Compressibility and Crystal Structure of Andalusite at High Pressure

American Mineralogist, Volume 69, pages 513-519,l9A

Compressibility and crystal structure of andalusiteat high pressure

RussBrr L. Relpn

Department of Geological Sciences, University of Washington Seattle, Washington 98195

Llnnv W. FIncEn, RoBEnr M. HezeN

Geophysical Laboratory, Carnegie Institution of Washington Washington, D. C. 20008

nxo SusRAre GnosB

Department of Geological Sciences, University of Washington Seattle, Washington 98195

Abstract

The unit-cell dimensions and crystal structure of andalusite Al2SiO5have been refined from X-ray data on single crystals mounted in a diamond anvil cell at pressuresof 12,25, and 37 kbar. Structure refinementswith anisotropic temperaturefactors yielded weighted R factors of 3.4, 4.9, and5.2%o respectively. The bulk modulusof andalusiteis 1.35t0.10 mbar and the axial compressionratios of orthorhombic unit-cell axes a:b:c are approxi- mately2.1:1.5:1.0. The relativelygreater compressibility of the A(IFOD bond resultsin a beingthe most compressibleaxis. Those bondsthat compress)3obetween I bar and 37 kbar at room temperature, are the bonds that also expand significantly between 25 and 1000"C at room pressure. Polyhedral bulk moduli for the Al(l) octahedron, the Al(2) trigonal bipyramid and the Si tetrahedronare 1.3t0.2, 1.6!0.5, and 4.1+1.5 mbar' respectively. Thus, the aluminum polyhedra are significantly more compressiblethan the silicon tetrahedron. The omega step-scanningtechnique of X-ray intensity data collection results in a significant improvement in accuracy and is recommended for structure determination with the diamond-anvil high-pressurecell.

Introduction spectroscopicdata, the phonon spectra ofandalusite and High pressurestructure determination contain valuable their temperaturedependence have been determined and data on the equations of state, interatomic forces and interpreted on the basis of a rigid-ion model by Iishi et al. chemical bonding in minerals. The Al2SiO5polymorphs, (1979). andalusite,sillimanite and kyanite, provide an interesting In this paper are presented data on the high pressure system where aluminum occurs in three types of coordi- structural response of andalusite to 37 kbar, as well as nations; in addition to the octahedral coordination found correlations between high-pressure changes and high- in all three minerals, aluminum also occurs in tetrahedal temperature response, elasticity, and phonon spectra. It coordination in sillimanite and in five-fold trigonal bipyra- has been possible to observe directly the structural ele- midal coordination in andalusite. Knowledge of the re- mentsof andalusitethat are responsiblefor the compress- sponse to pressure and temperature of these different ibility and, hence, the elastic constants. The present data types of Al-O bonds in the presence of relatively rigid on andalusite at high-pressure,combined with high-tem- SiOa tetrahedra is necessaryfor an understandingof the perature data of Winter and Ghose (1979),may be used to stability relations and phase transformation within the test the inverse relationship betwedn structural responses Al2SiO5system. The temperature efects on the crystal due to temperature versus pressure (Hazen and Finger, structures of andalusite, sillimanite and kyanite have 1982).Andalusite is a light-atom structure with a small been determinedby Winter and Ghose (1979).The elastic unit-cell and orthorhombic symmetry and thus also con- constants of andalusite and sillimanite have been deter- stitutes a test casefor the improvement in accuracy of X- mined by Vaughan and Weidner (1978), who used the ray intensity data collected at high pressureby the omega Brillouin scatteringtechnique. From infrared and Raman step-scanningtechnique. The resulting improvement in 0003-004)v84l0506-05l 3$02 .00 5I 3 514 RALPH ET AL.: ANDALUSITE AT HIGH PRESSURE

the data resulted in a successful refinement of the aniso- A. Auiomotic bockgroundposltlons tropic temperature factors in a complicated silicate structure at high pressure.

