The Symmetry of Vesuvianite: Optics and Diffraction

Home , Vesuvianite

6L7

The Canadian Mineralogist Vol.3l, pp. 617-635 (1,993)

THESYMMETRY OF VESUVIANITE

LEEA. GROAT Departmentof GeologicalSciences, University of British Columbia,Vancouver, British ColunbfuV6T 17A

FRANKC. HAWTIIORNE Departtnentof GeolagicalSciences, University of Maninba" Wilmipeg,Manitoba R3T2N2

T. SCOTTERCIT Mineral SciencesSection" Canadian Museam of Narure,Otnwa" Ontaio KIP 6P4

ANDREWPI.ITNIS Deparwunt of Eanh Sciences,University of Carnbridge,Cambridge CB2 3EO England

ASsTRAcr

The vesuvianitestrustur€ hss ideal symmetryP$/nnc, but manyvesuvianite samples show physicalproperties that indicate deviationsfrom this syffnefly. Here we examine76 samplesof vesuvianitefrom approximately50 different localities, and focus on their physical and chemicalproperties that are affectedby symmetry.Tbree groups are recognized,on the basis of optical properties:(i) normal crystalsof vesuvianiteshow uniform extinction and small (G-5") 2V; (ii) blocky crystalsof vesuvianite show inegularly shapedareas of variablebirefringence in a (001) section,with 2V valuesin the range5-35'; (iii) sector-zonedcrystals of vesuvianiteshow {001}, {101} and {100} sectorswith low (-5'), intermediate(2G-35") and high (40-60') valuesof 2V, respectively;some crystals may be more complex,with { 110} zones.X-ray precessionphotographs of fragments from each of the sectors show the number and intensity of the "glide-violating" reflections to increasein the sequence{ 101} -+ {001 } + { 100}; in addition,deviations from AlmnnI-ate symmetryalso were apparent.Difhrse streaking is associatedwith the'\,iolahng" reflections.Possible derivative space-groupscan be derived from the P$lnrc pwent grotp using groupreduction techniques.This showsthat severalspace groups previously suggestedare not possible.In addition, several ofthe derivative space-groupscan be eliminated,as the observedoptic orientationsare not compatiblewith thesesyrnme- tries. A combinationof optical and X-ray-dilfraction evidenceindicates that the symmetryof vesuvianiteis P2ln (or Pn),We suggestthat there is a continuous(or near-continuous)ferroelastic phase transition betweena high-temperatureP4lnnc stntc- ture and a low-temperafineP2Jn or Pn structure.Differential order of cationsover pai$ of sitesin the channelsof tle structure cannot drive the transition to ^F2llnsymmetry, as the associatedorder-parameter does not transform as the active irreducible relnesentationof this transition.The variety of optical types of vesuvianiteare a result of differeut relationshipsbetween the temperatureinterval of crystallizationand the temperatureof the phasetransition.

Keywords:vesuvianite, symmetry, ferroelastic phase transition, channel, degree of order.

Sol"naarns

La structue de la v6suvianitepossede une sym6trie idlzIe PLlnnc, mais les propri6t6sphysiques de plusieurs6chantillons t6moignentd'une sym6trie diff6rente.Nous examinonsici soixante-seize6chantillons provenant de cinquantelocalit6s diff6- rentes,en portantnotre attentionsur les propri6t6sphysiques et chimiquesqui sont affect6espar la symdtrie.Nous r6partissons les &hantillons en fois groupesselon leurs propri6t6soptiques: i) cristaux nonnau( montrantun angle d'extinction unifonne et un angle 2V faible (G-5"); ii) cristaux en blocs montrant des zonesd forme irr6gulihre, de bir6fringencevariable dansune section(001), avec2V entr:e5 et 35o,et iii) cristaux h zonationen secteurs,ayant des secteua {001}, { 101} et { 100} avec2V faible (-5), interm6diaire(20-35), et 6lev6 (40-600),respectivement. Certains de ces cristaux sont m6meplus complexes,et montrent des zones {110}. D'aprbs les clichds de pr6cession(en diffraction X) de fragmentsprovenant de chacun de ces secteurs,le nombreet l'intensitd desr6flexions en violation desplans de glissementaugmentent dans l'ordre { 101} + {001 } + { 100}. De plus, les &arts d la sym€tie deI,aue4lnmm sont dvidents.L'dtirement destaches est li6 i la pr6sencede r6flex- ions qui causentles vioLations.Irs groupesspatiaux d6rivatifs possiblesd6coulent du groupeparent P4lnnc par techniquesde r6duction de groupe.Plusieurs groupes spatiaux propos6s ant6rieuement ne sont pas des choix possibles.De plus, plusieun des groupesspatiaux d6rivatifs peuvent6tre dliminds i causede leur incompatibili€ avec les orientationsoptiques observ6es. Une combinaisondes 6videncesoptiques et en difhaction X montreque la sym6triede la v6suvianiteserajrt run (ou Pz). Nous croyonsqu'il existeune transitionfeno6lastique continue (ou presque)entre une structue P4lnnc stableI temp6rature6lev6e et une structureHJn or: Pz stableA faible temp6ratue. Une mise en ordre diffdrentielle des cationsimpliquant des paires de 618

sites dansles canauxde la structurene saurait6tre responsabled'une transition i la sym6trieP2ln, pwce que le parambtrede mise en ordre associ6ne se transformepas dansla reprdsentationactive irr6ductible de cette transition. I-,avai6tf des types optiquesde la v6suvianiter6sulte des relationsentre I'intervalle de tempdraturede cristallisationet la tempdraturede l'inver- sion. (fraduit par la R6daction)

Mots-cl6s:v6suvianite, sym6trie, transition de phaseferro-6lastique, canal, degr6 d'ordre.

