American Mineralogist, Volume 73, pages 766-774, 1988

Interlayer order in illite/smectite

SrBpnrN P. Ar,rlNBn, Cnllc M. BnrHrnDepartment of Geology, 1301 West Green Street, University of Illinois, Urbana, Illinois 61801, U.S.A.

Ansrntcr

Interlayer order in interstratified illite/smectite (I/S) has two seemingly contradictorydescriptions: the Markov theory developed to explain the X-ray difraction (xnn) patternsof I/S minerals and the theory of fundamental particles based on observations made bytransmission electron microscopy (rnrvr). According to Markov theory, I/S consists of crys-tallites about l0 nm thick or greater that are composed of stacked illite and smectiteinterlayers. The stackings are known as MacEwan crystallites. The theory of fundamentalparticles holds that I/S consists of much smaller crystallites that can accumulate duringxno experiments to give the appearance of MacEwan crystallites.

To test the relationship between the theories, we consider the fundamental-particlecontent of MacEwan crystallites. In our study we construct synthetic crystallites in whichillite and smectite interlayers are arranged by Markov theory. Our results show that Mar-kov theory predicts the size distributions of fundamental particles in randomly interstrat-ified I/S and in I/S with short- and medium-range order. Markov theory, however, poorlypredicts reu observations in some illite-rich I/S with long-range order. We suggest thatthe rEvr observations complement rather than contradict interpretations of the crystallog-raphy of most I/S minerals made on the basis of xnp studies. Apparent discrepanciesbetween the theories can be attributed to the effects of sample preparation for ruvr exper-rments.

INrnooucrroN

Illite/smectite (I/S) is an interstratified clay rnineral ofcommercial and geologic interest that exhibits propertiesof both illite and smectite. On the basis of X-ray diffrac-tion (xnn) studies, many petrologists have observed thatsmectite-rich I/S minerals in sedimentary (Perry andHower, 1970; Weaver and Beck, 197 1 ; Boles and Franks,1979) and contact metamorphic (Nadeau and Reynolds,1981; Pytte, 1982) environments change with time tomore illite-rich minerals upon burial and heating. Thereaction, termed smectite illitization, can drive petro-leum migration (Burst, 1969; Bruce, 1 984) and cause geo-pressures (Powers, 1967; Bethke, 1986) by liberating waterfrom smectite interlayers. The SiOr, Fe, and Mg producedduring smectite illitization are sources of cements in sed-imentary rocks (Towe, 1962; Boles and Franks, 1979).

Over the course of the reaction, an xRD peak appearsat low values of 20 and migrates to higher angles. Thepeak shift signals development of short and then longerranges of interlayer order (Hoffman and Hower, 1979:Bethke et al., 1986). The type ofinterlayer order in I/Scan be used as an indicator of the thermal histories ofsediments and rocks (Hoffrnan and Hower, 1979; Srodo6,1979; Horton, 1985; Burtner and Warner, 1986).

Interlayer order in I/S has two seemingly contradictorydescriptions. Hendricks and Teller (1942) and MacEwan(1956, 1958) introduced Markov theory to study inter-layer order in interstratified clays. Their approach con-

0003404x/88/0708-O766$02.00 766

sidered one-dimensional diffraction from infinitely thickinterstratifications of two types of interlayers. Reynoldsand Hower (1970) applied Markov theory to calculatexRD patterns in their study of the crystallography of I/S.In their model, I/S is composed of silicate layers about Inm thick that are separated by anhydrous illite and hy-drous smectite interlayers. The interlayers are arrangedalong the c* crystallographic axis to form MacEwan crys-tallites of various ordering types (Zen, 1967).

Interlayer fractions (P, and P") and junction probabil-ities (e.g., P, , and P, ,) quantifr the interlayer order aris-ing within MacEwan crystallites from interactions amongneighboring interlayers (Reynolds, 1980). A mineral'sReichweite describes the number of neighbor-to-neigh-bor interactions that must be considered to model its xnopattern (Jagodzinski, I 949; Reynolds, I 980). Random in-terstratifications have a Reichweite of 0 (R0) and showno interactions among neighbors. Reichweite I (Rl) min-erals are ordered by nearest-neighbor interlayers. Inminerals with Reichweite 2 and 3 (R2 and R3) order,next-nearest and thrice-removed neighbors further affectinterlayer occupancy. Reichweite generally increases withillite content in I/S suites. The Markov description ofinterlayer interaction provided the basis for previousstudies of the thermodynamic properties (Sato, 1965;Znn,1967) and, reaction kinetics (Bethke and Altaner, 1986)of interstratified clay minerals.

