American Mineralogist, Volume 63, pages 664_676, l97g

Multisyste_msanalysis of beryiliumminerar stabilities: the systemBeO-A[rOa_SiO2_H2O

DoNer.n M. Bunr Department of Geology, Arizona State (Jniuersitv Tempe,Arizona8528I

Abstract

seven commonly associatedminerals in the systemBeo-Alror-Sior-Hro includechry- soberyl,, ,, , kaolinite,and qiuit . The phaserule implies that not more than six of theseminerals can coexistat an invariantpoint, and, with the addition of an aqueousphase, the associationconstitutes an (n * 4; ptrase(negative two d-egreesof freedom)multisystem. The apparentincompatibility of taotinite with phenakite allowsthe splitting of this unwieldymultisystem into two smaller(n + 3) phasemultisystems, which may belabeled (Kao) and (phe).Moiar volumedata, compuier program RrlcrroN, and naturalassemblages can then be usedto derivethe presumablystabie cJnfiguration of these multisystemson p"-minus an isothermal pHro diagram. n, p-r diagramprojected through theaqueous phase shouldhave the sametopology, and cansimilarlf be drawn. on the resultingdiagrams, three . invariant-butpoinis rabeled tchrl, tBr;;, and [etz] arestable in the.multisystem (Kao), and threedistinct identically-fuU"i.Opoint, u.. stablein rhe multisystem(Phe). An implicationof this topologyvia ihe "r.tu.tubl"-rtable correspon- dence,"is that the assemblagephenakite + euclase* beryl(* aqueousphase) has a finite i'I;ix, ii,l'J.?lT"t' ::ff,,,j :r;: :":.T' ? ts why" euclase is muchrarer than bertrandite. and its stabilityfield, especially in the presence p t low and T. Most reactionsinvolving the bly occur at temperaturestoo low for conve_ 0.c).

Introduction The present paper representsa first attempt to derivethe topology of the stability fieldsof these berylliumminerals. The derivationdepends on natu- ral assemblages(cf. Beus, 1960; Vlasov, 1966: Burnol. t968; Cerny, t963), Fortran program RrncrroN (Fingerand Burt, 1972),molar volume data (Robie el al., 1967),and multisystemsanalysis (Korzhinskii, 1957).Reliable thermochemical or experimentaldata on mostof the phasesare lacking, so that the results areofnecessity topological rather than quantitative. Many of the resultswere collectivelyderived as a laboratoryassignment by my springterm 1977class in ore deposits at Arizona State University. The method, heresummarized in advance,consisted bas- icallyof the followingfive steps: (l) Thesystem BeO- AlrOs-SiOr-HrOwas searched for all possiblephases that occur as mineralsor that havebeen synthesized. A numberof thesephases were eliminated from con- 0o03-004x/ 7 8 /0708_0664$02. 00 664 BURT: STABILITIES 66s sideration,leaving seven plus an aqueous Table 2 Abbreviations,formulas, and molar volumes* of eight in the systemBeO-Al,Og-SiOz-H,O fluid. (2) The resultingeight-phase multisystem was additionalminerals pseudoternary system by simplified to a six-phase Nee Abblev. FotEula Molar Volwe* projectingthrough HrO and by noting that phenakite ( I oules/bar) Be0 0.831 and bertranditethen plot at the samepoint. (3) An Bronellite Bro Behoite Beh Be (OH) 2.22 isothermal P,-minus pHrO diagram was plotted for 2 corundun Cor A12O3 2.558 (4) Natural assemblages this simpler multisystem. Dlaspore Dsp A1o (OH) t.776 most likely intersectionof A1(ori) 3.196 were usedto determinethe Gibbsite 3 (on) .Hro the degeneratedehydration reaction of bertranditeto Beryllite B1r BerSlo4 2 phenakitewith the multisystem.(5) The resultingP"- Andalusite AI6 Ar2sio5 PvP At2si40lo(oH) 12.83 minus pHrO diagram was transformedinto a topo- Pyrophyllire 2 logically identical schematic Pr"o-T diagram. *Data from Roble et al-. (1967) excepE for behoite and pyrophytllte. Beholi-e from x-ray data for B-Be(OH)2 ln Rosa (isOi); pvropnvrlite recalcurated fron Dav (1975)' Phases

The quaternarysystem BeO-AlrOr-SiOr-HrO con- and water,mainly in channelpositions (Bakakin and tains, among others, the sevencommonly associ- Befov, 1962: Cerny, 1975; Hawthorne and Cerny, ated phaseslisted in Table l. Correspondingmolar 1977), and natural beryl and may also volumes are given in joules/bar. Eight additional contain Cr3+, Fe3*, V3+, Sc3+,and other ions sub- phases have been omitted from the present study, stituting for A13+.Based on availabledata, there are largely becausethey have never been reported in as- no indicationsof major compositionalvariations in sociation with beryl (Table 2). The compositionsand naturaleuclase, bertrandite, or phenakite' assumednatural compatibilitiesof anhydrousminer- als in the system BeO-AlrOr-SiOz are shown in Fig- Review of exPerimental studies ure I (Burt, 1975a a summary of evidenceappears studiesand the follow" under the discussionof natural assemblages).Simi- This reviewof experimental have been made as larly, the compositionsand known compatibilitiesof ing review of natural occurrences in order to succinctlysumma- most phases in the system BeO-AlzOs-SiO2-H2O, complete as possible, data initiallyavailable projectedthrough excessquartz, are shown in Figure rizein oneplace the conflicting Much of this 2. The dashedlines on this figurerefer to uncertainor on the system BeO-AlzOr-SiOr-HrO. for the multisystems conflicting assemblagesvariously reported in the lit- data is seen to be unnecessary and these two sections may erature (again, consult the sectionon natural assem- analysis that follows, during a first reading without blages). therefore be skimmed In the following discussion,the phasesin Table I much lossof continuitY. system AIrOB-SiOr-HrO will be assumedto be stoichiometric.Natural beryl Phase equilibria in the (1976'1978) may contain considerablealkalis (Na, Cs, and Li) have recentlybeen summarized by Burt

Table I Abbreviations. formulas, and molar volumes* of seven mineralsin the systemBeO-AlrOr-SiO,-H,O

Nane Abbrev. MoIa! volune 0""1eel!eE) Chrysoberyl Ch! BeAI204 3.432 +,002 Phenakite Phe Be2si04 3.719+.004

EucIa6e Euc BeAlSioO (Ol{) 4.657+.010 Btr Be4S1207 (0H) 9.217+.050(?) Bertrandite 2 Beryl BrI Be^A1^Si.O- ^ 20,355 +.O25 J 2 OL6 A12S1205(oH) 9 .952 +.026 Kao 1 init e Kao 4 Qtz si02 2.2688+.0001

