American Mineralogist, Volume 74, pages 352-359, 1989

High-pressurecrystal chemistry of and : Revisedprocedures for high-pressurediffraction experiments RonBnrM. HaznN,Llnnv W. FrNcrn GeophysicalLaboratory, CarnegieInstitution of Washington, 2801 Upton Street,N.W., Washington, D.C. 20008, U.S.A.

Ansrucr Modified single-crystalX-ray diffraction techniqueshave been adopted in the study of the structure of andradite at several pressuresto 19.0 GPa (190 kbar) and the compressionof a mantle pyrope to 6.0 GPa. Bulk modulus, K, of end-member natural andradite from Val Malenco, Italy, is 159 + 2 GPa (assumingdK/dP: 4), whereasthat of pyrope from Kakanui, New Z.ealand,is 179 + 3 GPa. In andradite, the Ca-containing 8-coordinated polyhedron, Fe3+-containingoctahedron, and Si-containing tetrahedron all display significantcompression. The larger Ca-containingpolyhedron, which is more com- pressible than Fe- or Si-containing polyhedra, has the same bulk modulus as the bulk crystal. Below l0 GPa, bond compressionis accompaniedby a significant decreasein Si- O-Fe angle. This behavior is similar to that of framework silicates, in which a corner- linked network of smaller, more rigid polyhedra (Si and Fe) collapsesabout a larger, more compressible polyhedron (Ca). At higher pressure,however, polyhedral distortion may play a significant role in garnet compression. We use an optimized procedurefor collecting X-ray diffraction data from single for which peak-to-backgroundratios are small, and the ratio of accessiblereflections to structural parametersis large. A subsetof reflections-those most influenced by variable atom positional parameters-is scannedat relatively slow rates.By counting a selectsubset of reflectionsfor longer times, we greatly increasedthe percentageof observedreflections, improved precision of refined positional parameters and interatomic distances,and re- duced the total diffractometer time for the data-collection experiment.

