Kinetics of dissolution of mechanically comminuted rock-forming oxides and silicates—I. Deformation and dissolution of quartz under laboratory conditions

Grorhtmacu PI Cormorhamks Aclu Vol. 45. pp 1665 lo 1674. 1981 Printed WI Great Britaw. All rqhts reserved

W16-7037’81 101665.IOM2OC:O CopyrIght C 1981 Per&wnon Press Lid

Kinetics of dissolution of mechanically cornminuted rock-forming oxides and silicates-I. Deformation and dissolution of quartz under laboratory conditions RADOMWPETROVICH Research & Development Department, Phillips Petroleum Company, Bartlesville. OK 74004, U.S.A. (Receired 27 February 1979; accepred in

reckedform

29 April

1981)

Abstract-The extensive evidence on the properties of ground quartz such as grain morphology and adherena and subsurface structural damage shows a consistent pattern, interpretable in terms of the competing processes of fracture and of local plastic deformation. The welldocumented pattern of dissolution of ground quartz in aqueous solutions is also consistent. At large undersaturations and constant other environmental variables. the apparent dissolution rate of ground quartz decreases exponentially with the increasing thickness of the equivalent dissolved disturbed layer, and the rate of release of adherent tiny fragments shows roughly the same dependence on the latter. At small undersaturations distribution of solubilities also needs to be considered.

INTRODUCTION

dence. This evidence is not only scattered through the largely non-geochemical literature; it also consists of THE RELATIONbetween mechanical deformation and data that usually cover only one aspect of a complex dissolution kinetics falls between well-established problem and accordingly have to be fitted together fields of geological inquiry. Consequently, mechanical like the pieces of a puzzle. This is done in the present comminution is usually considered by geochemists paper and its sequel by first examining the physical only as a process that changes interface areas. The properties and dissolution behavior of the extensively anomalies in the kinetics of dissolution of quartz that studied ground quartz then identifying the factors are caused by grinding were recognized by the early that determine the response of oxides and silicates to fifties (CLELLANDer al., 1952), and the use of etched grinding, and finally applying the acquired insight to quartz in dissolution experiments to eliminate such anomalies started twenty years ago (VAN LIER et al., the interpretation of the evidence on the effect of 1961). Yet the analogous anomalies in the kinetics of grinding on dissolution of silicates. The effort is justidissolution of ground silicates were not recognized as fied by the fact that a self-consistent pattern does emerge. such until the mid-seventies (F%TROVI~, 1976), and the Mechanical properties and dissolution behavior of parabolic kinetics of dissolution of feldspars and oliground quartz are examined in the present paper; the vines, actually caused by grinding were in the meangeneral pattern of deformation of rock-forming oxides time among the mainstays of the then fluorishing and silicates during mechanical comminution and the theories of diffusion-controlled dissolution of silicates. dissolution behavior of these minerals after such By now ample evidence has been presented for the parabolic dissolution kinetics of feldspars and oli- comminution are examined in its sequel (pEr~ov~~, 1981-herein referred to as Part II). Mechanical vines, as well as the parabolic release of silica during comminution of mineral grains in different environdissolution of pyroxenes and amphiboles, as artifacts caused by grinding (PErrtovrC et al., 1976; HOLDREN ments on the Earth’s surface and the implications of this comminution for simultaneous or subsequent disand BERNER,1979; BEWER er al., 1980; GRANDSTAFF, solution of its products, which by themselves make 1980). This raises the question of the future use of the the relation between deformation and dissolution bulk of the available evidence on the kinetics of silirelevant to geochemistry, are discussed in Part II. cate dissolution, obtained in experiments with ground but not etched solids. Should such experiments just be ignored as superseded, or should the information on CHARACTRRIZATION OF GROUND QUARTZ dissolution rates and mechanisms contained in their The following properties of ground quartz that are releresults be separated from artifacts of sample prepvant to its dissolution behavior will be considered here: (1) aration and put to good use? In my opinion. the the chemistry of its surface: (2) the shapes and microrelief second course is much more reasonable. Hence this of quartz fragments: (3) grain-size distributions of samples subjected to separation: (4) mutual adherence of quartz attempt to describe quantitatively and to understand the effect of grinding on the kinetics of dissolution of fragments. and (5) subsurface structural damage inflicted by grinding. These properties are functions of the mechrock-forming oxides and silicates. anics. chemical environment. and duration of grinding The approach adopted in this paper is that of critiwhich have to be explicitly considered when interpreting cal analysis of the already available experimental evithe experimental evidence. Note that dry grinding implies 1665

