vector representation of some mineral compositions in the ... - RRuff

449 Thc Canalian M ineralogi st vol. 32,pp. 449-457(1994)

OFSOMEMINERALCOMPOSITIONS VECTORREPRESENTATION GROUP, IN THEAENIGMATITE TO HOGTUVAITE WITHSPECIALREFERENCE DONALD M. BURT U.S.A. Arizona85287'1404, Tempe, Departtnent of Geology, Ari4ornStateUniversity,

ABSTRACT wheret8lAcationsareNa and Ca, t6J3-" t"z*, Aenigmatite-groupcompositionsconformto the generalformulaA 2B6T6O2p, Fe3*,Mg, Al, Cr, Ti, and Sb5r,and talz are Si, Al, B, and Be in namedend-members.Theseinclude the sodic mineralsaenigmatite,krinovite, and wilkinsonite,and the calcic mineralsrhdnite, serendibite,dorrite, welshite,and h6gtuvaite(a new Be-bearingend-member:Grauchet al. 1994).Graphicalrcpresentafionof the compositionalrelationsamongthesephasesis madepossibleby the vector method,which has recently beenapplied to a numberof other mineral groups.The fundamental principle is that a chemicaldisplacementsuchas CaAl(NaSi)-1,having both direction and magtitude, can be thoughtof as a vector of unit length and arbitrary orientation.Compositionalrelations are simplified by condensingon vectorsof isovalent substitution,suchas Fe3*Al-, and Fe2+Mg-r.In vector diagrams,bound vectorsare attachedto a point and show the relations amongbasisand derived vectors.The conespondingfee vectorsgeneratethe accessiblecompositionalrange(e.g., triangle, quadrilateral,or pentagon),startingfrom an initial formula or composition(additive componentof J.B. Thompson,Jr.). When this approachis usedon the aenigmatitegroup,the compositionsof the main mineralsare derivedftom that of aenigmatiteby applicationof the basisvecton CaAl(NaSi)-1,Al2(MgTi)-,, and Al2(MgSi)-r.Hogtuvaiteis derivedby BeSiAl-2actingon rhtlnite, and welshite by AlSbBe(MgTiSi)_1acting on hpgtuvaite. Other theoretical end-memberscan be generatedby the vector method;in the aenigmatitegroup,many areprobablyunstablewith regmdto a mixture of clinopytoxeneplus olivine or spinel,especiallyif they lack Ti or excessA1. Keywords:exchangevectors,aenigmatitegroup,hpgruvaite,beryllium.

Sotwtans La compositiondesmin6rauxdu groupede I'aenigmatiter6pondI la formule g1ndraleA286T60ro,danslaquelleNa et Ca occupentla position t81A,Fe2+,Fe3r,Mg, Al, Cr, Ti et Sb5i, la position t6lB,et Si, Al, B et Be, 1aposition [4lr dansle casdes p6lesqui sont d6jbhomologu6s.Parmi ceux-ci se trouvent les min6rauxsodiquesaenigmatite,krinovite et wilkinsonite, et les min6rauxcalciquesrhOnite,serendibite,dorrite, welshiteet hogtuvalte,cettedemidre6tantle pdle i Be: (Grauchet al. 1994). Une repr6sentationgtaphiquedes relations compositionnellesparmi ces phasesest renduepossiblegrdce tr la m6thodedes vecteurs,qui a rdcernment6t6 appliqu6eavec succdsi d'autres groupesde min6raux.Le principe fondamentalveut qu'un d6placementcompositionnel,par exempleCaAlQ.{aSi)-1,poss6dant} la fois une direction et une amplitude,s'exprime sous forme de vecteurd'une longueurunitaire et d'orientation quelconque.Les relationsparmi les compositionssont simplifiables en termesde vecteursde substitutionisovalente,par exempleFe3*Al-l et Fe2+Mg-l.Dans les diagrammesvectoriels,les vecteursrattachdstr un point d6montrentles relationsparmi le vecteurde baseet les vecteursd€riv6s.t e vecteurlibre correspondantd6finit l'6tendueaccessibledansl'espacecompositionnel(c'est-i-dire, un triangle,un quadrilatdreou un pentagone),d partir d'une formuleou d'une compositioninitiale (composant additif de J.B. Thompson,Jr.).Dansle contextedu groupede I'aenigmatite,la compositiondes min6rauxprincipauxest ddriv6eh partir de celle de l'aenigmatitepar l'applicationdes La h6gtuvalted6coulede l'application du vecteurBeSiAl-2 vecteursopdrationnelsCaAl(NaSi)-r, Al2(MgTi)-, et Al2@4gSi)-1. agissantsur le p6le rhrinite,et la welshiterdsultede l'application du vecteurAlSbBe(MgTiSi)-t agissantsur le p61ehggnrvalte. On peut pr6dire la compositionde p6les nouveauxpar la m6thodedes vecteurs;dansle cas du groupede I'aenigmatite, plusieursseraientinstablespar rapport i un m6langede clinopynoxbne+ olivine ou spinelle,surtout s'ils sont d6pourvusde titaneou contiennentun excdsd'aluminium. (Iraduit par la Rddaction) Mots-cl6s: vecteurs d'&hange, groupe de I'aenigmatite, hpgtuvalte, b6ryllium.

