small due to the shallow nature of the pits, causing a secondary intluence on the dissolution rate. Changes in surface roughness cannot, therefore, explain differences in our observed dissolution rates. It has been argued for some time that grinding of materials produces changes such as phase transformations ( JAMIESON and GOLDSMITH, 1960; DANDURANDet al., 1982) and mechanical deformation (BUCK, 1960). Enhanced dissolution rates in dry-ground calcite powders have been related to high dislocation densities observed near grain surfaces (FERRET et al., 1987). SANGWALand ARORA (1979) found that mechanical polishing of MgO plates produced a deformed surface layer consisting of microcracks and dislocation loops to depths of -200 pm, explaining a dissolution rate increase (<2X) in polished samples. Concentrations of etch pits are seen at cracks resulting from scratches in our 600-g& experiments (Fig. 6b), but high dissolution rates persist even after the cracks dissolve away. Increased dissolution rates would be expected if the ground surfaces were not parallel to the cleavage plane (COMFTONet al., 1986), but should have remained high after deep etching with 10e3 M HCl. This leaves dissolution at grinding-induced dislocations or microscopic cracks as the cause for high rates with the 600-g& surfaces. The similar rates for ground strained and unstrained samples suggest a highly deformed surface layer, similar to the lattice of the strained sample. Removal of a deformed layer could explain why deep etching of the rough surface with 10e3 M HCl yielded a dissolution rate comparable to a cleaved surface (Table 1). Simulations of Dissolution Based on Surface Morphology Evolution We observed low initial dissolution rates in experiments which were not exposed to the atmosphere due to frequent photography stops. The lower initial rate before the surface becomes “fully reactive” has also been observed by COMFTON et al. ( 1986) and COMPTONand UNWIN ( 1990). In this early

period a considerable portion of the surface is still flat. At -3 h the surface is covered with intersecting pits, leaving a minimal amount of flat surface. At this time the bimodal size distribution is established and the dissolution rate reaches steady state. Once steady state is reached, there is little change in the appearance of the surface. The steady state surface morphology is characterized by the following constant features: ( 1) constant bimodal pit distribution, (2) constant ratio of flat to inclined surface (Cl pit walls and cleavage traces), and (3) constant slope of inclined surfaces. According to terrace-kink-ledge models, the dissolution rate is proportional to the total ledge length or density on the surface (HIRTH and POUND, 1957). This is supported for calcite by the observation that dissolution rate increases for surfaces cut at increasing angles to the cleavage face, exposing a higher density of ledges to the solution (COMPTON et al., 1986 ) . If dissolution rates are proportional to ledge density, steady state rates will only be observed for constant ledge density. In our experiments, the ledge density must be low early in the runs, and as pits nucleate and grow on the surface, ledge density must increase. Attainment of steady state dissolution kinetics implies ledge creation and annihilation also reaches steady state. The observed steady state pit size distribution and pit slope suggests that the ledge density on the surface is constant over the steady state dissolution period. A semi-quantitative relation between the ledge density resulting from changes in surface morphology and the evaporation rate has been carried out for arsenic by DOWELLet al. ( 1977). We use their approach to tally the contribution of morphological elements to the overall dissolution rate. Initial rate

We estimate the initial dissolution rate after 30 min dissolution at 25°C based on the initial density of pointed (pb - lo4 - cm-*) and flat (pk - lo5 - cm-‘) pits. Approximating the pointed pits as square right pyramids of width 2x and depth z (volume I’d) with velocities of u, for opening and u, for deepening (Table 2), the rate of volume change ( dVi/dt) for a single pointed pit can be calculated: (10) dV$ 4 = 5 (2zxu, dt

(11)

+ x%,).

By normalizing to moles ( n ) per unit area (A ) , we calculate the contribution to the dissolution rate from pointed pit growth (RL) in’moles~cm-2-s-‘:

(12) Similarly, flat pits are treated as truncated square pyramids of depth zF and wall slope 8’ averaged from the steep and shallow walls (Fig. 8) to calculate the contribution of flat pits to the dissolution rate ( R&): vb=

4(3z&

3zgx/tan

8’ + zg/tan’

0’)

(13)

I. N. Machnis and S. L. Brantley

1124 dV$ = 4v,( 2z,x - z$/tan dt

_

dvb dt

0’)

(14)

-I

-Ph*vln.