*Data flom Roble et af. (1957) except for berttandite' The Cor bertrandite value vas calculated fron unit cel-I dinensions given BeO Chr by Solovreva and Belov (1951), and cited in Ross (1954). Sttghlly different unit cell dimenslons in Solov'ewa and Belov (1964) give a value of 9,177; use of densitles measured on natulal Eaterials Fig l. Moderate P and f mineral compatibilitiesdeduced for (2.60+.03) gives a value of 9.16+.10. lhe system BeO-AlrOr-SiOr, based on natural assemblages' BURT,, BERYLLIUM MINERAL STABILITIES

determinedthat beryl breaksdown to chrysoberyl, phenakite, and cristobalite between 1300 and 1400.c. Studiesof beryl synthesisat high pressureswere initiatedby Wilson (1965),who reporteddirect syn- thesisof beryl from its melt at pressuresto 20 kbar. Beryl and phenakitereportedly were synthesizedby ----:115:: Takuboet al. (1971)to 20 kbar at 1600.C.The phase characterizations(or quenchingprocedures) in the abovetwo studiesare questionable(cf, Nassau, 1976) in light of the resultsof Munson(1967). His recon- naissancestudies indicated that naturalberyl breaks Hzo down to chrysoberyl,phenakite, and quartz at ap- proximately15.5 kbar and l340oCand to chrysobe- Fig. 2. Compatibilitiesamong some minerals in the system ryl, phenakite,and coesiteat 45.5kb, 1050"C.As BeO-AlrOr-SiO,-HzO, basedon natural assemblages.euartz is discussedbelow, this high p subsolidusbreakdown of assumedpresent. Dashed lines indicateuncertain or conflictins berylis consistentwith molarvolume data (Table mineralcompatibilities. I ). Studiesof the completequaternary BeO_AlzOr_ SiOr-HrO initially involvedhydrothermal syntheses and Day (1976,1978),and little needbe addedhere. of beryl and .Van Valkenburgand Weir (1957)synthesized beryl between 500 and g50"C at I to 2 kbar, but reportedlyobtained phenakite plus glassabove 900"C. Wyart and Scavnicar(1957) syn- thesizedberyl between400 and 600oCat 400-1500 bars.At 600'C theyobtained beryl * chrysoberyl* assumedto be unstable at low to moderatetemper_ phenakite,and with the additionof CrrO, to replace atures.Studies of therelated binary system BeO_SiO, Al2Os,beryl * phenakitet quartz* Cr2O3.Frondel by Morgan and Hummel (1949) phenakiti revealed and Ito (1968)readily obtained beryl at 6g0oand 2 as the only intermediatephase; it melts incongru- kbar, and also synthesizedthe Sc-Fe analogueof ently.In thebinary systemBeO-HrO, Newkirk (1964) beryl(bassite), with phenakite,quartz, and . dehydrated behoiteto bromelliteat l70oC, 1.3kbar Other synthesesare reviewedby Nassau(1976). and200oC, 4. I kbar,but thisreaction was not reversed. Beuse, al. (1963)studied the hydrothermalaltera- In the ternary BeO-SiOr-HrO,Bukin (1967)readily tion of berylin variousHF-bearing solutions between synthesized both bertranditeand phenakitebetween 500 and 600"C. They alteredberyl to quartz,to ber- 300 and 500oC, 720 atm, but bertranditeappeared trandite,and to bertrandite* .A similar favoredbelow 400"C. seriesof leachingexperiments was performed by Syr- The anhydrousternary BeO-AlrOr-SiO,has been omyamnikovet al. (1972).They alteredberyl to chry- soberyl* phenakiteat temperaturesabove 300"C and 500 kg/cm2(approximately 500 bar). They also leachedphenakite in alkalinesolutions to producea surfacecoating of chkalovite,NarBeSi2Ou. A synthesisstudy of the completesystem BeO_ hydrothermalsyntheses underunspecified conditions AI,OB-SiOz-HrObetween 300 and 700"C. I kbar is (500-600'C, 0.7-1.4 kbar accordingto Nassau, reportedby Ganguliand Saha(1967). They produced 1976). beryl, chrysoberyl, phenakite, bromellite, ber- Studiesof the incongruentmelting behaviorof trandite, quartz,mullite, pyrophyllite,and kaolinite. beryl by Ganguli and Saha(1965) and Miller and They hydratedphenakite to bertranditeat about Mercer(1965) were confirmedby Rieblingand Duke 500'C and broke beryl down to bertranditesolid (1967). Liquid immiscibilityoccurs in the melts. solutionplus pyrophyllite at about485oC. The prob- Ganguliand Saha (1965) delineateda ternaryeutectic able lack of equilibriumin theseexperiments is in- at 151515'C involvingchrysoberyl, phenatite, and dicated by the fact that they reportedly grew py- cristobalite,and Ganguli(1972) in a subsolidusstudv rophylliteto 550oC,which is about200o above the I BURT: BERYLLIUM MINERAL STABILITIES 66'r kbar equilibrium dehydration temperature deter- ity of beryl). Four reported bromellite occurrences minedby Haasand Holdaway(1973). are mentionedin Burt (1975b);a fifth from Chinais Ganguli and Saha'sexperiments involving py- mentionedby Chao (1964) and is describedby rophyllite are also inconsistentwith natural assem- Shabynin(197 4, P. 228). blages,as shown by thefollowing compositional rela- Natural assemblagesinvolving the hydrousphases tions (abbreviationsin TablesI and 2): could be shown on a tetrahedron,but most assem- blagesinvolve quartz,so that a triangulardiagram in 2 Brl * 2Btr + 5 Pyp : 14Euc -t 22Qtz (l) the presenceof excessquartz should be adequate Phe*PYP:2Euci3Qtz (2) initially(Fig. 2). Solidlines on Figure2 depictwell- 7 Phe* Pyp + 2 Btr * 2 Brl (3) Qrz: documentedand/or common natural assemblages; 3Btr + PVP:4Brl *7Kao * (4) Qtz dashedlines indicate poorly documented and/or con- Btr * 9Pyp:4Chr * 5 Kao * 28Qtz (5) flictingassemblages. Unfortunately, most of the un- Brl +4Pyp:3Chr *2Kao * lSQtz (6) certaintieisagain involve euclase. Brl * PYP: Chr * 2Euct (7) Qtz As examplesof theseuncertainties, consider that As discussedbelow, most of the assemblageson the the assemblageberyl-bertrandite-kaolinite has been right sidesof the aboveequations have been reported describedor implied (Aver'yanova,1962; Gallagher from nature;the alternativeassemblages involving and Hawkes,1966), but the conflictingassemblage pyrophyllite are unknown, and pyrophyllitewas euclase-quartzis morecommon, with beryl(Gallag- thereforeomitted from the multisystemsanalysis. her and Hawkes,1966), kaolinite (Olsen, l97l; Cas- In summary,virtually all experimentalstudies in- sedanne,1970), or bertrandite* beryl(Strand, 1953; volved short-durationsynthesis runs rather than Mirtensson, 1960;Sharp, 196l). The assemblages equilibrium(stable or metastable)reversals. Never- euclase-bertrandite(Sainsbury, 1968) and euclase- theless,it appearsthat beryl breaks down both at bertrandite-beryl(Komarova, 1974) are alsoknown high 7'and at highP, andthat bertranditeis stableat from silica-undersaturatedenvironments. lower temperaturesthan phenakite.It is alsoprob- The extremelycommon assemblagebertrandite- able (Wyart and Scavnicar,1957, and later studies) beryl rules out the assemblagephenakite-euclase- that beryl-phenakite-quartz, beryl-chrysoberyl- quartz,which has apparentlynot beendocumented, phenakite,and lessclearly beryl-chrysoberyl-quartz althoughall three mineralsmay occur in the same are stable assemblagesat moderateP and T, as deposit(Mirtensson, 1960, and others).In silica-un- shownon Figure l. None of the abovestudies in- dersaturatedenvironments, however, euclase-phena- volvedthe synthesisof euclase,and thus its rolein the kite assemblagesare described from the SovietUnion aboveequilibria will haveto be answeredfrom natu- (Kalyuzhnayaand Kalyuzhnyi, 1963; Novikova, ral assemblages. 1964:1967: Getmanskaya, 1966; Komarova, 1974; Ginzburg et al., 1974). Natural assemblages Kaolinite-berylassemblages are also described The moderateP and T compatibilitiesamong the (eerny, 1968;Kerr,1946; Kayode,l9Tl); the alterna- anhydrousberyllium mineralshave been deduced tive assemblagechrysoberyl-euclase-quartz has ap- from numerousnatural occurrences(Fig. l; cf. Burt, parentlynot beenreported. A bertrandite-kaolinite- 1975a).Examples of the incompatibilityof berylwith quartz assemblageis reported by Levinson (1962) the aluminosilicateminerals in pegmatitesare given and chrysoberyl-kaoliniLe-qxartz assemblages prob- by Heinrichand Buchi(1969); the stableassemblage ably occur in hydrothermal alteration zones (cf is chrysoberyl-quartz.Chrysoberyl-phenakite (+ beryl) Govorov, 1968;Sainsbury, 1968), although they are assemblagesare reviewedby Okrusch(1971), who not definitelyreported. also reviews chrysoberyl-corundumand chryso- As regardssome of theminerals in Table2, behoite beryl-aluminosilicatelocalities. To the best of my is known from only two localities(Montoya et al., knowledge, beryl has not been found with bro- 1964;Ehlmann and Mitchell, 1970);at neither does it melliteor ,although Bank (1974)has ap- occur with any of the mineralsof Table l. In the parentlyfound corundum(), beryl (emerald), systemBeO-SiOr-HrO, it presumablyis stablewith and chrysoberyl(alexandrite) in a singlehand speci- bertranditeand bromellite, but not with phenakiteor men. Similarly, phenakite,chrysoberyl, and qvartz quartz.In the systemBeO-AlrOs-HrO it presumably may occuras associatedminerals, but theyhave not is stablewith diaspore,but not with chrysoberyl. all beenfound in directcontact (implying the instabil- Theseremain conjectures. 668 BURT.' BERYLLIUM MINERAL STABILITIES

