kinetics of dissolution of mechanically comminuted rock-forming oxides and silicates—ii....

Kinetics of dissolution of mechanically comminuted r~k-formic oxides and siIicates-41. ~efo~ati~

and dissolution of oxides and silicates in the taboratory and at the Earth’s surface

RAWMIR PETROVICH

Research & Development Department. Phillips Petroleum Company, Bartlesville, OK 74004. U.S.A.

(Recrit’ed 27 February 1979; accepted in revised form 29 April 1981)

Abstract-Comparison of the patterns of fracture under tensile stress, indentation, and scratching of periclase. quartz, and corundum indicates that the properties relevant to dissolution of rock-forming oxides and of rock-forming non-layer silicates should be changed by mechanical comminution in essentially the same way as those of quartz. The changes are accomplished by brittle fracture under the tensile component of the stress field. which does not generate subsurface damage. and by microplastic behavior under local stresses with high net compressive and shear components, which does.

Mechanical comminution should therefore affect the apparent rates of dissolution (rates calculated with respect to the initial interface area) of rock-forming oxides and of rock-forming non-layer silicates in essentially the same way in which it affects the apparent rate of dissolution of quartz. This is supported by the available evidence on the effect of dry grinding on the kinetics of dissolution of feldspars. pyroxenes, and olivines in aqueous solutions.

Different effects of mechanical comminution on solubilities and dissolution rate constants can be related to certain measured or calculated properties of the considered minerals. Notably. the effect of grain size on the dissolution rate constant can be rigorously related to the Kelvin effect.

The available evidence on the mechanical comminution at the bases of dry-based glaciers, in high- gradient segments of streams. in certain high-energy coastal and epeiric ennronments. and in sandy deserts indicates that such mechanical comminution should significantly affect the simultaneous or subsequent dissolution of the comminuted material

INTRODUCTION

IN THE previous paper of this series f&T’ROVKH,

198I--herein referred to as Part 1). changes in some properties relevant to dissolution and the kinetics of dissolution of a reference oxide, quartz, in aqueous solutions were considered in some detail. Quartz was selected as the reference material because the properties and dissolution behavior of ground quartz have been extensively studied and the bonding within it has some essential similarities both with the bonding in other rock-forming oxidei and with the bonding in silicates.

The present paper is an attempt to answer three interrelated questions:

1. How similar are the patterns of changes introduced by mechanical comminution of other rock forming oxides and of silicates that lack planes of extreme weakness to the pattern of changes introduced by mechanical co~inution of quartz?

2. How similar are the effects of mechanical comminution on the kinetics of dissolution of rock- forming oxides other than quartz and of silicates that lack planes of extreme weakness in aqueous solutions to the effect of mechanical comminution on the kinetics of dissolution of quartz?

3. Are natural processes of mechanical comminution likely to have a significant effect on the kinetics of dissolution of rock-forming oxides and silicates in

some environments on the Earth’s surface that deserve our attention?

MODES OF DEFORMATION OF ROCK-FORMING OXIDES AND

SILJCATIB DURING MECHANICAL COMM~NUT~ON

It was shown in Part 1. that mechanical comminution of quartz during such grinding treatments as mortar-and-pes- tle grinding and vibration milling can be resolved into a multitude of individual events belonging to two processes:

1. Fracture, caused by the tensile component of the stress at the crack-tip (cf. LAWN et al., 1980). and

2. Local plastic deformation, caused by high local stresses with net compressive and shear components (cf Law74 ef af.. 1980).

Both fracture under tensile stress and microplastic behavior have been studied in the cases of three oxides that span the range of mechanical properties of interest for the present study: the semi-brittle and moderately hard (Moh5 hardness 53) periclase (MgO), the brittle and moderate11 hard quartz, and the brittle and very hard corundum (the designations semi-brittle and brittle refer to room-tempera. ture behavior). Mechanical behavior of these oxides ir examined below as a key to the behavior of other oxide: and silicates of interest.

Fracture under mueroscopic tensik stress

Cleavage fractures propagate in all three oxides withoul introducing dislocations at temperatures up to at leas 250°C (MARTIN, 1972; WIEDERHORN et al.. 1973; AKASHI f975; MARTIN and DURHAX, 1975). In periclase dislocatior arrays are introduced not only in regions of plastic defer

<I(* 45 10 R 1675

1676 RADOMIR PETROVICH

mation in which fracture starts, but also at steps on cleavage surfaces (FUTAGAMI and .L\KASHI, 1972); however, in quartz dislocations are not introduced either along cleavage steps or along the lines of change in slope that give curvature to conchoidal fractures (BURSIL and MCLAREN, 1965; MARTIN and DURHAM, 1975). Accordingly, dislocations are not to be expected at steps on cleavage surfaces of corundum either. LAWN er al. (1980) have observed partial healing of arrested cracks in corundum which leaves arrays of mismatch dislocations in the crack plane; such arrays are to be expected near the tips of cracks that branch from cleavage surfaces of all three oxides.

lndenration and scratching

In periclase, symmetric dislocation arrays spread from indentation marks and narrow dislocation networks underlie scratch marks (BROOKES and GREEN, 1973; ALLEN et al..