RADOMIR FTTROVICH

1666 in this paper. as usually. exposure its moisture.

to atmospheric

air with

Room-temperature crushing of quartz under high vacuum (lo-’ Pa and below) produces surfaces at which the silicon-oxygen tetrahedra have so tilted that almost all broken Si-0 bonds have been reconstituted into new strained bonds, only about 1”” of silicon atoms in the surface tetrahedra possessing a dangling sp3 orbital with an unpaired electron or carrying an oxygen atom with seven electrons in its outer shell (HOCHURASSER and ANTONINI, 1972: RADTSIG and BYSTRIKOV. 1978). However. the surface of quartz exposed during the fracture to liquid water or to atmospheric air with its moisture is hydroxylated, the hydroxyl ions completing the tetrahedra that had lost by fracture an oxygen atom or the connection with a further silicon atom (ST~BER. 1956: GALLEI. 1973). Gruin

shupes

und microrelief’

ST~BER

and ARNOLD’S (1961) micrometer-size quartz fragments, separated from quartz samples dry-tumbled for a week in a rubber-coated container. were angular and bounded by conchoidal fractures: blade-like edges were common and even awl-like points occurred. On the other hand, the micrometer to tenth-of-micrometer stze fragments separated by SAKABE rt al. (1960) from quartz samples subjected to dry mortar-and-pestle grinding for 2 min to 24 hr showed marked changes of shapes with time. from angular and often flaky shapes to well-rounded ones. Obviously the shapes of fragments are determined by competing processes of macroscopic fracture (splitting, crushing) and of abrasion. Micrometer-size quartz fragments produced by moderately long mortar-and-pestle grinding under water have angular shapes dominated by conchoidal and possibly cleavage fractures. similar to those of quartz fragments obtained by moderately long dry mortar-and-pestle grindmg (BERGMAN et al., 1962, 1963). Gram-size

distributions

und mutuul

udherencr

o/fragments

They are most conveniently treated together. because the former is affected by the latter. Silica fragments 0.01-0.1 pm across (herein: tmy fragments) of unidentified structure were sttcking even after repeated sedimentation to micrometer-size quartz fragments obtained by ST~BER and ARNOLD (1961) by dry-tumbling in a rubber-coated container, to micrometer-size quartz fragments obtained by BERGMAN et ul. (1963) by dry mortar-and-pestle grinding, and to tenth-of-micrometer size quartz fragments obtained by S&ER (1967) by dry ball-milling. However. BERGMAN ct ul. (1963) found that if they ground a quartz sample under water and elutriated it immediately after grinding. relatively few tiny fragments were sticking on their micrometer-size fragments. The phenomenon was extensively studied by REBINDER and KHODAKOV (1962). who vibration milled quartz for tens of minutes under standardized mechamcal conditions but immersed in different liquids or atmospheric air. When vibration milling under water gave a certain ?&, r (mean grain size calculated from low-temperature gas adsorption). vibration milling for the same time under acetone. benzene. or ethanol gave a rather larger ZRk,-r. and dry-vibration millin&for the same time gave an even larger ZR,,, r. Moreover, 2RHi. r of the material ground under acetone. benzene. or ethanol could be reduced by It.&30sec of vibration milling under water to the mk,.r that would have been obtained if all grinding had been done under water. but this treatment could not bring&r of dry-ground material even close to the latter: also the decrease in zk,r of quartz subjected to dry vtbration milling becomes conspicuously slow onIy after the atmospheric moisture is consumed on newly created surfaces. Considered together with the evidence on the surface