INIRoDucrroN completehomogeneity in al1major elements(Ca" Si, Al, Mg, Fe) (Arem 1973).(v) Somevesuvianite Vesuvianite is a common rock-forming and acces- crystals show a lamellar $tructurethat, in Arem's sory silicate mineral. In most texts on mineralogyand opinion,is dueto twinning. optical mineralogy, it is describedas tetragonal,with Much work has beenpublished on the optical prop- the occasionalcomment that optically anomalous erties of vesuvianiteoand there is sufficient repro- and biaxial varieties also are known. In fact, there are ducibility from locality to locality as studiedby differ- major uncertaintiesin the symmetry, structureand ent investigatorsto indicate that the differences chemistryof vesuvianite,uncertainties that have in optical propertiesare real. resistedconsiderable effort to clarify and understand them. As part of a generalinvestigation of vesuvianite Dffiaction evidence (Groat et al. L992a,b), we here examinethe structural aud physical characteristicsthat pertain to the question Warren & Modell (1931) solvedthe crystal struc- of symmefy and the factorsthat affect it. ture of vesuvianite in the space-grotp P4lnnc. T\is symmetry was assumedto be correct until the work Pnsuous WoRK of Arem & Bumham (1969). Using precessionphotography, theseauthors showed that one or more of the There aretwo principal typesof experimentalinfor- glide-plane extinction criteria f.or P4lnnc symmetry mation that have been used in the derivation of are violated in many samplesfrom a variety of local- the symmetry of vesuvianite: optics and diffraction. ities; thus a variety of space-groupswere proposed We will review the publishedwork in some detail, (Table 1). Vesuvianitesamples from severallocalities as it indicatessome of the ways in which the problem have P4lnnc symmetry; for some other localities, tle canbe approachedfrom new directions. symmetry is reduced.The space-grorpP4lnmm ww proposed,with the deviations from P4lnnc symmetry Optical evidence characterizedas'ostrong" and "weak". Violations of the z-glide perpendicularto [001] also were Vesuvianitecommonly occurs as very large and observedin three samples,giving the possible space- well-developedeuhedral crystals that exhibit tetra- groupsP4lmmm, P42m, P4m2, P4mm and P422; for gonal morphology. Nevertheless,examination one samplefrom Asbestos,Quebec, a positive piezo- in tansmitted light showsthem commonlyto be biax- electric responseeliminated P\lmrnm as a possibility ial, and some show complex sector-zoning.These featureswere discussedin detail by Arem (1973), and it is apparentfrom his review that vesuvianiteshows BB 1. !On-!4/@ SPACBm BEPolm I]' InSVXOUSslgDrtg an extremely wide variation in optical properties: "no two idocrasespecimgns seemed to give the same sPeoa crouP (:.969) results". TmFortantoptical featuresof vesuvianiteare ?4/@ - 'a6e8" Bl&L Ia&6, Qr4- ed & Bcnb& &larai,e, Qe. summarizedas follows: (i) Somevesuvianite samples h61, Qb. are uniaxial. (ii) Many vesuvianitesamples are biaxial, hll!.U€, E - t4/@ "wah' Fod& S@, IelY w\th 2V varying in the range 0-62". (ii| Some vesu- Tel@!L, [oFey vianite crystals are sector-zoned,the sectorsbeing F e6l1ttr. N &bostoB , qra . related to the bounding crystal faces.The sectorsare Etodr$agh, P6&l€b subtendedby a specific face at the surfaceof the crys- 8e gad& Co., & Poltstbos , C!6€c€ SaP6sls A (aggF (1980) lal, and sectorsmay be idenffied by the Miller indices A1a Ptedrcsr, IEly C1@opD6ttl & kt (1983) of the subtendingface (or form). (iv) Some vesu- Asbas@, qu€. A1168 i hrnbe (1983a, b) vianite crystals pattem (if Edo uiIk, E show an iregular zonal cut fr Ede nl1s, w A11e (1985) normal to the Z axis), with the different zonesextin- &b6sFs, Qu6. Ft*gateld at al. (1986b) guishing in different positions; thesecrystals show 8e balb &. , 6 lLESerald ot aI. (1987) TIIE SYMMETRY OF YESIIVIANITE 6L9

P4ln P4nc The proposeddifferences in the various domains are OR OR associatedwith different schemesof order at the partly occupiedI(1) and X(4) sites in the channelsof the o(10)A Yo)A o00)A x4)B o(ro)A x(4)B q10)A Y(1)A o(10)B x(4)A o(r0)B Y(l)B o00)B Y0)B o00)B x(4)A structure. These and previous argumentshave not x{4)A O0o)B Y(l)B O(r0)B x{4)A o(10)B Y(r)B O(r0)B specifically addressedthe non-tetragonalaspects Y(l)A o(1OA x(4)B o(r0)A Yo)A o(10)A x(4)B o0o)A ofthe vesuvianitestructure; this is donehere.

ABCD E:esRnfiI.nAL Fto. 1. Possibilitiesfor orderamong channel cationsin the Groat et al. (1992a)characterized the chemistry of vesuvianitestructure; affangements A and B arecompa- a wide tible with P4ln symmetry,C andD arecompatible with range of vesuvianitesamples that form the P4zcsymmetry, and a statisticalcombination of all four basisfor the work presentedhere. Selectedsamples anangementsis compatiblewth P4lnncsymmenry. The ftom this set are examinedby optical methodsopreces- notationof sitesis fromGroat et al. (1992a). sion photography,single-crystal X-ray diffractometry and high-resolutiontransmission elecfton microscopy (HRTEM).

(althoughthe ubiquity of quartz as inclusionsin vesu- Optics vianile makesthis a very difficult experiment). Sapountzis& Katagas(1980) assignedthe space- Sectionswere preparedboth parallel to (001) and group P4lnnm to a vesuvianite sample from Greece. (100), generally 250 Fm in thickness.For most of Allen (1985) suggesteda further set of non-teftagonal the sampleslisted by Groat et al. (1992a),2V was space-groups(Table 1) as possible symmetr.iesfor measuredby the method of Tobi or Kamb (Bloss vesuvianite,based on the fact that many samplesare 1961).To check on the reliability of thesemeasure- biaxial rather than uniaxial as required by tetragonal ments,2V also was measuredon a spindle stagewith symmetry. a filtered source(1, = 590 nm), using the program Giuseppetti&Mazzi (1983)were the first to attack EXCALIBR @loss1981). For crystalsin which sector the problem of non-P4/nnc vesuvianite,refining the zoning was observedoserial sectionswere cut such structure of a vesuvianite crystal from Val d'Ala, that the three-dimensionalnature of the sectorzonins Piemonte,in the space-grcupP4ln. This particular could be recorded. crystal showedlarge numbersof weakly observed Somesimple heatingexperiments were donewith a reflections of the type lfil, h + ft odd, and hhl, I odd, Fluid, Inc. fluid-inclusion heating stage on a Nikon consistentwith the space-groupP4ln,Tlis reduction Optiphotmicroscope. A (001) sectionof sampleV12 in symme0ryallows additional ordering of the cations was heatedin air from 25 to 500'C and simulta- that occupythe chamel sitesin tle structure.The pos- neouslyexamined in cross-polarizedlight to observe sibilities for such ordering are shown in Figure 1; the effect of temFeratureon the deviation from uni- arrangementsA and B are compatiblewith P4lz sym- axial optics. meffy, ilrangements C and D are compatible with P4nc symmetryoand a statistical combination of all Prec e s s ion photography four arrangementsis compatiblewith P4lnnc syrnmetry. For P4ln symmety, each channel site equivalent Following detailed electron-microprobeanalysis tn P4lnnc is split into two nonequivalentsites of simi- of oriented sections,specific fragmentsof the crystal lar geometry. Site-occupancyrefinements by were removedfrom the thick sectionfor precession Giuseppetti& Mazzi (1983) showedthat there is sig- photo$aphy; in this way, the chemistry and optical nificant ordering over the pseudo-equivalentsites in propertiesof the fragmentwere known prior to the dif- the cha::nel.More recentrefinements n P4/n andp4 fraction experiment.In addition, this enabledspindle- were reported by Allen (1985), Allen & Burnham stagemeasurements of 2V to be comparedwith analo- (1983a,b) and Fitzgeraldet al. (1986, 1987),and gous values obtainedby the Tobi or Kamb methods. various discussionsof possibleschemes of order com- Thesefragments were groundinto spheresto eliminate patible with different tetragonalsym_metries have been differential absorptionas a function of crystal orienta- given. Allen & Burnham(1992)have further devel- tion, as this can be a sourceof apparentdeviations in opedthe schemeof Giuseppetti&Mazzi (1983).They diffraction intensities from the true (Laue) symmetry proposedthat vesuvianiteconsists of ordereddomains of the crystal. basedon P4/n, P4, P4nc or lower symmetry.Crystals These crystals were mounted on glass fibers and witl equal volumes of domains show P4lnnc (long- examinedon a conventionalprecession camera witl range) symmetry,whereas crystals with unequal filtered MoKcr X-radiation. Long-exposurezero- and volumes of (differently ordered) domains show sym- upper-level precessionphotographs were taken with 'tonsistent o'wef'fitn. mefiry with the preferredscheme of ordet''. All photographswere taken at two differ- 620 TIIE CANADIAN MINERALOGIST ent values of the precessionangle (usually 25" and NS 3. Om6 BW OF 8rum lmm m 30) in order to identify possible Renninger(double- 2V <')' diffraction) effects. slclt Zdq ML *, !.C.t. 7 (s!e)' E'19 (rb) n0 Jgffey &, qs. 9-24 (coio) ' 32.8(4) (tb) CeIl dimensions (rtu) n1 , 30-33 (@r€), 37'4 n5 "39 n5 Groat et al. (L992a) measuredcell dimensions !20 . 62.1(3) a2L on all their chemically characterizedsamples using , (rh) 722 x3-21 (ooe), 4.7(2) (rb) single-crystalX-ray diffractometry. However, they €1 C&ft€xd ro@biP, Qud. 0"10 (oora), 14'23 constrainedtheir cell dimensionsto ietragonals)rlnme- v49 Ul!ffqb, P*166 try (a = b). We rerefinedthese data without any metric seerr zdag v aht &, Qe. 6'9 (rb) consftaintson the cell dimensionsso that the refine- n2 Jaff,rey &, Q!6. 0-10 (cot6)' 36 ((1011), 60-62 bg|M &1 Jeo, ldoo ment results are free to reflect any metric deviations i72 & 8113, q of the unit cell from tetagonal symmetry. w5 gl1d Usr, !.8.4.4. 0"10 (@16)' 10-25 (t101) d !e)

