Multisyste_ms analysis of beryilium minerar stabilities:the system BeO-A[rOa_SiO2_H2O

DoNer.n M. Bunr

Department of Geology, Arizona State (JniuersitvTempe, Arizona8528I

American Mineralogist, Volume 63, pages 664_676, l97g

The present paper represents a first attempt toderive the topology of the stability fields of theseberyllium minerals. The derivation depends on natu-ral assemblages (cf. Beus, 1960; Vlasov, 1966: Burnol.t968; Cerny, t963), Fortran program RrncrroN(Finger and Burt, 1972), molar volume data (Robie elal., 1967), and multisystems analysis (Korzhinskii,1957). Reliable thermochemical or experimental dataon most of the phases are lacking, so that the resultsare ofnecessity topological rather than quantitative.

Many of the results were collectively derived as alaboratory assignment by my spring term 1977 classin ore deposits at Arizona State University. Themethod, here summarized in advance, consisted bas-ically of the following five steps: (l) The system BeO-AlrOs-SiOr-HrO was searched for all possible phasesthat occur as minerals or that have been synthesized.A number of these phases were eliminated from con-

Abstract

seven commonly associated minerals in the system Beo-Alror-Sior-Hro include chry-soberyl, phenakite, euclase, bertrandite, beryl, kaolinite, and qiuit . The phase rule impliesthat not more than six of these minerals can coexist at an invariant point, and, with theaddition of an aqueous phase, the association constitutes an (n * 4; ptrase (negative twod-egrees of freedom) multisystem. The apparent incompatibility of taotinite with phenakiteallows the splitting of this unwieldy multisystem into two smaller (n + 3) phase multisystems,which may be labeled (Kao) and (phe). Moiar volume data, compuier program RrlcrroN, andnatural assemblages can then be used to derive the presumably stabie cJnfiguration of thesemultisystems on an isothermal p"-minus pHro diagram . n, p-r diagram projected throughthe aqueous phase should have the same topology, and can similarlf be drawn.. on the resulting diagrams, three invariant poinis rabeled tchrl, tBr;;, and [etz] are stable inthe. multisystem (Kao), and three distinct

-but identically-fuU"i.O point, u.. stable in rhemultisystem (Phe). An implication of this topology via ihe "r.tu.tubl"-rtable correspon-dence," is that the assemblage phenakite + euclase * beryl (* aqueous phase) has a finite

i' I;ix, " ii,l'J.?lT"t' ::ff ,,,j :r;: :":.T' ?ts why euclase is much rarer than bertrandite.and its stability field, especially in the presencet low p and T. Most reactions involving thebly occur at temperatures too low for conve_0.c).

Introduction

0o03-004x / 7 8 /0708_0664$02. 00 664

BURT: BERYLLIUM

siderat ion, leaving seven minerals p lus an aqueousf lu id. (2) The resul t ing e ight-phase mul t isystem was

simplif ied to a six-phase pseudoternary system byprojecting through HrO and by noting that phenakite

and ber t randi te then p lot at the same point . (3) An

isothermal P,-minus pHrO diagram was plotted for

th is s impler mul t isystem. (4) Natura l assemblageswere used to determine the most l ikely intersection of

the degenerate dehydration reaction of bertrandite to

phenaki te wi th the mul t isystem. (5) The resul t ing P"-

minus pHrO diagram was t ransformed into a topo-logically identical schematic Pr"o-T diagram.

Phases

The quaternary system BeO-AlrOr-SiOr-HrO con-ta ins, among others, the seven commonly associ -

ated phases l is ted in Table l . Corresponding molar

volumes are g iven in joules/bar . Eight addi t ionalphases have been omitted from the present study,

largely because they have never been reported in as-

sociation with beryl (Table 2). The compositions and

assumed natura l compat ib i l i t ies of anhydrous miner-

als in the system BeO-AlrOr-SiOz are shown in Fig-

ure I (Burt, 1975a a summary of evidence appears

under the d iscussion of natura l assemblages) . Simi-

lar ly , the composi t ions and known compat ib i l i t ies of

most phases in the system BeO-AlzOs-SiO2-H2O,projected through excess quartz, are shown in Figure

2. The dashed lines on this figure refer to uncertain or

conflicting assemblages variously reported in the l it-

erature (again, consult the section on natural assem-

blages) .In the fo l lowing d iscussion, the phases in Table I

wi l l be assumed to be sto ich iometr ic . Natura l bery l

may conta in considerable a lka l is (Na, Cs, and L i )

Be0

Be (OH) 2

A12O3

A1o (OH)

A1(ori) 3BerSlo4 (on)

2 .Hro

Ar2s io5

At2si40lo (oH) 2

*Data from Roble et al- . (1967) excepE for behoite

pyrophyt l l te. Behol i -e from x-ray data for B-Be(OH)2

( i s O i ) ; p v r o p n v r l i t e r e c a l c u r a t e d f r o n D a v ( 1 9 7 5 ) '

andln Rosa

and water , main ly in channel posi t ions (Bakakin and

Befov, 1962: Cerny, 1975; Hawthorne and Cerny,

1977), and natural beryl and chrysoberyl may also

conta in Cr3+, Fe3*, V3+, Sc3+, and other ions sub-

stituting for A13+. Based on available data, there are

no indicat ions of major composi t ional var iat ions in

natura l euclase, ber t randi te, or phenaki te '

