Ostwald Ripening and Interparticle-Diffraction Effects for Illite Crystals

American Mineralogist, Volume 73, pages 1335-1345, 1988

Ostwald ripening and interparticle-diffraction effects for illite crystals

DnNNrs D. ErBnr, U.S. Geological Survey, Federal Center, Mail Stop 404, Denver, Colorado 80225, U.S.A. J.q.NSnoooN Institute of Geological Sciences,Polish Academy of Sciences,3 I -002 Krak6w, Senacka3, Poland

Ansrnncr The Warren-Averbach method, an X-ray ditrraction (xno) method used to measure mean particle thicknessand particle-thicknessdistribution, is usedto restudy sericite from the Silverton caldera. Relative mean particle thicknessesdetermined by this method for the Silverton illites correlate well with cation-exchangecapacity, with fixed interlayer chemistry, with an xRD intensity ratio, with the wave number of a 824-834 cm-' infrared absorption band, with the Kubler index, and with the apparent K-Ar agefor the samples. Apparent particle-thicknessdistributions indicate that the clays may have undergoneOst- wald ripening and that this process has modified the K-Ar ages of the samples. The mechanism of Ostwald ripening can account for many of the features found for the hydrothermal alteration of illite. Expandabilities measured by the xno peak-position method for illite/smectites (VS) from various locations are smaller than expandabilitiesmeasured by transmissionelectron microscopy (rer',r)and by the Warren-Averbach (W-A) method. This disparity is interpreted as being related to the presenceofnonswelling basal surfacesthat form the ends of stacks of illite particles (short-stack efect), stacks that, according to the theory of interparticle diffraction, diffract as coherentX-ray scatteringdomains. Previous determinations of the chargeof the illite interlayer have been based on expandability measurementsthat have not been corrected for the presenceof these nonswelling surfaces.Thus, the value for the illiteJayer charge,previously thought to be about -0.75 equivalentsper Oro(OH)r, needsrevision. By using revr methods for measuringmaximum expandabilities,the fixed cation content of illite layers in I/S is determined to be approximately -0.9 equivalents per O,o(OH)r. This charge is independent of illite origin and expandability. Based on a long extrapolation, the mean charge on exposedbasal surfacesofillite particles from the Silverton caldera is approximately -0.48 equivalents per O'.(OH)'.

INrnooucrroN Appr,rclrroN oF THE W,l,nnnN-AvERBACH In a recentpaper, Eberl et al. (1987) discussedthe min- TECHNIQUE eralogy of sericite from the Silverton caldera (Colorado) The Warren-Averbach X-ray diffraction technique was in terms of the theory of interparticle diffraction (Nadeau developed originally for the investigation of cold-work et aI., 1984a, I 984b). This paper was, in part, a searchto distortion of metals. This technique has been used by find a superior technique for studying this commonly oc- metallurgists for more than 35 years, and, in the words curring material. In the present paper, the Warren-Av- ofKIug and Alexander(1974), "A vast amount ofexpe- erbach method (Warren and Averbach, 1950) is used to rience . . . supportsthe pre-eminenceof the Fourier meth- measureillite-particle thicknesseswith greater precision od of Warren and Averbach in this field." The Warren- than was possible in the previous work. The better cor- Averbach (W-A) method separatesthe effects of X-ray relations found using these measurements,together with diffraction (xno) peak broadening related to particle size additional rervrthickness measurementsof other illites, (or X-ray scattering-domainsize), which is not a function extend our knowledge ofthe relations between structure oftwo-theta angle,from peak broadeningrelated to strain and chemistry for these and similar clays. In addition, in the crystal structure, an effect that is angular depen- apparentparticle-thickness distributions suggesta mech- dent, by analyzirgdiffraction profiles for two or more 00/ anism for the formation and evolution of illites in hvdro- peaks. thermal systems. The presentapproach, which is empirical, assumesthat 0003404x/88/ll 12-l335$02.00 I 335 r336 EBERL AND SRODON: OSTWALD RIPENING AND ILLITE

ARTICULATEDILLITE DISARTICULATEDILLITE CRYSTALS CRYSTAL

Non-swsllingsurface

1.0nm illite layerwith fixed Fof lhls partlcle: cations T=8.0nm

Fundamentalpartlcle X-rayscattering domain size = 4.0 nm vlewDolnl Expandability= 0%

Mineral= illite N=4

T= 4.0nm 1.7nm swelling (wilh glycol)with <- Stackingtaull s=3 exchangeable cations Max.expandability = 25%

N=12

MacEwan Crystatllte vlewpolnt

Mineral= illite/smectite

Ordering= R3

Expandability= 18%

Fig. l. A diagram that comparesthe fundamental-particleconcept with the MacEwan crystallite conceptof I/S and that presents other conceptsdiscussed in the text. The c* axis is parallel to the stacks.The crystallographicorigin for the stackingfault is strictly speculative. particle-size xRD peak broadening for illite is related to The assumption that most of the particle interiors are fundamental-particlethicknesses and that, typically, this fault-free is supported for the Silverton sericites by the broadening is influenced minimally by stacking faults data of Eberl and Velde (in prep.). This technique,which within particles that would tend to give a smaller X-ray plots an xno intensity ratio (Srodori, 1984) versus the scattering-domainthickness than the fundamental-parti- Kubler index (Kisch, 1983), indicates that most of these cle thickness.A hypothetical example of a stacking fault sericiteshave xno defect-freedistances parallel to c* that is diagrammed on the right side of Figure 1: the illite are equal to or greaterthan the mean particle thicknesses fundamental-particle thickness in this figure is 8 nm, (defect-freedistance : 20 to >40 illite layers).This tech- whereas the X-ray scattering-domain thickness is ap- nique also indicates that illites from other areas(e.9., il- proximately 4 nm. The interiors of the particles are as- lites from the Niger Delta basin) have defect-free dis- sumed to be strain-free. Strain broadening for basal xno tancesthat are less than particle thicknesses(defect-free reflections is assumedto arise entirely from interparticle distance 5 to l0 illite layers), in which case the W-A swelling (the 1.7-nm spacingsin the left side of Fig. l). techniquemay give spuriously small mean particle thick- This "strain" is kept constant at about 1.7 nm by Sr sat- nesses. uration and glycolation. The assumption of strain-free interiors seemsreason- EBERL AND SRODON: OSTWALD RIPENING AND ILLITE 1337

