American Mineralogist, Volume 72, pages 724-738, 1987

Modulated 2:1 layer silicates: Review, systematics, and predictions

SrnprrnN Guccturrcrlr Department of Geological Sciences,University of Illinois at Chicago, Chicago,Illinois 60680, U.S.A. R. A. Eccr-nroN Department of Geology, Australian National University, P.O. Box 4, Canberra,A.C.T. 2600, Australia

AssrRAcr A continuous or nearly continuous octahedralsheet places important constraints on the geometry and topology of the attached tetrahedra in modulated 2:l layer silicates.A plot of the average radius size of the tetrahedral cations vs. the average radius size of the octahedralcations shows the distribution of structureswith respectto misfit of tetrahedral and octahedral (T-O) sheets,with modulated structuresforming when misfit is large. It is tentatively concluded that such misfit is a requirement for modulated structuresto form. It is evident that misfit of T-O sheetsis a limiting factor for geometrical stability. On the basis of tetrahedral topology, modulated 2;l layer silicates are divided into two major categories,islandlike (e.g., zussmanite, stilpnomelane) and striplike (e.g., minnesotaite, ganophyllite) structures.Bannisterite, which is more complex, most closely approximates islandlike structures.The plot involving cation radii is useful as a predictive tool to identify modulated structures,and parasettensiteand gonyeriteare identified as possiblenew mem- bers of the group. Diffraction data suggestthat parsettensite has a variation of the stilpnomelane structure with smaller islandlike regions and gonyerite has a modulated chlorite structure. Chemical mechanismsto eliminate misfit of T-O sheetsusually involve Al substitutions. Becausemodulated 2:l layer silicatescommonly occur in Al-deficient environments, struc- tural mechanisms are usually a requirement to eliminate misfit of component sheets. Besidesa modulated tetrahedral sheet, structural mechanisms include (l) a limited cor- rugation of the interface between the T-O sheetsthat allows for a continuously varying stmctural adjustment, (2) distortions of the octahedral-anionarrangement located at strip or island edges,and, at least in one case,(3) cation ordering. Near end-member compositions, modulated 2:l layer silicates usually have Al in tet- rahedral coordination, when Al is present,rather than in octahedral sites. It is concluded that a continuous edge-sharingoctahedral sheetwith large cations has a constraining in- fluence on the size of possible substituting cations. This effect may explain the lack of octahedral ordering schemesin hydroxyl-rich micas where a small cation might occupy the M(l) site and a large cation might occupy the M(2) sites that surrounded M(l).

INrnooucrron kaolin group. Except in the talc-pyrophyllite and the ser- Silicatesin which SiOotetrahedra are linked by sharing pentine-kaolin groups, adjacent layers may be separated three corners to form infinite two-dimensional sheets by cations, hydrated cations, metal-hydroxyl octahedral constitute a major category of rock-forming minerals sheets,organic compounds, or various other interlayer known as the layer silicates. Pauling (1930) outlined the material. general features of the micas and related layer-silicate The generalizedmodel for l: I and 2:l layet silicatesas minerals. These features usually include a layer com- outlined by Pauling was firmly establishedby later work- prised of two types of sheets;octahedrally coordinated ers. However, Zussman (1954) found that such a model cations form a sheetby sharing edges,and tetrahedrally does not hold in all cases.For example, the serpentine coordinated cations form a sheet by sharing corners. If antigorite (Zussman, 1954; Kunze, 1956) shows an in- two tetrahedral sheetsoppose each other with the octa- version and relinkageoftetrahedral apicesacross the ide- hedral sheetbetween, then a 2: I layer is described,where- ally vacant regions between l:1 layers. Since that time, as if only one tetrahedral sheetis linked to the octahedra, the serpentineJike minerals caryopilite (Guggenheim et the result is a 1:I layer. The former layer type is common al., 1982),and greenalite(Guggenheim et al., 1982), the to the talc-pyrophyllite, mica, smectite, vermiculite, and talc-like mineral minnesotaite (Guggenheim and Eggle- chlorite groups, and the latter is found in the serpentine- ton, 1986a), and the micalike minerals zussmanite 0003-004x/87l0708-{724$02.00 724 't25 GUGGENHEIM AND EGGLETON: MODULATED 2:1 LAYER SILICATES