Nadeau et al. (1984a, 1984b, 1984c; 1985) and Nadeau(1985) used a Pt-shadowing technique to study dispersed

ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE 767

I/S by transmission electron microscopy (reu). Theirstudies showed that I/S is composed of "fundamentalparticles," each of which is a small but integral numberof nanometers thick along c*. The particles are consid-erably thinner than the crystallite sizes of about 10 to 20nm commonly inferred from xno studies. Nadeau et al.proposed that interfaces between fundamental particlescan hydrate so that random accumulations of fundamen-tal particles formed during sample preparation for xnpexamination can behave as MacEwan crystallites. Inter-layers internal to the fundamental particles act as illite,and the hydrous interfaces between particles form smec-tite interlayers.

The distribution ofparticle thicknesses provides an al-ternative description of interlayer order in I/S. In the sim-plest examples, populations of particles that include only2-nm-thick particles yield Rl-ordered I/S with 500/o illite,3-nm-thick particles yield R2-ordered I/S with 670lo illite,and 4-nm-thick particles yield R3-ordered I/S with 7 5o/oillite.

Figure I summarizes the relationship between the twotheories. On the left, a MacEwan crystallite is representedas six stacked silicate layers. Order type is determined bythe arrangement of the five illite and smectite interlayers.On the right, the same crystallite is represented as anaccumulation of three fundamental particles. The sizes ofthe particles determined possible interlayer arrange-ments.

Previous investigations have emphasized apparent dif-ferences between the Markov and fundamental-particletheories (e.g., Klimentidis and Mackinnon, 1986; Ahnand Peacor, 1986). Mackinnon (1987) questioned theprecision of measuring fundamental particle thickenessesalong the c*-axis with the rnu shadowing method. In thisstudy, we test the relationship of the theories quantita-tively. Our calculations show broad agreement betweenboth descriptions of interlayer order for most I/S min-erals and help to provide a conceptual link between xnoand reu experiments.

MnrnonsWe use a stochastic method to calculate the size distributions

of fundamental particles that are predicted by Markov theory tooccur within MacEwan crystallites. Our method uses a random-number generator to build a large population of MacEwan crys-tallites in the memory of a computer. The crystallite interlayersare arranged stochastically according to the illite content andjunction probabilities (Reynolds, 1980) of the mineral in ques-tron.

Two examples illustrate our technique. In a mineral with 600/oillite and random (R0) interstratification, P,: P,. : P5 I : 0.6.MacEwan crystallites for this mineral are created by choosingillite as the first interlayer in a crystallite 600/o of the time andsmectite 400/o of the time. Succeeding interlayers also have a 600/ochance of being set to illite. On the other hand, to build a crys-tallite with 75olo illite interlayers and complete Rl order, the firstinterlayer has a 750lo chance of being set to illite (Pr : 0.75).Occupancy of succeeding interlayers depends on the previousinterlayer. For Rl-ordered I/S, a smectite interlayer is alwaysfollowed by an illite (Ps , : 1.0). An illite interlayer, however, is

FundomenlolPorlicles

3nm

Fig. l. MixedJayer illite/smectite depicted as a MacEwan

crystallite (left) and an accumulation of fundamental particles

(right). Anvils represent 2: I silicate layers, balls represent K cat-

ions in illite interlayers, and wavy regions represent water re-gions that span smectite-interlayer regions'

followed by another illite only 670/0 of the time because

P , , : | _ P ' ' ! " ' : 9 . 6 7Pr

(Reynolds, 1980). MacEwan crystallites with longer ranges of

order were modeled in the same manner, except that junction

probabilities accounting for twice- and thrice-removed neigh-

bors (e.g., P,,, and Prrrr) were used. Results in this study are

based on populations ofat least 10000 crystallites, each ofwhich

contains l5 interlayers (i.e., 16 silicate layers).Once a population of crystallites has been constructed, mea-

suring the distances between smectite interlayers gives the sizes

of the fundamental particles of which the crystallites are com-posed. Because the silicate layers (between interlayers) are aboutI nm thick, the separations are integral numbers ofnanometers.For example, clay minerals composed entirely of smectite inter-layers yield only l-nm particles, and those with regularly alter-nating illite and smectite interlayers produc€ particles 2 nm thick.