maximum pressure.A third difficulty is the reduction in '.rrnonucrroN peak-to-backgroundratios resulting from the use of small Garnet is one of about half a dozen silicate structure crystalsat higher target pressures.A crystal must be thin- types thought to constitute most of the Earth's upper ner than about 25 pm if it is to be preserveduncrushed mantle and transition zone. Pyrope (MgrAlrSirO,r) and at pressuresabove l0 GPa. Futhermore, thicker Be seats (CarAlrSirO,r) were thus among the first sili- are required; thus peak-to-background ratios are often cates to be examined with high-pressure single-crystal small in high-pressuresingle-crystal experiments. X-ray diffraction techniques (Hazen and Finger, 1978). Improvements in -cell design and operation Those studies, which employed the triangular Merrill- have greatly reducedthe first two problems. The rangeof Bassettdiamond anvil cell, were limited to about 6 GPa availablehydrostatic pressure has beenincreased to above (60 kbar). It was not possible to resolve some important 30 GPa through the use of solidified gas as the pressure details of the structure response(the compressionof Si- medium (Mills et al., 1980; Jephcoatet al., 1987). Jeph- O bonds, for example) from those data. coat et al. (1988), for example, have obtained Raman Until recently, researcherswere limited to an upper spectroscopicmeasurements on a singlecrystal of BeO to pressurerange of about l0 GPa for single-crystalexper- pressuresapproaching 50 GPa using a lever-arm dia- iments in the laboratory. At least three factors contrib- mond-anvil cell and the gas-mediaprocedures. In these uted to this limit. First, all of the standard hydrostatic experiments, the open cell is placed in a steel bomb, which pressurefluids, mixtures of alcohols and water, become is pressurizedto 0.2 GPa with the appropriate gas. The solid and stiff at pressuresbetween l0 and 14 GPa (Fu- diamond cell is closed by a remote-controlled motorized jishiro et al., l98l). Single crystals strain and become gear assembly. H, He, Ne, and Ar have been used suc- uselessfor diffraction experiments under these condi- cessfully as media in single-crystal experiments, with tions. The secondlimitation is the difficulty of operating higher hydrostatic pressuresresulting from the lighter the standard Merrill-Bassett diamond cell (see,e.g., Ha- gases. zen and Finger, 1982) above l0 GPa. Diamond align- The design of the X-ray cell has also been improved ment is not well controlled in the three-screw,triangular with strongerBe support disks and better diamond align- pressurecell,andsogasketdeformationusuallylimitsthe ment (see,e.g., Mao and Bell, 1980).Single crystals of 0003-o04x/89/0304-0352$02.00 352 HAZEN AND FINGER: ANDRADITE STRUCTURE REFINEMENT AT 19 GPa 353 wiistite have been studied to 22 GPa in a cell designed obtained from the Smithsonian collections fNMNH for X-ray diffraction experiments (Hazen et al., l98l). number ll934l). The mantle-derivedspecimen, a frag- The principal objective of this study was to employ our ment of a monomineralic megacryst,was collected from improved single-crystalpressure cell and gas-mediatech- an eroded volcanic neck. The composition of the un- niques to determine the and compress- zoned crystal, as reported by Mason (1966) and Jarosew- ibility of andradite garnet to above 15 GPa. Andradite ich (1972), is (Mg, ooCa. rnMno o, Fefr .{) (Al, r* Fel.d.Ti"orr)- (CarFerSi.O,r)was selectedbecause of its relatively high (Si, e,5Al0 'ss)O,r. This composition, representedas frac- averageelectron density compared to other common gar- tions of end-member ,is as follows: 0.670 pyrope, net species.At the same time, we undertook compres- 0. 197 , 0. 105 grossular,0.025 andradite, and sional studies to 6 GPa in the standard Merrill-Bassett 0.006 .This optically isotropic sample is free diamond cell of a natural, mantle-derived pyrope garnet ofvisual defectsand possessesa deep red color. Studies from Kakanui, New Zealand. We wished to determine of the cation ordering of megacrystsfrom the whether the natural sample-with composition approxi- same locality (McCallister et al., 1975) suggestequilibra- mately 670/opyrope,2Oolo almandine, 10.50/ogrossular, and tion above 1300'C and subsequentrapid eruption and 2.5o/oandradite-has a compressibility significantly dif- cooling of the Kakanui samples. ferent from that of end-member pyrope. Both the andradite and pyrope experiments were af- Room-pressuredata collection and structure refinements fected by the problem of collecting X-ray intensity data Room-pressure crystal-structure analysis was per- on small crystals with poor peak-to-backgroundratios. formed on eachgarnet prior to the high-pressurestudies. Andradite data collectionswere limited by the small size Equant 100-pm fragments were mounted on glasscapil- of crystals that can be preserved at pressuresabove l0 laries and centered on an automated four-circle difrac- GPa, whereas pyrope data suffer from the intrinsically tometer with graphite-monochromatizedMo radiation (tr weak X-ray scatteringby elements with Z less than 15. : 0.7093 A;. notn samplesdisplayed cubic unit-cell di- Conventional high-pressuredata-collection procedures, mensions within two estimated standard deviations. The by which all accessiblereflections are measured using room-pressurea cell edgesfor andradite and pyrope are moderate scan speeds,proved ineffective. The resulting 12.031+ 0.001 and I1.548 + 0.001,respectively, based refinements were of poor quality and lacked the resolu- on positions of centered reflections. We employed the tion necessaryto identify significant pressure shifts in procedure ofKing and Finger (1979), by which each re- atomic positions. flection is centeredin eight equivalent positions and there- A secondaryobjective of this garnet study, therefore, by correctedfor crystal centeringand diffractometer zero was to find an alternative data-collection algorithm. We EITOTS. decided to identifu an "optimal" subsetof accessiblere- Cubic andradite and pyrope garnetsadopt spacegroup flections that are most strongly affectedby atomic posi- Ia3d. Three cations-Si at (3/e,0,1/a),the octahedralcation tions and to collect those select reflections with slower at (0,0,0),andthe 8-coordinatedcation at (h,O,Vt)-are in scan rates. The garnet structure is ideally suited to test fixed special positions, whereasoxygen is in the general this new high-pressureX-ray procedure. Garnet's cubic position. Intensity data for three-dimensionalrefinements unit-cell edge of - 12 A yields a large with as were collected with omega step scans of 0.025" and 4.0 many as 1500accessible reflections corresponding to more secondsper step.We collectedan octant of data to sin d/tr than 100 symmetrically distinct reflectionsin a diamond- r 0.7 for andradite and a hemisphereof data for pyrope. cell experiment. Yet garnet has only three variable posi- Digitized data wereintegrated by the method of Lehmann tional parameters (the x, y, and z of oxygen). An opti- and Larsen (1974). Intensity data were correctedfor Lo- mized data-collectionalgorithm allows the difractometer rentz and effectsand specimen absorption, to spend most of its time measuringan influential subset and the resulting structure factors were averagedto yield of reflections,rather than on unobservedreflections that 2 17 symmetrically independent reflections for andradite would be rejected during refinement. and 154 for pyrope.l Structurevariables, including a scalefactor, an isotropic extinction parameter (Becker and Coppens, 1974), three ExppnrprnNrAl DETATLs oxygen positional parameters,and thermal coefficients, Sample description were refined using a modified version of program nrmrr Andradite garnet from Val Malenco, Italy, was ob- (Finger and Prince, 1975). The fully ordered andradite tained from the Smithsonian Institution's National Mu- structure was refined with isotropic thermal parameters, seum of Natural History collections (NMNH specimen whereasin the pyrope analysiswe included I 2 anisotropic number 129741).Euhedral dodecahedralcrystals, trans- parent and of a pale lime greencolor, were collectedfrom t hydrothermally deposited veins in a serpentinite. The a *pV of the observedand calculatedstructure factors may be orderedas DocumentAM-89-396 from the Business specimen is of near ideal composition: CarFe2Si3Or2. Office, MineralogicalSociety ofAmerica,1625I Street, N.W., Suite 414, Crystals are optically flawlessand isotropic. Washington,D.C. 20006,U.S.A. Please remit $5.00in advance Pyrope garnet from Kakanui, New Zealand. was also lor the microfiche. 354 HAZEN AND FINGER: ANDRADITE STRUCTURE REFINEMENT AT 19 GPA