1976: CHAUDHRI et al., 1980). At high loads, such subsurface damage is generated in periclase even by indenters and sliders that are softer than periclase (of Knoop hardnesses down to l/4 of that of periclase), and it appears before visible surface damage (ALLEN et al., 1976).

size of the abrasive, and after the surface is smoothed by polishing with cerium oxide powder lattice strains in the subsurface can be detected by both electron and X-ray diffraction (SEKIGUCHI and F~NAKUBO, 1974). When LAZ~RINA and SOROKA (1974) etched mechanically

In quartz, enhancement of the blue cathodoluminesccnce that corresponds to the enhancement of cathodoluminescence at dislocations in periclase (6. CHAUDHRI et al.. 1980) was observed by HANUSIAK and WHITE (1975) around scratch marks produced under high vacuum. Mechanical polishing of single crystals of quartz with alumina powders generates surface relief with a height of about l/10 of the

Given access to dislocations. water molecules and or products of their dissociation within quartz and silicate crystals facilitate plastic deformation of these crystals by their bond-breaking effect (GRIGGS, 1967). However. durmg mechanical comminution water molecules from the atmos- phere or immersion medium have much readier access to crack tips. Accordingly, as m the experimentally studied case of quartz (MARTIN and DURHAM. 1975). the presence of water vapor or liquid water facilitates brittle fracture of oxides and silicates in general. The presence of liquid water or other immersion liquids also reduces local heating and with it dislocation mobility, decreasing the tendency towards microplastic behavior. Therefore mechanical comminution of rock-forming oxides and silicates m general under water favors brittle fracture at the expense of plastic deformation. as documented in the case of quartz (see Part I).

Liquid water and to a lesser extent organic solvents such as acetone must decrease the tendency of fragments of rock-forming oxides and silicates to stick to each other during mechanical comminution, for the reasons already stated in discussing their effect on sticking of quartz fragments (see Part I).

KINETICS OF DISSOLUTION OF GROUND SILICATES

.

It was shown in Part I that when ground quartz

L dissolves at constant temtxxature and oressure in an aqueous solution that satisfies the following conditions,

(1) activities of catalytically active species are constant. and

polished quartz faces in hydrofluoric acid, they found that dislocation density as indicated by etch pits was much higher in a thin surface layer than in the interior of the crystal.

In corundum. three-dimensional dislocation networks are generated in the central deformation zone under Vickers indentation and particle-impact marks (LAWN et al.. 1980). Threedimensional dislocation networks underlie Individual scratch marks on corundum surfaces; as the surface is repeatedly crisscrossed by the abrading grains, these networks merge into a zone of high dislocation density whose thickness is roughly commensurate to the size of the abrasive (HOCKEY. 1971. 1972).

(2) saturation with respect to the dissolving solid IS not approached. its apparent dissolution rate .i’ (i.e. dissolution rate calculated using the initial surface area of the totally immersed solid sample) shows the following dependence on the thickness I* of the equivalent dissolved disturbed layer (for which see Part I):

J = k.4,,.4”

+ (h.dkA,rAO)exp(-~*‘i,) for <* d L,, lia)

Thus the pattern of brittle fracture under a large tensile component of stress, but microplastic behavior under high

j = !G-l,,A,,

local stresses with dominant compressive and shear com- for <* > L, (lb) ponents is common to all three oxides. Since they span the range of mechanical properties and dominant bond types of the common rock-forming oxides and the common

where 240 and & (m’) are the initial and steady-state

rock-forming silicates other than layer silicates. the proper- interface areas. k (mol rn-’ set- ‘) is the rate constant ries rrlruant IO dissolution of rhr common rock-firming for dissolution of the undisturbed solid in that par- o.uides and non-layer silicatrs must c,hange wirh mechanicai titular solution. L,, (ml is the thickness of the equival- comminution in essenriallp the same way as those of quurrz.

The rudimentary evidence on the relevant properties of ent disturbed iaye; (for which see Part I). and i, (m)

rock-forming silicates is consistent with this conclusion, and I\‘~ are constants characteristic of the sample. It

but shows that quartz is not always the closest analogue to was also shown that for closed-system dissolution in a silicates. Micrometer- and submicrometer-size albite frag- solution initially devoid of silicic acid, this results in a ments stuck tenaciously to coarser albite fragments, still largely bounded by good cleavage surfaces, which HOL-

dependence of the molality mzsio, of the total dis-

DREN and BERNER (1979) had obtained bv drv armding: solved silicic acid on time r of the form

accordingly aibite. with i;s three-dimensional aiumino-sifi- cate framework related to that of coesite and large cations in its cavities. behaves in this respect very much like quartz (see Part I). On the other hand, room-temperature propa-

mLsioI = mXsio,lr) + C(t - f~) for r > rL c2b)

gation of conchoidal fractures in zircon iniroduces -arrays of dislocations along the lines of change in slope (BURSIL where a, b, and C* are constants. The purpose of this

and MCLAREN. 1965); accordingly the island silicate zircon. section is to determine how similar the effect of grind- though harder. is more ductile than quartz. ing on the kinetics of dissolution of non-layer silicates

Kinetics of dissolution of oxides and silicates-11 1677

is to the effect of grinding on the kinetics of dissolution of quartz.

To separate unambiguously the effect of grinding on the kinetics of dissolution of silicates from the effects of changing compositional variables. one has to use data from dissolution experiments that satisfied not only conditions (1) and (2). but also the additional condition:

(3) the rates of change in the monitored molalities are proportional to the apparent dissolution rate, i.e. dissolution is either congruent, or incongruent with the overall precipitation rate proportional to the overall dissolution rate.

Dissolution experiments with ground silicates that satisfy al! these conditions are scarce, but not al- together lacking.

Some stepwise dissolution experiments at constant pH of CLELLAND et al. (1952) that were done with dry

e 06

H ; 06

ground quartz, orthoclase, and olivine were probably the earliest attempt to compare the effects of grinding on the kinetics of dissolution of quartz and silicates. The results of these experiments are shown in Fig. 1: the variables plotted as functions of the cumulative dissolution time t are Znpiol,,, the sum of molalities of molybdate-reactive silica reached at the ends of successive dissolution steps, and Z@ro,,i, the sum of virtual molalities of the SiOl component contained in suspended particles that remained in the decanted solution at the ends of successive dissolution steps.

