ORIGINAL PAPER

Eva Scholtzova Æ Lubomır Smrcok

On local structural changes in lizardite-1T : {Si4+/Al3+}, {Si4+/Fe3+},[Mg2+/Al3+], [Mg2+/Fe3+] substitutions

Received: 14 December 2004 / Accepted: 6 April 2005 / Published online: 31 August 2005� Springer-Verlag 2005

Abstract Geometrical changes induced by cation sub-stitutions {Si4+/Al3+}[Mg2+/Al3+], {2Si4+/2Al3+}[2Mg2+/2Al3+], {Si4+/Fe3+} [Mg2+/Al3+] or [Mg2+/Fe3+], where {} and [] indicate tetrahedral and octahe-dral sheet in lizardite 1T, are studied by ab-initioquantum chemistry calculations. The majority of themodels are based on the chemical compositions reportedfor various lizardite polytypes with the amount of Al inthe tetrahedral sheets reported to vary from 3.5% to 8%in the 1T and 2H1, up to �30% in the 2H2 polytype.Si4+ by Fe3+ substitution in the tetrahedral sheet withan Al3+ (Fe3+) in the role of a charge compensatingcation in the octahedral sheet is also examined. Thecation substitutions result in the geometrical changes inthe tetrahedral sheets, while the octahedral sheets re-main almost untouched. Substituted tetrahedra are tiltedand their basal oxygens pushed down from the plane ofbasal oxygens. Ditrigonal deformation of tetrahedralsheets depends on the substituting cation and the degreeof substitution.

Keywords Ab-initio Æ Pseudopotential Æ Plane wavesÆ Lizardite Æ Substitutions

Introduction

The crystal structures of the vast majority of 1:1 and 2:1sheet silicates are usually described by simplified struc-tural models ignoring possible cation ordering in tetra-hedral and/or octahedral sheets. This fact is quiteunderstandable if we take into account the very closescattering power of Si and Al for X-rays or, the absence

of supercell diffractions indicating cation ordering. As aconsequence, the nature of local changes induced by thesubstitution of a smaller cation by a larger one or areplacement of a cation by another with a similar size,but with different formal atomic charge remain mostlyhidden to us.

In contrast to diffraction methods, which averagestructural information over a relatively large irradiatedvolume, quantum chemistry methods provide a chanceto study local changes in crystal structures. Due to thenature of these methods it is, however, not possible touse a standard crystallographic tool, like variableoccupancy parameters. As a result, the so called com-putational cells derived from the basic crystallographiccells must be expanded several times in order toaccommodate all required atoms and the structures’symmetry usually reduce to P1. Whereas for micas sucha practice could in many cases lead, due to the largevariety of cations in their structures, to a disaster, it iseasier to base the computational models on the 1:1 sheetsilicates. In their structures Si usually fills all, or almostall, tetrahedral sites and the variability of cation sub-stitution in their octahedral sheets is, compared to the2:1 sheet silicates, low. For the 1:1 sheet silicates it isthus conceivable to propose models, which considercation substitution in both tetrahedral and octahedralsheets, but still remain computationally tractable at arelatively high level of theory.

Changes in the distribution of electron density in li-zardite caused by octahedral Mg2+ for Fe3+ substitu-tion were studied by 3D HF SCF method (Dovesi et al.1996) by Scholtzova et al. (2000) who found that the Fe–O bonds were (surprisingly) more ionic than Mg–Obonds. Bosenick et al. (2001) reviewed the basic ap-proaches ranging from empirical potentials to ab-initioquantum chemistry for the determination of energies ofordering of cations in several minerals. The applicationsof the individual methods are illustrated by the examplesof Al/Si, Mg/Ca and Mg/Al ordering.

Palin et al. (2001) investigated the nature of Al/Siordering in muscovite using various computational

E. Scholtzova (&) Æ Lubomır SmrcokInstitute of Inorganic Chemistry, Slovak Academy of Sciences,Dubravska cesta 9, SK-845 36 Bratislava, Slovak RepublicE-mail: uacheva@savba.skTel.: +421-2-59410457Fax: +421-2-59410444

Phys Chem Minerals (2005) 32: 362–373DOI 10.1007/s00269-005-0006-5

techniques and deduced two-dimensional orderingschemes. For energy calculations they used empiricalinteratomic (Buckingham type and three body) poten-tials. The same method was later used by Palin et al.(2003) in the computational study of tetrahedral Al/Siand octahedral Al/Mg ordering in another mica,phengite. The Monte Carlo simulations of cationordering indicated presence just of a short-range order.