(15)

With our measured values at 30 min (x = 12.6 pm, v, = 54 X IO-” m-s-‘, z = 0.8 pm, v, = 2.7 X lo-” rn.s-‘, zF = 0.3 pm, 8’ = 8.9’) we calculate Rd = 0.24 X lo-” 10-‘0mol~cm-2~s-‘togive mol*cm-2-s-’ andRk=2.2X the total initial dissolution rate RI, = 2.4 X lo-” ‘. Our measured initial rate ( - 1.1 X lo-” mol-cm-2.smol. cmm2.s-‘) falls within the limits of this calculation considering that the error in p& alone is - +0.2 log units. Steady state rate

The rate calculation at steady state is based on the constant bimodal size distribution and pit wall slope at 2Y’C. The surface area can be divided into predominantly flat areas covered with G2 pits (AJ~,) and steep areas comprised of the walls of Gl pits and cleavage steps (Aimlined). We define the fraction of steep area, F ( = Ainc/lned/Alor,A,,, = total surface area). The steep-walled area is calculated as one large pyramidal etch pit whose base has the area Ainclined(=cA,,,) with average wall slope 6” ( from Fig. 8 ) . Noting that tan 8” = z/ x, we can write the following expression for the volume of one pointed etch pit at steady state ( V $&ed) and its growth rate ( d V $,lined/ dt ) : 4

4

V”,nc/,md

=

-

3

zx

2 = j tan esyx3

(16)

&I””

Inclmd dt

= 4 tan Psx2vX = Ainclinedtan Pv,.

The contribution rate ( R $c/in&) is RF

of the steep-walled area to the dissolution

dnl& rnclrned

(17)

= (

”

dt

1 mclined

Equation 18 reduces to a linear retreat rate of v,& as expected for intersecting pointed pits. The contribution from the areas covered by small G2 pits ( Rjfo,) is calculated from the background surface retreat rate (vb, Table 2):

= W&( 1 - t) = vb( 1 - 8 A/I,, J’m

(

19j

VT?l

or a linear surface retreat rate of vb( 1 - [). This background surface retreat rate represents dissolution at point defects and perfect surface (all surface not affected by growth of GI pit walls). For the following measured values (with t = 0.52 at 43 h total dissolution, vb = 0.5 X lo-” m-s-‘, 8” = 3.2”) we rncl,ned = 4.25 X lo-” mol. cmm2- s-’ and Rza, = calculate RSs

0.65 X lo-” mol -cm-’ - s-’ and the total steady state dissolutionrate(RF,)=4.9X 10-‘0mol~cm-2~s-‘.Thisrate is about 50% higher than our measured steady state rate. With a conservative 10% error estimate in this calculation, the measured rate lies within two standard deviations of our calculated rate. According to this calculation, 85% of the total dissolution occurs at inclined (high ledge density) surface at 25°C. What Controls Steady State? A simple numerical simulation incorporating our etch pit growth data was used to produce cross-sectional surface profiles and dissolution rates for comparison with our observations (Fig. 5 ). The pit eccentricity and slope variation were ignored for simplicity. The simulation uses our measured pit growth rates for v, and v, (Table 2). “Dislocations” were oriented normal to the surface and equally distributed (pd = 10’ - cme2) along the profile. In Fig. 5c, flat surface with no dislocations recedes at vb, but the pointed dislocation pits (GI) eventually intersect to produce a “sawtooth” profile. The calculated dissolution rate (Fig. 5f) increases linearly until the GI pointed pits intersect, when a steady state rate of 7.3 X lo-lo mol. cme2 - s-’ begins. This rate is -2.4 times our observed steady state rate and is comparable to our strained sample initial rate, or our rough surface rates. Changing the dislocation density in the simulation changes the initial transient rate, but does not affect the steady state rate since it is only defined by v,. G2 pits were incorporated into the calculation (Fig. 5d) by approximating point defect clusters as surface normal zones of fast dissolution (0.5 pm long, separated by 0.05 pm, randomly started at the surface) and equally spaced (pc = 10 ’ - cm-2) between the dislocations. Pointed pits grow at these defects at the surface, becoming flat at the end of the segments, producing a rate of recession comparable to vb in the areas between dislocations. However, the sawtooth profile is still produced, with little change in the dissolution rate curve (Fig. 5f). The only way to produce a steady state surface characterized by a constant bimodal pit distribution and constant 6 is to introduce some characteristic that causes pit nucleation at dislocations to turn on and off. Dislocations which contain discontinuous impurities, bends or branchings could cause discontinuous dissolution, and these are simulated in Fig. 5e by 5 pm dislocation segments separated by 5 pm along the dislocation line. This results in terraced GI pits and never produces a sawtooth pattern. The dissolution rate reaches a lower steady state value than the “sawtooth” rate after a shorter transient period. This rate is comparable to our measured steady state rate. An increase in the density of discontinuously dissolving dislocations will increase .$,and as a result, the steady state rate, but only up to the limit for the sawtooth profile. The inclusion of point defects and discontinuous dissolution at dislocations in our simulation produces a profile and steady state dissolution rate similar to our observations. If a small fraction of the dislocations (even a single dislocation) were continuous, the profile would ultimately become