The experiments with orthoclase whose results are plotted in Fig. 1 satisfied conditions (1) to (3) (Appen-

dix A). Figure la shows that the shape of the GnrsiO,Vi vs t curve for the orthoclase sample is indistinguish- able from the shapes of the corresponding curves for the two quartz samples. Figure lb shows that like the two quartz samples, the sample of ground orthoclase

0 20 40 60

IO

06

0 20 40 60

Fig. 1. (a) &IO~K),,~ as functions of time and (b) Zmj&,,.i as functions of time in four stepwise dissolution experiments of CLELLAND et al. (1952). done at 37°C with dry-ground rock crystal (rc), an orthoclase (or), and an olivine (00, and as-received Lochahne quartz sand (Ls) and with an HsBOs-NasBOs aqueous solution of pH 7.5. Microscopically determined mean grain sires of about 250~ in a)) four cases.

Separation of solids between dissolution steps by sedimentation. Empirical curves.

1678 RAWMIR PETROVICH

released a large quantity of tiny fragments in the first dissolution step: in view of the relation between dm,siojdt and J’ established in Appendix A, only Zoo/, of m&2,, could have consisted of precipitate). The amounts of particulate material released in the first step by the orthoclase sample and the identically treated sample of ground quartz (rock crystal) are similar: they correspond to layers 21 and 16 nm thick, respectively, on the average coarse fragment.

The Xmsio,,i vs time and Zm&o,,i vs time plots for Clelland and coworkers’ dissolution experiments with olivine are qualitatively similar to the corresponding plots for orthoclase and quartz. Quantitative interpretation of these plots will not be attempted here because with the oxidation of dissolved iron, the unknown MgjSiOz ratio of the olivine critically affects the possibly changing dm,sioi’(J’dt) ratio.

Further extensive information on the kinetics of dissolution of dry-ground alkali feldspars, including direct observation of adhering tiny fragments by scanning electron microscopy, was recently obtained by HOLDREN and BERNER (1979) in a series of room-temperature. constant-pH, closed-system dissolution experiments with dry-ground albite. The sets of (t,mzsio,) points obtained during the first 510 hr of their experiments are shown in Fig. 2. Their differently treated albite samples are denoted here as follows: a&)-the

14O-210pm size fraction of albite dry-ground in a disc grinder: ab(cw)-L&(C) ultrasonically cleaned in and washed with acetone; ab(cwe)-&cw) etched for 2Omin in a 59, HF-0.09 N H2S04 aqueous solution; ub(f)--a&) ground in a mechanical agate mortar until it was ‘*dominated by particles less than 2 pm in di- ameter”; ab(fe)-ah(j) etched like ab(cwe) for 15-20min. Also shown and denoted with or is a : t,m~io,i set obtained by WOLLAST (1967) in a closed- system dissolution experiment at the same temperature and pH. with a solution differing from the preceding one only in having 52% of K’ ions replaced by Na+ ions. When comparing different mrsioI vs time plots in Fig. 2 it should be kept in mind that Holdren and Berner’s experiments with coarse albite were done with 70 g of a&c), or what remained of 70 g of a&c) after further treatments, per 975 ml of solution; their experiments with fine-grained albite with 50 g of a&f), or what remained of 50 g of ab(f, after etching, per 1OOOml of solution; and Wollast’s experiment with 50 g of orthoclase. per 950ml of solution. All these experiments satisfied conditions (1) to (3) during the pre-steady-state and steady-state stages of dissolution (Appendix A).

The first thing to note in Fig. 2 is the fact that all Holdren and Bemer’s m5io, vs time plots. as well as the pre-steady-state and steady-state stages of Wol-

Frg. 2. jnLsi02 as a functton of time m room-temperature. closed-system dissolutton experiments wtth dry-ground alkali feldspars and aqueous solutions of pH 6.0. ah(c), ah(cwL *xperiments of HOLDREX and BERNER (1979). done with dry-ground albite used with or without further treatment as stated in the text and a 0.050 M K-biphthalate-O.045 M KOH solution. or(c)--an experiment of WOLLAST (1967). done with an orthoclase sample containing 59,, quartz, presumably dry-ground. and a 0.050 M K-

biphthalate-0.045 M NaOH solution. The shapes of curves are given by eqn (2).

Kinetics of dissolution of oxides and silicates--II 1679

last’s plot- are well fitted by mrsio,(t) curves whose shape is given by eqn (2); the agreement is especially significant in the case of the very well defined curves for oh(f) and ab(fe). It follows that eqn (l), the empirical equation introduced to describe the effect of grinding on the kinetics of dissolution of quartz. also describes accurately the dependence of the dissolution rate on <* in the case of high-undersaturation dissolution of dry-ground feldspars.

Comparison of different mpio,(t) curves in Fig. 2 and HOLDREN and BERNER’S (1979) information on the morphology of their albite grains after different treatments makes possible certain inferences about the material that caused the pre-steady-state variation in the apparent dissolution rate p. Holdren and Berner have certainly demonstrated that 50% of the material contributing to the thickness Ld of the equivalent disturbed layer on L&(C) was in adherent fine and ultrafine fragments [compare MC) and L&(W)]. Drawing their steady-state asymptotes to mBio2 vs time plots for a&), ab(cw), and ub(cwe) so as to average, rather than follow, the long-term fluctuations in -i’ that took place during the 1340 hr of dissolution experiments with these materials, Holdren and Berner also conclude that, in my terminology, etching completely eliminated the ‘disturbed’ material. From this and the elimination of adherent fine and ultrafine fragments accomplished by etching they conclude that all of the ‘disturbed’ material resided in the adherent fine and ultrafine fragments. However. the steady-state asymp- tote to the mssio,(t) curve for &-we) can be reason- ably drawn so as to leave an L~b(cWC) that is equal to

0.25 Lib”) (Fig. 2); moreover, the etched coarse albite fragment in Holdren and Berner’s Fig. SC shows unmistakeable signs of dissolution, such as cavities under overhanding cleavage-step ledges. Accordingly. the coarse fragments may have contributed 20-30% 01 ,;btcl.