Sainz-Diaz et al. (2001) analyzed the influence ofcation substitution on the position of the –OH group (cisvs trans) in dioctahedral illites and smectites. In theircalculations they used transferable empirical potentialsto calculate total energies of the configurations, in whichAl3+ was substituted by Mg2+ and Fe2+, Si4+ by Al3+

in octahedral and tetrahedral sheets, respectively. Theeffect of cation substitution in the constituting sheets onthe structures of 2:1 dioctahedral phyllosilicates (pyro-phillite, illite and smectite) with the different interlayercharges were studied using ab-initio (DFT) calculations(Sainz-Diaz et al. 2002). They found that Fe3+ cationshad a tendency to clustering.

Trioctahedral 1:1 mineral lizardite is a very goodguinea pig for computational studies for several salientreasons. First, the crystal structures of its three poly-types 1T, 2H1 and 2H2 have been reliably determined(Mellini 1982; Mellini and Zanazzi 1987; Mellini andViti 1994; Brigatti et al. 1997) providing very accuratesets of starting and/or reference atomic coordinates.Second, presence of strong covalent (Si–O) and strongionic (Mg–O) bonds side by side with the rather weakinterlayer hydrogen bonds in one compound still pro-vide a challenge for a computational method (see e.g.Smrcok and Benco 1996). Third, due to a low degree ofcation substitution in their structures they provide agood chance to study local geometrical changes.

The aim of this study is to find structural changes inboth tetrahedral {} and octahedral [] sheets of 1:1 sil-icates originating from the following cation substitu-tions : {Si4+/Al3+}, {Si4+/Fe3+} and [Mg2+/(Al3+ orFe3+)]. The majority of the models used in the studyare based on the chemical compositions reported forthe lizardite polytypes. The amount of Al in the tet-rahedral sheets of those structures is reported to varyfrom 3.5% to 8% in the 1T and 2H1, up to �30% inthe ‘‘aluminian’’ lizardite 2H2. Although the amount of{Si4+/Fe3+} substitutions in the above-mentioned li-zardites does not exceed 5%, such a substitution is notrare (O’Hanley and Dyar 1993). An attempt is, there-fore, also made to replace a Si4+ by an Fe3+ in thetetrahedral sheet, with an Al3+ in the role of a chargecompensating cation replacing a Mg2+ in the octahe-dral sheet. Not to leave the last stone unturned themodel where octahedral Mg2+ is replaced by Fe3+

instead of Al3+ is also examined. Such a model is astep towards another 1:1 layer silicate, cronstedtite(Smrcok et al. 1994; Hybler et al. 2000), full descriptionof which electronic structure is not possible at thecurrent status of theory due to the specific nature ofFe–Fe interactions.

Computational details

The calculations were performed by the ab-initio pro-gram package VASP (Kresse and Furthmuller 1996)for periodic systems using pseudopotentials and planewaves. The calculations were based on the densityfunctional theory (DFT) (Jones and Gunnarsson 1989)using generalized gradient approximation (GGA) inexchange-correlation functional (Perdew et al. 1992).The interaction between ions and electrons was de-scribed using projector augmented wave method(PAW) (Kresse and Joubert 1999; Bloechl 1994) withplane wave cut-off of 400 eV. The optimizations of thestructures were done by the method of conjugatedgradient in 12k points (Teter et al. 1989; Bylander et al.1990). The atomic reference configurations were asfollows : Fe—(3d7 4s1), Si—(3s2 3p2), Al—(3s2 3p1),Mg—(3s2 3p0), O—(2s2 2p4). The configuration for H isobvious.

The basic computational cell with the formulaMg12Si8O36H16 was based on the unit cell of the 1Tpolytype doubled in the A and B directions, that is,a=b=10.664 A, c=7.233 A (Fig. 1a). All calculationswere done in the P1 space group with the cell param-eters fixed and all atomic coordinates allowed to vary.In such a cell there are eight tetrahedral cation posi-tions, that is, the smallest degree of substitution in thetetrahedral sheet is 12.5%. A further enlargement ofthe mesh of possible tetrahedral cation positions tobetter mimic the reported compositions would lead tolarge, computationally intractable cells. Besides, it wasassumed that such an enlargement would not bring toomuch of improvement as far as description of localchanges is concerned. However, since there was a riskthat in the case of slowly decaying variations in thegeometry of the sheets induced by a substitution somechanges would not be accurately described, one set ofcalculations was made also with a cell with 3a=3blattice vectors (see below). All derived structuralparameters (interatomic distances, angles, etc.) werecalculated using the PLATON program (Spek 2004).