chemistry of ground quartz, these data suggest that the mutual adherence of quartz fragments IS caused by reconstitution of some broken Si-0 bonds across grain-to-grain contacts, which is impeded by the presence of solvent molecules and prevented by prompt hydroxylation. Mutual adherence of quartz fragments ground under water but left immersed in it for some time (BERGMAN er ~1.. 19631 is probably due to Si-0 bonds established by precipttatton of silica from the solution. supersaturated because of grinding (see below,. Subsurface

structural

damage

Five percent of E’ paramagnetic centers (unpaired eiectrons in dangling sp’ orbitals of silicon atoms bonded to only three oxygen atoms) obtained by HOCHSTRASSER and ANTONINI (19721 by room-temperature. high-vacuum crushing of quartz were inaccessible to CO2 molecules; the corresponding broken Si-0 bonds in the interior of quartz fragments had to be located along dislocations and or leading edges of cracks. The case for an amorphous layer under the surface of quartz fragments subJected to moderately long mortar-and-pestle gsinding was destroyed by TALBOT and KEMPIS (1960). but SAKABE et al. (1960) have shown that during protracted mortar-and-pestle grinding of quartz submicroscoptc fragments acquire a fraction of amorphous silica that increases both with the grmding time and with the decreasing grain size at constant grmding time. In a detarled study of dry vibration mtlling of initially micrometer-size quartz fragments. SCHRADER and DUSDORF (1966) found that from the beginning of milling lattice strain (as manifested by differential changes in X-ray diffraction peak intensities) increased and the size of diffracting crystal domains (as manifested by peak broadening) decreased. During the first few hours both lattice strain and the amount of produced amorphous silica increased approximately proportionally to the increase in the low-temperature-gas-adsorption surface area of the sample; with further milling the amount of amorphous silica continued its steady increase although the increase in the surface area became much slower (cf. the results of REBINDER and KHODAK~V). The amorphous silica produced by vibration milling of quartz under atmospheric air or an inert gas contains appreciable concentrations of subsurface paramagnetic centers indicative of broken St-0 bonds (VOLAND er ul.. 1969: JEDAMZIK et ul.. 1980). but it preserves to a large extent the short-range order characteristic of quartz (STEINIKE et al.. 1979). In other words. the transformation of quartz mto amorphous silica caused by vibration milling takes place by an excessive proliferation of dislocations, and implies a gradual buildup of dislocations by localized plastic behavior (microplastic behavior). When SCHRADER and DUDORF (1966) repeated the described vibtatton-mtlling experiments with a quartz-water slurry. the mean lattice strain at first increased with time but then levelled off and no amorphous material was detectable. Similarly. STEER and FUERSTENAU (1976) found that comminution of quartz fragments is faster. but lattice strains are lower, when vibration milling is done with water-wetted quartz. These results are consistent with the expected cooling and bond-breaking effects of water (see Part II). It can be seen from the evidence presented here that yrinding qf‘quurt-_. whether with u morrar und pestle or m u rihrution mill. (‘~ii he resolrrrl into u multlrudr o/ mdictdurtl PI c11i3 helonyiny to two comperrny processes. I, Fructuru under the tensile component qf’thr .srrcss ut the truck tip. wfhich in its pure form produces angular fragments without significant subsurface damage (cf. YASHIMA 1’1(I/.. 1979; LAWN et d., 19801. and whl& occur.5 within plustrc de~ormution. 2. Loculi:ed domuin.5 suhjrctrd to whstantiul ~vmpres.~iw und .&rrr 5tres.s hl. creutiorl und motcon of disloc~atiorrs and accordingly