Experimental

A fragment of a gem-quality andalusite crystal from Minas Gerais, Brazil, (from the samesample used by Winter and Ghose (1979)for their high-temperatureexperiments) was usedfor high- pressurestudy. A square crystal plate approximately 100 x 100 x 50 g,m was selectedand mounted along with small ruby chips Iqsls in a diamond-anvilhigh-pressure cell of the Merrill-Bassett type "3893 (Merrill and Bassett, 1974)modified (1977). by Hazen and Finger B. Monuolbockground posltlons The pressuremedium was a 4: I methanol:ethanol mixture. The ruby fragmentswere used for the pressurecalibration by the R1 ruby flourescencetechnique. The andalusitecrystal was mounted with its (001) plane approximately parallel to the diamond faces and was securedwith a small dot of petroleumjelly. The first data set at 37 kbar was collected at the University of Washington on the Syntex Pf four-circle automatic diffractometer with the d-20 techniqueand MoKa radiation monochroma- tized by reflecting from a graphite "single" crystal. All other Is61s.341 .32i7 data s€ts were collected at the Geophysical Laboratory on an Isslg automatedfour-circle diffractometer and Nb-filtered MoKa rad! Fig. l. Comparison of manual and automated background ation. All accessiblereflections for which sin 0/)r < 0.70 were selection for evaluation of integrated X-ray intensities: (a) collected. The data were corrected for specimenand diamond- continuous omega scan, automatic background selection; (b) cell absorption as well as Lorentz and polarization factors. omega step-scan, manual background selection. Integrated Results of unit-cell refinements at the pressures studied are intensities procedures, shown in Table 1. for weak reflections are similar with both but strong reflections, which may have white radiation Data at 12 kbar w€re collected first with continuous omega shoulders, axe often overestimated with automatic background scansand background measurementswere determined from the selection. intensities at the extremes of the scan. (Omega scans axe necessaryin diamond-cell studies because beryllium, which is used to support the diamonds, produces powder rings that modified manually prior to integration. Reflections were again interfere with 0-20 scans.)Data from symmetrically equivalent corrected for absorption, and symmetrically equivalent reflec- reflections were averagedprior to least-squaresrefinement with tions were averaged. Refinement based on 312 observed data the program nrrNe4 (Finger and Prince, 1975).Neutral scattering from the step-scanprocedure yielded a significantly improved (3.4% factors of Cromer and Mann (1968)and coefficientsfor anoma- anisotropic model, with a weighted R factor of 3.4Vo lous scatteringfrom Cromer and Libermarl (1970)were used for unweighted). all atoms. Refinement of a model with anisotropic atoms (46 Ofi-line selection of background positions, as facilitated by parameters, including scale factor, extinction parameter, 14 om€ga step-scandata collection, is an improvement over auto- p positional and 30 thermal parameters), based on 380 observed mated backgroundcollection for at least two reasons. When averagedreflections (I > 2 o) yielded a weightedR factor of 4.3Vo filtered radiation is used with a moving-crystal fixed counter (7.2Votnweighted). technique, shouldersof intensity are observed in the vicinity of Intensity data for andalusiteat 12 kbar were recollected with the Bragg peak (Fig. l). As the crystal is rotated away from the stepwiseomega scans (4 secondcounts at0.025"intervals). Step- scan data were processedand displayed visually on a graphics CRT for each reflection; backgroundpositions were selectedby Table 2. Refinement conditions and refined extinction the technique of Lehman and Larsen (1974), but could be parametersfor andalusiteat high pressure

lZ kbar 12 kbar 25 kbar 37 kbar Continuous Sterscan Steo-Scen Table l. Unit-cell parametersof andalusite l{umberof observatlons I> 2o) 380 312 2A7 351 t{eightedR(X) + 4.3 I barr 12 kbar 25 kbar 37 kbar 3.4 4.9 S.z 8(t) +i t.z 3.4 6-2 5.4 7.79W(71 7.7599(',r8)7.7382(10) 7.7ue(6) r* (xror) "(l) l.o(3) 2.8(4) 1.4(4) 0.8(3) b(A) 7.9031(r0) 7.873s(17) 7.8571(241 7.8375(r6) s.ss66(s) 5.s440(17) s.5338(40) 5.5262(r3) + "([) r"ightea R = [r{Fo - rrl2lx,roz]llz v(i3) 342.4s(6) 338.72(rs) 336.46(27) 333.71(l I ) i+ R-rllFol - IFcll/ rl Fo Parentheslzedfigures represehtesd's. r Fm Uinter and chose (1979) RALPH ET AL.: ANDALUSITE AT HIGH PRESSURE 515

