American Mineralogist, Volwne 71, pages277-300, 1986 Phase equilibria andthermodynamic properties of minerals in the BeO-AlrO3-SiO2-H2O (BASH) system, with petrologic applications Mlnx D. B.qnroN Department of Earth and Space Sciences, University of California, Los Angeles,Los Angeles, California 90024 Ansrru,cr The phase relations and thermodynamic properties of behoite (Be(OH)r), bertrandite (BeoSirOr(OH)J, beryl (BerAlrSiuO,r), bromellite (BeO), chrysoberyl (BeAl,Oo), euclase (BeAlSiOo(OH)), and phenakite (BerSiOo) have been quantitatively evaluatedfrom a com- bination of new phase-equilibrium, solubility, calorimetric, and volumetric measurements and with data from the literature. The resulting thermodynamic model is consistentwith natural low-variance assemblages and can be used to interpret many beryllium-mineral occurTences. Reversed high-pressure solid-media experimentslocated the positions of four reactions: BerAlrSiuO,, : BeAlrOo * BerSiOo + 5SiO, (dry) 20BeAlSiOo(OH) : 3BerAlrsi6or8 + TBeAlrOo + 2BerSiOn + l0HrO 4BeAlSiOo(OH) + 2SiOr: BerAlrSiuO,, + BeAlrOo + 2H2O BerAlrSiuO,, + 2AlrSiOs : 3BeAlrOa + 8SiO, (water saturated). Aqueous silica concentrations were determined by reversedexperimentsat I kbar for the following sevenreactions: 2BeO + H4SiO4: BerSiOo + 2H2O 4BeO + 2HoSiOo: BeoSirO'(OH), + 3HrO BeAlrOo * BerSiOo + 5H4Sio4: Be3AlrSiuOr8 + loHro 3BeAlrOo + 8H4SiO4: BerAlrSiuOrs + 2AlrSiO5 + l6HrO 3BerSiOo + 2AlrSiO5 + 7H4SiO4 : 2BerAlrSiuOr8 + l4H2o aBeAlsioloH) + Bersio4 + 7H4sio4:2BerAlrsiuors + 14Hro 2BeAlrOo + BerSiOo + 3H4SiOo : 4BeAlSiOr(OH)+ 4HrO. The results of these experiments were combined with the heat capacitiesand entropies determined in a companion study and with data from the literature to estimate the ther- modynamic and thermophysical properties of the beryllium minerals. Eighty-six data sets containing over 1000independentobservations were evaluated using the program eHASE2o. The values of G!rr,, (kJ/mol) and S!rr., (J/(K.mol)) with their uncertainties (2o) arebehoite -827.3(6.7),45.57(0.18); bertrandite -4300.6(1.6), I72.ll(0.77); anhydrous beryl -8500.4(3.8),346.7(4.7); chrysoberyl -2176.2(1.5), 66.25(0.30); euclase -2370.2(r.l), 89.1l (0.a0); and phenakite - 2028.4(0. 9), 63.43(0.27 ). The effect of water on the stability of beryl is treated as a purely volumetric interaction Gr, r ty*ous ueryt : Gp, Ii anlyarcu. t" ryl - P noiaZu, where Z*" is an effective volume for the fluid occluded by the beryl structure (14.1 cm3/ mol). Not only doesthis simple "bottle model" work as well for beryl as alternative, more sophisticated models, in part owing to the lack of hydration data, it also appears to work reasonably well for cordierite. Beryl has a wide stability range consistent with its relative natural abundance. The stability field of beryl is greatly increased by high fluid pressures and by alkali-containing solid solutions. The assemblage chrysoberyl + quartz is stableonly at relatively high tem- peratures(>600"C) or with Poro ( P,.o,.At moderate pressures with decreasing temper- ature, euclase becomes stable around 400'C. Euclase replaces beryl in aluminum silicate- bearing assemblages in the 300'C range. In the 200"C range, phenakite and bromellite hydrateto bertrandite and behoite,respectively, and pure beryl reacts to euclase + quartz + bertrandite or phenakite. The predicted phaserelations are in good qualitative agreement 0003-004x/86 /0304427 7 $02.00 277
Transcript
American Mineralogist, Volwne 71, pages 277-300, 1986
Phase equilibria and thermodynamic properties of minerals in theBeO-AlrO3-SiO2-H2O (BASH) system, with petrologic applications
Mlnx D. B.qnroNDepartment of Earth and Space Sciences, University of California, Los Angeles, Los Angeles, California 90024
Ansrru,cr
The phase relations and thermodynamic properties of behoite (Be(OH)r), bertrandite(BeoSirOr(OH)J, beryl (BerAlrSiuO,r), bromellite (BeO), chrysoberyl (BeAl,Oo), euclase(BeAlSiOo(OH)), and phenakite (BerSiOo) have been quantitatively evaluated from a com-bination of new phase-equilibrium, solubility, calorimetric, and volumetric measurementsand with data from the literature. The resulting thermodynamic model is consistent withnatural low-variance assemblages and can be used to interpret many beryllium-mineraloccurTences.
Reversed high-pressure solid-media experiments located the positions of four reactions:
The results of these experiments were combined with the heat capacities and entropiesdetermined in a companion study and with data from the literature to estimate the ther-modynamic and thermophysical properties of the beryllium minerals. Eighty-six data setscontaining over 1000 independent observations were evaluated using the program eHASE2o.The values of G!rr,, (kJ/mol) and S!rr., (J/(K.mol)) with their uncertainties (2o) are behoite-827.3(6.7) ,45.57(0.18) ; ber t randi te -4300.6(1.6) , I72. l l (0 .77) ; anhydrous bery l-8500.4(3.8),346.7(4.7); chrysoberyl -2176.2(1.5), 66.25(0.30); euclase -2370.2(r.l),
89. 1 l (0.a0); and phenakite - 2028.4(0. 9), 63.43(0.27 ).The effect of water on the stability of beryl is treated as a purely volumetric interaction
Gr, r ty*ous ueryt : Gp, Ii anlyarcu. t" ryl
- P noiaZu,
where Z*" is an effective volume for the fluid occluded by the beryl structure (14.1 cm3/mol). Not only does this simple "bottle model" work as well for beryl as alternative, moresophisticated models, in part owing to the lack of hydration data, it also appears to workreasonably well for cordierite.
Beryl has a wide stability range consistent with its relative natural abundance. Thestability field of beryl is greatly increased by high fluid pressures and by alkali-containingsolid solutions. The assemblage chrysoberyl + quartz is stable only at relatively high tem-peratures (>600"C) or with Poro ( P,.o,. At moderate pressures with decreasing temper-ature, euclase becomes stable around 400'C. Euclase replaces beryl in aluminum silicate-bearing assemblages in the 300'C range. In the 200"C range, phenakite and bromellitehydrate to bertrandite and behoite, respectively, and pure beryl reacts to euclase + quartz +bertrandite or phenakite. The predicted phase relations are in good qualitative agreement
0003-004x/86 /0304427 7 $02.00 277
278 BARTON: PHASE EQUILIBRIA IN THE BeO-A1,O,-SiO,-H,O SYSTEM
with natural associations. Consideration of the effect of solid solution in beryl improvesthe agreement.
In most geologic environments, externally imposed chemical potentials govern the sta-bility of beryllium minerals. As a result, minerals in this system are perhaps most usefulas indicators of metasomatic variables. Euclase, for example, has a broad P-f shbilityrange, but is stable only in environments with unusually high alumina activities, thusaccounting for its relative rarity.
INrnoouc:ttoN
Beryllium, one of the geochemically less abundant ele-ments, occurs as an essential component in more than 50minerals (Fleischer, 1980). Although rarely composingmore than a small portion of any rock, beryllium mineralsare fairly common, especially in differentiated felsic ig-neous and related metasomatic rocks. The variety of be-ryllium minerals and their widespread occurrence meanthat they can be useful petrologic indicators.
Ofthe beryllium minerals, the most common and hencethe most petrologically and economically important be-long to the system BeO-AlrOr-SiOr-HrO (BASH). Overtwenty phases occur in this system, and those of geologicinterest are listed in Table l. The AlrOr-SiOr-HrO systemhas been intensively studied, and its phase relations arewell understood (see recent data and reviews by Hemleyet al., 1980; Perkins et al., 19791, thermodynamic com-pilation by Robinson etal.,1982). These studies proposesimilar phase diagrams for the ASH system and thus pro-vide a reasonable basis for addition of the componentBeO.
Relatively few thermochemical data are available forberyllium-bearing phases. In this study, phase equilibriumand solubility experiments were performed to provide theinformation needed along with data from the literature toderive an internally consistent thermodynamic model forphases in the system. This model, in turn, is used to cal-culate a petrogenetic grid for the BASH system and re-actions in more complex systems. From these calcula-tions, deductions can be made about the petrogenesis ofrocks containing minerals in this system.
Figure I shows the phases consideredin this study pro-jected from water. Of these phases, only beryl has a widelyvariable composition. The aluminum silicates can acceptsmall amounts of transition metals, and kaolinite, pyro-phyllite, and diaspore may contain small amounts ofhalo-gens substituting for hydroxyl, but their compositionalvariations are small. Chrysoberyl can contain substantialiron, chromium, and manganese substituting for alumi-num, but in most cases this substitution is small (Vlasov,1967, Vol. III). Euclase and phenakite are uniformly closeto their ideal compositions. Ganguli and Saha (1967) re-ported that synthetic bertrandite can contain Be(OH)considerably in excess of the ideal formula, but analysesof natural bertrandites show no evidence of nonstoi-chiometry.
Beryl, in contrast to the other phases, exhibits a widerange of compositional variation, as a consequence oftwo
kinds ofsubstitutions: species occupying channel sites andspecies substituting for the tetrahedral or octahedral cat-ions. The alkalies occur in beryl in amounts up to severalweight percent, occupying channel sites with charge bal-ance being accomplished by substitution of other cationsin the framework sites and accompanied by adjoiningwater molecules in the channels (Hawthorne and eerni,1977). Lithium, in coupled substitution with the channelalkalies, replaced beryllium (Hawthorne and eern!, 1977).Water, in addition to accompanying the alkalies, also oc-cupies the channel cavities in a manner similar to that incordierite (Schreyer and Yoder, 1964; Aines and Ross-man, 1984). Both of these substitutions have a profoundeffect on the stability of beryl. In addition to the alkaliesand water, up to several weight percent of magnesium,manganese, iron, and chromium are found in some beryls.The iron occupies both channel positions and substitutesfor aluminum in the octahedral sites, whereas chromium,magnesium, and manganese substitute for the aluminum(Goldman et al., 1978; Nassau and Wood, 1968; Woodand Nassau, 1968; Gibbs et al., 1968). Helium, carbondioxide, and argon have also been found in beryl (Beus,l 966).