ft'"'6"i!-*+ eallE d6 st:&d &datl@ n!6 obdd dd a 4do.sba€'-dl nz (rbi Tobt's htu) Er6 &t6dd utE b'3 bM Measarernentof dffiacrton intensirtes (aX@6 1951).

Crystalswere mounted on aNicoletR3mautomated four-circle diffractometer equippedwith a molybde- REsuLTs num X-ray tube and a highly orientedgraphite-crystal monochromatormounted in equatorial geometry. Optics Twenty-five reflections were automatically centered, and least-squaresrefinement produced the cell dimen- 2V measurements.Yaiations in birefringence are sions (Table 2) and an orientation matrix relating a prominent feature of some samplesof vesuvianite; the crystal axes to the dilfractometer axes. Intensity we describethese variations with the terms "low"o data were collectedin e - 2e scanmode according "intermediate"andofigh", emphasizingthat higS bire- to the procedureof Groat et al. (L99'2b).Complete sets fringenceis of the order 0.003.Values of.2V fot of selectedequivalent reflections (in 4lrnmmLaue selectedsamples are given in Table 3; values vary symmetry) were collected in order to quantitatively from 0 to over 60o. It should be noted that where 2V comparethe intensity distributions with the possible is small (<5o),the isogyrestend to be ratherdiffuse, Iaue elementsof symmetry.Intensities systematically and it is difficult to ffierentiate betweentrue uniaxial absetttn P4lnr?csymmetry also were collected. behaviorand slight biaxiality. There is good agree- ment betweenthe spindle-stageand thin-section High-resolution transmission electronmicroscopy measurementsof'2V, indicating that the latter are reasonablyaccuiate (perhapst2'). A1l samples A (100) sectionof Yl2 was examinedwith an of boron-freevebuvianite are optically negative;all Hitachi 100 kV transmissionelectron micloscope, boron-bearingSamples are optically positive. This equipped with a tilting stage.An ion mill was used confirms the.observationsof Oftedal (I9&), Khotina to make an edge thin enough to allow transmission (1968)andSerdyuchenko et al. (1968).At boroncon- of the electron beam. Both HRTEM images and tents someivhatless than the minimum (1.25 atoms selected-areadiffraction (SAD) patternswere obtained per formtll'a'unit) found by Groat et al. (1992a) fromthe samole. in crystalsof boron-bearingvesuvianite, there must be an isotropic vesuvianite(assuming complete solid- solution between boron-free and boron-bearing vesuvianites). Textural Opes.T\e vesuvianitesamples examined TAB1I 2. UNCON9IIA]INEDCEI,L DIUENSIONSFOR V12' in thin (thick) section show a variety of textures in both plane- and cross-polarized[ght. They can be Vl2 core 912 l!i6r. v12 rta divided into three basic types: (i) Normal vesuvianite: thesecrystals show uniform extinction and usually a (A) 15.515(2) 15.5X8(2) L5.522(2> b (A) x5.52r(1) 15.s19(2) 15.s48(2) have a small 2V; the majority ?95Vo) of vesuvianite . (A) 11.800(2) 11,810(1) 11.8r5(2) samplesare of this type. An example is shown c (") 90.00(1) 89.99(1) 8e.96(x) in Figure 2a (Y40, Monte Somma,Italy). Although p (") 90.05(1) 90.05(9) 90.05(1) there is uniforrn extinction, a pronouncedoptical zon- Y (") 89.97(1) 90.02(1) 90.07(1) ing is present.A BSE image @g. 2b) showsthe opti- Y (43) 284L.9<7> 2844.L(6' 285L.6(7t zoning to correspondto differencesin meanatomic aa (A) 0.005 0,001 0.026 cal number.(ii) Bloclcyvesuvianite: the (001) sectionis 'Sauplo mubere are fr@ cr@t et af. (f992ar. divided into irregularly shapedareas of variable bire- TIIE SYMMETRY OF YESUUAN]TE 621

Frc.2. (a) (001) sectionof a normalvesuvianite (x30; V40, Monte Somm4 Italy) in plane-polarizedlight, showing optical zoning; (b) BSE image of the core of V40' showingcompositional zoning. Scalebar: 500 pm. fringence, 2V and optical orientation; these areas tend birefringence rim and a rudimentary low-birefringence to have sfiaight boundaries, but do not seem to sho\r core may be present. These features are illustrated in any prefened crystallographic orientation. A high- Figure 3a for a sample from the Jeffrey mine, Quebec 622 THB CANADIAN MINERALOGIST

Ftc.4. Sketchof (001)section through Vl2, asseen in cross- polarizedlight.

One particular type-(iii) samplefrom the Jeffrey mine (Vl2) is translucent,pale brown, and forms {100} prismssingly terminated by {101} and {001} forms. A single crystal was sectioned,and a sketch is shownin Figure4.Each zonein the (001) section can be associatedwith a face of the crystal; these zoneswill be henceforthdenoted by the corresponding face-symbolor form-symbol.The {001} sector(core) haslow birefringence;2Vvuies from 0 to 10o,andthe optic axis is parallelto Z. T\e {101} sectorshave intermediatebirefringence and 2V = 36o with strong dispersion(r rrv). The {100} sectors(rim) havehigh birefringence (-0.003); 2V is approximatelyequal b 6442" .In all sectors,the optic axialplane is,oriented orthogonalto the sectorboundaries [l'.e., I | (010) in ard sectorsl.This was characteristic Hc. 3. (a)(001) section (X20) of Y22 vesuvianire.; {101} {100} @locky of all crystalsand all examined. in cross-polarizedligh! showingoptical zoning; (b) BSE samples Precession imageof onecorner of Y22, showingcompositional photographyconfirmed that the principal morpho- 2eningbetween the rim andthe rest of thecrystal. Scale logical form presentis { 100} rather than { 1I 0 }. bar:500 pm. SarnpleV75 from the Wilui River, former U.S.S.R., occursas large doubly terminatedcrystals with prominent {100} and {101} andless prominent {001} and (Y22; note that samplesfrom this locality are very {110}, set in an extensivelyserpentinized matrix. variable with regard to all properties).A highly bire- Figure 5 showspart of a (001) section;the core has fringent zone (2V = 48o) surroundsa blocky zone a cross-hatchedpattern (possibly due to trvinning), and with undulose extinction and variable birefringence the rim and {110} sectorsshow fine striations.The (16 <2V < 21.").A BSE image(Fre. 3b) showssignifi- {001} sectorhas a low birefringence,and 2V varies cant compositional differences between the rim and from 0 to 10'; the {100} sectorshave higher birefrin- the rest of the crystal. (iii) Sector-zonedvesuvianite: gence,and 2V variesin the range 10-25. Again, all (001) sectionsof thesecrystals shorr a low-birefrin- sectorsrue optically positive, and V75 is an example gence core and a high-birefringence rim, with addi- of boron-bearingvesuvianite. BSE irnagesindicate the tional sectorsor zonesthat vary from sampleto presenceof chemical differencesbetween the various sample; some show an intermediate-birefringence sectors.The sector-zonedvesuvianite V44 from zone around the core, whereas others show distinct Mexico closelyresembles V75; both have weakly sectorsalong the [1 10] directionsof the crystal. developedsector-zoning, are optically positive and TIIE SYMMETR.YOF VESWIANTTE 623