TaBLE1, Meanparticle thickness (in nm) parallel to d measured TABLE2, Meanparticle thickness parallel to d for sericitesam- for the Silvertonsericites bv the Warren-Averbachand pleRM22 as a functionof interparticlechemistry rEMmethods InterparticlechemistrY Thickness(nm)

Sr-saturated,glycolated 10 Warren-Averbach Arithmetic Weighted Ca-saturated,glycolated 11 Smoothed mean mean Mg-saturated,glycolated 11 Na-saturated,glycolated 10 AR1 60 18.6 K-saturated,glycolated 15 AR1R 19 Natural,glycolated 13 LF7 14 sr-saturated,air-dried 13 IQ LF1O 4.4 Ca-saturated,air-dried 20 RM3 23 19 Mg-saturated,air-dried 16 RM4 15 Na-saturated,air-dried v aa RM5 12 K-saturated,air-dried 12 RM6 12 Natural,air-dried I RM8 11 A1 'l 'l RM1.I Nofe: Measurementswere made by the Warren-Averbachmethod' RM12 12 RM13 11 8 RM21 11 RM22 10 RM28 15 7.4 particle mea- RM30 14 11 8 Comparisons between mean thicknesses RM31 17 sured by the xno W-A method (raw data) and by the rnu *arith- RM35A 11 4'l Pt-shadowing method (Table l, column labeled RM35C 12 RM35D 12 1.6 metic mean") indicate that the methods are comparable SG1 13.5 for three samples, although the W-A method generally JU+ 29 20.0 43 28 givesgreater thicknesses. However, it would be more correct to use the weighted means rather than arithmetic means as a measure of mean thicknesses.rru particle- able in applying the W-A method to sericite,because any thickness distributions needed for this calculation were deviation in lattice spacing (from the previously mea- available for only two samples(Table l, column labeled sured value of 9.99 A; ttrat is associatedwith strain with- "weighted mean"). Thus, becausethere are insufficient in particles would be negligible compared with the large reu thicknessmeasurements to calibrate the W-A thick- "strain" related to swelling between particles. The as- nessmeasurements, mean thicknessesand particle-thick- sumption that strain broadeningis equivalent to swelling ness distributions determined by the W-A method are between particles-and, therefore, that its effect on xnp consideredto be correct in a relative senseonly, although peak breadth can be removed for crystallite-sizeanalysis there is some evidence from cation-exchange'capacily by the W-A method-is supported by correlations that measurementsthat the mean thicknessesmay be correct follow. in an absolute sense,as will be discussed.Particle-thick- Weighted mean particle thicknessesfor samples (Sr- ness distributions calculated from the raw data, rather saturated, glycolated, <2-pm size fractions) that were than from the smoothed data (Table l), were used in studied previously by other methods (Eberl et al., 1987) subsequentanalyses because the raw data set is more were determined by the W-A method from the samexRD complete. patternsused previously (Table l, column labeled"raw"). During application of the W-A method, it is important This analysisused the 002 and 005 xno reflections, Na- that the thickness of interparticle expanding layers be tional Bureau of Standards standard referencematerial uniform (i.e., constant "strain"). The effect of changing 675 (synthetic fluorophlogopite mica powder) as a cali- the interparticle chemistry on measured particle thick- bration standard both for two-theta position and to re- nessesfor a sericite sample is shown in Table 2' Air-dry move the effectsof machine broadening,and a Siemens- sericites may contain swelling layers of diferent thick- Allis' automated D-500 diffraction systemequipped with nesses(one or more water layers in the swelling com- a Diffrac V/R S software program named cRysrzthat au- plexes),and glycolated samplesthat have exchangecat- tomatically performs the W-A analysis. In addition, ions of low hydration energy(e.g., K*) also may contain weighted mean particle thicknesses(Table l, column la- two types of swelling layers (1.4 arl,d1.7 nm), as well as beled "smoothed") and particle-thickness distributions layers that have collapsed reversibly around the cation. were determined for selectedsamples using SiemensDif- Measurementshave indicated that the interparticle Sr- fract 500 software from additional xno data that had been glycol complex yields uniform swelling@berl et al., 1987). smoothed prior to Fourier analysisby using a Split-Pear- Evidence that the W-A technique gives reasonablemean son function. particle thicknessesis given by the correlationspresented in Figure 2. The origin of the correlation between maximum expandability and an infrared absorption band (Fig. t The use of brand names is for identification purposesonly and doesnot constituteendorsement by the U.S. GeologicalSur- 2F) is not known. Similar correlations were made in a vey. previous paper by using other, less precise methods to l 338 EBERLAND SRODON:OSTWALD RIPENING AND ILLITE

s10 r A D I I G8 I r I E

;6 I E I t l^ I ln o z2 I r R^2=0.83 Y*0.36+078x Y=988.01- 1.1843x R^2= 0.81 6o 0+ 2 4 6 I 10 12 14 824 826 828 830 832 834 CEC(meqper100g) WAVENUMBER (l/cm)

oQto 12 tlt x IT 10 E8 r tt I ;6 I E I t ;4 I I o z2 1l I o. y - 33.91- 34.46x B^2= 0.48 R^2=0.69 XA Y-'3.57+156x ltl 0.6 0.7 o.B 0.9 1.0 2 3 4 5 6 7 I 9 10 FIXEDK + Na (eq. per half.unit cell) KUBLERINDEX (delta two-theta x 10)

s10 10 x E8

o ts I o 4 o z 2 y = -7.'13+ 0.76x R^2= 0.96 4 y= -8.11 +9.82x-I 38,x^2 R 2 =0-94 x t! 0 23 4121416182022 INTENSITYRATIO APPARENTK-ATAGE (MA)