Kinetics of calcite dissolution a sawtooth,

with the maximum rate of 7.3 X lo-” mol*cm-*.s- ’ . However, the dissolution could appear to be at steady state over long time periods as the rate very slowly increased, approaching the sawtooth limit. Our simulation shows that there should be no increase in steady state rate with increasing dislocation density, after an initial transient period, if a sawtooth profile is produced. The possibility that dissolution rates would not be affected by dislocation density if etch pits intersected was predicted by LASAGAand BLUM( 1986) and was used to explain the results of SCHOTTet al. ( 1989). However, the fact that increases in dislocation density cause increased dissolution rates in this and other studies suggests that discontinuous dissolution at dislocations in the unstrained samples lowers the steady state rate from that of the sawtooth profile (Fig. 5e). In the case of calcite, the maximum possible increase for dissolving a sample with Pd = lo3 - cm-*, compared to a dislocation-free sample, is only a factor of -5.4 since there is significant background dissolution from G2 pits (ub) at defect clusters. The importance of dissolution at impurities has also been proposed by BLUM et al. ( 1990) for the lack of dependence of quartz dissolution rate on dislocation density. The preferential etching at microcracks and twin boundaries in the strained sample indicates that the distribution of defects has a profound effect on the dissolution morphology, and hence the dissolution rate, as has been pointed out in other studies ( SCHOTTet al., 1989; MEIKE, 1990). The main effect of regularly spaced zones of high defect density separating relatively undeformed parts of a crystal would be to increase the surface area, or the roughness factor, by dividing large grains into many smaller grains. It is clear that more work is needed to definitively identify the cause of the morphological features we have observed. Innovative techniques such as in situ atomic force microscopy ( HILLNERet al., 1992) should finally shed light on this problem at the atomic scale. CONCJJSIONS

We have measured a factor of 2.3 increase in the dissolution rate for strained (Pd = 6 X 10 8 - cm-*) over undeformed (& - 10 3 - cm-*) calcite single crystals. Dissolution rates of unstrained crystals are initially transient until a steady state is reached. Rates for mechanically ground surfaces are higher than for deeply pre-etched ground surfaces. Pm-etched ground surfaces dissolve at a steady state rate comparable to that of cleaved samples. This suggests that surface preparation affects dissolution rates through enhanced dissolution at cracks and dislocation loops produced in the grinding process. Ground surfaces and strained samples dissolve at roughly the maximum dissolution rate predicted from etch pit growth kinetics. Steady state dissolution rates occurred when the surface had a constant bimodal etch pit size distribution and time-independent slope for inclined surfaces (constant ledge density at etch pit walls and cleavage steps). Gl pits consist of large pointed and terraced pits possibly corresponding to straight and bent or branching dislocations, respectively. G2 pits include abundant, short-lived, small etch pits, attributed to nucleation at impurity or defect clusters. Calculated dissolution rates and surface profiles based on etch pit growth rates are

1125

in reasonable agreement with our observations. An abundance of nondislocation nucleation sites in the undeformed calcite explains the relatively small increase in dissolution rate for highly strained samples. Acknowledgments-This

project was started with support for SLB from the Petroleum ResearchFund of the American Chemical Society and Research Corporation funds. SLB also acknowledges support from the David and Lueile Packard Foundation and NSF grant EAR8657868. We would like to also thank Sue Barta, Linda Bliss, Brian Evans, Henry Gong, Mike Machesky,Robert Pangbom, Gary Rowe, Deane Smith, Don Voigt, and Tess Wilson for their help. Discussions

with Brian Evans, Andy Gratz, Rich Reeder, David Rickard, and Katsuo Tsukamoto, and pre-prints from Richard Compton were very helpful. We especially thank Maria Borcsik for the calcite samples, Brian Evans for preparing the strained sample, and Rich Reeder for the TEM analysis of dislocation density. The paper was greatly improved by reviews by Annemarie Meike, John Morse, and Rich Reeder. Editorial handling:

T. Pates

REFERENCES BARWISEA. J., COMPTONR. G., and UNWINP. R. ( 1990) The effect of carboxylic acids on the dissolution of calcite in aqueous solution. Part 2: d-, I-, and meso-Tartaric acids. J. Chem. Sot. Faraday Trans. 86, 137-144.

BENNEMAP. and VANENCKEVORT W. J. P. ( 1979) On the occurrence of a critical driving force for dissolution: Theory and experimental observation on KDP and other crystals. Ann. Chim. Fr. 4, 45 l459. BERNERR. A. ( 1978) Rate control of mineral dissolution under earth surface conditions. Amer. J. Sci. 278, I2 14- 123 1. BERNERR. A. and HOLDRENG. R. ( 1979) Mechanism of feldspar weathering--II. Observations of feldspars from soils. Geochim. Cosmochim. Acta 43, 1173- 1186. BERNERR. A. and MORSEJ. W. ( 1974) Dissolution kinetics of calcium carbonate in sea water, IV. Theory of calcite dissolution. Amer. J. Sci. 274, 108-134. BERNERR. A. and SCHOTTJ. ( 1982) Mechanism of pyroxene and amphibole weathering-II. Observations of soil grains. Amer. J. Sci. 282, 1235-1252.

BIANCHETTIS. F. and REEDER R. J. ( 1985) Variable dissolution rates of deformed and undeformed calcite (abstr.) Geol. Sot. Amer. Prog. Abstr. 17, 522.

BLUM A. E., YUND R. A., and LASAGAA. C. ( 1990) The effect of dislocation density on the dissolution kinetics of quartz. Geochim. Cosmochim. Acta 54,283-298.

BRANTLEYS. L., CRANES. R., CRERARD. A., HELLMANNR., and STALLARDR. ( 1986) Dissolution at dislocation etch pits in quartz. Geochim. Cosmochim. Acta 50,2349-236 1. BRIEGELU. and GOETZEC. ( 1978) Estimates of differential stress recorded in the dislocation structure of Lochseiten limestone (Switzerland). Tectonophysics 48, 6 l-76. BUCK T. M. ( 1960). Damaged surface layers-semiconductors. In The Surface Chemistry of Metals and Semiconductors (ed. H. C. GATOS), pp. 107-135. J. Wiley & Sons. BUSENBERGE. and PLUMMERL. N. ( 1986) A comparative study of the dissolution and crystal growth kinetics of calcite and aragonite. In Studies in Diagenesis (ed. F. A. MUMPTON);USGS Bull. I5 78, pp. 139-168. CABRERAN. and LEVINEM. M. ( 1956) On the dislocation theory of evaporation of crystals. Phil. Msg. 1, 450-458. CASEY W., CARR M. J., and GRAHAMR. A. (1988) Crystal defects and the dissolution kinetic8 of rutile. Geochim. Cosmochim. Acta 52, 1545-1556.

L., CARRELSR. M., and WOLLASTR. ( 1989) Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals. Chem. Geol. 78,269-282.

CHOU

1126

I. N. Maclnnis and S. L. Brantley

COMPTONR. G. and DALY P. J. ( 1984) The dissolution kinetics of Iceland Spar single crystals. J. Colloid Interface Sci. 101, 159- 166. COMPTON R. G. and PRITCHARD K. L. ( 1990) The dissolution of calcite at pH > 7: Kinetics and mechanism. Phil. Trans. Roy. Sot. London A330,47-70. COMFTON R. G. and UNWINP. R. ( 1990) The dissolution of calcite in aqueous solution at pH < 4: Kinetics and mechanism. Phil. Trans. Roy. Sot. London A330, I-45. COMPTON R. G., DALY P. J., and HOUSEA. W. ( 1986) The disso-

lution of Iceland Spar crystals: The effect of surface morphology.