Bragg position, the white radiation from the tube is ditrracted ture factors are adjustedin such a way that the discrepanciesfor into the counter first. Eventually the limits of the counter strong reflections are minimized at the expenseofweaker ones. aperture are reached and the only radiation observed is general As a result, the eflect on unweightedR is much greater than for scatteredradiation. Usually the scanlimits are chosento be large weighted R. in order to reduce sensitivity to small shifts in crystal orientation; A secondadvantage to manual selection of background posi- thus backgrounds are measured outside the shoulder regions. tions is the opportunity to view the shapeof each peak in detail. For weak reflections there is little difference in the intensities Anomalies in peak shapedue to diamond or ruby diffraction or measured with continuous versus step-scan procedures. The other interference, are quickly identified and those aberrent effect is significantfor a strong reflection for which the measured reflectionsmay be rejectedfrom the data set prior to refinement. intensity is too large for continuous scan methods. In the Subsequentrefinements of andalusiteat 25 kbar employed the refinement process, however, the scale factor and the tempera- omega steFscan procedure for data collection. Refinementcon- ditions and refined extinction parametersfor andalusiteappear in Table 2. Refined positional and thermal parameters appear in Table 3. Refined positional and thermal parameters for Table 3. while observedand calculatedstructure factors for four andalusite sets of andalusiteintensity data appear in Tables 4a to 4d.t I bar' 12 kbar l2 kbar ?5 kbar 37 kbar t contlnuous step-scan step-scan Contlnuous To obtain a copy of Tables4a to 4d, order Document Am-84- 239 from the BusinessOffice, Mineralogical Society of America, Ar(r) 2000 Florida Avenue, N.W., Washington, D.C. 20009. Please x0 0 remit $5.00in advancefor the microfiche. voo 00 0 z .2419(l) .2414(6) .24r6(5).24re(7) .24r4( 5) (continued) pir .002r(r) .003r(3) .0026(2).0035(4) .0029(3) Table 3. 9zz .ooze(r) .@20(2) .oor7(2) .0025(4) .0018(3) 12 kbir l2 kbar 25 kbar 37 kbar Bgg .0023(2).00s8(r2) .0035(9).0007(r5) .00r3( r 2) contlnuous step-scan steD-scan Continuous Btz .000s('r'r).0004(2) .0004(2).0009(2) .000r(2) Btso0 00 0 08 Bzto0 00 0 x .4246(2't .4247(5) .424s(41 .4260(7) .4269(s) r"q .46(2) .65(4) .4e(4) .s3(6) .42(s) .3629(2') .362r(6) .3623(s) .3608(8) .3s98(6) z 00 000 Al(2) 'll .00rr (2) .0030(7) .0026(5).oo2s(7) .0027(s) x .3705(l) .3593(3) .3102(2) .3702(31 .36ee(2) 9zz .0031(2) .0022(7) .oo2o(s).0035(e) .oo2r(6) y . 1391(l ) .1390(2) . r39r(2) . r386(3) . r387 (2) Bgs .003r(4) .0060(29) .0026(22).00r7(37) .0037(28) z .5 ,5 .5 .J .5 "12 -.0006(2)-.0005(6) .ooo7(4)-.ooos(7) -.ooo2(5) BIr .0009(r) .0022(3) .ool4(2) .0022(3) .0016(2) 8tg 00 000 Bzz .0025(l) .oor9(3) .oors(2) .oo2o(4) .0020(3) Bzg 00 000 .0028(2) .0054(r3) .0045(e).00s2(15) .0022(1',r) Bgg n-eq. .44(5) .57(lo) .48(8) .56(r3) .45(e) g,tz .oooo(r) .ooor(3) -.0003(2)-.0003(3) .0004(2) Btg o o 00 0 0zgoo 00 0 0. r"q. .34(2) .ss(5) .42(41 .s5(6) .38(5) x . ro3o(2) . ro34(6) . r031(4) . ro3r(7) . r034(s) .4003(2) .4004(5) .4000(4).3999(7) .4008(5) si 2 00 000 x .2460(l) .2461(3) .24se(2).2460(3) .2467(2) Btr .00r0(2) .00r8(7) .0015(5).0036(8) .oo2r(s) y .2520(1) .2515(3) .2s14(2).2s0s(3) .2500(2) '22 .0027(21 .0027(tl .oor3(s) .0025(e) .ooro(6) 200 00 0 '33 .0085(s) .0059(28) .0066(22).0068(37) .oo6s(29) Brr .0007(r) .00r9(2) .00r5(2).0019(3) .00r2 (2 ) Btz .0002(2) .oool(5) -.0003(4)-.00r2(7) .000r(4) Bzz .0024(r) .0020(2) .00r2(2),0019(3) .00rs( 2) 6.ts 00 000 Bgo .0025(2) .0041(10) .0041(8).0047(14) .0050(r l ) '23 00 000 Brz .0000(1) .0002(2) -.0002('r) .0000(2) .000r( r ) -eq.R ,60(5) .61(lo) .sr(8) .78(r3) .5r(ro) Bls o o 00 0 92g00 00 0 0D r"q. (2) (s) .3r .4e(4) .3e(3) .sr .42(4) x .2305(2) .22s8(31 .2303(3).2303(5) .22e6(31 .133e(2) .r337(4) .1327(3). r324(5) .r308(4) z .2394(2) .2389(8) .2389(6) .2387(9) .2399(7) % .00r6(2) .0024(4) .0025(4).0030(6) .0024(4) x .4233(2) .4222(5't .4?2t(41 .4220(71 .4203(s) 'l I .0032(2) .0032(4) .oor8(3) .oo3o(7) .oo2o(4) v .3629(2) .3531(6) .3634(4).3632(8) .3639(s) '22 .0030(3) .0036(22) .0045(r6).00r7(29) .0033(2) z .5 -.ooo4(1 -.ooos(4) .ooo0(3)-.0004(8) -.0003(3) Ftt .00r8(2) .0034(7) .0024(5).0025(8) .0024(5) -12 ) .,13 -.ooo4(r)-.ooor(7) -.'0007(5)-.0003(8) -.0010(6) .0028(2) .00r6(7) .002r(s) .0027(e) .00r9 (6 ) "22 .ooo5(2) .0002(7) .ooro(s) .ooo0(7) .ooro(s) '33 .0030(4) .00s9(2e) .0009(22).0066(36) .0027(5) '23 R .61(8) .54(5) .55(l0) .4e(7) Btz -.0003(2)-.000r (6) -.0003.(4) .0004(7)-.00r| (5) 'eq. .4e(3) Bts 00 00 0 '23 00 00 u 'Frm l{lnter and Ghose(1979). -eq.R .46(s) .64(t0) .4r(8) .6e(13) 0 5t6 RALPH ET AL.: ANDALIJSITE AT HIGH PRESSURE

