the identification of naturally occurring tio, (b) by ... · the identification of naturally...

American Mineralogist, Volume 76, pages 343-353, 1991

The identification of naturally occurring TiO, (B) by structure determinationusing high-resolution electron microscopy, image simulation, and

distanceJeast-squares refi nement

Jrr-r,r,tN F. BlNrrnr,or* D.Lvro R. Vrsr-nNDepartment of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.

Davrn J. SrvrrrnCenter for Solid State Science and Department of Physics, Arizona State University, Tempe, Arizona 85287, U.S.A.

Ansrru.cr

Semicoherently intergrown lamellae of a new TiO, mineral have been identified inanatase crystals from Binntal, Valais, Switzerland. This unnamed mineral has been re-ported previously as the synthetic polymorph TiO, (B) (Marchand et al., 1980). We haveinterpreted high-resolution electron micrographs to determine the positions of columns ofTi cations within the unit cell as determined by electron diffraction. The model structure,which consisted of Ti cations octahedrally coordinated by O, was tested by comparingcomputer-generated images with experimental micrographs from two orientations. Sim-ulations were calculated for defocus and thickness conditions necessary to match the ex-perimental and calculated images of the host anatase. The model structure was then refinedusing a distance-least-squares (DLS) program to adjust all interatomic distances simulta-neously to values comparable with those found in anatase and rutile. The image simula-tions for this DlS-improved structure match the experimental images for both orienta-tions. The DlS-improved model closely reproduces the detailed polyhedral distortionsfrom the ideal structure that were predicted by Catlow et al. (1984) using energy mini-mization techniques. The TiO, (B) structure, composed of edge- and corner-linked pairsof edge-sharing octahedra, can be generated from the anatase structure by regular shearparallel to (103) ofanatase, which is the observed orientation ofthe interface between thetwo minerals. High-resolution heating experiments carried out within the electron micro-scope showed that the TiO, (B) polymorph was converted to anatase either by growth ofsteps (<l nm high) on the lamellar maryins that removed the shear component relatingthe two structures, or by a bulk mechanism when anatase nuclei were scarce or absent.This reaction occurs in the microscope at a furnace temperature of approximately 700 "C,approximately 100 "tC below the anatase-rutile transformation. The irreversible TiO, (B)- anatase and anatase - rutile reactions may be useful indicators of peak temperaturesif it can be established that both minerals are common in low-grade metamorphic rocks.

INrnonuctIoN

There are seven known polymorphs of TiOr, six ofwhich have distinct structures (Table l). Three of thesepolymorphs, rutile, anatase, and brookite have been foundpreviously in nature. In this paper we report the charac-terization of lamellae of a polymorph, currently knownas TiO, (B) (Marchand et al., 1980), which has been foundin natural anatase crystals.

Because these lamellae occupy a small volume of theanatase crystals, our attempt to characterize their struc-ture using X-ray precession photographs was unsuccess-ful. Consequently, we applied a number of electron mi-

croscopic techniques to derive a structural model, adjustedthe model until computer image simulations approxi-mately matched the atomic-resolution images, and finallyrefined the model using a distance-least-squares (DLS)structure modeling program. This approach is thus shownto be a useful alternative to those ofCatlow et al. (1984)and Theobald et al. (1984) for solving structures whenonly small quantities of material are available. Previousmethods combine electron or powder X-ray diffractionwith energy minimization modeling based on the Bornmodel for the ionic solid. However, they do not take ad-vantage of the capabilities of very high-resolution elec-tron microscopes that produce images which are inter-pretable using image simulation techniques (O'Keefe,1984) in terms of atomic positions.

The nature ofgrain boundaries between different phasesis of considerable interest because the structure of these

* Present address: Department of Geology and Geophysics,University of Wisconsin-Madison, 1215 West Dalton Street,Madison, Wisconsin 53706, U.S.A.