450

TIIE CANADIAN

InrnolucloN

MINERALOGIST

M8W

M5,tt46

M7

M1-M4

T1-76

(Ca,Na)z (Fe2*,Mg)z (Mg,Fe3+,Ti4)3 (Ti4*,Fe3*) (Si,Al)6O20.

Vectors,by definition, have both a direction and magnitude.An exampleof a vector quantity is the The large irregular M8 andM9 polyhedra,in addition physical displacementrepresentedby walking five to being crystallographicallydistinct from eachother, metersnorth. Ionic substitutionsin minerals likewise are quite different in shapein rhtinite (calcic) and haveboth a direction(or "sense")anda magnitude(or aenigmatite(sodic:Bonaccorsiet a\.1990). This fea'oextent");therefore,althoughit is not yet conventional ture explainsthe lack of completesolid-solution (Burt 1991) betweenthe two and presumablywhy natural phases to do so, thesechemicaldisplacements also canbe treatedas vectors,a concept,if not a termi- tend to be either Na-dominant(aenigmatite,krinovite, nology,that originatedwith W.L. Bragg (Thompson and wilkinsonite:Duggan1990)or Ca-dominant (rhdnite,serendibite,welshite,dorrite, and hggtul98l; cf. Smith 1959). Aenigmatite-groupminerals, although relatively vaite). The six octahedrallycoordinatedsitescan be rare, occur in a variety of high-temperatureenviron- subdividedamongthe largerM5 andM6 sites,typicalments, ranging from volcanic and plutonic to ly with divalent cations,the smallerM1-M4 sites,and metamorphicand metasomatic;they also occur in the still smallerM7 site,typically with a high-valence meteorites(e.g.,Deeret al. 1978).The purposeof this cation such as Ti or Sb5+.A variety of tetrahedrally paperis to apply vector methodsto the graphical coordinatedcationsoccupy the T1-76 sites;this helps representationof complexcoupledsubstitutionsin the explain why coupledsubstitutionsin this group canbe aenigmatitegroup;algebraic vector representations of quitecomplex(cl Johnston& Stout1985).Significant mineral compositionsin the aenigmatitegroup were vacanciesat cation sites or heterovalentsubstitutions given by Johnston& Stout (1985).Emphasiswill be involving anionshave not been described,however, placedon coupledsubstitutions involvingBe andSb5* which at least makesthe aenigmatitegroup simpler (which were not consideredby Johnston& Stout) and thanthetourmalinegroup,for example@urt 1989). on derivationof tle new Be end-memberh@gtuvaite A further complicationis that many potential endcompositions,especially describedin the accompanying article (Grauchet al. memberaenigmatite-group 1994).To the best of tfie author'sknowledge,this is those lacking Ti or Al, are unstablewith respectto a the lrst new mineral whoseinitial descriptionis based mixture of clinopyroxeneplus spinel or olivine (or on the vectormethod. both). Table 2b showsthis relation for somesimple Structuraland crystal-chemicalfeaturesin this Ti-free compositions.This complicationcan be group have recentlybeenreviewedby Deer et al. (1978)and Bonaccorsiet al. (1990).The idealized IN THE TABLE2. STABLNY AND INSTABLTTY compositionsof mineralend-members recognizedto dateare Iisted in Table 1. The formula of this group is AENIGMATITE GROUP generally given as t81A2t61B6IqT6O2e, with A = Na or General:A2B676AD = 2BTzOa +2B2TO4 Ca,B = Fe2+,Mg, Fe3*oAl, Cf*, Ti3+,Ti4, or Sbs*, and 7 = Si, Al, Fe3+,B, or Be. Structuralrefinements a) Examplm of Stability: by Bonaccorsiet al. (1990)revealthat a more accurate 2NaFe3+Si206+ 2Fe2SlO4= Na2(Fe2+4Fe3+2)Si6020 representationfor rhdnite, a common memberof the wllklnsonilo Fayalite Aeglrine group,is 2Naoratgi2o6 + 2Mg2SiO4 = Na2(Mg4Cr3+2)Si6O2o Kosm@hlor TABLE 1. MINEMLS IN THE AENIGMATTTEGROUP