Kinetics of dissolution of oxides and silicates-I results in si~ifi~nt subsurface structural damage (cf. LAWN et Of., 1980). The character of fragments obtained in a given grinding time reflects the changes in the relative importance of the two processes with the time and with the grain size at constant time; but note that these changes depend both on the severity of grinding and on the fluid surrounding the fragments, if there is one. KINETIC!3 OF DlSSOLUTlON OF GROUND QUARTZ TWO types of dissolution experiments are considered here: (1) closed-system dissolution experiments, in which the solid is exposed to the same

volume of solution throughout the experiment, and (2) stepwise dissolution experiments, in which the solid sample is repeatedly exposed to identical volumes of solution. Dissolution experiments with ground quartz considered in this paper were ail done at constant temperature and pressure and constant activities of water and of dissolved species other than the sihcic acid or fhrosihcic acid molecules and ions. The measured dissolution rates are apparent dissoiution rates J’, obtained by dividing the rate of transfer of silica across the solid/solution interface by the measured or estimated initial surface area of the totaffy immersed sohd sample. Even given an accurate knowkdge of the initial surface area, y need not be equal to the actual dissolution rate; where the surface area of a ground quartz or silicate sample was followed during dissolution, it changed appreciably even when judging from the dissolved fraction of the sampie it should not have done so (BERGMAN et al., 1962; GRANDSTAFF,1978). Quartz dissolves in fluoride-free acid to neutral aqueous solutions according to the relation SiOzt9, + 2HtOtt) * H*SiOl(,,,

(1)

(STUMMand MORGAN, 1970, pp. 395-396). If the temperature, pressure, activities of water and of dissolved species other than the silicic acid molecules and ions, and the surface morphology (macroscopic and microscopic) of quartz grains are constant, the actual mean dissolution rate f (mol m-* set-‘) can be written as f = f; - &zu&o*

(21

where x (mol me2 set- ‘) is the rate constant for the transfer of SiOl units from the solid to the solution, set- r) is the rate constant for the return E(molm-* of SiOz units from the solution to the solid, and aruSiO( the nondimensional molar activity of H&Oh molecules in solution. At equilibrium f is equal to zero; therefore the above relation can be also written as f = k(l - ~H~SrO*/&z3iOJ

(3)

where k (no1 m- * set- ’ ) is the macroscopic rate constant for quartz dissolution and is identical to E, and &&SO, is the equilibrium value of OuIstcI.

1667

DOWNSet al. (1976) have ex~rimenta~ly demonstrated the validity of eqn (3) under the stated conditions; the deviation from this relation in the initial stage of their experiments is easily understood as due to the use of ground samples (see below). If the grains of which the sample consists have nonuniform dissolution properties, eqn (3) obviously cannot provide an adequate description of the apparent dissolution rate. The material exposed to the solution at different elements of the interface can differ in several properties, each of which inthrences the local dissolution rate: crystallographic orientation of the interface element, initial microrelief, and the character, distribution, and density of dislocations that reach the interface. For simplicity, consider a sample in which a single parameter x determines all local dissolution properties. By analogy with eqn (3), the apparent mean dissolution rate j’ (mol m-* set- *) can be written as f’=

l& a@;S)b,&f f

(

f - -%SiO,W asio,(X) >

dX

(41

where A0 (m’) is the initial area of the solid/solution interface; < (m) is the apparent mean distance of retreat of the ~iid/~iution interface, defined as the ratio of the volume of solid dissolved by the considered time and the area Ae; a(x;C) is dA/dx at the time when 4 has the indicated value, A being the solid/solution interface area at that time; OH&to,(<)is the value of enSfOI that is reached when 1: reaches its indicated value; &&to,(x) is the value of anLio, that corresponds to equilibrium (in general metastable) with the solid of the indicated value of x: k,,+.(X) (moi m-’ set- ‘f stands for the rate constant for dissolution when ausio,(~) < ~~,s~o~~~)and for the rate constant for growth (not necessarily identical to the former) when ~,,,s~,(s) > Up’ic,k)t both for material of the indicated value of x. The progress of dissolution, expressed through <. affects 5’ in two ways: through the change in the grains themselves, expressed by ab: 51, and through the change in au.sio,. which affects both the sign and the magnitude of the factor in brackets (the change in sign of this factor with the change in cu,sron corresponds to the change from dis~~ution of the more solubte grains or parts of grains to growth of the less soluble ones). In the present context the critical issue is the shape of a(X; <); therefore the present discussion can be limited to the case of dissolution far from saturation, when eqn (4) is reduced to