Review of exPerimental studies

This review of experimental studies and the follow"

ing review of natural occurrences have been made as

complete as possible, in order to succinctly summa-

r ize in one p lace the conf l ic t ing data in i t ia l ly avai lable

on the system BeO-AlzOr-SiOr-HrO. Much of this

data is seen to be unnecessary for the multisystems

analysis that follows, and these two sections may

therefore be skimmed during a first reading without

much loss of cont inui tY.Phase equil ibria in the system AIrOB-SiOr-HrO

have recent ly been summarized by Burt (1976' 1978)

Abblev. FotEula Molar Volwe*( I o u l e s / b a r )

Bro

Beh

Cor

D s p

B 1 r

AI6

P v P

MINERAL STABILITIES

Table 2 Abbreviat ions,

add i t i ona l m ine ra l s

66s

formulas, and molar volumes* of e ight

in the system BeO-Al ,Og-SiOz-H,O

Nee

Bronel l i te

Behoite

corundun

Dlaspore

Gibbsite

B e r y l l i t e

Andalusi te

Pyrophyl l i re

0 . 8 3 1

2 . 2 2

2 . 5 5 8

t . 7 7 6

3 . 1 9 6

1 2 . 8 3

Table I Abbreviat ions. formulas, and molar volumes* of seven

minerals in the system BeO-AlrOr-SiO,-H,O

Nane Abbrev. MoIa! volune

0""1eel!eE)Chrysoberyl

Phenakite

EucIa6e

Bertrandite

Beryl

Kao 1 init e

quartz

BeAI204

Be2si04

BeAlSioO (Ol{)

Be4S1207 (0H) 2

B e ^ A 1 ^ S i . O - ̂J 2 O L 6

A12S1205 (oH) 4

s i02

3.432 + ,002

3 . 7 1 9 + . 0 0 4

4 . 6 5 7 + . 0 1 0

9 . 2 1 7 + . 0 5 0 ( ? )

20 ,355 + .O25

9 .952 + .026

2.2688+.0001

Ch!

Phe

Euc

B t r

B r I

Kao

Q t z

*Data f lom Roble et af . (1957) except for bert tandite ' The

bertrandite value vas calculated fron unit cel- I dinensions given

b y S o l o v r e v a a n d B e l o v ( 1 9 5 1 ) , a n d c i t e d i n R o s s ( 1 9 5 4 ) . S t t g h l l y

di f ferent uni t cel l dimenslons in Solov'ewa and Belov (1964) give

a value of 9,177; use of densit les measured on natulal Eater ials

( 2 . 6 0 + . 0 3 ) g i v e s a v a l u e o f 9 . 1 6 + . 1 0 .

BeO

Fig l . Moderate P and f mineral compat ib i l i t ies deduced for

lhe system BeO-AlrOr-SiOr, based on natural assemblages'

ChrCor

Fig. 2. Compatibilities among some minerals in the systemBeO-AlrOr-SiO,-HzO, based on natural assemblages. euartz isassumed present. Dashed lines indicate uncertain or conflictinsmineral compatibi l i t ies.

and Day (1976,1978), and little need be added here.

assumed to be unstable at low to moderate temper_atures. Studies of the related binary system BeO_SiO,by Morgan and Hummel (1949) revealed phenakitias the only intermediate phase; it melts incongru-ently. In the binary system BeO-HrO, Newkirk (1964)dehydrated behoite to bromellite at l70oC, 1.3 kbarand 200oC, 4. I kbar, but this reaction was not reversed.In the ternary BeO-SiOr-HrO, Bukin (1967) readilysynthesized both bertrandite and phenakite between300 and 500oC, 720 atm, but bertrandite appearedfavored below 400"C.

The anhydrous ternary BeO-AlrOr-SiO, has been

hydrothermal syntheses under unspecified conditions(500-600'C, 0.7-1.4 kbar according to Nassau,1976).

Studies of the incongruent melting behavior ofberyl by Ganguli and Saha (1965) and Miller andMercer (1965) were confirmed by Riebling and Duke(1967). Liquid immiscibility occurs in the melts.Ganguli and Saha (1965) delineated a ternary eutecticat 151515'C involving chrysoberyl, phenatite, andcristobalite, and Ganguli (1972) in a subsolidus studv

MINERAL STABILITIES

determined that beryl breaks down to chrysoberyl,phenakite, and cristobalite between 1300 and1400.c.

Studies of beryl synthesis at high pressures wereinitiated by Wilson (1965), who reported direct syn-thesis of beryl from its melt at pressures to 20 kbar.Beryl and phenakite reportedly were synthesized byTakubo et al. (1971) to 20 kbar at 1600.C. The phasecharacterizations (or quenching procedures) in theabove two studies are questionable(cf, Nassau, 1976)in light of the results of Munson (1967). His recon-naissance studies indicated that natural beryl breaksdown to chrysoberyl, phenakite, and quartz at ap-proximately 15.5 kbar and l340oC and to chrysobe-ryl, phenakite, and coesite at 45.5 kb, 1050"C. Asdiscussed below, this high p subsolidus breakdown ofberyl is consistent with molar volume data (Table I ).