Within the AI(l) octahedron,the long Al(l)-Oo bond lengthdecreases most with pressure(1.97% at 37 kbar), the intermediate bond A(1)-OB remains unchanged,and the shortest A(1)-OA bond decreasesslightly (0.66% at 37 kbar). Hence, the compressibility of a bond length is not necessarilyalways a direct function of magnitude. A similar behavior is reflected at high temperature, where the Al(lFOo bond increasesthe most, the Al(lfOs bond remains unchanged and the A(1)-OA bond increases slightly (Winter and Ghose, 1979).At pressure the aver- (A) age (Al(llO bond length changesfrom 1.935Aat I bar to 1.916Aat 37 kbar and the octahedralvolume correspond- ingly changesfrom 9.538to 9.28143. Within the Al(2) trigonal bipyramid, all of the bond lengths decrease with pressure, the longest Al(2)-Oc tA3t bond decreasingthe most. Winter and Ghose (1979) observed this bond to increase the most with temperature. With pressure, however, the difference in Al(2lO bond lengths decreases only slightly, and there is no 332 significant changein O-AI(2!-O bond angles. Hence, for the Al(2) polyhedron, no tendency to become more 010203040 regular pressure. ( is observed at high P kbor) Within the SiOa tetrahedron, the longest Si-O- bond, Fig. 2. Variations of the unit cell dimensionsand volume with Si-OB, decreasesfrom 1.645Aat I bar to 1.633Aat 37 pressure.The error bars (one standarddeviation) are indicated in kbar, which is significant. In contrast, the shorter Si-Oq termsof crosses. and Si-Op bonds do not show any decreasewith pressure.Shortening ofSi-O bondshas also been observed in diopside by Levien and Prewitt (1981).At high tempera- Results ture, the Si-Os bond in andalusiteis observedto increase Unit-cell parameters slightly from 1.645(4)Aat room temperature to 1.650(2)A at lfi)0'C (Winter and Ghose, 1979).In view of the fact All three unit-cell dimensions decreasewith pressure that the thermal vibrations at high temperatureresult in a (Fig. 2). The data points at I atmosphereare from Winter and Ghose (1979). The compressibility of andalusite is strongly anisotropic; the coefficients of linear compression (p/ : AlllLp) for three unit-cell axes are 3.2i'0.4, 2.2!0.4, and 1.510.5 x l0-a kbar-r for Bu.fo and B. respectively.Axial compressionratios for a:b:c are thus 2.1:1.5:1.0.The bulk modulusof andalusiteobtained for a Birch-Murnaghan equation of state (K' = 4) is 1.39a0.10mbar.