TABLE1. Refinementconditions, refined positional parameters, TABLE3. Unit-cell parameters of pyrope and andradite versus and equivalent isotropic temperature factors for py- oressure rope and andradite at room conditions Pressure VIVo Val Malenco (GPa) a (A) v(4") Parameter Kakanui pyrope andradite Val Malencoandradite <0.01in cell 12.045(1 1747.6(51 1.00000 No. of obs. (/ > 2o) 12'l 155 ) 11 .992(1 17247(31 0.98690 B(%\. z.o 2.9 20 ) 11.9546(6) 17084(3) 0.97757 wR (ohl'- 2.5 z.o 5.0 11 .915(2) 1691.4(10) 0.96784 a (A) 11 .548(1 12.031(1) ) 11 .785(1) 1636.6(2) 0.93648 v(A') 1s39 9(2) 1741 5(s) 12.5 16.0 11.707(21 1604.3(7) 0.91800 Extinction(cm x 105) 0.67(5) 2.6(2) 170 11.680(4) 1593.6(14) 0.91188 19.0 11.669(3) 1s888(11) 0.90913 Si x Te Va v 0 0 Kakanui pyrope z V4 1/t <0.01 in cell 11 5423(15) 1537.7(6) 1.0000 B 0.71(3) 0 54(3) 0.95 11 .5218(8) 1529.5(3) 0.9947 2.15 11.493(8) 1518.6(3) 0.9876 Al or Fe3* X 0 0 11.476(1) 1511.3(5) 0 9828 0 0 3.15 11 457(1 1s03.8(5) 0.9780 z 0 0 410 ) 11 .4345(1 0) 1491.1(4) 0.9697 B 0.66(1) o.57(2) 600 Mg or Ca x VB l/a v 0 0 z '/4 V4 B 0 95(3) 0.66(2) Oxygen x 0.0341(1) 0.039s(2) High-pressure study of Kakanui pyrope 0.0490(2) 0.0488(1 ) fragment of pyrope, approxi- z 0.6530(1) 0 6s56(1) We selecteda flattened B 0.95(4) 0.60(3) mately 150 x 100 x 40 p.m,forhigh-pressure study' The Note:Parenthesized figures represent estimated standard deviations crystal was mounted in a Merrill-Bassett-type diamond- ' R: >lF. - F.llzn. anvil cell with an Inconel 750X gasket(400-prn-diameter .'Weighted : B l>w\F. F.flZwFf,lil2. hole). The garnet crystal and several l0-pm chips of pressurecalibrant were securedagainst one anvil facewith a small dot of the alcohol-insoluble fraction of Vaseline. thermal parametersand two variable occupancyparam- A 4: I mixture of methanol : ethanol served as the pres- eters related to the distribution of Fe, Mg, and Al among sure-transmitting medium. the 4-. 6-. and 8-coordinated sites. Conditions ofrefine- Unit-cell parameterswere obtained at 0.95, 2.15,3.15, ment, final atomic coordinates,andisotropic thermal pa- 4. I 0, and 6.00(all + 0.05GPa), as well asat room pressure rameters for both garnets are given in Table l, whereas while the crystal was still mounted in the diamond cell- the anisotropic thermal parameters and vibration-ellip- Fifteen to twenty reflections with 33" < 20 < 4lo were soid data for pyrope appear in Table 2. Note that the centered for unit-cell refinement. Initial unit-cell refine- constraint relations for the 8-coordinated cation as given ments weremade without constraint (i.e., astriclinic). The by Novak and Gibbs (1971) are applicableto the site at resultant dimensions conformed to cubic symmetry at all (O,Vr,Vt),but not for (h,O,r/n),our choice for the Mg, Ca pressures,thus indicating that no phase transitions oc- coordinates. curred and hydrostatic conditions obtained. Final cell pa-

TABLE2. Anisotropicthermal parameters (x 105)and magnitudesand orientationsof pyropethermal ellipsoids Anglewith

Atom Thermal parameters* B x 10u Axis r, with unique axis parallelto DI 0., 150(1 3) 1 0.091(1) Uniaxialellipsoid 124(9) 2 0.091(1) t1001 2 P12-P13-P23 0 0.101(4) with axis parallelto Al or Fe P11-P22-P23 124(8) 1 0.088(2) Uniaxialellipsoid unique

P12-P13-P23 8(10) 2 0.088(2) [111] 3 0.0s7(3) Mg or Ca 0,, 121(11) 1 0.090(4) 0 90 90 214(S) 2 0.11 2(3) 90 135 45 o - D - a --i 45 45 P23- P12 P13 v 28(8) 3 0.128(3) 90 Oxygen 0u 203(15) 1 0.102(s) 89(13) 52(23) 38(23) d 169(1 s) 2 0.11 0(5) 85(26) 142(924\ 53(23) 161(16) 2 0.117(4\ 5(26) 87(221 e3(1s) 2(11) R -2('t2) -13(12) HAZEN AND FINGER: ANDRADITE STRUCTURE REFINEMENT AT 19 GPa 355