Spectroscopic data on beryl and cordierite suggest thatwater occupies two distinct positions at low temperatures,one with the H-H vector normal to c and "sitting" in therings between the large cavities (Type II), the other withthe H-H vector parallel to c and located in the large cav-ities (Type I, Wood and Nassau, 1968). The abundanceof Type II water correlates well with the alkali content;this correlation leads to the suggestion that there is bond-ing between them (Goldman et al., 1978; Hawthorne andCern!, 1977; Wood and Nassau, 1968). Aines and Ross-man (1984) have shown that with increasing temperaturethese two types of water decrease in quantity with equi-librium partitioning favoring a third state that has thespectroscopic characteristics ofa gas (not bonded or ori-ented on an IR time scale).
Many crystallographic structure refinements have beendone on phases in this system (Ross, 1964; R. M. Hazenet al., unpub.). None suggests that there is any disorderamong the tetrahedral species. The mineralogic propertiesof the beryllium minerals were recently reviewed by Burt(1982).
Thermodynamic data have been measured for some ofthe beryllium phases in this system. Low-temperature heat-capacity measurements have been performed on phen-akite by Kelley (1939) and on chrysoberyl by Furukawa
Table 1. Names, abbreviations, and formulas of some phases
of geologic interest in the BeO-AlrOr-SiOr-HrO system
A b b r . F o m u l a Abbr. Fomul a
279
Alro,Proiected {rom water
Fig. l. Minerals in the BeO-AlrO3-SiOr-H2O system pro-jected from HrO. Abbreviations from Table l.
other investigators, although Miller and Mercer (1965)
did synthesize what they believed to be a beryllian mullite
in their experiments at higher temperatures.
In addition to the experimental data, a number of com-
pilations of the observed parageneses of beryllium min-
erals exist (Beus, 1966; Vlasov, 1967, Vols. II and III;
Burt, 1978). Burt (1978) derived a detailed topological
model for phase equilibria in the system based on natural
associations. Burt (1 975a, 197 5b, I 976, I 980), Franz and
Morteani (1984), and Kupriyanova (1982) discussed the
stability ofthese minerals in more complex systems. Franz
and Morteani (1981) also discussed the topology of the
reactions in the system in light of their experimental re-
sults.
ExpnnrvrnNTAl- METHoDS AND RESULTS
High-pressure, solid-media phase-equilibrium and silica-buff-
ering solubility experiments were done to provide the basis for
derivation of a thermodynamic model for the BASH system.
Starting materials
Natural materials were used in all the experiments with the
exception of synthetic bromellite (l- to 3-mm crystals grown in
lithium molybdate flux, NMNH 115234). Cell parameters for
the starting materials are listed in Table 2. A cell refinement was
not done for BeO because of its toxicity. Crystallographic datawere collected by powder-ditrraction methods using Ni-filtered
Cu Ka radiation and were reduced with the program ofBurnham(1962). Qrafiz and corundum served as internal standards.
Partial chemical analyses were performed on an automatedARL-EMX microprobe at the University of Chicago. Spectrom-eter analyses were done under operating conditions of I 5 kV and
l5 pA. Data reduction was accomplished using a ZAF-type cor-
rection program written by I. M. Steele of the University of
Chicago. Standards used were fluor-topaz (for A1, Si, and F in
bertrandite and euclase), hematite (for Fe in all but beryl), albite,
microcline, pollucite, and synthetic Rb-feldspar (for Na' K' Cs'
and Rb, respectively, in the Minas Gerais beryl). Only the chryso-
beryl and beryl contain detectable impurities' The chrysoberylcontains 3.1 wto/o FerO, corresponding to about 2.5 mo10/o Be-
FerOo. Analyses of the beryl used are given in Table 3. Water
contents of the Brazilian beryl and the bertrandite were deter-
BARTON: PHASE EQUILIBRIA IN THE BeO-AIO,-SiO,-H,O SYSTEM
A l u m i n u m s i l i c a t e A l s
A n d a l u s i t e A n d
B e h o i t e B h
Bertrandite Bt
Beryl Be
Beryl l ' i te Bl
Bromel I i te Br
chrysoberyl ch
Corundum co
At 2s io5Al^s i0 .
Be(0H) zBe4s iz07(0H)2
Be3Al 25i 601 8.nH20
Be3s i04(0H)2 .H20
Be0
BeAl "0,
A t ̂ 0 .
D i a s p o r e D i
E u c l a s e E u
G i b b s i t e G b
K a o l i n i t e K a
Kyanite Kya
P h e n a k i t e P h
P y r o p h y l l i t e P y
Quartz Qz
Si I I imani te Si I
Aro(olr )
BeAl Si 04(0H)
Ar (0H) 3
Ar2s iZ0s(oH)4
A I 25 i05
8e,,5 i 0,
A r 2 s i 4 o t o ( o H ) 2
s i02
At 2s i05
and Saba ( I 966). Hemingway et al. ( I 9 86), in a companionstudy, measured the low- and high-temperature heat ca-pacities of bertrandite, beryl, chrysoberyl, euclase, andphenakite. Ditmars and Douglas (1967) measured the heatcontent of chrysoberyl from 298 to I173 K. Enthalpies offormation of chrysoberyl are available from Robie et al.(1978) and from Holm and Kleppa (1966). Holm andKleppa (1966), Bamberger and Baes (1972), and Schuilingetal. (1976) gave values for the reaction 2BeO + SiOr:BerSiOo obtained from oxide-melt calorimetry and phaseequilibria. Thermodynamic data for BeO are tabulated inRobie et al. (1978). Kiseleva et al. (1984) reported heatsof formation of bertrandite, beryl, chrysoberyl, euclase,and phenakite based on heat-of-solution experiments.
Although there are many studies concerned with syn-thesis of phases in this system, especially beryl, few havedealt with elucidating the phase relations. In the systemBeO-SiOr-HrO, Bukin (1967) synthesized bertrandite upto temperatures of 500'C and phenakite at similar andhigher temperatures. Ganguli and Saha (1967) performeda number of synthesis experiments in the quaternary sys-tem. Beus and Dikov (1967) and Syromatnikov et al.(1971) studied the stability of beryl and other berylliumphases in the presence of alkalies and fluorine-bearingspecies, but none of their experiments were reversed.
The high-temperature stability of beryl and its meltingrelations have been investigated by Franz and Morteani(1984), Ganguli (1972), Ganguli and Saha (1967), Millerand Mercer (1965), Van Valkenberg and Weir (1957), andMunson (1967). Unfortunately, these and other studieson beryl and related phases have been synthesis studiesand are therefore of limited value in the derivation ofthermodynamic properties.
Franz and Morteani (1981), Hsu (1983), and Seck andOkrusch (1972) studied several reactions by reversal ex-periments. Their data, although limited to only a fewreactions, place limits on the upper thermal stabilities ofberyl, euclase, and bertrandite. Franz and Morteani ( 198 l)reported a new phase in the quaternary system that ismore aluminous than chrysoberyl plus quartz and moresilicious than beryl plus andalusite. This phase was notobserved in this study and has not been reported by any
And,Kya,Sil
280 BARTON: PHASE EQUILIBRIA IN THE BeO-AIO,-SiO,-H,O SYSTEM
Table 2. Crystallographic data for the BeO-AlOr-SiOr-H,O starting materials
Cel I Parametersl
b (A ) c (A ) e ( i l v ( 43 )
source2
l '4atenia I a (A)
A n d a l u s i t e
Bertrandi te
Beryl
Beryl
Ch rysobe ryl
E u c l a s e
P h e n a k i t e
Quartz
7.7e28114) 7 .8980( te )
B.71 92( l6 ) t5 ,2722(23)
9 . 2 1 0 4 ( t 4 )
9 .2 I 84{ 09 )
5 . 4 8 0 r ( 0 3 ) 9 . 4 l l e ( 0 7 )
4 .7703 l .29) r4 .3235(s4)
12.4722(10\
5 . 5 5 3 9 ( l 9 )
4 .s624(17)
9 . r 9 0 3 ( r 3 )
9 . r 678( s8)
4 .4288(03)
4 . 6 3 1 7 ( 3 9 )
8.2532(19)
- 3 4 1 . 8 3 ( 1 2 )
- 6 0 7 , 9 r { 1 6 )
- 675.18(22\
- 674.70(37)
- 228.43(02)
r 0 0 . 4 1 6 ( 6 2 ) 3 i l . 2 6 ( 3 9 )
| i l . 8 2 ( 2 r )
B l a c k H i l l s , S o u t h 0 a k o t a
A l b a n y , t 4 a i n e ( F . 1 4 . N . H .#6969)Robertson ToMship, Quebec( N , t r l . N . H . # 1 2 3 2 0 7 )M i n a s G e r a i s , B r a z i I( p r o v i d e d b y R . G a i n e s )C o l a t i n a , E s p i r i t o S a n t o ,B r a z i l ( N . 1 4 . N . H . # R 1 5 2 3 1 )! 1 i n a s G e r a i s , B r a z i l( N . 1 4 . N . H . # l 2 l 3 5 0 )San l t l i guel di Pi raci caba ,B r a z i l ( N . l ' l . N . H . # B 2 l l 5 2 )u n k n o w n ( U n i v e r s i t y o fC h i c a g o # 2 0 9 9 )
I E r r o r s g i v e n i n p a r e n t h e s e s ( l o )
I t l . l l . r u . l . = N a t i o n a l M u s e u m o f N a t u r a l H i s t o r y , F . M . N . H . = F i e l d M u s e u m o f N a t u r a l H i s t o r y
mined by loss on ignition (average of 5 samples each). The ber-trandite results are consistent with normal bertrandite stoichi-ometry and limit the substitution of Be(OH), for SiO, (proposedby Ganguli and Saha, 1967) to <30/0. The Quebec beryl was usedin the silica-buffering experiments and the Brazilian beryl wasused in the high-pressure experiments.
The minerals were separated from impurities by coarse crush-ing and hand-picking. On examination in oils, both beryl sampleswere found to have moderately abundant (0.010/o to 0.10/o byvolume) fluid inclusions. The other phases have few inclusionswith the exception of the chrysoberyl which contains some oxideinclusions (which may contribute to the observed iron content).
High-pressure experiments
Piston-out piston-cylinder reversal experiments were per-formed to determine the temperatures as a function of pressurefor Reactions I to 4:
The starting materials (Tables 2 and 3) for each ofthese reactionswere mixed together in stoichiometric proportion with equalmasses of reactant and product assemblages. The mixes wereground under acetone to an average particle size of 5 pm (deter-mined by examination in oil). For Reaction 1, the beryl wasdehydrated at 1400"C for I h. Although this is above the l-barstability limit of beryl (Ganguli, 1972), optical and X-ray ex-amination showed no evidence of decomposition. After grinding,the mixtures were loaded into 6-mmJong platinum capsules.Approximately 2 mg of water were added to each of the capsulesfor the water-containing experiments. The capsules were sealedby arc welding and folded in halfto fit into the pressure assembly.Before sealing, the capsules for Reaction I were crimped andplaced in an oven at 800'C for several hours to drive off anyvolatiles acquired during the mixing and loading steps. Devol-
atilization ofthe mix could not be done at 1400t because thestarting mix reacted rapidly to give beryl (which should be meta-stable relative to chrysoberyl + cristobalite + phenakite).