MORSE J. W. ( 1986) The surface chemistry of calcium carbonate minerals in natural waters: An overview. Mar. Chem. 20,9 I- 112. MURPHYW. M. ( 1989) Dislocations and feldspar dissolution. Eur. J. Mineral. 1, 3 15-326. MURR L. E. and HISKEYJ. B. ( 198 1) Kinetic effects of particle-size and dislocation density on the dichromate leaching of chalcopyrite. Metall. Trans. 12B, 255-267.

PAQUETTEJ. and REEDERR. J. ( 1990) New type of compositional zoning in calcite-insights into crystal-growth mechanisms. Geology 18, 1244-1247.

J. Colloid Interface Sci. 113, 12-20. COMFTON R. G., PRITCHARDK. L., UNWIN P. R., GRICG G.,

PATELA. R. and GOSWAMIK. N. ( 1962) Etching of calcite cleavages.

SILVESTERP., LEES M., and HOUSEW. A. ( 1989) The effect of carboxylic acids on the dissolution of calcite in aqueous solution. Part I :-Maleic and fumaric acids. J. Chem. Sot. Faraday Trans.

PLESKOVYu. V. and FILINOVSKIV. Yu. ( 1976) The Rotating Disk Electrode. Consultant Bureau. PLUMMERL. N., WIGLEYT. M. L., and PARKHURSTD. L. ( 1978) The kinetics of calcite dissolution in CO*-water systems at 5” to 60°C and 0.0 to 1.0 atm CO*. Amer. J. Sci. 278, 179-216. PLUMMERL. N., WIGLEYT. M. L., and PARKHURSTD. L. ( 1979) Critical review of the kinetics of calcite dissolution and precipitation. In Chemical Modelling of Aqueous Systems (ed. E. A. JENNE), Vol. 93, pp. 538-573. Amer. Chem. Sot. RICKARD D. and SJ~BERG E. L. ( 1983) Mixed kinetic control of calcite dissolution rates. Amer. J. Sci. 283. 8 15-830. RWHOW T. G. and ROCHOWE. G. ( 1979) An Introduction to Mi-

g&4335-4366. CYGAN R. T., CASEY W. H., BOSLOUGHM. B., WESTRICHH. R., CARR M. J., and HOLDRENG. R. ( 1989) Dissolution kinetics of experimentally shocked silicate minerals. Chem. Geol. 78, 229244. DANDURANDJ. L., GOUT R., and SCHOTTJ. ( 1982) Experiments

on phase transformations and chemical reactions of mechanically activated minerals by grinding; petrogenetic implications. Tectonophysics 83, 364-386.

DOWELLM. B., HULTMANC. A., O’NEALH. R., and ROSENBLATT G. M. ( 1977) Changes in surface morphology and vaporization rate upon vaporization of arsenic ( 111) cleavage surfaces. J. Chem. Phys. 66, 1875-1886. FERRETJ., GOUT R., KUHNY., and SEVELYJ. ( 1987) The influence of grinding on the dissolution kinetics of calcite. Phys. Chem. Minerals 15, 163- 170. GILMANJ. J. ( 1960) Discussion to the article: Etching of metals and semiconductors. In The Surface Chemistry of Metals and Semiconductors (ed. H. C. GATOS), pp. 172-173. J. Wiley &Sons. HARI BABUV. and BANSIGIRK. G. ( 1969) Branching and bending of dislocations in sodium chloride crystals. J. Appl. Phys. 40,43064312.

HEU;ESONH. C., MURPHYW. M., and AAGAARDP. ( 1984) Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta 48,2405-2432.

HILLNERP., MANNES., GRATZ A., and HANSMAP. ( 1992) AFM images of dissolution and growth on a calcite crystal. Ultramicroscopy (submitted).

HIRTHJ. P. and POUNDG. M. ( 1957) Evaporation of metal crystals. J. Chem. Phys. 263, 1216-1224.

IVESM. B. and MCAUSLANDD. D. ( 1968) On the slope of etch pits. Surface Sci. 12, 189-207.

JAMIESONJ. C. and GOLDSMITHJ. R. ( 1960) Some reactions produced in carbonates by grinding. Amer. Mineral. 45,8 19-827. JOSHI M. S., KOTRUP. N., and ITITAKHEN M. A. ( 1978) Revelation of stepped dislocations in amethyst crystals by hydrothermal etching. Amer. Mineral. 63, 744-746. KEITH R. E. and GILMAN J. J. ( 1960) Dislocation etch pits and plastic deformation in calcite. Acta Met. 8, l-10. LASAGAA. C. ( 1983) Kinetics of silicate dissolution. In Fourth Znternational Symposium on Water-Rock Interaction, pp. 269-274. Misasa, Japan. LASAGAA. C. and BLUMA. E. ( 1986) Surface chemistry, etch pits and mineral-water reactions. Geochim. Cosmochim. Acta 50,23632379.