Clay minerals with more complicated interlayer arrangementsgive particles in distributions of sizes. Thus, a synthetic sizedistribution of fundamental particles can be calculated from theprobability coefrcients of Markov theory.

We applied our technique by analyzing the xno patterns ofI/S minerals. First we determined the Markov coefficients (in-

terlayer fractions and junction probabilities) that best modeled

the xno pattern of each sample studied. In this step, we calcu-lated xno patterns using a Fourier series technique (Reynolds,

1980; Bethke and Reynolds, 1986) that describes diffraction from

oriented clay mounts. We used the resulting interlayer fractions

and junction probabilities to calculate the size distribution of

fundamental particles for each of the samples, applying the Monte

Carlo technique already described. The calculated size distri-

butions allowed us to compare the predictions of Markov theory

directly with the rnv observatrons.

Srupr,n TNTERSTRATTFICATToNS

First we consider the interlayer arrangements and fun-

damental particle contents of simple Markov interstrati-

] , " ,

' {

' {

768 ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE

Fig. 2. Arrangements of smectite and illite interlayers withinMacEwan crystallites as predicted by Markov theory for ran-domly interstratified and R1-, R2-, and R3-ordered I/S withvarious illite contents. Each row represents a MacEwan crystal-lite with the crystallographic c*-axis projected horizontally. Irepresents an illite and . a smectite interlayer.

fications. Figure 2 shows typical structures of MacEwancrystallites over the range of compositions and orderingtypes commonly observed in natural I/S. The crystalliteswere constructed stochastically using the Monte Carlomethod. In I/S with random interstratification and con-taining 20, 40, and 600/o illite (Figs. 2a,2b, and 2c), clus-tering (e.g., SSS... or III.. .) and alternation (ISISIS. ..)of interlayers are apparent in the synthetic crystallites.Illite interlayers have a greater tendency to form clustersas illite content increases, so that clusters of more than

several interlayers are common in the crystallites con-taining 600/o illite. Disarticulating the crystallites at smec-tite interlayers, each cluster would form a fundamentalparticle whose thickness in nanometers is the number ofillite interlayers in the cluster plus one.

Figures 2d-2f show typical interlayer arrangements ofI/S with complete Rl ordering and illite contents of 50,60, and 70o/o. In the case of half illite interlayers, all ofthe crystallites appear in the regular alternation (ISNIS. . .) characteristic ofrectorite. As illite content increases,however, alternations become less dominant and illiteclusters more common. There are no clusters of smectiteinterlayers because Ps s : 0 in Rl-ordered I/S. Notably,Rl-ordered I/S with 700/o illite, a common interstratifi-cation in nature, has little tendency for interlayer alter-nations of more than two cycles. For example, the pos-sibility of encountering six interlayers in the triplealternation ISISIS (or its inverse) in this mineral is aboutl0l0. Thus, this mineral would not resemble rectorite inlattice-fringe images although both minerals have the sametype of ordering and similar illite contents.

In a comparable manner, R2-ordered I/S composed of670/o lllite (Fig. 2g) and R3-ordered I/S wirh 750lo illite(Fig. 2j) show ordered affangements in which smectiteinterlayers are separated by 2 or 3 illite interlayers, re-spectively. I/S with illite contents greater than these ex-amples (Figs. 2h, 2i, 2k, 2l), however, shows progressiveloss of the alternation structure of the end members anddevelopment of interlayer clusters that dominate thecrystallite structures.