rameters were calculated with cubic constraints (Ralph TABLE4. Comparison of refinementsof conventionaland opti- and Finger, 1982)and are listed in Table 3. mizedstep-scan data for Kakanuipyrope at 2.15 GPa A full set of intensity data was collected at 2.15 GPa. Conventional Selecteddata All accessiblereflections to 60 20 (a total of 1274 re- flectionsincluding Time per refl 3.5 min 13.2min standards),were measured with normal Number of refl 87 33 0.025" steps and 4.0 seconds-per-stepcounting times. Numberof obs 48 31 Structurerefinement basedon this full data set converged Total time 68.9 h 62.6 h quickly, but the resulting errors in oxygen positional pa- B(%) 5.8 4.6 rameters-approximately +0.01 Weighted R (%) J.J 2.9 A alongall threeaxes- Oxygen x 0.0345(8) 0.03s2(s) are too largeto determinethe relative cqmpressionofMg- Oxygeny 0.0497(8) 0.0477(7) O, Al-O, and Si-O bonds. Betweenroom pressureand 6 Oxygen z 0.6519(9) 0.6s2s(6) GPa, garnetsundergo --3o/o volume change,or an av- 1.636(9) 1.620(6) eragelinear changeof - - lol0. oat o 1.880(1 0) 1.880(7) With bond-distanceerrors (d"n-) 2.292(3) 2.303(7) as large as +0.50/0,we cannot identify many structwal AngleSi-O-Al 131.9(6) 133.1(4) changesofsignificance (other than uniform compression). Our previous study of a pure synthetic pyrope (Hazen and Finger, 1978) suffered from similar difficulties. Experi- the leverageof the observation on the value of the param- mentsto higherpressures-above l0 GPa-might reveal eter. To minimize the sizeof the standarderrors, we select differential changes,but at those pressures,smaller crys- those observationswith the largest magnitudes of lever- tals must be used. The consequentreduction in peak-to- agesfor the parameters of interest. Note that the target backgroundratio would further increaseoxygen positional set ofreflections does not always have the strongest-nor errors. We concluded that a revised data-collection pro- even necessarilyobserved- intensities. Rather, it consti- cedure is essentialif meaningful high-pressurestructure tutes the subset of reflections whose intensities most data are to be obtained. strongly influencethe variable parametersin question.To One way to enhancepeak-to-background ratio is to count calculateleverages and choosean optimized set, the par- each reflection for longer times. It is not practical, how- tial derivatives ofthe test observationswith respectto the ever, to spendseveral weeks collecting every data set.We parameters and the variance-covariancematrix for the decided, therefore, to apply the method of Prince and parametersmust be known. The former can be calculated Nicholson (1985) to identifu an optimal subsetof acces- from the structure;however, the latter is usually obtained sible reflectionsthat are most influencedby the structural from a conventional data collection and refinement.After parameters of interest, in this instance the x, y, and,z the reflections are selectedfrom the asymmetric unit in fractional coordinates of oxygen. reciprocal space;all symmetry equivalents for the Laue group are generated. Identifying an optimized data set The optimized data-collection procedure, applied to In high-pressurestudies we are primarily concernedwith Kakanui pyrope at 2.15 GP4 yielded a substantial im- identifying the subtle shifts in relative atomic positions provement in the structure refinement, as documentedin that reflect differential polyhedral compression and cat- Table 4. We collected only 412 reflections, representing -oxygen

Tlele 5. Refinementconditions, refined parameters, cation-oxygen interatomic distances, and Si-O-Fe angle for Val Malenco andradite at several pressures

Presssure(GPa) Room 2.O 3.0 12.5 19.0

No. of refl. 217 191 32 32 t16 114 No. of obs 155 88 32 32 38 38 R(%)- 2.9 15.4 3.9 3.9 2.9 5.8 wB(/"1.. 2.6 10.7 3.0 3.4 2.O 2.9 Step increment(') 0.025 0.025 0.02 0.02 0.025 0.025 Time per step (s) 3.0 4.0 16.0 16.0 4.0 4.0 Extinction(cmx 10s) 2.6(2) 4.(41 11(2) 3(1) 4(1) 3(1) si a 0.54(3) 0.s4t 0.s41 0.541 0.541 0.s4t FeB 0.57(21 0.57t 0.571 0,571 0.571 0.57f CaB 0.66(2) 0.661 0.66t 0.661 0.661 0.661 Oxygen x 0.039s(2) 0.38408) 0.0388(4) 0.392(5) 0.0395(7) 0.0365(10) Oxygen y 0.0488(1) 0.0504(16) 0.0498(5) 0.0504(6) 0.0510(6) 0.0479(10) Oxygen z 0.6s56(1) 0.6577(15) 0.6559(4) 0.6s66(5) 0.6561(6) 0.6581(8) Oxygen I 0.60(3) 0.601 0.601 0.601 0.60f 0.601 d., . [4] 1.643(2) 1.634(21 ) 1.638(5) 1 625(6) 1.613(7) 1.589(1 0) d.. [6] 2.O16121 2.039(17) 2.011(5) 2.015(5) 1.990(6) 1.974(8) " d""-o[4] 2.358(21 2.331(2Ol 2.336(5) 2.32s(71 2.312(9) 2.238(121 d.. oI4l 2.494(2) 2.469(20l 2.46q6) 2.452(71 2.419(8) 2.427(121 1Si-O-Fe 133.4(1) 131 .5(1 2) 132.4(3) 132.0(4) 131.95(5) 132.O(7\ A/ote-'Parenthesizedfigures representesd's. Bracketedfigures representbond-distance multiplicities. - R: >lF. - F"ll>F. -- - Weighted R : l>w(F. F.)21>WP11P. t lsotropic temperaturefactors were constrainedto room-pressurevalues.