I,lG. 5. Part of a (001) sectionof V75 in plane-polarizedlight ( x 15), showing { 100} and {110} sectors. boron-bearing,whereas V12 and V71 have strongly on the indices of the reflectionsthat can be observed, developedsector-zoning, are optically negative and and ooviolations'oof such restrictions indicate that the areboron-free. symmetry elementi5 not present.PLlnnc has several Heating experiments.At room temperafure,V12 elementsof translationalsymmg6y' theseand their shows sectors of different birefringence when violating reflections are listed in Table 4. Following observeddown [001] in cross-polarizd light; in parti- Allen (1985),we designatethese violating reflec- cular,the {101} and {100} sectorsshow strongbire- tions as being of types a, b or c for convenienceof fringence. With increasing temperature,the birefrin- expression. genceof thesesectors decreases, until at -500oC, the It should be noted that symmetry violation can sectorsare almost extinct. This finding suggeststhat be coupledbetween these two types.Thus violation the deviation from uniaxial optics decreaseswith of glide symmetryalso violatesthe correspondingmir- increasing temperature;accurate measurements ror symmetry of the Laue group. This connectionis of birefringence atd 2V as a function of temperature of some importance,as it provides supportingevi- are desirable. dencefor the absenceof a glide plane. This is neces- sary, as the occurrenceof double diffraction can give Prec e s sion photo graphy rise to additional intensity at any point in the reciprocal lattice; if the point in the reciprocal lattice has Four crystalswere examinedin detail. The spectac- zero primary Bragg intensity becauseof the presence ular optical zoning and large variation in 2V prompted of elementsof translationalsymmetry, this additional examinationof eachsector in V12 from the Jeffrey intensity can give the appearanceof glide-violating mine; crystalsfrom the {001} core, {101} intermedi- (or screw-violating)reflecfions. As indicatedabove, ate,and {100} rim sectorsare designatedY72c,YI2i all precessionphotographs were taken at two different and V12r, respectively.In addition, the core zone precession(p) angles,as this changesthe conditions of V75 from Wilui was examinedbecause of the pres- enceofboron andthe low contentofOH. There aretwo typesof diffraction symmetrythat we TABLE 4. P4/mc F'rtLNCIloN CoNDITIoNS can examineby precessionphotography: (l) Inue sym- synboL cltdo P1@ Vlolathg metry: with regard to vesuvianite,we searchedfor C@dlttoG violations of the standard4lmmm symmetry on all levels. (ii) Translational symmetry.'all elements r gllds perpendicul-d to c hko; & * & odd of translationalsymmstry (glides, screws)give rise n gl-lde perpendicuL& to a h07, A + i odd to "systematicabsences"; in practice, the presence 0kl,k+7odd ! gltde perpondlcular to ]thl, I odd of such elementsof symmetryimposes restrictions [1101 624

for double diffraction to occur while leaving the con- reflectionsobserved in any of the precessionphoto- ditions for the occumenceof Bragg reflections graphs.As shownin Figure 7, all reflectionsare sharp unchanged.As an exampleofthis, Figures6a, b show and round, and there is no observables6eaking (dif- two (h0l) zero-levelphotographs taken for Y12c at fuse intensity). Close visual inspection showedequal a p of 25' and 30", respectively.Note that the promi- intensify of reflectionsrelated by 90o rotationsaround nent (702) reflection in Figure 6a is absentin Figure tbeZ axis,and reflections related by the horizontal and 6b, indicating that it is causedby double diffraction; vertical mirror planes.Thus the Laue symmetry note also that this reflection is sharperthan the rest is 4lrnmm,and the space-groupsymmetry detennined ofthe normal Bragg reflections,a featurethat is char- by precessionphotography is P4lnnc. acteristicof Renningerreflections. Reflection (702) In V12c (Figs. 6a, b, c), the reflectionsare not violates all n-glide criteria tn P4lnnc (Table 4), show- as sharp as those for V75c (Fig. 7), and somedilfrrse ing the impofiance of confirming that symmetry- streakingis apparent.There is a significantnumber violating reflections are actually true Bragg reflec- of b-type reflections (Table 5); some are quite strong tions, and not causedby doublediffraction. le.S.,(604)1, but most are relatively weak and show For vesuvianiteV75c, there are no true violatino streakingin the a" direction.Streaking also is asso- T}IE SYMMETRY OF VESIIVIANTTE 625

Ftc. 6. Precessionphotographs, sample YL2: (a) n (h0D zero-levelphotograph of Y12c (p = 25', 84 hours expo- sure); (b) the sameas (a), but with p = 30" (82 houn); (c) an (ltlc0) zero-level photographof Vl2c (84 hours); (d) an (i04 photographof V12i (83 hours); (e) aa (hn) photographof V12i (84 hours); (f) n (h0D photograph of Vl2r (87 hours); (g) an (fttO) photographof. Yl2r (87 hours).

oonon-violating" ciated with reflectionsoand is espe- Correspondingprecession photographs of V12i cially noticeableon tle zero-level,being prominent (Figs. 6d, e) show most of the featurespresent around (004), (008) and along (103) and (ft06) rows. in V12c. However,the violating reflectionsare con- The (ftft0) zero-level(Fig. 6c) showsfaint diagonal siderablyweakero although the sameLaue group sym- streakingle.e., | | [110] around(440) and (480)1. All metry and "space-groupextinctions" are observed. reflectionsrelated by 90orotations aboutZ have equal A similar streakingis apparentin thesephotographs, intensities(as judged by eye).However, this is not the although it is less prominent than in the photographs casefor reflections related by vertical mi:ror planes; from thecore {001} region. weak high-index reflections (such as 7 1l 0 and Precessionphotographs for V12r are shown 11 7 0) show notabledifferences in intensity, a feature in Figures 6f, g. Inspection showsfar more violating that is also seenon upper-level(hkl) ad (ftt3) photo- reflectionsthan in Yl2c and V12i: theseare listed graphs. Violating reflections of type c also are in Table 5. The violating reflections are more intense observedin theseupper levels, which is consistent and much less diffrrse than is the casefor analogous with the loss of the diagonal vertical mirror planes reflections in the core and intermediatesectors. Very in the Laue symmetry. little streakingis apparentin the photographs.The 626 TI{E CANADIAN MINERAI,OGIST

Frc. 7. hecession photographs,sample V75: (a) an (/rOf photograph(102.5 hours); O) an (l*0) photograph(81 hours).

sameLaue group symmetry is observed;the fourfold synrmeff.yofthe Laue group is retained.There is also axis is retained,but there is non-equivalenceacross no diffraction evidencefor the loss of fourfold rota- the vertical mirrors. tional symmetry I I Z aespitethe fact that 2V ranges From the precessionphotography and optical up to 62o. The precessionphotographs thus indicate results, we can make the following statementsabout that the maximamsymmetry of V12 is P4ln, and show the symmetryof vesuvianitecrystals V75 and V12: (i) no evidenceof deparnre from tetragonalsymmetry. in V75c, no reflections seenon the precessionphoto- graphsviolate P4lnnc symmeffy, even though 2V cart Single - cry stal intensity datt rangeup to 10o;(ii) all sectorsof V12 show b- and c-type violating reflections,together with loss of verti- Thesedata provide two types of evidencecon- cal mirror-plane Laue symmetry; howevernno a-fype cerning the diffraction symmetryof vesuvianite: reflections were observed.and the horizontal mirror (i) systematicinvestigation of Laue symmetry,and (ii) complete and quantitative measurementof violating reflections,