Calculated interlayer arrangements such as those inFigure 2 can be compared with the interlayer arrange-ments observed in high-resolution rrvr investigations.Both clustering and alternation have been observed inlattice-fringe images of I/S minerals that have been treat-ed chemically to hold smectite interlayers expanded un-der vacuum (Klimentidis and Mackinnon, 1986; Ahn andPeacor, 1986; Vali and Koster, 1986). Calculated struc-tures should prove useful for interpreting the results ofsuch experiments.

Figure 3 shows the size distributions of fundamentalparticles in I/S of the ordering types and illite contentsconsidered in Figure 2. The size distributions were de-termined by measuring the distances between smectiteinterlayers in 10000 crystallites with stochastically deter-mined interlayer anangements. Randomly interstratifiedI/S is composed of particles over a range of sizes. Therange of sizes and the number of particles more than sev-eral nanometers thick increase with illite content. Thethicker particles appear in Figure 2c as clusters of illiteinterlayers.

Rl-, R2-, and R3-ordered I/S minerals with 50, 67,and 7 5o/o illite, however, contain fundamental particles ofa single size within crystallite interiors. Combining theseparticles gives the regular interlayer arrangements ofISIS..., IISIIS.'., and IIISIIIS... that appear in Figure 2.The minerals also contain smaller particles that appearonly at the ends of crystallites. These particles occur be-

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ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE 769

Rondom

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ll.- lh.--"J , : : : : : " '

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TI 752

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60-

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Fig. 3. Size distributions offundamental particles predictedby Markov theory for randomly interstratified and R1-, R2-, andR3-ordered I/S with various illite contents. By Markov theory,most I/S minerals contain a distribution of particle sizes. Sizesare in nanometers and represent the number of illite interlayersalong c* within a particle. Open bars represent particles occur-ring at crystallite ends.

cause the synthetic MacEwan crystallites contain a fixednumber of interlayers. Markov theory describes finite se-ries within infinitely long sequences and was applied ex-actly in Hendricks and Teller's (1942) study of infinitelythick crystallites. Reynolds and Hower (1970) and Reyn-olds (1980) modified the theory slightly to describe in-tedayer arrangements within the finite sequences thatmake up MacEwan crystallites. In our analysis, assuminginterlayer sequences of finite length results in the possi-bility that truncated fundamental particles can occur atthe ends of crystallites. Particles that occur only at crys-tallite ends are shown by open bars in Figure 3.

As illite content increases from the end-member casespresented, particle sizes fall in increasingly broad distri-butions. The breadth of the distributions represents in-creasing likelihood of encountering clusters of illite inter-layers within ordered MacEwan crystallites. Thus, evenI/S with complete short- or long-range ordering, exceptin end-member cases requiring perfect alternation, con-tains fundamental particles of a variety of thicknesses.

AN.c.Lvsrs oF NATURAL sAMPLES

We applied our method of analysis to a suite of I/Sminerals studied by Nadeau et al. (1985). The suite con-tains samples WWB, CCB, NCB, LPB, RAN, and TGB,which effectively span the range of I/S compositions and

20-(n

j o z ' o I ' 0 " 2 o 1 2 3 4 5 6 7 8 9 > 9

Fig. 4. Observed xRD pattern for ethylene glycol-solvatedsample WWB (Nadeau et al., 1985) with observed size distri-bution offundamental particles (top), and calculated xRD patternfor I/S with 300/o illite and random interstratification, with par-ticle-size distribution resulting from Markov theory (bottom).Peak spacings on xRD patterns are given in nanometers.

ordering types common in nature. Nadeau et al. (1985)measured the thicknesses of between 22 and 78 funda-mental particles from each sample. To analyze these sam-ples, we determined the interlayer fractions and junctionprobabilities that gave the calculated xno patterns thatmost closely matched the actual patterns of the I/S min-erals (Table l). We used these values to synthesize inter-layer arrangements in MacEwan crystallites and the cor-responding particle-size distributions, using the MonteCarlo technique. We then compared the calculated dis-tributions to the distributions determined by rEM mea-surement.

Figure 4 shows xno patterns and size distributions offundamental particles for sample WWB, a Cretaceousbentonite from Westwater, Utah. WWB contains about300/o illite and is typical of randomly interstratified I/S.The top ofthe figure shows the observed xRD pattern andmeasured distribution of particle sizes. The bottom of thefigure shows the calculated xno pattern that best matchesthe observed pattern and the synthetic particle-size dis-tribution.