0003-O04X/9 l/03044343$02.00 343

344 BANFIELD ET AL.: NATURALLY OCCURRING TiO, (B)

Tlele 1. List of the TiO, polymorphs with distinct structures

Structure Space groupDensity(9'cm-"1 Unit cell data (nm) Reference

RutileAnataseBrookiteTio, (B)Tio, llTio, (H)

P4Jmnm14llamdPbcaC2lmPtun14lm

4.133.793.993.644.333.46

a:0 .459, c=0.296a : 0.379, c: 0.951a : 0.917, D : 0.546, c : 0.514a : 1.216, b : O.374, c : 0.651, P : 1O7.29a : 0.452, b : 0.550, c : O.494a : 1.018, c: 0.297

Cromer and Herrington (1955)Cromer and Herrington (1955)Baur (1961)Marchand et al. (1980)Simons and Dachille (1967)Latroche et al. (1989)

Note.'The CaCl, structure is related to that of rutile by a second order phase transtormation

boundary regions controls diffusion rates and transfor-mation mechanisms. Based on interpretation of atomic-resolution images, it is possible to deduce the bondingconfiguration at the boundary between the anatase andTiO, (B)-phase. Furthermore, the obvious structural re-lationship between these phases, first noted by Brohan etal. (1982), can be used to interpret images with nearatomiclevel resolution that show the phase transforma-tion mechanism observed directly (at high temperature)in the electron microscope.

S.Lupr,r DEScRrprroN AND ExpERTMENTALMETHODS SAMPLES

The anatase crystals examined in this study are fromtwo localities near Binntal, Valais, Switzerland (46'20'N,8"12'E). The first sample was from the collection of How-ard Belsky. The second sample was from the collectionof Carl Bosch, U.S. National Museum, Division on Min-eralogy, Smithsonian Institution, Washington, DC (Mu-seum Number 86134) and is from the Alp Lercheltiniarea. The anatase crystals occur in a mica-rich gray paru-gneiss that experienced upper greenschist facies meta-morphism approximately 30-40 Ma (S. Graeser, writtencommunication). Graeser states that the anatase clearlyformed after the climax of metamorphism and suggests adate based on K-Ar determinations for fissure mineralsof approximately I I m.y. Electron microprobe analysesfor both samples (K. Livi, analyst) show them to be >990/oTiO, with small amounts of Fe and Al, and traces of Mnand Cr. No compositional difference between the coex-isting polymorphs could be detected using either analyt-ical electron microscopy (AEM) or by repeated electronmicroprobe analyses from crystals known to contain la-mellae. When examined optically (using reflected andtransmitted light microscopy), the crystals appear to behomogeneous, coarsely twinned anatase.

X-ray diffraction

Single crystal X-ray diffraction patterns were obtainedwith a precession camera using Zr-filtered MoKa X-rays.Zero- and firstJevel b-axis films were exposed for up toI week to enhance possible weak reflections associatedwith the TiO, (B)-phase. Although reflections attribut-able to the B-phase were not detected in these experi-ments, a careful powder X-ray diffraction study by J. Postrevealed that small diagnostic TiO, (B) peaks could beidentified in sample 86134.

Elechon microscopy

The anatase and lamellae were initially characterizedusing a Philips 420T transmission electron microscope(TEM) operated at 120 keV. Samples were prepared bycrushing small crystals; a suspension of the material inalcohol was deposited on a holey carbon grid. Selected-area electron diflraction (SAED) patterns and convergent-beam electron diffraction (CBED) pattsrns were obtainedboth from thin edges of crystals containing anatase andlamellae and from areas comprised only of lamellae. AEMdata were obtained using an EDAX Li-drifted Si detectorwith a Be window and analyzed using a Princeton Gam-ma-Tech System IV X-ray system.

High-resolution electron micrographs were recordedwith a 400-kev JEM 4000EX TEM with a point resolu-tion of close to 0.17 nm (Cs : 1.0 mm). Through-focusseries were recorded for two orientations at magnifica-tions of 500 000 and 800 000 x .

Heating experiments were carried out on crushed grails

mounted on holey carbon films. The sample was heatedto a furnace temperature of 800 'C in a single-tilt HrO-cooled Gatan holder. In some cases, partly reacted ori-ented crystals were examined by transferring the sampleto a double-tilt holder after cooling.

Computer-simulated images for anatase and modelstructures were calculated using the SHRLI programsversion 80F (O'Keefe et al., 19781' O'Keefe, 1984; Selfand O'Keefe, 1988).

Distance-least-squares refi nernent

The DLS refinement was carried out using the DLS-76program originally written by C. H. Baerlocher and A.Hepp, revised by Brund Guigas, and adapted for an IBMcomputer by S. L. Lawton and E. L. Wu. The DLS pro-

cedure is described by Burnham (1985).