Two pressure assemblies were used. An assembly consistingalmost entirely of NaCl was used for the water-bearing experi-ments which were all conducted below 800qC. This salt assemblyhas been shown by Holland (1980) to be friction-free withinexperimental uncertainty. Experiments on Reaction 1, which wereconducted between ll50 and 1450qC, used an assembly con-sisting largely of pyrex glass. The pyrex assembly has an appre-ciable friction requiring pressure calibration. Consequently, re-versals were done on the reaction anhydrous cordierite:sapphirine + quartz. This reaction has been reversed at 1250Cbetween 7000 and 7500 bars in an internallyheatedgas apparatusby R. C. Newton (pers. comm., 1980). For the calibration re-versals, the cordierite and sapphirine + qluartz, were prepared inthe manner of Newton (1972). Care was taken to ensure that thecordierite-sapphirine-quartz mix was completely dry before seal-ing the capsules. The "true" position of the reaction at othertemperatures can be obtained from the 1250'C bracket and theClausius-Clatpeyron slope (derived from the thermodynamic datapresented by Newton et al., 1974). Table 4 gives the results ofthe calibration experiments. These experiments and others athigher pressures using this same pressure assembly (Perkins andBarton, unpub.) indicated that the pressure correction is approx-imately -100/0. A pressure correction of -100/o was applied toall experiments using the pyrex assembly.
Tungsten-rhenium thermocouples were used for the high-tem-perature experiments. Chromel-alumel thermocouples were usedfor the lower-temperature experiments. The position of the ther-mocouple was checked on dissection of the assembly after eachrun, and any nrn in which the thermocouple was more than Imm from the capsule was rejected. No pressure correction hasbeen applied to the temperature measurements. Uncertainty inthe pressure measurements is estimated to be about 200 bars.The salt-assembly experiments maintained constant pressure af-ter an initial period ofexpansion that accompanied the attain-ment of a thermal steady state. The pressure for the pyrex-as-sembly experiments often drifted considerably with time requiringpressure adjustments over long periods. The estimated precisionof the temperature measurements is +5'C.
For all experiments, reaction direction was determined by com-paring X-ray scans ofthe run products with those of the starting
BARTON: PHASE EQUILIBRIA IN THE BeO-AI,O,-SiO,-H,O SYSTEM 281
Table 3. Analyses of the beryls used in the experiments
quebecl( N . M . N . H . # r 2 3 2 0 7 )
Table 4. Results for beryl breakdown and pyrex-assemblycalibration
B e - 1 6 4 1 7 . 0 1 2 8 5 6 ' 5 - 7 . ? 6 . 2 0 s t r o n g c h + p h + q zBe-165 6 .0 1350 5 .8-6 .2 5 .40 modera te beBe- l 66 5 .5 I 350 6 .8 -7 .2 6 .30 s t rong ch+ph+qzBe-167 20 .0 1225 7 .3-7 .7 6 .75 nodera te ch+ph+qz
B e - 1 7 2 4 . 0 l 4 l 0 6 . 8 - 7 . 2 5 ' 4 0 n 0 r e a c t i o nB e - 1 7 5 1 8 . 0 1 2 0 0 6 . 8 - 7 . 2 6 . 3 0 w e a k b eB e - l g 8 4 - 5 l 4 l 0 6 . 4 - 6 . 8 5 . 9 5 v e r y s t r o n g c h + p h + q zB e - 2 0 1 4 . 5 l 4 l 0 5 . 6 - 5 . 9 5 . l 5 w e a k b eB e - 2 0 2 1 6 . 0 1 2 5 0 6 . 2 - 6 . 6 5 . 7 5 w e a k b e
Be-204 lB .0 1250 6 .9-7 .2 6 .30 no reac t ronBe-205 8 .0 ]450 5 .6-5 .8 5 . ' l5 s t rong ch+ph+qzB e - 2 0 8 1 8 , 0 l l 5 0 7 . 0 - 1 , 4 6 . 5 0 w e a k b eBe-234 48 .0 l l50 7 .1 -8 .0 7 .05 s t rong ch+ph+qzB e - 2 3 5 3 . 0 ] 4 5 0 5 . 5 - 5 . 7 5 . 0 5 s t r o n g b e
Be,A l rS iUOln= BeAl ZO4+ Be25 i04+ 55 i02 water -sa tura ted , sa l t assemblv
1 Ana lys is by R.E. S tevens , p rov ided by !1 . F le ischer (U.S. Geo1og ica lSurvey) .
2 Detemined by loss on ign i t ion .
mixes. The anhydrous charges were well sintered, homogeneouspellets that were quite difrcult to grind, whereas the hydrouscharges were loose powders ofrather coarsely recyrstallized phas-es. A reaction was considered to have taken place if there wasmore than a 20o/o change in the relative peak intensities ofphaseson one side of the reaction versus the other. If any of the peaksindicated an inconsistent direction ofreaction, the run was con-sidered to indicate no reaction. The relative intensities of thepeaks for Reaction 4 were sensitive to the degree ofgrinding. Itwas possible to change the apparent direction of the reactionfrom beryl + kyanite to chrysoberyl + quartz with moderategrinding for experiments near equilibrium, As a result, only thoseexperiments for which extent ofreaction was strong (peak ratioschanged by more than a factor of two) to very strong (peaks ofthe reactant assemblage nearly gone) were used (determined byXRD after slight gnnding). For some runs, grain mounts weremade and optically examined, but they were used to determineonly the presence or absence ofphases and not the direction ofreaction. For the water-bearing experiments, only those runs inwhich water was unambiguously present on opening of the cap-sule were used.
Table 4 gives the results for Reaction I and for the cordieritecalibration reactions. The critical experiments for Reaction I areplotted in Figure 2 along with the position of the equilibriumcalculated from the thermodynamic model presented later. Sev-eral experiments conducted on Reaction I (Table 4) in the pres-ence of excess water gave complete reaction to beryl in less thanI d at 700 and 800"C at pressures up to 20 kbar. The uncertaintyassociated with the impurities in the beryl could have been avoid-ed by using synthetic beryl; however, the ease with which com-plete yields of medium-grained beryl can be obtained by thismethod was not discovered until too late in the study.
Results for Reactions 2-4 are given in Table 5 and are plottedin Figures 3-5. These results agree reasonably well with those ofHsu (1983) and Franz and Morteani (1981). The slightly highertemperatures found in this study may be due to the alkali contentof the beryl used in these experiments. Franz and Morteani andHsu used synthetic beryl that presumably was alkali free. Asdiscussed in the Thermodynamics section, the alkali content ofberyl should have a significant efect on its stability. The effectofalkalies has been taken into account in the calculated curvesfor Figures 2-5.
Cord ie r i te = Sapph i r ine + Quar tz d ry , pyrex assembly
B e - 2 1 5 1 0 . 0 1 2 5 0 7 . 9 - 8 . 1B e - 2 1 1 ] 0 . 0 1 2 5 0 8 . 1 - 8 . 3B e - 2 l B 1 0 . 5 1 2 5 0 7 . 7 - 7 . 9R e - 2 2 1 4 . 0 | 3 8 0 7 . 8 - 8 . 0R e - 2 2 7 4 . 0 I 3 8 0 8 . I - 8 . 3
c o m p l e t e b ecompl ete bec o m p l e t e b every strong be
n o r e a c t i o nweaK cow e a k s p + q zvery strong cds t r o n g s p + q z
Another possible source of error is that the water content ofberyl may not have reached equilibrium values during the ex-periments. Jochum et al. (1983) found that hydration and de-hydration in cordierite proceeds rapidly at temperatures above400"C and pressures above 1 kbar (times on the order ofa fewhours or less). It therefore seems likely that beryl achieved anequilibrium water content during the experiments. Alkalies inberyl, however, inhibit dehydration (Ginzburg, 1955) and thuspossibly slowed hydration in these experiments,
Silica-buffering experiments
An extensive series of aqueous silica-buffering experimentswere performed at I kbar on various assemblages from the BeO-
Fig.2. The dry breakdown of beryl at high temperature. Theopen rectangles indicate reaction to chrysoberyl + phenakite +quartz, tlre filled rectangles indicate reaction to beryl, and thehalf-filled symbols indicate no reaction. The ideal line is calcu-lated for pure beryl; the corrected line takes into account theimpurities in the experimental beryl. See the text for details.Abbreviations from Table 1.
(t,
(!-o.:(o
o(t,(D
G
282 BARTON: PHASE EQUILIBRIA IN THE BeO-AI,O,-SiO,-H,O SYSTEM
Table 5. Results for high-pressure, water-saturated reactions
R u n N o . T j m e T e m p .
( h ) ( " c )
Pres su re
(bars )
R e s u l t s
4 8 e A r S i 0 4 ( 0 H ) + 2 5 i 0 2 = B e 3 A l 2 5 i 6 0 t B + B e A l 2 0 4 + 2 H 2 0
o
J
o
u)oo(L
Be-l 53 96 500Be-188 48 520B e - l g l 3 6 5 5 5Be-l 93 24 590B e - 1 9 5 2 4 5 8 0
Be-l 99 48 545B e - 2 0 0 2 4 5 8 5
B e - 2 6 2Be -265B e - 2 6 9
80008u00
I 0000I 2000I 2000I 0000l 2000
I 5000I 5000r 6500I 7000
moderate eu + qzvery strong be + chmoderate be + chvery strong be + chweak eu + qz
moderale eu + qzn 0 r e a c ! 1 0 nweak eu + qzn o r e a c t r o nweak be + ch
moderate eu + qzvery strong be + ch
s t r o n g e ustrong be + ch + phmoderate be + ch + phs t r o n g e umoderate be + Ch + ph
n 0 r e a c t t o nweak euno react i onweak euweak be + ch + ph
weak euweak be + ch + ph
moderate be + kyas t r o n g c h + q zstrong be + kyavery strong ch + qz
Be-224 21 640 I 5000B e - 2 2 8 2 0 6 5 0 1 5 0 0 0
t0000r 00008000
I 20{.J0| 2000800080008000
I 5000I 5000
2 o 8 e A l 5 i 0 4 ( 0 H ) = 3 B e 3 A l 2 S i 6 0 t B + 7 B e A l 2 0 4 + 2 B e Z S i 0 4 + 2 H Z 0
B e - 1 7 9 6 0 5 8 0B e - 1 8 3 3 6 5 9 0B e - l 8 5 4 8 5 5 0B e - l d 6 2 4 6 1 0Be-l 92 12 625
B e - l 9 6 4 8 5 4 0B e - 2 1 0 4 8 5 3 5B e - 2 1 4 4 8 5 4 5Be-223 20 665Be-225 20 680
300 350 400 450 500 550 600 650 700 750 800
Temperature (oC)
Fig.4. Experimental results on the breakdown ofeuclase tquartz. The ideal line is calculated for pure beryl; the correctedline takes into account the impurities in the experimental beryl.See the text for details. Abbreviations from Table l.
the charge in order to make opening the capsules easier at theend ofthe experiments. Platinum was used because gold capsulestended to anneal themselves to one another when run together.Charges consisted of 15-35 mg of silica solution or distilled waterloaded using a microsyringe and l-2 mg of the solids that com-posed the buffering assemblages. After loading, the capsules werecrimped shut, the crimped ends clipped straight, and then sealedby arc welding. At each stage the capsules were weighed in orderto determine the masses of the reactants and to detect losses. Atthe end ofa run, any capsule that differed by more than 0. I 5 mgfrom its prerun weight was rejected. Most capsules varied by lessthan 0.10 mg.