where kfX) is the rate constant for dissolution. If under these conditions there exists a steady-state limit

where < -+ 00 should be taken in the microscopic

RAIXMIRF’ETR~VICH

1668

sense (obviously such a limit cannot exist once < begins to approach the mean radius of the dissolving grains). eqn (51 can be written as

= jls + A&(;)

(7)

i.e. as a sum of a steady-state term that corresponds to dissolution of material of uniform properties at an interface of effectively constant relief and a transient term due to deviations in surface area. microrelief. and mechanical state of some or all of the material exposed in the early stage of dissolution from the steady-state surface area. microrelief. and mechanical state. In closed-system dissolution experiments with ground samples of quartz or of other polymorphs of silica. the variable followed as a function of time t (set) is usually the molality mBiOL (mol SiO,;kg H20) of the total dissolved silica, occasionally the dissolved fraction fdipr of the starting solid sample. Figure I shows mrsio,(t) curves obtained by STABBERand ARNOLD (1961) in three successive dissolution experiments with the same sample of dry-ground quartz (obtained by tumbling in a rubber-coated ball mill without balls) of gas-adsorption mean grain size of 0.25 pm; the experiments were done at room temperature, with a NaCI-NaHC03 aqueous solution of pH 8.3. It can be seen that in each experiment a stage of pre-steady-state dissolution. in which the initially high dissolution rate gradually decreases. abruptly passes into a steady-state stage. The extent to which the

sample dissolves differently from a sample of the same nominal surface area that has from the beginning the steady-state surface area. microrelief, and mechanical state can be conveniently expressed by the thickness & (m) of the equivalent disturbed layer and the shape of the pre-steady-state curve. The equivalent disturbed layer is defined here as a uniformly thick layer, of surface area equal to the initial surface area of the totally immersed solid sample and of density equal to that of the undisturbed solid, whose dissolution would produce the observed msio,-intercept or f,,,,-intercept of the steady-state asymptote to the msio:(t) or f;i,,lt) curve; the shapes of pre-steadystate curves are treated below. Having reached a steady-state configuration in one experiment. the sample passes again through a pre-steady-state stage in the next. This shows that the dissolving grains had formed aggregates that survived the slow rolling around to which they were exposed during the dissolutidn experiments, but were in part disrupted by the centrifuging by which they were separated from the solution after the first and the second dissolution experiment. Somefdi.,(t) curves obtained by BERGMAN(1962) in closed-system dissolution experiments with micrometer-size fragments of quartz. tridymite, and cristobalite and an HF aqueous solution are shown in Fig. 2. The shape of the curves is the same as in Fig. 1. although the mean grain size is about three times as large and, more importantly, the solids were prepared by grinding under water. That quartz fragments up to about 0.1 pm across. and in the case of thin flakes up to several tenths of a

Fig. 1. mZSIOl as a function of time in three closed-system dissolution experiments of ST~BER and ARNOLD (19611. done at room temperature with the same sample of dry-ground quartz of gas-adsorption mean grain size of 0.25 pm. exposed successively to three volumes of a 0.9”” NaCIkO.I”, NaHCO, aqueous solution of pH 8.3. The shapes of the curves are given hy eqn (15).