Fig.2. Relation betweenmaximum expandability, measuredby the Warren-Averbach method, and crystal chemical properties of the Silverton sericites. measure expandability (Eberl et al., 1987). For conve- ticle-thicknessmeasurements (4 in nm) from the equa- nience, maximum expandability, rather than mean par- tion ticle thickness,is usedon the vertical axesin thesefigures, Maximum expandability : 100/7. (l) becausemaximum-expandability plots yield relationsthat are more linear than do particle-thicknessplots. Maxi- Maximum expandability is the expandability that would mum expandabilities can be calculated from mean par- be measuredif the stacksof illite particles were infinitely thick (i.e., all exposedbasal surfacesofillite particles are involved in swelling),as will be discussed. TABLE3. Mean particlethickness (in nm) for severalsericite samplesas a functionof the pairof xRDreflections "Maximum expandabilities" rather than "expandabil- usedin the Warren-Averbachanalysis ities" are plotted in the figures, becauseexpandabilities measuredby the conventional xRD peak-position meth- Reflections LF7 RM3 RM8 RM13 RM3O RM35A SG4 od depend on factors such as the thickness of the clay 001-002 12 20 2 812724 specimen,the arrangementof particles in the specimen, 001-003 12 20 3 812724 the saturating cation, and the relative humidity (Eberl et 001-005 13 20 3 912825 002-003 11 17 I 912724 al.,1987). Expandability is a measureof how much a clay 002-005 14 23 11 11 14 11 29 swells; as such, it would be a precise measurement,for 003-005 67 38 59 74156 example, in soil engineering studies where one is con- EBERL AND SRODON: OSTWALD RIPENING AND ILLITE r339 cerned that clays might crack foundations. However, for should lead to bimodal particle-size distributions. The understanding the problems in clay-mineral petrology second mechanism is progressive recrystallization by (e.g., the thermodynamics and kinetics of illite forma- Ostwald ripening of the older clay during the younger tion), the mineralogically important parametersare max- event. Particle-thicknessdistributions indicate that the imum expandability, mean particle thickness,and parti- relation in Figure 2F, which could be discussedonly qual- cle-thicknessdistribution. titatively in the previous paper (Eberl et al.' 1987), most Additional evidence that mean thickness measure- likely results from progressiverecrystallization by Ost- ments given by the W-A method are precise is given in wald ripening (Ostwald, 1900), with a resulting partial Table 3. Different combinations of 00/ reflections were loss ofradiogenic Ar and a progressiveincrease in particle used for particle-thickness determinations for several thickness. samples. The 003-005 combination gives spurious re- According to Baronnet (1982), Ostwald ripening is sults. All of the other combinations give good results, characterizedby the simultaneousgrowth and dissolution except for combinations containing 001 reflections for of particles of a mineral within a single medium. After sample RM8, which is one of the most expandablesam- nonexplosive nucleation (i.e., nucleation that takes place ples. The 002-005 pair is the one of choice for thesesam- over a significant length of time), a system may contain ples for consistentresults and for avoiding the I 0 I qtrattz a greatmany crystallites of ditrerent sizes.The tendency reflection. then is to minimize surfacefree energy by dissolving small In addition to mean particle-thicknessmeasurements, particles and growing large particles as matter is trans- the W-A method also can give particle-thicknessdistri- ferred from the former to the latter through solution. By butions. One can be confident that the W-A method gives this mechanism, the averagesize of the particles will in- precise mean particle-thicknessmeasurements for these creasewith ripening time, and the size distribution of the samples,based on the good correlations given in Figure particleswill spreadout. 2. In addition, extrapolation of the CEC (Fig. 2A), the Apparent particle-thicknessdistributions for some of intensity ratio (Fig. 2C), and the Kubler index (Fig. 2E) the dated samplesare given in Figure 3. RM8, which is curves to 00/oexpandable gives reasonablevalues for non- the oldest sampledated, also gives the simplest thickness swelling illite: a CEC of aboul zero, an intensity ratio of distribution. This distribution may representthe original about 1.0, and a Kubler index of about 0.25" 20. The particle-sizedistribution formed by the older hydrother- latter value is that cited for the anchizone-epizonebound- mal event. As the apparent age of the clays becomes ary, at which expandabilityis lost (Kisch, 1983,p.3a9). younger, the particle-thickness distributions become However, there is no direct evidence to prove that the skewed progressivelytoward thicker particles, as would particle-thicknessdistributions are correct. Confirmation be expectedfor continued ripening ofthe older clays by of thesedistributions by revr, for example,would require the youngerevent. The correlation betweenmean particle about a thousand particle-thickness measurementsper thicknessand apparent age(Fig' 2D thus is a function of sample(Exner and Lukas, l97l; Baronnet,1974). (Many the extent ofripening: radiogenic Ar loss from the older fewer measurementsare required for mean thicknessde- clays is related to mass transfer by ripening' terminations.) Furthermore, there is at least one obvious Ostwald ripening can be identified, and the recrystal- problem with the W-A method: it is limited at the thick lization mechanism can be determined, by replottinggain- end ofthe distribution by particles that diffract as though sizedistribution histograms(Fig. 3) to a plot that usesthe they are infinitely thick (particles approximately >100 reduced coordinates:f/f^.", and r/r^"n, where/is the fre- nm thick). These particles cannot broaden xno peaks as quency of a given particle radius, fi"- is the maximum a function ofparticle size. Also, there is a greaterchance frequency encountered,r is the particle radius, which is for thicker particles to be broken into coherently diffract- equal to Yzthe particle thickness, and r-"u. is the mean ing domains that are smaller than the fundamental-par- particle radius (Baronnet, 1982). Indirect proofthat Ost- ticle thickness.However, if the relative particle-thickness wald ripening has taken place is given by a steady-state distributions are adopted, then the mechanism for seri- profile that is independent of ripening time and of initial cite formation can be understood. grain-sizedistribution (Lifshitz and Slyozov, I 96 I ; Wag- ner, 196l). The shapeand position of the normalized distribution are indicative of the growth-controlling Osrwar-n RIPENINGBY SERICITE mechanism (Baronnet, 1982, 1984). Mean particle thicknesses determined by the W-A Such normalized particle-radius histogramsfor several method reveal a linear relation between apparent K-Ar dated sericite samples and for two other illites are pre- ageand maximum expandability (Fig. 2F). In accordance sented in Figure 4. Three types of steady-stateprofiles with the available mineralogic and stable-isotope evi- were found for the Silverton sericites(Figs. 44' 48, and dence(Eberl et al., 1987),two mechanismscould explain 4C), two of which are very similar. The steady-stateshape this relation. The first mechanismis mixing of clay formed of the profiles from sample to sample is indicative of during the older (22Ma), cooler (180'C) hydrothermal Ostwald ripening in a closed system.The position of the event with clay that nucleated during the younger (12 maximum and the general shape of the distributions, Ma), hotter (320'C) hydrothermal event. Such an origin however, do not fit any ofthe calculatedprofiles for var- I 340 EBERL AND SRODON: OSTWALD RIPENING AND ILLITE

