American Mineralogist, Volume 69, pages 176-185, 1964

Crystal structure of ilmenite (FeTiOs) at high temperatureand at high pressure

B,q,nny A. WecHsr-Enl ANo Cnenr_rs T. pnewrrr

Department of Earth and Space SciencesState University of New YorkStony Brook, New York 11794

Abstract

The structures of two single crystals of synthetic ilmenite were refined using X-rayintensity data collected at24,4ffi,600, 800, and 1050'c (l atm) and 0.fi)1, 25.4,34.6, and46.1 kbar (room temperature). Thermal expansion of the unit cell was nearly isotropic,whereas compression was relatively anisotropic, with cla decreasing linearly with incrias-ing pressure. The isothermal bulk modulus and its pressure derivative determined from cellvolume data are Ko = 1.7\7) Mbar, Ki : 8(4), or Ko : 1.77(3) if K"' is assumed to be 4(l).Mean Fe-O and Ti-O distances increased linearly with temperature and decreased linearlywith pressure, (Fe-o) being about twice as expandable and compressible as (Ti-o). Th;responses of the two octahedral sites to temperature and pressure were quite different fromone another, however. The longer of the two independent Fe-o bonds was moreexpandable and less compressible than the shorter one, whereas the opposite was true forthe Ti site. The Ti atom was displaced toward the centroid of its coordination polyhedron athigh temperature, but the Fe atom moved further away from its centroid position. Cationshifts were much smaller with pressure than with temperature. These results indicate thatthe reponses of the ilmenite structure to temperature and pressure are not inverse incharacter. The cation sites remained fully ordered at all temperatures and pressuresstudied.

Introduction

Ilmenite (FeTiOl) occurs as an accessory mineral in awide variety of igneous and metamorphic rocks (Hag-gerty, 1976i El Goresy, l976a,b; Rumble, 1976). One ofits most valuable characteristics for petrogenetic studieshas been the use of compositions of coexisting hematite-ilmenite and magnetite-ulvdspinel solid solutions as anindicator of temperature and oxygen fugacity at the timeof last equilibration (Lindsley, 1963; Buddington andLindsley, 1964). More recently, other geothermometershave been based upon coexisting ilmenite and olivine orpyroxene (Andersen and Lindsley, 19'19: Bishop, 1980)and have utilized solution models to extend the experi-mental calibrations. The ilmenite structure may also be animportant one for metasilicates undergoing high-pressuretransformations in the Earth's mantle (e.g., Ringwood,1969; Liu, 1977a). In order to improve thermochemicalmodels, understand crystal-chemical partitioning behav-ior, and characterize the pressure-temperature systemat-ics of compounds with the ilmenite structure. it would be

I Present address: Hughes Research Laboratories. 30ll Ma-libu Canyon Road, Malibu. California 90265.

0003-004)vE4l01024176$02.00 t76

useful to determine the effects of elevated temperatureand pressure upon the crystal structure of ilmenite.

The ilmenite structure was determined by Barth andPosnjak (1934). Shirane et al. (1959) determined themagnetic structure at low temperature using neutrondiffraction, and the structure of lunar ilmenite was studiedby Raymond and Wenk (1971). Numerous other investi-gations have elucidated the magnetic properties of ilmen-ites and hematite-ilmenite solutions (e.g., Ishikawa,195E,1962; Shirane and Ruby, 1962; Shirane et al.,1962;Thorpe et al.,1977) and have suggested the possibility ofan order{isorder transformation at high temperatures asis observed for intermediate compositions. Burton (1980)studied such a transformation in an intermediate hema-tite-ilmenite by single-crystal X-ray diffraction.

Recently, high-pressure structure refinements havebeen reported for several materials with the closelyrelated corundum structure (Finger and Hazen, 1980).Compression of ilmenite has also previously been studiedby X-ray diffraction (Liu et al., 1974) and Mrissbauerspectroscopy (Vaughan and Drickamer, l%7) on poly-crystalline specimens. A number of other studies haveconsidered the elasticity, crystal-chemical systematics,and high-pressure phase transformations in other com-pounds possessing the ilmenite structure (Liebermann,

WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE 177

1976; Liu, 1977b; Kirfel et al., 1978; Ito and Matsui,1979\.

The present study was undertaken to characterizechanges in the crystal structure of ilmenite with tempera-ture and under isothermal, hydrostatic compression andto compare this behavior with that found for similarmaterials.

Experimental procedures

Synthesis of samples

The ilmenite used in this study was synthesized byD. H. Lindsley (run no. L679). The starting material wasa stoichiometric mix of Fe * Fe2O3 + TiO2. It was loadeddry into a Ag capsule and reacted in a piston-cylinderapparatus at 20 kbar, 1000"C for I day, 22 hours. The runproducts consisted of single crystals of ilmenite, generallyequant and subhedral, -50-150 trr.m in diameter.

Precession camera studies

A single crystal cemented to a quartz glass fiber andsealed in an evacuated silica capillary was studied at hightemperature on a precession camera. Precession photosofthe ftOl orientation were exposed for -24 hours each at500, 700, 900, 1000, and 1150'C. Three relatively weakbut observable reflections _which are allowed in spacegroup R3 but forbidden in R3c were found to be present atall temperatures. The reflections monitored were 201,l07,and 205, which are excluded by the condition I : 2nin R3c. This evidence precludgs the gossibility of a spacegroup transformation from R3 to R3c, which would beindicative of complete cation disorder, to 1150t20'C. Nodecomposition or loss of resolution in diffraction spotswas observed throughout the heating experiment.

High temperature data collection

Another ilmenite crystal from the same synthesis runwas studied at high temperature on an automated four-circle difractometer. Three-dimensional X-ray intensitydata were collected at24,400,600, 800, and 1050"C, andagain at room temperature after heating (nreH). Thecrystal was held at temperature for 3 to 4 hours beforedata collection was begun. All reflections with two theta

Table 1. Unit-cell parameters of ilmenite at high temperature

? ( ' c ) a ( E ) c (A) v (A3 l c /a

less than 70o for graphite-monochromated MoKa radia-tion were measured. At room temperature, data werecollected in a hemisphere of reciprocal space, while athigh temperatures, only one quadrant ofreciprocal spacewas studied in order to minimize the total exposure athigh temperature. Intensity data were converted to struc-ture factors by correcting for background and Lorentz-polarization factors. Following the collection of intensitydata at each temperature, 20 values of from 12 to 15reflections were measured, and the average of the posi-tive and negative 20 values was used in a least-squaresrefinement of the unit-cell parameters (Table l).

High pressure data collection

A third crystal from the same synthesis run was select-ed for high pressure study. Precession and Weissenbergphotos showed the sample to be a single crystal withsharp diffraction spots.

Three-dimensional X-ray intensity data were collectedat room temperature and pressure. All reflections with 20less than 70'were measured in one hemisphere of recipro-cal space. Structure refinement based on these data (seebelow) yielded essentially identical parameters to thoseobtained from the crystal used for high-temperaturestudy. The crystal was then placed in a Merrill andBassett-type miniature opposed anvil diamond cell (Mer-rill and Bassett, 1974) for high pressure diffraction mea-surements. An Inconel X-750 gasket was used (0.25 mmthickness) with a 0.35 mm hole for the sample chamber.The crystal was attached to one diamond face with asmall amount of the alcohol-insoluble fraction of petro-leum jelly, which partially covered a portion of thecrystal. The pressure-transmitting medium was a 4:lmixture of methanol:ethanol (Piermarini et al., 1973\. Aruby crystal -30 pm in diameter was placed in the samplechamber to monitor the pressure. Pressure was calibratedby measuring the shift of the R1 ruby fluorescence line(Barnett et al., 1973; Piermarini et aI., 1975; King andPrewitt, 1980). The estimated precision of the pressuredetermination is t0.5 kbar. Pressure was determinedimmediately after loading the diamond cell at each pres-sure and again following data collection. In general, atleast 24-48 hours elapsed between loading and the start ofdata collection, during which time some relaxation oc-curred. The pressures quoted for each experiment werethose determined following the completion of data collec-tion.