Kinetics of dissolution of oxides and silicates--l micrometer across. can remain in colloidal suspension even after centrifuging for 30 min at 3C00 rpm was shown by SAKABE et al. (1958). Progressive release of such material. originally attached to the selected size fraction of ground quartz, was followed by CLELLAND et al. (1952) in a series of stepn+sr dissolutiort exprriments with dry-ground rock crystal and with asreceived quartz sand of Cretaceous age. in which the coarse fraction (grain sizes of the order of 1OOpm) was separated from the solution after each dissolution step by apparently brief sedimentation (‘all dusts used settled completely in less than one minute’-CLELLAND et al.. 1952, p. 32). Figure 3a shows the cummulative release of dissolved (molybdate-reactive) silica in two series of these experiments; note that the solubility of quartz under the conditions in question is 0.15mmoUkg HZ0 (FOURNIER.1973). so saturation with respect to quartz was not approached in individual dissolution steps. The obtained Xmrsio,.i vs time plots are strikingly similar to theSdir, vs r and mrsiol vs t plots obtained in closed-system dissolution experiments. Figure 3b shows the corresponding plots of cummulative release of suspended particulate silica (operationally defined as the difference between the total silica in the supernatant solution and the molybdate-reactive silica). expressed as the sum of virtual molalities m&>,,, as a function of time. The rate of release of particulate silica is comparable to the rate of dissolution, and roughly proportional to it, until most of the disturbed material is gone.

The dependence

1669

of the apparent

dissolurion

rate on

is implied in the above plots, the amount of silica transferred to the solution being proportional to <. However. this dependence is more directly given by .? vs < plots obtained in stepwise dissolution experiments with ground quartz. Such plots were first obtained by SAK.-BE et al. (1960). but BAUMANN'S (1971 I plots, obtained with micrometer- and submicrometer-size quartz fragments. define the relation between .? and < much more precisely are the only ones considered here. In Baumann’s experiments, as in those of SAKABEet al. (1960), the solids were separated from the supernatant solution after each dissolution step by centrifuging. Baumann does not give the duration and rotation rate of centrifuging, and in view of the results of SAKABE ef al. (1958) colloidal fragments may have been present in his solutions and given a post-separation contribution to the dissolved silica. Figure 4 shows the results of Baumann’s experiments with some asreceived quartz dust; it can be seen that if one introduces the thickness S* of the equivalent dissolved disturbed layer, the thickness qfthe

equivalent

s*

4

c

f

.

dissolved layer

kA,, P -

-----Z

t.

(8)

Ao

where A,(m’) is the steady-state interface area and pq (m3 mol-‘) is molar volume of quart& the dependence of j’ on <* is closely approximated by

03 I

Fig. 2. Dissolved fractions of ground silica samples as functions of time in three closed-system dissolution experiments of BERGMAN (1962), done at 25’C with silica polymorphs ground under water and with 0.1 M hydrofluoric acid. Starting solids of Stokes diameters between 0.5 and l.Opm. The shapes of curves are given by eqn (15).

1670

RAWMIR

F~~ovrcn

t , days

ib)

I

L

i

i

20

40

h

i

60

?,daYS Fig. 3. la) Wsioi., as a function of time. and (b) Em&i,, as a function of tune. m two series of stepwise dissolution experiments of CLELLAND cr ul.(1952). done at 37’C with dry-ground rock crystal (rc) and as-received Lochaline quartz sand (tst and an H,BO,-Na,BO, aqueous solution of pH 7.5. Microscopically determined mean grain sizes m the lGO-4GO/lrn range. free particles smaller than 5Opm were removed by repeated sedimentation. Separation of solids between dissolution steps also done by sedimentation. The shapes of curves given by eqn (I 5).

the relation

3’ = kA,,;&

J’ = k/4,, ,‘&)

+ (~~i,k4,,‘.4,)exp(-;*

>.d)

for ;* ,< Ld

(9a)

for i” > Ld

(9b)

where the constants xJ and i., (m) depend only on the quartz sample. and L, is, as before. thickness of

the equivalent disturbed layer. The results plotted in Fig. 5 were obtained by Baumann with quartz samples prepared by ball milling of a quartz-water slurry in an agare ball mill. The dependence of J’ on 2:* is again approximated by the relation (9). but as steady state is approached J’ does not decrease with increasing < nearly as rapidly as in the preceding case. For closed-system dissolution in a solurion that initially contained no dissolved sitica. the reduced moia-