21.5Ma t7,4 Ma * RM8 RM28

z1^ u rv f o IIJ

21.1Ma 13.8Ma I RM5 sG4

o z1^ of U

20.0Ma 12.1Ma s RM3O AR1

o z4^ u rv uo E E

RELATIVE THICKNESS (nm) RELATIVETHICKNESS (nM)

Fig. 3. Apparent particle-thicknessfrequency distributions for severaldated samplesfrom the Silverton caldera. ious reaction mechanisms(Chai, 1974, 1975),some of the sericitesin Figures 4A and 48 come closeto fitting is which are presentedas solid curves in Figure 4. that measuredfor Fisher reagentcalcite (Fig. 4D) by Chai There are several possibilities for this lack of correla- (1975).The meaning,ifany, for this apparentcorrelation tion betweenexperiment and theory: (l) The steady-state is obscure.The reducedprofiles for samples35A and 35D plots in Figure 4 are artifacts of the measurementtech- fig. aC) resemble those described by Baronnel (1974) nique. This possibility seems unlikely, becauseseveral for a synthetic phlogopite system for particles formed at different steady-stateprofiles have been measuredby the short run times (10 min to 3 d at 600 "C and Pno: I W-A technique. (2) The experimental plots are for rate kbar). The distribution was interpreted by him to be tran- laws that have not yet been calculated theoretically. (3) sitional betweena nucleation-controlled distribution and The plots actually representcord distributions, rather than a ripening-controlled distribution (Baronnet, I 982). Sam- true particle-radiusdistributions, becausethe W-A meth- ples RM35A and RM35D were collected from a broad od may give apparent thickness distributions that have alteration zone that was severalmeters wide, rather than been modified by the presenceof stackingfaults. A math- from cracks as were the other sericites, and, therefore, ematical method for relating radius distributions to cord they may have undergone less ripening because the distributions has been outlined by Exner and Lukas plumbing was not as well developed. A very different (1971), who have made the calculation for reaction by reducedprofile is given by sampleMF54 (Fig. 4C), which first-order kinetics, but the calculation for second-order is an illite from the central Alps (Hunziker et al., 1986). kinetics has not yet been attempted. It seemslikely that The end of Ostwald ripening, which almost never is the Silverton sericitesshould have reacted by a second- reached,would be the formation of one single,large crys- order rate law, because Baronnet (1974, 1982, 1984) tal (Baronnet, 1984), or, more practically for clays, a found that the basal surfacesofphlogopite grow by sec- number of crystals having a single, relatively large par- ond-order kinetics (spiral-growth mechanism) in hydro- ticle size.The thickest particles should record a complete thermal systems.(4) Calculationsfor the theoreticalcurves history of the recrystallization, becausethey never have Gig. a) are based on crystals having spherical geometry undergone dissolution. They should be zoned from an and may not be applicable to the plate geometry of clay. older core to a younger rim, and this zonation should be The only published profile that the reduced plots for repeatedgoing from the thinnest, oldest particlesto thick- EBERL AND SRODON: OSTWALD RIPENING AND ILLITE r341