Studies of the complete quaternary BeO_AlzOr_SiOr-HrO initially involved hydrothermal synthesesof beryl and emerald. Van Valkenburg and Weir(1957) synthesized beryl between 500 and g50"C at Ito 2 kbar, but reportedly obtained phenakite plusglass above 900"C. Wyart and Scavnicar (1957) syn-thesized beryl between 400 and 600oC at 400-1500bars. At 600'C they obtained beryl * chrysoberyl *phenakite, and with the addition of CrrO, to replaceAl2Os, beryl * phenakite t quartz * Cr2O3. Frondeland Ito (1968) readily obtained beryl at 6g0o and 2kbar, and also synthesized the Sc-Fe analogue ofberyl (bassite), with phenakite, quartz, and hematite.Other syntheses are reviewed by Nassau (1976).

Beus e, al. (1963) studied the hydrothermal altera-tion of beryl in various HF-bearing solutions between500 and 600"C. They altered beryl to quartz, to ber-trandite, and to bertrandite * muscovite. A similarseries of leaching experiments was performed by Syr-omyamnikov et al. (1972). They altered beryl to chry-soberyl * phenakite at temperatures above 300"Cand 500 kg/cm2 (approximately 500 bar). They alsoleached phenakite in alkaline solutions to produce asurface coating of chkalovite, NarBeSi2Ou.

A synthesis study of the complete system BeO_AI,OB-SiOz-HrO between 300 and 700"C. I kbar isreported by Ganguli and Saha (1967). They producedberyl, chrysoberyl, phenakite, bromellite, ber-trandite, quartz, mullite, pyrophyllite, and kaolinite.They hydrated phenakite to bertrandite at about500'C and broke beryl down to bertrandite solidsolution plus pyrophyllite at about 485oC. The prob-able lack of equilibrium in these experiments is in-dicated by the fact that they reportedly grew py-rophyllite to 550oC, which is about 200o above the I

BURT,, BERYLLIUM

Hzo

----:115::

BURT: BERYLLIUM MINERAL STABILITIES

kbar equilibrium dehydration temperature deter-mined by Haas and Holdaway (1973).

Ganguli and Saha's experiments involving py-rophyllite are also inconsistent with natural assem-blages, as shown by the following compositional rela-tions (abbreviations in Tables I and 2):

2 Brl * 2Btr + 5 Pyp : 14 Euc -t 22Qtz ( l )P h e * P Y P : 2 E u c i 3 Q t z ( 2 )

7 Phe * Pyp + Qrz: 2 Btr * 2 Brl (3)3 B t r + P V P : 4 B r l * 7 K a o * Q t z ( 4 )

B t r * 9 P y p : 4 C h r * 5 K a o * 2 8 Q t z ( 5 )B r l + 4 P y p : 3 C h r * 2 K a o * l S Q t z ( 6 )

Br l * PYP: Chr * 2Euct Qtz (7 )

As discussed below, most of the assemblages on theright sides of the above equations have been reportedfrom nature; the alternative assemblages involvingpyrophyllite are unknown, and pyrophyllite wastherefore omitted from the multisystems analysis.

In summary, virtually all experimental studies in-volved short-duration synthesis runs rather thanequilibrium (stable or metastable) reversals. Never-theless, it appears that beryl breaks down both athigh 7'and at high P, and that bertrandite is stable atlower temperatures than phenakite. It is also prob-able (Wyart and Scavnicar, 1957, and later studies)that beryl-phenakite-quartz, beryl-chrysoberyl-phenakite, and less clearly beryl-chrysoberyl-quartzare stable assemblages at moderate P and T, asshown on Figure l. None of the above studies in-volved the synthesis of euclase, and thus its role in theabove equilibria will have to be answered from natu-ral assemblages.

Natural assemblages

The moderate P and T compatibilities among theanhydrous beryllium minerals have been deducedfrom numerous natural occurrences (Fig. l; cf. Burt,1975a). Examples of the incompatibility of beryl withthe aluminosilicate minerals in pegmatites are givenby Heinrich and Buchi (1969); the stable assemblageis chrysoberyl-quartz. Chrysoberyl-phenakite (+ beryl)assemblages are reviewed by Okrusch (1971), whoalso reviews chrysoberyl-corundum and chryso-beryl-aluminosilicate localities. To the best of myknowledge, beryl has not been found with bro-mellite or corundum, although Bank (1974) has ap-parently found corundum (ruby), beryl (emerald),and chrysoberyl (alexandrite) in a single hand speci-men. Similarly, phenakite, chrysoberyl, and qvartzmay occur as associated minerals, but they have notall been found in direct contact (implying the instabil-

ity of beryl). Four reported bromellite occurrencesare mentioned in Burt (1975b); a fifth from China is

mentioned by Chao (1964) and is described byShabynin (197 4, P. 228).

Natural assemblages involving the hydrous phases

could be shown on a tetrahedron, but most assem-blages involve quartz, so that a triangular diagram inthe presence of excess quartz should be adequateinitially (Fig. 2). Solid lines on Figure 2 depict well-documented and/or common natural assemblages;dashed lines indicate poorly documented and/or con-flicting assemblages. Unfortunately, most of the un-certaintieis again involve euclase.