Krinovitg

Forstgrite

2caAl2sio6 + 2MgFe3+2oa = cadMg2Fe3+4)(AlaSiio26 'CATS' Magnesloterrlte Donite

Gsngral: tslA2t6iB6t4lTSO20 Mineral Name

ldealized ComoGition

Aenigmatite

Na2(Fe2+sT)si6o2o

Dorrite

Ca2(Mg2Fee+ a)(Al4Si2)O2o

Hogtuvaite

Ca2Fe2+sTDFoSis)O2o

= 2CaFeSizOo+ ZFesOa Ca2(Fe2+4Fe3+2)(Fe3+2Sia)O2q

Krinovite RhOnite

Na2(Mg4or3+2)Si6O2o Ca2(Fez+5TD(Al2Si4)O2o

ca2(Mg6)si6o20= 2GaMgsieoo+ 2Mg2sio4

Serendlbita

ca2(M&Al3xBt.5Al1.5sijo26

Wolshito

+Sb5r XB62Si4)O2o Ca2(Mg4Fe3

Wilkinsonite

Na2(Fez+4Fe3+2)Si6O20

b) Examples ot Instabillty: = 2CaMgSi2O6+ 2MgAl2Oa Ca2(Mg4Al2XAl2Sia)O2s Diopsid€

Spinel

Hedenbergito Magnetito

Diopslde

For6terlte

= 2NaAlSlot + 4Al2Og Na2(Ald(Al4Si2)Oeo Neohellne

Gorundum

'\

VECTORREPRESENTATIONS IN TITEAENIGMATTTEGROUP

45L

Taking twice the first and subtractingthe secondleads to Ca2MgTi(NaSi)-2,a vector of zeroAl (labeledAlt). Lines of constanttotal Al (slope-/z) are parallel to this vector on the compositiondiagrambelow. The horizontalbasisvectoris a vectorof constantMg, Ti, and octahedrallycoordinatedAl; the vertical one is one of constantNa, Ca, Si, and tetrahedrallycoordinatedAl. The correspondngfreevectors,that operatefreely on the plane (Hoffmann 1975),rf allowed to do so on Appncenoll ro CoMMoNSussrrrurroNs a single arbitrary initial formula [additive composition of Thompson(1981, 1982),here chosenas "Mgplanar the accessible For purposesof graphicalsimplification,all compo- analogof aenigmatite"l,generate sitionsdepictedwill be "condensedon" or projected compositiondiagram (triangle,quadrilateral,or pentadown vectorsof isovalentsubstitution(such as gon in the examplesbelow), which is boundby lines Fe2+Mg_,and Fe3+Al_l).This is doneto allow com- ofzero contentofvariouselements(Burt 1991).These plex coupledsubstitutionsto be emphasizedand is not chemicallimits are generallymore extensivethan meantto imply that the Na{a-Mg-Ti-Sb-Be-Al-Si crystal-chemicallimits providedby considerationof end-membersderived are representativeof Fe-rich typical coordinationnumbersin crystals(Burt 1991). nanrralcompositions,or evenare stable. For example,in Figure 1, the chemicallimits define a On the planar vector diagramsderivedbelow, an quadrilateralboundedby lines of zero Na, Ca, Al, and inset showsvarious bound vectors (e.g., Hoffmann Ti, but the lowermostcompositionhas tetrahedrally 1975)that are attachedto a fixed point; it depictsthe coordinatedMg and Ti and is thereforepresumably relations among the two basis vectors and various unstable.More reasonableand restrictivecrystalother vectorsderivedby taking linear combinations. chemicallimits are providedby the solid rectangle. For example,in Figure 1, the nvo basisvectors,arbi- The remaining figures are drawn in a similr fashion trarily drawn orthogonal and of the samelengtl for andhavesimilar properties. easeof plotting, are CaAl(NaSi)_,and Alr(MgTi)_,. Actually, the compositionto the upper right is explainedby the observationthat the rh