1.0

0.8

0.6

1.0

0.2

0.0 012345 012345 r/r mean / r mean Fig. 4. Normalized apparentparticle-radius histograms for K-Ar-dated sericitesamples from the Silverton caldera,for the Silver Hill illite, and for an illite from the central Alps (MF54). The solid curves in A, B, and C are theoretical profiles expectedfor Ostwald ripening by various reaction mechanisms.The solid curve in D is an experimental curve for Fisher reagentcalcite (see Chai.1975). er, younger particles,provided that the blocking temper- an artifact of the expandability measurement,an artifact ature for Ar loss has not been exceeded. that is related to the arrangement of illite fundamental particles on the xnp slide. pARTTCLES Drs.l,nrrcur,ATED rLLrrE AND Using the NEwMoDprogram of R. C. Reynolds (De- SHORT STACKS partment of Earth Sciences,Dartmouth College, Hano- The presenceof disarticulated illite particles was hy- ver, New Hampshire 03755, U.S.A.), one can calculate pothesized in the original paper (Eberl et al., 1987) in the effectsthat disarticulatedillite particlescould have on order to reconcile expandability measurementsmade by expandability measurements.The program's MIXERop- the conventional xRD peak-position method with those tion was used to add together appropriate illite and I/S made by rEM. Expandabilities that were calculated by compositions. To test the illitic end of the curve, 100/o Equation I from rnrvr particle-thickness measurements expandable,R3 I/S was mixed with illite composed of generally were larger than those measured by xno. The crystallites8-10 layers thick (the thicknessthat would be problem is presentedagain in Figure 5, where W-A, rath- expectedfor disarticulatedillite particles in an I/S having er than rnr'r, particle-thicknessmeasurements are used. this expandability). The patterns were added in the pro- Disarticulated illite particles do not swell (Fig. l). There- portion 850/oI/S + l5o/oillite. The resulting pattern does fore, they causethe "I/S" xno peak to migrate to a two- not show a peak for discrete illite, and the 17" two-theta theta position that representssmaller expandabilities than those calculated from Equation l, an equation that assumesthat all basal surfhcesare involved in swelling. s12 If the concept of disarticulated illite particles is valid, ri 10 o lt then this effect should influence the xno patterns of all E plot 8 mixed-layer clays. Figure 64, is a of expandability tl EA versus fixed-cation content for I/S from a variety ofen- J vironments and ages.Maximum expandabilities for the I E4o I upper curve in Figure 6A were determined by rnrraand z Y=2.02+0.92xR^2=0.81 Equation l. Expandabilities for the lower curve were o. I x measuredby the peak-position method of Srodori (1980, utu 1984). In a previous paper, the xRD curve was thought o 2 4 6 I l0 12 EXPANDABILITY(Conventional, o/o) to be composedof two straight lines and to offer evidence for the existenceof two types of illite layersin I/S (Srodori Fig. 5. Relation between maximum expandability, deter- et al., I 986); but with the additional rpvr evidence,it now mined by the Warren-Averbachmethod and Eq. 1, and expand- seemslikely that the lower position of the xnp curve is ability determined by the xno peak-position method. 1342 EBERL AND SRODON: OSTWALD RIPENING AND ILLITE