The powders for the buffering assemblages were prepared bygnnding the reagents to coarse powders and then sieving andwashing with distilled water to concentrate the 30- to 150-pmsize fraction. Bromellite, however, was only coarsely crushedunder acetone in a glove bag due to its toxicity. The beryl usedin these experiments was not dehydrated.
Distilled water and Ludox (ammonia-stabilized colloidal silica)were used to prepare starting silica solutions of various concen-trations. The experiments were "reversed" by starting with silicaconcentrations on the high and low sides ofthe equilibrium value.Because aqueous silica is the most abundant-but not the only-species in such solutions, approaching equilibrium from bothdirections with respect to silica transferred the greatest amountofmass in both directions. ln other words, even though analogousbuffering reactions involving rhe solid phases and the aqueousberyllium and aluminum species can be written, the amount ofsolution and reprecipitation necessary to buffer their concentra-tions is considerably smaller than that needed to buffer the con-centration of silica. Therefore, by forcing the silica values tochange substantially from either direction, rnuch more materialis dissolved and precipitated than would be necessary to butrerthe other species alone. These experiments should then be asclose to "true" reversals as many conventional phase-equilibriumexperiments in which there are one or more degrees of compo-sitional freedom.
After their preparation the capsules were loaded in groups offour into standard cold-seal bombs. Running four capsules to-gether allowed multiple determinations of the same equilibriumwhile eliminating the effect of variations in temperature and pres-sure between runs. Internal chromel-alumel thermocouples were
Be-230 72 500 6000Be-23f 72 515 6000B e 3 A l 2 5 i 6 0 t 8 + 2 A l 2 s i 0 5 ( K y a ) = 3 B e A l 2 0 4 + 8 5 i 0 2 ( w i t h e x c e s s r a t e r )
24 775t20 80020 85020 850
AlrO3-SiOr-HrO system and from the BeO-SiOr-HrO subsystem.In these experiments, the solid-phase assemblage bufers the con-centration of aqueous silica in solution. Given a measured silicaconcentration and the assumption that aqueous silica obeys Hen-ry's law over the concentration range ofinterest, the equilibriumconstant of the reaction (and hence the free energy) can be ob-tained directly. This method has been used exrensively by J. J.Hemley and coworkers in studies of the MgO-SiOr-HrO andAlrO3-SiOr-HrO systems (Reed and Hemley, 1966; Hemley etal., 1977a, 1977b, 1980).
In this study the method has been modified somewhat fromthat of Hemley et al. (1977a) to permit much smaller samples.Capsules were made from 2-cm lengths of 3-mm-diameter plat-inum tubing. The tubing was carefully annealed prior to loading
2 0 E u = 3 B e + 7 C h + 2 P h + t o w
C$
eo
> V< < This study
i"'< Hsu (1983)< Franz and Morteani (1981)< Seck and Okrusch (1972)
- Calculated ( ideal)
300 350 400 450 500 550 600 650 700 750 800
Temperature (oC)
Fig. 3. Experimental results on the breakdown ofeuclase. Theideal line is calculated for pure beryl; the corrected line takes intoaccount the impurities in the experimental beryl. See the text fordetails. Abbreviations from Table l.
o(u
I
o
oo0)
n
4 E v + z Q z = 1 B e + 1 C h + 2 W
1Be + 2Als = 3Ch + 8Qz //
> This Study-- Calculated (corr.)ts Seck and oirusih . /'
Mtstbl w/ And (id )> Franz and Modeani- Mtstbl Ext ( ideal)- Calculated ( ideal)
BARTON: PHASE EQUILIBRIA IN THE BeO-ALO'-SiO,-H,O SYSTEM
Table 6. Results for silica-bufering experiments
283
R u n N o . T ' i m e ( " C ) l o g r H o s i o o R u n n o . T i m e ( ' C ) l o 9 t l 4 s i 0 4
d a y s i n i t i a l f i n d l d a y s i n i t i a l f i n a l
Fig. 5. Experimental results on the water-saturated break-down ofberyl + aluminum silicate. The aluminum silicate phaserelations are calculated from the data in Robinson et al. (1982).All the other curves are calculatedfrom the thermodynamic mod-el. The calculated (corrected) curve is for the alkali-containingberyl used in this study. The solid curve that intersects the kya-nite-sillimanite reaction is for pure beryl and the stable aluminumsilicate polymorph, whereas the dotted and the dot-dash curvesare for the metastable reactions with pure beryl appropriate tothe experiments Franz and Morteani (1981) and Seck and Okrusch(1972), respectively. Abbreviations from Table 1.
used with the tip of the thermocouple at the midpoint of thecapsules. The thermocouples were calibrated against a standardthermocouple which was in turn calibrated against the meltingpoints ofNaCl and ice. Temperatures are believed to be accurateto within +5'. Bourdon tube-type gauges were used to measurethe pressures. These gauges were intercalibrated with one another.Calibration was also performed against a new gauge certified bythe factory to !.2%. Pressures are believed to be accurate within470 (40 bars) ofthe reported values.
Run times varied from a few days at the highest temperaturesto over 3 mo at the lowest temperatures. The length of run wasdetermined by experience. In general, the higher the temperatureand the smaller the mass of silica that needed to be transferred,the less the time that was required to reach equilibrium.
Quenching was done at constant pressure by cooling the bombas rapidly as possible with an air blast. A few runs were quenchedby immersion of the bomb in water. In all cases the temperaturewas below 300'C within 30 s ofthe start ofthe quench and belowl00qC within 2 min. The capsules were then removed from thebomb, weighed, washed, and analyzed.
Analysis consisted of first opening the capsules in distilledwater and carefully washing to recover all the charge. The so-lutions were then diluted to 50 mL with distilled water and ana-lyzed by using the molybdate blue method (Strickland and Par-sons, 1972). Althoug*r the opening and dilution ofthe runs wasdone in glass containers, large variations in silica concentrationsbetween duplicate runs were detected only in a few analyses whereNaOH solutions were used in the washing step or where analysistook place more than I d after opening. Such runs were rejected.The estimated uncertainty in the molality of aqueous silica is+0.05 log units. This compares with +0.02 log units for theexperiments of Hemley et al. (1977a, 1977b, 1980) in which themass of solution was about 50 times larger. Better results couldhave been obtained using rapid-quench bombs and the microan-alytical techniques described by Frantz and Hare (1973).
After many of the runs, grain mounts of the buffer assemblages
were examined optically for new phases or for the complete de-composition of the starting phases. The high-temperature limitsfor experiments on euclase and bertrandite were determined inthis manner, although it was usually clear from the silica analysesthat something anomalous had happened. No additional phaseswere observed in any of the experiments. Nothing was detectedthat might correspond to the "hybrid" phase of Franz and Mor-teani (1981). None of the assemblages used contained the bulkcomposition of the "hybrid" phase; even if it is stable it may nothave been able to nucleate.
Several ofthe reactions studied were metastable relative to oneor more alternative assemblages; however, careful checking es-tablished that in many cases it was possible to maintain themetastable assemblage without nucleation of the stable phase(s)throughout the course of the experiment. Table 6 presents theresults for these experiments. The results are plotted in Figures6-8.
Aqueous silica concentrations measured for two butrers (ber-yl + chrysoberyl + andalusite, beryl + chrysoberyl + euclase)were consistently below the values predicted using all the other
Be-94aBe-94bBe-94cBe-94dB e - l 2 l dB e - 1 2 6 d
Y This Study (Ph/Br) This Study (Bi/Br)I Hemley et al (1977a,1980)> Hsu (reversal)(1983)
Metastable- Calculated
284 BARTON: PHASE EQUILIBRIA IN THE BeO-Al,O,-SiOr-H,O SYSTEM
370 380
I
o
o
I
E
o
Temperature (oC)
Fig. 6. Silica-buffering results in the BeO-SiO,-H2O systemat l-kbar water pressure. The l-kbar bracket of Hsu (1983) isshown for comparison. Abbreviations from Table 1.
results (Fig. 6). These two assemblages, which have the highestsilica concentrations ofthose studied, probably precipitated somesilica during quench, although no evidence was seen in the grainmounts. Calculations based on the results ofRimstidt and Barnes(1980) support this argument. The 540"C experiments on chryso-beryl + andalusite + beryl were water quenched unlike theothers, and perhaps this procedure accounted for their closerapproach to the calculated equilibrium. Air-quenched experi-ments at 600'C scattered widely below the calculated equilibriumvalue. The results for these two reactions were not used in de-riving the thermodynamic properties.
There is a large discrepancy in the position of the reactionbertrandite : phenakite + water between the reversed results ofthis study using silica buffering techniques and the results ofHsu(1983) using conventional reversal techniques (Fig. 6). Hsu foundthat the reaction takes place in the mid-300eC range at pressuresfrom 500 to 3500 bars. In contrast, the results here require thetemperature ofreaction to be less than 300"C, probably in themid-200'C range. There is no obvious cause for this difference;other results from the two studies on the euclase breakdownreaction agree well (Figs. 3, 7, 8). Both data sets are compatiblewith the entropy and heat-capacity data on the phases. Severalpossibilities exist. First, the results of Hsu may represent meta-stable recyrstallization ofbertrandite from finely ground to coarsermaterial at a rate much faster than the (stable) growth of phen-akite. This is consistent with the much better cleavage in ber.trandite that would tend to make it grind easier than phenakite,but would require that the precipitation of bertrandite from so-lution be kinetically favored. Bertrandite spontaneously decom-poses between 450 and 500'C; previous attempts to determinethe reaction have either yielded bertrandite stability limits in thisrange from synthesis-type experiments (Bukin, 1967; Ganguliand Saha, 1967) or found the growh of bertrandite very difrcultto achieve (this study; P. Renders, personal communication, 1984).Hsu's brackets indicate a higher Clapeyron P-7 slope than pre-dicted by the entropy and volume data; however, because hisbrackets are wide, a curve can be constructed that is compatiblewith the calorimetry and all but one of his experiments. A steep€rslope might indicate kinetic control of recrystallization whichshould be nearly independent of pressure (e.g., Wood and Wal-ther ,1983) .