The calculated distribution predicts predominance ofl-nm particles, and significant numbers of 2 nm and 3nm particles, in good agreement with the observed dis-tribution. Small differences between the calculated andobserved data-such as the slight depletion of thin par-ticles and enrichment of thick ones in the observations

TABLE 1. Predominant ordering type (Reichweite), illite interlayerfractions, and iunction probabilities for samples ana-lyzed

OrderingSample type Pt P,, Pn Pr,,

WWBNCBccBLPBRANt u b

RORO-R1RO-R1R1-R2

HJ

R3

.3

.55 .38

.5 .25

.75 .67 .63

.90 .89 .88 .86

.90 .89 .88 .86

770 ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE

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Fig. 5. Afransements of interlavers (a) carcurated _'yp* ,.1?,i;,*T1ltJ"l':lTilT::1il'# j:}j#iiji''jl,T'[13]_tically on the basis of Markov theory and (b) random accumu-

-.""i p"rilrf.s for sample NCB.lations of fundamental particles for sample WWB.

relative to the calculations-are not statistically signifi-cant because of the relatively small number of measure-ments. For example, one particle was observed for eachthickness of 4, 5, 6, and 8 nm. Each of these particlesrepresents about 3olo of the total population, a somewhatgreater fraction than is predicted by the calculated distri-butions. On the basis of counting theory (e.g., Bertin,1978), however, each of these measurements carries astandard deviation of l00o/o of the observed value. Forthis reason, discrepancies here are not necessarily signif-rcant.

Figure 5 shows interlayer arrangements in randomMacEwan crystallites, calculated from Markov theory asdescribed before, and those that would result from ac-cumulation of fundamental particles from the measuredpopulation. In the latter case, a computer randomly choseparticles and added them to an accumulation one at atime until the accumulation contained more than l0 in-terlayers. Interlayers internal to the particles form illitesand the interfaces between the accumulated particles makeup smectite interlayers. The representations are similar,showing common clusters of both illite and smectite in-terlayers. Illite clusters are somewhat more common inthe random accumulations because the four particles > 3

(a ) (b )

nm in thickness make up > l0o/o of the population ofobserved particles (and a considerably greater share ofthe population's volume).

Sample NCB (Fig. 6), a Cretaceous bentonite from NewCastle, Colorado, is representative of I/S with short-rangeorder. The xRD pattern of this sample is best modeledassuming a composition of 550/o illite and incomplete Rlorder. The calculated size distribution predicts that 2-nmparticles are predominant and that significant numbersof particles I nm and >3 nm thick occur. Except for someinflation of the population at I nm due to crystallite-endeffects, the calculated and observed distributions matchclosely. Synthetic interlayer arrangements (Fig. 7a) showa greater tendency for interlayer alternation than the pre-vious sample. The synthetic arrangements clearly resem-ble those that would result from the accumulation of fun-damental particles (Fig. 7b). Sample CCB (data notshown), a Cretaceous bentonite from Canon City, Colo-rado, is also representative ofI/S with short-range order.The xnp pattern of this sample is best modeled assuminga composition of 500/o illite and incomplete Rl order. Inthis sample, agreement between Markovian predictionsand rev observations is similar to that observed for sam-ple NCB.

40-

20-(z)

40-

20-(z)

40-

20-(z)

Fig. 6. Mineralogical observations for sample NCB (Nadeauet al., 1985) as described for Fig. 4 (top), and predictions ofMarkov theory for I/S with 550/o illite and 45o/o Rl order (bot-tom).

io z'o r'o 'zo

Fig. 8. Mineralogical observations for sample LPB (Nadeauet al., 1985) as described for Fig. 4 (top), and predictions ofMarkov theory for I/S with 75o/o illite, complete Rl order, and25o/o R2 order (bottom).