(Lopes-Vieiraand Zussman,19 69),stilpnomelane (Eggle- TABLE1. Calculatedand observedlateral di- ton, 1972), ganophyllite (Eggleton and Guggenheim, mensionsof octahedraland tetrahedralsheets I 986),and bannisterite(Threadgold, I 979)have been de- Compo- scribed as modulated structuresbased on the ideal struc- sition Mineral 4 (A) 4 (A) tures of serpentine, talc, or mica. The recent structure Octahedralsheet refinement of pyrosmalite (Kato and Tak6uchi, 1983) in- A|(OH)3 Gibbsite, 8.684,8.672 8.125 dicatesthat this structure may be classifiedas modulated, bayerite Mg(OH), Brucite 9.425-9.441 8.910 although its derivation directly from the traditional layer- Fe(OH), Synthetic 9 786 9.164 silicate group is more complex. Mn(OH), Synthetic 9.948 9.376 We define a modulated layer silicate as one in which a Tetrahedralsheet periodic perturbation occurs in the structure. Often, this Si4O1o None 9.15 (SisADOlo None 9.335 means that a superlattice forms. Although a prominent sublattice is present that approximates that of a normal Note:Observed b-axis dimensions, 4, arefrom Saal- feld and Wedde(1974),Zigan et al (1978),Zigan and type of layer silicate such as a serpentine,talc, mica, etc., Rothbauer(1 967), and Oswaldand Asper(1 977). Cal- the overall structure is more complicated and may in- culatedvalues, 4, are from Eqs.1 and 2 of text using volve tetrahedral connectionsacross the interlayer region ionicradii trom Shannon(1976). and/or discontinuities in the component sheets.For the purposeof this paper, we do not consider modulated lay- er-silicate structures to include those structures with discontinuities and out-of-planedisplacements in the oc- oxygensto form the lower portion ofthe octahedralsheet. tahedral sheetbecause such displacementsdisrupt the two- To complete the octahedral sheet in 2: I layer structures, dimensional layerlike aspectsof the structure. Therefore, a secondtetrahedral sheetis inverted to oppose the first the minerals sepiolite and palygorskite are not discussed so that a similar configuration of apical oxygensand OH further becauseof their prominent octahedraldiscontinu- groups surround the octahedralcation. In l:1 layer struc- ities. The serpentineJike mineral chrysotile (Jagodzinski tures, the octahedral cations complete their sixfold co- and Kunze, 1954; Whittaker, 1956a, 1956b)is not a ordination with OH groups only, which form an addi- modulated structure by the above definition, although its tional anion plane on one side of the octahedral cations structure is basedon principles similar to those outlined and which are not sharedwith the tetrahedral sheet. below. It is emphasizedthat the tetrahedral sheetis composed A continuous or nearly continuous octahedral sheet of three planes: the basal plane, the tetrahedral cation placesimportant constraints on the geometry and topol- plane (usually Si) and the apical oxygen + OH plane. This ogy ofan attached tetrahedral sheet.The purpose ofthis latter plane forms a common junction between the two paper is to explore the relationship between the tetrahe- sheetsand requires that the lateral dimensions of an oc- dral and octahedral sheetsby reviewing previous con- tahedral sheet be equal to the lateral dimensions of the cepts and by establishinga simple graphical approach to attached tetrahedral sheet.In addition to overall charge determine topological limits. Such limits are potentially balance,this relationship representsthe major constraint useful as a predictive tool to determine not only which 1o variations in chemistry in both octahedral and tetra- minerals require further study, but also to place con- hedral sheets. straints on the extent ofstructural adjustment. The degreeof fit between the tetrahedral and octahe- dral sheetsmay be estimated (see,e.g., Radoslovich and Trm rrrna,gEDRAL-ocTAHEDRAL RELATroNsHrp: Norrish, 1962) by comparing the lateral dimensions of Rnvrnw oF coNcEprs the two component sheetsin an unconstrained or free The tetrahedral sheet forms an ideally hexagonalnet- state. Lateral dimensions of the octahedral sheetmay be work with tetrahedra containing primarily Si and possi- eslimatedfrom the relation bly lesseramounts of Al3* or Fe3*. Each tetrahedron is b"",: 3(M-O)14, (l) linked to three other tetrahedral neighbors through shared corners, with these shared anions forming a basal plane. where M-O representsthe mean octahedralcation to an- The fourth corner or apical oxygenis directed away from ion distance.Equation I assumesthat the octahedra are the basal plane and is involved also in the linkage to the regular. The octahedral lateral dimensions as calculated octahedralsheet. The hexagonalmodel as describedcon- may be compared to naturally occurring octahedral sheets sists of sixfold tetrahedral rings forming a two-dimen- found as hydroxide minerals (Table l). Calculated and sional network. However, the tetrahedral sheet consists observed values differ significantly and suggestthe im- also of a hydroxyl (OH) group located at the same level portance of octahedral distortions (e.g., Radoslovich, as the apical oxygen and centered in the hexagonalring. 1963)in determiningthe lateraldimension. For example, Therefore, the apical oxygens and OH groups form a brucite has an observed b-cell length that is 60/olarger completeplane of anions.Larger cationsreside on another then that calculated assumingno distortions. plane immediately adjacent to this anion plane and are Tetrahedral sheetsdo not occur in an unconstrained coordinated to one OH group and two adjacent apical and free state,but it is possibleto calculatean ideal lateral 726 GUGGENHEIM AND EGGLETON: MODULATED 2:1 LAYER SILICATES extent basedon (Si,Al) content from the equation al., 1973)and by field-strengtheffects (the ratio ofvalence to cation radius) of neighboring octahedra(Lin and Gug- b(Si,-,AI,) = 9.15 + 0.74x, (2) genheim, 1983).Additional contributing factors to ry'and where x is the Al content. The assumptionsare that the r valueshave beenreported (cf., Hazen and Wones, 1972)' tetrahedral sheetis composedofhexagonal rings oftetra- Clearly, the misfit betweenthe two sheetsis only one of hedra, the tetrahedral anglesare ideal, the Al-O distance severalfactors contributing to the magnitude of thesepa' is 1.748A, and the Si-O distanceis 1.618A. The lateral rameters. dimensions of both component sheetswill be identical in Another notable distortion found in the octahedral sheet only certain specialcases depending on the compositions is the counterrotation of upper and lower oxygen triads ofeach sheet. (Newnham,l96l), designatedas c.r by Appelo (1978).Ra- doslovich (1963) suggestedthat shortened shared edges Comrnondistortions affecting sheet sizes causethis effect,but regressionanalyses by Lin and Gug- Reducingrelatively large tetrahedral sheets.The abun- genheim (1983) indicate that the difference in size be- dance of layer-silicate minerals with large variations in tween the adjacent octahedral sites is the controlling fac- tetrahedraland octahedralcomposition suggeststhat there tor. The resultsof the regressionanalyses imply that cation is a structural mechanism(s)that allows the tetrahedral charge and shared-edgelengths are important insofar as and octahedral sheetsto be congruent. The most impor- they affect polyhedral sizes. For structures that have a tant mechanism is distortion of the tetrahedral sheet by uniform chemistry for all of the octahedral sites, varia- in-plane rotation ofajacent tetrahedra in opposite senses tions in <.rvalues between octahedraare negligible. How- around the silicate ring (see,e.g., Guggenheim,1984). ever, octahedral-cationordering will affect