Initial loading was at 12.2 kbar, followed by datacollection at 25.4 kbar. After this, the diamond cell wasopened to move the crystal back to the center of thegasket hole. Following data collection at 34.6 kbar, thecell was again opened to move the crystal back to thecenter. Because of the thickness of the gasket at 12 kbar,a significant amount of shielding of the X-ray beamoccurred. Therefore, the refinements at this pressure willnot be considered further here. However, the unit-cell

2 4 5 . 0 8 8 4 ( r ) *

4 0 0 5 . 1 0 8 0 ( r )600 s .1 r .82 ( r )800 5 . r2S0 ( r )

1 0 5 0 5 . 1 4 1 2 ( 1 )RTAH** 5 .0889 (1 )

3 1 5 . S 4 ( 1 ) 2 . 7 6 4 2J r r . z ) t r l z . / o o u2 r 1 1 a f l \ a 1 e l d

3 2 3 . 0 8 ( 3 ) . 2 . 7 6 6 6J Z ) . O Z \ L t

3 r 5 . 0 8 ( 1 ) 2 . 7 6 9 4

1 4 . 0 8 5 5 ( 4 )14.L2A7 (6')14 . rs56 (6 )t 4 . r 8 7 ( r )t4.2250 (6't14 . 0933 (5 )

Standatd deviations ate given in patentheses and tefet to

the est i@ted erw in the - least s igni f icant uni ts. This

convention is fofTo|4ed in a-l-l tab.les.

Roon tenpetature aftet heating.

I78 WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE

determination at this pressure appears quite good. Subse-quent data collection at higher pressures was only mini-mally affected by gasket cutoff, resulting in a relativelysmall number of reflections which were excluded fromthe refinements.

Intensity data were collected in the fixed-phi mode andintensities were measured using the constant-precisionscanning technique (Finger et al., 1973). All accessiblereflections with 20 less than 90o in a sphere of reciprocalspace were collected. Due to the unfavorable orientationof the crystal at 35 and 46 kbar, only reflections withsmall values of / could'be measured, resulting in therelatively large uncertainties in the z coordinates for theserefinements. All intensities were corrected for absorptiondue to the diamond and beryllium in the pressure cell,using the method described by Finger and King (1978).

Unit-cell parameters were determined at both roompressure and at high pressures from the settings for20-24centered reflections corrected for errors in crystal center-ing and diffractometer zeroes using the procedures ofKing and Finger (1979). The triclinic cell, with no con-straints, was in every case consistent with rhombohedralsymmetry, suggesting that hydrostatic stress was main-tained during data collection. Unit-cell parameters arereported in Table 2.

Precession photos ofthe crystal were taken in both ftOland hl<n orientations following high-pressure data collec-tion. These suggest no deterioration of the crystal as aresult of compression nor was there any indication oftwinning as has been observed in shock-compressedilmenites (Sclar et al., 1973).

Absorption correction

Absorption corrections were applied to all intensitydata using linear absorption coefficients varying from106.3 to 103.1 cm-r for the high-temperature data and106.3 to 109.0 cm-r for the high-pressure data. Thecrystals studied at high temperature and high pressuremeasured -0.06 x 0.08 x 0.12 mm and -0.05 x 0.07 x0.10 mm, respectively. Extinction factors were also cal-culated for all reflections. Although it would have beenbetter to use a constant absorption coefficient for all datasets, we are confident that this inadvertent error has notsignificantly affected the final results. Examination of thetransmission and extinction factors indicates that the

Table 2. Unit-cell parameters of ilmenite at high pressure

principal effect of varying the absorption coefficient was asimple scaling, by a maximum of 2-3Vo for transmissionand 5JVo for extinction factors. The deviations in indi-vidual structure factors not accounted for by the overallscale factor and extinction parameter (r*) are smaller thanother sources of statistical uncertainties in the data.

All reflection data were averaged prior to refinement toproduce a set of symmetry-independent reflections. Forthe high-pressure data, a number of reflections thatdiffered significantly from their equivalents were omittedprior to averaging.

Structure refinements

Structure refinements were carried out using the least-squares program RFTNE4 (Finger and Prince, 1975). Start-ing coordinates were taken from Shirane et al. (1962), andthe neutral atom scattering factors of Doyle and Turner(1968) were used. Real and imaginary parts of the anoma-lous dispersion corrections were also included for allatoms. Reflections were weighted on the basis of count-ing statistics, and those with F < 3or Gigh temperature)or 1 ( 2o1 ftigh pressure) were excluded from therefinements. A scale factor, positional parameters, isotro-pic or anisotropic temperature factors, and an isotropicsecondary extinction correction were varied in the finalcycles of refinement. Final values of refined parametersare reported in Tables 3 and 4. Final observed andcalculated structure factors for all data sets are listed inTable 5.2 Selected interatomic distances and angles (un-corrected for thermal motion) and coefficients of expan-sion and compression are given in Tables 6 and 7.

In the final cycles of refinement of the high-tempera-ture data, the weighting scheme of Prince (1978) wasemployed. Although none of the refined parameterschanged significantly as a result of this weighting scheme,the statistical parameters were improved. Also, from 3 to5 observed reflections were rejected from each refine-ment on the basis of very high delta/sigma values. It isbelieved that these reflections may have been affected by"powder rings" arising from recrystallization of the high-temperature cement holding the crystal in place. For thehigh-pressure data, a few reflections having large del-talsigma values believed to have been affected by gasketcutoff were excluded.

The 35 kbar refinement is the most uncertain of thehigh-pressure results. The Fe atom z coordinate in thisrefinement is particularly anomalous, lying off the trenddefined by the I atm,25 and 46 kbar results by about 3esd. This may have resulted from the unfavorable orienta-tion ofthe crystal during data collection at this pressure,which was limited to reflections with / less than or equalto 5.

2 To receive a copy of Table 5, order Document AM-83-235from the Business Office, Mineralogical Society of America,2000 Florida Avenue, N. W., Washington, D. C. 2(M)9. Pleaseremit $5.00 in advance for the microfich€.

P ( k-bar )"

(A)

o . o o l 5 . 0 8 7 s ( s ) * L 4 . O A 2 ' | l 7 t 3 r 5 . 6 8 ( 4 ) 2 J 6 a I

I 2 . 2 5 . 0 7 8 5 ( s ) 1 4 . 0 3 5 8 ( . 1 7 ) 3 1 3 . 5 0 ( 6 ) 2 . 7 6 3 A

2 5 . 4 s . 0 6 9 1 ( 4 ) 1 3 . 9 8 4 9 ( 1 3 ) 3 I 1 . 2 1 ( 4 ) 2 . 7 5 A 9

3 4 . 6 s . 0 6 3 5 ( 2 ) 1 3 9 5 1 8 ( 1 6 ) 3 0 9 . 7 9 ( 4 ) 2 . 7 5 5 4

4 6 - 7 5 . O s 6 1 ( 4 ) 1 3 . 9 r 1 s ( 1 9 ) 1 O 7 . 9 9 ( 5 ) 2 . 7 5 1 4

Stanalatd deviations ate given in patentheses and tefer tothe estimted ettot in the Teast sifrificant units.This convention is foffowei! in aff tabfes.

WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE

Table 3. Final positional parameters and isotropic temperature factors (42) of ilmenite at high temperature

179

24o c 4oooc 6oooc goooc lo5ooc

x

za

txto51 fi

00 . 3 s s 3 7 ( 2 )0 . 5 8 2 ( 8 )

o

0 . 14640 (2 )0 . 4 s s ( 7 )

0 .31743 ( r8 )0 . 0 2 3 3 2 ( 1 7 )0 .24506 ( 5 )0 . 5 8 ( l ) r

r . 0 9 ( 5 )

0 . 0 r 50 , 0 1 9

00

0 . 3 5 5 0 5 ( 3 )1 . 1 7 ( r )

0o. 14676 (41

o. 31796 ( 29)o.02432128\o .24419 (B)r . 0 5 ( 2 ) t

0 , 9 6 ( 6 )

0 , 0 2 00 . 0 2 8

00

0.35650 ( 4 )r . 5 r ( 1 ) i

00

0. 14695 ( 4 )r . 1 0 ( 1 ) +

0 . 3 1 8 5 4 ( 3 4 )o . 0 2 4 3 8 ( 3 4 )0 .24479 ( 11)l . 3 1 ( 2 ) i

0 . 8 3 ( 6 )

0 .o240 . 0 3 6

00.3s689 (5 )l . s 5 ( 2 ) i

0

o . L47 22 (511 . 3 2 ( r ) f

0 . 31919 ( 39 )0 .02499 ( 36)o.24495(L3l1 . 6 s ( 3 ) +

0 . 8 4 ( 7 )

245o,0260 . 0 3 8

0

0 . 3 s 7 3 2 ( 6 )2 . 3 7 ( 2 1 +

0.14748 (6 )1 . 5 1 ( 2 ) t

0 .31857 (44)0 . 0 2 4 9 1 ( 4 3 )o.24475(L6l

r . os (8 )24A

0 . 0 2 8o.o47

0

0 . 3 5 5 4 2 ( 2 )o . s 7 ( l )

0

0 . 14545 ( 3 )0 , 4 7 ( r )

0 . 3 r745 ( 25)0 . 0 2 3 4 5 ( 2 5 )o .24485 (7 '0 . s 8 ( 2 ) i

0 . 4 6 ( 4 )

27L0 , 0 2 0o.o24

x

z

x

Iz

r t

n (obs)R (wt)R

I EqllvaTent isottoplc B.tt Secondtrg extlnction p4teetet.

Results

Unit-cell parameters

Thermal expansion was nearly isotropic between roomtemperature and 1050'C. The a cell dimension increasedlinearly with temperature, whereas c and the cell volumeappeared to increase somewhat more rapidly at hightemperature than at lower temperatures. However, be-cause our methods for determining lattice parameters ofthis crystal did not explicitly take account of possibleerrors in crystal orientation and centering, the reporteduncertainties are probably underestimated. It is likelythat the true standard deviations of the high-temperaturecell parameters are on the order of five times those

Table 4. Final positional parameters and isotropic temperaturefactors (A1 of ilmenite at high pressure

I aUtr 25.4 kba! 34.6 kbi ! 46,I l6d

reported, and possibly more. Therefore, we cannot beconfident about the curvature in the c-dimension withtemperature. A small increase was noted in c determinedat room temperature after heating. This may have beendue to misalignment of the crystal and is not believed tobe indicative of any structural changes resulting fromheating.

The c cell dimension in ilmenite was approximatelytwice as compressible as a between I atm and 46 kbar.The compression in both directions was curvilinear,decreasing slightly with increased pressure, while the c/cratio decreased linearly.

The volume compression data were fit to a Birch-Murnaghan equation of state (Bass er al., l98l), in orderto determine the zero-pressure isothermal bulk modulusand its pressure derivative. Since no rigorous constrainton Ki is available, both K. and Kl were varied, yieldingK" : 1.70(7) Mbar and Ki = 8(4). However, if Kl isassumed to be 4(l) (see discussion below), the derivedvalue of Ko : 1.77(3) Mbar. (The assumed uncertainty inKi was included in calculating the uncertainty of K..)This compares well with values determined for a naturalsingle crystal of ilmenite, Ko: 1.79 Mbar (Madelung andFuchs, l92l; Birch, 1966), and on a polycrystalline speci-men of magnesian ilmenite, K" : 1.68(12) Mbar (Lil etal., 1974). It is also in good agreement with the bulkmodulus vs. molar volume systematics for ilmenite-typecompounds (Liebermbnn, 1976), which suggest K = 1.74Mbar for FeTiO3 (R. C. Liebermann, pers. comm.).

Structural changes

The ilmenite structure is based on the R2O3 corundumstructure in which oxygens form a nearly hexagonalclose-packed framework. Layers of edge-sharing octahe-dral cation sites extend in the (001) planes. Each cationshares one octahedral face with a cation in an adjacentlayer, whereas the face opposite this is "shared" with a

F e x O 0

9 0 o

z 0 . 3 5 5 4 0 ( 1 ) 0 . 3 5 5 6 2 ( 3 )

r 0 . 6 2 s ( 8 ) t 0 . 6 8 ( 2 )

T i r O 0

9 0 o

z 0 . 1 4 5 3 8 ( 2 ) 0 . 1 4 6 3 ? ( 4 )

a 0 . 5 0 5 ( 8 ) r 0 , 5 3 ( I )

o x 0 , 3 1 7 1 9 ( r I ) o . 3 l s 9 6 ( 3 o )

9 o . 0 2 3 4 0 ( 1 2 ) 0 . 0 2 3 0 I ( 2 7 )

z 0 . 2 4 5 0 2 ( 4 1 o . 2 4 5 3 ? ( 1 1 )

B 0 . 6 2 ( r ) t o . G r ( 2 )

r* (xto5) f t 2.27 l to)

i l (obs) 308

R ( d ) o . o 2 2

R 0 . 0 1 5

0 0

0 0

0 . 3 5 5 3 0 ( 1 4 ) 0 . 3 5 5 8 0 ( 1 r )

0 . 6 3 ( 2 ) 0 , 6 3 ( 2 )

0 o

o o

0 . 1 4 6 5 0 ( 1 9 ) 0 , 1 4 5 4 4 ( 1 4 )

o , 5 o ( 2 ) o , 5 2 ( 2 1

0 . 3 1 6 5 ? ( 3 6 ) 0 . 3 1 6 4 9 ( 3 2 )

o.02284(291 O.O2L65126l

o.2452012A' O.24545125)

0 . 5 3 ( 3 ) 0 . 6 s ( 3 )

r . 3 6 ( 1 5 ) L . 3 2 l L 2 l

1 5 9 1

o . o 2 2 0 . 0 2 0

0 . 0 1 9 0 . 0 1 9

2 . 2 5 1 1 6 )

r4o

0 . 0 2 3

0 . 0 2 0

rEquivalat isotropic B.

fis*ondatg extinction patareter.

I8O WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE

Table 6. Selected interatomic distances (A), angles ("), and thermal expansion coefficients of ilmenite at high temperature

24oc 4oooc 6oooc eoooc losooc RTArr cr

F e - o 2 . 2 0 1 3 ( S ) 2 . 2 I 9 l L l 2 . 2 3 o 1 2 t 2 . 2 3 A 1 2 1 2 . 2 4 4 1 2 1 2 . 2 o 4 l I ) 2 0 . 6F e - o 2 , 0 7 7 4 ( A ) 2 . 0 8 5 ( I ) 2 . 0 A 6 1 2 , 2 . 0 8 8 ( 2 ) 2 . 0 9 3 1 2 \ 2 . 0 8 0 ( 1 ) 7 . I

<Fe-o> 2 .L396 2 . L52 2 .158 2 . 163 2 .L7L 2 . !42 14 . 3

r i - o 2 . 0 8 8 6 ( S ) 2 . 0 9 0 ( r ) 2 . 0 9 5 ( 1 ) 2 . L O O ( 2 1 2 . 0 9 9 ( 2 \ 2 . 0 8 7 ( 1 ) 4 . 8T 1 - O 1 . 8 7 4 4 ( 8 ) r . 8 7 9 ( I ) L . A A 2 | 2 \ 1 . 8 8 5 ( 2 ) L . e 9 2 1 2 ' , ) r . 8 t 4 ( 1 ) 9 . 1

< T i - o > 1 . 9 8 1 5 1 . 9 8 5 1 . 9 8 8 1 . 9 9 3 I . 9 9 6 1 . 9 8 0 7 . I

Q E * * ( F e ) 1 . 0 2 7 1 1 . 0 2 8 5 L . O 2 9 2 I . O 3 O O 1 . 0 3 1 1 L . O 2 7 2Q E ( T i ) L . 0 2 7 7 L . 0 2 7 3 r . 0 2 6 7 L . O 2 6 2 1 . 0 2 5 9 t . 0 2 7 8

reoa vo t . {83) L2 .562 t2 .766 r2 .s55 12 .930 13 .052 L2 .6o4

T i o 6 v o l , ( i r ) t o . o o t t o . o s t l o , l l 9 t o . 1 9 l r o . 2 3 8 9 . 9 7 8