Rnsur-rsSample characterization

Both anatase samples contained lamellae of the samesecond mineral. The samples differed only slightly in theabundance of the second phase (the Smithsonian samplecontained slightly more lamellae). Data presented belowwere obtained from, and are appropriate for, both sam-ples.

The electron micrograph in Figure I shows a crystal ofanatase in the [010] projection that contains lamellae of

345

Fig. 2. Image down [010] of the intergrown minerals showingareas of anatase (A) and a second mineral (X).

face is parallel to (103) anatase. The presence ofa reflec-tion from the lamellae just inside the 103 reflection ofanatase indicates that the interplanar spacings of latticeplanes parallel to the interface are not exactly equal.Moreover, from Figure 3b it is apparent that the ll2reflection of anatase associated with the pseudo-close-packed planes almost exactly overlies a reflection fromthe lamellar phase. The SAED patterns indicate that thereis misfit between the lamellae and anatase along theirinterface so that the intergrowth is probably semicoher-ent. The d-values measured from the electron difractionpatterns are listed in Table 2.

TABLE 2, List of dvalues measured from SAED patterns, cal-culations for TiO, (B), and indices

lO nm

Fig. I . Transmission electron micrograph down [010] of an-atase (A) showing two sets of lamellae of a second mineral Xparallel to {103} ofanatase.

the second mineral labeled "X," which is shown belowto be TiO, (B). The margins of the lamellae are parallelto the symmetrically equivalent {103} planes of anatase.In most areas, the lamellae were observed in only one ofthese two directions. Based on the absence ofreflectionsin X-ray precession photographs, the weakness of peaksin powder X-ray diffraction traces, and the projected ar-eas of lamellae in TEM images, it is estimated that thelamellae occupy less than l0lo of the sample. They rangefrom a few nanometers to hundreds of nanometers across.SAED and CBED patterns indicate that the lamellae havea three-dimensional reciprocal lattice distinct from thoseof anatase, rutile, and brookite. Furthermore, the imagecharacteristics extend to the edge ofthe sample (Fig. 2),indicating that the distinct unit cell is not the result oftwinning or a moir6 effect.

SAED patterns such as those in Figure 3 show that thereciprocal lattices of the two minerals have a well-definedorientation relationship. Figure 2 indicates that the inter-

BANFIELD ET AL.: NATURALLY OCCURRING TiO, (B)

this study

6.25.85 .13.73.33.23.23 .13.03.02.92.72.62.62.52.52.42.32.22.22.12.O2.02.0

4TiO, (B)cafculated' hkl

0012002012011 1 1202210,21000240i1 1 1 , 1 1 14003 1 0 , 3 1 03 1 1 , 3 1 i4022021124013ir1, 311312,3122og0035 1 15 1 160i

6.225.805.063.733.223 . 1 63.143.112.992.972.902.692.682.532.452.452.372.302.282 . 1 72.072.032.032.03

- Calculated from the cell dimensions given by Marchand et al. (1980).


Fig. 3. SAED patterns (a) showing [010] of anatase and the reciprocal lattice from mineral X in lamellae coexisting with anatase;(b) in [3lI] ofanatase, showing the relative orientation ofthe two reciprocal lattices. Reflections from mineral X are arrowed.

In situ heating experiments

A series of heating experiments was carried out withinthe Philips 420T electron microscope. Since these studiesinvolved the use of crushed grains on holey carbon films,the exact temperature achieved was not known. In gen-eral, a reaction was observed at a furnace temperature ofapproximately 700 "C for crystals that were located closeto the bars of the Cu support grid. In most cases, a com-bination of electron diffraction and imaging was used todetermine that the lamellar phase had been replaced byanatase. In rare cases, the product ofreaction ofanataseand the lamellae was rutile.

The transformation of X to anatase proceeded eitherby growh of subnanometer ledges of anatase along theinterface between the two phases or by propagation ofanatase at the expense ofthe second mineral along a broadfront. Where narrow lamellae of the second phase (X)were contained within anatase, or where there was abun-dant anatase intergrown with the wide lamellae, the re-action tended to proceed by motion of steps. In someinstances, the transformation occurred rapidly, and theinterface appeared to jump suddenly through the sample,as shown by the comparison of Figure 4a with 4b. Inregions predominantly composed of the second mineral,the bulk mechanism predominated.