ane can be representedapproximately by KouFeu- (si,AD(o,oH),,.2H2O. The structureof stilpnomelane(Eggleton,1972) is com- posed of a continuous octahedral sheet and modulated tetrahedral sheets(see Fig. 2). The tetrahedral sheetsar- ticulate to the octahedral sheet,but form nearly trigonal islands of six-member hexagonalrings of SiOotetrahedra. Each island consistsof seven complete six-member sili- cate rings and has a diameter of seven tetrahedra. The Fig. 2. An idealizedstilpnomelane structure (A) projected islands are separatedand linked laterally by an inverted plane (B) viewed (both onto the X-Y and along[110] modified single six-member silicate ring. In contrast to the hexag- from Eggleton,1972). onal rings within the islands, these rings have a more trigonal configuration. In a normal layer silicate, the in- tures with the triclinic form depleted in K and slightly terlayer spaceis vacant or contains the alkali cation. In enriched in Mn at the expenseof Fe. Polytypesmay form stilpnomelane, the interlayer region contains the alkali with both structures,and Jeferson (1976) has noted the cation and the inverted six-member trigonal silicate rings, occurrenceof numerousone- and two-layer varieties.Muir which link the islands and adjacent layers acrossthe in- Wood (1980),in a study on the same material, did not terlayer space.The interlayer has two trigonal ringsjoined find the inverse K to Mn variation in all cases,as was along Z through the apical oxygens and a resultant doo, reported by Jefferson (1976). In addition, he noted the value of 12.2L. occurrenceof zussmaniteJike (designatedas "2u2") ma- Bannisterite.Smith (l 948)and Smith and Frondel (1968) terial with cell parametersapproximately 80/osmaller and recognizedthat two different minerals had been confused with a chemistry of approximately KAlMn._,Fel[rSi,,- for ganophyllite.Smith and Frondel (1968) presented Oor(OH),o,by analogyto zussmanite. X-ray, chemical, and additional optical data for bannis- The zussmanitestructure (Lopes-Vieira and Zussman, terite that established it as a speciesin its own right. 1969) contains T-O-T layers defined by sixfold rings of Threadgold (1979) presenteda structural formula based tetrahedraopposing a continuous octahedralsheet. Three- on electron-microprobe analysisand a refinement of the fold tetrahedral rings laterally connect the six-fold rings structure. However, full details have not yet been pre- and connectadjacent T-O-T layersthrough a tetrahedral sented.Dunn et al. (198 l) chemically analyzedmaterial edgeacross what is the interlayer region in a normal layer from Franklin, New Jersey,and Plimer (1977) reported silicate (seeFig. l). Alkali ions reside in the hole formed on material from Broken Hill. Chemical formulae appear by two opposing sixfold rings in the interlayer region, but to rangefrom Caoo,GA., Nao'n) (Fe' MnorM& ')":,.(Si,or- the number of such sites is restricted by the presenceof Al,6),:,6O38(OH)s'2(H,O)for the Broken Hill material the threefold rings; there are only one-fourth as many (Treadgold, pers. comm.) to Ca.o3G<{o,Naoorr)(Fe,o.- alkali positions in zussmanite as compared to a normal Mnu,orMg,orrZn, oorFef,jr)":,o,ur(Si,o rrAl, rrFefrjo)":,uOrr- mrca. (OH),.6. l(HrO) for the Franklin material (Dunn et al., Stilpnomelane.Modern structural work on stilpnomel- 198l) with a structural formula of IQrCaorM,oT,uOrr- ane was initiated by Eggletonand Bailey (1965)in which (OH)8(HrO)r-6where M and T are the octahedraland tet- the subcell was defined and described. Eggleton (1972) rahedral cations, respectively. described the full cell and later (Eggleton and Chappell, Bannisterite (Threadgold, 1979) has a two-layer struc- 1978)compared chemistry to physical properties and cell ture with one-quarter of the tetrahedra inverted toward data. Crawford et al. (1977) found evidencefor two two- the interlayer space.These tetrahedra share their apical layer and many long-rangeperiodicities from an electron- oxygenswith similarly inverted tetrahedra from adjacent microscope study. layers. Sixfold rings are composed oftetrahedra that co- Stilpnomelaneis generallyrecognized as a group of min- ordinate directly to the octahedral sheet.Fivefold rings, erals, with the bulk of component Fe ranging from pri- very distorted sixfold rings, and sevenfold rings are formed marily Fe2* (ferrostilpnomelane)to primarily Fe3* (fer- also, but each ofthese rings contains two inverted tetra- ristilpnomelane).Although Mg-dominant stilpnomelanes hedra (Threadgold, pers. comm.). In this way, the close have beenknown for sometime, Dunn et al. (1984)des- proximity of highly chargedtetrahedral cations is elimi- ignated this speciesas lennilenapeite. A Mn-dominant nated in the fivefold and distorted sixfold rings. Similar speciesis known as parsettensife.(See Predicting Modu- fivefold and distorted sixfold rings are found in gano- Iated Structures,p. 735.) The end-member Fe varieties phyllite. have structural formulae dependenton the protonization of the hydroxyl groups:KFe?J (SiurAle)Or68(OH)o8.| 2HrO Strip structures for ferrostilpnomelaneand KrFelr*(Si63Ale)O2r6.36HrO for Minnesotaite. Gruner (1944) suggestedthat minneso- ferristilpnomelane. Eggleton and Chappell (1978) have taite was the Fe2+analogue of talc on the basis of X-ray suggesteda simplified formula basedon one-eighthof the powder photographs of impure material. However, al- structural formula so that, for example, ferrostilpnomel- though the doo,value of approximately 9.6 A suggestsa GUGGENHEIM AND EGGLETON: MODULATED 2:I LAYER SILICATES 729 lalc structure, Guggenheimand Bailey (1982) concluded X andtentetrahedra(4+ I + 4 + l) spannineoctahedra; from single-crystalphotographs of a twinned crystal that a P cell is produced. For the C-centeredcell, strip widths the structure is modulated. Further X-ray analysisand a alternate between three and four tetrahedra so that nine chemical and transmission-electron microscopy (rrrvr) tetrahedra (4 + I + 3 + l) span eight octahedra. The study by Guggenheimand Eggleton(1986a) supported this C-centeredcell has been found only in the most Fe2+-rich conclusion and outlined the details of the structure. sample. A minnesotaiteJike phase enriched in Mn was Guggenheim and Eggleton (1986a) showed that min- noted by Muir Wood (1980), but structural information nesotaitecrystallizes in two structural forms, which may is lacking. be designatedP and C in accord with the Bravais lattice Ganophyllite. The first careful optical study of gano- of the two respectiveunit cells.Crystallization ofthe struc- phyllite was made by Smith (1948). He found evidence tural forms appearsto be related to chemistry, and the that the term "ganophyllite" was being applied to two resulting misfit between the tetrahedral and octahedral separatelayer silicates.Smith and Frondel (1968) ditrer- sheets.A simplified structural formula for the C-centered entiated thesephases on the basis ofX-ray data and des- cell using the chemical data of Blake (1965) and Guggen- ignated them as ganophyllite and bannisterite (seeabove). heim and Eggleton(l 986a)on the basisofeleven oxygens The approximate chemical formula (Eggletonand Gug- 56(Mn,Fe,Mg)ro(Si3, is (Fe,,oMno ouMgo ,nAl. orxsi3 88Alo rr)Oro(OH), uo. Of the genheim,I 986) is (K,Na,Ca)u+7 5Al' s)- sevenspecimens studied, this samplewas the only C-cen- Or6(OH),6.2lHrOand Z: 8. Peacoret al. (1984)have tered example, and, furthermore, it was the only sample given the name of eggletoniteto sampleswith Na > K. that crystallized suffciently well to be studied by single- Dunn et al. (1983) have found that for the limited number crystal X-ray methods. Although the P-cell structure var- of samplesthey analyzed,there appearsto be little vari- ied somewhatin composition, a representativechemistry ation in the octahedral occupancy. is given by (Fe,,nMno o,Mg, o7)(Si3 eeAlo o,)Or.(OH)3. Smith and Frondel (1968) showed that ganophyllite Like talc. minnesotaite has a continuous octahedral crystallizesin the monoclinic spacegroup A2/a with cell sheet.There are adjacent Si tetrahedra on either side of parametersa : 16.60(5),b : 27.04(8),c: 50.34(15)A, this sheetto form an approximate2:l layer (seeFig. 3). P:94.2(2)'. Thereis a prominentmonoclinic subcell with However, in contrast to talc, strips of linked hexagonal spacegroup I2/a and cell parameters 4o : 5.53 : a/3, rings of tetrahedra are formed only parallel to L A dis- bo: 13.52: b/2,co:25.17 A: c/2,and B :94.2. continuity ofthe normal configuration ofthe tetrahedral Jefferson(1978) noted a triclinic polytype la: 16.54(5), sheetresults along Xbecause some of the tetrahedrainvert b : 54.30(9),c : 28.52(8)A, d: 127.5(3),0 : 94.1(2), partially (note Figs. 3a, 3b). Thesetetrahedra form a chain r : 95.8(2)'lin spacecroup IPI or Pll and interpreted extendingparallel to Iin the interlayer region. The chain variations in polytype as resulting from structural col- servesto link the adjacent strips within the basal plane umns that can be stackedalong {011} planes. and also links adjacent strips acrossthe interlayer space. Ikto (1980) determined the ganophyllite subcell struc- The latter linkage is achieved through a tetrahedral edge ture by using single-crystalX-ray data. He describedthe (approximately 2.7 L), which is dimensionally equivalent subcell (note resemblancesin Fig. 4) as having a contin- to the interlayer separationin a normal talc structure. In uous octahedralsheet with tetrahedral strips on both sides this way, the doo,value of minnesotaite closely approxi- of the octahedra.The strips are three tetrahedral chains mates the predicted value of an Fe-rich talc. However, wide and are extendedparallel to X. The strips are stag- the bonding ofadjacent layersacross the interlayer region geredacross the octahedralsheet so that the rifts between is much stronger in minnesotaite than the weak van der strips are offset. The rift pattern allows a marked sinu- Waal bonding in a talc structure. soidal curvature of the octahedral sheet and of attached The disposition of the tetrahedral strips is such that tetrahedra along }. According to the Kato model, large strips superposedirectly acrossthe interlayer space,but alkali cations connect adjacent layers by occupying sites are displaced parallel to X by one-half of a strip width where rifts opposeeach other acrossthe interlayer. acrossthe octahedralsheet. In a normal 2:1 layer silicate, Guggenheimand Eggleton(1986b) found that the large the octahedral sheet is held in tension between the two cations can be readily exchanged.These results are in opposing tetrahedral sheetsand, thus, is planar. In min- contrastto the predictedbehavior basedon the Kato mod- nesotaite,the strip displacementacross the octahedralsheet el. In that model, there is a high residual negative charge relaxes such tension and allows limited curving of the associatedwith the coordinating anions ofthe interlayer tetrahedral-octahedral interface to produce a wavelike alkali site, thereby making cation exchangeunlikely. Eg- stnrcture. gleton and Guggenheim(1986) re-examinedthe structure Tetrahedral strip widths in minnesotaite are dependent ofganophyllite using the Kato data set, several hundred on the component sheetchemistry. Hence, there are vari- additional weak reflections,and electron-diffraction data. ations in unit-cell size and symmetry. As the cations in They proposeda model (seeFig. 4) whose significant dif- the tetrahedra are essentiallyall Si, variations in octahe- ferenceis basedon the interlayer connectors.The triple- dral-sheet chemistry are the most critical. When the oc- chain strips are connectedby pairs ofinverted tetrahedra tahedral sheet is relatively small, as in the Mg-enriched that serveto connectboth adjacentlayers and neighboring sheets,a modulation occurs every four tetrahedra along strips. The alkali cations reside in the tunnels formed in 730 GUGGENHEIM AND EGGLETON: MODULATED 2:I LAYER SILICATES