F e - T i 2 . 9 4 3 5 ( 4 ) 2 . 9 5 7 0 ( 7 1 2 . 9 6 6 3 ( 8 ) 2 . 9 7 5 ( L \ 2 . 9 8 5 ( I ) 2 . 9 4 5 0 ( 5 ) 1 3 . 7F e - r e t t 3 . 0 0 2 ? ( r ) 3 , 0 1 8 2 ( 2 ) 3 , 0 2 5 9 ( 3 ) 3 . 0 3 5 2 ( 3 ) 3 . 0 4 5 7 ( 4 ) 3 . 0 0 3 3 ( 2 ) t 4 . OF e - F e 2 4 . 0 7 4 4 ( 4 ) 4 . O 6 7 7 ( 5 ' , ) 4 . 0 5 3 ( r ) 4 . 0 5 r ( 1 ) 4 . 0 5 9 ( r ) 4 . 0 7 5 2 ( 4 ) - 3 . 6r i - r i I 2 . 9 9 2 a ( L ) 3 . 0 0 2 3 ( 2 ) 3 . o o j 2 l 2 ' ) 3 . o l l 7 ( 3 ) 3 . o I B o ( 3 ) 2 . 9 9 2 9 1 2 1 a . 2r i - r i 2 4 . L 2 4 2 ( 4 ) 4 , 1 4 7 r ( g ) 4 . 1 6 1 ( r ) 4 . L 7 7 ( r \ 4 . r 9 6 ( t ) 4 , 1 2 7 9 1 6 ) 1 7 . 0

o - o t r i 2 . 7 0 r ( r ) 2 . 7 1 2 ( 2 ) 2 . 7 2 3 ( s t 2 . 7 3 L ( 3 ) 2 , 7 3 4 ( 3 ) 2 . 7 o r p l l r . 9o - o 2 3 . 2 1 6 ( 1 ) 3 . 2 3 4 ( 2 ) 3 . 2 3 8 ( 3 ) 3 . 2 4 - t ( 3 ) 3 - 2 5 7 ( 3 ) 3 . 2 L 7 ( 2 1 L 2 , 4o - o 3 3 . 0 5 1 ( r ) 3 . o ' t 2 l 2 l 3 . 0 8 0 ( 3 ) 3 , 0 8 5 ( 4 ) 3 . 0 9 8 ( 4 ) 3 . 0 5 8 ( 2 ) 1 5 . 0o - o 4 3 . 0 0 5 ( 1 ) 3 . 0 1 9 ( 2 ) 3 . 0 2 3 ( 3 ) 3 . 0 2 4 ( 3 ) 3 . 0 3 8 ( 4 ) 3 . 0 1 0 ( 2 ) 1 0 . 7o - o s 2 . 9 2 I ( I ) 2 . 9 2 5 ( 2 1 2 . 9 2 7 l 3 t 2 . 9 2 5 ( 3 ) 2 . 9 3 9 ( 3 ) 2 - 9 2 0 ( 2 1 5 . 0o - o 6 2 . 6 0 7 ( r ) 2 . 6 j 5 ( 2 ' , ) 2 . 6 1 r ( 3 ) 2 . 6 L 9 ( 4 ) 2 , 6 2 0 ( 4 \ 2 - 6 0 2 ( 2 1 4 . 9o - o 7 2 . 8 8 5 ( I ) 2 . a 9 2 1 2 1 2 . 8 9 6 ( 3 \ 2 . 9 0 7 ( 3 ) 2 . 9 U ( 4 ) 2 . e 8 2 ( 2 1 8 . 8

o - F e - o 7 5 . 6 8 ( 3 ) 7 5 . 3 5 ( 5 ) 7 5 . 2 6 ( 6 ) 7 5 . 2 0 ( 7 ) 7 4 , 8 8 ( 8 ) 7 5 . 5 5 ( 4 )o - F e - o 9 0 . 9 2 ( 3 ) 9 r . 0 2 ( 5 ) 9 r . 0 0 ( 6 ) 9 0 . 9 5 ( 7 ) 9 0 . 9 7 ( 3 ) 9 1 . 0 3 ( 4 )o - F e - o 8 9 . 1 5 ( 4 ) S 8 . 9 9 ( 6 ) 8 8 . 8 7 ( 8 ) 8 8 . 6 4 ( 9 ) 8 8 . 7 ( 1 ) 8 9 - 2 3 ( 6 1o - F e - O 1 0 1 . 4 0 ( 3 ) 1 0 1 . 6 5 ( 4 ) 1 0 r . 8 l ( 6 ) I O 2 . O 7 ( 7 ) 1 0 2 , t 8 ( 8 ) 1 0 1 , 3 2 ( 4 )

o - T i - o 8 0 . 5 6 ( 3 ) 8 0 . 8 8 ( 5 ) S 1 . 0 6 ( 7 ) 8 r . 1 3 ( 8 ) 8 I . 2 6 ( 9 \ 8 0 . 6 5 ( 4 )o - T i - o 8 2 . O 7 1 3 J S I . 8 4 ( 5 ) 8 1 . 8 9 ( ? ) 8 1 . 9 7 ( 8 ) 8 1 . 9 ( 1 ) 8 1 . 9 7 ( 4 )o - r i - o 9 3 . 2 8 1 4 1 s 3 . 3 7 ( 7 ) 9 3 , 3 3 ( e ) e 3 . s ( 1 ) 9 3 . s ( 1 ) 9 3 . 2 4 ( 6 )o - r i - o 1 0 2 . 3 5 ( 3 ) L 0 2 . 2 6 ( 5 ) 1 0 2 . 1 4 ( 6 ) 1 0 1 . 8 S ( 7 ) 1 0 1 . 8 8 ( 9 ) r O 2 . 4 O ( 4 )

r d = f t t / d , t d - d t t t o 2 6 l y l o 6 , o r - l r .- " ' ' - 2 4 " - 1 0 5 0 - 2 4 " " " '

, *Qvadtat ic eTonqat ion.fMetaL-reta7 distarces are indicated as fofJ.ows:

-l--across shared edge between ad.jacent retal sjtes,' 2--across vacant octahedraL lpsition, along lOOll.floxggen-oxggen atistances are Tnd.icated as foTLows:

7--Fe-f i shated face, 2--Fe sixe, face optrDsite the slRred facet 3--Fe 6i te, s lBted edge; 4--Fe si te, unshated. edge;5--Ti s i te, face opposite Xhe shared face; 6--Ti s i te, shated edge; 7--Ti s i te, unshared edge.

vacant octahedral position. In ilmenite, Fe and Ti are the TiO6 octahedron became more regular, as indicatedcompletely ordered into alternating layers along c, so that by the quadratic elongation (Robinson et al., l97l; seeeach cation shares three edges with other octahedral Table 6). Mean Fe-O and Ti-O distances increasedcations of the same type, but the common octahedral face linearly with temperature, with (Fe-O) increasing aboutis shared with a cation of the other type. On either side of twice as much as (Ti-O) between 24 and 1050"C.each vacant octahedral position along c lie cations of the The fractional coordinate z of the Fe atom increasedsame type. Both cation sites lie on threefold axes, and slightly with pressure, whereas the Ti e coordinate waseach has a single variable positional parameter, e. Devi- unchanged. Small shifts were found for all three oxygenations of z from 1/3 and 116 for Fe and Ti sites, respective- coordinates, with y changing the most and z the least withly, are indicative of "puckering" of the cation layers increasing pressure. The Fe and Ti sites were afectedabove and below planes parallel to (001). quite differently by compression. The longer of the two