Secondly, thicknesses of the equivalent disturbed layers on u&c) and ab(cw). calculated with respect to the surface area of the coarse fragments, are close to 1 nm, while thicknesses of the equivalent adherent layers on these materials, calculated with respect to the same surface area amount to tens of nanometers. Thus no more than a couple of percent of the adherent material contributes to the ‘disturbed’ material manifested in dissolution kinetics--a finding consistent with the attainment of steady state in dissolution experiments with micrometer-size quartz and feldspar fragments after only a fraction of a percent of the solid sample is dissolved.

Thirdly, the mean interface-area grain size. analogous but not necessarily equal to the mean gas- adsorption gas size, of o&f) at steady state can be obtained from the self-explanatory relation

dNf) (dmrsio,~dr)ss aWf)

0 (is

ZKpb(cwd

0.70(dm,i02/dt~~cWC) = F = e IK1M” (31

where Q, (m’/kg) is specific surface area at steady state, and the coefficient 0.70 takes into account the difference in albite/solution ratios. Taking for ziT:P”‘“‘) the mean size of the coarse fragments, about 180 m, one obtains for %$‘) the value of 28 man

Fig. 3. Concentrations of total dissolved silicon and magnesium as functions of time in a room- temperature, closed-system dissolution experiment of GRANDSTAFF (1977). done with a dry-ground Mg,,,,Fe,,,,Cao.ozSiOs bronzite of sieving size range 74-149 m and a 0.1 M HCI-KCl-0.17 mM KF

solution of pH 3.24. The shapes of curves are given by eqn (2).

1680 RADOMR PETROVICH

extremely high value for a material that was described in its original state as dominated by grains of 2R < 2 pm and that has since then lost only 0.03% of its mass. The conclusion is inevitable that like MBER and ARNOLD'S (1961) micrometer-size quartz, whose dissolution is documented in Part I, Holdren and Berner’s micrometer-size dry-ground albite was strongly aggregated. This also explains the simple scaling down of the mLSIOl(t) curve for fine-grained albite that was achieved by etching-instead of selec- tively dissolving the ‘disturbed’ material, the etchant was dissolving en masse the aggregated grains. Unfor- tunately, this also means that one cannot tell to what extent the relatively slow approach to steady state was due to the expected more extensive subsurface damage, and to what extent to grain-boundary diffusion.

It is more difficult to find results of dissolution experiments with ground chain silicates that satisfy conditions (1) to (3). The results of a closed-system dissolution experiment of GRANDSTAFF (1977) that was done with a dry-ground orthopyroxene and satisfied at least approximately all three conditions (Appendix A) are plotted in Fig. 3. It can be seen that m,(r) curves whose shape is given by eqn (2) fit both the [t,mM,: and :r,msi) set fairly accurately, indicating that eqn (1) also satisfactorily describes the dependence of the apparent dissolution rate on <* in the case of dry- ground pyroxenes.

Quantitative analysis of the effect of grinding on the kinetics of silicate dissolution will not be further pursued here, because unambiguously interpretable data are lacking for some important rock-forming silicates and interpretation of data for layer silicates is made difficult by the need to consider non-stoichio- metric dissolution (cf. THOMAssIN ef al.. 1977). How- ever, it is worth noting that the MzsioZ(t) curves recently obtained by HURD et al. (1979) in closed- system, constant-temperature, constant-pH dissolution experiments with dry-ground olivine and tremo- lite also have shapes given by eqn (2).

FACTORS THAT ENHANCE

DISSOLUTION OF MECHANICALLY

COMMINUTED OXIDES AND

SILICATES

As mentioned in Part I, mechanical comminution affects the kinetics of dissolution of solids in three ways: (1) by increasing the interface area. (2) by increasing the solubility of the solid and thus retard- ing the effect of the approach to saturation with respect to the dissolving solid. and (3) by increasing the rate constant for dissolution.

The direct tfkt of the interface urea on dissolution kinetics is obvious: other things being equal. the overall rate of transfer of the solute to the solution is proportional to that area.

Increase of solubility by a very small grain size (Kel-

negligible contribution of surface free energy to the molar free energy of the solid. The importance of this effect for the solubility of mechanically comminuted material was first recognized by STABBER and ARNOLD (1961), after they discovered the adherence of tiny fragments to micrometer-size fragments of dry-ground quartz. Provided Gibbs free energy ysL (mJ/m’) of the solid/solution interface is known. the increase in solubility of equant or sub-equant fragments can be calculated using the Kelvin equation adapted to solutions (aliar the Ostwald-Freundlich equation):