Figure 5 shows the region visible in Figure 4, now ori-ented with the electron beam approximately parallel to[010] of anatase after the sample was transferred to aroom temperature double-tilt holder. The area labeled A'corresponds to an unreacted region in Figure 4a. A nar-row strip of the unreacted phase (marked by an arrowand an X) has been preserved.

A partially reacted region present in the right part ofFigure 5 is enlarged in Figure 6. This micrograph showsa thin lamella of anatase that has replaced the secondphase (X) along a broad, but slightly serrated, front. Onthe right-hand side of this lamella, at least three ledgesless than I nm high (marked by arrows) can be observed.

Motion of these ledges along the boundary was observedat high temperature.

High-resolution electron rnicroscopy

Through-focus series of images were obtained from theintergrowths in two orientations. Images recorded aboveand below the optimum defocus (-48 nm for the JEM4000EX) for the [010] projection of anatase are shown inFigure 7, and the optimum defocus image from the [53I]zone of anatase is shown in Figure 8. An image of theboundary between anatase and X is shown at greatermagnification in Figure 9. Prolonged examination in the400-keV microscope caused the eirowth of a different phasealong the thin edge of the sample. This beam damage isillustrated in Figure 10.

Image simulation and distance-least-squares modeling

Anatase images were calculated for a range of crystalthickness and objective lens defocus values for the [010]and [531] zones. By matching the characteristics of theexperimental images with these simulations, it was pos-sible to establish the thickness and defocus conditionsthat were appropriate for the images of the intergrowths.

The optimum defocus images of anatase (Figs. 7c, 9)show that columns of pairs of Ti cations in the structureare clearly resolved. For this reason, we attributed pairsof similar spots in the image from the lamellae as repre-senting columns of Ti cations. We measured the positionof these columns within the unit cell suggested by electrondiffraction and derived a model for the cation positionsin the structure. Because of its low atomic scattering fac-tor compared with that of Ti, O will contribute little con-trast to the high-resolution images. Consequently, theprojected positions of O atoms can not be determineddirectly from the images. However, calculation of imagescorresponding to a structure that contained only Ti cat-ions indicated that the O atoms must contribute in a sub-tle way to the characteristics of high-resolution images in

BANFIELD ET AL.: NATURALLY OCCURRING TiO, (B) 347

-A->t

b

Fig.4. Images of the intergrowths recorded approximately at700 "C (furnace temperature) (a) immediately before, and (b)immediately after, the growth of the area of anatase (horizontalarrow) at the expense of the other polymorph (X). The verticalarrow marks a point of reference.

2 5 n m

Fig. 5. Image of the area in Figure 4, after the sample wascooled, transferred to a double-tilt holder, and oriented in the[010] anatase projection. On the left side ofthe figure the ar-rowed strip of the second polymorph, marked with an arrow andX, was preserved after the area to the right was converted toanatase (A'). The small arrowheads (on the far right-hand sideof the image) mark points shown in the enlargement of this areain Figure 6.

Fig. 6. Enlargement of the area marked in Figure 5 showinga strip of anatase that has replaced the other polymorph (X)along a wide front. Steps of anatase approximately 0.5 nm high(arrowed) were observed to grow along the interface at high tem-perature.

the [010] projection. This result suggests that matchingfine details in the simulations for the model with detailsof the experimental images could provide reasonably re-liable projected positions for the O atoms in the structure.

By analogy with anatase, rutile, and brookite, the struc-ture of the unnamed mineral can be anticipated to becomposed of octahedrally coordinated cations, with oc-tahedra linked only by edge and comer sharing. This con-straint led almost immediately to a single structure mod-el, from which image simulations were generated forcomparison with the experimental images in the through-focus series.

The moderately good match between the image simu-lations for the initial model and the experimental imageat the optimum defocus is illustrated in Figure lla. Themost obvious discrepancy of detail is within the lineararrangement of small white spots. In the experimentalimage, the break between groups of three small whitespots lies between two black spots (and offset from thelargest white splotches), whereas, in the simulation, thesebreaks overlie the largest white splotches. Furthermore,


Fig. 7. Through focus series of [010] anatase with superim-posed image simulations for anatase and the DlS-improvedmodel structure (a) defocus l2 nm, thickness 2.5 nm; (b) defocus-28 nm, thickness 2.5 nm; (c) defocus -44 nm, thickness 2.5nm; (d) defocus -60 nm, thickness 2.5 nm. Arrows show a de-fect in the new mineral (X) that can be seen in c to consist of athin strip of anatase (A).