The Fe and Ti atom z coordinates both increased independent Fe-O distances was somewhat less com-linearly with temperature, corresponding to movement pressible than the shorter Fe-O distance, whereas thetoward the centroid of the coordination polyhedron for Ti longer Ti-O distance was more than twice as compress-and away from the centroid position for Fe. "Puckering" ible as the shorter one (Table 7). However, overallof the Fe layer was significantly increased, and the Fe-Fe distortions of the FeO6 and TiO6 polyhedra, as measureddistance across the vacant octahedral site in the Ti layer by the quadratic elongation and octahedral angle vari-actually decreased at high temperatures. The longer of ance, were only slightly affected by pressure. Mean Fe-Othe two independent Fe-O bonds increased nearly three and Ti-O distances decreased linearly with pressure, withtimes as rapidly as the shorter distance, whereas for the the (Fe-O) distance about twice as compressible as (Ti-Ti atom, the shorter bond distance increased twice as O).rapidly as the longer one (see thermal expansion coeffi- Although the change in the oxygen e coordinate withcients in Table 6). Thus, the FeO6 octahedron became pressure is small, it reflects the diference in behaviorsignificantly more distorted at high temperature, while between the Fe and Ti sites. The octahedral height

WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE lE l

Table 7. Selected interatomic distances (A), angles ('), andcoefficients of compressibility of ilmenite at high pressure

(distance between upper and lower oxygen layers along c)is dependent upon the c length and the oxygen z coordi-nate. The slight increase in zo*y with increasing pressureindicates that the octahedral height of the Fe layerprobably decreases more than twice as rapidly as that ofthe Ti layer. This decrease is also more than twice thelinear compressibility in the a-direction. Thus, the Fe siteis "flattened" relative to the Ti site, which compressesabout equally along a and c. This is perhaps the reason forthe decrease in c/a with increasing pressure. The greaterc-axis compression is, of course, also associated withmore substantial shortening of metal-metal distancesalong c (i.e., Fe-Ti across shared face, Fe-Fe and Ti-Tiacross vacant sites) than between adjacent metal sitesacross shared edges.

Cation distribution

In order to determine whether any disorder between Feand Ti sites was present, direct cation site occupancyrefinements were performed on all data sets. Total occu-pancies were constrained to the stoichiometric composi-tion. No measureable disorder was found at any tempera-ture or pressure, with estimated standard deviations inthe occupancies of -+l-ZVo. The observed mean bonddistances of the octahedral sites are also consistent withcomplete order having been maintained under all condi-tions.

Temperature factors

Thermal ellipsoids calculated from all data collected atI atm pressure are presented in Table 8. Due to thepaucity of intensity data, no attempt was made to refineanisotropic temperature factors for the high-pressuredata.

I a h 25.4 kbar 34.6 k-bar 45.1 kbar

Fe-OFe-O

<Fe-O>

Ti-oTi-o

<Tt-o>

0E*r (Fe)

QE (r i )

reoo voL (13)

riol 'or. rfl3t

Fe-TiFe-Pe ltPe-Fe 2Ti-Ti ITi-Ti 2

2.2005 16)2 . 0 7 A 4 l 5 l2 . 1 3 9 5

2 . 0 8 7 1 ( 5 )1 . . 8 7 4 2 ( 5 )r . 9 4 0 5

r. o272L . O 2 7 9

1 2 . 5 5 8

9 . 9 8 4

2.9436t4)3 . 0 0 2 3 ( 3 )4 . O 1 2 7 l 3 l2 . 9 9 2 3 ( 3 14 . 1 2 2 9 ( 6 1

2 . 6 9 8 ( 1 )3 . 2 r 7 ( 7 13 . O s l ( r )3 . 0 0 s ( r )2 . 9 2 L ( 1 12 . 5 0 4 l 7 )2 . e 8 4 ( 1 )

7 5 . 6 L 1 2 )9 0 . 9 3 ( 2 )8 9 . 1 S ( 3 )

1 0 1 . 4 I ( 2 )

8 0 . 5 3 ( 2 )82.02 l2l9 3 . 3 r ( 3 )

r 0 2 . 3 8 ( 2 )

2 . 1 8 0 ( 3 ) 2 0 . 22 . O 5 2 t 2 t 2 7 . 62 , r r 5 2 3 . 8

2 . O ? 2 1 3 ) 1 5 . ?r , 8 6 9 ( 2 ) 6 . OI . 9 ? 0 t I . 6

r. o27 5r. o272

12.141

9 . 8 3 9

2 . 9 1 3 ( 3 ) 2 2 - 52 . 9 8 5 3 ( 7 ) 1 2 - 34 - O r 2 ( 3 ) 3 2 . 32.972914) L4.t4 - 0 7 4 ( 4 ) 2 5 . ' l

2 . 6 A 2 1 3 ' L 2 . 93 . r 8 5 ( 2 ) 2 r . 63 , O O 3 ( 6 ) 3 4 - 12 . 9 6 8 ( 6 ) 2 6 , 12 . 9 1 3 ( 2 ) 5 . 92 . 5 9 5 ( 6 ) 7 . 52 . 8 6 t ( 5 ) 1 7 . 3

7 5 . 9 0 ( 1 2 )9 0 . 3 3 ( 1 1 )8 9 . O 0 ( 1 2 )

t o l . 8 2 ( 1 I )

8 0 . 6 4 ( 1 2 )8 2 . 1 9 ( 1 4 )92.96 lL2)

1 0 2 . 4 1 ( 1 4 )

2 . 1 8 4 ( 1 ) 2 . r 8 r ( 3 )2 . 0 6 ? ( 1 ) 2 . 0 6 5 1 2 )2 . L 2 6 2 . t 2 3

2 . 0 7 6 ( r ) 2 . O 1 2 1 3 11 . 8 7 2 ( 1 ) l . S 6 8 ( 3 )t . 9 1 4 1 . 9 7 0

L . O 2 7 ? I . 0 2 5 8L . O 2 7 9 L . O 2 1 6

1 2 . 3 0 3 L 2 . 2 1 1

9 . 8 8 1 9 . 4 2 9

o - o 1 , ,o-o 2o-o 3o-o 4G O 5G O 6c o 7

2 . 9 2 6 3 1 4 t 2 . 9 1 3 ( 4 )2 . 9 9 2 3 1 3 1 2 . 9 8 7 0 ( S )4 . 0 3 8 ( 1 ) 4 . 0 3 8 ( 4 )2 . 9 4 1 2 ( 3 ) 2 - 9 1 7 1 r ' l4 . 0 9 4 ( 1 ) 4 . 0 8 8 ( s )

2 . 6 7 9 ( 2 1 2 . 6 5 2 1 3 13 . 2 7 4 ( 2 ) 3 . 2 0 0 ( 2 )3 . 0 2 2 ( 3 ) 3 . 0 2 0 ( 7 )2 . 9 4 2 1 3 ) 2 . 9 1 9 I ' t l2 . g r e t 2 ) 2 . 9 r 2 ( 2 12 . s 9 6 ( 3 ) 2 . s 9 0 ( 7 )2 . 4 1 ' t l 3 l 2 . 8 6 6 ( 6 1

7 s . 6 6 ( 6 ) 7 5 . 8 8 ( ] , 4 )9 0 . 5 6 ( 6 ) 9 0 . 6 3 ( 1 3 )8 9 . 0 4 ( S ) 8 9 . 0 5 ( r 3 )

r 0 1 . 7 6 ( 6 ) r 0 1 . 5 5 ( 1 2 )

8 0 . 3 7 ( 6 ) 8 0 . 6 5 ( r 4 )8 2 . 0 6 ( 6 ) 8 1 . 9 9 ( 1 6 )9 3 . 4 0 ( 8 ) 9 3 . 1 9 ( 1 3 )

1 0 2 . 3 9 ( 6 ) 1 0 2 - 4 r ( 1 7 )

O-Fe-O

o-Fe-o

O-Fe-O

O-Fe-O

o-Ti-oGTi-OGTi-O

o-Ti-o

g = - I ( ] / d ) ( d . - . - d ) / 4 6 . 1 1 x 1 o ' ( k b a r - ) .

., Quatlrat ic eTongation.

fileta]-reta] distarces ate inilicateal as foliows..

7 - actoss shateil eilge betveen ailjacent netai sites;

2 - ac toss vacant occahe i t ta l los i t ion , a long lo01 l .