As examples of these uncertainties, consider thatthe assemblage beryl-bertrandite-kaolinite has beendescribed or implied (Aver'yanova, 1962; Gallagherand Hawkes, 1966), but the conflicting assemblageeuclase-quartz is more common, with beryl (Gallag-her and Hawkes, 1966), kaolinite (Olsen, l97l; Cas-sedanne, 1970), or bertrandite * beryl (Strand, 1953;Mirtensson, 1960; Sharp, 196l). The assemblageseuclase-bertrandite (Sainsbury, 1968) and euclase-bertrandite-beryl (Komarova, 1974) are also knownfrom silica-undersaturated environments.

The extremely common assemblage bertrandite-beryl rules out the assemblage phenakite-euclase-quartz, which has apparently not been documented,although all three minerals may occur in the same

deposit (Mirtensson, 1960, and others). In silica-un-dersaturated environments, however, euclase-phena-kite assemblages are described from the Soviet Union(Kalyuzhnaya and Kalyuzhnyi, 1963; Novikova,1964: 1967: Getmanskaya, 1966; Komarova, 1974;Ginzburg et al., 1974).

Kaolinite-beryl assemblages are also described(eerny, 1968;Kerr, 1946; Kayode,l9Tl); the alterna-tive assemblage chrysoberyl-euclase-quartz has ap-parently not been reported. A bertrandite-kaolinite-quartz assemblage is reported by Levinson (1962)and chrysoberyl-kaolini Le-qxartz assemblages prob-ably occur in hydrothermal alteration zones (cfGovorov, 1968; Sainsbury, 1968), although they arenot definitely reported.

As regards some of the minerals in Table 2, behoiteis known from only two localities (Montoya et al.,1964; Ehlmann and Mitchell, 1970);at neither does itoccur with any of the minerals of Table l. In thesystem BeO-SiOr-HrO, it presumably is stable withbertrandite and bromellite, but not with phenakite orquartz. In the system BeO-AlrOs-HrO it presumablyis stable with diaspore, but not with chrysoberyl.These remain conjectures.

66'r

668 BURT.' BERYLLIUM MINERAL STABILITIES

Beryllite, reported from a single locality (data sum-marized in Kuz'menko, 1966), is compositionallyequivalent to a mixture of bertrandite, behoite, andwater, but it only occurs with the poorly character-ized phases "sphaerobertrandite" and ..gelbertran-

dite" (hydrated bertrandites, more or less). Like be-hoite it is probably stable only at such low tem-peratures that it can safely be neglected.

As mentioned in the review of experimental stud-ies, pyrophyllite presents a particular problem amongthe hydrated aluminous minerals, inasmuch as it ap-parently has never been reported as occurring withany beryllium mineral. I have tentatively shown it asbeing compatible only with chrysoberyl in silica-satu-rated environments.

Finally, diaspore, like andalusite and corundum, isknown only with chrysoberyl (Apollonov, 1967;Sainsbury, 1968), and, like the other minerals inTable 2, will not be considered further.

To summarize, the natural assemblages have notelucidated the unknown role of euclase. The assem-blage beryl-bertrandite-kaolinite suggests that eu-clase is unstable with quartz, but euclase typicallyoccurs with quartz. The assemblage euclase-phena-kite suggests that euclase is stable at higher temper-atures than bertrandite (chemically, hydrated phena-kite), but euclase is much less common thanbertrandite.

These ambiguities suggest that there may existsolid-solid, P- and ?'-dependent reactions among theBe-bearing phases; such reactions can be investigatedby means of multisystems analysis (Korzhinskii,1959; Burt, l97l) and a computer program to gener-ate the relevant reactions (e.g., RnecrroN: Finger andBurt, 1972).

Multisystems analysis

S implifu ing the multisystem

In the quaternary system BeO-AlrOr-SiO2-H2O,not more than six phases can stably coexist at aninvariant point. If HzO fluid is added to the sevenphases in Table l, the resulting eight-phase associa-tion constitutes an (r * 4)-phase multisystem, wherer is the number of components. In terms of the phaserule, this multisystem has negative two (-2) degreesof freedom.

Such a multisystem is unwieldy; how can it besimplified? A first step is to recognize that only equi-libria occurring in the presence of aqueous fluid areof practical interest; "projecting through water"eliminates one of the eight phases and topologically

reduces the number of components by one, to three.Nevertheless, an (n * 4)-phase multisystem still re-mains, and previous analytical considerations ofthree-component systems (Zen and Roseboom, 1972;Day, 1972) have only considered (n * 3)-phase multi-systems. Another simplification is needed. [Note that"projecting through quartz" still leaves an (n -f 4)-phase binary multisystem, and results in a loss ofgenerality.l

The second simplification is made possible by thefact that, projected through HrO, two of the phases,bertrandite and phenakite, plot at the same point(Fig. 3). A P-T diagram will therefore be split in twoby the degenerate dehydration reaction convertingbertrandite to phenakite. Reactions involving eitherphase will be refracted as they cross this line, but theunderlying topology will be unaffected. For topologi-cal purposes, then, the system already constitutes an(tr + 3)-phase multisystem. It belongs to chem-ography type Qc of Zen and Roseboom(1972, Figs. 3and 8) and Day (1972, Fig. 8).