Beryllite,reported from a singlelocality (data sum- reducesthe numberof componentsby one,to three. marized in Kuz'menko, 1966),is compositionally Nevertheless,an (n * 4)-phasemultisystem still re- equivalentto a mixtureof bertrandite,behoite, and mains, and previous analyticalconsiderations of water, but it only occurswith the poorly character- three-componentsystems (Zen andRoseboom, 1972; ..gelbertran- ized phases"sphaerobertrandite" and Day, 1972)have only considered (n * 3)-phasemulti- dite" (hydrated bertrandites,more or less).Like be- systems.Another simplification is needed.[Note that hoite it is probably stableonly at such low tem- "projecting through quartz" still leavesan (n -f 4)- peraturesthat it can safelybe neglected. phasebinary multisystem,and resultsin a lossof As mentionedin the review of experimentalstud- generality.l ies,pyrophyllite presents a particularproblem among The secondsimplification is made possibleby the the hydratedaluminous minerals, inasmuch as it ap- fact that, projectedthrough HrO, two of the phases, parently has neverbeen reported as occurringwith bertranditeand phenakite,plot at the samepoint any berylliummineral. I havetentatively shown it as (Fig. 3). A P-T diagramwill thereforebe splitin two beingcompatible only with chrysoberylin silica-satu- by the degeneratedehydration reaction converting ratedenvironments. bertranditeto phenakite.Reactions involving either Finally,diaspore, like andalusiteand corundum, is phasewill be refractedas they crossthis line, but the known only with chrysoberyl(Apollonov, 1967; underlyingtopology will be unaffected.For topologi- Sainsbury,1968), and, like the other mineralsin cal purposes,then, the systemalready constitutes an Table 2, will not be consideredfurther. (tr + 3)-phasemultisystem. It belongsto chem- To summarize,the natural assemblageshave not ographytype Qc of Zen and Roseboom(1972,Figs. 3 elucidatedthe unknownrole of euclase.The assem- and 8) and Day (1972,Fig. 8). blage beryl-bertrandite-kaolinitesuggests that eu- claseis unstablewith quartz,but euclasetypically occurswith quartz.The assemblageeuclase-phena- Usingmolar uolumedata kite suggeststhat euclaseis stableat highertemper- Purely topological approachesto multisystems aturesthan bertrandite(chemically, hydrated phena- analysiscan become exceedingly cumbersome (Burt, kite), but euclaseis much less common than 1978).A lesscumbersome procedure in the present bertrandite. caseis to usethe molar volumedata in Table I to These ambiguitiessuggest that there may exist constructan isothermalP"-minus pHrO diagram solid-solid,P- and ?'-dependentreactions among the (Marakushev,1973, and earlier papers going back to Be-bearingphases; such reactions can be investigated 1964;cf. Zen,1974).This constructionis basedon the by means of multisystemsanalysis (Korzhinskii, thermodynamicrelation 1959;Burt, l97l) anda computerprogram to gener- - an=Yzo atethe relevantreactions (e.g., RnecrroN: Finger and ( ='r+=) : (8) Burt, 1972). \ 0pH2Ol7 AV" whereArHrO is the numberof molesof water in- Multisystemsanalysis volved in a dehydrationreaction, and AZ" is the reactionvolume change for thesolids. If it is assumed Simplifu ing the multisystem that decreasingpHrO correspondsto increasing7, In the quaternarysystem BeO-AlrOr-SiO2-H2O, this diagramshould, in general,have the sameto- not more than six phasescan stably coexistat an pologyas a P-T diagramin the presenceofan aque- invariant point. If HzO fluid is added to the seven ousfluid. phasesin Table l, the resultingeight-phase associa- The main advantageof the isothermalP"-minus tion constitutesan (r * 4)-phasemultisystem, where pH"O diagramis that the reactionslopes are deter- r is the numberof components.In termsof thephase minedby the molar volumesof the solids,as shown rule,this multisystemhas negative two (-2) degrees by equation(8) above.If compressibilitiesand solid of freedom. solutionare neglected,the slopesare constant(i.e., Such a multisystemis unwieldy;how can it be the reactionsdefine straight lines). This constraintis simplified?A first stepis to recognizethat only equi- analogousto the compositionalconstraints that fix libria occurringin the presenceof aqueousfluid are the slopeson, e.g.,a pHrO-pCO2diagram involving of practical interest; "projecting through water" pure substances(l Korzhinskii,1957). eliminatesone of the eight phasesand topologically On such fixed-slopediagrams, any (n * 3)-phase BURT: BERYLLIUM MINERAL STABILITIES 669 multisystemhas only two alternativetopologies, re- lated to each other by an interchangeof stableand metastableinvariant points (Korzhinskii, 1957). The useof molar volume data to constructa P"-minus pHzO diagram therefore yields only two possible topologiesfor each (n + 3)-phasemultisystem-a <%\ simplificationwhen comparedto the severaltopol- ogiesyielded by compositionalconsiderations alone 1."t\ (cf. Day,1972). metastable-stablecorrespondence The \t.- - \ \. --- For each topology, the labels of the invariant a points that are metastablecorrespond to the phase assemblagethat is stable,and uice uersa (Burt, 197l). This propositioncould be called the metastable- stable correspondencefor (n f 3)-phase multi- systems.A simplederivation is givenbelow' The first stepof the derivationconsists of noting that an (n + 3)-phasemultisystem can be derived from an invariantpoint involving an equalnumber of phasesby subtractingone degree offreedom (i'e.,by arbitrarily fixing one of the intensiveparameters at a value to one side or the other of its value at the Fig. 4 Schematic isothermal P"-minus pHrO diagram of the invariant point). By this treatmentthe univariant multisystem of Table 1, if kaolinite-phenakite is unstable and reactionsaround the invariantpoint transforminto phenakite-euclase-beryl is stable. Solid circles indicate stable points. points stableand metastable invariant points in theresulting invariant points, open circles metastable Invariant by absent (non-participating) phases in the and divariantfields transform into uni- are labeled multisystem, multisystems (Kao) and (Phe), which are, respectively, above and variantlines. An exampleof sucha transformationis below the BtrlPhe line. Lines are labeled by their slopes(in bars/ givenin Burt (1971,p.192-193). In the presentstudy, joule/mole of ArO). Corresponding reactions are listed in Table 3. a more complicatedexample involves the derivation The saturation line for pure HrO is not shown. of the two multisystems(Phe) and (Kao)on Figure4 by fixing the temperatureat its valueat the left mar- gin of Figure6. 68), one might experiencesome conceptual difficulty Without invokinga magneticfield or otheruncon- in derivingmultisystems on PE-f diagramsby this ventionaldegree of freedom(cl Pippard,1957,p.63- method.Nevertheless, the analogousnature of the constraintsimposed on the slopes,and the identical suggestthat such multisystemsshould Qtz topologies, obeythe samerelations as thoseon LL-u.and p-(or P) diagrams. The secondstep of the derivationconsists of point- ing out that a straightline cutting an invariantpoint dividesthe immediatevicinity of the invariantpoint into two sectors,in which stableand metastableuni- variant reactions are interchanged(as they pass throughthe invariantpoint). This line corresponds to the value of the "fixed" intensiveparameter at the invariantpoint. If the line is movedslightly in one direction,one configurationof the resultingmulti- Bro, / Cor, if it is movedin the other BehJ- Dsp systemnet results;and BeO Chr AlO1.5 direction, the alternative configuration ("residual now remainsto demonstratethat the Fig. 3. Projected compositions of some phases in the system net") results.It BeO-Al,O'-SiOz-HzO, in the presenceof H,O. labelsof the univariantreactions that are metastable o/u BURT: BERYLLIUM MINERAL STABILITIES