Colculoted

ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE

I I . I I I I I ' I I I

I I I I . I I I . I I

I I ' I . I I I ' I . I I

l . l . t . t . t . l l l l l

t . i l l t ' l i l . l l l

I I . I I I I . I I I

I I . I I ' I I . I I I I I

I I . I . I I I I ' I I

I I I ' I ' I . I . I I

I I ' I I . ' I I I I I

r ' t ' i l . 1 . r . rI I . I I . I I I ' I I I

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l i l l . i l t . l l

( b )

771

' I I . I I . I I ' I I I I I

u i l t . t ' l l l l l l .

I I I ' I I I . I . T I . I .

I ' I . I I I I I . I I I I I

I . I I I . I . I I I I I ' I. I I I I I I I I . T I I I .

I I . I I . I I . I I I I I T

I I . I I I I . I I I ' I I I

I I I I I I ' I I I . I . I .

I I I I ' I . I I ' I I I . I

I I . I I I I I I I ' I . I I

I . I I I I . I I ' I I I I I

. I I ' I I I I . I I I . I I

I . I I I I I I ' I I I I I .

( a )

40-

Fig. 9. Arrangements ofinterlayers (a) calculated on the ba-sis of Markov theory and (b) random accumulations of funda-mental particles for sample LPB.

Sample LPB (Fig. 8), a Cretaceous bentonite from LasPiedras, Colorado, is typical of I/S with short- to inter-mediate-range order. The xno pattern of this sample isbest modeled assuming 750lo illite with complete Rl orderand partial R2 order. The corresponding size distributionpredicts a broad distribution ofparticle sizes with 2-nmand 3-nm particles in greatest abundance. Significantclustering of illite interlayers and some alternation arepredicted (Fig. 9a). Again, the Markovian predictionscompare well with the observed size distribution and cal-culated interlayer arrangements, except for some inflationof l-nm and 2-nm populations due to the effects of as-suming fixed crystallite sizes.

Samples RAN (a Permian sandstone from the southernNorth Sea basin) and TGB (a Devonian bentonite fromMohawk Valley, New York) are typical of I/S with long-range order (Fig. l0). The xno patterns for these samplesare best modeled assuming 900/o illite with complete R3order. Calculated xno patterns, however, fail to modelthe observed patterns exactly. In particular, significantdifferences occur in the diffracted intensity near l.l and0.48 nm.

Markov theory predicts size distributions for samplesRAN and TGB that are qualitatively different from theobserved distributions. Whereas the calculated distribu-tion predicts numerous particles >7 nm thick, such par-ticles are rare in TGB or RAN. In addition, these samplescontain significant populations of2- and 3-nm particles,whereas these particles occur only at the ends of Mac-Ewan crystallites ordered by Markov theory. CalculatedMacEwan crystallites (Fig. I la) contain longer and moreabundant clusters of illite interlayers than arrangementscalculated from size distributions of fundamental parti-cles (Fig. I lb). Apparently, Markov theory, which hasnot been completely successful in describing xnD patternsof I/S minerals with long-range order (Reynolds, 1980,p.297), cannot predict even qualitatively the reu obser-vations of these minerals.

INrnnr-.lysn coNTENT or I/S

To test further the relationship between the Markovmodel and the concept of fundamental particles, we com-pare the estimate of the fraction of illite interlayers in I/S

a---lh'r---r 2 3 4 5 6 7 E 9 > 9

t3r.rrrttJ1 2 3 4 5 6 7 8 9 > 9

Fig. 10. Mineralogical observations of samples RAN andTGB (Nadeau et al., 1985) as described for Fig.4 (top), andpredictions of Markov theory for I/S with 90o/o illite and com-plete R3 order (bottom). The observed and predicted size dis-tributions are qualitatively different.

(Pr) resulting from Markov analysis of xno patterns tothe interlayer content of accumulations of fundamentalparticles. The latter can be calculated directly from mea-sured size distributions of fundamental particles.

Consider a population of { particles of known thick-ness. There are Nr particles I nm thick, N, particles 2mm thick. and so on. so that

N,: > N, .

MacEwan crystallites are stacked arrangements of theparticles. Within the crystallites, illite interlayers are in-ternal to the particles, and smectite interlayers occur atthe interfaces between particles. Arranging the i/, parti-cles into N, MacEwan crystallites, then,

f r , : N , + 2 N 2 + 3 N r + " - l / ,

where n, is the total number of interlayers. N, is subtract-ed from the summation because there is one fewer inter-layer than silicate layer in each crystallite.