Using molar uolume data

Purely topological approaches to multisystemsanalysis can become exceedingly cumbersome (Burt,1978). A less cumbersome procedure in the presentcase is to use the molar volume data in Table I toconstruct an isothermal P"-minus pHrO diagram(Marakushev, 1973, and e arlier papers going back to1964; cf. Zen,1974). This construction is based on thethermodynamic relation

( ='r+=) : - an=Yzo (8)\ 0pH2O l7 AV"

where ArHrO is the number of moles of water in-volved in a dehydration reaction, and AZ" is thereaction volume change for the solids. If it is assumedthat decreasing pHrO corresponds to increasing 7,this diagram should, in general, have the same to-pology as a P-T diagram in the presence ofan aque-ous fluid.

The main advantage of the isothermal P"-minuspH"O diagram is that the reaction slopes are deter-mined by the molar volumes of the solids, as shownby equation (8) above. If compressibilities and solidsolution are neglected, the slopes are constant (i.e.,the reactions define straight lines). This constraint isanalogous to the compositional constraints that fixthe slopes on, e.g., a pHrO-pCO2 diagram involvingpure substances (l Korzhinskii, 1957).

On such fixed-slope diagrams, any (n * 3)-phase

BURT: BERYLLIUM MINERAL STABILITIES 669

multisystem has only two alternative topologies, re-lated to each other by an interchange of stable andmetastable invariant points (Korzhinskii, 1957). Theuse of molar volume data to construct a P"-minuspHzO diagram therefore yields only two possibletopologies for each (n + 3)-phase multisystem-asimplification when compared to the several topol-ogies yielded by compositional considerations alone(cf. Day,1972).

The metastable-stable correspondence

For each topology, the labels of the invariantpoints that are metastable correspond to the phaseassemblage that is stable, and uice uersa (Burt, 197l).This proposition could be called the metastable-stable correspondence for (n f 3)-phase multi-systems. A simple derivation is given below'

The first step of the derivation consists of notingthat an (n + 3)-phase multisystem can be derivedfrom an invariant point involving an equal number ofphases by subtracting one degree offreedom (i'e.,byarbitrarily fixing one of the intensive parameters at avalue to one side or the other of its value at theinvariant point). By this treatment the univariantreactions around the invariant point transform intostable and metastable invariant points in the resultingmultisystem, and divariant fields transform into uni-variant lines. An example of such a transformation isgiven in Burt (1971, p.192-193). In the present study,a more complicated example involves the derivationof the two multisystems (Phe) and (Kao) on Figure 4by fixing the temperature at its value at the left mar-gin of Figure 6.

Without invoking a magnetic field or other uncon-ventional degree of freedom (cl Pippard, 1957,p.63-

Qtz

Cor,Dsp

Chr AlO1.5

Fig. 3. Projected compositions of some phases in the system

BeO-Al,O'-SiOz-HzO, in the presence of H,O.

Fig. 4 Schematic isothermal P"-minus pHrO diagram of the

multisystem of Table 1, if kaolinite-phenakite is unstable and

phenakite-euclase-beryl is stable. Solid circles indicate stable

invariant points, open circles metastable points. Invariant points

are labeled by absent (non-participating) phases in the

multisystems (Kao) and (Phe), which are, respectively, above and

below the BtrlPhe line. Lines are labeled by their slopes (in bars/

joule/mole of ArO). Corresponding reactions are listed in Table 3.

The saturation line for pure HrO is not shown.

68), one might experience some conceptual difficultyin deriving multisystems on PE-f diagrams by thismethod. Nevertheless, the analogous nature of theconstraints imposed on the slopes, and the identicaltopologies, suggest that such multisystems shouldobey the same relations as those on LL-u. and p-(or

P) diagrams.The second step of the derivation consists of point-

ing out that a straight line cutting an invariant pointdivides the immediate vicinity of the invariant pointinto two sectors, in which stable and metastable uni-variant reactions are interchanged (as they pass

through the invariant point). This line corresponds tothe value of the "fixed" intensive parameter at theinvariant point. If the line is moved slightly in onedirection, one configuration of the resulting multi-system net results; and if it is moved in the otherdirection, the alternative configuration ("residualnet") results. It now remains to demonstrate that thelabels of the univariant reactions that are metastable

Bro, /BehJ-

BeO

<%\1."t\

\ t . - - \\ . a - - -

o / u BURT: BERYLLIUM MINERAL STABILITIES

on one side of the dividing line correspond to thephase assemblage that is stable on this side of the line,and uice uersa. This proposition could be called thestable-metastable correspondence for invariantpoints.

This latter proposition is a rather trivial con-sequence of the Morey-Schreinemakers rule (Zen,1966, p. l0-ll) and of Schreinemakers' concept ofthe univariant scheme (Zen, 1966, p. 12-14). Theinterested reader may verify its applicability to anyinvariant point involving univariant reactions thatare approximated by straight lines.

It has thus been demonstrated that the correcrtopology for each (n + 3)-phase multisystem onfixed-slope diagrams is specified by the choice be-tween the stabilities of two alternative mineral as-semblages. For pt-1t" diagrams, the two alternativeassemblages are related to each other by a balancedsolid-solid univariant reaction (Burt, l97l); for p"-minus pHrO diagrams a reaction (or relation) can be

stated, but not balanced chemically. (The same seemsto be true for P"-T diagrams.) The above statementsare illustrated by the examples that follow.