on one side of the dividingline correspondto the stated,but not balancedchemically. (The same seems phaseassemblage that isstable on thisside of theline, to be true for P"-T diagrams.)The abovestatements and uiceuersa. This propositioncould be calledthe areillustrated by the examplesthat follow. stable-metastable correspondence for invariant For thisdiscussion, angled brackets ( ) will beused points. to enclosethe namesor abbreviations(Table I ) of the This latter propositionis a rather trivial con- non-participatingphases labeling multisystems, sequenceof the Morey-Schreinemakersrule (Zen, squarebrackets [ ] will similarly label invariant 1966,p. l0-ll) and of Schreinemakers'concept of points,and parentheses ( ) will labelreactions. This the univariantscheme (Zen, 1966,p. 12-14).The usagefollows Burt (1971). interestedreader may verify its applicabilityto any invariantpoint involving univariantreactions that P"-minuspH2O diagram areapproximated by straightlines. At low temperaturesor high valuesof pH2O,ber- It has thus been demonstratedthat the correcr tranditeis stablerelative to phenakite,and the phena- topology for each (n + 3)-phasemultisystem on kite-absent(n + 3)-phasemultisystem (Phe) can be fixed-slopediagrams is specifiedby the choice be- considered.Computer program RnecrroN (Finger tweenthe stabilitiesof two alternativemineral as- and Burt, 1972)is usedto calculateall possiblereac- semblages.For pt-1t"diagrams, the two alternative tionsin this multisystem(Table 3, in part).The reac- assemblagesare relatedto eachother by a balanced tion slopes(in bars/joule/moleof HrO) are then solid-solidunivariant reaction (Burt, l97l); for p"- obtainedfrom equation8 andthe molar volume data minuspHrO diagramsa reaction(or relation)can be in Table L