o

a=284-t

Fig. 3. (A) Perspectivsview ofthe idealized P-cell structure of minnesotaite.The interlayer tetrahedra sharecorners to form a chain parallel to Y, which is more clearly seen in (B) in the (001) plane drawing. (C) Diagrammatic illustration of the C-cen- teredcell ofminnesotaite. Note the alternation offour- and three- tetrahedra-widestrips along X The strips are joined by a cor- ner-sharing chain along I similar to that shown in (B) (from c Guggenheimand Eggleton, 1986a). the "interlayer" region between the inverted tetrahedra. Thesesites are numerous and poorly defined and may be DrscussroN comparedto the exchange-cationsites in zeolites.Overall, Excessiveout-of-plane tilting oftetrahedraas observed the structuremay be classifiedas a modulated mica struc- in the 1: I layersilicate chrysotile (e.9., Whittaker, 1956b) ture. cannotoccur in normal 2:l layersilicates; opposing tet- z 1l 4l

A ooooooo Ou oo ooo

B c

Fig. 4. (A) Ganophyllite structure projected down X; (B) and (C) Configuration of the tetrahedral sheet for Z : 0 and Z: Y+,respectively, for the monoclinic form. Symmetry elements(e.g., open circles indicate symmetry centers)for A2/a are also D given in (B) and (C). (D) A triclinic linkage. (From Eggletonand Guggenheim,1986.) 732 GUGGENHEIM AND EGGLETON: MODULATED 2:1 LAYER SILICATES

_ o28 *11 h l1 32 1 (A 6) o27

o26

A 0.65 o.70 075 o80 o85 -r"6) ro(A) o30

i=0325 muscovite o29 i = 0.535 trilithidt€ i = 0.648 (,-i ganophyllite o28 I1 chak'odtts-i I l1 6) cnabo'dite(res t 6) o27 o.27 (J ''nn"-'"n" o26

n D o85 0.65 070 075 o'80 o.8s 065 070 075 o8o r"(A) ro(A) Fig. 5. A series of plots of the averageradius of cations occupying the tetrahedral sites (r,) vs. the averageradius of cations occupyingthe octahedralsites (r") basedon ionic radii from Shannon(1976) and observedcompositions. Lines a and Dare explained in the text, and octahedralvacancies are ignored in the calculations(see text, also). (A) and (B) Compositions of stilpnomelanewith calculationsbased on reported Fe3+values (A) or recalculatedassuming that all Fe is Fe'?*(B). Chemical analysesare taken from Eggletonand Chappell (1978, Table l), Eggleton (1972, Table IVa), and Dunn et al. (1984) and show a wide range of chemical variations. Labeled points refer to analysesin the original sources.(C) Confining compositional regionsfor islandlike structuresfor stilpnomelane(from Fig. 68), zussmanite,and bannisteriteand individual points for chalcodite,gonyerite, and parsettensite.These regionsdo not necessarilyshow maximum limits of geometricalstability. Boxes(labeled 1-5) are talc compositions for ideal (1) and Fe-rich talcs (2, Robinson and Chamberlain, 1984;3, Forbes, 1969;4, Lonsdaleet al., 1980; 5, as no. 2 with all Fe as Fe2*).Analyses: zussmanite,Muir Wood (1980,p. 614); bannisterite,Dunn et al. (1981),Threadgold (unpub.); and gonyerite,Frondel (1955).(D) Showsa plot analogousto (C), but for striplike structures.Analyses: minnesotaite, Guggenheim and Eggleton(1986a); ganophyllite, Eggletonand Guggenheim(1986). rahedral sheetsacross a common octahedral sheet hold lateral dimensions. For example, the ratio of tetrahedral the octahedralsheet flat under tension.However. a limited to octahedralcations increases from l. 33: I in talc to I .40:I corrugation in modulated 2:l structures is possible be- in zussmanite,1.50: I in stilpnomelane,1.60: I in bannis- causetension is relieved at the point of modulation where terite, and 1.67:l in ganophyllite. These variations are a the tetrahedral inversions occur. It is noteworthy that the direct result ofthe tetrahedral configurational changeand structure simulates a l:l layer silicate at these inversion correspondto the large lateral size ofthe octahedralsheet. points. Therefore, modulated 2:l layer silicatesinvolve a continuously varying structural adjustment that compen- The I, vs. P. plot sates for differencesin component-sheetlateral dimen- The use of r, vs. r. plots to delineate geometrical "sta- sions. It is emphasized,however, that the corrugation is bility" fields may be justified for the modulated 2:l layer limited in range and that a conflgurational change in- silicates.Obviously, the variations in the ratios of tetra- volving tetrahedralinversions is a requirement. hedral to octahedral cations and the structural compen- Tetrahedral inversions usually involve "extra" tetra- sation for differencesin the lateral dimensionsof the com- hedra that serve to span ever-increasingoctahedral-sheet ponent sheetssuggest the utility of such plots. Unlike the GUGGENHEIM AND EGGLETON: MODULATED 2:1 LAYER SILICATES 733