IABLE 5. EE LEcf,IoNg VIOIATINC Er[lNCIlOtr COtrDXf,IOlls EOR P4/@. Allen (1985) reported that a crystal of vesuvianite FRoU X-BAY PR!0E88I6I nroroctsAnr' (Vt2) from Eden Mills (Vermont) showsan unequaldistib-

hb7 a' b' c' hhl e' b' c' hht ution of intensities over the (hkl) set equivalent in Laue gtovp lrnrnrn,and concludedthat this sample r.n 2 @!s has Laue group symmety 4lm. Table 6 showsthis O 14 * 441 Aa I x O t 6 a 5O2 a 991 ! particular set ofreflections for all four crystals(V75c, 1O4 3 506 t lo o 3 : I 06 a 661 lolo I a Y12c,YL2r, V12r) examinedin detailhere; only half 1 O12 N 7 7 | tlll I x 2OO a 8O3 i lSlS I a 306 a

\42 hr@dlat€ TABII 6. INTE{SITIE8 (cps a 10-s) FOR 346 AID EqUnIAI]EA'T NEFLECfiONS (P4/tuc) I O t x 203 x 5O2 : I 04 a 2os x 66 t a W5 co!6 V12 core V12 Lobi. Vl2 rta 106 x

VI2 rts lsB 2L5<3t t 99(4) 235<3' 290(3) 2t7 496(4) 229(3' 293(3) 0 4a3 4aa03a Aa6 <1' 0 6x3 6 x AB I a d46 214(3) 490<4) 228<3) 263(3) 8 9 o 9x3 i OIO a /,95(4) o 12ag 12 x 9 012 a 346 219(3) 233(3) 257<3' o 14 a 4 I a lO O 3 x oa6 211(X) 484<4) 225Q) 298(3) I .las 2xl0OZx I 6as 6 x lOlO I x 346 215(3) 476<4' 228<3) 299<3) grs I 8 t ll O 2 x 436 2L6(3) 482<4) 227<3' 260(3) I 12a5 3 a lllr I a 2 3i5 I i l2l2 | : 436 213(3) 484<4) 223<3) 264(t' TI{E SYMMETRY OF YESUVIANTTE 6n of ttre reflections \ryeremeasured. as the other half way as all allowed Bragg reflections;thus we measure of the set are the Friedel equivalents.For V75c, there the intensity of all potentially violating reflections.All is no significant variation in iniensify; the mean value violating reflections exceeding5o (basedon counting is 215, with a dispersionof t 4, as comparedwith the statistics)are shownin Table 7. Certainly for YlZc standarddeviation of 4 for an individual intensity. and V12r, there are many observedostensibly viol- Similar calculationsfor the variouszones of V12 show ating reflections.However, thesemay be due to dou- significant differencesin the intensitiesof potentially ble diffraction, and it is necessaryto confirrn at least equivalent reflections. This is particularly noticeable someof them as Bragg reflections.This may be done for Vl2r, in which the reflectionssplit up into two by monitoring the reflection intensity as tle crystal equivalentsets of meanintensities, 295(4) nd26l(3t, is rotated about the psi vector. When the crystal is in respectively;this differenceof 34 can be compared the Bragg diffracting position, the direction orthogonal with the pooled standarddeviation of 4.6 to indicate to the plane of the reflection is called the psi direction that this difference is highly significant. Similar rela- (or vector). If the crystal is rotated about the psi tions occur for other specific sets of reflections (e.g., vector, the conditions for Bragg diffraction remain {L241,{1261, {133} and {137} areparticularly unchanged;however, the conditionsfor double notable in this regard), witl much larger deviations diffraction do not remain so; consequently,reflections than for {346}. However,for VL2, they only split due to double diffraction can be detectedby loss up into the sametwo setsas {346}; the 4-fold rota- of intensity upon crystal rotation about psi. Some of tional symmetryis preservedfor all setsof reflections the stronger violating reflections in Table 7 were examined.It should be noted that fle glide-violating examinedin this fashion to confirm their validitv reflections do not show tlis samerelationship; they as Bragg reflections.Figure 8 showsresults of psi- seemto obey complete4lmmm Laue symmetry.Thus scansfor reflections210 from Yl2i and reflections for V12r, all vertical mirror planes are lost from the 333, 540,and 10.03from V12r. For reflections Laue group 4lmmm,resulting tn4lmLaue symmetry. 210 and 540, the observedintensities scatter about In the collection of the single-crystalintensity data zero as the crystals are rotated around psi; double for all four crystals, reflections systematicallyabsent diffraction is apparentas sharp spikesabove back- in P4lnnc were collected and processedin the same ground (where the doubly diffracted beam coincides

TABIa 7. RXI'l,EctIoNs VIOIATINC ErrInoTIoN CoNDITIoNS FOR p4/nc FRO{ X-RAy INrENsrTr DATASSIS(r/oF > 5.O0)

F/aF r/6F F/oF a' b' c, hhl F/aF F/oF F/aF a, b, c' !12e' Vf2t 1L2t V12c vt2t vl2r

I3 o 2 10.73 x o ro - 6.00 - 10.07 a o5 - 10.09 a o lo 3 5,45 - 9.46 a o3 - 9.38 o rr a 9.45 a zz - 8.7L a o ll 2 - 8.68 E 7 3 5.93 x o ll 3 5.08 7 7 5.04 - 11.20 x o 14 ll 5,70 :: E - 10.65 r0a 7.38 - L4,64 a o3 - 9.35 x roZ - 8.01 x 33- - x0.48 x ro4 6.17 - L7,92 x 33 - LO.79 a l l lr 5.03 23 - 10.63 a 2oF 5.02 23 8.14 9.84 a 223 - 8.56 x oA - L0.07 a 223 - t0.t6 x o 1 6.94 - 15.20 x 3 0 6- 7.4L o 4 5.X9 - L4,84 x 33- - 10.06 x

- 8.64 x 333 - 8.19 i oTT - 10.s6 xx 405 - 8.95 a o5 5.23 xt 403 - L4.77 x o lr - 11.44 xx 665 5.20 r 6 5.03 x 7 0lo 6.99 r 4 6.20 - 16.55 a 277 - 8.05 - L4.73 a 777 - 8.87 43 - t0.50 x loo3- - 11,02 x 43 - t0.28 x loo3 - 9.72 x 7Z 9.42 x rl o Z 9.62 x 76 5.66 a 19 0 2 9.77 x

"c - corg, I - lntemdLals zoDo, r - rl! 628 T}IE CANADIAN MINERALOGIST

- 4C[) ctl, cL g 2oo b o0 c o S.aoo

125 150 17s an 25Nn53Np5 Psi f)

.D.m o. d > t8cx, at g 9rmc

1400

laD 333 (v12r)

lm 125 150 175 N % 2g n5 S0 345 350 Psi(") with the position of the Bragg peak) and sharpspikes symmetry P4lnnc, and thus any simple structural below background(where the doubly diffracted beam modification of this can only occur in a spacegroup coincideswith the position of a backgroundmeasure- that is a subgroup or supergroupof this basic sym- ment). For reflections 333 and 10.03,the observed metry. There are no three-dimensionalspace gloups intensitiesscatter about positive values (-1500 and that are supergroupsof PLlnnc. this limits the possible 2000 cps, respectively);thus although double diffrac- space-groupsymmetries to subgroupsof P4lnnc. tion doesoccur at somevalues ofpsi, giving the char- These may be derived from the group multiplication acteristic sprky profile to the scan, these two reflec- table for ,P4lnnc (Table 8) by systematicdeletion tions arevalid Braggreflections. of elements,such that the remaining elementssatisff the basic axioms of group theory and henceconstitute Possiblespace-groups a spacegroup; note that asP4lnnc is of rank 16; derivative space-groupsmust have ranks of 8, 4, 2 or l. The basic structureof vesuvianitehas space-gtroup Iteration of this procedurethrough all possibilities TIIE SYMMETRY OF VESI'!'IANTTE 629