Of the total number of interlaYers,

tx,: N. + 2N3 + 3N. + "'

are illite interlayers. The intedayer fraction Pr(f.p.) is theratio of the number of illite to total interlayers determinedon the basis of the size distributions of fundamental par-

ticles for the samples in question:

: ) 'ry - n',

: ) 1 i - r )N ,

772

I I I I I . I I I I I I I I I

I I I I I I I I I I . I I I I

I I I I I I I . I I I I T I I

I I I I I I I I I I I I I I .

I I . I I I I I . I I I ' I I

I I I I I I I ' I I I I I I I

I I I I I I . I I I I I I I I

I . I I I I . I I I I I I I I

I I I . I I I ' I I I I T I I

I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I

I I I I . I I I I I I I T I .

I I I I I I . I I I I . I I I

I I I I I . I I I I I I I I I

( a )

I I I I I I I I I I I I

I I I I I I . I I I I

I I I I I I . I I I I I I

I I ' I I I I I I ' I I I

I I . I I ' I I I I . I I

I I I . I I I . I I I I I

I I I I I . I I I I ' I

I . I . I I I . I I I

I T I T I T I T I I I I

I i l l t ' i l i l 1 1

l i l i l l . t . l r r

I I . I I I I I ' I I

I I I ' I I I I I . I I I

I I . I I I I . I I . I I I

( b )

Fig. 1 1. Arrangements of interlayers (a) calculated on thebasis of Markov theory and (b) random accumulations of fun-damental particles for sample TGB.

Here, f, is the fraction N i/ N, of particles i nm thick, andNo is the average number of particles N, / N*per crystallite.This equation is similar to Equation I in Eberl et al.(1987) and the equations on p. 508 in Nadeau (1985),except for the l/N, term that accounts for the finite num-ber of particles constituting a crystallite. Equation I givesinterlayer fractions directly from the particle-size distri-butions/ determined by rnru experiments.

Figure 12 shows the relationship of P, (f.p.) given byEquation I from measured particle-size distributions withP, (Markov) estimated by modeling the xno patterns ofthe samples studied. Values agree well for I/S and Rl-and R2-ordering types (samples CCB, NCB, and LPB).This correlation argues that Markov theory accurately de-scribes interlayer abundances in this type of I/S. SampleWWB, which has R0 order, gives a value of P, (f.p.) sig-nificantly greater than P, (Markov). We suggest that thisdiscrepancy is due to the overestimate of large particles,which might be more easily imaged by shadowing tech-niques. For example, ignoring the four measured particles> 3 mm thick in this sample (a total of l2o/o of the mea-sured population) gives near perfect agreement, as shownby the open circle in Figure 12.

For sample TGB, P, (Markov) > & (f.p.) and for sam-ple RAN, P, (Markov) >> & (f.p.). Notably, these twosamples have xno patterns and distributions of funda-mental particles that are poorly modeled by Markov the-ory. These differences in determination of interlayer con-tent are consistent with our suggestion that Markov theorypoorly describes the structure of VS with interpreted long-range order.

DrscussroN

Results in this study show broad agreement betweenthe predictions of Markov theory and the observed sizedistributions of fundamental particles for I/S with ran-dom and short ranges ofinterlayer order. This agreementindicates that the precision ofthe reu technique is ade-quate for measuring c*-axis thicknesses of Pt-shadowedsamples, despite the concerns raised by Mackinnon (1987).On this basis, we conclude that rErvr measurement of thethicknesses of fundamental particles for these minerals

ALTANER AND BETHKE: INTERLAYER ORDER IN ILLITE/SMECTITE

'^b +iLPB

c c B

lwwB

W W B , i : 1 , 3

. 2 . 4 . 6 . 8 1 . 0

R ( t . P . )

Fig. 12. Fraction of illite interlayers in I/S for samples ana-lyzed. Illite contents are from analysis of xno patterns usingMarkov theory P, (Markov) and calculations based on the sizedistributions of fundamental particles P, (f.p.) according toEquation 1. Closed symbols represent illite contents based onmeasurements of fundamental-particle size. Open symbol forWWB represents an illite content calculated on the basis of pop-ulations ofparticles 1 to 3 nm thick.

support rather than contradict interpretations of interlay-er order made on the basis of xno studies.