l: I layer silicates,the 2:l layer silicateslack stronglayer- and octahedralsheets is necessaryto producea modulated toJayer interactions either through H bonding or by elec- structure should be consideredtentative until additional trostatic interactions caused by cation substitutions. In data are obtained for analysis no. 33. Clearly, however, contrast to the serpentines,tetrahedral sheetsin the mod- misfit of tetrahedral and octahedral sheetsis a geomet- ulated 2:l layer silicatesface tetrahedral sheetsacross the ically limiting factor. Whereas (Fe2*,Fe3+)stilpnome- interlayer. Also, in somecases, the layer-to-layerdistances lanes may have a large compositional range, there is a are quite largebecause ofone or more tetrahedrainvolved geometrical limit in which the misfit between the two in linkagesacross the interlayer region. Figure 5 shows a kinds of sheetsprevents the formation of the structure (at seriesofsuch plots, where r, is the weighted-averagetet- higher averageoctahedral-cation sizes). It is noteworthy rahedral-cation radius and r. is the analogousparameter that all modulated structureshave compositional regions for the octahedral cations. Representativelayer-silicate that fall to the right of lines a or b, the two approximations minerals have been plotted in Figure 5c using ionic radii for the limitation of the congruencyof nornal tetrahedral data from Shannon (1976). In order to make the plot and octahedralsheets. Therefore, when compositions fall useful as a predictive tool (seebelow), octahedralvacan- to the left of these lines, the modulated structure(s)re- cies are not included in the calculations, as the number quires readjustmentsthat involve lateral reductions in the of such vacancies would be unknown in an unknown dimensions of the tetrahedral sheet, such as tetrahedral structure. rotation or possibly sheetthinning or thickening, etc. A single line separatingthe region of geometrical sta- The use of the r, vs. F"plot requires that the chemistry, bility of normal layer silicatesfrom that of the modulated including the oxidation state of the constituent cations, 2:l layer silicatescannot be defined.Approximations can has been determined and that the structural formula is be made from theoretical considerations (line a) as cal- known or known approximately. It is assumedthat alkali culated from Equations I and 2 and from experimental cations have no or little effect on the linkage betweenthe studies (line b) such as Hazen and Wones (1972) and tetrahedral and the octahedral sheets.Of particular im- Forbes (1969). Line a is basedon the assumptionthat portance is the allocation of Al, which may commonly neither the octahedra nor the tetrahedra are distorted. occur both tetrahedrally or octahedrallyin layer silicates. Line b does not have this restriction but does suffer from However, examination of the ideal formulae of all mod- the fact that experiments may not reflect conditions that ulated structures(see above) indicates that Al is tetrahe- maximize misfit. It is noteworthy that Fe-rich talcs (Rob- dral. Examination of the chemical composition of natural inson and Chamberlain,1984; Lonsdale et al., 1980)plot phasessuggests that Al occurs only in the tetrahedral site generallybetween the extremesset by lines a and b. Gug- at end-membercompositions, i.e., when the averageoc- genheim (unpub. data) has shown by revr that these Fe- tahedral-cation size is large relative to Al. This relation- rich phasesare true talcs and not minnesotaite structures. ship suggeststhat there are geometric constraints in- It is noteworthy also that the oxidation state for the Fe volved. has not been characterizedadquately in all cases.Fur- thermore, it is emphasized that these lines are approxi- Cation partitioning mations and that no sharp boundary delineating fields of In a continuous trioctahedral sheet,the octahedrashare geometrical stability has been determined. In part, these edgesand thus have a constraining effect on the size of lines are approximations becausethe plot representscom- neighboring octahedra.In an octahedral sheetcomposed positional effectsonly and doesnot considerthe ionic radii primarily of large cations, an isolated octahedron con- of the cations at temperaturesand pressuresof formation. taining a much smaller cation will be unstable. This in- In addition, errors associatedwith composition and es- stability results from the larger sharededges between the pecially the oxidation stateof Fe may be large.These and octahedron containing a small cation and its six large other considerationsare discussedin more detail below. octahedralneighbors; small cations do not usually reside The compositions of the modulated structures cluster in cavities that are too large. Therefore, for modulated to the right of line a and D \,\riththe notable exception of layer silicateswith primarily Fe2* or Mn in the octahedral the stilpnomelanes(Fig. 5a). The large range of compo- sheet,Al should prefer the tetrahedral sites. The differ- sitions for the stilpnomelanesmay be a result of postcrys- encesin radii betweenneighboring Al3+ and p"z+ 1-300/o) tallization oxidation (seeHutton, 1938 Zen, 1960). Fig- or Al3* and Mn2+ (-:SoUo;would effectivelyenlarge an Al ures 5a and 5b show the effect of calculating 7" and 7, octahedralsite to an unacceptabledegree. However, when valuesbased on both Fe3* (0.65 A; and p"z+ 10.72A) sufficient AI3+ is present so that there is a coalescenceof values.With the exceptionof one analysis(no. 33),which smaller-sizeoctahedra, this effect is minimal and site as- is very Al-rich, all points falling to the left of line D have signmentis more uncertain. It is also unclear whether the significant octahedral vacancies.If such vacancies (at a effectwould be important for syntheticphases where equi- "radius" of 0.82 A) are included in the ro term, all these librium has not been acheivedor for structureswhere the points would shift significantly to the right near line b. octahedral sheet is discontinuous, as cations could pref- Ignoring octahedral vacanciesin the z" term produces a erentially enter sites at sheetedges. greater spread in points for the other plots in Figure 5 For an octahedralsheet composed oflarge cations, it is also. The conclusion that misfit between the tetrahedral arguedthat an isolated octahedroncontaining a relatively 