2q) - (tl, o o. d > -an cQ I .{00 c

€00

150 175 m 23 Psi f)

at, ci tooo d

o F r+m -g

1003 (V12r)

o x 50 75 'l(x) 125 '150 175 N % 2n z75 3C[) 82s 350 Psi(') Frc. 8. Psi scans:(a) 210 from V12i, (b) 333from V12r,(c) 540 from V12r, and(d) t0'03 from Vl2r. gives the spacegrcups of Table 9, which hence con- was milled through the samplein such a way that all tains all possiblespace-group symmetries for vesu- threesectors ({100}, {101}, and {001}) could vianite structnres.Note that severalspace-groups sug- be examined.A carefrrl searchof each sectorshowed gestedby previous authors are tuotpresenl and hence no evidenceof domain structtueor variable intensity. suchproposals cannot be correct. However,in moving from one sectorto another,it was necessaryto tilt the stage in order to recenterthe Hi gh-res olution tTanenission electron micro sc opy image of (001). Further investigation showedthat in the { 101} and {001} sectors,Z tilts inward(toward A (100) sectionof V12 was examinedusing high- the centerof the crystal) by as much as 3o.This agrees resolution transmissionelectron microscopy. A hole with optical observations. 630 TTIE CANADIAN MINERALOGIST

TABLE 8. I{TLTIPLICATION !;t&LE EQR P4/mc

2t c

I I | 4t 42 4t nz at at 2. nr 2t nt 2, n, 2, c

I I I 4t R. V" 42 4t 45 n' 2' n, 2t n. 2. c 2r

4r 4t Zt 42 43 I a" nt | 2t c 2' n' 2x n' 2Y nt

42 42 n' 43 I 4t t As Vt 2v nt n' 2, c 2' n'

4a 48 au | 4, 42 Vt I n, 2, n, 2, c 2t nt 2r n

nr 42 Z3 t At I 4t 4t n, 2t n' 2' c 2t n' 2'

v' at 4, nr At t 4 42 I c 2, n, 2, ns 2r n, 2t

4' Au 4t I Z' n 4t I 42 n' 2' c 2t nt 2t a' 2,

n' 2' 2t 2t nt n' c I t 42 n' 4' 4t 4e Ae -4u n n' nt c 2t 2' 2, t I n' 42 A, 4t 4t

2t 2t n, 2t 2. 2' nu c n' 42 ns I t 4t 43 4t A,

n, n, 2t c nx n 2, 2' nz 42 i I V" 43 Vt 4!

2' 2' n' 2Y 2, c nt n' 4t Ze 4t Vt I l 42 nz

a' n' 2' nt c n, 2t 2y 2, V. 4. 4t 4t I I n 42

2t 2, c 2x 2' 2Y n' ns nt 4' At 43 Z3 42 nt t t

c c 2t n' n' n, 2' 2' 2t 4t 4t A" 4t 12 42 t I

TABIS 9. sItBGROIrPsOF P4/wc D$cussIoN

Totrag.ml ?422 P4/n Thesymmetry of vesuvianite P4nc P4 ,an2 P4 pVzc Different crystals of vesuvianite show different degreesof deviation from P4lnnc symmetry.With O!thorboubtc regard to this, the following questionsare pertinent: (i) do any samFlesof vesuvianitebave P4lnnc symme- Pnnn Pn6' Pctn try at room temperature?(ii) do all non-tetragonal

P222 P2,22' P22t2 vesuvianitecrystals have the same space-groupsymmetry? Both of questions Pnd2 Pnc2' Pcn2 these are difficuft to answel Pn2a Pn2n' Pc2rn as very small deviationsfrom a specific syrnmetryare difficult to chatacteize. Perhaps a more pragmatic P2nn P2 tct' P2nn answerto the first questionis that somesamples show llorccl-lnLc only minor to negligible deviationsfuom P4lnnr sym-

P2"/n metry, and the structure can be adequatelydescribed rn in this spacegroup; structure refinement in a lower

P2'l P2tttot P2tt,oj symmetry shows no detectabledeviations from P4lnnc. For the secondquestion, the samediffrculties Trlqltnlc apply. What is definite is tlat somesamples show con- siderabledeviations ftom P4lnnc symmefiy, and the PI important thing is to decide on the correct (or most appropriate)space group(s) for thesestructures, which 'Prlnclpal s6a at 45o to th€ tetragoEl a ses. we refer to collectivd as the low-symmetrystructure. lsuporscripcs for lha @nocllnLc epace gror4re A combination of optical and diffraction observa- lndisaCe th.E ori.EDgation of ttle prhcl,pel uls relatlre co tb6 Ld€al tEcragoel a6a . tions with tle group-subgroup argumentslimits the THE SYMMETRY OF VESIIVIAMTE 63r spacegroups possible for low-symmetryvesuvianite various constraintsimposed by symmetryon the coef- to a small number of possibilities. The following ficients of this expansion,and usefiil expressionsfor observationsare pertinent: (i) diffraction evidence the free energy thermodynamicpotential can be showsthat when comparedto the ideal P4lnnc sftac- derived.Thus the physicalidea that underliesthis type ture, all glide-planesymmefries are violated exceptfor of treatmentis quite straightforward,although the the n-glide perpendicularto Z; (i) optical examination algebraicaspects of a quantitativetreatment can shows vesuvianite to be biaxial; (iii) the optic axial be rather complicated.This approachhas beenused plane is parallel or perpendicularto the axes of by Saljeand coworkers(Salje 1985,1987, Salle et al. an ideal tetagonal crystal; and the (iv) possiblespace 1985,Redfern & Salje 1987)and by Hatch and groups (Hatch of vesuvianitemust be subgroupsof P4lnrrc. coworkers et al. 1987" Hatch & Ghose 1989a Combinationof thesepoints gives the possible b, Hatch & Griffen 1989) for the analysisof phase space-groupsof low-symmetryvesuvianite as P2ln transitionsin someminerals. or its subgroups.For P2ln syrnmetry,the unique axis is Z (tetragonal),and all subgroups(Pn, P2, PI, PI) Applic ation to ve s uv ianit e are possiblewith this orientation.However, the space group P2 also is possiblewith the unique axis along 11s limited information on the temperaturedepen- X or I (tetragonal). denceof the optical data showsthe (spontaneous)bire- It seemsworthwhile to make some fairly general fringencedown [001] to decreasewith increasingtem- remarksabout the symmetryaspects of vesuvianite perature.This finding, togetherwith the symmetry before specific physical and chemical details are con- relationships in vesuvianite, suggesta continuous sidered. Here we have a situation where there is transition betweena high-symmetryphase and a low- an obvious prototype structure (with P4lnnc symme- symmetry phase,from a high-temperaturetetragonal try), and most (or all) of the structureshave sometype (uniaxial) structure to a low-temperature(biaxial) of subgrouprelationship to this prototype.For the pre- structure.There may, in fact be more than one transi- sent,\re allow the possibility that individual structures tion in this system,as the high symmetryof the parent of vesuvianitemight adoptdifferent space-goupsym- structurecould allow a seriesof continuoustransitions menie$, dependingon details of chemistry or history with decreasingtemperature. Such a possibility can of crystallization and equilibration. This strongly only be examinedby detailedquantitative measure- suggeststhat there is a continuoussecond-order phase ments of order parameter(s)as a function of tempera- transition betweena (high-temperature)P4lnnc stttc- ture. At present,it is sufficient to identify the presence ture and a lower-symmetrymodification. Such situa- of a transition. and consider which of the unusual tions are best consideredwithin the framework feafuresof vesuvianiteare a result of this transition. of Landau theory (Tol6dano & Tol6dano 1980, Salje In a P4lnnc -->P2ln transition. the translational 1990). symmetry remains unchanged,and the critical point of the Brillouin zone is the origin. Thus the primary Inndau theory order-parametermust transformunder a I point (zone- center)represefianot of PLlnnc.Inspection of Table 1 The basic ideasof this theory are fairly simple. For of Stokes& Hatch (1988) showsthat the active order- a continuousphase-transition, the difference between parametermust transformaccording to the one-dimen- the high-symmery phaseand the low-symmetryphase sional representationT5+ of P$/nnc. This is a pure is zero at the transition. As conditions change away ferroelastictransition (Aizu 1969,Tol6dano 1979), from the transitioninto the field of stability of the low- and bottr Landau and Lifshitz frequencies ate zero, symmetryphase, tle differencebetween the high-sym- as requiredfor a continuoustransition. Hence the basis metry phaseand the low-symmstryphase increases. functionsof the active ireducible representationtrans- If we normalize the difference such that its possible form as the componentsof the spontaneousstrain. values are in the range G-1, this difference is called Schlenker et al. (L978) gave the generalized the order parameter; note that we have not yet speci- Lagrangiansftain tensor components.Using the stan- fied the physical nature of the order parameter.In dard axesof vesuvianite,the componentsof the spon- a continuousphase-transition, the order parameter taneousstrain are: changescontinuously from zero to non-zerovalues, ey= (ar- a)lq, e22=(a1- b^)lat, ezz= and thesenon-zero values are small phase close to the (cr-c^\c, (1) transition. We can expressthe free energyof tle system in terms of the free energyof the part conespond- where the subscripts denote the symmetry of the ing to the high-symmetryphase plus the free energy structure,Assuming that (a. + c^)12= a, and ct = cmo of the distortionsfrom the high-symmety phase,that we may calculate the spontaneousstrain from the is, the order parameter.As the order parameter metrically unconstrainedcell-dimensions of the vesu- is small, we can expand the free energy as a Taylor vianite semplesofGroat et al. (1992a).This correlates series in terms of the order parameter.There are strongly with the 2V values measuredfor thesecrys- 632 THE CANADIAN MINERALOGIST