= 10312-2ll 58x+107 3312 R'2=0 9E expandability measurements.The concept may apply to x'"" very illitic clays such as the Silverton sericites,but does y.98.28- | 10.70,1xR'2= not seemto work for Rl clays. =Rn Thus, the conceptofdisarticulated illite particles needs to be modified to include the concept of "short stacks" z1v (MacEwan crystallites).A completely disarticulated illite CL particle interlayers. A stack ofillite par- xzv has no swelling IJJ ticles that contains two particles has one swelling inter- 0 (one the top and one on - 0.0 0.2 0.4 0.6 0.8 1.0 layer, but two basal surfaces on A FIXED K + Na (eq. per half-unit ceil) the bottom of the stack) that do not swell. Thus, for a given mean particle thickness, the fewer the particles in a stack, the larger the proportion of nonswelling basal surfaces,and the smaller the expandability. In a stackthat contains a large number of particles, rnu expandability x calculatedfrom Equation I should be approachedby xno )- expandabilitymeasured by the peak-positionmethod. The = relation is xno expandabilitv : 100(,5- l)/(^SZ - l), (2) z f/o) where S is the mean number of illite particles in a stack x IJJ and Z is the mean thickness(in nm) of the illite particles 0 00 02 04 06 08 10 as measuredby rnr'r. Theseconcepts are depicted in Fig- B FXEDFIXED K + Na (eg.per half-unit ce!l) ure l. The hypothesis that the divergenceof the two curyes Fig.6. (A) Relationbetween expandability and fixed K + Na in Figure 6.4 is related to the presenceofshort stackswas for expandabilitiesmeasured by the rru technique(maximum tested by using Equation 2 to calculate the S required to expandability particle calculatedfrom weightedmean thick- shifl the rEu line in Figure 6,{ to match the xnp curve. nesses,upper curve),and by the xno peak-positionmethod For expandabilities >400/0,for which rnrrathickness data (conventionalexpandability, lower curve).Data for the upper in Figure 6,4 curvecomes from Eberlet al. (1987),Nadeau and Bain (1986), are lacking, the linear-regressionequation andthree unpublished analyses ofSilurian bentonites.Data for was used to relate fixed-cation content to expandability, thelower curve comes from Srodoriet al. (1986).(B) The upper and particle thicknessthen was calculatedfrom Equation curveis correctedfor the effectof shortstacks (stacks were as- l. The calculated curve for S : 2 is compared with the sumedto containtwo particles)by useof Eq.2. The calculation measured curve in Figure 68. The xno curve can b€ shiftsthe uppercurve, for whichexpandabilities were measured matched exactly by assumingthat S varies regularly be- by mur,downward to approximatelyfit the lowercurve, for which tween 1.4 for I/S of small expandability and >5 for I/S expandabilitieswere measured by the xno peak-positionmeth- of large expandability. In other words, the thinner illite od. particles stack better than the thicker particles. An S less than 2 implies that the sample contains disarticulated illite particles. reflection is displacedby an amount that is equivalent to If the particles are free from defects, then the mean a decreasein expandability of about 3olo(see Fig. 4 in number of coherently diffracting unit cells parallel to c* Eberl et al., 1987),which is approximatelythe value ar- should be N : S?". Thus, according to the short-stack rived at by deconvolution (see Table 3 in Eberl et al., hypothesis,a 400/oexpandable clay should have N: 5 (i" 1987). Thus, disarticulation could explain the discrep- : 2.5 from Eq. l, and S : 2 from Fig. 68), which seems ancy between curves in Figure 6A for the highly illitic small (by a factor of lessthan two) when compared to the end. ly' needed to model real xnp patterns of I/S (Reynolds, When a similar calculation was attempted for clays 1980).On the other hand, the calculatedvalues for a 200lo having larger expandabilities, however, the discrepancy expandableI/S (Z: 5, S : 2, N: l0) fall within the betweencurves (Fig. 6A.) could not be reconciled. When range required by Huff et al. (1988) to model the xnp 250loexpandable, Rl I/S and discrete illite (3-5 layers pattern of a K-bentonite having this expandability (12 > thick) were added together in proportions up to 150/oil- N > 5) and to explain selected-areadiffraction results (7. lite, the illite did not appearas a discretepeak, but neither : 5 to 10).The modeledxRD pattern of Hutret al. (1988) did it shift the positions of the I/S peaks. On the other also required the incorporation of some segregationbe- hand, a peak for coarse-grainedillite was clearly visible tween illite and I/S, which may be evidencefor the pres- in such a mixture, even if present in much smaller pro- ence of disarticulated illite particles. A conclusive solu- portions. These calculations imply that the disarticulat- tion to the problem presented by Figure 6,{ probably ed-illite concept may, at best, be only a partial explana- awaits more data on the relation between particle size tion for the discrepancy between xRD and rEM and X-ray scattering-domain size, and incorporation of EBERL AND SRODON: OSTWALD RIPENING AND ILLITE r343 the interparticle-diffraction concept into Reynolds' pro- stacksof 2-nm-thick illite particles,should appearat 50o/o gram. expandableI/S (Eq. l). Likewise, R3 ordering usually ap- The regressionequations in Figure 6.4 can be solved pearsat about l5o/oexpandable I/S (e.g.,Velde and Bruse- simultaneously to relate maximum expandability to ex- witz, 1982), whereas the fundamental-particle concept pandability measuredby the conventional xno peak-po- predicts that this type of ordering, which results from sition method (X). The empirical relation is swelling between particles that are 4 nm thick, should appear at 25o/oexpandable I/S. Equation 3 may resolve Maximum expandability: 55.35(0.037X+ 0.041)'h this difficulty, becausea32o/o expandable clay (xno peak- - 10.87. (3) position method) has a maximum expandability (from Mean particle thickness(O then can be calculated from Eq. 3) of 500/0,and a l2o/o expandableclay has a maxi- Equation I, and mean number of particles per stack (S) mum expandability of 280/0.Na-rectorite has an expand- can be calculatedfrom Equation 2. ability (xnn peak-position method) that is close to 500/o Equation 3 assumesthat the relation betweenexpand- and a fundamental-particle thickness that is approxi- ability and S varies regularly for all illite/smectites, but mately 2 nm. S must be relatively large for this situation some clays may not fit this equation becauseof the efects to occur. on S of differing particle geometry, sample preparation, LAYERSAND PARTICLE and crystallization history. Keeping in mind this limita- CH,lncrs oF ILLITE tion, the data ofAltaner et al. (1988)can be used as an SURFACES independentcheck ofthe accuracyofEquation 3 for sam- The precision of the presentdata permit calculation of ple RM30. These authors determined that RM30 has a the chargesfor illite interlayers and exposed basal sur- maximum expandability of 22o/o+ 4olofrom a Nun in- faces. The generally accepted charge for illite layers is version/recovery technique. An expandability of 6.60/o approximately 0.75 equivalents per O'.(OH), for diage- measured for this sample by the xno peak-position netic clays (Hower and Mowatt, 1966; Velde and Bruse- method (Eberlet al., 1987)yields a maximum expanda- witz, 1986) and a somewhat larger value for hydrother- bility of 190/ofrom Equation 3, a value that lies within mal clays(e.g., Eberl et al., 1987).The presentapproach, the error range of the rvun technique. There seemsto be however, indicates that thesevalues need revision. Based no justification for the equation used by Altaner et al. on rEM particle-thickness measurements(Fig' 6,{), the (1988)to correctxRD expandabilitydata for sampleRM30 best extrapolated value for the mean charge of an illite for the presenceof MacEwan crystallites (short stacks). layer is about 0.9 equivalents,a value that appearsto be Even assuming that their equation is correct, using the independent of both illite origin (with the exception of weighted mean particle thickness for this sample as de- illite layers formed by wetting and drying; see Eberl et termined by revr (Table l), rather than the averagecrys- al., 1986) and expandability. This fixed-interlayer-cation tallite size used by Altaner et al. (1988), their equation content is smaller than that of muscovite, and therefore givesa maximum expandabilityof l8o/o(rather Ihan l4V$, illite may warrant a separate mineral name based on close to the Nnanvalue. Therefore, the hypothesis that chemistry alone.The proposal that the illite interlayer has this samplecontains smectite sitesin the interiors of illite a larger chargethan previously suspectedalso is