Structural changes at high pressure Andalusite is orthorhombic, space group Pnnm, with four Al2SiO5units in the unit cell. The crystal structure of andalusiteconsists of tetragonally distorted Al( l) octahedra sharing edgesto form chains along the c-axis. These chains are located at the corners and the middle of the unit cell, the orientation of the long octahedral axes (direction of the Al(1)-Oo bond) being approximately 30' to the left and right ofthe a axis. These octahedralchains are linked through SiOatetrahedra and edge-sharingpairs of Al(2)-trigonal bipyramids (Taylor, 1929;Burnham and Buerger,1961) (Fig. 3). Under pressuresup to 37kbar, no Fig. 3. Projection ofthe andalusitecrystal structure on (001) phase transitions or changes in structural topology are after Burnham and Buerger, 196l). Atoms are represented by observed, but several significant changes in bond dis- striped circles at z = 0, stippled circles at z : l/4, and clear tances are evident. circles at z = ll2. Chains of Si and Al(2) polyhedra are outlined. RALPH ET AL.: ANDALUSITE AT HIGH PRESSURE 5t7

cy:2.334,c22:2.890 and ca3:3.801mbar havebeen correlated with the crystal structure by the authors, who suggestthat the Al(l) octahedra control the elasticity in these directions, and thus are more compliant than the lower-coordinatedpolyhedra. The data on thermal expansion and compressibility are in accord with the measured elasticconstalts c11( c221 ci;. The andalusitestructure is most compressiblealong the a-axis and least compressiblealong the c-axis. This effect is principally the result of compressionof the long Al(lF Op bond, which lies on the ab-planeat 30'to the a-axis.A similar interpretation of the thermal expansionin andalusite has already been ofered by Winter and Ghose (1979). The intermediatecompressibility along the b-axis is most likely a consequence of the compression of the long A(2)-Oc bond, which lies parallel to the b-axis. The bulk data (1.39 0.9? 0.98 0.99 r.00 r.0r t.02 modulus measuredfrom static compressibility mbar) is in agreementwith the zero pressurevalue of 1.33 v/vo mbar obtained by Brace et al. (1969), but not with the Fig. 4. Plotof unit cell t/t6v€rsuS y/yo demonstratethat axial Reussbound value (1.580mbar) of Vaughanand Weidner vaxiationsaxe similar for temperatureand pressurechanges. (1978).The correction between isothermal and adiabatic High-temperaturedata are from Winterand Ghose (1979). moduli (Anderson, 1966)is on the order of 0.17oand is too small to explain this discrepancy. lower value of the Si-O bond length than its true value, P olyhedral bulk- moduli in andalus it e the small increaseof the Si-Os bond length with temperature may be significant and in accord with shortening of The observed bulk moduli for the Al(1) octahedron, this bond at high pressure. Al(2) trieonal bipyramid and the SiO4 tetrahedron are 13t0.2, 1.6+0.5and 4.1+1.5mbar respectively.These valuesare considerablyless than those predictedfrom the Discussion linear bulk modulus-polyhedral volume relationship, Inverse relationship between pressure and temperature effects When the unit-cell dimensions and bond lengths (X) |.03 normalized with respect to X6 under ambient conditions are plotted against V/Vq, where Vs is the unit-cell volume at room temperature and pressure, a roughly inverse r.02 behavior is commonly observed. As Levien and Prewitt (1981)have shownin the caseof diopside,however, this l.0l relationship does not strictly hold becauseofthe different responseof the structure to pressureand temperature. In andalusite a similar behavior is observed. Among the l.oo unit-cell dimensions, c deviates most strongly from such inverse behavior (Fig. a). In terms of the long A(I)-OD 0.99 bond, which compressesthe most, a strictly inverse behavioris alsonot observed(Fig. 5). This observationis 0.98 not surprisingin view ofthe fact that at high temperature, the anharmonic thermal vibrations of the atoms increase considerably. It is this effect that may explain the non- reciprocity of the P and I responseof the silicate struc- o.9? 0.98 o.99 1.O0 l.ol Loz tures. v/ vo The elasticity of andalusite: relationship Fig. 5. Plots of bond distance d/da versus unit cell VlVn for polyhedra of with thermal expansion and compressibility. the longest bond in each of the three cation andalusite. High-temperature structural variations mirror The elastic constantsofandalusite have been measured approximately those at high pressure;but the changeof slope at by the Brillouin scattering technique by Vaughan and the origin indicates that the "inverse relationship" is not exact. Weidner (1978). The principal elastic constants: High temperaturedata from Winter and Ghose (1979). 5lE RALPH ET AL.: ANDALUSITE AT HIGH PRESST]RE