Results and discussion

Optimization of the unsubstituted 1T polytype

To assess the overall accuracy of the computationalmethod the positions of all atoms in the un-substitutedcell of the 1T polytype were optimized first. The con-vergence was smooth and the most dramatic changeswere, as expected, in the positions of hydrogen atoms,whose starting values derived from X-ray data lackeddesired accuracy. A comparison of optimized andexperimental (Mellini 1982) bond lengths and angles isin Table 1. From the first two rows it is seen that thecomputational method clearly distinguished between Si–Oapical and Si–Obasal bonds, slightly overestimating the

363

former and underestimating the latter. However, theabsolute difference of �0.01 A represents a goodagreement between calculated and experimental dis-

tances. The optimized Mg–(OH) distances in octahedraare indistinguishable from the experimental values,considering the estimated standard deviations of thelatter. A greater than expected Mg–Oapical bond length isan acceptable computational compromise betweenstrong covalent and ionic bonds. A good agreement inthe bond angles is also evident from the narrow intervalsgiven in Table 1. A good correspondence of distancesand angles is corroborated by the negligible deviationsof the atoms from the nearest reference planes (Fig. 1b).Those auxiliary planes perpendicular to c(=c*) axis cutthe structure at the z-levels equal to the z-coordinates ofthe respective atomic ‘‘layers’’ in the lizardite-1T. Cal-culated deviations from the nearest planes are in generalin the range of hundredths of A, the largest values being�0.06 A (an Obasal), �0.03 A (a Si) and �0.04 A (anOapical), respectively. Finally, calculated deviations fromthe ideal 120� angles (/ angles) expected for a ‘‘hexa-gon’’ of SiO4 tetrahedra are ±4.3� (Fig. 1c). This valueis to be compared to ±1.7� (Mellini 1982) and isacceptable. The thickness of the tetrahedral sheet (Dstet)calculated as a difference between the Cartesian z-coordinates of basal and apical oxygens negligibly in-creased from 2.20 A derived from the experimental datato 2.22 A. Similarly, Dsoct =(zapical�zouter) followed thattrend and increased from 2.12 A to 2.16 A. Consideringthe results summarized above the method is suitable forfurther study of structural changes caused by atom-by-atom substitutions.

Fig. 1 Projections of the structure of the computational double cellto ab—(a) and ac—plane (b), respectively. The meaning of thesubscripts in (b) is as follows : basal, apical—the oxygens formingthe tetrahedral; inner, outer–hydroxyl group(s), pointing towardsthe basal oxygens of the 1:1 layer or pointing outwards the 1:1layer. The auxiliary planes (symbolized by tiny arrows) are fit to cutthe structure at the z-levels typical for the respective groups ofatoms. c the / angles define the deviations from the ideal value(120�) and are a rough measure of tetrahedral sheet deformation.Shading of polyhedra in (a) and (b) cases has no special meaninghere

Table 1 Calculated and experimental values of bond distances andangles

Bond dcalc [A ] dexpa [A ]

Si–Oapical 1.604 1.616(5)Si–Obasal 1.660 1.646(3)Mg–Oouter 2.024 2.021(5),2.026(5)Mg–Oinner 2.089, 2.094 2.082(5)Mg–Oapical 2.148 2.121(3)Bond angles \calc½�� \exp½��Oapical–Si–Obasal <111.7;112.0> 110.6Obasal–Si–Obasal <106.9;107.0> 105.5, 108.3, 111.0Oapical–Mg–Oouter <83.9;84;2> <82.8;84.0>Oapical–Mg–Oouter <174.5;176.1> <175.4;177.2>Oapical–Mg–Oinner <91.5;93.1> <93.1;94.1>Oouter–Mg–Oouter <98.7;100.3> <98.8;99.2>

aMellini 1982

364

For further comparison some accurate referencevalues of bond lengths are essential. For the purpose ofthis study our choices are as follows (in A): tetrahedrald(Si–O)�<1.62;1.65> (Mellini 1982) and d(Al–O)�<1.77;1.80> (IT 1962), octahedral d(Al–O) �<1.85;1.98> (IT 1962) and d(Mg–O)�<2.02;2.15>(Mellini 1982), tetrahedral d(Fe–O)=1.89 and octahe-dral d(Fe–O)=2.06 (Fleet 1981), respectively.