support- fundamental particles is unsupported. The W-A method ed by an extrapolation of the W-A data for the Silverton gives a somewhatsmaller maximum expandability (140lo) sericites (0.98 equivalents, from a correlation having a for this sample, and this expandability correlates well with lot of scatter,Fig. 2B), by a combination of Nun and xnn that measuredby the reNamethod (130/o).Clearly, more data for sample RM30 (0.95 equivalents, Altaner et al., data are needed before the xun technique for measuring 1988, and Eberl et al.,1987), and by chemicalanalysis maximum expandabilitiescan be reconciledwith the oth- of the Kaube sericite, a nonswelling illite for which sur- er methods. face effectsshould be minimal (0.87, Srodoriand Eberl' Equations 2 and 3link the fundamental-particle con- l 984). cept (Nadeauet al., 1984a, 1984b)with the MacEwan The mean chargeofthe exposedbasal surfacescan be crystalliteconcept (Reynolds, 1980; Altaner et al., 1988) estimated from an extrapolation of the curve of maxi- of mixed-layer clays. The two models can yield diferent mum expandability versus cation-exchangecapacity (CEC, expandabilitiesfor the same sample (Figs. I and 6), but Fig.2A), assumingthat the W-A thicknessmeasurements both models are valid: the fundamental-particle model (raw data, Table 1) are correct in an absolute sense.Two yields maximum expandabilities,whereas the MacEwan apparently spurious CEC measurementsat 22 and 24 crystallite model yields expandabilities that are partly a meq/100 g have been omitted from Figure 2A. An ex- function ofthe presenceofnonswelling basalsurfaces that trapolation to zero percent expandableI/S gives a CEC arise from the presenceof disarticulated illite particles of approximately zero, thereby indicating that all of the and short stacks. detectableCEC for the illite particles is related to basal It has been puzzling that Rl ordering for I/S usually surfaces.This extrapolation agreeswith the determina- appearsat about 350/oexpandable (e.g., Perry and Hower, tion ofNadeau (1987) that basal-surfacearea represents I 970), becausethe fundamental-particleconcept predicts 950/oof the total surfacearea of micaceousclays. The long that Rl ordering, which results from swelling between extrapolation of the CEC versusmaximum-expandability t344 EBERL AND SRODON: OSTWALD RIPENING AND ILLITE curve to 1000/oexpandable I/S yields a value of 128 meq/ modynamic parameter of particle size is to be deter- 100 g for the expanding surfaces,a smectite CEC. This mined. Finally, if it is proven that a sericite (or any other CEC is equivalent to a mean chargefor the basal surfaces clay) has reactedby Ostwald ripening, then the challenge of about -0.48 equivalentsper half unit cell, which is is to separatefrom a single sample the various particle identical to the chargecalculated for the surfacesof sam- sizes for independent chemical, structural, and isotopic ple RM30 when the surface tetrahedral charge deter- analysis. Thereby, the nucleation and recrystallization mined by Nrvrn(-0.34, Altaner et al., 1988)is addedto history of a sample can be determined. the octahedralcharge determined by xnr (-0.14 from Table 8 in Eberl et a1.,1987). Note added in proof. It has been found that the choice of a standard is crucial for determining the shapeof the CoNcr,usroN W-A particle-thicknessdistributions (Figs.3 and 4). When The mineralogy of sericite from the Silverton caldera a better standardwas chosen (i.e., ground muscovite, which can be understood in terms of the presenceof illite mi- gave sharper XRD peaks than NBS 675), the reduced crocrystals having various particle sizes. These crystals profiles (Fie. a) more closely approached,although did probably formed initially within the illite stability fietd, not match exactly, the theoretical curve for reaction by but thermodynamic equilibrium was not achieved be- second-orderkinetics (spiral growth, shown in Fig. 4C). causesurface free energywas not minimized. Such a dis- It may be that if a perfect, defect-freestandard could be equilibrium would lead to crystal dissolution and to crys- found and if the XRD peaks for this standard could be tal growth according to the theory of Ostwald ripening. modeled exactly by the smoothing function, then the re- The degreeof ripening undergoneby a particular sample ducedplots for most ofthe Silverton sericiteswould match most likely was a function of temperatureand of time of the theoretical second-ordercurve. Choice of standard, exposureto hydrothermal fluids. Thesevariables, in turn, however, does not greatly influence mean particle-thick- may havebeen controlled by distancefrom the heat source nessmeasurements. We thank Myron Smith at Chevron and by plumbing. But time and temperature are not the for his help in determining the revised distributions. only factors that can affect the degreeofripening. Many of the factors that have been found to influence expandability in I/S (seeEberl et al., 1987) can be under- Acrc'lowr,rocMENTS stood in terms of Ostwald ripening. For example, ripen- Cntical reviews and comments by S Altaner, A Baronnet, A. Inoue, ing kinetics will be enhancedby increasingtemperature, P Nadeau, R. Pollastro,R Sanford,G Whitney, and B. Velde are grate- by the presenceof mineralizing salts that tend to increase fully acknowledged.We thank Fred Paillet for his help with a calculation, the solubility ofthe clay, by increasingporosity and per- David Bish and SteveChipera for the useof their laboratory, and Manin meability, by stirring and flow, by fluctuations in concen- Frey for supplying sample MF54 J.S acknowledgessupport from The Polish Academy Program trations (e.g.,wetting and drying), by fluctuations in tem- ofSciences CPBP 03.04. perature,etc. (Baronnet,1982). Conversely, crystal growth can be retarded by the presenceofinhibitors. Rrrnneucns crrpo From the viewpoint of Ostwald ripening and the theory Altaner,S.P., Weiss, C.A., Jr., and Kirkpatrick,R.J. (1988) Evidence from of interparticle diffraction, it is possible to understand 'Si NMR for the structureof mixedJayer illite/smectite clay minerals. why the reaction of smectite to illite has proven to be Nature, 33 I , 699-702 Baronnet,A. (1974)Etude en microscopie6lectronique des premiers stades difrcult to reverse, why illite passesthrough a swelling de croissanced'un mica synth6tique, la phlogopite hydroxylee. Ph6- phaseas particles thicken to form nonswelling mica, and nomdnesde coalescenceet de murissementdans le systCmeferm6 con- why sru and rnu data indicate that illite both dissolves servatif: KrO-6MgO-AlOa6SiOaexcis HrO High Temperatures-High and grows in a single diagenetic or hydrothermal fluid Pressures,6.675-685 - ( ripening The (Pollastro,1985; Inoue I 982) Ostwald in solution. caseof calcite and mica. et al., 1987).However, Ostwald EstudiosGeol6gicos (Madrid), 38, 185-198. ripening theory is not strictly applicable to burial diage- - (l 984) Growth kinetics ofthe silicates.A review ofbasic concepts. netic sequencesif the systemsare open, or if other reac- Fortschritte der Mineralogie, 62, 187-232 tants are involved in the illite recrystallization process. Chai, B.H.T. (1974) Mass transfer of calcite during hydrothermal crys- Conclusionsdrawn in this study with respectto use of tallization. In A.W. Hoffrnann and B.J. Giletti. Eds.. Geochemical transportand kinetics, p. 205-2 I 8. CarnegieInstitution ofWashington, the W-A method for measuringthe thicknessesof swell- Washington,D.C. ing clays must remain tentative until this technique can -(1975) The kinetics and masstransfer of calcite during hydrother- be calibrated by other techniquesofparticle-size analysis, mal recrystallizationprocess Ph D thesis, Yale University, New Ha- such as rerra.AIso, although the present approach indi- ven, Connecticut. Eberl,D.D, and Northrop,H.R. (1986)Potassium fixation in catesthat the W-A Srodoi, J., method works empirically, the W-A smectite by wetting and drying. In J.A. Davis and K.F. Hayes, Eds, theory needsto be applied rigorously. The W-A method Geochemicalprocesses at mineral surfaces.American Chemical Society works best for clays of small expandability (< 100/o), SymposiumSenes, 323, 296-326. whereasthe xnp peak-position method is more precise Eberl,D.D, Srodo6,J , ke, M., Nadeau,P H , and Northrop, H.R. (1987) for clays of larger expandability. Expandabilities mea- Sericitefrom the Silverton caldera,Colorado: Correlation among structure, composition, origin, and particle thickness.American Mineralo- sured by the latter method, however, must be corrected gist, 72, 914-934. for the presenceof short stacks if the important ther- Exner, H.8., and Lukas, H.L (l 97 l) The experimentalverification of the EBERL AND SRODON: OSTWALD RIPENING AND ILLITE 1345