16.0, 17.5, and 19.0 GPa, as well as at room pressure A;. We thus applied our new approach and collected op- while the crystal was still in its high-pressuremount. At timized data sets(a selectset of 32 symmetrically distinct the two lower pressures,cell parametersrefined without reflections,measured with 0.02" stepsand 16 s per step) constraints conform to cubic dimensions. At 12.5 GPa, at 3.0 and 5.0 GPa. Conditions of refinement, refined for example, all three axesare I 1.785 + 0.002 A, and all parameters,and selectedinteratomic distancesand angles three angles are within 0.02' of 90". At the two highest appear in Table 5. As in the pyrope refinements,we ob- pressures,however, axes differ from each other by more served a dramatic improvement in the quality of refine- than 0.01 A, and one angledeviates by 0.14" from 90". ment with the optimized data set. Errors in atomic co- Thesesmall, but significant,distortions-more than 3 es- ordinates, interatomic distances,and the Si-GFe angle timated standarddeviations from cubic dimensionality- were reduced by a factor of four, and total diffractometer may be indicative of a slightly nonhydrostatic crystal en- time was reduced from 66 to 56 h. vironment, or they may signal the onset of a displacive Rnsulrs AND DrscussroN phasetransition to a symmetry lower than cubic. Complete sets of intensity data were collected in the Roorn-pressurerefinements conventional way (all accessibledata,0.025 steps,4.0 s Refined oxygen parametersand isotropic temperature per step) at 12.5 and 19.0 GPa. Averageddata yielded 38 factors for andradite are in closeagreement with those of independentobserved structure factors at both pressures. Novak and Gibbs (197l), who also studied an Italian We refined only five variables:extinction parameter,scale specimen from Val Malenco (identified as Valmalen in factor, and three oxygen coordinates.The isotropic ther- their ). Their cation--oxygendistances, for example, mal parameterswere fixed at the room-pressurevalues, agree within 0.008 A of our reported values, and both basedon the observationsthat silicatethermal parameters studiescite 133.4'for the Si4Fe angle. vary little with pressure(Hazen and Finger, 1982) and Novak and Gibbs (197l) presented refinements of a that these parameterswere not emphasizedin the opti- pure synthetic pyrope garnet as well as a natural chromian mizeddala set.Both refinementsproceeded normally and garnet obtained as an inclusion in diamond. The Kakanui achieved convergenceat weighted residualsof 2.0o/oand pyrope ofthe presentstudy differs substantiallyfrom these 2.9o/o,for 12.5 and 19.0 GPa data, respectively. previously examined . The molar volume of Ka- A secondandradite crystal, approximately 120 x 90 x kanui pyrope is 2.4o/olarger than the pure end-member, 40 p,m,was mounted in a Merrill-Bassett-type triangular owing primarily to its greater grossular and almandine cell. Unit-cell parameterswere determined at 2.0,3.0,and components.Si-O distancesare virtually identical (1.634 5.0 GPa. A complete set of intensity data was obtained vs. 1.636 A), Uut the other cation