Computational models—an overview

When a Si4+ atom from the tetrahedral sheet is replacedby an Al3+ (Fe3+), either the computational proceduremust compensate for an extra (�1) charge, or, to pre-serve electroneutrality, a Mg2+ in an octahedron shouldbe replaced by a trivalent atom, Al3+ being, consideringthe method in use, the best first choice. The strategy weused is the second one, since the energy convergence

process in a charged system is as a rule slower and couldturn to be less stable. Inasmuch as it would be unac-ceptably time consuming to evaluate all mutual posi-tions of the substituting atoms in the double cell, onlyfour representative models (Figs. 2, 3) were considered.Figure 2 shows the models A and B, which differ only inthe position of a charge balancing octahedral cation.While in the A case both substituted polyhedra are in aclose contact by sharing an Oapical, in the B case a distantoctahedron was selected to be built around Al. In the Cand D cases two tetrahedral Si atoms are substituted(Fig. 3). Whereas the mutual position of the substitutingcations in the configuration C is similar to the A case,the D model is an extreme with two substituted neigh-boring octahedra. A comparison of the total energiesshows that in both cases the configurations withsubstituted tetrahedron and octahedron in close contact(A and C) are more stable. For the sake of completenesswe report that total energy of A structure is lower than

Fig. 2 The models A and Bused to study singlesubstitutions. a A-sharedpolyhedra, b B-unsharedpolyhedra. Substitutedpolyhedra are painted in gray,large gray filled circles indicatepositions of the octahedralcations

365

that of B by �226 kJ/mol, and that of C is lower thanthat of D by �72 kJ/mol. The models B and D weretherefore not further considered. In the case of tetrahe-dral {Si4+/Fe3+} substitution, the differences between Aand B models are 24.3 or 48.4 kJ/mol in favor of A,depending on which octahedral substitution was used :[Mg2+/Al3+] or [Mg2+/Fe3+], respectively. Note thatalthough values may seem large, they represent justsmall fractions of the total energies—the difference be-tween the models A and B is only �0.5% of the totalenergy (Etot) obtained for A. The difference between Cand D represents only �0.2% of Etot (C) and the dif-ferences for Fe substituted lizardites are even smaller :�0.05% or �0.11% of Etot(A) for the layer substitutions{Si4+/Fe3+}[Mg2+/Al3+] or {Si4+/Fe3+}[Mg2+/Fe3+],

respectively. The electronic structure of Fe atoms wassextet for {Si4+/Fe3+}[Mg2+/Al3+] and septet for{Si4+/Fe3+} [Mg2+/Fe3+], respectively.

{Si4+/Al3+} [Mg2+/Al3+] substitution: 2·2 model

Although the cation substitutions result in some changesin both the constituting sheets, their nature is ratherlocal than global and are more pronounced in the tet-rahedral sheet. Tetrahedral Al–O bond lengths opti-mized to 1.75–1.77 A, which is in full accord with theexpected values. There are no significant changes in theSi–O bond lengths—even in the tetrahedra adjacent tothe substituted one the absolute deviations from theexpected values are within the interval 0.02–0.04 A.

Fig. 3 The models C and Dused to study doublesubstitutions. a C-two sharedpolyhedra, b D-sharedoctahedra. Substitutedpolyhedra are painted in gray,large gray filled circles indicatepositions of the octahedralcations

366

Those values are comparable to the inherent limits of thecomputational method (see above). Similarly, the tetra-hedral T–O–T (T=Si, Al or Fe) angles deviate from theexpected no more than for 1–3� absolute. Such a smallchanges of bond distances and angles clearly indicatethat T-O tetrahedra are stiff bodies, not easily deform-able.

Quite an interesting result is that while in the Si–Otetrahedra it holds that d(Si–Obasal)> d(Si–Oapical) as inthe un-substituted polytype, there is not any obviousorder in the Al–O bond distances. The most interestingfact, however, results from the analysis of the deviationsof the atoms from the reference planes defined inFig. 1b. The fact that all Oapical remains in a plane de-spite longer Al–O than Si–O interatomic distance pointsto more dramatic changes in the positions of atoms‘‘below’’ (Fig. 1b). First, the Al atom drops from theplane of central atoms (T) in tetrahedra for �0.1 A,pushing down the Obasal atoms forming its coordinationpolyhedron (Fig. 4). Deviations of their Cartesian z-coordinates from the corresponding reference plane are�0.10, �0.16 and �0.21 A, respectively, that is, the Al-substituted tetrahedron is tilted (Fig. 4a). To quantify

the tilt we note that whereas in the unsubstituted lizar-dite-1T the Si–Oapical bonds are almost parallel to the c-axis (deviations range from �0.08� to �0.05�), the dec-linations of the T–Oapical bond lines now are within<�3.9�;�0.6�> (Fig. 4b). The maximum deviation(�3.9�) is found just for the substituted tetrahedron. TheSi-atoms bonded to Obasal atoms remain in the planewith the median deviation �0.04 A. Local distortions inthe tetrahedral sheet also lead to significant changes inthe / angles (Fig. 4a)