o.00@

j {.0cx}c +6 I tl ".0* I r {9 o.oma 1t

.0.(x)10 +r

{.0012 10 2v f) Flc. 9. Variation of spontaneousstrain with optic axial angle(2V for selectedcrystals of vesuvianite. tats (Fig. 9), and also shouldcorrelate with the sponta- have shown significant ordering of cations over sites neousbirefringence. that are equivalentrn P4lnnc. Specifically,the channel The componentsof the spontaneousstrain trans- sites [abeled Ca(4)A and Ca(4)8, and M(3)A and form as tle order parameterfor tle representationf5*, M(3)Bby Giuseppetti&Mazxi (1983)lhave split into and hencethe spontaneousstrain could drive the tran- two sets of two equivalent sites, ratler than one set sition. However, all suggestionsas to the possible of four equivalent sites in the P4lnnc structure.It is symmetry-lowering mechanismin vesuvianite have instructive to examinethe expressionfor the structure involved cation ordering;we will considerthis next. factor in P4ln, and see the effect of ordering on the diffraction characteristics.Using standardterminology Ordering of channelcations as an order pararneter (InternationalTables for X-ray Crystallography,

There have been severalsuggestions that lowering of symmetry in vesuvianiteprimarily involves ordering of cations over the channel sites X(4)A + X(4)B IABI.E 10. CIIANNBL SITES AS A FI'NCTTON OF and I(1)A + f(l)B (Table 10). However, the order TUMRISY parametersassociated with such mechanismsdo not transform as the 15+ irreducible representation P4/ffic P4/n P2/a, Pn, P7 P2, Pl of P4/nnc, and hence connot drive a (ferroelastic) P4lnnc -+ P2/n phase tansition. Tbey can drive a x('r)A' -+ x(4)a r(4)A ferroic transition,P4lnnc P4/n, but the basic prob- x(4)A' lem in vesuvianiteinvolves breaking of tetragonal symmetry, and such channel ordering cannot be the x(4)B' causeof this (unlessthe lower symmetryis P2 rather x(4)D x(4)B that P2ln, in which case ordering over quartets x(4)8. of channelsites (Table l0) would occur and could Y(r.)A' drive the transition). Y(r.)A Y(l)A Y(1)a" Ordering of chnnnelcations and dffiaction symrnetry Y(I,)B' There have been several refinementsof the struc- Y(1)B Y(r-)B fure of vesuvianite in space group P4ln, and these Y(1)B' TTIE SYMMETRY OF VESI'VTANITE 633