Kinetics of dissolution of oxides and silicates-l

1671

*I 0

to5

t

Fag I 8 0

-0.5

-c-----

.----------_----------~~

I

I

/

I

2

3

Cnm

Fig. 4. Log @,/j:.) as a function of i in a stepwise dissolution experiment of BAUMANN (1971). done at room temperature with a sample of as-received quartz dust and an aqueous solution of pyrocatechol of pH 8.5. Initial mean diameter of quartz grains calculated from the specific surface area was equal to 0.19 m: separation of solids between dissolution steps was done by centrifuging.

Fig. 5. Log(df,,Jdt) as a function offdiSS in five stepwise dissolution experiments of BAUMANN (1971), done at room temperature with different quartz samples and a 0.1 M NaCI aqueous solution. Mean grain size of the reference material was apparently 2pm: the other starting solids were obtained by b~i-milting of the reference material in the presence of water in an agate bat1 mill for the indicated times. Note that at constant y, df.,Jdt increases with increasing ball-milling time because of the increasing surface area.

1672

RADOMIR

lity t&o, of total dissolved silica, defined as the contribution of ‘disturbed’ material to the total molality of dissolved silica, is equal to n&o, = mrsio, - rkPl,, M,JJ)~

(IO)

where MHO (kg) is the mass of water in the solution. Under these conditions (11) and m&o,

(12)

= C(pgrlo)i(MSiO,MH,O)l~*

FTTROVICH

(t. Xtn& !,,I points in Fig. 3. Excellent fit is obtained with both sets of pomts for the as-received Lochaline sand and wtth the It. &I~,~,.,) set for the dry-ground rock crystal, but the (r,Xn~&&~,~) set for the latter materiai is fitted only approximately. the rate of release of particulate silica from that material decreasing slower than predicted as the steady state is approached. Note that exact correspondence between the curves for dissolution and for release of particulate matter both in shape and in the factor multiplying time in the logarithmic term would imply that

(16) +A,., = const:mrsio,,,. where pq (kg m- 3, is density of quartz and !astlslol (kg mol - t) is molar mass of silica. Substituting eqns In closed-s~~cern di.~~lution rxperiments with ground (9a). (10) and (12) in eqn (11).one obtains the relation quartz in which .~atururion bvith respect to disturbed materiul is upprouchrd. still at constant temperature. fiSiO~MM* m&o1 dm&io, = he dt. (13) pressure. and activities of water and of dissolved speev cies other than stlicic acid molecules and ions. the Pq&.40 nzo dependence of mSiO, on time is a function of the relaIntegrating and using the initial condition that tive rates at which the disturbed material is being m&io, = 0 when I = 0. one obtains the relation used up and saturation is being approached. If the / available disturbed material is used up before the pqndAo ln( 1 + (14) approach to saturation seriously affects the mean dis4ssi0z = fiSiO~MH~Cl ‘_ solution rate. as in the experiments of DOWNSet al. (1976), the mrSiO,(t)curve can be approximated by the and using eqn (10) and the relation between the relation steady-state value of the apparent dissolution rate constant k;, and the actual dissolution rate constant k. k;, = kA,,,‘Ao. ?q&Ao

lnjl+ mzSio2= fisio2!14H:0 ,

Kdk;r.tiSiO

Pq4

2t

’ ,

for f < tt, (15a)

mrsio

2

=

mrsio,(tL)