For this discussion, angled brackets ( ) will be usedto enclose the names or abbreviations (Table I ) of thenon-participating phases labeling multisystems,square brackets [ ] will similarly label invariantpoints, and parentheses ( ) will label reactions. Thisusage follows Burt (1971).

P"-minus pH2O diagram

At low temperatures or high values of pH2O, ber-trandite is stable relative to phenakite, and the phena-kite-absent (n + 3)-phase multisystem (Phe) can beconsidered. Computer program RnecrroN (Fingerand Burt, 1972) is used to calculate all possible reac-tions in this multisystem (Table 3, in part). The reac-tion slopes (in bars/joule/mole of HrO) are thenobtained from equation 8 and the molar volume datain Table L

Tab le3 . Poss ib le reac t ions(andcor respond ingmolarvo lumechangesfor theso l ids in jou les /bar )amongwaterandthephases inTab lel, assuming that phenakite-kaolinite is an unstable assemblage. This is the output of computer p.ogt"r RrncrroN (Finger and Burt,

1972\

QtzBr l H2o

-2

1-5

____L999

- J

-4

-1

-11-2-1-4

-1-4

L08

-2

-50-4

t

4-1

z

75

z4

2

z1

1

J

11

4I

IL1

- 4

o-4

8

-10

4-4

-4-2

-4

-26

-2

1

-2

9

- l

J

- 267

-10-10

10

- r q

-6

- 2

- 11-1- 3-5

- I J

-2

- 4-9-1- l

- 3-2

- J

- 3

-9

-2

-10

6 . t z t- 4 . s70s . 9 5 5

-3 .184

L9 .25219.664-2 .481 ,

6 . 0 3 9

7 . 2 7 512 .609- 1 . 9 4 1

5 . 3 3 4

15 . 0393 .327

-o,62L2 .O84

6 . ) - L d

0. 6988. 584

-2 .629

- t .1663.26L

-26.9r8L .239

0. 613-2 .379

- 7-)

-13- 1

-23

18

- 3

-3

24

10

-88

-106

204

504

204

20

-1

- l

- 1

- 7

- 2-10

- J

J

- 3

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-9-18

- 3

-3

BURT: BERYLLIUM MINERAL STABILITIES 671

The next step is to plot the multisystem (Phe) on anisothermal P,-minus rrHzO diagram. When this isdone (as seen in the lower left part of Fig. 4), the twoalternative topologies are given by the following rela-tion among the stable and metastable invariantpoints:

Qtz + Chr * Btr * Kao : Brl * Euc (9)

As discussed above, beryl-euclase is a relatively com-mon assemblage, whereas the alternative four-phaseassemblage quartz-chrysoberyl-bertrandite-kaolin-ite is unknown. The two invariant points labeled [Brl]and [Euc] must then be metastable, as shown, and thepoints [Qtz], [Chr] [Btr], and [Kao]are stable. (Point

[Kao], labeled [Phe] on Fig. 4, becomes metastablewhen phenakite is considered, as described below.)On Figure 5, an enlargement of the stable part ofFigure 4, the assemblage beryl-euclase is stable insidethe closed polygon formed by joining the two pointslabeled [Qtz], the two points labeled [Chr], and theupper point labeled [Btr].

The final step is to determine how the degeneratedehydration reaction Btrl Phe cuts the multisystem(Phe) determined above. Inspection of Figure 4 re-veals that it may do so (l) below point [Qtz], (2)between [Qtz] and [Chr], (3) between [Chr] and [Btr],(4) between [Btr] and [Kao] (labeled [Phe] on Fig. 4because this is where I placed the reaction), or (5)above point [Kao] (labeled [Phe] on Fig. 4). Possi-bilities (l) and (2) above would imply that phenakite,rather than bertrandite, would typically occur withkaolinite and euclase (in other words, that ber-trandite would have a very low dehydration temper-ature indeed). This implication conflicts with thewidespread natural occurrences of bertrandite, andpossibilities (l) and (2) may therefore be rejected.Poss ib i l i t y (3 ) i s fo r p rac t ica l purposes in -distinguishable from possibility (4), because the de-hydration reaction BtrlPhe is independent of the Btr-absent point [Btr].

The above arguments leave only possibilities (4)and (5). In other words, the dehydration reactionBtr/Phe can intersect the multisystem either above orbelow the point [Kao] (labeled [Phe] on Fig. a).These alternatives correspond to a second (r + 3)-phase multisystem (Kao), the two topologies of whichare given by the relation

Chr * Qtz * Btr : Phe f Brl * Euc (10)

Neither the left nor the right assemblage has beenreported from nature. Phenakite, beryl, and euclaseare, however, known as associated minerals (cf. MFr-

Fig. 5, Enlargement of the central part of Fig. 4, showing stablereactions and invariant points. Inset shows chemography (c/. Fig.3). Tie lines to kaolinite are omitted in the upper right area of thediagram where other aluminosilicates probably become stable.

tensson, 1960; Kalyuzhnaya and Kalyuzhnyi, 1963).Tentatively then, phenakite-beryl-euclase is assumedto be a stable assemblage, and Figure 4 has beenconstructed accordingly from the data in Table 3.The rarity of phenakite-beryl-euclase is probablydue to the fact that it is a quartz-absent assemblage.