Compared to the tetrahedral sheet, there are justtrifling changes in the octahedra. The Al–O bond dis-tances optimized to the values very close to the expected,d(Al–O) �<1.89; 2.04 A >. Shorter Al–(O, OH) thanMg–(O, OH) distances force small changes in the bondangles within the substituted octahedron, but none ofthe absolute differences exceeds 5�. The oxygen atomsforming octahedra (Oouter, Oinner and Oapical) remain inthe planes, but the Al atom dropped for 0.08 A from theplane of central Mg atoms. Finally, the thickness valuesDstet=2.22 A and Dsoct=2.15 A are in fact identicalwith Dstet=2.20 A and Dsoct=2.12 A calculated fromthe experimental data (Mellini 1982).

Fig. 4 Pictorial presentation ofthe most important changes inthe tetrahedral sheet. The emptylarge circle indicates theposition of the substitutingoctahedral cation, thesubstituted tetrahedron is ingray. Deviations of the basaloxygens from their referenceplane are proportional to thearea of the dark circlespositioned at the places of thebasal oxygens (a). Similarly, thedeviations of the T–Oapical

bonds from the c axis are shownas the circles positioned insidethe tetrahedra (b). The smallestdots in (b) represent the tilt of �0.1�, no dots are zero deviations.The values inscribed in (a) arethe / angles

367

{Si4+/Al3+} [Mg2+/Al3+] substitution : the model 3·3

Because there was a risk that the ‘‘2·2’’ computationalcell could be too small to reveal how far the changes inthe cell caused by a local perturbance (cation substitu-tion) could spread, some calculations in a single substi-tuted tripled (3a=3b, C; Mg27Si18O81H36, a=b=15.996 A, c=7.223 A, P1) computational cell weredone. Two mutual positions of the substituting andcharge balancing cations were tried as given above. Eventhough the model with the neighboring cations (equiv-alent to the A model discussed above) is energeticallyfavorable, the difference is small, � 97 kJ/mol, whichcorresponds to � 0.1% of Etot.

The most important changes are, as in the 2·2 modelcase, in the tetrahedral sheet. Al-substituted tetrahedronis tilted and the three coordinating basal oxygens arepushed down below the plane of Obasal (Fig. 5a). Fromthe figure it is obvious that those three oxygen atoms arethe only exceptions among the others, since the largestcalculated negative, median and positive deviations ofall Obasal from the reference plane (in A) are �0.191,

�0.004 and 0.020. The Al atom drops from the plane oftetrahedral cations for �0.1 A, that is, as in the 2·2 case.From Fig. 5a it is also seen that changes are local ratherthan global and in fact disappear in the second shell oftetrahedra surrounding the substituted tetrahedron.Inclinations of the T–Oapical bonds from the c axis(Fig. 5b) are within the interval <�4.1�;�0.1�>, i.e.very similar to those found for the doubled cell. Theother characteristic quantities as layers thicknesses anddeviations of T atoms from the reference plane areidentical to the values from the ‘‘2·2’’ model within theerrors of the computational procedure. As in the pre-vious ‘‘2·2’’ case, there is no significant structuralchange in the octahedral sheet.

Although the model based on the tripled cell has notbrought any new essential information compared to themodel based on a doubled cell, it has provided a betterpicture of the spread of the changes in geometry.However that additional information was paid by such alarge increase of machine time needed to complete cal-culations that the ‘‘3·3’’ models were not further con-sidered.

Fig. 5 Deviations of the basaloxygens from their referenceplane and / angles (a),deviations of the T–Oapical

bonds from the c axis (b)

368

{2Si4+/2Al3+} [2Mg2+/2Al3+] model substitution

Geometrical analysis of the double Al-substitutedpolytype shows that the changes are of the same kind asin the single Al-substituted structure. As before, nosignificant changes are recognized in the octahedralsheet and all major changes are just in the tetrahedralsheet (Fig. 6a, b).