(4)

where s(R) (mol;kg H20) is the solubihty of grains with the inscribed-sphere radius R (m), p(m’!‘mol) is the molar volume of the solid, .# (Jmol-’ K-‘) is the gas constant, and T (K) is absolute temperature. This relation was used by ST~BER and ARNOLD (1961) to calculate the solubility enhancement for tiny quartz fragments, and a slightly modified version of it by HOLDREN and BERNER (1979) to calculate the solubility enhancement for tiny feldspar fragments. .4t present there are two problems with quantitative evaluation of the Kelvin effect in the case of mechanically comminuted oxides and silicates. The first is to obtain reliable ysL values. ST&ER and ARNOLD (1961) used an estimated ;sL value for quartz of 420 mJ/m’. and HOLDREN and BERNER (1979) an estimated value for feldspar of 6OOmJi’m’. For comparison, analysis of nucleation rates gives for the interface between amorphous silica and its aqueous solution ysL values of 46 and 100 mJ/m’ (ILER, 1980). and for the interface between the relatively insoluble oxysalt barite and its aqueous solution a ;‘s[. value of 135 mJ/m’ (NIELSEN and .%HNEL, 1971). while the directly measured room- temperature ;!sL for the muscovitelwater interface is 12OmJ;m’ (SCHULTZ cf al.. 1977a. 1977b). At room temperature, 3 ;‘sL value of 120mJjm2 would double the solubility at a grain size of 25 nm. and increase it ten times at the grain size of 7.6 nm. The second prob- lem, which also makes determination of ysL from solubility measurements very difficult. is that of determin- mg the effective mean grain size of the finest surviving size fraction. which actually determines the solubility (cf. ADAMSON. 1976. pp. 334335). It is clear. however. that the effect is very important.

The analogous increase in solubilirv of‘ the material in blade tdyrr and shot-p points by the wry .srnull radius of’curc.oturr (ST~BER and ARNOLD, 1961) should be in principle calculable from the more general form of the Kelvin equation (ADAMSON. 1976, p. 51).

where R, and R2 are the maximal and minimal radius of the surface.

rin effect or Gibbs-Thomson &kr) is due to a non- Increuse in sohrhi/ir 1’ h!, suhatrf&~r .~trucfurul

Kinetics of dissolution of oxides and silicates--II 1681

damage is difficult to quantify until domains of amorphous material are formed (note that as with tiny grains, the most soluble material controls the meta- stable solubility of the sample). Structurally closest to fused silica (cf. STEINIKE et al., 1979, or Part I), domains of amorphous silica produced by grinding should have a solubility within the range between the solubilities of precipitated amorphous silica and cris- tobalite; this gives a room-temperature enhancement of solubility of severely dry-ground quartz by at least a factor of 12 (cf. FOURNIER, 1973). Comparable solubility enhancements are to be expected in silicate samples in which domains of amorphous material have been produced. Evaluation of this effect in less severely deformed oxides and silicates is at present impossible, because it requires not only characterization of dislocation populations under abraded surfaces, but also determination of the unknown relation between the observed dislocation populations and the solubilities of oxides and silicates. The evidence reviewed in Part I (under Characterization of Ground Quartz) shows that subsurface structural damage is concentrated under abraded (as opposed to cleaved) surfaces and in particular in the finest size fractions, that it increases both with the increasingly severe grinding conditions and increasing grinding time, and that it is reduced by the cooling effect of water, acetone, etct. However, BERGMAN et al. (1%3X who have managed to free micrometer-size fragments of quartz ground under water almost entirely of the tiny fragments by prompt ultrasonic dispersion and repeated washing report no significant differences in “either easily soluble layer or disturbed layer” between samples contaminated with tiny fragments and samples free of them. Accordingly it appears that subsurface structural damage is a significant cause of solubility enhancement even in samples subjected only to moderate grinding.

The macroscopic rate constant k (mol m-’ &c- ‘) for dissolution can be expressed as the product of the surface density n* (mm2) of reaction sites (about which more below) and the single-site dissolution rate constant k* (mol set-‘)

k = n*k*. (6)

In dealing with the effects of mechanical comminution on k. the effects on n* and on k* can be sometimes separated.

Increase of rho macroscopic dissolurion rate canstant bJ the eflecr of grain size on the single-site dissolution rate constant was implicitly invoked by HOLDREN and BERNER (1979) when they argued that the calculated substantial increase in the solubility of their tiny feld-

t Compare the use of acetone to prevent solid-state transformations in mineral samples ground for powder X-ray diffractometry.

: Note that one is not dealing here with diffusion-controlled dissolution, in which dissolution rate is proportional to the difference between the solubility and the con- centration of the solute in the bulk solution.

spar fragments by the Kelvin effect implied a substantial increase in the rate constant for dissolution of these fragments:. There is no experimental evidence for this effect, but its relation to the Kelvin effect can be simply shown on the example of a solid that con- sists of one kind of atomic groups, transferable to the solution as entities (i.e. a solid such as quartz). Let the term ‘transfer-ready groups’ denote atomic groups that are located at reaction sites and are next in line for the transfer to the solution. Addition of one transfer-ready group in its lowest-freeenergy state to the solid increases the free energy of the solid more when that transfer-ready group is backed by a grain of a rather small radius R than when it is backed by a semi-infinite solid. Let that difference in Gibbs free energy G (J) per group be AG,i,(R). Hence the Kelvin effect

(7)

where k (J/K) is the Boltzmann constant. When the new transfer-ready group is added in the state that corresponds to the saddle-point in the free energy barrier that retains it in the solid, the free energy of the solid is also raised more if the group is backed by a grain of a rather small radius R than if it is backed by a semi-infinite solid. Let this difference in free energies with the representative point of the system at saddle point be AC,,(R). Then it follows from the transition state theory (VINEYARD, 1957; LAILXER, 1965, pp. M-90) that the single-site rate constant k* is higher when the grain has a rather small radius R than when the grain is semi-infinite by a factor

k*(R) w,) = exp

AC.,(R) - AG,i.(R)

k7 >- (‘3)

It follows that compared with the Kelvin effect, the increase in k* with decreasing grain size is a second- order effect. Since both AC,, and AG,i, are due to interaction over distances of tens of nanometers,

(AG,, - AC,,) cannot be expected to be as large as AC,,, and accordingly the relative increase in k* with decreasing grain size cannot be as large as the relative increase in solubility. Should [AC,,(R) - AC&R)] be equal to AG,,(R)/n, where n is a constant greater than unity, k*(R)/k*(co) would be equal to [sjR)/sfw)]““; but at this time even this cannot be ascertained.