Table 5. Selectedinteratomic distancesand anglesfor andalusite chargesof Al(1) and Al(2); in fact the Al(l)-O bonds should be slightly more ionic than the A(2)-O bonds on the basis of average Al-O bond lengths within the Al(l) Al(l )-0A(xz) 1.827(3) l.8Zt(4) l.8Zl(3) 1.819(s) r.Bt5(3) octahedron and the Al(2) trigonal bipyramid. The Si-O -0, (x2) 1.891(3) 1.89t(4) t.8se(3) l.ss8(s) 1.889(3) bond, on the other hand, was considered tobe onlv 50Vo -00 (x2) 2.086(2) 2.071(3) z.oto(zl 2.0G3(4) 2.045(3) ionic (Pauling, 1960). AYg. 1.935 l.92g t.g2t L923 1.9t6

Al(2)-0A l.el6(4) t.sll(5) l.8ll(4) r.810(7) t.808(5) Lattice vibrations and soft modes -0c 1.83e(4) 1.839(5) 1.833(4) r.828(5) r.826(4) -0c 1.899(4) t.8eo(4) t.894(3) r.886(6) 1.875(4) Phonon spectra of andalusitehave been measuredwith -00 1.8t4(3) (rz) l.8ll (1) l.8lo(3) r.806(s) L799(4) polarized Ramanand infrared spectroscopyand interpret- Ayg. 1.836 t.832 1.832 1.827 t.822 ed on the basis of a rigid-ion model by Iishi et al. (1979). -0A From this study, Iishi et al. concluded that the dynamical st r.645(4) t.637(5) L640(4) r.640(6) L633(4) -0c structure r.618(4) t.613(s) 1.612(4) 1.513(5) 1.617(4) of andalusite is given by rather rigid SiOa -oD (x2) 1.630(2) 1.622(4) r.625(3) 1.620(5) 1.527(41 tetrahedra, linked together by much weaker and more Avg. 1.63f 1.624 1.625 l.623 1.626 ionic (70%) O-AI-O bonds. This conclusion is in accord with the high-temperatureand high-pressureresponse of the andalusite structure as previously elaborated. Iishi et aI. (1979)have found that the 4 phonon modes, Angles(') I bartl 12 kbart 12 kbar* 25 kbar* 37 kbar+ usually representing the totally symmetric stretching Ar(r)-0^-At(2)r2'r.s(2) r2r.s(2) 121.7(2)12t.6(3) 122.2(7) modes of a tetrahedron, are split in andalusite. Its high- Ar(r )-0x-st il1.2(l ) ilr.3(2) tll.l(2) lil.l(3) lll.2(2) At(2)-0;-si r26.s(2) 126.4(l) 126.2(1\r26.3(3)12s.6(2) energy branch, both in A and,Bry symmetry, has been e6.5(r) 96.6(l) e6.7(t) 96.3(2) e5.5(I ) assignedmainly to the stretchingof the shortest Si-O (Si- 3l:liII i:31 88.6(l) 88.3(2) s0.4(l) 89.0(2) 8s.e (2 ) o;-Ar(r )-0; er.5(7) el.8(2) et.6(2) e2.1(21sz.r(2) Oc) bond, whereas the low-energy branch has been 0--si-o assigned to the stretching of the longest Si-O (Si-OB) l0r.3(2) r0r.2(2) 101.3(2)'109.4(3)r0r.4(3)r01.2(2) o:-si-6 r09.3(r) r09.5(2) l0e.I (2) r09.r(3) bond. Ifthis assignmentis pressure, 0;-sr-0c ilr.4(r) 1il.2(r) lll.5(l) ilr.4(2) il1.4(t) correct,then at high where the Si-Os bond decreasessignificantly, one would 0.