stationary Wagner-Lifshitz distribution of coarseparticles. Metallog- - (l 984b) Interstratifiedclays as fundamentalparticles Science,225, raphy,4,325-338 923-925 Hower,J., and Mowatt, T.C. (1966)The mineralogyof illitesand mixed- Ostwald.W. (1900)Uber die vermeintliche Isomeriedes roten und gelben layerillite-montmorillonites. American Mineralogist, 5 l, 825-854. Quecksilberoxydsund die OberflSchenspannungfester Korper. Zeit- Hufl, w.D, Whiteman,J.A, and Curtis,C D (1988)Investigation of a schrift fiir PhysikalischeChemie, Stdchiometrie und Verwandschafts- K-bentonite by X-ray powder diffraction and analytical transmrssron lehre,34, 495-503. electronmicroscopy. Clays and Clay Minerals,36, 83-93. Perry, E., and Hower, J. (1970) Burial diagenesisin Gulf Coast pelitic Hunziker,J C., Frey,M., Clauer,N , Dallmeyer,R.D, Friedrichsen,H., sedimentsClays and Clay Minerals,18, 165-177 Flehming,W, Hochstrasser,K., Roggwiler,P., and Schwander,H. (1986) Pollastro, R.M. (1985) Mineralogical and morphological evidencefor the The evolulion of illite ro muscovite: Mineralogical and isotopic data formation of illite at the expenseof illite/smectite. Claysand Clay Min- from the Glarus Alps, Swtzerland. Contributions to Mineralogy and erals,33, 265-274. Petrology,92,157-180 Reynolds,R.C (1980)Inrerstratified clay minerals In G.W Brindley and Inoue,A., Kohyama,N, Kitagawa,R., and Watanabe,T (1987)Chem- G Brown, Eds., Crystal structures of clay minerals and their X-ray ical and morphologicalevidence for the conversionofsmectite to illite. identification, p. 249-303 Mineralogical Society,London. Claysand Clay Minerals,35, I I l-120. Srodofi (1980) Preciseidentification of illite/smectite interstratifications Krsch, H J. (1983) Mineralogy and petrology of burial diagenesis(burial by X-ray powder diffraction. Clays and Clay Minerals, 28,401411' metamorphism) and incipient metamorphism in clastic rocks In G. - (1984) X-ray identification of illitic materials Claysand Clay Min- Larsen and G.V Chilingar, Eds, Diagenesisin sediments and sedi- erals,32, 337-349. mentary rocks, Developmentsin Sedimentology25B, p. 289494. El- Srodoir,J., and Eberl, D.D (1984)Illite MineraloglcalSociety ofAmerica sevier,New York. Reviews in Mineralogy, 13, 495-544. Klug, H P , and Alexander, L.E. (1974) X-ray diFraction proceduresfor Srodoir,J., Morgan, D J , Eslinger,E V., Eberl, D D., and Karlinger, M.R. polycrystallineand amorphous materials. Wiley, New York. (1986) Chemistry of illite/smectite and end-member illite. Clays and Lifshitz,LM., and Slyozov,V.V. (1961)The kineticsof precipitationfrom Clay Minerals, 34, 368-378 supersaturatedsolid solutions. Physics and Chemistry of Solids, 19, Velde, B, and Brusewitz,AM (1982) Metasomaticand non-metaso- 35-50 matic low grademetamorphism of Ordovician meta-bentonitesin Swe- Nadeau, P.H. (1987) Relationshipsbetween the mean area, volume and den Geochimicaet CosmochimicaActa, 46,447452. thicknessfor dispersedparticles ofkaolinites and micaceousclays and -(1986) Compositionalvariation in componentlayers in natural their application to surfacearea and ion exchangeproperties. Clay Min- illite/smectite. Clays and Clay Minerals, 34, 651-657. erals.22. 351-356. Wagner, C (1961) Theorie der Alterung von Niederschliigendurch Um- Nadeau,P.H , and Bain, D.C. (1986) Composition of somesmectites and l6sen (Ostwald-reifung).Zeitschrift fiir Elektrochemie,65, 58l-59 l. diageneticillitic claysand implications for their origin Clays and Clay Wanen, B.E, and Averbach,B.L (1950)The effectofcold-work distor- Minerals,34,455464. tion on X-ray patlerns.Journal ofApplied Physics,21,595-599- Nadeau,P.H., Wilson,M.J, McHardy, W.J., and Tait, J.M (1984a)In- terparticledifraction: A new conceptfor interstratifiedclays Clay Min- MeNuscnryr REcEIvEDM,qncu 21, [988 erals,19,757-169 MnNr.rscnryrAccEprED Jurv 27. 1988