The final optimized bond lengths are similar to thosefound in the case of single substitution. The bond anglesin tetrahedra (Oapical-T–Obasal) oscillate for ±5� aroundthe values found for unsubstituted polytype. It is thehigher degree of substitution which causes largerdeformations, because for single substitution the chan-ges were limited just by ±3�. Tilt of tetrahedra (<�4.2;�1.2�>) results in deformation of all the sheet leadingto the deviations of the basal oxygens from the referenceplane limited by the interval <�0.2;0.02>A, the med-ian value being �0.04 A. Note that even though theinterval of the tilts has boundaries close to the limits for

the single Al-substituted layer, the mean (median) valuesdiffer remarkably : �0.75� (single) versus �2.7� (double)(Fig. 6b). The double substitution also lead to largersheet deformation measured through the / angles,compared to that observed for single substitution(Fig. 6a). Calculated values of the layers’ thicknessesDstet=2.21 A and Dsoct =2.14 A clearly show that theyare insensitive to the degree of substitution.

{Si4+/Fe3+}[ Mg2+/Al3+] model substitution

Preliminary calculations show that lizardite cell is toosmall to accommodate a tetrahedral Fe atom. Structureoptimization was unstable and resulting Fe–O inter-atomic distances were unrealistically short: <1.75–1.79>A. New cell parameters were therefore sought bya step-by-step manual optimization, where the latticeparameters constrained to a=b were stepwise increasedin five steps starting from those of lizardite-1T up tothose of cronstedtite-3T, in which �18% of tetrahedral

Fig. 6 The most importantchanges in the tetrahedral sheetin the case of doublesubstitution. The empty largecircle indicate the position ofthe substituting octahedralcations, the substitutedtetrahedra are in gray.a Deviations of basal oxygensand / angles, b tilt of tetrahedra

369

cation positions are occupied by Fe3+ (Smrcok et al.1994). In every step a full optimization of the structurewas done and the resulting values of the total energieswere fit by a parabola. From its first derivative a newestimate of a=b=10.783 A was found and the structurewas re-optimized with those new values.

The final interatomic distances in the substitutedtetrahedron (1.82 A for Fe3+–Oapical and 1.85–1.90 Afor Fe3+–Obasal, respectively) are in full accord with thereference distances (Fleet 1981). The Si–Obasal bonds inthe tetrahedra bonding to the substituted tetrahedronshorten for �0.04 A and Si–Oapical lengthens for�0.02 A. Even if those values were not on the edge ofthe method in use we could conclude that the bondlengths in the neighboring tetrahedra were not remark-ably changed (see also the paragraph on {Si4+/Al3+})substitution.

Even though an FeO4 tetrahedron is larger that anAlO4 one, the deviations of basal oxygens from thereference plane are similar as in all previous cases, thatis, (�0.26; �0.03; 0.02) A (Fig. 7a). Such a similaritysuggests existence of a maximum deviation from theplane acceptable by the sheet. Such an assumption can

be further supported by the values of sheet thicknesses,which are in total agreement with those found forAl-substituted sheets: Dstet=2.21 A and Dsoct=2.14 A.The bond angles (O–T–O’) are for T=Si, Fe similar tothose found for the {Si4+/Al3+} model, that is, do notdiffer for more than one degree absolute, except forObasal–Fe–Obasal, where the maximum difference is+2.5�. The substituting Fe atom is ‘‘pushed’’ below theplane of tetrahedral cations for 0.14 A, while the rest ofthe cations keep their z-coordinates within the accuracyof the computational method.

A rather large tilt of Fe-substituted tetrahedron(�5.3�) induces noticeable tilts of all tetrahedra withinthe computational cell : <�4.3�; �0.8�> (Fig. 7b).Note that equivalent deformational changes appear onlyin the double {Si4+/Al3+}) substituted cell <�4.2�;�1.3�> A. Larger deformations of the sheet than ap-peared for single {Si4+/Al3+} substitution are under-lined by larger values of / angles (Fig. 7a), which liebetween the values for single and double {Si4+/Al3+}substitution. Geometry of the octahedral sheet is nottouched by tetrahedral substitution as in previous cases.Optimized Al–O distances in octahedra are within

Fig. 7 Deviations of the basaloxygens from their referenceplane and / angles (a),deviations of the T–Oapical

bonds from the c axis (b)

370

1.89 A and 2.03 A, that is, in accord with the expected.The deviations of all atoms belonging to the octahedralsheet from the reference planes have a random nature,being close to zero within the accuracy of the compu-tational method.