-Ar(2)-0" 74.0(21 74.0(21 74.0(2' 74.2(31 73.9(21 0;-Ar(2)-0x 86.7(2) 86.8(2) 86.8(r ) 86.7(21 87.3t21 predict the low-energy branch to increase in frequency. q-Al(2)-01 r05.I (2) t06.2(21 r06.2(z) ro0;g(t) roo.o(zl 0;-Ar(2)-o; 9e.r(r) e9.0(r) ee.z(l) 99.1(2) ee.40) Iishi et al. have also found that the Raman spectra of Ar(2)-0-st 123.7l2l 123.4(2) t23.8(2) 123.7(3)t23.3(2) andalusitereveal two modesat 1,065cm-r (211)and242 (2)-0-Al Al (2) r06.0( 2) 106.0(2) 106.0(2) 10s.8(3) 106.0(2) cm-t (zrg) with a strongtemperature dependence of their scatteringfrequencies. Both lines show 41" symmetry; f Continuousscan r Step-scan the temperature coefficients are both ca. 5.10-2 lFrm (cm-16-t;. Iinter and Ghose(1979). The other 41, modesat 553 cm-r and 718 cm-l shift with increasingtemperature to lower values. Thesecritical phonon branchesshow considerablecontri- butions ofthe repulsive Fl force constant to their respec- which are 3, 3.8 and 7 mbar, respectively (Hazen and tive effective force constants. The potential term Fl is Finger, 1979). The octahedral bulk modulus of the 4,106 related to the nearest oxygen-{xygen distance (Oc-Oc) octahedron in corundum, which is more compact and 2.2474 at room temperature. These edges lie in the ab regular than that in andalusite, is 2.4-+0.2 mbar (Finger plane and only phonons with normal coordinatespredom- and Hazen, 1978). The bulk modulus of the SiOatetrahe- inantly parallel to these edges contribute to the critical dron prewitt, in diopsideis 4 mbar (Levien and lggl). In behavior(Iishi et al..1979\. qtartz, however, where considerable bond bending is If 211is correlated with the oxygen--oxygeninteraction observed, the experimental SiOa tetrahedral bulk modu- along the Oc-Oc edge, it will soften at high temperature lus is 7 mbar (Levien et al., 1980).The discrepanciesin due to the increase(l.lVo at 1000'C)in the Oq-Os edge the experimental values of polyhedral bulk moduli and length. This edgedoes not decreasesignificantly, howev- those predicted from linear bulk modulus-polyhedral er, at high pressure up to 37 kbar. Therefore, the high- volume relations may be explained by the fact that the pressure efect on the frequency of the 211 will be first-approximation assumption of Hazen and Finger negligible. The z11amode representsthe rotation of the (1979)that all cation oxygen bonds have the sameionicity silicate tetrahefua, which may be causedby the increase is invalid. In the case ofandalusite,Iishi et al. (1979)have of the Al(llOp bond length (or the OgOD edge of the obtained best fit to the phonon spectra in their rigid-ion Al(2)-polyhedronparallel to the b-axis) with temperature. calculations by assumingthe effective ionic charges for At high pressure the Al(l)-Op bond length cecreases Al, Si and O to be -0.476 0.952,0.476and respectively. considerably and the Oc-Op edge decreasesby 3.7Voat On this basis,the Al-O bonds are consideredtobeT0% 37 kbar. Hence, if this assignmentis correct, z11ashould ionic. They did not distinguish betweenthe effective ionic increasein frequency at high pressure. RALPH ET AL,: ANDALUSITE AT HIGH PRESSURE 5t9