++otgg"n-o*9g"n ilistances ate inilicateil as foTlows:

l--Fe-?i shareil facei 2--Fe sixe, face opposite the

slEteil face; 3--Fe site, ahateil edge, A--Fe Eixe,

unslared eilgei 5--Ii site, face oppsixe the shated

face; 5--Ti sjte, shared eilgei 7--Ti site, uDslEaed

edge.

Table 8. RMS amplitudes of vibration (A) and orientation of thermal eltipsoids

24o c 4oooc 6oooc goooc t0500c

Fe aton!Perpendiculu to c

Paral lel to c

li atom:Paral lel to c

Perpendiculu to c

Oxggen aton:Axis I

Argle with aAngle with DAngle with c

Axis 2Angle with aAngle wlth DAngle wlth c

AJ(18 3Angl6 {ith aAngle with DAngI6 with c

0. 0876 (6 )0 . o9r5 (9 )

0 . o84r (10)0 . 077s ( 6 )

0 . o8o3 ( 14)52 ( r r ) * *70 (10)

ro4 (6 )

0 . 0 8 5 0 ( r 3 )4 I ( I I )

143 (7 )64 (5 )

o , too3 ( 13)102 (3 )

6 0 ( 3 )3 0 ( 3 )

0 .0860 . 0 8 6

0 . 0 7 60 . 0 7 5

o.077 (2 ' , ,2A 16',,9s (12)78 ( Is )

0 . 0 8 2 ( 2 )84 (17)

1 2 6 ( 5 )39 (8 )

o , o 9 7 ( 2 1LL7 (4)

3 6 ( 5 )s4 (s )

o . L 2 2o . L 2 2

0 . t o 50 . r 0 5

0 . 1 0 4 ( 3 )5 s ( 1 7 )53 (9 )

t2o (14)

o . 1 r0 ( 3 )r41 (14)

57 (10)r29 (13)

0 . 1 3 2 ( 3 )l l a l E l

37 (4 )s4 (4 )

0 . 1 3 6 ( r )0 . r 4 3 ( r )

0 . 1 1 7 ( I )0 . 119 G)

o . u s ( 3 )3 3 ( 7 4 )

r17 (s6)57 (67 |

0 . r 2 0 ( 3 )112 (95)r r 8 ( 5 5 )

s8 (58)

0 . I 4 7 ( 3 )l I3 (4 )

4 r ( 4 )49(4 l

o. rso ( r )o. r50 ( l)

o. L26 (2't0 . r31 ( r )

0 . 1 2 S ( 3 )

a2(71r01 (8 )

0 . 1 4 3 ( 3 )s9 (10)

L27 (7' '4 r ( 8 )

0_ 160 (3 )112 (5 )

3 8 ( 7 )52 t7l

0. os50.085

o.o77o .o71

o .076 (3 )60 (2Al? 1 1 1 q \

1,23 (L7l

0 . r59 ( r )0 . 1 8 2 ( r )

o . L42 (21o. 143 ( r )

0 . 1 4 3 ( 4 )74(2s l6 r (15)

r30 (13)

0 . r 4 8 ( 3 ) 0 . 0 8 r ( 3 )lss (r9) 144(221

51 ( l5 ) 59 (10)r I2 (18) 12s ( r8 )

0 . I s 2 ( 3 ) 0 . 0 9 9 ( 3 )ro5 (4 ) 108 (6 )

43 (4 ) 38 (s )4 8 ( 3 ) s 3 ( 5 )

rcrgstal used fot hlqh-ptessuEe atualg reasuieit at toon tenpetature and pressure..rAngles gl,ven in itegtees.

lE2 WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE

For the crystal studied at high temperature, thermalvibration of Fe and Ti was found to be essentiallyisotropic at room temperature and 400"C and only slightlyanisotropic at higher temperatures. However, the roomtemperature and pressure refinement of the high-pressurecrystal did indicate slightly anisotropic vibration of Feand Ti, with the longer axes parallel to c. The oxygenellipsoid was significantly anisotropic at all temperatures,with the direction of maximum vibration lying in the a-+plane, about 50-55' from c for the high-temperaturecrystal and 30'from c for the high-pressure crystal. Thediscrepancies between the two crystals at room tempera-ture and pressure are not serious. Due to improved datacollection procedures, we feel that the ellipsoids deter-mined for the high-pressure crystal are probably some-what more reliable.

Equivalent isotropic temperature factors (Hamilton,1959) for the high-pressure crystal are slightly higher thanthose for the high-temperature crystal at room tempera-ture. The B"o for Ti increased linearly with temperature,whereas those for Fe and O increased more rapidly athigher temperatures. Isotropic temperature factors for allatoms were essentially unchanged with pressure.

Discussion

Mean Fe-O and Ti-O distances. uncorrected for ther-mal motion, increased linearly with temperature. Theincrease in (Fe-O) distance was twice as great as that for(Ti-O). Values of thermal expansion coefficients (Table 6)compare well with measured values of mean Fe2+-Odistances in fayalite (Smyth, 1975), wiistite (Carter,1959), orthoferrosilite (Sueno et al.,1976), and hedenber-gite (Cameron et al., 1973). The mean Tia*-O distanceexpansion was also comparable to values for this speciesreported for anatase (Horn er al., 1972), rutile and brook-ite (Meagher and Lager, 1979), and titanite (Taylor andBrown, 1976). The lower rate ofexpansion for octahedral(TF+-O) is consistent with the greater Pauling bondstrength (cation charge/coordination number) of Ti4"-Obonds. However, as was also pointed out by Meagher andLager (1979), the expansion coefficients for (Ti4*-O)distances are substantially greater than those expectedfrom the trend pointed out by Hazen and Prewitt (1977).

The polyhedral bulk moduli, Ke : ll3B (Hazen andFinger, 1979), of the Fe and Ti sites in ilmenite are 1.4(1)and 2.9(5) Mbar, respectively. The Fe value compareswell with values derived from compression of wustite(Clendenen and Drickamer, 1966; Will et a/., 1980) ofabout 1.6 Mbar. Ko for the Ti site is also consistent withthe value of 2.2(8) reported by Hazen and Finger (1981)for TiO2. The value determined in this study indicatesthat the TiO6 polyhedron is among the least compressibleoctahedra yet found. The polyhedral bulk modulus for theFe site is compatible with the semiempirical relationderived by Hazen and Finger (1979), although the Ti sitehas a somewhat smaller Ko than is predicted by this

relation. Hazen and Finger (1981) also noted that Kovalues for tetravalent ions show systematic deviationsfrom the trend suggested by Hazen and Finger (1979).

The ilmenite structure is derived from the corundumstructure by ordering of the octahedral sites into twononequivalent layers. It is thus interesting to comparethese results with those for R2O3 corundum structuresreported by Finger and Hazen (1980). The compression inilmenite is relatively anisotropic, with cla decreasingabout twice as rapidly as in Fe2O3, as compared with nochange with pressure for Al2O3 and Cr2O3, and a rapidincrease for V2O3. The decrease in cla ratio and change inFe coordinate in ilmenite are indicative of further depar-ture from hexagonal close packing and the ideal corun-dum structure with increased pressure. However, this ispartially offset by the changing oxygen y and z coordi-nates, which become more corundum-like at high pres-sure. Whereas the structural parameters for Fe2O3,Cr2O3, and Al2O3 remain essentially constant as pressureis increased, somewhat more distortion is observed inilmenite, presumably due to the presence of two non-equivalent cation sites.

The bulk modulus and its pressure derivative areindicative of the mechanism of compression of crystalstructures (Hazen and Finger, 1978). In a fully edge-linked structure such as that of ilmenite, the compressibil-ity is expected to be mainly determined by shortening ofM-O bonds. The fraction of the unit-cell volume occupiedby the cation polyhedra in ilmenite is, in fact, constantbetween I atm and 46 kbar, as it is betweel24 and 1050'Cas well. Thus, although some distortion of the structureoccurs under pressure, the overall rate of compressionmust be controlled by the compressibilities of the compo-nent polyhedra themselves. This being the case, it isreasonable to suggest that the actual Ki for ilmenite isprobably in the range of 4 to 5, as is observed in similarmaterials. Therefore, the bulk modulus determined withKi constrained to be 4(l), which gave K" : 1.77(3) Mbar(see above), may provide a slightly better estimate thanthe value determined with both K. and Ki allowed to vary(K" = r.70(7), Kl : 8(4)).