Increase of the macroscopic dissolution rate constant by the e$ect ojsurface microreliefon the surface density of reaction sites

Reaction sites are sites from which ions or atomic groups of the solid can be immediately transferred to the solution. On low-index crystal faces, whether generated by growth or by cleavage fracture, surface density n* (m-‘) of such sites is low; these sites are kinks that move along the steps that sweep the retreating face (cf. BURTON et al., 1951). On irregular fracture surfaces, and in particular on abraded sur-

1682 RAD~MIR PEIX~VICH

faces. n* can be higher than in the preceding case by orders of magnitude, because a large fraction of surface ions or atomic groups may be exposed in such a way as to be immediately transferable to the solution. In the case of reaction-controlled dissolution these high n* values are ephemeral : as dissolution proceeds, the crystal/solution interface retreats faster in regions of higher n*. so that a set of low-index faces is gradu- ally developed (CL BERGMAN ef al., 1%2: HEIMANN

and WILLGALLIS. 1%9; HEIMANN et al., 1969; HEI- MANN, 1975, pp. 146-202). Accordingly, the macroscopic dissolution rate constant decreases rapidly with the approach towards the steady-state surface microrelief. and then more slowly with the approach towards a steady-state macrorelief. The effect of the changing microrelief on the macroscopic dissolution rate constant of ground oxides and silicates is obviously important, and probably dominant in the cases of lightly to moderately severely ground materials: the slower approach towards the steady- state macrorelief cannot affect the dissolution rate significantly when the thicknesses of equivalent dissolved layers are as small in comparison with grain sizes as in the experiments considered in this paper.

Increase of the macroscopic dissolution rate constant

by subsurface structural damage was first suggested as the explanation of the observed transient increase in the apparent dissolution rate constant k’ when it was thought that an amorphous Iaycr generally formed under the surface of ground quartz (GIBB et al.. 1953). ST~~BE~I and ARNOLD (1961). who attributed the enhanced solubility of ground quartz to the Kelvin effect caused by the presence of adhering submicrometer fragments, considered subsurface structural damage to be the probable cause of the transient enhancement of the apparent dissolution rate constant. HOLDREN and BERNER (1979). who attribute the transient enhancement of k’ entirely to adherent submicrometer fragments, consider subsurface structural damage a possible contributor to the enhancement of the dissolution rate constants of such fragments.

The effect of subsurface structural damage on the dissolution rate constant is directly demonstrable when the original crystalline solid has been in part transformed into amorphous state. SCHRADER and DUSDORF (1966) who used among the other methods of monitoring of the state of their vibration-milled quartz etching under standard conditions and for a standard time. found that the rather light etching with an HCI aqueous solution dissolved amounts of silica proportional to the sample surface area, but the more drastic etching with an HF aqueous solution removed quantitatively the amorphous material without affect- ing appreciably the remaining crystalline material.

Dislocattons in a crystal act during dissolution as sources of retreating steps: in the case of screw dislocations. spiral steps that rotate around the dislocation outcrop (cf. BURTON et (II.. 1951; HEIMANN, 1975, pp. 43-60). and in the case of edge dislocations, closed- contour steps nucleated at the dislocation outcrop

(CAFBRERA, 1956; SCHAARWACHTER. 1965: HEIMANN, 1975, pp. 43-60). The effect of dislocations on dissoiu- tion kinetics obviously depends not only on the surface densities of outcrops of dislocations of different types, but also on the availability of steps from other sources: it is maximal in the case of dissolution of a low-index face of large dimensions, and minimal in the case of an irregular surface with a sharp relief. However. even in the latter case if the face is under- lain by a dislocation network, the rate of approach towards the steady-state interface configuration will be affected by the dislocations.

Implications of the observed dependence of the apparent dissolution rate on the thickness of the equivalent dissolved disturbed /aver ‘* 1 z

As pointed out in Part I, eqn (1) formally describes the rate of dissolution of mechanically comminuted material as consisting of two contributions. a steady- state contribution & that corresponds to the steady- state surface configuration and a transient contribution A.& that is due to ‘disturbed maternal’ with whose disappearance steady state is reached. If all ‘disturbed material’ had uniform properties but were non-uniformly distributed. one would expect a linear decrease of the transient contribution with the increasing thickness <* of the equivalent dissolved disturbed layer, which is a measure of the dissolved amount of ‘disturbed material’. One observes instead an exponential decrease of A& with increasing <*. which corresponds to faster dissolution of the material that deviates more from the steady-state configuration. Once experimentally obtained. this result is intuitively obvious. At this time it is not clear whether it can be used to identify the dominant contribution, if one contribution is dominant, to the anomalous dissolution rate of ground quartz and siti- cates.