Fig. 8. Image in anatase [53I] showing a lamella of tlre sec-ond polymorph and image simulations calculated for a defocusof -48 nm and crystal thickness of approximately 2.5 nm. Thesimulation for anatase is shown enlarged in the inset.

Fig. 9. Image of a lamella boundary and simulations for thestructures of the two minerals. Careful examination [sighting ata low angle parallel to (001) anatasel ofthe arrangement ofblackspots (corresponding to columns of Ti cations) indicates thatcoherency is attained locally by small atomic displacements atthe boundary.


Fig. 10. Micrograph showing a crystalline product (arrowed)ofTiO that resulted from electron-beam irradiation. The prod-uct has a square lattice and replaces both anatase and X, partic-ularly at their interface.

thc calculated interatomic distances for the initial modelstructure were rather variable, many of them being largeror smaller than those found in anatase, rutile, and brook-rte.

In order to adjust the atomic coordinates and thus im-prove the consistency between expected and model in-teratomic distances, we used a distanceleast-squares cal-culation. This comparatively simple structure modelingapproach has been used successfully in conjunction withX-ray diffraction to solve otherwise intractable problems(see review by Burnham, 1985). DLS should be an effec-tive technique for optimizing TiO, structures, given thegeneral topology and the size and shape ofthe unit cell,because of the number of existing polymorphs that alldisplay relatively uniform Ti-Ti and Ti-O distances(however, the O-O distances for both shared and un-shared edges are less predictable).

We tested this hypothesis by specifiing a set of atomiccoordinates (not related by symmetry) for anatase thatwere somewhat displaced from their known positions (upto 100/o), allowing the program to adjust the interatomicdistances to approach those found in rutile. Generally wefound that the program converged on a set ofcoordinateswithin lolo of those found in the known structure. The

Fig. ll. Optimum-focus image and simulations (a) for theinitial model of the unknown structure; (b) for the DLS-im-proved model structure.

convergence was not strongly dependent on the weightsassigned to the distance specifications.

When applied to the model of the new structure, theprogram again rapidly converged regardless of whetherthe lengths for the shared edges were specified to be closeto those in rutile or anatase. Modeling of the O-O dis-tances by comparison with those found in the well-estab-lished polymorphs is complicated by the fact that theycontain octahedra that share different numbers ofedges,in a variety of configurations. We attempted to approachthe most physically reasonable structure by adjusting theO-O distances to reflect these considerations (modeledwith O-O unshared : 0.3 nm compared to 0.295 in rutileand 0.303 in anatase; O-O : 0.26 or 0.27 nm for sharededges, depending on the arrangement of shared edges,compared with O-O shared edges of 0.241,0.254,0.277nm in anatase and rutile).

The phase grating calculated by the SHRLI image sim-ulation package (see Fig. I 2) shows the projected arrange-ment for the Ti (large black spots) and O atoms (smallgray spots) for the final DlS-improved model (Fig. I lb).

Fig. 12. Phase grating output from the SHRLI programsshowing the projected positions of columns of Ti (large grayspots) and O atoms (smaller gray spots). Filled circles emphasiz-ing the positions of the Ti atoms, open circles emphasizing thepositions ofthe O atoms. Coordination polyhedra and axes aresuperimposed.


Tlsle 3. The (x z) coordinates for the 4i site (C2lrn) for theidealized VO2 structure, the lattice-energy-minimiza-tion-predicted structure (LEM), and the DLS-modeledprimitive structures

Site ldealized' DLS*

Fig. 13. Image simulations calculated for both anatase (up-per set) and the DlS-improved model structure (lower set) atthicknesses of approximately 2.5 nm at defocuses of L2, -28,-44, and -60 nm.

The superimposed polyhedral diagram shows that thisstructure is composed ofcornerlinked pairs ofedge shar-ing octahedra. These octahedra have a regular size andshape, and they have similar interatomic distances andvolumes to those found in anatase and rutile.