Some of the difference in compressional behavior be-tween the Fe and Ti sites can perhaps be understood byconsidering the nature of the structure in the a and cdirections. The ilmenite structure consists of alternatinglayers of edge-sharing Fe and Ti octahedra stacked alongc. Compression along a is constrained by the more rigidpolyhedron, i.e.,Ti, and both cation sites are compressedat virtually identical rates in this direction. Parallel to c,however, the two cation layers may be compressed moreor less independently of one another. Therefore, differ-ences between the overall volume compressibilities of thetwo sites may be expected to be expressed mainly in the cdirection. Of course, this does not necessarily require achange inthe cla ratio unless one of the sites compressesequally in both directions, as Ti does in ilmenite. Similar

c (a)

WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATT]RE AND PRESSURE

> o l

I

o t

o 9 8

c/o

lE3

5.O9q ( A ) o 97L

400Fig. l. Variation of ilmenite cell parameters with V/V".

behavior may also pertain to compression of other miner-als having the ilmenite structure.

Comparison of temperature and pressure effects

Hazen and Prewitt (1977) suggested that in compoundswhere all component polyhedra have similar values ofalB, the mechanism of compression will be essentiallyequivalent to that of cooling, i.e., compression and ex-pansion have inverse efects. Although this criterion issatisfied in ilmenite, clearly the mode of compression isnot the inverse of expansion. In Figure l, a, c, and cl a areplotted against VlVo (unit-cell volume at T, P divided byvolume at24"C, I atm). The striking difference betweenexpansion and compression is clearly demonstrated bycla.The linear decrease with pressure is contrasted with asmall decrease followed by an even smaller increase withincreasing temperature. Whereas the high-temperaturebehavior is characterized by nearly isotropic expansion ofthe unit cell and significant structural distortion, at highpressure the structural changes are smaller and the unit-cell compression is quite anisotropic.

Figure 2 demonstrates the linear relationship betweenmean Fe-O and Ti-O distances and VlV" in ilmenite.

>o l O l

I

402 4c,4 4.06 4.o8 4.lO 412 414 416 48 4?O

DISTANCE (A)

Fig. 3. Variation of Fe-Fe and Ti-Ti distances across vacantoctahedral sites in ilmenite with VIV".

Thus, the difference between expansional and compres-sional behavior is not related to the mean M-O distances.It is interesting, however, to observe the individual bonddistances which make up the coordination polyhedra. Inboth the Fe and Ti sites, the more expandable of the twoindependent M-O bonds are also the less compressibleones, the opposite of what might be expected if the ratesof expansion and compression were proportional to indi-vidual bond strengths. The latter notion is reasonablyuseful when considering mean bond distances, however.

The oxygen coordinates vary approximately inverselywith temperature and pressure, although changes in thecation coordinates are decidedly noninverse. As withincreasing pressure, the octahedral height (along c) oftheFe layer probably changes much more rapidly than that ofthe Ti layer at high temperature. However, the netexpansion along c is about equal to the expansion along a.This is perhaps due to metal-metal repulsion betweenadjacent Ti sites, resulting in increased separation andconsequently greater expansion of the Ti layer along athan c.

The displacement of the Fe position at high tempera-ture may also reflect the importance of metal-metalrepulsions. The retreat of the Fe position away from theTi across the shared face is suggestive of a significantrepulsive interaction. This results in greater "puckering"ofthe Fe layer and an increase in Fe-Fe distances acrossshared edges. On the other hand, this shift also results ina decrease in the Fe-Fe separation across the vacantposition along c at high temperature (Figure 3). Presum-ably the Fe-Fe interaction in this direction is weaker thanthe corresponding Ti-Ti repulsion, resulting in the ten-dency of the Fe site to distort in this fashion.

Acknowledgments

D. H. Lindsley provided the ilmenite crystals used in thisstudy, and his thoughtful comments are appreciated. Assistancefrom and discussions with Kenneth Baldwin, Jay Bass, BenjaminBurton, Robert Hazen, Hubert King, Louise Levien, Robert

//

.T i -O, - /

Lo 9 7

| 96 t97 198 t99 212 2 t3 214 215 216

DISTANCE (A)

Fig. 2. Variation of mean Fe-O and Ti-O distances inilmenite with VIV".

217 214

I- - are - re \

\\\

t/'

"l

T i - T iI

l '

!

/'I

184 WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE

Liebermann, and Alexandra Navrotsky contributed measurablyto the results. This research was supported in part by NSF GrantNo. EAR8I-20950.

ReferencesAndersen, D. J. and Lindsley, D. H. (1979) The olivine-ilmenite

thermometer. Proceedings of the Lunar and Planetary ScienceConference. l0th. 493-507.

Barnett, J. D., Block, S., and Piermarini, G. J. (1973) An opticalfluorescence system for quantitative pressure measurement inthe diamond-anvil cell. Review of Scientific Instruments. 44.t-9.

Barth, T. F. W. and Posnjak, E. (1934) The crystal structure ofilmenite. Zeitschrift ftir Kristallographie, AEE, 265-27 0.

Bass, J. D., Liebermann, R. C., Weidner, D. J., and Finch, S. J.(1981) Elastic properties from acoustic and volume compres-sion experiments. Physics of the Earth and Planetary Interi-ors, 25, 1,1,0-158.

Birch, F. (1966) Compressibility; elastic constants. In S. P.Clark, Jr., Ed., Handbook of Physical Constants, p.97-173.Geological Society of America Memoir 97.

Bishop, F. C. (1980) The distribution of Fe2* and Mg betweencoexisting ilmenite and pyroxene with applications to geother-mometry. American Journal of Science, 280,46-77.

Buddington, A. F. and Lindsley, D. H. (1964) Iron-titaniumoxide minerals and synthetic equivalents. Journal of Petrolo-gy ,5 , 310-357.

Burton, B. (1980) Crystallography of the ilmenite-corundumorder-disorder transformation for an intermediate ilmenite-hematite solution. (abstr.) EOS, 61, 40E.

Cameron, M., Sueno, S., Prewitt, C. T., and Papike, J. J. (1973)High-temperature crystal chemistry of acmite, diopside, he-denbergite, jadeite, spodumene, and ureyite. American Miner-alogist, 58, 594-618.

Carter, R. E. (1959) Thermal expansion of MgFe2Oa, FeO, andMgO . 2FeO. Joumal of the American Ceramic Society, 42,324-327.

Clendenen, R. L. and Drickamer, H. G. (1966) Lattice parame-ters of nine oxides and sulfides as a function of pressure.Journal of Chemical Physics, 44, 4223-4228.

Doyle, P. A. and Turner, P. S. (1968) Relativistic Hartree-FockX-ray and electron scattering factors. Acta Crystallographica,424.390-397.

El Goresy, A. (1976a) Oxide minerals in lunar rocks. In D.Rumble, Ed., Oxide Minerals, p. EG-I-EG-46. MineralogicalSociety of America Short Course Notes, 3, Washington, D.C.

El Goresy, A. (1976b) Opaque oxide minerals in meteorites. InD. Rumbfe, Ed., Oxide Minerals, p.EG-47-8G72. Mineralogi-cal Society of America Short Course Notes, 3, Washington,D.C.

Finger, L. W. and Hazen, R. M. (19E0) Crystal structure andisothermal compression of Fe2O3, Cr2Or, and V2O. to 50kbars. Journal of Applied Physics, 51, 5362-5367.

Finger, L. W. and King, H. E., Jr. (1978) A revised method ofoperation of the single-crystal diamond cell and refinement ofthe structure of NaCl al 32 kbar. American Mineralogist, 63,337-342.

Finger, L. W. and Prince, E. (1975) A system of ronrur IVcomputer programs for crystal structure computations. U. S.National Bureau of Standards Technical Note E54.