NATURAL MECHANICAL COMMINUTION AT THE EARTH’S SURFACE AND

ITS EFFECT ON THE KINETICS OF

MINERAL DISSOLUTION

An important question that was left unanswered until this point is whether mechanical comminution in certain natural settings produces significant amounts of material whose kinetics of dissolution in the same environment or after transport are significantly affected by that comminution. I shall discuss below the material from several environments on the Earth’s surface for which this appears to be true; but before turning to this material one should note that besides oxides and silicates other minerals. notably carbonates. undergo during mechanical comminution changes that must affect their dissolution behavior (cf. FRIES and MARHIC. 1973; MOMOTA et al., 1980). and that mechanical comminution obviously affects mineral dissolution in at least one other geological setting of importance. namely shear zones in the Earth’s crust (of. KERRICH et (I/.. 1980).

Kinetics of dissolution of oxides and silicates-II 1683

At present, glaciers supply about 7% of terrigenous sediment that reaches the sea (LISITSYN, 1978, p. 116). The shear at the glacier base causes abrasion of the glacier base by rock and mineral fragments in traction (B~ULTON, 1974), as well as the amply documented crushing and abrasion of these fragments (DRAKE, 1972; KRINSLEY and DCXXNKAMP. 1973, pp. 11-12 and 4450; KRINSLEY and SMALLEY, 1973; HAMMOND

et al., 1973; WHALLEY and KRINSLEY, 1974; BOULTON, 1978; FLAGEOLLET and VASZOU, 1979). Mechanical comminution under wet-based glaciers is comparable to grinding under water, while the more important comminution under dry-based glaciers is subject to the cooling effect but lacks the liquid phase needed for simultaneous dissolution. As a result. subglacial morraine material typically shows almost no signs of chemical weathering (LISITSYN, 1978, p. 118). Some lo-30% of such material consist of grains smaller than 1Opm (LISIIXYN, 1978, p. 117) and contribute to the extensive silty sediments of circumpolar seas (LISITSYN. 1978. pp. 122-130). The importance of mechanical comminution for the kinetics of dissolution of glacial material was recogneed more than a hundred years ago by DAUB&E (1867); in recent years it was investigated by HIJRD (1977) and by HURD

et al. (1979).

Fluviatile material

Abrasion of pebbles and larger clasts in high-gradient streams, which takes place by impact (KUENEN, 1956). certainly affects the rate of dissolution of the abraded material. Abrasion of sand-size and smaller grains transported by rivers is insignificant (KUENEN. 1959).

Marine material

Rocky coasts are eroded largely by the abrasion caused by impacts of boulders, pebbles, and coarse sand thrown at the rocks by the surf and dragged down the wave-cut platform on their return (BRAD-

LEY. 1958; DAVIES, 1977, pp. 78-99); the steady-state erosion rate is reached at an optimal abundance of such material in the surf zone (ESIN, 1980). In the same time, the coarser fragments thrown by the surf must suffer abrasion and the finer fragments crushing (cf. KUENEN, 1956). This obviously affects the subsequent dissolution of the shallow subsurface of the different clasts.

The rates of abrasion of rock and mineral ciasts transported in traction by moving water rapidly decrease with the decreasing clast mass, and good rounding of sand-size grains by currents of common river velocities would require transport over trajectories of hundreds of thousands of kilometers (TWEN-

HOFEL, 1945; KUENEN, 1959). Trajectories of adequate length obviously can be traversed by repeated for- ward and reverse transport under the action of tidal

currents of some epeiric seas and blys. because good rounding of not only quartz but also the chemically unstable feldspar is achieved in Recent coarse-grained sands of the Bay of Fundy (BALAZS and KLEIN, 1972) and was widespread in the Cambrian, Ordovician, Pennsylvanian-Permian, and Jurassic epeiric seas of eastern North America (ODOM, 1975; ODOM et al., 1976). It is obvious that the kinetics of feldspar dissolution under such conditions are strongly influenced by the rate of abrasion. The characteristic pattern of surface damage on quartz sand grains from high- energy coastal environments (KRINSLEY and D~ORN- KAMP, 1973, pp. 12-15 and 53-58) indicates that abrasion of sand grains takes place in a variety of such environments. The very fine-grained and to some extent structurally disturbed material abraded from quartz sand grains in the above coastal and epeiric environments probably dissolves to some extent because of its enhanced solubility.

Eolian material

The intense abrasion suffered by mineral surfaces exposed to wind-blown sand has been recognized for some time (e.g. TWENHOFU, 1945; WHITNEY and DIE- TRICH, 1973), but the intense structural damage suffered by the outer micrometer or two of the mineral grains under such surfaces was recognized only relatively recently (KRINSLEY and DOORNKAMP, 1973. pp. 15-17 and 6372; KALDI et al, 1978). These changes must strongly affect the kinetics of mineral dissolution in the highly saline solution films that adhere to exposed mineral grains after the infrequent rains. The fine fragments abraded from sand-size and coarser clasts and rock surfaces obviously contribute to the wind-blown mineral dust carried out of arid regions, which according to LISIEYN (1978, pp. 109-l 10) contributes more to pelagic sedimentation than the clas- tic material of fluviatile origin. The kinetics of dissolution of such micrometer-size material (LISITSYN, 1978, pp. 80-83)--calcite, quartz feldspar, etc. (Ltsrrs~, 1978, pp. 83-89)-must be strongly affected by the surface and subsurface properties which it has acquired during comminution.

CONCLUSIONS

The following conclusions can be drawn from the examined evidence :

1. The properties relevant to dissolution of rock- forming oxides and of rock-forming non-layer silicates are changed by mechanical comminution in essentially the same way as those of quartz. The changes are accomplished by brittle fracture under the tensile component of the stress field, which does not generate subsurface mechanical damage, and by microplastic behavior under local stresses with high net compressive and shear components, which does.