The simulations calculated for [010] anatase at severaldefocus values and a thickness (2.5 nm) that matches theimage characteristics at the edge of the sample (Fig. 7)are reproduced in Figure 13, together with the simula-tions for the model structure (at the same defocus valuesand thickness). In Figures 7 and 8, these simulations havebeen superimposed onto the experimental images. Thematches for all examples are quite good. The detailedmatch of the [010] optimum defocus image (Fig. I lb) ismuch improved relative to that for the initial model (Fig.I la); the break between groups of three white spots isnow positioned correctly. Furthermore, the simulationsshow areas with lighter contrast corresponding to O atompositions (see phase grating in Fig. 12) that duplicateregions with light contrast in the high-resolution images.

Table 3 illustrates the comparison between the ideal-ized structure (no polyhedral distortion; as reported byCatlow et al., 1984), the TiO, (B) structure predicted byenergy minimization modeling (Catlow et al., 1984), andthe Dls-optimized TEM structure for the mineral re-ferred to above as X. Because the Dls-structure wasmodeled using a primitive rather than C-centered unitcell, duplicate results for equivalent positions were ob-tained.

For the VO, structure, Catlow et al. (1984) report 6values for the atomic coordinates (powder X-ray minusideal) of 0.01-0.07 and between the energy minimizationand X-ray structures of less than 0.01-0.04. For the TiO,(B) structure, the differences between the (n, z) coordi-nates of the ideal and DlS-optimized structure (averagevalues) range between 0.0 and 0.03, and those betweenthe energy minimization and DLS structure range be-tween 0.00 and 0.06 (all except one result that is within0.04). In every case in which the DlS-optimized coor-dinates are not intermediate between those of the idealand energy-minimized structures, they are equal to them.

Note; (a) and (b) are independent results for equivalent sites in theC-centered unit cell.

'Catlow et al. (1984)."- Average for three DLS calculations.

DrscussroN

The structure of the unnamed mineral in the lamellae(X) in anatase was determined by electron microscopicand modeling techniques. This study has established thatX is the equivalent of the synthetic Ti-oxide known asTiO, (B), and thus that TiO, (B) occurs in nature.

The TiO, (B) mineral converted to anatase on heating,suggesting either that it primarily contained tetravalentTi or that interaction of the electron beam caused oxi-dation of trivalent Ti in the structure. Both the results ofprevious studies on TiO, beam damage and the results ofthis study (discussed below) suggest that damage involvesreduction rather than oxidation of the specimen. Conse-quently, thb heating experiments are interpreted to indi-cate that TiO, (B) primarily contains tetravalent Ti. Itwould be unusual indeed to find appreciable trivalent Tiin metamorphic rocks such as those from which the sam-ples were taken.

The possibility that the lamellae could have formed asa result of electron irradiation during examination wastested by deliberately exposing the intergrowths to a highand prolonged electron dose (in the 400-keV JEM4000EX). No evidence was found to suggest that the beampromoted the development of TiO, (B). Indeed, an alter-native crystalline product developed from both TiO, (B)and anatase along the edge of the sample (Fig. l0). Thisreaction product has spacings of approximately 0.21 nmbetween its square lattice fringes, consistent with its iden-tification as TiO (NaCl structure). This product devel-

T(1) xz

r(2) xz

o(2) xz

qo) xz

O(4) xz

o.220.33

0.380.33

0.220.3t!

0.450.67

0 .180.28

0.400.26

0.630.01

0.240.34

o.440.63

0.650.72

0.670.00

0.610.67

O(1) xz

(al 0.220.3ril

(b) 0.200.31

(a) 0.400.33

(b) 0.380.31

(a) 0.660.01

(b) 0.660.00

(a) 0.250.35

(b) 0.230.31

(a) 0.450.65

(b) 0.430.63

(a) 0.630.69

(b) 0.620.66


oped on both the anatase and TiO, (B), reflecting thetendency of the electron beam to reduce the Ti in bothminerals.

The development of TiO as a result of beam damage(radiolysis) of TiO, (rutile) has been previously describedby Smith et al. (1987). McCartney and Smith (1989) alsonoted the development of TiO, II, the high-pressure phase,as a result of electron irradiation of rutile. This interestingand rather surprising observation was not made in thedamaged anatase and TiO, (B). Figure l0 shows that theTiO develops preferentially at the interface between TiO,(B) and anatase. This probably indicates that the interfacehas a higher reactivity because of the coherency strainassociated with it.