We refined two occupancyparameters for Kakanui py- rope while constraining the bulk composition. The vari- 164 able parameterscorrespond to the Fe/Al value t62 in the tet- I rahedron and the FelMg value for the octahedron. The F) 160 refined model is consistentwith a tetrahedralsite occupied 158 by only Si and Al, yielding a composition of (Si'e72Aloo2r). 202 This is consistentwith that of R. Luth et al. (per- zoo sonal communication) who measuredMiissbauer I spectra o 198 of mantle-derived pyropes. They found that tetrahedral 196 Fe3*commonly occursin pyropes with relatively low Fe3+/ 244 )Fe, whereasFe3+-rich samples contain octahedralFe3+. o o 240 We assumedthat all remaining Al and all Ti enter the O 236 octahedral positions, with Fe and Mg accounting for the (u balance.The refined octahedraloccupancy, assuming the O 232 site is completely filled, gives a composition of 05101520 (Alon.rMgo oroTio o,rFeo -r). The indication of significant octahedral Mg in this high-pressuregarnet parallels ob- Pressure,GPa servations of ordered octahedral Si and Mg distributions Fig. l. Variationofandradite cation-oxygen bond distances in majorite garnet (MgSiO.). Octahedral Mg must, there- vs.pressure. Distance vs. pressure points arejoined by unweight- fore, be considered a possible component in any high- ed regressionlines. pressuregarnet with appreciablepyrope content. The large site contains most of the Mg as well as all Ca, Fe2+, and Mn. The resulting large-site formula is in air, whereas the high-pressurevolumes were deter- (MgouroFeo,r,uCao ,roMno oor). mined with low-angle reflections on a crystal in the dia- Anisotropic thermal-vibration ellipsoids for oxygen and mond cell. Swansonet al. (1985) have demonstratedthat the 4- and 6-coordinated cations are close to isotropic unit-cell volumes measuredin a single-crystalX-ray ex- (Table 2), as they are in most other silicategarnets (Novak periment often difer depending on the range of 20 em- and Gibbs, l97l). The 8-coordinated Mg cation displays ployed. High-angledata can yield significantlygreater vol- more anisotropy, consistent with the vibration of rela- umes (and usually more accuratevalues) than low-angle tively small Mg atoms in the elongatedtriangular dodeca- data. The resulting Zo values (referencevolumes at STP) hedron. for our earlier garnet study were thus systematicallylarge relative to the high-pressuremeasurements, giving bulk Andradite pyrope and bulk moduli moduli that were too small. In subsequenthigh-pressure Pressure-volumedata (Table 3) were fit to a Birch-Mur- studies, we obtained room-pressurevolumes on crystals naghanequation of state,with an assumedvalue of 4 for still mounted in the pressurecell, and we measuredthe dK/dT. Our eight andradite pressure-volumedata points same set ofreflections used for high-pressurecell refine- yield a bulk modulus of 159 + 2 GPa, compared to the ments. This procedure eliminates one major source of 158 + 2 valuereported by Bass(1986), who usedBrillouin systematicerrors. scatteringmethods on a similar Italian specimen.The bulk modulus of Kakanui pyrope, calculatedfrom our six pres- High-pressure crystal chemishy of andradite sure-volumedata points to 6.0 GPa, is 179 + 3 GPa, Five of our andradite structure refinements-those for consistentwith the 177 GPa value for pure Mg.AlrSirO,, data collectedat room pressureand 3.0, 5.0, 12.5, and reported by kitner et al. (1980), who employed Brillouin 19.0 GPa-are sufficiently preciseto reveal compression scattering methods. We concur with the conclusion of mechanismsof the garnet structure. Selectedinteratomic Leitner et al., therefore, that the incorporation of about distancesand anglesfor andradite at theseconditions are l0o/ogrossular arl'd20o/o almandine in the natural garnet listed in Table 6 and shown in Figure l. (The conventional has little effect on the bulk modulus. 2.0-GPa refinement was not well behaved. and conse- Our pressure-volumedata are too few and representtoo quently that refinement is omitted from Table 6.) small a pressurerange to obtain meaningful valuesof both The Ca-containing 8-coordinated polyhedron, Fe3+- bulk modulus and its curvature, dK/dP. Refinement of containing octahedron,and Si-containing tetrahedron all the eight andradite P-V data points, for example, yields show significantcompression. Between room pressureand K : 146 + 15GPaand dK/dP : 6.1 + 2.3.The six pyrope 19.0 GPa, total compressionamounts for averageSi-O, P-V data points give K: 163 + 3 GPa and dK/dP : 12 Fe-O, and Ca-O bonds are 3.1, 1.9, and 4.0ol0,corre- +2. sponding to polyhedral bulk moduli of200, 330, and 160 We previously reported garnetbulk moduli of 135 GPa GPa (all + 100/o),respectively. Note that the bulk modulus for both pyrope and grossular(Hazen and Finger, 1978). of 160 GPa for the large Ca-containing site is identical to Thesevalues are in error becauseroom-pressure volumes that of the 159-GPamodulus observedfor the bulk crys- were determined using high-anglereflections on a crystal tal. This situation obtains in many orthosilicatesand other 358 HAZEN AND FINGER: ANDRADITE STRUCTURE REFINEMENT AT 19 GPA

TABLE6. Interatomic distances and angles for Val Malenco andradite at several pressures