The {Si4+/Fe3} [Mg2+/Fe3+] model substitution

This model differs from the previous one by a slightlylarger substituted octahedron, because the octahedralFe–O bond lengths are for � 0.1 A longer than Al–O.The nature of the changes in the tetrahedral sheet ishowever similar as in the case of the model with [Mg2+/Al3+] octahedral substitution: deviations of basal oxy-gens from the reference plane are within<�0.27;�0.04;�0.02>A (Fig. 8a), the Si–Obasal bondsin the neighboring tetrahedra are shorter for 0.04 A thanexpected and the bond angles Oapical–T–Obasal notice-ably changed for ±6� compared to un-substitutedpolytype. The Fe–O bond lengths in the tetrahedron arein accord with the expected: Fe–Oapical=1.85 A and Fe–

Obasal vary within 1.87–1.89 A, respectively. Deviationsof the T–Oapical bonds from the c-axis are within theinterval <�3.8; �0.8>�, with the median value of�1.7� (Fig. 8b). Compared to the model with compen-sating Al3+ in octahedra, the octahedral Fe3+ droppedfrom the plane of reference cation plane for �0.1 A.There are no changes in the thickness of the octahedralsheet caused by [Mg2+/Fe3+] substitution.

Hydrogen bonds

In the interlayer bonding in lizardite a prominent role isplayed by hydrogen bonds formed by oxygen (donor, D)and hydrogen atoms of the outer hydroxyl groups froma layer bonded to basal oxygens (acceptors, A) of anadjacent layer (Fig. 1b). The comments in this para-graph are however restricted to the H-bonds leading toObasal of the substituted tetrahedra. For the unsubsti-tuted polytype the calculated Oouter–H (D–H),H....Obasal (H....A) bond distances as well as D–H....Abond angles are equal within the limits of the method

Fig. 8 Deviations of the basaloxygens from their referenceplane and / angles (a),deviations of the T–Oapical

bonds from the c axis (b)

371

(Table 2). As due to the substitutions in the tetrahedralsheet some Obasal are (unequally) pushed below the ref-erence plane, the corresponding hydrogen H....A bondsshortened for �0.1–0.2 A. Despite those changes allhydrogen bonds in substituted lizardite belong to thecategory of middle strong hydrogen bonds (Hibbert andEmsley 1990). Substitutions in the octahedral sheetshave no effect on the geometry of hydrogen bonds.

Conclusion

Detailed geometrical analysis shows good agreementbetween the experimental and calculated bond distancesand angles for 1T polytype, although the accuracy of thecalculated is noticeably lower. The overall accuracy ishowever sufficient for study of geometrical changes in-duced by substitutions of central cations. The analysisclearly shows that both constituting sheets are built ofstiff bodies, which are not ready for any large defor-mation. This is clearly proved also by calculated vol-umes of SiO4 tetrahedra in the substitutedstructures—they vary within 2.22–2.28 A3. While thelocal substitutions in the octahedral sheet result in neg-ligible changes in the geometry of the sheet, the tetra-hedral sheet adapts to larger cations by largerdeformations—the larger is the cation, the larger is forinstance, deformation expressed through deviationsform the ideal ‘‘hexagon’’ formed by tetrahedra. Incor-poration of Fe atom causes such large stress in the sheetthat the new cell parameters must be used. Notice,however, that while the volume of AlO4 tetrahedronrepresents �122% of SiO4 unit, a FeO4 occupies asmuch as �144%. Negligible changes in the octahedralsheets can be explained by the hypothesis that its size ismainly controlled by O–O repulsion. Such a rigid O–Olayer can easily accommodate Mg, Fe and Al cations,even though the octahedral volumes vary: �9.5 A3 forMgO6 or FeO6 vs �9.4 A3 for AlO6.

Acknowledgments The authors wish to express their thanks to Prof.M. Mellini and an anonymous Referee for their valuable remarksand recommendations and to Prof. J. Hafner for providing themwith a copy of VASP program.

References

Bloechl PE (1994) Projector augmented-wave method. Phys Rev B50:17953–17979

Bosenick A, Dove MT, Myers ER, Palin EJ, Sainz-Diaz CI, GuitonBS, Warren MC, Craig MS, Redfern SAT (2001) Computa-tional methods for study of energies of cation distributions:applications to cation-ordering phase transitions and solidsolutions. Mineral Mag 65(2):193–219

Brigatti MF, Galli E, Medici L, Poppi L (1997) Crystal structurerefinement of aluminian lizardite-2 H2. Am Mineralogist82:931–935

Bylander DM, Kleinman L, Lee S (1990) Self-consistent calcula-tions of the energy bands and bonding properties of B12C3.Phys Rev B42:1394–1403