An alternative interpretation is that the silica concentrationsfor bertrandite are too high. This might result from unusuallyhigh surface energies on the bertrandite or from unexpected com-
400 410 420 430
Temperature (oC)
Fig. 7 . Silica-butrering results for euclase-bearing assemblagesat l-kbar water pressure. Abbreviations from Table 1.
plexes in solution. Surface energies should not have been a prob-lem because the reactants were quite coarse and the reactionscould be tightly reversed at 350rc and above. If the pH in theexperiments were strongly basic, then significant concentrationsof polymeric silica species could have been present. BeO, how-ever, is amphoteric and thus the solutions should have been nearneutral. Furthermore, the same effect should have occurred forthe phenakite-bromellite assemblage and should not have changedthe intersection ofthe two reactions. Interference ofBe-contain-ing species in the analytical method is another possibility, butshould be ruled out for the same reason as pH.
Thete seems no obvious experimental reason to prefer one setofbertrandite results over the other. Free energies ofbertranditeare derived using both sets in the following section, and theimplications of each are discussed in the Calculated Mineral Sta-bilities section.
TtrnnuonvNAMrc MoDEL
In order to make maximum use of the experimentaldata from this study and the experimental and calori-metric data from the literature, and then to extrapolatethese results to nature, it is necessary to construct a modelofthe thermodynamicproperties ofthe phases in the BASHsystem. The derivation of such a model is discussed inthis section, along with a review of how it compares withearlier estimates of the thermodynamic properties of min-erals in the BASH system. The model is based on a least-squares fit of published phase-equilibrium and calori-metric data and the data presented here. The method ofHaas and Fisher (1976) was used. Because water has asignificant effect on the stability of beryl, it is first nec-essary to discuss ways by which the energetic effect ofwater can be taken into account.
Hydration of beryl
Natural beryl contains up to several weight percent wateroccurring in the channels in the structure. Other volatilespecies as well as cations (principally alkalis and alkalineearths) are found in the channels (Beus, 1966; Cern!, 1975;Goldman et al., 1978; Hawthorne and -ernf, I 977). Sim-ilar channel constituents are common in cordierite (Gold-
a Ch + Ph/Eu Be/Eu + PhI Hemley et al (1977a,'- Metastable ext s- Calculated
BARTON: PHASE EQUILIBRIA IN THE BeO-AI,O,-SiO,-H,O SYSTEM 285
man et al., 1977; Cohen et al., 1977), and their presencehas a major effect on cordierite stability raising the high-pressure stability by several kilobars (Kurepin, 1979;Newton, 1972; Newton and Wood, 1979). Similar resultsfor beryl were anticipated by Burt (1978) and were, infact, found in this study. The results of several experi-ments on the hydrous and anhydrous breakdown ofberyl(Table 4) demonstrate that the stability field of beryl isgreatly expanded by the addition of water. The volumeof reaction apparently chang,es sign for several importantreactions (see below). A number of experimental studieshave been made on the substitution of volatiles in cor-dierite (e.g., Mirwald and Schreyer,1977 Mirwald et al.,1979; Johannes and Schreyer, l98l), but none have beenmade on the substitution of volatiles or other species inberyl.
The significant effect of channel water on the stabilityof beryl requires that hydration be taken into account inderiving a thermodynamic model for the BASH systemand in discussing the stability relations of beryl in nature.Three hydration models were considered: (l) ideal solu-tion between end-member anhydrous and hydrous beryls;(2) zeolitic water modeled using adsorption isotherms,and (3) a nonenergetic, volume-only interaction ("bottlemodel").
Newton and Wood (1979) and Kurepin (1979) modeledwater-containing cordierite as a solid solution betweenanhydrous cordierite and a hydrous cordierite of fixedwater content. The mixing properties of this solution wereassumed to be ideal with the number of sites available formixing per mole the same as the number of water mol-ecules per mole of the hydrous cordierite end member.This model was examined for beryl because of the struc-tural similarity between beryl and cordierite. Reaction 5is an analogous hydration reaction written for beryl,
BerAlrSiuO,. * nHrO: BerAlrSiuO,r-nHrO, (5)
where z is the number of moles of water per mole ofhydrous beryl. The equilibrium condition for this reactionis given by Equation 6
380 410 440 470 500 530
Temperature (oC)590 620
Fig. 8. Silica-buffering results for high-temperature assem-blages in the BeO-AlrOr-SiOr-HrO system at l-kbar water pres-sure. See text for discussion. Abbreviations from Table 1.
solute uncertainty in these values, but varying any of theparameters by more than 100/o gives a considerably worsefit to the experimental data, given the other assumptionsnecessary. These values produce reasonable agreementwith the cordierite hydration data of Mirwald and Schrey-er (1977), although they systematically underestimate thewater content at low pressures. Newer data on the watercontents of cordierite given by Mirwald et al. (1979) sug-gest that the variation of water with pressure and tem-perature may be more complex than that predicted by theNewton-Wood hydration model.
Martignole and Sisi (1981) evaluated the activity ofanhydrous cordierite by Gibbs-Duhem integration of theactivity over the pressure ranges of interest. Their tech-nique is similar to those used for evaluating adsorptionof water in zeolites. Although their calculations are basedon the cordierite hydration data of Schreyer and Yoder(1964), which are probably less accurate than more recentdata, the calculations based on the adsorption model arein somewhat better agreement with phase equilibria thanare calculations based on the Newton and Wood model.Unfortunately, this technique cannot now be applied toberyl because the required hydration measurements arenot available.
An alternative, simple model is to consider the cavitiesin the beryl (or cordierite) structure as "bottles" that cancontain water, but with no energetic effect: the differencein Gibbs free energy between an anhydrous beryl and aberyl saturated with water would be -V",,(P - l), where2""" is the efective volume of the "bottle." This modelpredicts that the isohydrons (lines of constant water con-tent) parallel the isochores of water, which is generallyconsistent with the cordierite experiments. In addition,the simplicity of this model greatly facilitates the appli-cation ofpHAszo or similar data-reduction techniques be-cause this model is linearly related to the Gibbs free en-ergy, unlike the first two discussed. One consequence ofthe bottle model is that the nominally water-free reactionssuch as Reactions I and 7
BerAlrSiuO,, + 2AlrSiOs:3BeAlrOo + 8SiO, (7)
o'
E
LIib - ZAS. +
where X^" and X"" are the mole fractions of anhydrousand hydrous beryl and the values of n, A,Ho, ASF, and AZneed to be determined for beryl. For beryl, as for cor-dierite, the volume of the anhydrous and hydrous phasesare the same within uncertainty and thus A Z : 0. Becauseno hydration data are available for beryl, the water modelis constrained only by the efect that varying its parametershas on the internal agreement of the phase equilibria andsolubility data. At an earlier stage of this study (Barton,l98l), an iterative frt of this model with other (then avail-able) thermodynamic data gave n: 1.2, AH: -53 840J/mol, and A,S : -136.6 J/(K.mol). These values fallwithin the stated uncertainty of the Newton and Woodvalues for cordierite. It would be difrcult to give an ab-
P v
LV dP + nRT ln :;"H;B : 0,)(eslnro (0)
*f' ' ' l - -'" "' l---
. . O B e + A n d / C ha Belch + Ph Be/Ph + And (mtstbl)I Hemley et al (1977a,1980)
Metastable ext s- Calculated
286 BARTON: PHASE EQUILIBRIA IN THE BeO-ALO,-SiO,-H,O SYSTEM
will be nearly free of curvature because the only changeis the addition of a constant volume (although there willbe minor curvature resulting from differences in expan-sivity and compressibility). In contrast, the Newton andWood (1979) and Martignole and Sisi (1981) models pre-dict substantial curvature at low pressures.
The cordierite hydration data of Mirwald et al. (1979)are somewhat more consistent at low pressures with theideal-solution model than with the bottle model. A con-sistency test is not appropriate for the adsorption methodbecause the adsorption isotherms are calculated directlyfrom the hydration data. The bottle model agrees reason-ably well with the hydrarion data of Mirwald et al. (1979)for cordierite at pressures above I kbar, excluding theirfour highest-pressure experiments below 600"C. The cal-culated V*" for cordierite is 16.2 + l.l cm3 based on 30measurements (excluding the highest- and lowest-pressuredata). The value for all 42 measurements given by Mir-wald et al. is 19.2 + 6.9 cm3. These values compare fa-vorably with 14.l cm3 estimated here for beryl. The bottlemodel, therefore, appears to be reasonable for both cor-dierite and beryl, at least to a first approximation if ac-curate water contents are not needed at low pressures.
The simplicity of the bottle model is its great advantage;however, there are some observations that are inconsis-tent with the simplistic interpretation of no energetic in-teraction. Spectroscopic investigations of water in cor-dierite and beryl clearly show that there is an energeticinteraction between the water and the structure of themineral (e.g., Aines and Rossman, 1984). Available evi-dence, however, suggests that the energy ofthis interactionis low (Langer and Schreyer, 1976; Aines and Rossman,1984), and thus it should contribute little to the Gibbsfree energies ofthe hydrated phases at moderate to hightemperatures and pressures. This contribution could be-come important at low temperatures and pressures. Thesomewhat poorer agreement of the calculated phase re-lations with natural assemblages could be a consequenceof this interaction (see following sections) as could thedifferences between the model and the cordierite hydra-tion data. The molecular sum of alkalis and water com-monly exceeds l.0 per formula unit in alkali-rich naturalberyls (e.g., Beus, 1966) further demonstrating that thesimplistic volume-for-volume replacement relationshiphypothesized here cannot be correct in detail. Lackingexperimental constraints on the hydration of pure andalkali-bearing beryl, however, the development of moreelaborate hydration models would be purely speculative.
Beryl hydration is accommodated in thermodynamiccalculations by adding an additional water volume to thevolume of reaction. This formulation should hold for oth-er volatile (noninteracting or weakly interacting) com-ponents in the beryl structure. It is clear that for volatile-saturated systems, the whole volume should be added andthat for volatile-free systems, no cavity volume should beadded. The case of 0 < Puro ( P,o*r requires discussion.The effective volume for fluid-undersaturated cases isV-"Prr,id/P,oot. This can be seen by imagining a reaction
taking place in a system with an osmotic membranepermeable only to the fluid. The total volume of reactionwill include Vu,but in calculating the Gibbs free energychange from the standard state, the AZ,"uo" will be inte-grated from I to P,oo,, whereas Z*" will only be integratedfrom I to Pou,o. Then, to the extent that 2""" is independentof pressure, the contribution to AG from the fluid will beVu,Po.^.
The efect of water on the stability of beryl is consid-erably more pronounced than the effect of water on thestability ofcordierite. This is because in cordierite-break-down reactions. an increase in aluminum coordinationgenerally leads to a large volume of reaction favoring thestability of the high-pressure phases, whereas, in beryl-breakdown reactions. there is no aluminum-coordinationchange and consequently a smaller AZ.oro.. This is illus-trated by two reactions: the breakdown ofberyl to chryso-beryl, phenakite, and quartz (Reaction I , discussed above)and Reaction 7. Figure 9 shows calculated curyes for Re-action 7 for P"ro : Proor,0.5P.rr, and 0. Decreasing waterpressure reduces the stability ofberyl * aluminum silicateby several hundred degrees at moderate pressures. Thisdecreased stability results from an approximately 90'change in the Clapeyron slope at any pressure. Differencesin the predicted low-pressure phase equilibria might pro-vide a way to test the difference between the alternativehydration models.