With regard to the multisystem (Kao), shown in theupper right part of Figure 4, the metastable invariantpoints are then [Phe], [Brl], and [Euc], and the stableones are [Chr], [Qtz], and [Btr]. The metastable point

[Phe] of multisystem (Kao) corresponds to theformerly stable point [Kao] of the multisystem (Phe).(Strictly speaking, with regard to the full (r + 4)-phase multisystem of Table l, the point [Phe, Kao] ismetastable.)

On Figure 5, the assemblage phenakite-beryl-eu-clase is stable only inside the small triangle whoseapices are labeled [Chr], [Qtz], and [Btr] in the multi-system (Kao). The size of this area could be enlargedby moving the BtrlPhe line down, even to below thelower point [Btr]. As long as this line does not inter-sect the lower points [Chr] and [Qtz], the mineralcompatibility relations, and the fundamental to-

A-/9. l$\ f/bNr.

"Y'q*

'oo

A

U,., AA\

672 BURT: BERYLLIUM MINERAL STABILITIES

pology of the diagram, remain unchanged. The areaof stability of the assemblage was made small becausethe assemblage is not yet described from nature.

Incompatibilily of phenakite and kaoliniteThe two multisystems (Phe) and (Kao) are stable on

opposite sides of the BtrlPhe line (Figs. 4 and 5).Extending somewhat the generalization that stablearrays of points correspond to unstable asSbmblages,consider that stable arrays of multisystens also corre-spond to unstable assemblages (Burt, l97l). That is,phenakite-kaolinite must be an unstable assemblageat the temperature considered. (A close examinationof Figure 5 also reveals that phenakite-kaolinite mustbe unstable.)

In order to justify this more-or-less a posterioriobservation, the following compositional relationsshould be noted (cf. Fig.2):

2 Kao * l1 Phe * 5 Qtz : 4 B t r * 2 Br l ( l l )

K a o * 3 P h e : 2 E u c * B t r * Q t z ( 1 2 )

7 Kao * 26 Phe : l0 Euc * 9 Btr t - 2Brl (13)

The left-hand assemblages are unknown; the right-hand assemblages ale well-known, as describedabove. Kaolinite-phenakite could therefore be sub-mitted as the only incompatibility when program Rn-AcrIoN was used to generate the reactions in Table 3.

P,-T diagram (fluid-absent )The stable multisystems (Kao) and (Phe) on P"-

minus pHrO diagrams (Figs. 4 and 5) can also bedrawn as the stable invariant points [Kao] and [phe]on a P"-T diagram that omits water. The result isseen on Figure 6, part of a possible (n t 3)-phasemultisystems array for the seven minerals in Table l.Each water-absent line on Figure 6 corresponds, ingeneral, to an invariant point on Figure 4. The ex-ception is the degenerate line (Btr, Euc) which is alsoa line on Figure 4.

The left axis of Figure 6 is positioned at the tem-perature for which the isothermal diagrams Figures 4and 5 were drawn; Z could either increase or decreaseto the right (as shown by the label t Z on the hori-zonal axis). Unfortunately, with only molar volumeinformation available, it is unknown whether thepoints [Kao] and [Phe] are stable or metastable ifwater is added to this multisystem, or whether otherinvariant points exist stably or metastably.

At this point it can be noted that on Figure 6,

Fig. 6. Schematic fluid-absent P"-T diagram of part of themultisystem of Table l. The left axis is drawn at the temperaturefor which Figs. 4 and 5 are drawn; Z might increase or decrease tothe right. lnset shows chemography for quartz-saturated equilibria(cf. Fig. 2).

invariant point [Kao] corresponds to type IV-21 ofDolivo-Dobrovol'skii (1969; type III-5 if projectedthrough quartz) and that point [Phe] corresponds totype IV-13 (type III-2 if projected through quartz).Projected through qvarlz, as shown on the inset, theoverall chemography of this multisystem belongs totype Q3 of Day (1972, Fig. 8). The multisystems nettype of Figures 4 and 5 corresponds to type 2 of Day(1972, Fig.7).

P-T diagram (fluid-present )As stated above, the topology of Figures 4 and 5

should be equivalent to that of a P-T diagram drawnfor excess water, because decreasing pHrO should, ingeneral, correspond to increasing 7. This relation isevident on Figure 7. Topologically, there is a one-to-one correspondence between Figures 5 and 7 (Fig. 7was so drawn).

Of course, some of the invariant points on Figure 7may be metastable, due to the participation of otherphases, or they may be physically unrealizable (i.e.,they may occur at negative pressures). Most natural

Ato [5 ,

Pvp

BURT: BERYLLIUM MINERAL STABILITIES

assemblages appear to form at pressures above thetwo invariant points labelled [Qtz] on Figure 7. Thatis, euclase and euclase-phenakite seem to be stablewith regard to the alternative assemblages Chr-Brl-Btr-Kao and Chr-Brl-Btr (cl Fig. 6). Natural as-semblages further appear to form below the lowerpoint labeled [Btr] on Figure 7. That is, beryl-kaolin-ite seems to be stable relative to Chr-Euc-Qtz. Onlythe invariant point [Chr]seems to fall within the P-Trange normally involved in the formation of hydro-thermal beryllium deposits. Nevertheless, as dis-cussed below, the presence of bertrandite-beryl-ka-olinite instead of euclase-quartz could be due tosupersaturation of low-temperature solutions withamorphous silica in place of quartz.