Table3.Possiblereactions(andcorrespondingmolarvolumechangesforthesolidsinjoules/bar)amongwaterandthephasesinTable l, assumingthat phenakite-kaoliniteis an unstableassemblage. This is the output of computerp.ogt"r RrncrroN (Fingerand Burt, 1972\

Brl Qtz H2o

-2 ____L999 J -4 4 L0 -11 6. tzt o -2 -1 8 -1 -4. s70 -4 1 z -2 -3 s.955 8 1 -4 -5 -3.184

-10 4 -2 7 -IJ L9.252 I 6 5 -26 19.664 1 4 -2 7 -2 -2.481, -5 -4 6.039

-J 1 z -10 -4 7.275 -4 I 4 -10 -9 12.609 L -2 10 -1 -1.941 -1 1 2 -l 5.334 -11 -4 9 z -50 15.039 -2 2 1 -4 -3 3.327 -1 4 -l t -2 -o,62L -4 10 1 2.O84 -1 -8 J -rq 6. )-Ld -4 8 -1 -6 -J 0. 698 -10 a -3 8.584 6 -l -1 -2 -2.629

-7 -1 -J -9 -t -) 20 .166 4 J -18 3.26L -13 50 -7 -3 -9 -26.9r8 -1 4 -3 -2 L.239

-2 20 -3 -10 0.613 3 4 -2 -3 -2.379 18 20 -10 -3 BURT: BERYLLIUM MINERAL STABILITIES 671

The next stepis to plot the multisystem(Phe) on an isothermalP,-minus rrHzO diagram.When this is done(as seenin the lower left part of Fig. 4), the two alternativetopologies are given by the followingrela- tion among the stable and metastableinvariant points: Qtz + Chr * Btr * Kao : Brl * Euc (9) A-/ discussedabove, beryl-euclase is a relativelycom- As q*9. l$\ f/ mon assemblage,whereas the alternativefour-phase bNr. 'oo assemblagequartz-chrysoberyl-bertrandite-kaolin- "Y' ite is unknown.The two invariantpoints labeled [Brl] and [Euc]must then be metastable, as shown, and the points[Qtz], [Chr] [Btr],and [Kao]are stable.(Point A [Kao], labeled[Phe] on Fig. 4, becomesmetastable when phenakiteis considered,as describedbelow.) On Figure 5, an enlargementof the stablepart of Figure4, the assemblageberyl-euclase is stableinside the closedpolygon formed by joining the two points labeled[Qtz], the two points labeled[Chr], and the upperpoint labeled[Btr]. The final step is to determinehow the degenerate U,.,A dehydrationreaction Btrl Phe cuts the multisystem (Phe)determined above. Inspectionof Figure 4 re- A\ vealsthat it may do so (l) below point [Qtz], (2) part Fig. 4, showingstable between and (3) between and Fig. 5, Enlargementof the central of [Qtz] [Chr], [Chr] [Btr], reactionsand invariantpoints. Inset shows chemography (c/. Fig. (4) between[Btr] and [Kao] (labeled[Phe] on Fig. 4 3). Tie linesto kaoliniteare omittedin the upperright areaof the becausethis is whereI placedthe reaction),or (5) diagramwhere other aluminosilicatesprobably become stable. abovepoint [Kao] (labeled[Phe] on Fig. 4). Possi- bilities(l) and(2) abovewould imply that phenakite, tensson,1960; Kalyuzhnaya and Kalyuzhnyi,1963). rather than bertrandite,would typically occur with Tentativelythen, phenakite-beryl-euclase is assumed kaolinite and euclase(in other words, that ber- to be a stableassemblage, and Figure 4 has been trandite would havea very low dehydrationtemper- constructedaccordingly from the data in Table 3. ature indeed). This implication conflicts with the The rarity of phenakite-beryl-euclaseis probably widespreadnatural occurrencesof bertrandite,and dueto the fact that it is a quartz-absentassemblage. possibilities(l) and (2) may thereforebe rejected. With regardto the multisystem(Kao), shown in the Possibility (3) is for practical purposesin- upper right part of Figure4, the metastableinvariant distinguishablefrom possibility(4), becausethe de- pointsare then [Phe], [Brl], and [Euc],and the stable hydrationreaction BtrlPhe is independentof the Btr- onesare [Chr], [Qtz],and [Btr].The metastablepoint absentpoint [Btr]. [Phe] of multisystem (Kao) correspondsto the The above argumentsleave only possibilities(4) formerly stablepoint [Kao] of the multisystem(Phe). and (5). In other words, the dehydrationreaction (Strictly speaking,with regard to the full (r + 4)- Btr/Phe canintersect the multisystemeither above or phasemultisystem of Tablel, the point [Phe,Kao] is below the point [Kao] (labeled[Phe] on Fig. a). metastable.) Thesealternatives correspond to a second(r + 3)- On Figure 5, the assemblagephenakite-beryl-eu- phasemultisystem (Kao), the two topologiesof which claseis stableonly insidethe small trianglewhose aregiven by the relation apicesare labeled [Chr], [Qtz], and [Btr] in themulti- system(Kao). The sizeof this areacould be enlarged Chr * * Btr : Phef Brl * Euc (10) Qtz by movingthe BtrlPhe line down,even to belowthe Neither the left nor the right assemblagehas been lowerpoint [Btr]. As long asthis line doesnot inter- reported from nature.Phenakite, beryl, and euclase sect the lower points [Chr] and [Qtz], the mineral are,however, known as associatedminerals (cf. MFr- compatibility relations, and the fundamental to- 672 BURT: BERYLLIUM MINERAL STABILITIES

pologyof the diagram,remain unchanged. The area of stabilityof theassemblage was made small because the assemblageis not yet describedfrom nature. Incompatibilily of phenakiteand kaolinite The two multisystems(Phe) and (Kao) are stable on oppositesides of the BtrlPhe line (Figs.4 and 5). Extending somewhatthe generalizationthat stable arraysof pointscorrespond to unstableasSbmblages, considerthat stablearrays of multisystensalso corre- spondto unstableassemblages (Burt, l97l). That is, phenakite-kaolinitemust be an unstableassemblage at the temperatureconsidered. (A closeexamination of Figure5 alsoreveals that phenakite-kaolinitemust be unstable.) In order to justify this more-or-lessa posteriori observation,the following compositionalrelations shouldbe noted(cf. Fig.2): Ato[5 , 2 Kao * l1 Phe (ll) * 5 Qtz: 4 Btr * 2 Brl Pvp

Kao* 3Phe:2Euc* Btr* Qtz (12)