734 GUGGENHEIM AND EGGLETON: MODULATED 2:I LAYER SILICATES small cation will be avoided. Such an argument applies between 2:l layers. For example, interlayer distancesare to all trioctahedral 2:l layer silicates, including the hy- characterizedby weaker bonds in these layer silicates. droxyl-rich micas. For these micas, the general cation- Therefore,interlayer-volume reduction is high when com- orderingpattern (Guggenheim, 1984, p. 7l) showsa trend pressiveforces are applied along Z*. These results imply of a larger M(l) site relative to M(2). In a typical mica, that hydrostatically applied stress to the system is not site M(1) is surrounded by six M(2) sites, whereaseach necessarilytransmitted through the structure isotropical- M(2) site shares edgeswith three other M(2) sites and ly, but is generally controlled by and transmitted along threeM(l) sites.Thus, the M(l) may be considered"iso- bonds. In contrast,the inverserelationship generallyholds lated" in the sensethat it is sharing edgeswith only one for increasing temperature, with interlayer volume in- type of octahedralsite, M(2). Hence, the constraining ef- creasinggreatly. fect of M(2) dictatesthat a smaller cation avoids entering Unlike normal layer silicates,modulated 2: I layer sil- M(1), as is generallyobserved. icateshave tetrahedral connectorsacross interlayer space There are severalnotable exceptionsto the generalor- and, therefore, should be significantly stiffer alotg Z*. dering pattern, namely (l) clintonite (Tak6uchi and Sa- Thus, the interlayer region cannot act as an efficient pres- danaga, 1966), which has been described with a small sure "buffer." Instead, the tetrahedral connectorswould M(1) site containing Al and relatively large M(2) sites be expected to transmit pressure more efrciently along containing Mg, and (2) some Li-rich micas (e.g.,Guggen- Z*. Becausethe tetrahedra are very rigid, an octahedral heim and Bailey, 1977 ; Guggenheim,I 98 I ) with one small site in a modulated structure would be expectedto have Al3+ octahedral site and two large sites. Recent neutron a different compressibility than the analogous site in a diffraction (Joswiget al., 1986)and X-ray diffraction stud- normal layer silicate. Assuming that compressiveforces ies (MacKinney and Bailey, in prep.) of clintonite suggest are transmitted to the octahedral sites efrciently and are that the earlier work is in error and that clintonite does not greatly attenuated by T-O-T bending (see the sug- conform to the normal ordering pattern of a relatively gestionby Vaughanin Hazen and Finger, 1982,p. 155- largeM(l) site. In the Li-rich micas,sufficient F, univalent 156), a high-pressure,low-temperature environment cations, and vacanciesexist to prevent a uniform geom- should efectively promote a reducedmisfit of tetrahedral etry from developingin the octahedralsheet. For example, and octahedral sheets.These conditions apparently pre- octahedral sites containing vacanciesand univalent cat- vailed during the formation of zussmanite(Agrell et al., ions readily distort to accommodate their trivalent Al 1965),which is found in the FranciscanFormation of neighbor.Thus, they cannot act to constrain sizesofneigh- California and is believedto be ofblueschist-faciesorigins. boring octahedral sites. Furthermore, F substitution for Of course, although misfit of tetrahedral and octahedral (OH) favors being associatedwith a smaller site (Gug- sheetsmay be a geometrically limiting feature of these genheimand Bailey, 1977). structures, thermal stability is not based necessarilyon More direct evidence that octahedra may effectively this feature alone. constrain the sizeofneighbors with sharededges has been given by computer modeling simulations by Baur et al. Modulations along preferred directions (1982) in the rutile-type structure. For this case it was Variations in the topological arrangementof the tetra- found that a larger VFu octahedron would be reduced in hedra must have important consequencesin how the mis- size by about 0.250loif surrounded by smaller MgFu oc- fit betweenthe two sheetsis relieved. Strip structureswith tahedra.Although rutile is composed of edge-sharingoc- tetrahedral strips ofset on alternatesides ofan octahedral tahedra forming chains rather than sheets,it is clear that sheet(e.g., see Fig. 3a or 4a)allow the octahedralsheet to the argument is similar, and it would be expectedthat the be wavelike and, hence, allow the distance from apical effect is greaterfor a sheetlikearrangement. oxygento apical oxygen to increase.This increaseresults in tetrahedra tilting out ofthe (001) plane and effectively Effect of temperatureand pressure increasesthe lateral dimensions ofthe tetrahedral sheet. The f, vs. r" plot requires precisevalues for ionic radii Furthermore, the changein the configurationofthe sixfold at the temperature and pressureof mineral formation, if ring relieves the strain along one axis. Whereas these the plot is to represent the true upper limits of misfit mechanismsare suitable for relieving misfit in one direc- between the tetrahedral and octahedral sheets.However, tion, they do not explain why there is no modulation of not only are these values difficult to obtain, it is often the strip structure parallel to either I as in minnesotaite difficult to ascertainthe environmental conditions of min- or X as in ganophyllite, i.e., why is the hexagonal ring eral formation. Therefore, the regions of delineating geo- strip continuous?Eggleton and Guggenheim (1986) sug- metric stability are only approximations, asthe ionic radii gestedthat Al preferentially occupies the central contin- used for these plots are basedon ambient conditions. uous tetrahedral chain ofthe triple chain in ganophyllite. High-temperature studies of fluorophlogopite (Takeda This substitution sufficiently increasesthe chain dimen- and Morosin,1975) and high-pressurestudies of phlog- sion so that it may span the octahedra alongX. Evidence opite and chlorite (Hazen and Finger, 1978) have dem- that this substitution occurs comes from (l) tetrahedral- onstrated strong anisotroic temperature and pressurere- site size considerationsand (2) the position ofthe inter- sponsesthat relate to diferences in bonding within and layer cation, which is located predominantly near the tet- GUGGENHEIM AND EGGLETON: MODULATED 2:1 LAYER SILICATES 735