Dovesi R, Saunders VR, Roetti C, Causa M, Harrison NM, Or-lando R, Apra E (1996) CRYSTAL95. University of Torino,Torino

Fleet ME (1981) The structure of magnetite. Acta Cryst (1981)B37:917–920

Hibbert F, Emsley J (1990) Hydrogen bonding and chemicalreactivity. Adv Phys Org Chem 26:255–379

Hybler J, Petrıcek V, Durovic S, Smrcok L’ (2000) Refinement ofthe crystal structure of cronstedtite-1T. Clays Clay Minerals48:331–338

International Tables for X-ray Crystallography (1962) The KynochPress, Birmingham, England, pp 262–269

Jones RO, Gunnarsson O (1989) The density of functional for-malism, its applications and prospects. Rev Mod Phys 61:689–746

Kresse G, Furthmuller J (1996) Efficient iterative scheme for ab-initio total energy calculations using a plane-wave basis set.Phys Rev B54:11169–11186

Kresse G, Joubert J (1999) From ultrasoft potentials to the pro-jector augmented wave method. Phys Rev B 59:1758–1775

Mellini M (1982) The crystal structure of lizardite �1T: hydrogenbonds and polytypism. Am Mineralogist 67:587–598

Mellini M, Viti C (1994) The crystal structure of lizardite-1T fromElba, Italy. Am Mineralogist 79:1194–1198

Mellini M, Zanazzi PF (1987) Crystal structures of lizardite �1Tand lizardite 2 H1 from Coli, Italy. Am Mineralogist 72:943–948

O’Hanley DS, Dyar DM (1993) The composition of lizardite-1Tand the formation of magnetite in serpentinites. Am Mineral-ogist 78:391–404

Palin EJ, Dove MT, Redfern SAT, Bosenick A, Sainz-Diaz CI,Warren MC (2001) Computational study of tetrahedral Al–Siordering in muscovite. Phys Chem Miner 28:534–544

Palin EJ, Dove MT, Redfern SAT, Sainz-Diaz CI, Lee WT(2003) Computational study of tetrahedral Al–Si and octa-hedral Al–Mg ordering in phengite. Phys Chem Miner30:293–304

Perdew J, Chevary A, Vosko SH, Jackson KA, Pedersenm MR,Singh DJ, Fiolhais C (1992) Applications of the generalizedgradient approximation for exchange and correlation. Phys RevB46:6671

Sainz-Diaz CI, Laguna AH, Dove MT (2001) Theoretical mod-eling of cis-vacant and trans-vacant configurations in theoctahedral sheet of illites and smectites. Phys Chem Miner28:322–331

Sainz-Diaz CI, Timon V, Bottela V, Artacho E, Hernandez-La-gina A (2002) Quantum mechanical calculations of diocta-hedral 2:1 phyllosilicates: effect of octahedral cationdistributions in pyrophyllite, illite, and smectite. Am Miner-alogist 87:958–965

Table 2 Selected hydrogen bonds [A ] and angles [�]. The D-Hbonds are not given here, because they all were within the interval<0.97; 0.99> A.

Model H...A D...A D–H–A

Experiment a 2.240 3.032 158.0Unsubstituted 2.022 2.966 163.51Si/1Al 1Mg/1Al 1.909 2.878 169.3

1.824 2.805 172.51.932 2.894 165.9

2Si/2Al 2Mg/2Al 1.877 2.852 171.21.836 2.816 171.61.908 2.878 167.5

1Si/1Fe3+ 1Mg/Al 1.890 2.863 171.31.809 2.792 173.51.859 2.828 166.5

1Si/1Fe3+ 1Mg/1Fe3+ 1.834 2.807 170.11.737 2.731 178.11.883 2.826 158.6

aMellini 1982

372

Scholtzova E, Smrcok L’, Tunega D, Turi Nagy L (2000) Ab-initio2D periodic Hartree-Fock study of Fe-substituted lizardite-1T—a simplified cronstedtite model. Phys Chem Miner 27:741–746

Smrcok L’, Benco L’ (1996) Ab-initio periodic Hartree-Fock Studyof Lizardite-1T. Am Mineralogist (1996) 81:1405–1412

Smrcok L’, Durovic S, Petrıcek V, Weiss Z (1994) Refinement of thecrystal structure of cronstedtite-3T. Clays ClayMinerals 42:544–551

Spek AL (2004) PLATON, A multipurpose crystallographic tool.Utrecht University, Utrecht

Teter MP, Payne MC, Allan DC (1989) Solution of Schrodinger’sequations for large systems. Phys Rev B40:12255–12263

373