L974),the structurefactor may be written as hansition driven by ordering of cations over quariets of channel sites, as in that case,one might expect A = Scosn(li- lilx + + ldy - hl2)cosn(lh+ [h a direct relationshipbetween the intensitiesof the viol- l*x - lh - kly - H2)cos2n(lz+ (2) [h+1414) ating reflectionsand 2V. This also suggeststhat we For the Z(1)A and Z(1)B sites, x = ! = 1.14,and, will not identify the principal order-parameteruntil equation(2) reducesto there has been an adequatestructural refinement of (work progress). a=8cos2n(1il4+H4+lz) (3) 4 meaqslinisvesuvianite in As this is symmetricalin fr and k, Ahkr= Akr,1for x = Twinningin vesuvianite y = L/4, and ordering over I(1)A (L14, ll4, z) and Y(I)B (L/4, ll4, z') doesnot break 4lmmm Laue sym- Many investigatorshave proposedthat twinning metry. Thus the deviationsfrom 4lmmrnLaue symme- occursin vesuvianite,both to accountfor the appear- try noted abovemust be causedby other structural anceof somesamples in transmittedlight, and factors than ordering over the I(1)A and I(1)B sites. to accountfor its unusual physical and diffraction On the otherhand, such ordering can produceintensity properties.We regard it as possible tlat many vesu- for reflectionsof the type h\l, h + I = 2n + L, and vianite samplesmay be twinned. However, this is not hencethe occlurenceof vertical-glide-violatingreflec- the reason why vesuvianite deviatesfrom tetragonal tions could be due to orderingover I(1)A and I(1)8. synmelry. There are 1rrs imfortant points that result from the Twinning of the kind usually proposed,for vesu- above sonsiderations:(i) the argumentgeneralizes vianite (e.9.,by reflectionacross a mirror | | {110}) to a// channelsites, and hencechannel ordering of any will. increasethe apparentsymmetry for most physical kind is not sufncient to describea changein symmetry processessuch as transmissionof light or diffraction from P4lnnc to P4ln. There must be significant of X rays, provided that the scale of the twinning is changesin order or atomic positions at sites lying off fine relative to the energeticor spatialresolution ofthe the channelsthrough the structure,possibly occurring process.Hence twinning will tend to reducethe opti- as relaxation in responseto ordering of channel cal or diffraction o'anomalies"of a mineral and cannot cations. Also, the only diffraction information on normally contribute to such features. Thus although order of cationsin the channelslies in the ghde-viol- twinning may be presentin vesuvianite,it cannotbe a ating reflections. (ii) Ordering of channel cations causativefactor for the "anomalous" featuresof this of this type cannot accountfor the deviationsfrom mineral. tetragonalsymmetry (as shown abovewhen consider- ing the group-theoryaspects of aP4lnnc -+ Y2lntran- Antiphasedomnins sition). In principle, ordering of channelcations such that f(1) splits into four distinct sites could drive Severalsamples of vesuvianitehave been refined in a P4lnnc -+ P2 transition,and it is perhapssignificant the space-groupP4/n, with the resulting patterns that Allen & Burnham (1992) rcportedpositive SHG of order amongchannel cations distinct from those (SecondHannonic Generation)signals from samples expectedrn P4lnnc symmetry.In the transitionP4lnnc of vesuvianite showing shong glide-violating reflec- -->P4ln, there are two possibleorigins of the P4ln celT tions, suggestingnon-centrosymmetric space-group relative to the parent P4lnnc cell: (0,0,0) and synmerry. (1./2,0,1.12).Thence there is the possibility of the As noted above,ordering of cationsover pairs developmentof antiphasedomains of P4ln structure of channelsites cannot dive a P4lnnc -+ Y2/n f:ansi- with a relativedisplacement of. (0,0,1/2). tion. However, such ordering does contribute to the Veblen & Weichmann(1991) have recently shown intensity of reflections of types a, b and c (Table 4). that a vesuvianitecrystal from Crestmore,California" Inspection of Tables 5 and 7 shows the relationship is madeup of domainslG-50 nm wide elongateparal- betweenthe intensitiesof the violating reflections and lel to [001]. This particularspecimen shows selected- the deviation from tetragonalsymmetry, as measured area electron-diffractionpatterns consistent with P4ln by 2V n the {001} (2V = G-10'), {L}ll (2V = 36) symmetry, but is weakly optically biaxial; Veblen and { 100} (2V = 6L") zonesof sampleV12. Although & Weichmann(1991) suggested that the true symme- the violating reflectionsare strongestfor the {100} try of this vesuvianiteis P2/n or lower. On the other zone, where 2Vis largest,the violating reflections are hand, our IIRTEM examinationof vesuvianiteV12 weakestfor the {101} zone, whete 2V is still quite from the Jeffrey mine, Quebec,shows no sign of any large (36'), and intermediatebetween these two for antiphasedomains. In particular,the {100} sector the {001} zone,where 2V is small.Thus thereis nor showsstrong deviation from tetragonalsymmetry and a l:L correlationbetween tle intensity of the violating uniaxial optical behavior (2V * 60'), in line with the reflections and the deviation from tetragonalsynme- absenceof domain structure(as the twin relationship try as measuredby the observed2V values.This betweendifferent domainswill tend to averageout tlrows somedoubt on the presenceof a P4lnnc -->Y2 deviationsfrom tetagonal behaviorin macroscopicor 634 TIIE CANADIAN MINERALOGIST long-range properties). This is in line with the idea of crystallizationoverlaps the temperatureof the tran- of a high-temperature (>500'C) phase transition, sition. In this case,vesuvianite initially crystallizes where crystalsforming abovethe transition will invert with P$lnnc symmetryas in case(i). However, as the to the lower symmetrythrough the transition,forming temperature falls through that of the transition, finely twinned domains(c/. Veblen & Weichmann a lower-symmetrydrangement begins to crystallize, 1991), whereascrystals forming below the transition and the inrtial P4lnnc structue inverts to the lower will be untwinned and will have the lower-symmetry form with a polysynthetically twinned arrangement. structuralalrangement over the long range. This processproduces a pseudo-tetragonalcore with an overgtowthof stronglybiaxial vesuvianite. Theorigin of sectorzoning Cowcl-ustoNs Sectorzoning is observedin many minerals,and hasbeen explained as a result of differencesin compo- (i) Optical examination shows virtually all vesu- sition or degreeof order that relate to differential vianite samplesto be biaxial, with 2y varying in the interaction of componentswith different crystai- rangeO-62o. growth faces of a mineral. This mechanismcan (ii) X-ray data show no discernabledeviation from be invoked here to mlisnalizs sector-zonedvesuvian- tetragonalsymmetry. ite, as our chemical data show small but significant (iii) If comparedto the ideal P\lnnc structure,all compositionaldifferences between sectors. glide-plane symmetriesare violated except for the As yet, there has not been a successfulrefinement n-glide perpendicularto Z. of the structure of a non-tetragonalvesuvianite (cur- (iv) Sector-zonedvesuvianite shows compositional rently under investigation by us), and thus the com- and optical (2V1differences between sectors. plete details of the physical mechanismassociated (v) The optic axial plane is parallel or perpendicular with the (tetragonal)symmetry-breaking transition are to the axesof an ideal tetragonalcrystal this discounts not known. In terms of crystal growth, the attitude severalorthorhombic and monoclinic subgroups,with of the structure with respectto the growing faces of principal axesat 45o to the ideal tetragonalaxes. the crystal is of obvious importance in terms of the (vi) Optical and diffraction data indicate tlat vesu- characterofthe order parameterthat drives the transi- v\ailtehas P,ln or Pn space-groupsymmetry. tion. (vii) We suggestthat vesuvianiteundergoes a ferroelastic phase-transitionat high temperatures(>500'C) Temperaturerange of crystallizption from a P4lnnc structureto a P2ln or Pn structure. (viii) Orderingofchannel cationsover nonequivalent The presenceof a (continuous)phase transition pairs of I(1) and X(4) sites cannotbe the order para- accountsfor many (but not all) of the physicalfeatures meter that drives the P4lnnc -+ P2ln transition, as observedin vesuvianite,the key aspectbeing the rela- it does not transform as the active irreducible repre- tionship of the temperatureof transitionto tle temper- sentationof this transition. ature interval of crystallizationof the specific sample. (ix) We proposethat the different optical types of We can recognizetbree situations:(i) The temperature vesuvianitearise from different relationshipsbetween interval of crystallizationis abovethe temperature the temperaturerange of crystallization and the of the transition. In this case,the vesuvianitecrystal- temperatureof the ferroelasticphase-transition. lizes with P4lnnc symmetry. On cooling, it passes through the [ansition and inverts to a lower symme- ACKNOWLEDGEN{B.ITS try, which producesfine-scale twinning. This produces the *normal" vesuvianitewith uniform extinction and This work was funded by the Natural Sciencesand small (< 5") 2V. The fact that 2V doesnot equal zero EngineeringResearch Council of Canadain the form indicatesthat the true symmetryis not tetragonal(1.e., of a PostgraduateFellowship and operating grant the crystal is not uniaxial), but the fine-scaletwinning to the fint author, a University ResearchFellowship, servesto simulate (pseudo-)tetragonaloptical behav- an OperatingGrant, a Major EquipmentGrant and an ior. Such a twinned structurehas been observedby InfrastructureGrant to the authorwith the overly large Veblen & Weichmann(1991) in vesuvianitefrom housecat.The authorsthank F.M. Allen and J.C. Crestmore(Califomia) that formed close to a contact Rucklidgefor their helpful reviewsof the manuscript. with a quartzmonzonite (i.e., at a relatively high temperature).(ii) The temperatureof crystallization is completelybelow the temperatureof the transition. RnrensNcEs In this case,vesuvianite crystallizes witl non-tetragonal symmetry,and the complexitiesthat are Avu, K. (1969):Possible species of "ferroelastic"crystals observedmust be due to crystal growth; this leads to andof simultaaeouslyferroelectric and ferroelastic crys- sector-zonedvesuvianite. (iii) The temperature tals.J. Phys.Soc. Japan27,387-396. TIIE SYMMETRY OF VESTIVIANTTE 63s

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INrnnnanoxar- Tasus FoRX-RAy Cnysrauoonepny. Vol. ReceivedMay 1, 1991, revised manuscript accepted fY 1J974):Kynoch hess, Birmingharn,England. December21. 1992.