Roomoressure 3.0 GPa 5.0 GPa 12.5GPa 19.0GPa Si tetrahedlon si-o I4l 1.643(2) 1.638(5) 1.62s(6) 1.613(7) 1.589(1 0) o-o t2l 2.562(41 2.5s1(9) 2.528(131 2.535(17) 2.416(22) o-o [4] 2.741(4) 2.736(8) 2.715(11l. 2.69s(13) 2.680(19) o-si-o [2] 102.5(2) 102.2(3) 102.1 (5) 103.1(6) se.0(9) o-si-o t4l 113.1(1) 113.2(2) 113.3(3) 112.7(3) 115.0(5) Fe octahedron Fe-o[6] 2.016(2) 2.011(5) 2.01s(5) 1.990(6) 1.974(8) o-o t6l 2.876(3) 2 855(7) 2.860(10) 2.818('t2) 2.794(17}. o-o t6l 2.826(3) 2.831(7) 2.839(10) 2.797(12) 2.789(16) o-Fe-O[6] 8e.0(1) 89.5(2) 8s.6(3) 89.6(3) 89.9(5) O-Fe-o[6] 91.0(1) 90.s(2) 90.4(3) s0.4(3) 90.1(5) Ca site Ca-O [4] 2.358(21 2.336(5) 2.329(7) 2.312(91 2.238(12l- Ca-O [4] 2.494(2) 2.466(6) 2.452(7) 2.419(81 2.427(12) Mean Ca-O 2.426 2.401 2.391 2.366 2.333 o-o t2l 2.562(4) 2.551(e) 2.528(131 2.535(17) 2.416(221 o-o t4l 2.876(3) 2.855(7) 2.860(10) 2.818(1 2) 2.794(17) o-o t4l 2.929(41 2.879(9) 2.85302) 2.831(1 5) 2.840(241 o-o t2l 2.847(4\ 2.820(9) 2804(13) 2.747(16\ 2.778(21) o-o [4] 3.477(11 3 451(3) 3.432(4) 3.405(6) 3.341(7) o-ca-o [2] 65.8(1) 66.1(2) 65.8(3) 66 3(4) 65.3(5) O-Ca-O [41 72.6(1) 72.9(2) 73.5(3) 73.1(3) 73.0(4) O-Ca-o [4] 742(1) 73.6(2) 73.3(21 73.5(3) 73.3(4) o-ca-O [2] 69.6(1) 6e.8(2) 6e.8(3) 69.3(4) 71.6(6) o-ca-o 91.5(1) e1.8(1) 9171(2) 92.1(2) 91.4(3) [4] 't12.9(21 o-ca-o [2] 113.1(1 ) 113.1(3) 113.4(4) 11 1.5(5) Si-Fe [6] 3.3628(1) 3 3418(1) 3.3292(1) 3.2938(1) 3.260s(2) Si-Ca [4] 3.0078(1) 2.9890(1) 2.9778('1',) 2.9461(1) 2.9163(2) Fe-Ca [4] 3.3628(1) 3.3418(1) 3.3292(1) 3.2938(1) 3.2605(2) Si-O-Fe 133.4(1) 132.4(3) 132.0(4) 131.9(s) 132.0(7) 95.9(1) e5.8(2) 96.1(3) s5.3(4) e7.8(5) Si-O-Ca 't24.6(11 Si-O-Ca 125.1(2) 125.7(3) 125.8(3) 124.3(s) Fe-O-Ca 95.8(1) 96.1(2) e5.s(3) 96.s(3) 95.1(4) Fe-O-Ca 100.2(1) 100.1(2) 99.8(2) se 6(3) 101.2(4) Ca-O-Ga s8.8(1) 99.3(2) 99.4(2) 99.4(3) s9.8(4) Nofe. Bracketed figures representbond distance and angle multiplicites.Parenthesized figures representesd's. compounds in which one large cation polyhedron ac- The interpolyhedral angle between tetrahedra and oc- counts for most of the crystal volume. tahedra (the Si-O-Fe anglein Table 6) undergoesthe larg- The significant compressionof the silicate tetrahedron est change-a decreaseof 1.5'betweenroom pressureand is of special interest. In previous high-pressurestructure 5.0 GPa. At higher pressures,however, this angleappears studies,which were limited to lower pressures,significant to be constantat -132'. Hazen and Finger (1979, 1985) Si-O compression was seldom observed. This behavior demonstratedthat the principal compressionmechanism prompted Hazen and Finger (1982) to suggesta value for in most framework silicatesis T-O-T bond bending (i.e., the tetrahedral bulk modulus in silicates of > 300 GPa. framework distortion) coupled with compression of al- The 200-GPa value observedin this garnetstudy, coupled kali-oxygen and alkaline earth--oxygen bonds. Cation- with the 190-GPavalue reported by Kudoh and Tak6uchi oxygen bond compression was shown to be strongly in- (1985) for the silicate tetrahedron in forsterite (studied to fluenced by Coulombic effects:bond compression is in- 14.5 GPA), revealsthat a much lower silicate tetrahedral versely proportional to cation charge.Thus, although in- bulk modulus is appropriate, at least in the case of or- dividual framework-forming tetrahedra are relatively rigid, thosilicates. the large monovalent and divalent cation sites typical of At pressuresup to 12.5 GPa, the O-Si-O and O-Fe4 , feldspathoids, zeolites, and other framework anglesare essentiallyunchanged, and the O-Ca-O angles aluminosilicates display significant compression. vary by only about 0.5o.Several intrapolyhedral anglesin Garnet may be visualized as a framework structure, the 19.0-GParefinement differ significantly-by as much with a three-dimensionalnetwork of cornerlinked silicate as 4o in the caseof one O-Si-O angle-from lower-pres- tetrahedra and Fe3+octahedra (Gibbs and Smith, 1965; sure results. It is not clear whether these differencesrep- seeSmyth and Bish, 1988,Fig. 4. l, which emphasizesthis resentsystematic errors in the 19.0-GParesults, or wheth- linkage). The high-pressurebehavior of andradite up to er polyhedral distortion, not generallyseen below l0 GPa 5.0 GPa is thus similar to that of framework silicates,in (Hazen and Finger, 1985), is an important compression which a cornerJinked network of smaller,more rigid poly- mechanism at higher pressures. hedra "collapses" about larger, more compressiblepoly- HAZEN AND FINGER: ANDRADITE STRUCTURE REF.INEMENT AT 19 GPa 359 hedra. Polyhedral tilting, however, appears to be a less Gibbs, G. V., and Smith, J. V. (1965) Refinementof the crystal structure significantcompression mechanism at pressuresabove l0 of synthetic pyrope. American Mineralogist, 50, 2023-2039. Glazer,A.M., and Ishida, K. (1974) Cation displacementsand octahedral GPa. tilts in NaNbO3: Part I. Determination from X-ray difference reflections. Ferroelectrics.6. 