+

k;,clo (t - tL) MH:O

for t > tL (15b) where tL is the time at which 5” reaches Ld. Equation (15) can be conveniently titted to sets of (f. mLSiOI) data points by interpolating into such sets two points of which the second has an m&,,,-value twice as high as that of the first (Appendix A). The mrsio2(t) curve for dry-ground quartz in Fig. 1 was fitted in this way, using for the steady-state slope the slope of the mrsio,(r) curve after eight or ten days (visually estimated). Using the relation .fdirs = m’sioLMsio~QHdQSOio:.where Q” (kg is the initial amount of soiid silica in the system, eqn (15) can be also used for fitting pre-steady-state segments of fdis,(r) curves obtained in closed-system dissolution; this was done with the three sets of experimental points in Fig. 2. It can be seen that eqn (15) predicts both the shapes of the pre-steady-state segments of mato, andfdi,,(t) curves and the breaks in slopes of jdi,,(t) curves that occur at the transition to steadystate dissolution. Curves of the shape given by eqn (15) were also used to fit the sets of experimental (r. Esio,.,) and

where tr&,or corresponds to equilibrium with undisturbed quartz. However. if the mean dissolution rate IS appreciably decreased by the approach to saturation before the supply of disturbed material is exhausted. as in some experiments of VAN LIER et al. (l!%O), ST&ER and ARNOLDI1961 ). and ST~~BER (1967). description of dissolution kinetics requires the use of the complete eqn (4). The kinetics of dissolution of ground quartz under such conditions will not be discussed here. but one of their aspects should be mentioned. Although the disturbed material on or under the surface of the average quartz fragment does not form a continuous layer. well defined apparent solubilities up to 14 times as high as the solubility of well crystallized quartz have been observed (VAS LIER et al.. 1960; ST~BERand ARNOLD.1961; ST~BER. 1967). This indicates low rate constants for growth on undisturbed and slightly disturbed quartz surfaces, in agreement with the evidence that at low temperatures quartz can be grown only at relatively low supersaturations (MACKENZIEand GEES. 1971). tts surface becoming covered with amorphous silica at high supersaturations (ST~~BER. 1967: BAUMASX.1971). CONCLUSIONS The considered evidence on the surface chemistry, grain morphology. mutual adherence of grains. and subsurface structural damage of ground quartz forms a consistent pattern. interpretable in terms of the

Kinetics of dissolution of oxides and silicates--l

competing processes of fracture and of local plastic deformation. The evidence on the kinetics of dissolution of ground quartz in aqueous solutions also shows a consistent pattern. At large undersaturations and constant other environmental variables, the apparent rate of dissolution of ground quartz decreases exponentially with the increasing thickness of the equivalent dissolved disturbed layer, and the rate of release of adherent tiny fragments shows roughly the same dependence on the latter. At small undersaturations prediction of the kinetics of dissolution of ground quartz requires consideration of the distribution of solubilities.

Acknowledgement-I thank the management of Phillips Petroleum Company for permitting me lo publish this paper.

REFERENCES

BAUMANN H. (1971) Herstellung reiner und gestiirter Quarzoberflkhen und ihr Verhalten nach unterschiedlicher Behandlung. Forrscljrirrsber. Kolloide Poly. 55, 37-44. BERGMAN I. (1962) Silica powders of respirable size. II. Dissolution rates in dilute hydrofluoric acid. J. Appl. Chem. 12, 336-341. BERGMAN 1.. CARTWRIGHT J. and BENTLEYR. A. (1962) A mechanism for the dissolution of ground quartz powders in dilute hydrofluoric acid: an ‘easily soluble’ core and its relation to the ‘easily soluble layer’. Nature 1%. 248-250. BERGMAN1.. CARTWRIGHT J. and CASSWELLC. (1963) The disturbed layer on ground quartz powders of respirable size. Br. J. Appl. Phys. 14, 399-401.

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A. CURVE

FITTING

In fitting a curve of the shape

m = aln(1 + br) + cr

IA.1)

RAOOWR&lROVICH

1674

one needs first to determine the slope of the baseline m’ = cr. Then defining m” by the relation m” I m - kt, one has to determine the parameters of the curve m” = aln(l

+ br).

(A.3

Choosmg two values of m”, namely m; and m’;. such that my = 2m; and both m’; and m; can be determined with a

reasonable accuracy, one can obtain a and b from the relations 11 - 3, b=--it1

‘=

m; InIl + br,)’

L4.3) (A.41