Ani sotropic t he rmal v ibr ation s Brace, W. F., Scholz, C. H., and La Mori, P. N. (1959). Isothermal Compressibility of kyanite, andalusite, and silli- The shapes and orientations of the thermal vibration manite from synthetic aggregates.Journal of Geophysical ellipsoids do not show any clear monotonic trends with Research,7 4, 2089-2098. pressure; however, the general nature of some of the Burnham, C. W. and Buerger,M. J. (l%1) Refineinentof the vibrations can be discerned. The maximum vibration crystal structure of andalusite.Zeitschrift ftir Kristallographie, direction of Al(l) lies along the Op-Al(l)-Op bond axis; rrs,269-290. that of 06 is normal to the plane of Si and two Al(2) atoms Cromer, D. T. and Liberman, D. (1970)Relativistic calculations bonded to it, and that of Op in a plane normal to the line ofanomalous scatteringfactors for X-rays. Journal ofChemi- between Al(2) and Si atoms most closely bonded to it. It cal Physics,53, lE9l-lE9E. is clear that current techniques are not yet sufficiently Cromer, D. T. and Mann, J. B. (1968)X-ray scattering factors precise, becauseoflimited accessto reciprocal space, to computedfrom numerical Hzirtree-Fockwave functions. Acta Crystallographica,A24, 321:324. extract any but the most obvious information from aniso- Finger, L. W. and Hazen, R. M. (197E)Crystal structure and tropic temperature factors refined from high-pressure compressiohof ruby to 46 kbar. Journal of Applied Physics, data. 49,5823-5826. Finger, L. W. and Prince, E. (1975) A system of Fortran IV Conclusions computer programs for crystal structure computations. Na- Although functional relationships among thermal ex- tional Bureau of Standards (United States) Technical Note, pansion, compressibility and elasticity of andalusitehave 854. now beenestablished, a more fundamentalunderstanding Hazen, R. M. (1977) Temperature, pressure and composition: of the thermodynamic behavior of andalusitewill require structurally analagous variables. Physics and Chemistry of Minerals,1, 83-94. a knowledge of the phonon dispersion relations as a Hazen, R. M. and Finger, L. W. (1977) Modifications in high function pressure of and temperature and the nature of pressure single-crystaldiamond-cell techniques. CarnegieIn- chemical bonding. Certain conclusions, however, can be stitutign of Washington Year Book, 76,655-656. drawn basedon this and previous studies: Hazen, R. M. and Finger, L. W. (1979)Bulk modulus-volume 1. The values of compressibility, thermal expansion relationship for cation-anion polyhedra. Journal of Geophysi- and elasticity of andalusite are determined primarily by cal Research,84, 6723-6728. the more compliant Al(l) octahedron (particularly the Hazen, R. M. and Finger, L. W. (1982) Comparative Crystal lone Al(l)-Op bond) and secondarily, by the Al(2) trigo- Chemistry. John Wiley and Sons, New York. nal bipyramid; the SiOatetrahedron behaveslike a rather Iishi, K., Salje, E., and Werneke, C. (1979)Phonon spectraand rigid group. rigid-ion model calculationson andalusite.Physics and chemistry of minerals,4, 173-18E. 2. The inverse relationship between pressureand tem- King, H. E. and Finger, L. W. (1979) Diffracted beam crystal perature effects on the crystal structure of andalusite is centeringand its application to high-pressurecrystallography. only approximately correct. The deviation from this Journal of Applied Crystallography, 12, 174-378. relationship may be the result of increased anharmonic Lehman, M. A. and Larsen, F. K. (1974)A method for location thermal vibrations at high temperatures. of the peaks in step-scan-measuredBragg reflections. Acta 3. The softeningof two phononmodes (zrr 1,065cm-l CrystallographicaA30. 580-584. arid vla 242 cm-t) with temperature (Iishi et aI., 1979) Levien, L, and Prewitt, C. T. (1981) High-pressure structural can be correlated with the increase in two non-bonded study of diopside.American Mineralogist, 6,315-323. oxygen-oxygen distances (respectively the Os-Os and Levien, L., Prewitt, C. T., and Weidner,D. J. (1980)Structure properties OeOo edges of the Al(2) trigonal bipyramid). With and elastic of quartz at pressure.American Mineral- ogist, 65, 920-930. pressure the Oq-Os edge does not change appreciably, Merrill, L., and Basset,W. A. (1974)Miniature dibmondanvil whereas the Og-OD edge decreasesby 3.7Voat kbar. 37 pressure cell for single crystal X-ray ditrraction studies. Re- Hence,with increasein pressure,the 211mode is predict- view of Scientific Instruments, 45,290-294. ed to be virtually unchanged, whereas the z11amode Pauling, L. (l%0) The Nature of the Chemical Bond, 3rd should increase in frequency. Edition. Cornell University Press. Taylor, W. H. (1929)The structure of andalusite.Zeitschrift fiir Acknowledgments Kristallographie, 7 l, 2O5-218. This work has been supported by National Science Founda- Vaughan, M. T. and Weidner, D. J. (197E)The relationship of tion grants EAR El-15517(Finger and Hazen) in part and EAR elasticity and crystal structure in andalusite and sillimanite. 79-04886and EAR 82-06526(S. Ghose). Physics and Chemistry of Minerals, 3,133-144. Winter, J. K. and Ghose, S. (1979)Thermal expansionand high- temperature crystal chemistry of the Al2SiOs polymorphs. References American Mineralogist, @, 573-586. Anderson, O. L. (1966). The use of ultrasonic measurem€nt under modest pressure to estimate compressionat high pres- Manuscript received,April 12, 1983; sure. Journal of Physics and Chemistry of Solids, 27, 547-565. acceptedfor publication, December 20, 19E3.