LEFAUCHEUXF. and ROBERTM. C. ( 1977) Defects revealing the two growth processes for a face case of hydrothermal synthetic calcite. J. Crystal Growth 38, 29-37. MEHTAB. J. and THUMARB. T. ( 1986) Different types of eccentricity of etch pits on calcite cleavages. Surf: Coatings Tech. 27,37 l-377. MEIKEA. ( 1990) A micromechanical perspective on the role of dislocations in selective dissolution. Geochim. Cosmochim. Acta 54, 3347-3352.

MORSEJ. W. ( 1983) The kinetics of calcium carbonate dissolution and precipitation. In Kinetics of Geochemical Processes (ed. R. J. REEDER); Reviews in Mineralogy 11, pp. 227-264. Mineral. Sot. Amer.

Acta Cryst. l&47-49.

croscopy by Means of Light, Electrons, X-Rays, or Ultrasound.

Plenum Press. SANGWALK. ( 1987) Etching of Crystals. North Holland. SANGWALK. and ARORAS. K. ( 1979) The anisotropy of grinding damage, chemical polishing and etching in MgO crystals. J. Phys. D: Appl. Phys. 12,645-650.

SCHOTTJ. ( 1990) Modelling of the dissolution of strained and unstrained multiple oxides: The surface speciation approach. In Aquatic Chemical Kinetics: Reaction Rates ofProcesses in Natural Waters (ed. W. STUMM), pp. 337-365. J. Wiley & Sons.

SCHO~TJ., BRANTLEYS., CRERARD., GUY C., BORCSIKM., and WILLAIMEC. ( 1989) Dissolution kinetics of strained calcite. Geochim. Cosmochim. Acta 53, 373-382. SEGNIT E. R., HOLLANDH. D., and BISCARDIC. J. (1962) The

solubility of calcite in aqueous solutions: I. The solubility of calcite in water between 75” and 200” at CO2 pressures up to 60 atm. Geochim. Cosmochim. Acta 26, 1301-1331.

SHAHA. J. and PANDYAJ. R. ( 1985) Chemical dissolution of calcite cleavages in aqueous solutions of sodium hydroxide. Crystal Res. Technol. 20, 8 13-8 17. SJOBERGE. L. ( 1978) Kinetics and mechanism of calcite dissolution in aqueous solutions at low temperatures. Stockholm Contrib. Geol. 32, l-96.

SJ~BERGE. L. and R~CKARDD. ( 1983) The influence of experimental design on the rate of calcite dissolution. Geochim. Cosmochim. Acta 47,228 I-2286.

SJOBERGE. L. and RICKARDD. ( 1984) Temperature dependence of calcite dissolution kinetics between 1 and 62°C at pH 2.7 to 8.4 in aqueous solutions. Geochim. Cosmochim. Acta 48, 485493.

TANNERB. K. ( 1976)X-ruy Dtflaction Topography. Pergamon Press. THOMASJ. M. and RENSHAWG. D. ( 1965) Dislocations in calcite and some of their chemical consequences. Trans. Faraday Sot. 61,79 l-796.

WHITE A. F. and PETERSONM. L. ( 1990) Role of reactive surface area characterization in geochemical kinetic models. In Chemical Modelling of Aqueous Systems ZZ(ed. D. C. MELCHIORand R. L. BASSETT);ACSSymposium Series 416, pp. 461-475. Amer. Chem. sot.

WINCHELLH. (1956) The unit cells of calcite. Amer. J. Sci. 254, 65-70.

ZARKAA. ( 1972) Etude de defaults de croissance darts des carbonates rhombddriques naturels. Bull. Sot. Fr. Mineral. Cristallogr. 95, 24-32.

ZHANGJ. W. and NANCOLLAS G. H. ( 1990) Mechanisms of growth and dissolution of sparingly soluble salts. In Mineral- Water Znter.face Geochemistry (ed. M. F. HOCHELLA,Jr., and A. F. WHITE); Reviews in Mineralogy 23,

pp. 365-396.

Amer. Mineral.

Sot.