Finger, L. W., Hadidiacos, C. G., and Ohashi, Y. (1973) A

computer-automated, single-crystal x-ray difrractometer. Car-negie Institution of Washington Year Book, 72,694-699.

Haggerty, S. E. (1976) Opaque mineral oxides in terres-trial igneous rocks. In D. Rumble, Ed., Oxide Minerals,p. Hg-l0l-Hg-300. Mineralogical Society of America ShortCourse Notes, 3, Washington, D.C.

Hamilton, W. C. (1959) On the isotropic temperature factorequivalent to a given anisotropic temperature factor. ActaCrystallographica, 12, 609-6 10.

Hazen, R. M. and Finger, L. W. (1978) Relationships betweencrystal structure and compressibility in oxides and silicates.Carnegie Institution of Washington Year Book, 77, E48-850.

Hazen, R. M. and Finger, L. W. (1979) Bulk modulus-volumerelationship for cation-anion polyhedra. Journal of Geophysi-cal Research, 84, 6723-6728.

Hazen, R. M. and Finger, L. W. (1981) Bulk moduli and high'pressure crystal structures of rutile-type compounds. Journalof Physics and Chemistry of Solids, 42, 143-151.

Hazen, R. M. and Prewitt, C. T. (1977) Etrects of temperatureand pressure on interatomic distances in oxygen-based miner-als. American Mineralogist, 62, 309-j15.

Horn, M., Schwerdtfeger, C. F., and Meagher, E. P. (1972)Refinement of the structure of anatase at several tempera-tures. Zeitschrift ftir Kristallographie, 136, 27 3-2E1.

Ishikawa, Y. (195E) An order-disorder transformation phenome-non in the FeTiO3-Fe2O3 solid solution series. Journal of thePhysical Society of Japan, 13, 828-E37.

Ishikawa, Y. (1962) Magnetic properties of the ilmenite-hematitesystem at low temperature. Journal of the Physical Society ofJapan, 17, 1835-1844.

Ito, E. and Matsui, y. (1979) High-pressure transformations insilicates, germanates, and titanates with ABO3 stoichiometry.Physics and Chemistry of Minerals, 4,265-273.

King, H. E., Jr. and Finger, L. W. (1979) Diffraqted beam crystalcentering and its application to high-pressure crystallography.Journal of Applied Crystallography, 12, 374-378.

King, H. E., Jr. and Prewitt, C. T. (19E0) Improved pressurecalibration system using the ruby R1 fluorescence. Review ofScientific Instruments, 51, 1037-1039.

Kirfel, A., Hinze, E., and Will, G. (1978) The rhombohedralhigh-pressure phase of MgGeO3 (ilmenite): synthesis andsingle-crystal structure analysis. Zeitschrift fi.ir Kristallogra-phie, 14E, 305-317.

Liebermann, R. C. (1976) Elasticity of ilmenites. Physics of theEarth and Planetary Interiors, 12, P5-P10.

Lindsley, D. H. (1963) Fe-Ti oxides in rocks as thermometersand oxygen barometers. Carnegie Institution of WashingtonYear Book, 62,60-66.

Liu, L.-G. (1977a)The system enstatite-pyrope at high pressuresand temperatures and the mineralogy of the Earth's mantle.Earth and Planetary Science Letters, 36,237-245.

Liu, L.-G. (1977b) Ilmenite-type solid solutions between MgSiO3and Al2O3 and some structural systematics among ilmenitecompounds. Geochimica et Cosmochimica Acta, 41, 1355-1 3 6 1 .

Liu, L.-G., Bassett, W. A., and Takahashi, T. (1974) Isothermalcompressions of a spinel phase of CozSiOr and magnesianilmenite. Journal of Geophysical Research, 79, llTl-1174.

Madelung, E. and Fuchs, R. (1921) Kompressibilitatsmessungenam festern korpers. Annalen der Physik (Berlin), 65, 2E9-309.

Meagher, E. P. and Lager, G. A. (1979) Polyhedral thermalexpansion in the TiO2 polymorphs: refinement of the crystal

WECHSLER AND PREWITT: ILMENITE AT HIGH TEMPERATURE AND PRESSURE lE5

structures of rutile and brookite at high temperature. CanadianMineralogist, l7 , 77-85.

Merrill, L. and Bassett, W. A. (1974) Miniature diamond anvilpressure cell for single crystal X-ray diffraction studies. Re-view of Scientific Instruments, 45.290-294.

Piermarini, G. J., Block, S., and Barnett , J. D. (1973) Hydrostat-ic limits in liquids and solids to 100 kbar. Journal of AppliedPhysics, 44, 5177 -5382.

Piermarini, G. J., Block, S., and Barnett, J. D. (1975) Calibrationof the pressure dependence of the R, ruby fluorescence line to195 kbar. Journal ofApplied Physics, 46,2774-2780.

Prince, E. (1978) A test of robust/resistant refinement on syn-thetic data sets. (abstr.) American Crystallographic Associa-tion. Program and Abstracts, 6, 37.

Raymond, K. N. and Wenk, H. R. (1971) Lunar ilmenite(refinement of the crystal structure). Contributions to Mineral-ogy and Petrology, 30, 135-140.

Ringwood, A. E. (l%9) Phase transformations in the mantle.Earth and Planetary Science Letters, 5,401-412.

Robinson, K., Gibbs, G. V., and Ribbe, P. H. (1971) Quadraticelongation: a quantitative measure of distortion in coordina-tion polyhedra. Science, 172, 567-570.

Rumble, D. (1976) Oxide minerals in metamorphic rocks. In D.Rumble, Ed., Oxide Minerals, p. R-l-R-24. MineralogicalSociety of America Short Course Notes, 3, Washington, D.C.

Sclar, C. B., Bauer, J. F., Pickart, S. J., and Alperin, H. A.(1973) Shock effects in experimentally shocked terrestrialilmenite, lunar ilmenite of rock fragments in l-10 mm fines(10085,19), and lunar rock 60015,127. Proceedings of theLunar Science Conference, 4th, l, 841-E59.

Shirane, G., Pickart, S. J., Nathans, R., and Ishikawa, Y. (1959)Neutron diffraction study of antiferromagnetic FeTiO3 and its

solid solutions with o-Fe2O3. Journal of Physics and Chemis-try of Solids, 10, 35-43.

Shirane, G. and Ruby, S. L. (1962) Mcissbauer study of FeTiO3and its solid solutions with oFe2O3. Journal of the PhysicalSociety of Japan, 17, Suppl. B-I, 133-135.

Shirane, G., Cox, D. E., Takei, W. J., and Ruby, S. L. (1962) Astudy of the magnetic properties of the FeTiO3-Fe2O3 systemby neutron diffraction and the Mcissbauer efect. Journal of thePhysical Society ofJapan, 17, 1598-1611.

Smyth, J. R. (1975) High-temperature crystal chemistry offayalite. American Mineralogist, 60, 1092-1097 .

Sueno, S., Cameron, M., and Prewitt, C. T. (1976) Orthoferrosi-lite: High-temperature crystal chemistry. American Mineral-og is t ,61 ,38-53.

Taylor, M. and Brown, G. E. (1976) High-temperature structuralstudy of the P2 Ja = A2la phase transition in synthetic titanite,CaTiSiO5. American Mineralogist, 61, 435447.

Thorpe, A. N., Minkin, J. A., Senftle, F. E., Alexander, C.,Briggs, C., Evans, H. T., and Nord, G. L., Jr. (1977) Celldimensions and antiferromagnetism of lunar and terrestrialilmenite single crystals. Journal of Physics and Chemistry ofSolids,3E. 115-123.

Vaughan, R. W. and Drickamer, H. G. (l%7) High-pressureMcissbauer studies on a-Fe2O3, FeTiOr, and FeO. Journal ofChemical Physics, 47, 1530-1536.

Will, G., Hinze, 8., and Nuding, W. (1980) The compressibilityof FeO measured by energy dispersive X-ray diffraction in adiamond anvil squeezer up to 200 kbar. Physics and Chemistryof Minerals. 6. 157-167.

Manuscript received, August I l, 1982;acceptedfor publication, July 22, 1983.