7 Kao * 26Phe : l0 Euc* 9 Btr t- 2Brl (13) Fig. 6. Schematic fluid-absent P"-T diagram of part of the The left-handassemblages are unknown;the right- multisystem of Table l. The left axis is drawn at the temperature hand assemblagesale well-known, for which Figs. 4 and 5 are drawn; Z might increaseor decreaseto as described the right. lnset shows chemography for quartz-saturated equilibria above.Kaolinite-phenakite could thereforebe sub- (cf. Fig. 2). mitted as the only incompatibilitywhen program Rn- AcrIoNwas used to generatethe reactions in Table3. invariantpoint correspondsto type IV-21 of P,-T diagram (fluid-absent [Kao] ) Dolivo-Dobrovol'skii(1969; type III-5 if projected The stablemultisystems (Kao) and (Phe)on P"- throughquartz) and that point [Phe]corresponds to minuspHrO diagrams(Figs. 4 and 5) can also be type IV-13 (type III-2 if projectedthrough quartz). drawnas the stableinvariant points [Kao] and [phe] Projectedthrough qvarlz, as shownon the inset,the on a P"-T diagramthat omits water.The result is overallchemography of this multisystembelongs to seenon Figure 6, part of a possible(n t 3)-phase typeQ3 of Day (1972,Fig. 8). The multisystemsnet multisystemsarray for the sevenminerals in Tablel. type of Figures4 and 5 correspondsto type2 of Day Eachwater-absent line on Figure6 corresponds,in (1972,Fig.7). general,to an invariantpoint on Figure4. The ex- P-T (fluid-present ceptionis the degenerateline (Btr, Euc) whichis also diagram ) a line on Figure4. As statedabove, the topology of Figures4 and 5 The left axisof Figure6 is positionedat the tem- shouldbe equivalentto that of a P-T diagramdrawn peraturefor whichthe isothermal diagrams Figures 4 for excesswater, because decreasing pHrO should,in and 5 weredrawn; Z could eitherincrease or decrease general,correspond to increasing7. This relation is to the right (asshown by the label t Z on the hori- evidenton Figure7. Topologically,there is a one-to- zonal axis).Unfortunately, with only molar volume one correspondencebetween Figures 5 and 7 (Fig. 7 information available,it is unknown whetherthe wasso drawn). points [Kao] and [Phe] are stableor metastableif Of course,some of theinvariant points on Figure7 wateris addedto this multisystem,or whetherother may be metastable,due to the participationof other invariantpoints exist stably or metastably. phases,or they may be physicallyunrealizable (i.e., At this point it can be noted that on Figure 6, they may occurat negativepressures). Most natural BURT: BERYLLIUM MINERAL STABILITIES assemblagesappear to form at pressuresabove the two invariantpoints labelled [Qtz] on Figure7. That is, euclaseand euclase-phenakiteseem to be stable with regard to the alternativeassemblages Chr-Brl- Btr-Kao and Chr-Brl-Btr (cl Fig. 6). Natural as- semblagesfurther appear to form below the lower point labeled[Btr] on Figure7. That is,beryl-kaolin- ite seemsto be stablerelative to Chr-Euc-Qtz. Only the invariantpoint [Chr]seemsto fall within theP-T rangenormally involved in the formationof hydro- thermal beryllium deposits. Nevertheless,as dis- cussedbelow, the presenceof bertrandite-beryl-ka- olinite insteadof euclase-quartzcould be due to supersaturationof low-temperaturesolutions with amorphoussilica in placeof quartz. The low P and T reactionson Figure 7 are sche- maticallyshown in moredetail in Figure8. Possible positionsfor the two dehydrationcurves involving the creation and destruction of pyrophyllite are markedby dashedlines. The pyrophyllitecurves are drawn consistentwith the assumptionthat chrysobe- ryl is the only Be-bearingmineral stable with py-

Fig. L Enlargementof the low pressurepart of Fig. 4, showing dehydrationreactions and invariantpoints possibly encountered in nature. Dashed lines show a permitted stability field for pyrophyllite.

rophyllite.In other words,kaolinite-quartz assem- blages are assumed to break down at higher temperaturesthan kaolinite-berylor kaolinite-eu- clase assemblages,as shown. Chrysoberyl-quartz- kaoliniteis stablein the intermediatezone. The py- rophyllite curves could easily be moved to higher temperatureson Figure 8. Discussion Heinrichand Buchi (1969) have shown that berylis unstablewith aluminosilicates,the stableassemblage being chrysoberyl-quartz.This fact explainsthe oc- currence of chrysoberyl in alumina-contaminated .The presentstudy suggeststhat chryso- beryl-quartzremains a stableassemblage to fairly low temperatures,but eventuallyis replacedby kaolinite- euclaseor, more probably, kaolinite-beryl. The stabilityrelations of beryl itselfare of particu' lar interest.It hasearlier been shown (Burt, 1975b) that under high fluorine activitiesberyl breaksdown Fig. 7. Schematic,fluid-present P-? diagramof themultisystem to the assemblagephenakite--quartz or, in the of Table 1, drawn topologically identical to Figs. 4 and 5. PzOuactivities, to Metastablepoints and linesare omitted. Inset shows chemography presenceof fluorapatiteand high (cf. Fig. 3). (CaBePOrF)-topaz-quaftz.The present 674 BURT: BERYLLIUM MINERAL STABILITIES