The identification of TiO, (B) as intimate intergrowthsin anatase suggests that these minerals are genetically re-lated in nature. Although we have no evidence as to howcommon the TiO, (B) polymorph is, Banfield (1990)demonstrated that it does develop in the weathering en-vironment. TiO, (B) may form commonly in nature atlow temperatures. The study of sample B6l 34 by J. Post(personal communication) indicates that although TiO,(B) may comprise a very small proportion of a sample,this mineral is sufficiently abundant that it can be iden-tified by powder X-ray diffraction.

By comparing the image simulations with the experi-mental image in Figure 9, the structure of the boundarybetween TiO, (B) and anatas€ can be inferred. Electrondiffraction patterns indicate that there is some misfit be-tween the two lattices parallel to their interface. This wasalso noted by Brohan et al. (1982), who observed thatpartly reacted synthetic crystals of TiO, (B) are subdivid-ed into small domains that are believed to have formedas a result of this misfit. Examination of grain boundariesin the samples described here indicates that despite thedifferences between the lattice parameters, the interfacescontain broad areas ofcoherency. Figure 9 illustrates dis-tortion or slight atomic displacements that occur at theboundary. Although the simplified diagram of the bound-ary (Fig. 14) does not show this distortion, it does illus-trate that the boundary region is highly structured, withmany polyhedra shared by both phases. The arrangementof dark spots in Figure 14 can be compared with thosein the high-resolution image (Fig. 9). The dashed linemarking the boundary between TiO, (B) and anatase inFigure 14 marks the furthest extent of polyhedra in anarrangement consistent with the anatase structure. Theboundary could be considered to (approximately) extendacross the region shown to contain polyhedra commonto both structures.

The TiO, (B) polymorph is known to have a structurethat is systematically related to that of anatase (Brohanet al., 1982). It has been shown that the synthetic materialconverts to anatase with increasing temperature (Brohanet al., 1982). Brohan et al. reported that samples trans-formed as a result of either increased temperature or pres-sure (550 'C and I atm, or 60 kbar and room tempera-ture). Our heating experiments demonstrated that the

Fig. I 4. Polyhedral representation ofthe structure ofanatase,TiO, (B), and their boundary. Black dots mark positions of Tiatoms; compare the arrangement at the boundary with that seenin Figure 9.

reaction can be induced in situ in the microscope underlow-pressure conditions. In nature, the reaction almostcertainly proceeds at much lower temperatures, probably

only partly as a result ofthe greater pressure (a few kilo-bars).

Brohan et al. (1982) proposed a TiO' (B) - anatasetransformation mechanism based on the identified to-potactic relationship and the observation that anatase canbe derived from the TiO, (B) phase by a process similarto crystallographic shear in the Magn6li phases, with theshear eliminating equal numbers of cationic and anionicvacancies.

Our in situ observations of the TiO, (B) - anatasereaction indicate that it may proceed either by growth ofindividual steps on the lamellar margins or by movementof a front through the sample, which occurs at times quiterapidly. The transformation by growth of steps is gener-ally in accord with the mechanism proposed by Brohanet al. (1982), insofar as the transformation involves sys-tematic displacement of octahedra parallel to the bound-ary. Dynamic observations, as well as micrographs fromthe quenched reaction (Fig. 6), suggest that this processoccurs by growth of steps approximately 0.5 nm high.Our interpretation of the mechanism, illustrated in Fig-ure 15, indicates that these steps correspond to the slabsthat must be displaced to create one structure from theother.

The TiO, (B) lamellae may either have formed by si-multaneous growth with anatase or have remained afterthe incomplete prograde replacement of TiO, (B) by an-atase. It is probable that with increasing temperature, an-atase in nature would completely replace TiO, (B), as itdid in our experiments. Two sequential reactions antici-


(103) ANATASE

O ti "t

y = 0,1 -lAnatase or transtormed

O Ti at y - 0.5 J T|O2(B)

O I r, ,n Tiq (B) before transformationO J

Z

* 'f'UEi:J'"":i::"J "'Fig. 15. Diagram illustrating the displacement that relates

the two structures. The width of the displaced slabs correspondsto the height of the anatase ledges during the transformation.

pated in low-grade metamorphic rocks are the transfor-mation of TiO, (B) - anatase and anatase - rutile.