Application of pn-Lszo
The program nHAS2o (Haas and Fisher, 1976) utilizes aweighted least-squares method to enable simultaneous es-timation and correlation of the thermodynamic propertiesofrelated phases. Data that can be evaluated by the pro-gram included heat capacities, heat contents, entropies,volumes, compressibilities, expansivities, heats of reac-tion, free energies ofreaction (e.g., from phase equilibria),and EMF voltages. Other types of data can be incorpo-rated by means of user-written subroutines if they can berelated to the underlying functions in a linear way. TheBASH system is well suited for application of pnaszo.Eighty-six data sets containing more than 1000 indepen-dent observations were used. The data sets include alldata types except EMF. The system is greatly overdeter-mined for the seven species ofinterest and therefore suit-able for a least-squares fitting procedure.
Linear progmmming methods represent an alternativeway to extract thermodynamic properties from a large setof experimental data (e.g., Halbach and Chattet'ee, 1984).These methods have the advantage of treating reversalexperiments as the inequalities that they are (in AG),whereas regression methods are better suited to data thathave a regular distribution about the true value (e.9., ca-lorimetric results, solubilities). In this study, only regres-sion techniques were used, although the ideal solutionmight combine a weighted linear programming methodfor phase-equilibrium reversal data with a regression tech-nique for other data. Reversal brackets were treated in-dependently with each half-bracket included in the data
BARTON: PHASE EQUILIBRIA IN THE BeO-ALO,-SiO,-H,O SYSTEM 287
set weighted by its P-I estimated accuracy. This resultsin a relatively even weight being applied throughout theinterval between the brackets (Demarest and Haselton,l98l) and thus should help minimize unjustified bias to-ward the midpoints of the brackets in the final fit.
The data of Robinson et al. (1982) for phases in theASH system were accepted as fixed values for the eval-uation of the thermodynamic properties of the berylliumphases. The data for BeO given in Robie et al. (1978) werealso used without modification. Free energies of water atelevated temperatures and pressures were calculated froma program based on Haar et al. (1979, l98l). All otherparameters were allowed to vary including the Gibbs freeenergy ofaqueous silica at I kbar.
The available heat-capacity, heat-content, and calori-metric-entropy data were fit first without employing anyof the other data. The volumetric data also were fit in-dependently. The results for the heat capacities and vol-umes were then fixed in the preliminary fitting of thephase-equilibrium and heat-of-reaction data. This pre-vented the program from diverging. Following the prelim-inary fit, all the regressed terms were allowed to vary toobtain the final fit. A few data were rejected in the processas it became apparent that they were inconsistent with thebulk of the information. It is possible to justify theseexclusions in all but one case. The data were all weightedin the regression by the author-reported uncertainties.
Results and discussion
In this section, the derivation of the thermodynamicproperties and their agreement with other thermodlnamicdata are discussed. The thermodynamic model reproducesmost of the experimental results within stated uncertain-ties; calculated phase relations based on the model are ingood agreement with observations on natural assem-blages. Comparison of the predictions of the model withnatural assemblages, however, is deferred to the next sec-tron.
The thermodynamic properties from the final pHnszo fitare summarized in Table 7. The thermophysical prop-erties are summarized in Table 8. nEcroN, a Fortran pro-gram written by John Haas (U.S. Geological Survey), wasused in conjunction with pxaszo to provide estimates ofthe errors in the thermodynamic properties. Hemingwayet al. (1986) have provided more complete tables for thethermochemical properties of the beryllium minerals.
Volumetric data. Thermal expansivities and compress-ibilities were incorporated in the model. Data for phasesin the ASH system were taken from Robinson et al. (1982).Hazen et al. (1983, personal communication) determinedvolumes of bertrandite, beryl, bromellite, chrysoberyl, eu-clase, and phenakite as functions ofpressure at room tem-perature. The compressibility of behoite was estimatedfrom the data for bromellite. Expansivity data for berylwere obtained from Schlenker et al. (1977), for bromellitefrom Skinner (1966), and for chrysoberyl from Woolfrey(1973) and Cline (1979). Thermal expansivities for be-hoite, euclase, and phenakite were estimated from the data
25o 310 370 oto r"*o"r"rrre (tc)
Fig. 9. The low-temperature stability limits of chrysoberyl +qwftz at water pressure equal to different fractions of the totalpressure. See the text for details. Abbreviations from Table l.
for bromellite. All the volumetric data were consistentwith the final model within 0.2o/o, nearly all within 0.10/0.
Heat-capacity and third-law entropy data. Hemingwayet al. (1986) determined the heat capacities and thirdlawentropies of bertrandite, beryl, chrysoberyl (only high-temperature heat capacity), euclase, and phenakite bycombined adiabatic and differential scanning calorimetry;they discussed the compositional corrections applied tothe data for beryl and chrysoberyl. Furukawa and Saba(1966), Kelley (1939), and Kostryukov et al. (1977) mea-sured the low-temperature heat capacities and calculatedthe thirdJaw entropies of, respectively, chrysoberyl, phen-akite, and behoite. High-temperature heat capacities forbehoite were taken from the compilation of Stull andProphet (1974). Ditmars and Douglas (1967) determinedthe heat content of chrysoberyl from 273 to ll73 K. Be-cause all the heat-capacity measurements were done at800 K or less, it proved necessary to estimate values be-tween 800 and 1500 K so that the fitted polynomialsvaried smoothly in that range. This was done using anextrapolator method developed by G. R. Robinson, Jr.(U.S. Geological Survey), and by oxide sum methods(Helgeson et al., 1978). All the heat-capacity and entropydata fell within two (author-reported) standard deviationsof the measurements in the final fit.
Silica-buffering data. For the silica-buffering reactions,standard Gibbs free energies of reaction were calculatedfrom the relation
LGr: -RZ ln fttk$iocfllzo
where nt"o*o o and n are the molality and stoichiometriccoefficient of aqueous silica, ,Cro is the fugacity of waterat the temperature and pressure of the reaction, s is thestoichiometric coefficient of water. b is the stoichiometriccoefficient of beryl, and AZ*'* and V*" are, respectively,
o
j
ofooc)
* J'{at*,,* + bv*)dP, (8)
B e + 2 A l s = 3 C h + 8 Q zVariable Water Pressure
Hro- ' total
288 BARTON: PHASE EQUILIBRIA IN THE BeO-AI'O'-SiO,-H,O SYSTEM
Table 7. Thermochemical properties of some phases in the BeO-AlrOr-SiOr-HrO system
P h a s e N a m e Gzggi , t ru" 5z9sx
J / m o l J / K - m o 1
C P * *
c
J / K - m o l
VZsg Source
G S c p v
J /ba r
Andal usi te -2444564( 4 5 6 )
Behoite -a27288( 6 7 3 4 )
B e r t r a n d i t e - 4 3 0 0 6 2 5- 4 3 0 6 3 7 5
( 1 6 2 e )
E e r y l - 8 5 0 0 3 6 0( a n h y d r o u s ) ( 3 7 9 6 )
* E r r o r s g i v e n h e r e a r e 2 0 f o r f r e e e n e r g i e s o f r e a c t i o n f r o m t h e o x j d e s f o r a l l
* * c p = a + b T + c x 1 0 6 T - 2 + d x 1 0 - 5 T 2 + s 1 - 0 - 5
l R o b i n r o n e t a l . ( 1 9 8 2 ) 2 R o b i e e t a l . ( 1 9 7 8 ) 3 T h i s s t u d y 4 s t u l l a n d P r o p h e t
6 s e i t z e t a l ( 1 9 5 0 ) T H e m i n g w a y e t a l . ( 1 9 8 5 ) 8 H a z e n e t a l . ( i n p r e p )
p h a s e s e x c e p t t h e o x j d e s ,
( 1s7+ ) sHaas e t a1 ( 1980)
9 - 1 " ' s s t u d y , 6 r r " 6 6 n t l 5 u ( - 9 8 3 )
the volume change of the solids in the reaction and thevolume of the cavity. H4SiO4 is used as the aqueous silicaspecies because it is the one most commonly accepted(e.g., Hemley et al., 1977a). The actual identity of thespecies is not needed in the modeling as long as the activitycoemcient ofaqueous silica is constant over the concen-tration range of interest. This assumption is reasonablefor neutral species in aqueous solutions of low to moderateconcentrations. In this study the thermodynamic prop-erties of aqueous silica were constrained by the experi-mentally determined quartz solubilities of Hemley et al.(1977a, 1980). Their values are quite similar to the sta-tistical fit by Walther and Helgeson (1977) to much of theearlier silica solubility work. Only the data of Hemley andothers were used in the least-squares fitting in order tomaintain consistency with the data of Robinson et al.(1982) on the ASH system. Aqueous silica can then beeliminated from all the reactions by adding the Gibbs freeenergy of Reaction 9
SiO, (quartz) + 2H2O: HoSiOo (9)
thereby converting the free energies ofthe aqueous silica
reactions to Gibbs free energies of quartz-bearing reac-tions.
A correction for solid solution in the experimental berylwas applied to the free energies ofthe silica-buffering re-actions. This correction has a trivial effect on the fit andthe calculated curves. Several sets of silica-buffering re-sults were not used in the final fit. These include the datafor the beryl + chrysoberyl + andalusite and beryl +chrysoberyl + euclase experiments discussed under Ex-periments. Also eliminated were some experiments at310"C on the bertrandite + bromellite buffer. Only thoseexperiments that started near the final silica value wereused. The other experiments, which started much fartheraway from equilibrium, did not converge sufrciently toprovide good estimates of the equilibrium values. Thefinal model agrees well with all the silica-bufering resultsexcept for the two silica-rich reactions mentioned above.
Phase-equilibrium data. Free energies of reaction forthe high-pressure experiments were extracted using therelation
T,'AG?,, : -RZln fi,,o + (A4d0" + bV*,) dP. (10)
BARTON: PHASE EQUILIBRIA IN THE BeO-AI,O,-SiO,-H,O SYSTEM 289
The symbols are the same as for Equation 8. The Gibbsfree energies for the beryl-bearing reactions done in thisstudy were corrected for slight decreases in the activity ofberyl due to solid solution in the starting materials andfor the portion of the cavity volume occupied by alkalisand thus unavailable to water. The activity correctionamounted to 1.8 J/(K.mol) (: 4ln c*.,) for the Brazilianberyl and 0. 5 J/(K. mol) for the Quebec beryl, Ideal mixingwas assumed in the activity calculations, with the cations(Table 2) mixing on sites consistent with the crystal-struc-ture data (Hawthorne and Cemy,1977). The combinationofthese two factors accounts for the crossing at about 4kbar ofthe calculated "ideal" and "corrected" curves inFigures 3 and 4. This crossing implies that the reversedberyl-bearing reactions determined in this study are slight-ly metastable relative to the reactions in the pwe system.Decreasing the entropies and the volumes of these reac-tions (i.e., treating the beryl as if it were pure) degradesthe fit ofthe data and predicts unrealistically low valuesfor V*".It is the prediction of an unrealistically low cavityvolume that is the main reason for including the com-positional correction. This correction, however, is prob-ably well within the total uncertainties, and thus it isretained even though it leads to what must be an imperfectinterpretation of the true phase relations.