studysuggests that berylshould hydrate at moderate tranditeand euclasein silica-saturatedand unsatu- pressuresto bertrandite-euclase-q\artz,or at low ratedsolutions. The recenteconomic importance of pressures to bertrandite-kaolinite-qvartz. These and bertranditeas an ore of berylliumwould justify such more complicatednatural hydrothermalalterations a study. A difficulty might be the low temperatures of beryl are extensivelyreviewed by Cerny (1968, involved-probably below 400oC.Should such ex- r970). perimentsbe impractical,carefully-documented stud- When this analysiswas first performedI wasun- ies of selectednatural assemblagesmight still prove awareof the reconnaissanceexperimental work on to be the besttest of the multisystemtopology here berylstability at highpressure by Munson(1967) and proposed.Assemblages of diasporeor pyrophyllite at high temperatureby Ganguli(1972).It was there- with Be mineralsother than chrysoberyl,or of ka- fore gratifying that the multisystemsanalysis cor- olinitewith phenakite,would be especially interesting rectlypredicted the high P and Z breakdownof beryl in this regard. to chrysoberyl* phenakite* quartz(Figs. 4 and5). The experimentaldata explain the steep negative Acknowledgments slopeof the breakdowncurve shown on Figure7. The Interlibrary Loan Service,Aizona State University Li- brary,is to bethanked for their The fact that berylis unstableunder upper mantle helpin locatingnumerous obscure references.Howard W. Day, John R. Holloway,John M. Ferry, conditionsis undoubtedlyof someacademic interest, and DouglasThorpe provided useful reviews. I am alsograteful to althoughgeologists appear to agreethat beryl-bear- Tom Young for computingassistance, as well asto Cyndi Gordon ing pegmatitesare crustalphenomena. In any case, for typing the manuscriptand to Sue Selkirk for drafting the the exact high P and T breakdowncurve of beryl figures.Partial support for this researchwas obtainedfrom the FacultyGrant-in-Aid Program,Arizona remains to be determined.Inasmuch as hydro- StateUniversity. thermally-grownberyl is somewhathydrous (Flani- References gen et al., 1967),anyone undertakingsuch experi- (1967) mentsshould be preparedto Apollonov,V. N. Morphologicalfeatures of the chrysober- encountersome of the yf from Sargardon. (in Russian) Zap. VsesoyuznogoMineral. problemsstudied by Newton(1972). He studiedthe Obs hches tua. 96. 329-332. influenceof wateractivity on thehigh pressure break- Aver'yanova,I. M. (1962) of beryl alterations.(in downof cordierite,another low-density silicate. Russian)Mater. po Mineral. Kol'sk Poluostoua,Akad. Nauk Moving on to the hydrousphases bertrandite and SSSR,Kol'sk Fllial,2 , 140-142(not seen;extracted from Chem. Abstracts,59, 96'19h,1963). euclase,what doesthe analysishave to say? # First, it Bakakin,V. V. and N. V. Belov(1962) chemistry of beryl. providestwo plausible explanationsfor the com- Geo kh i miy a, n o. 5, 420-433.ltr ansl.G e o c he mi s t ry no. 5, 484-500 parativerarity of euclase.Figures 7 and 8 showthat (1e62)1. euclase,although stable to highertemperatures than Bank,H. (1974)Smaragd, Alexandrit and Rubinals Komponen- bertrandite,is stableonly over a limitedrange of p ten einerParagenese vom Lake Manyarain Tansania.Z. dtsch. gemmologischen Gesellschaft, 2 3, 62-63. and T. Its stability is reducedin the presenceof Beus,A. A. (1960)Geochemistry of Berylliumand GeneticTypes of quaftzto a narrow sliceof P-Z possibly space, with a BerylliumDeposits. Akad. Nauk SSSR,Moscow. [transl. Free- pressureminimum at the point [Chr] (Fig. 8). Super- man,San Francisco (1967)1. saturationof hydrothermalfluids with amorphous -, B. P. Sobolevand Yu. P. Dikov (1963)Geochemistry of silicamight further reduce its stabilityin naturalenvi- beryllium in high temperaturepostmagmatic mineralization. ronments,and might Geokhimiya,no. f,297-304. [transl.Geochemistry, no. 3, 316- alonebe responsiblefor its fail- 326(1963)1. ure to appear(i.e., it would metastablyshift the fol- Bukin, G. V. (1967)Crystallization conditions of phenakite-ber- lowingreaction at invariantpoint [Chr] to the right: trandite-quartzassociation (experimental data). Dokl. Akad. 22 Euc + 26 SiO, (amorphous)- Btr * 6 Brl f 5 Nazl< S,SSR,176, 664-66'1. ltransl. Dokl. Acad. Sci. USSR, Kao). Earth Sci.Section, 176, l2l-123 (1968)1. (1968) Assemblages Burnol, L. Le beryllium.Bull. Bur. RecherchesGeol. Mini- that couldtake the placeof euclase- bres,secI.2, no 2, l-75. quartz include bertrandite-kaolinitewith falling Z, Burt, D. M. (1971)Multisystems analysis of the relativestabilities and beryl-kaoliniteor beryl-chrysoberylwith rising of babingtoniteand ilvaite. CarnegieInst Wash.Year Book, 70, 7. Euclaseitself probably dehydrates to bertrandite- t89-t97. - chrysoberyl-berylor (moreprobably, or with rising 11975a)Natural fluorinebuffers in the systemBeO-AlrOr- (abstr.). P) to phenakite-chrysoberyl-beryl. SiOr-F,O-r Trans.Am. Geophys.Union, 56, 46'1. - (1975b)Beryllium mineral stabilities in the model system Thesehypotheses could be testedby a carefulex- CaO-BeO-SiOr-PrOs-F,O-1and the breakdownof beryl.Econ. perimentalstudy of the dehydrationequilibria of ber- Geol..70. 1279-1292. BT]RT: BERYLLIUM MINERAL STABILITIES 675