rahedral rings at the center ofthe strip. These tetrahedra variables, it becomesof interest to determine if it is still would have undersaturated basal oxygens. Tetrahedral possible to identify modulated structures from chemical chains lateral to the central Al-bearing tetrahedral chain considerationsalone. Furthermore, it is useful to deter- are lengthenedby the addition ofthe inverted tetrahedra mine if it is possible to predict or construct reasonable (seeFig. 4). Ganophyllite representsthe first modulated models basedon chemical or limited other data. layer silicate refined sufrciently to reveal that cation-or- dering effectsmay play an important role in establishing PnnucrrNc MoDULATED sTRUCTURES the stability of a modulated 2:l structure. Eggletonhas listed (Table IVb of Eggleton, 1972) anal- In minnesotaite, misfit of tetrahedral and octahedral yses that do not seem to conform to the stilpnomelane sheetsis relieved along the strip direction by distortions structural model. Some of theseanalyses are old and pos- within the octahedral sheet (Guggenheim and Eggleton, sibly erroneous,whereas other have been clearly linked 1986a).Apparently, the structurecan accommodategreat- to structures that have been shown to be unrelated to er misfit when strip edgesare numerousbecause ofnarrow stilpnomelane. Two analyses(no. 46

Fig. 6. Electron-diffraction pattern of the basal plane (beam parallel to Z*) ofparsettensite(t.fO .o*pur.O to stilpnomelane (right). poor, Fe- and Mn-rich chlorite known as gonyerite. If Si, can affect misfit in a chlorite. In addition, it is unclear Al, and Fe3* are tetrahedrally located to conform to a how H bonding in the interlayer region may affect com- chlorite structural formula (total tetrahedral occupancyof parisons to other modulated structures. However, with 4.0 cations per formula unit), the chemistry may be plot- theseconstraints and even ifall small octahedral cations ted on a lr vs. l. plot (Fig. 5). We emphasize,however, and all largetetrahedral cations are partitioned within the that the normal chlorite structure consists of two octa- 2:1 layer, there is still considerablemisfit. hedral sheets,and it is likely that elemental partitioning Examination of transmission-electrondiffraction pat- terns of the gonyerite basal plane shows, in addition to reflections attributed to the heavy octahedral cations, weaker reflections indicating a superlattice presumably related to tetrahedral modulations (seeFig. 7). The lattice is basedon a hexagonalcell indicating an islandlike struc- ture. Difraction data involving 00/ reflections are con- sistent with a 28-A c cell parameter. It is notable that patterns show strong / : odd reflections, and these re- flections probably indicate that the (two-layer) unit cell is not composedof similar 2: I layers.High-resolution trans- mission-electronmicroscopy (Hnrrv) has confirmed this interpretation. Gonyerite is considerably more complex than a normal two-layer chlorite in which a two-layer sequenceis a result of stackingvariations. Becauseof the complexity of a chlorite structure,we would be premature to suggesta modulation description.Both the parsettensite and the gonyerite structuresare to be describedin more detail at a later time. The possibility of using the plotted position (Fig. 5) of a modulated structure relative to lines a ot b to predict the island size or strip width is limited. The nature of the tetrahedral perturbation at either the island or strip boundary, the extent of out-of-plane tetrahedral tilting, the possibility of cation ordering, etc., all serve to make Fig. 7. Electron-diffraction pattern of the basal plane of go- such predictions on an a priori basis difficult. However, nyerite. if additional information such as cell parametersor sys- GUGGENHEIM AND EGGLETON: MODULATED 2:I LAYER SILICATES 737 tematic variations in overall diffraction intensity is known, - (l 984)The brittle micas MineralogicalSociety ofAmerica Reviews it is possibleto constructpossible models for the structure. in Mineralogy,13, 6l-104 -(1986) Modulated 2:l layer silicates(abs.) IntemationalMiner- alogicalAssociation, l4th GeneralMeeting, 116-117. AcxNowr,npcMENTS Guggenheim,S., and Bailey,S.W. (1977) The refinementof zinnwaldite- We thank S. W. Bailey, F. Wicks, and R. M. Hazen for reviewing the lM in subgroupsymmetry. American Mineralogist, 62, 1158-1167. - manuscript and M. Vaughan,University of Illinois at Chicago,for helpful ( | 982) The superlaticeofminnesotaite. CanadianMineralogist, 20, discussions.We gratefully acknowledgethe ResearchResources Center of 579-584. the University of Illinois at Chicago and B Hyde, Australian National Guggenheim,S , and Eggleton,R A. (1986a) Structural modulations in University, Canberra,Australia, for the use of the transmrssion-electron Mg-rich and Fe-rich minnesotaite. Canadian Mineralogist, 24, 479- mlcroscopes. 49'7 - ( I 986b) Cation exchangein ganophyllite.Mineralogical Magazine, RnrnnrNcos 50. 51 7-520 Guggenheim,S., Bailey, S.W., Eggleton, R.A., and Wilkes,P. (1982)Struc- Agrell, S O., Bown, M.G, and McKie, D. (1965)Deerite, howieite and tural aspectofgreenalite and related minerals. Canadian Mineralogist, zussmanite,three new minerals from the Franciscanof the Laytonville 20. l-18 district, Mendocino Co., Califomia (abs.) American Mineralogist, 50, Hazen,R.M., and Finger,LW (1978)The crystalstruclures and com- 278 pressibilitiesoflayer minerals at high pressure.II. Phlogopiteand chlo- Appelo,C.A. (1978)Layer deformationand crystalenergy of micasand rite. American Mineralogist, 63, 293-296 relatedminerals I Structuralmodels for lM and 2Mr polytypes.Amer- -(1982) Comparative crystal chemistry. Wiley, New York, 231 p ican Mineralogisr, 63, 782-7 92. Hazen, R M., and Wones, D R (1972) The effect of cation substitution Bates,T F. (1959) Morphology and crystal chemistry of I : I layer lattice on the physical properties of trioctahedral micas American Mineral- silicates.American Mineralogist, 44, 78-l | 4 ogist,57, lO3-129 Baur, WH., Guggenheim,S., and Lin, J-C. (1982) Rutile-typecom- Hutton, C.O (1938) The stilpnomelanegroup of minerals Mineralogical pounds. VI Refinement of VF, and computer simulation of V:MgFr. Magazine,25, 172-206. Acta Crystallographica,B38, 35l-35 5. Jagodzinski,H., andKunze, G. (1954)Die rollschenslrukturdes chrysotils. Blake,R.L. ( I 965)Iron phyllosilicatesofthe Cuyunadistrict in Minnesota. I Allgemeine Beugungstheorieund Kleinwinkelstreuung.Neues Jahr- AmericanMineralogist, 60, 148-169. buch fiir Mineralogie Monatshefte,4, 95-108 Chernosky,J.V. (1975) Aggreagaterefractive indices and unit cell param- Jakob, J (l 923) Vier Mangansilikataus dem Val d'Err (Kt Graubunden). etersof syntheticserpentine in the systemMgO-Al,O,-SiOr-HrO Amer- SchweizerischeMineralogische und PetrographischeMitteilungen, 3, ican Mineralogist, 60, 200-208. 227-237 Crawford,E S., Jefferson,D.A., and Thomas,J M. (1977)Electron-mi- Jefferson,D.A. (1976) Stacking disorder and polytypism in zussmanite. croscopeand diffraction studies of polytypism in stilpnomelane.Acta American Mineralogist, 6 l, 470-483. Crystallographica,A3 3, 548-553. - (1978) The crystal structureof ganophyllite,a complex manganese Donnay,G., Morimoto,N , Takeda,H., andDonnay, J.D.H. (1964) Trioc- aluminosilicate. L Polytypism and structural variation. Acta Crystal- tahedral oneJayer micas I Crystal structure of a synthetic iron mica. lographica,434, 491-497. Acta Crystallographica,17, 1369-l38 I Joswig,W., Amthauer,G, and Tak6uchi,Y. 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