The value of V. "
was allowed to vary with only looseconstraints applied (the value was estimated for the pur-poses of the refinement as 20 + l0 cm3). This value waschosen because it is consistent with the range of watercontents observed in natural beryls and cordierites andthe amount found to enter cordierite in experiments. Thethermal expansion and compressibility of y.," were con-strained to equal those of beryl. The final estimate (14.1cm3) is consistent with maximum water contents of aboutone mole water per mole of beryl, somewhat less thanthat found for cordierite and that predicted for beryl usingthe Newton and Wood model (Barton, 1981).
The results agree reasonably well with the data of Franzand Morteani (1981) and Hsu (1983) on euclase-bearingreactions that were used in the fit. Because the "hybrid"phase was not observed in this study, direct commentcannot be made on its stability. The phase appears to bemetastable for several reasons. The phase has not beenreported from nature although appropriate bulk compo-sitions exist. Also, the field of occurrence for the hybridphase shown by Franz and Morteani cannot be a stablefield even considering only their other experimental re-sults.
Franz and Morteani (198 l) and Seck and Okrusch (1972)did experiments on Reaction 4. Their results, taken to-gether, indicate that this reaction under water-saturatedconditions has a low negative slope (Fig. 3). A negativeslope in the kyanite field is incompatible with the resultsof this study (Fig. 3) and with the calculated LV. Theaccuracy of the other determinations is not clear-Seckand Okrusch may not have reversed their reaction; in thisstudy the direction of reaction was found to be difficultto determine by X-ray ditrraction methods-hence, they
Table 8. Thermophysical properties of some phases in theBeO-A1,Or-SiO2-H2O system
Phdse NameC o e f f i c i e n t s f o r V o l u m e E q u a t i o n
a b c d
Andal usi te 50.0729
Behoi te 21 .8476
B e r t r a n d i t e 9 0 . 0 3 1 1
B e r y l 2 0 2 . 7 4 7 6
B r o m e l I i t e 8 , 2 1 6 7
Chrysoberyl 33.6087
c o r u n d u m 2 5 . 2 0 1 7
D i a s p o r e 1 7 . 4 0 5 8
Eucl ase 46,2613
K a o l i n i t e 9 8 . 4 1 9 6
K y a n i t e 4 2 . 3 1 7 4
Phenaki te 36.6712
P y r o p h y l l i t e 1 2 6 . 8 1 9 0
0 Q u a r t z 2 2 . 1 8 1 9
g Q u a r t z 2 3 . 5 7 9 4
Si I 1 i inani te 49, I 338
Vdummy 14.2420
were not heavily weighted in the refinement. These resultsand Hsu's (1983) bertrandite experiments were the onlydata that could not be made consistent with the model orjustifiably eliminated from consideration.
Several factors probably contribute to discrepancies be-tween the thermodynamic model and the phase-equilib-rium data. The most important is almost certainly theinadequacy of the simple beryl hydration model to fullyaccount for the energetic contribution ofwater and othervolatiles. This is illustrated by the relatively poor fit ofthe model to the reversals for Reaction 4 (Fig. 3). Reaction4 is nominally independent of water and has only a smallA Z.or;a" and AS; therefore the calculated position of theequilibrium is sensitive to Y*, The calculated slope forReaction 4 could be brought into agreement with the re-sults of this study by changing AV by +0.4 J/bar. Errorsof this magnitude could result from either uncertainty inVu or in the volumes of the phases (the total volume forone side of the reaction is about 29 J/bar). An additionalenergy contribution from the interaction of water with theberyl framework is another possibility, as suggested incordierite by the higher-than-predicted (bottle model) watercontents at low pressures and the ordering found by spec-troscopic studies.
The phase-equilibrium experiments of Hsu (1983) onthe reaction bertrandite : phenakite + water and the sil-ica-bufering results reported here are inconsistent. Pos-sible reasons for this were discussed under Experiments.The values in Table 7 represent individual fits to two setsof data using the calorimetric entropy and heat capacities.The Gibbs free energy of bertrandite given in Table 7 is1000 kJ more negative than the least-squares fit. Thisresult is still well within the experimental uncertainty andgives more reasonable breakdown temperatures (aboutl5.C higher).
On the basis of sl,nthesis experiments, Ganguli (1972)
290 BARTON: PHASE EQUILIBRIA IN THE BeO-AI'O,-SiO,-H,O SYSTEM
suggested that at I bar, beryl becomes unstable relativeto chrysoberyl + phenakite + cristobalite between 1300and 1400'C. The equilibrium temperature predicted fromthe data in Table 7 and Robinson et al. (1982) is about970'C. The large difference may be because Ganguli's syn-thesis experiments did not approach equilibrium. Gan-guli's results were not used in the data reduction.
Heat-of-solution and other data. Free energies ofreac-tions involving phenakite are presented by Schuiling etal. (1976) and by Bamberger and Baes (1972). Schuilinget al. (1976) did a series ofhalf-reversals at 1000 K in-volving phenakite, bromellite, and several other oxidesand orthosilicates. They estimated that the free energy ofreaction for bromellite + quartz: phenakite was be-tween - 14.3 I and - 6.48 kJ. This range agrees well withthe value of -7.97 kJ (1000 K) calculated from the ther-modynamic model. Bamberger and Baes used silica glassas the reference material for silica, and they were not ableto achieve equilibrium in their beryllia-rich experiments.As a result their results are diftcult to compare directly,but their calculated Gibbs free energy of formation is- 1967 .4 kJ, 6 I kJ larger than the value derived here. TheBamberger and Baes value was not used in the evaluation,whereas the data ofSchuiling and others were used.
Holm and Kleppa (1966) and Kiseleva and Shuriga(1981) measured the heats of solution ofbromellite, phen-akite, and qtartz and, derived enthalpies of reaction forbromellite + quartz: phenakite of -19.7(2.5) and-25.7(4.4)kJ at 968 K, respectively. The Afln., calculatedin this study is - I 3.8 kJ, slightly greater than two standarddeviations larger. Although there is no obvious reason forthis discrepancy, the source probably lies in the solutioncalorimetry (O. J. Kleppa, pers. comm.). The more neg-ative values of Holm and Kleppa ( I 966) and Kiseleva andShuriga (1981) are not consistent with the occurrence ofbromellite with talc in metasomatized ultramafic rocks(Klementyeva, I 969) -the calorimetric values predict thatphenakite * periclase or brucite would be stable instead.The phenakite heat-of-solution measurements were notincluded in the final data reduction.
Calorimetric enthalpies for the reaction bromellite +corundum : chrysoberyl (Holm and Kleppa, I 966; Robieet al., I 978) used in the data reduction agree with the finalvalue within two standard errors. This result is importantin demonstrating the overall consistency of the thermo-dynamic model in that the Gibbs free energies of theberyllium phases are tied to that of corundum throughboth andalusite and chrysoberyl within experimental error.
Kiseleva et al. (1984) determined heats of formationfor bertrandite, beryl, chrysoberyl, euclase, and phenakiteby high-temperature oxide-melt solution calorimetry.Their enthalpies were not used in the pnnszo fit becauseonly derived parameters are given in their abstract. I. A.Kiseleva (pers. comm., 1984) indicated that their oxidedala are consistent with those of Robie et al. ( I 978) per-mitting a comparison of their results to this study.rri'iBf ""u' - f/t'i5"*"t"'" : 16.7(13.4),31.4(12.1), -6.5(3.8),
ll.4(4.6), and ll.3(4.2) kJ/mol for, respectively, beryl,
bertrandite, chrysoberyl, euclase, and phenakite, wherethe numbers in parentheses are one standard deviationreported by Kiseleva et al. (1984). Ifthe uncertainties inTable 7 are included, then the two sets fall within abouttwo standard deviations of each other. The differencesare, however, still somewhat larger than expected, and fullinterpretation must await publication of the experimentalresults by Kiseleva and others.
The free energy ofbehoite was calculated from the av-erage of the three heats of formation given by Stull andProphet (1974) and the entropies from Robie et al. (1978)and Kostryukov et al. (1977).
The free eneryies and entropies estimated in this studyare quite similar to those estimated in an earlier version(Barton, 1981). Only the entropy of euclase difers by anunexpectedly large amount, being l0 J/K'mol lower inthis study. The difference in the estimated entropy foreuclase leads to significant differences in the positions ofsome euclase-bearing equilibria.
Cll,cur,.q,rnD MTNERAL STABILITIES
The fitted thermodynamic properties can be used tocalculate beryllium-mineral stabilities in the BASH sys-tem and, in conjunction with data from other sources,equilibria in more complex systems. In this section, sev-eral calculated phase diagrams are presented, discussed interms of their agreement with natural assemblages, andcompared with phase relations proposed for the BASHsystem by Burt (1978), Franz and Morteani (1981), andHsu (1983). Figures 10, ll, and 12 show, respectively,pressure-temperature, log 4"n$oo-temperature, and log4Ar2oj-temperature projections of the phase relations.
The overall pressure-temperature stabilities for the stoi-chiometric beryllium minerals are well defined (Fig. l0).With decreasing temperature, beryl * aluminum silicatereplaces chrysoberyl + qvartz under water-saturated con-ditions. In the 300-400oC range, beryl + aluminum sil-icate assemblages are replaced by euclase-containing as-semblages. About 100'lower, pure beryl + water reactsto euclase- or bertrandite-bearing assemblages and phen-
akite + water goes to bertrandite. In general, the uncer-tainty in the reactions increases with decreasing temper-ature mainly because the hydration model is likely to beless adequate. A related problem is the increased uncer-tainty associated with extrapolation of the Gibbs free ener-gies to temperatures lower than those of the experiments.Overall. +30"C seems a conservative estimate of the un-certainty in the reactions that are not directly constrainedby experiments. Because the uncertainties are highly cor-related, the overall topology of the phase diagrams shouldnot vary greatly.
Although the overall sequences and temperatures arewell defined, some details of the topology remain uncer-tain. The uncertainties mainly involve reactions that markthe high-temperature limit of euclase + quartz. There aremany possible confrgurations because the pertinent re-actions involve the aluminum silicates and fall within thesame range where aluminum silicate phase transitions oc-
P(wa te r )=P ( to ta l )
BARTON: PHASE EQUILIBRIA IN THE BeO-AI'O,-SiO,-H,O SYSTEM
-1
9 - 1
I
O ) r
-2
291
o(!