Laboratory transformation of anatase to rutile occursat high temperature. Rao (1961) stated that below ap-proximately 6 l0 'C the transformation is infinitely slow.We can infer from the observations of Hunziker et al.(1986) and others that the anatase - rutile transforma-tion probably occurs at temperatures below approxi-mately 400'C in metapelites from the Swiss Alps. Al-though the exact temperatures of the TiO, (B) - anataseand anatase - rutile transformations will largely reflectkinetic factors (Shannon and Pask, 1965, showed that theanatase - rutile transformation temperature is stronglyinfluenced by impurities and defect), we anticipate thatthey will occur sequentially in low-grade metamorphicrocks.

It has been often suggested that rutile, anatase, andbrookite form as weathering products of Ti-bearing min-erals such as biotite (Morad and Aldahan, 1982), amphi-bole, pyroxene (Loughnan, 1969), and ilmenite (Grey andReid, 1975). Other possible precursors include amor-phous Ti-oxide or Ti(OH)o (Loughnan, 1969). It is inter-esting to note that TiO, (B) can be synthesized by dehy-dration and structural rearrangement of HrTioOe.HrO(Tournoux et al., 1986). Feist et al. (1988) further discusssynthesis from a variety of structurally related Na and Cscompounds via intermediate H compounds. We suggestthat, if analogous hydrous Ti-oxide compounds occur innature, their dehydration and collapse during diagenesisor very low-grade metamorphism may result in the for-mation of TiO, (B) and, by extension, anatase and rutilein metamorphic rocks.

CoNcr,usroNs

This study has shown that the structure of a mineralthat occurs in submicroscopic quantities can be deter-mined using an approach that combines AEM, electrondiffraction, high-resolution imaging, image simulations,and DLS reflnement. Image simulation showed that thepositions of columns of Ti cations could be readily de-termined from the high-resolution images and that thedistribution of diffuse intensity in optimum-defocus im-ages could provide a first estimate for the anion positions.DLS refinement of the initial model resulted in a struc-ture containing polyhedra similar to those found in ana-tase and rutile. A very close match between the simulatedimages for the DlS-optimized structure and experimen-tal images was demonstrated. Not only did the DLS-op-timized structure correspond to the general structure ofthe synthetic phase TiO, (B), but the octahedral distor-tions from the ideal structure closely resembled those pre-dicted for TiO, (B) using energy minimization techniques(Catlow et al., 1984).

The unnamed mineral represents the fourth naturallyoccurring TiO, polymorph. It is known that TiO, (B) canbe synthesized by dehydration and collapse ofa hydroudprecursor. Consequently, it is possible that reactions con-verting similar precursor compounds to TiO, (B) in na-ture represent the first steps that may result in the for-mation of up to three TiO, polymorphs in low-grade rocks(all polymorphs may also be formed directly in somecases). Further systematic study is needed to establishhow common the TiO, (B) polymorph is. Given the prob-able irreversible nature of the reactions TiO, (B) - ana-tase and anatase - rutile, these minerals may proveuseful indicators of peak metamorphic temperatures inlow-grade rocks.

AcxNowr-nocMENTs

Thanks are expressed to Ken Livi for providing the initial anatase sam-ple, discussions, and microprobe data; to Renu Sharma for discussion ofthe chemical literature; to JeffPost for assistance with the DLS prog'am,access to powder X-ray diftaction results, and discussion; to M. O'Keefefor providing the SHRLI software; and to Stefan Graeser for informationon the geological history ofthe anatase-bearing rocks. Dirnitri Sverjenski,George Guthrie, and Peter Davies provided constructive comments onthe manuscript. Tamsin McCormick is thanked for her review and edi-torial help. This research was supported by NSF grants EAR-8609277,EAR-8903630, and DMR-861 1609.

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MeNuscmrr REcETVED JtrNe 20, 1990MeNuscnrrr AccEprED Jer.ruenv 7, l99l

BANFIELD ET AL.: NATURALLY OCCURRING TiO, (B)

the identification of naturally occurring tio, (b) by ... · the identification of naturally...

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