- (1976) Hydrolysis equilibria in the systemK,O-Al,Os- Sokolov, Ed., Zonal'nost' gidrotermal'nykh rudnykh mestorozh' SiOr-HrO-C'lrOr:comments on topology.Econ. Geol., 7l, 665- denii,I, 239-266,Izd. Nauka, Moscow. 671. Govorov, I. N. (1958)Features of the mineralogyand genesisof - (1978)Discussion: a working model of someequilibria in the tin-beryllium-fluoritedeposits of the Far East. Izuestiya the systemalumina-silica-water. Am. J. Sci.,278, 244-250. Akad. Nauk SSSR, Ser. Geol., no. l, 62-73. llransl. Izuestia Cassedanne,J. (1970)L'euclase au Bresil.Bull. Assoc fr. Gemmol- Akad Nauk SSSR, Ser. Geol.,4'l-55 (1958)l' ogie,no.24, 10-12. Haas,H. and M. J. Holdaway(1973) Equilibria in the system Cerny,P. (1968)Beryllumwandlungen in Pegmatiten-Verlaufund AlrO,-SiOr-HrO involving the stability limits of pyrophyllite' Produkte.Neues Jahrb. Mineral. Abh., 108,166-180 and thermodynamicdata of pyrophyllite.Am. J Sci.'273 ' 449- - (1970) Reviewof some secondaryhypogene parageneses 464. after early minerals. Freiberger Forschungshefte,C Hawthorne,F. C. and P. Cerny(1977) The alkali positionin Cs-Li 270, 47-67. beryl. Can Mineral., l5, 414-421 - (1975)Alkali variationsin pegmatiticberyl and their pet- Heinrich,E. W. and S. H. Buchi(1969) Beryl-chrysoberyl-sillima- rogeneticimplications. Neues Jahrb. Mineral. Abh., 123, 198- nite paragenesisin pegmatites.Indian Mineral , l0' l-7- 2r2. Kalyuzhnaya,K. M. andV. A Kalyuzhnyi(1963) The paragenesis Chao, Chuen-Lin(1964) Liberite (LLBeSiOr), a new -be- of accessoryberyl, phenakite,and euclasein topaz-morion ryllium silicatefrom the Nanling ranges,South China.Ti Chih (black smoky quartz) pegmatites.(in Russian)Mineral. Sb. H suehPao (Acta Geol. Sinica),44 , 334-342(not seen,extracted (L'vov),17,136-147. from Chem.Abstructs,6l, # l584ld, 1964). Kayode, A. A. (1971)A kaolinitegreisen from Dorowa-Babuje, Day, H. W. (1972)Geometrical analysis of phaseequilibria in northernNigeria. Econ. Geol', 66, 811-812. ternarysystems of six phases.Am. J. Sci, 272,711-734. Kerr, P. F. (1946)Kaolinite after beryl from Alto do Giz, . - (1976)A working model of someequilibria in the system Am. Mineral. 3l. 435-442. alumina-silica-water.Am. J Sci. 276. 1254-1284. Komarova,G. N. (1974)Typomorphic minerals of aposkarngrei- - (1978)A working model of someequilibria in the system sens.(in Russian)In N. V. Pavlov,Ed., Problemyendogennogo alumina-silica-water:reply. Am J. 9ci.,278, 250-253. rudoobrazouaniya,p. 222-234. Izd. Nauka, Moscow. Dolivo-Dobrovol'skii,V V. (1970)Types of invariantpoints of Korzhinskii,D. S. (1957)Physicochemical Basis of theAnalysis of physical-chemicalsystems and order geometry.(in Russian) the Paragenesisof Minerals,Izd' Akad. Nauk SSSR'Moscow' Oche rki Fiziko- Khi miches ko i Petologi i, 2, 281-296. Izd. Nauka, [transl.Consultants Bureau, New York (1959)]. Moscow. Kuz'menko,M. V. 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1043. r 40, t086-1089( l 963)1. Newton, R. C. (1972)An experimentaldetermination of the high - and - (1964)Precise determination ofthe crystalstruc- pressurestability limits of magnesiancordierite under wet and ture of bertrandite-Ben(SirOr)(OH)2.Kristallog rafiya, 9, 55| - dry conditions.J. Geol.,80, 398420. 553. [transl.Souiet Phys.-Crystallogr., 9, 458-460(1965)]. Novikova,M. I. (1964)Euclase from pneumatolytic-hydrothermalStrand,T. (1953)Euclase from lveland,occurring as an alteration depositsof the Far East. (in Russian)Trudy. Mineral. Muz., productof beryl.Norsk Geol.Tidsskrift, 3l, l-5. Akad. Nauk SSSR, 1J, 223-228. Syromyamnikov,F. V., A. P. Makorovaand I. l. Kupriyanova - (1967)The processesof phenakitealteration. (in Russian) (1971)Experimental study of beryl and phenakitestability in Zap. VsesoyuznogoM ineral. Obshchestua, 96, 418-424. aqueous solutions. Zap. VsesoyuznogoMineral. Obshchestua, Okrusch,M. (1971)Zur GeneseVon Chrysoberylund Alexandrit- 100,222-225.ltransl. Int. Geol.Reu., 14,837-839 (1972)1. Lagerstlitten.Eine Literaturiibersicht.Z. Dtsch. Gemmologisch- Takubo,H., S. Kume and M. Koizumi(1971) Crystal growth of en Gesellschaft,20, ll4-124. somesilicate minerals under high pressure.Mineral. Soc.Japan, Olsen,D. R. (1971)Origin of topaz depositsnear Ouro Preto, Spec.Pap., I,47-51 (Int. Mineral.Assoc., 7th Gen. Meet., 1970, Minas Gerais,Brazil. E con.G eol., 66, 627-631. Pap.Proc.). Petkol B. (1976)Beryllium. ln Mineral Factsand Problems,i'975 Van Valkenburg, A. and C. E. Weir (1957) Beryl studies edition U.S. Bur. Mines Bull. 667. 3BeO.AI,OB'6SiOz(abstr.). Geol. Soc. Am. Bull.,68, 1808-1809. Pippard, A. B. (1957) Elements of Classical Thermodynamics. Vlasov, K. A., Ed. (1966) Geochemistryand Mineralogy of Rare CambridgeUniversity Press, Cambridge. Elementsand Genetic Types of their Deposits.Yol. 3, Genetic Riebling,E. F. and D. A. Duke (1967)BeO.Al,O,.SiO, system: Typesof Rare-elementDeposits. Izd. Nauka, Moscow. [transl. structuralrelationships of crystalline,glassy, and moltenberyl. IsraelProgram for Sci.Translations, Jerusalem (1968). J. Mater. Sci.,2,33-39. Wilson, W. (1965)Synthesis of beryl under high pressureand Robie,R. A., P. M. Bethkeand K. M. Beardsley(1967) Selected temperature.J. Appl Phys.,36,268-270. X-ray crystallographicdata, molar volumes,and densitiesof Wyart, J. and S. Scavnicar(1957) Synthdsehydrothermale du minerals and relatedsubstances. U. S. Geol.Suru. Bull 1248. beryl. Bull. Soc.fr. Mineral. Cristallogr., 80, 395-396. Ross,M. (1964)Crystal chemistry of beryllium.U. S. Geol.Swu. Zen, E-an (1966)Construction of pressure-temperaturediagrams Prof. Pap.468. for multicomponentsystems after the method of Schreinema' Sainsbury,C. L. (1968)Tin and berylliumdeposits of the Central kers-a geometricapproach. U. S. Geol.Suro. Bull. 1225. Yotk Mountains,western Seward Peninsula, Alaska. In J. D. - (1974)Prehnite- and pumpellyite-bearingmineral assem- Ridge, Ed., Ore Depositsin the United States, 19i3-1967, blages,west side of theAppalachian metamorphic belt, Pennsyl- Graton-Salesuolume, vol.2, p. 1555-1512.AIME, New York. vaniato Newfoundland.J. Petrcl.,j,5,l9'l-242. Shabynin,L. I. (19'14)Rudnye mestorozhdeniya uformatsii magne- - and E. H. Roseboom,Jr. (1972) Some topological relation- zial'nykhskarnou. Izd. Nedra, Moscow. shipsin multisystemsof n I 3 phasesIIL Ternarysystems. lz. Sharp,W. N. (1961)Euclase in greisenpipes and associateddepos- J. Sci..272.677-'110. its,Park County, Colorado. Am. Mineral.,46,1505-1508. Solov'eva,L. P. and N. V. Belov(1961) of the mineralbertrandite, Be.SLO'(OH)r. Dokl. Akad. Nazft SS,SR, Manuscript receiued, September 9, 1977; accepted 140,685-688.ftransl. Dokl. Acad. Sci.USSR, Earth Sci.Section for publication, December 6, 1977.