The low P and T reactions on Figure 7 are sche-matically shown in more detail in Figure 8. Possiblepositions for the two dehydration curves involvingthe creation and destruction of pyrophyllite aremarked by dashed lines. The pyrophyllite curves aredrawn consistent with the assumption that chrysobe-ryl is the only Be-bearing mineral stable with py-

Fig. 7. Schematic, fluid-present P-? diagram of the multisystemof Table 1, drawn topologically identical to Figs. 4 and 5.Metastable points and lines are omitted. Inset shows chemography(cf. Fig. 3).

Fig. L Enlargement of the low pressure part of Fig. 4, showingdehydration reactions and invariant points possibly encountered in

nature. Dashed lines show a permitted stability field forpyrophyllite.

rophyllite. In other words, kaolinite-quartz assem-blages are assumed to break down at highertemperatures than kaolinite-beryl or kaolinite-eu-clase assemblages, as shown. Chrysoberyl-quartz-kaolinite is stable in the intermediate zone. The py-rophyllite curves could easily be moved to highertemperatures on Figure 8.

Discussion

Heinrich and Buchi (1969) have shown that beryl isunstable with aluminosilicates, the stable assemblagebeing chrysoberyl-quartz. This fact explains the oc-currence of chrysoberyl in alumina-contaminatedpegmatites. The present study suggests that chryso-beryl-quartz remains a stable assemblage to fairly lowtemperatures, but eventually is replaced by kaolinite-euclase or, more probably, kaolinite-beryl.

The stability relations of beryl itself are of particu'lar interest. It has earlier been shown (Burt, 1975b)that under high fluorine activities beryl breaks downto the assemblage phenakite-topaz-quartz or, in thepresence of fluorapatite and high PzOu activities, toherderite (CaBePOrF)-topaz-quaftz. The present

674 BURT: BERYLLIUM MINERAL STABILITIES

study suggests that beryl should hydrate at moderatepressures to bertrandite-euclase-q\artz, or at lowpressu res to bertrandite-kaolinite- qvartz. These andmore complicated natural hydrothermal alterationsof beryl are extensively reviewed by Cerny (1968,r970).

When this analysis was first performed I was un-aware of the reconnaissance experimental work onberyl stability at high pressure by Munson (1967) andat high temperature by Ganguli (1972).It was there-fore gratifying that the multisystems analysis cor-rectly predicted the high P and Z breakdown of berylto chrysoberyl * phenakite * quartz (Figs. 4 and 5).The experimental data explain the steep negativeslope of the breakdown curve shown on Figure 7.

The fact that beryl is unstable under upper mantleconditions is undoubtedly of some academic interest,although geologists appear to agree that beryl-bear-ing pegmatites are crustal phenomena. In any case,the exact high P and T breakdown curve of berylremains to be determined. Inasmuch as hydro-thermally-grown beryl is somewhat hydrous (Flani-gen et al., 1967), anyone undertaking such experi-ments should be prepared to encounter some of theproblems studied by Newton (1972). He studied theinfluence of water activity on the high pressure break-down of cordierite, another low-density ring silicate.

Moving on to the hydrous phases bertrandite andeuclase, what does the analysis have to say? First, itprovides two plausible explanations for the com-parative rarity of euclase. Figures 7 and 8 show thateuclase, although stable to higher temperatures thanbertrandite, is stable only over a limited range of pand T. Its stability is reduced in the presence ofquaftz to a narrow slice of P-Z space , possibly with apressure minimum at the point [Chr] (Fig. 8). Super-saturation of hydrothermal fluids with amorphoussilica might further reduce its stability in natural envi-ronments, and might alone be responsible for its fail-ure to appear (i.e., it would metastably shift the fol-lowing reaction at invariant point [Chr] to the right:22 Euc + 26 SiO, (amorphous) - Btr * 6 Brl f 5Kao).

Assemblages that could take the place of euclase-quartz include bertrandite-kaolinite with falling Z,and beryl-kaolinite or beryl-chrysoberyl with rising7. Euclase itself probably dehydrates to bertrandite-chrysoberyl-beryl or (more probably, or with risingP) to phenakite-chrysoberyl-beryl.

These hypotheses could be tested by a careful ex-perimental study of the dehydration equilibria of ber-

trandite and euclase in silica-saturated and unsatu-rated solutions. The recent economic importance ofbertrandite as an ore of beryllium would justify sucha study. A difficulty might be the low temperaturesinvolved-probably below 400oC. Should such ex-periments be impractical, carefully-documented stud-ies of selected natural assemblages might still proveto be the best test of the multisystem topology hereproposed. Assemblages of diaspore or pyrophyllitewith Be minerals other than chrysoberyl, or of ka-olinite with phenakite, would be especially interestingin this regard.

AcknowledgmentsThe Interlibrary Loan Service, Aizona State University Li-

brary, is to be thanked for their help in locating numerous obscurereferences. Howard W. Day, John R. Holloway, John M. Ferry,and Douglas Thorpe provided useful reviews. I am also grateful toTom Young for computing assistance, as well as to Cyndi Gordonfor typing the manuscript and to Sue Selkirk for drafting thefigures. Partial support for this research was obtained from theFaculty Grant-in-Aid Program, Arizona State University.

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Manuscript receiued, September 9, 1977; accepted

for publication, December 6, 1977.