219-225. Coucr-usroNs Hazen, R.M., and Finger, L.W. (1978) Crystal structuresand compress- Improvements in diamond-cell design and hydrostatic ibility ofpyrope and grossularto 60 kbar. American Mineralogist, 63, media have enabled us to obtain high-pressurerefine- 297-303. - (1979) Polyhedral tilting: A common type ofpure displacivephase ments on andradite up to 19.0 GPa, the highest pressure transition and its relationship to analcite at high pressure. Phase Tran- thus far attained in a crystal-structure determination. These sitions,l, l-22. high-pressurerefinements reveal significant compression -(1982) Comparative crystal chemistry. Wiley, New York. - ofSi-O bonds and changesin interpolyhedral anglesnot (l 985) Crystalsat high pressure.Scientific American,252, 5, ll0- often previous 117 seenin experiments. Hazen, R.M., Mao, H.K., Finger, L.W., and Bell, P.M. (1981) Irreversible We also developed new proceduresfor identifuing in- unit-cell volume changesof wiistile single crystals quenched from high fluential subsetsof accessiblereflections and collecting pressure.Carnegie Institution of Washinglon Year Book 80, 274-277. those reflections with relatively slow scan rates. This re- Jarosewich,E. (1972) Chemical analysisoffive for microprobe vised data-collection strategyresults in dramatically im- standards.Smithsonian Contributions to the Earth Sciences, SciencesInvestigations, I 969-l 97 l, 83-84. proved precision of refined parameterswhile reducingthe Jephcoat,A.P., Mao, H.K., and Bell,P.M. (1987)In G.C. Ulmer and H.L. total experiment time. This method is by no means re- Bames, Eds., Hydrothermal experimental techniques,469 p. Wiley, stricted to the garnetstructure. Garnet is typical of mantle New York. silicates, most of which possessrelatively simple struc- Jephcoat,A P., Hemley, R.J., Mao, H.K., Cohen, R.E., and Mehl, M.J. (1988) tures. positional parameter Raman spectroscopyand theoretical modeling ofBeO at high Only one atomic is required pressure.Physical Review, 837, 4'12747 34. to describe the or structures, only two for King, H.E., and Finger, L.W. (1979)Diftacted beam crystalcentering and corundum or , and only threefor garnetor . its application to high-pressure crystallogaphy. Journal of Applied Lower-symmetry silicates usually have more variable Crystallography,12, 374-37 8. (1985) atomic coordinates; olivine and clinopyroxene, for ex- Kudoh, Y., and Tak6uchi, Y. The crystal structure of forsterite MgrSiOounder high pressureup to 149 kbar. Zeitschrift fiir Kristallo- ample, require ll and 16 positional parameters,respec- graphie,l7l,29l-302. tively. Nevertheless,for all of thesephases there are many Lehmann, M.S., and [:rsen, M.K. (1974) A, method for location of the more symmetrically independent accessiblereflections peaks in step-scan-measured Bragg reflections. Acta Crystallographica, (asmany as 50 times more) than there are variable atomic A30. 580-584. Weidner, Liebermann, R.C. (1980) Elasticity coordinates. By kitner, B.J., D.J., and of combining the higher-pressure capa- single crystal pyrope and implications for garnet solid solution series. bilities of the gas-media pressure cell with optimized Physicsofthe Earth and PlanetaryInteriors, 22, lll-121. data-collection procedures, we anticipate dramatic im- Mao, H K, and Bell, P.M. (1980) Design and operation of a diamond- provements in the precision and range of high-pressure window, high-pressue cell for the study of single-crystal samples loaded diffraction studies. cryogenically.Carnegie Institution of Washington Year Book 79,4O9- 4lt. Mason, B. (1966) P-vrope,augite, and homblende from Kakanui, New AcxNowr,nocMENTS Zealand.New ZealandJournal ofGeology and Geophysics,9,476477 . McCallister, R.H., Finger, L.W., and Ohashi, Y. (1975) The equilibrium We thank P. M. Bell for the garnet samplesand H.-K. Mao for help in cation distribution in Ca-rich clinopyroxene. Carnegie Institution of sample mountinC. C. W. Burnham, G. V. Gibbs, R. W. Luth, and C. T. Washington Year Book 74,539-542. Prewitt contributed perceptive, constructive reviews of the manuscript. Mills. R.L., Liebenberg,D.H., Bronson, J.C., and Schmidt, L.C. (1980) This work was supported in part by NSF gants EAR8419982 and Procedure for loading diamond cells with high-pressure gas. Review of EAR8708192 and by the CarnegieInstitution ofWashington. Scientific Instruments. 5 l. 891-895. Novak, G.A., and Gibbs, G.V. (1971)The crystal chemistry of the silicate RnrnnrNcns crrrn garnets.American Mineralogist, 56, 79 1-825. Prince, 8., and Nicholson, W.L. (1985) The influence of individual re- Bass,J.D. (1986) Elasticity ofuvarovite and andradite garnets.Journal of flections on the precision of parameter estimates in least squares re- GeophysicalResearch, 91, 7505-7 516. finement. In A.J.C. Wilson, Ed., Structure and statisticsin crystallog- Becker,P.J., and Coppens,P. (1974)Extinction within the limit ofvalidity raphy, p. 183-196. Adenine Press,Guilderland, New York. of the Darwin transfer equations. I. General formalisms for primary Ralph, R.L., and Finger, L.W. (1982)A computer program for refinement and secondary extinction and their application to spherical crystals. of crystal orientation matrix and lattice constants from diffractometer Acta Crystallographica,A30, 129-147. data with lattice symmetry constraints. Joumal of Applied Crystallog- Finger, L.W., and Prince, E. (1975) A system of Fortran IV computer raphy, 15,537-539. programs for crystal structure computations. U.S. National Bureau of Smyth, J.R., and Bish, D.L. (1988) Crystal structuresand cation sites of StandardsTechnical Note, 854, 128 p. rock-forming mienrals. Allen and Unwin, Boston. Fujishiro, I., Piermarini, G., Block, S., and Munro, R.G. 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