2. Mechanical comminution should therefore affect the apparent rates of dissolution of rock-forming oxides and of rock-forming non-layer silicates in

1684 RADOMIR PETROVICH

essentially the same way in which it affects the apparent rate of dissolution of quartz. At constant temperature, pressure, and activities of catalytically active dissolved species and large undersaturations with respect to the dissolving solid this implies a transient component of the apparent dissolution rate that decreases exponentially with the increasing thickness c* of the equivalent dissolved disturbed layer. This is supported by the available evidence on the dissolution of dry-ground feldspars and pyroxenes. The rate of release of adherent fine fragments of dry-ground minerals of the above groups from coarse fragments under the above conditions should show roughly the same dependence on {*: this is observed in dissolution of dry-ground feldspar and olivine.

3. Different effects of mechanical comminution on solubilities and dissolution rate constants can be related to certain measured or calculated properties of the considered minerals. Notably, the effect of grain size on the dissolution rate constant can be rigorously related to the Kelvin effect.

4. Mechanical comminution at the bases of dry- based glaciers, in high-gradient segments of streams, in certain high-energy coastal and epeiric environments, and in sandy deserts should significantly affect the simultaneous. or subsequent dissolution of the cornminuted material.

.&knowledgement--I thank the management of Phillips Petroleum Company for permitting me to publish this pap+=

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APPENDIX A. VERIFICATION OF THE CONSTANCY OF THE (dmddldtllj RATIO

AND OF THE INDEPENDENCE OF j FROM CHANGES IN SOLUTION

COMPOSTlION

Experiments of CLELLAND et al. (1952) wirh orthoclase

Approximating the composition of the orthoclase by KAISilOa and usina KHARAKA and BARNES’S (1973) SOLMNEQ program-for calculation of mineral-solution equilibria. one finds that if the orthoclase had been dissolving congruently, the solution would have become substan- tially supersaturated with respect to both muscovite and phillipsite (with ionic activity quotient/equilibrium constant ratios equal to 7 x lo5 and 4 x lo’, respectively) already at mss,ol = 0.01 mmoI/kg. Therefore during almost the entire length of each dissolution step orthoclase must have dissolved incongruently in accordance with a relation

f686 RAWMIR PEWOVICH

such as

KAISi308 ,“,, + 0.74 H&, + 3.56 H1O,,, +

0.37 Ko.~~A1,.~,Si~.~,Q1~(QH)2,,,,

f 0.74 K,“,, + 1.78 H4Si04,.q, (A.1)

(cf. BUSENBERG and CLE-CY, 1976; PETROVIC, 1976a). Note that dm,,‘dt is proportional to the apparent dissolution rate whether mCIDl includes only the dissolved silica or also includes precipitate particles that remain in the decanted solution and are redissolved at the low pH of complexing with molybdate. It is easily shown, using the SOLMNEQ program and considering the reduction in mZAI that takes place with incongruent dissolution of the inferred type, that equilibrium with respect to the dissoiv- ing orthoclase could not have been approached even at the highest observed ntssios,.

Experiments of WOLLAST (1967) and of HOLDREN and BERNER (1967) with alkaiifeldspars at pN 6.0

Numerical modeling of the evolution of a closed system consisting of pure maximum microcline and WOLLAST’S (1967) pH 6.0 solution at 2% (done using ULBIU~H and MERINO’S (1974) Set I muscovite free. energy, for consist- ency with BU+ENBERG and CLE~~~NCY’S (1976) experimental results) indicates the following sequence: first congruent dksolution until rnmol = 0.01 junoljkg then incongruent dissolution with precipitation of gibbsite until msiO 2 = l.t~mol/l~g, finally incongruent dissolution with pr~ip~tation of muscovite until equilibrium with microcline is reached at msio, = 0.72 mmoI/kg. Actuilly an iltite would have been precipitating instead of muscovite, in accordance with eqn (A.l), but dmoio,/dt would still have been proportional to the apparent dissolution rate over the entire range of measurable mgio,. Comparing the composition of Wollast’s solution (0.050 M K-biphthalate,

0.0454 M NaOH) with that of Hoidren and Berner’s soi- ution (0.050 M K-biphthalate, 0.0454 M KOH), one can see that over the range of measurable mPiOt dissolution of Holdren and Berner’s alblte at pH 6.0 must also have been accompanied by precipitation of illite. with dmsio,idt proportional to the apparent dissolution rate

NaA&Os,,,, + 0.74H&, f 0.26K,:,, t 3s6rit0,,, -.

0.37Ko.~A1~ vS~> &to(OH)~,,,, + Na&,

f 1.78 H,SiO,,,,, (A.2)

The post-steady-stare decrease in the apparent dissolution rate is observed only in the late stage of dissolution of OF@).

GRANDSTAFF‘S (IYE’) experiment F3

The plot in Fig. 8, which was recalculated to a constant solid/solution ratio. shows after the first five hours of dissolution net addition of magnesium and silicon at a steady molar ratio of 1.26 untii this ratio is suddenly changed to 2.35 after 147 hr of dissolution; whether this change is due to an error in the [Si] value or the onset of ~ecip~tation of a new phase cannot be determined. The Mg/Si ratio of 1.26 is close to 1.33, the value that corresponds to stoichio- metric dissolution of GrandstafT’s bronzite with precipitation of pure ferripyrophyllite

Z/lg,.--Fe~,l,Ca,,,,SIO,,,,, + I.58 H,:,,

f 0.475 H20,,, t 0.052 O2 ($, --+

0.105 Fe2Si*0,010H)1 flPY, c 0.77 M&i;,

+ O.O2Ca$ + 0.58 H+SiO,,,,,. (A.3)

pH remains constant throughout the experiment.

kinetics of dissolution of mechanically comminuted rock-forming oxides and silicates—ii....

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