Markov theory, however, cannot explain the abun-dance of particles <4 nm thick and the paucity of parti-cles >7 nm thick in illite-rich I/S intepreted to have long-range (R3) order. On the basis of the relative abundancesof 5-nm to 7-nm particles in samples RAN and TGB,illite-rich I/S might contain especially long ranges of or-dering (R4-R6), which are difficult to describe using cur-rent formulations of Markov theory. The significantnumber of particles just 2 and 3 nm thick in these sam-ples suggests that the very long range order would beincomplete. Lattice-fringe imaging of illite-rich VS shouldprovide important insights into the nature of these min-erals.

An unresolved question is whether Markov theory orthe fundamental-particle concept best describes the crys-tallite sizes of I/S minerals in nature. MacHardy et al.(1982) estimated crystallite thicknesses of filamentous I/Sfrom sandstone pores using scanning electron microsco-py. They concluded that these clays have thiclcresses moresimilar to fundamental particles than to MacEwan crys-tallites. Lattice-fringe images of I/S from bentonites, how-ever, show crystallites that are closer in thickness toMacEwan crystallites than to fundamental particles (Leeand Peacor, 1986; Vali and Koster, 1986; Klimentidisand Mackinnon, 1986). Sampling bias, however, couldaccount for the lack of published lattice-fringe images offundamental particles. For example, dispersed funda-mental particles may be difficult to image because of theirsmall thicknesses.

These observations might be reconciled if smectite in-terlayers disarticulate by osmotic swelling after the Na-

oJ

o=

o-

or Li-saturation process used in preparing samples for Pt-shadowing analysis. Osmotic swell ing might causeMacEwan crystallites to cleave along smectite interlayers.Ahn and Peacor (1986) made a similar suggestion, al-though they proposed that large MacEwan crystallitescleave along smectite interlayers because of grinding dur-ing sample preparation rather than osmotically. Severalstudies have shown that water-rich suspensions of smec-tite exchanged with Li and Na dissociate into individual1-nm-thick particles (Norrish, 1954; Foster et al., 1955;Suquet etal.,1975), although the degree ofdissociationis reduced as salinity increases (Norrish and Rausell-Co-lom, 1963). Disarticulation arises from the large hydra-tion energies of Na and Li cations and from the greatersalinities in the interlayers relative to the solutions usedin sample preparation.

Because Ca, Mg, K, and Ba ions have low hydrationenergies, smectites saturated with these cations do notexhibit significant osmotic swelling (Suquet et al., 197 5).Disarticulation into fundamental particles would not beexpected under these conditions. This observation mayexplain why dispersed samples of untreated I/S show largervalues of mean particle thickness (Inoue et al., 1987) thanLi- or Na-exchanged I/S with the same illite content (Na-deau et al., 1985). Apparently, the untreated samples re-tain poorly hydrated ions such as Ca in their interlayersand do not disarticulate completely. Because these cat-ions are abundant in most groundwaters, I/S may also berelatively articulated in nature.

In the laboratory, disarticulation seems to be sufficient-ly reversible to reform MacEwan crystallites upon dryingwhen the clay is dispersed in dilute solutions. For ex-ample, Nadeau et al. (1984a,1984b, 1984c, 1985) ob-served that accumulations of fundamental particles fromNa- and Li-exchanged I/S appear as MacEwan crystallitesin xnp experiments, giving rise to their interpretation ofinterparticle diffraction. From these considerations, wepropose that osmotic swelling could explain the apparentdual nature ofI/S: the thin particles observed in Pt-shad-owing experiments after dispersion in Na and Li solu-tions and the thicker crystallites observed in xno exper-iments and lattice-fringe images.

Acruowr,pocMENTS

We thank R C. Reynolds for many discussions as well as the use ofhis MOD-4 computer program, I.D.R. Mackinnon and an anonymousreviewer for reviewing the manuscript, and the University of Illinois forthe use of its computers This research was supported by NSF grants EAR85-52649 and EAR 86-01 178

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