!
o
U)U)o(L
2oo 260 320 "'tJ;;"':t.."uu,o't,u'o
680 74o 800
Fig. 10. Calculated water-satuated phase relations in the BeO-Al2O3-SiO2-HrO system. Abbreviations from Table l.
cur. For example, the invariant point at about 3500 barsand 400"C among the phases beryl, euclase, kyanite, py-rophyllite, qtarlz, and water could be several kilobarshigher in pressure or so much lower in pressure as to bemetastable.
The log activity-temperature relations (Figs. ll, 12)present useful alternative projections ofthe BASH phaserelations at I kbar. These are calculated from the ther-modynamic model using the relation AG'r,, : - RT In a,,where a, is the activity of the species of interest. Theuncertainties in these diagrams are probably <0. 15 logunits.
Figure 12 is a nonconventional projection that deservessome comment. The activity of alumina is rarely consid-ered an independent variable in petrology, perhaps be-cause of the relative immobility of aluminum in mostgeologic environments. The activities of other compo-nents such as silica, the alkalis, alkaline earths, or hydro-gen ion are used instead. Most complex equilibria in-volving aluminosilicate phases (feldspars, micas, chlorites,clays, etc.) can, however, be written with the activity ofalumina as an independent variable. The advantage ofdoing this is that the stability limits of one set of minerals(in this case, beryllium minerals in the BASH system) canbe shown with a wide variety of completely different re-actions. For example, even though only the K-feldspar-muscovite buffer is shown on Figure I l, many other al-umina buffers could be shown including serpentine-clino-chlore-talc, albite-paragonite, topaz-quartz, and anor-thite-zoisite-quartz, each of which is of interest in certainberyllium deposits.
Solid solution in beryl should have a substantial effecton the phase relations. Figures llB and l2B show thecalculated phase relations for the activity of beryl : 0.1.Activities of this magnitude are reasonable for naturalalkali beryls assuming ideal mixing on the appropriatecrystallo$aphic sites. Alkali beryl commonly forms at latestages in pegmatite replacement zones replacing earlier,purerberyl and persisting to lowertemperatures than wouldpure beryl (Beus, 1966).
- 1 3
o - 1 6
IF
o - 1 g
240 2aO 320 360 400 440 480 520 560 600
Temperature (oC)
Fig. 11. Log nt*.,oo-temperature projection of phase rela-tions at I kbar. (A) Calculated phase relations for the pure system.(B) Calculated phase relations for ao*,:0.1. Note the large ex-pansion ofthe beryl fields at the expense ofthe others. The curvesare the same as in (A) except where labeled. (q Path consistentvdth the sequence ofassemblages seen in the Lost River, Alaska,beryllium deposits. The curves are the same as in (A). See textfor discussion. Abbreviations from Table l.
Compatibility with natural assemblages
A critical test of the calculated phase relations is howwell they agree with observed beryllium-mineral para-geneses. A large number of occurrences of two or threeminerals in the BASH system have been described (see,
o , ^-
o)O - 1 9
- 2 52OO 24O
Activity Beryl = O.1 (B)
292 BARTON: PHASE EQUILIBRIA IN THE BeO-Al,O,-SiOr-H,O SYSTEM
o
(g
o
200 250 300 350 400 450 500 550 600 650 700
Temperature (.C)
Fig. 12. log 4^ror-temperature projection of BASH phaserelations at I kbar. (A) Calcuiated phase relations for the puresystem. AIso shown is the curve for the reaction muscovite :K-feldspar * alumina + water. (B) Calculated phase relations fora*r, : 0. I . The curves are the same as in (A) except where labeled.Note the effect of the expansion of the beryl stability fields. (C)Projection of the stability fields of euclase (horizontally ruled)and euclase + quartz (vertically ruled) with dbvr : l. The curvesare the same as in (A). Note that euclase is incompatible withK-feldspar. See text for further discussion. Abbreviations fromTable l.
for example, Beus, 1966). Table 9 summarizes key, well-described associations of two or more minerals in theBASH system. The observed and calculated phase rela-tions correspond well overall, but several associations have
Table 9. Proposed natural assemblages in the BeO-AlrOr-SiOr-HrO system
Assembl ages 0ccurrence References
C h + P h + B e
C h + D i
C h + Q z + s i t
C h + Q z + B e
E u + D i ( ? )
C o + B e
K a + B e
K a + B e + B t
K a + Q z + B t
K a + Q z + E u
B e + B t + E u
Q z + B t + E u
Q z + B t + B e
Q z + P h + B eB e + P h + E u
pegmati tes
gre isens , pegmat i tes
pegmati tes
pegna ti tes
grer senspegmat i tes
gre i sens , pegnat i tes
pegmati tes
vo l canogen ic depos ' i t sgrer senspegmat i tes , g re j sens
peqnatites
pegmat i tes , g re i senspegmat i tes , g re isens
pegmat i tes , g re isens
pegnat t tes
0 k r u s c h ( l 9 7 1 )
S a i n s b u r y ( 1 9 6 8 ) , A p p o t l o n o v ( 1 9 6 7 )
He inr ich and Buch i (1969) , S tanek(1978) , F ranz and l lo r tean i (1984)
H e i n r i c h a n d B u c h i ( 1 9 6 9 )
Sa insbury (1968)
G r a z i a n i a n d D i c i u l i o ( 1 9 7 9 )
Kayode (197 ' ) ) , Ker r (1946)
Cerny (1968)
Gal lagher and Hawkes (1966)
L e v i n s o n ( 1 9 6 2 ) , L i n d s e y ( 1 9 7 7 )
0 l s e n ( 1 9 7 1 )
Gai I agher and Hawkes ( I 966 ) ,Ka lyuzhnaya and Ka lyuzhn i (1963)
St rand (1953) , Konarova ( , l974)
l la r tensot r (1960) , Hawley (1969)
many references
Adans (1954) , Kupr iyanova (1970)
Ka lyuzhnaya and Ka lyuzhn i (1963)
small or nonexistent fields of stability, at least for activitiesof beryl near unity. These associations, discussed here,include corundum + beryl, kaolinite + beryl and/or +bertrandite, and beryl + bertrandite.
No pyrophyllite-beryllium-mineral assemblages havebeen described, which is unfortunate because pyrophylliteis a key phase in the predicted equilibria in the 300"Crange. The activities ofalkalis, alkaline earths, or fluorineare apparently high enough in the environments wherethe beryllium minerals form to replace pyrophyllite bymicas, feldspars, or topaz.
Corundum * beryl. Corundum crystals have been re-ported as inclusions in a beryl crystal from Brazil (Gra-ziani and Di Giulio, 1979). Because identification wasmade solely on the basis of electron microprobe analyses,which would not detect beryllium, and because some ofthe "corundum" was surrounded by quartz (Graziani andGuidi, 1979) it seems plausible that the mineral may bechrysoberyl. If it is corundum, then the association withquartz would indicate a disequilibrium assemblage. Ascan be seen from Figures I lA and I lB, only low activitiesof beryl (.0.01) can be compatible with corundum.
Kaolinite * bertrandite. Kaolinite * bertrandite hasbeen reported from volcanogenic beryllium deposits (Lev-inson, 1962; Lindsey, 1979). This assemblage is stablerelative to euclase I qtartz only at moderate pressuresand low temperatures. Cogenetic silica in these depositsis represented by a poorly crystalline polymorph, indi-cating an unusually high silica activity at the time of for-mation. Hydrothermal K-feldspar is present with the ka-olinite, also indicating metastability (with respect tomuscovite). Silica activities much higher than quartz sol-ubility are well known in geothermal waters and can sig-nificantly displace some equilibria such as the hydrolysis
o
(to)o
Temperature (oC)
Activi ty Beryl=0.1
BARTON: PHASE EQUILIBRIA IN THE BeO-Al,OrSiO,-H,O SYSTEM 293
of K-feldspar (Meyer and Hemley, 1967). The pertinentreaction here is 4BeAlSiO.(OH) + 2SiO, * 3HrO:BeoSirOr(OH), + 2AlrSirO,(OHL. Silica activities greaterthan that of quartz will drive the reaction to the right.Calculations based on the thermodynamic data indicatethat a supersaturation of +0.6 (this study) or *0.2 (Hsu,1983) log units will stabilize the right-hand side at I barand 100.C. These concentrations are below that of amor-phous silica at the same conditions, lending credence tothe model. The abundant fluoride in these deposits mayalso help stabilize bertrandite (Hsu, 1983).
Bertrandite * beryl. Bertrandite very commonly re-places beryl, usually with a sheet silicate taking up thealuminum. The bertrandite + beryl assemblage, however,has only a small stability field in the simple system (Fig.l0). There are several possible explanations for this: ahigher-temperature breakdown of bertrandite than pro-posed here; an underestimate of the stability of pure berylat low temperatures; or the stabilization of beryl by solidsolution. If the decomposition of bertrandite is close tothe conditions indicated by Hsu (1 983), the I 00" increaseover Figure l0 would dramatically broaden the field ofcoexistence of bertrandite and beryl. Two lines of evi-dence, however, support the lower-temperature break-down proposed in this study. In an extensive fluid-inclu-sion study ofbertrandite and phenakite from one deposit,Kosals et al. (1973) found that the bertrandite formedbelow 290'C and the phenakite above 200"C. Their esti-mate of the total pressure was 700 bars. Breakdown ofbertrandite above 300'C would also preclude a stable fieldfor the observed assemblage muscovite + phenakite +quartz (Franz et al., pers. comm.; Stager, 1960; cf. Fig.t2A).
As discussed above (Thermodynamics), the beryl hy-dration model is most likely to be inadequate at low tem-peratures and pressrues leading to an underestimate ofthestability of beryl. Thus it is possible that beryl * ber-trandite could be much more extensive even with thelower-temperature bertrandite-breakdown reaction. Ex-pansion of the beryl-stability field by solid solution, how-ever, seems the most likely interpretation. Reasonabledecreases in the activity of beryl greatly expand the beryl-stability field and hence the region of coexistence withbertrandite (Figs. I I, l2).
Kaolinite * beryl. Beryl most commonly alters to claysor micas plus otherminerals. Cernf (1968), Kayode (1971),and Kerr (1946) documented the alteration of beryl tokaolinite. The calculated phase relations indicate that thisassociation is not stable at high activities of beryl (Figs.I lA, l2A), but that it does become stable with reasonabledecreases in the activity of beryl (Figs. llB, l2B). Thisinterpretation is partly supported by the fact that the peg-matitic beryls discussed by Ken (1946) and eern! (1968)tend to be alkali-rich and thus should have activities sig-nificantly less than l. The association kaolinite + beryl +bertrandite (Gallagher and Hawkes, 1966) can be ration-alized by silica supersaturation (Burt, 1978) only at lowactivities of beryl.
Comparison with alternative topologies
Burt (1978) proposed a detailed, general model for phaserelations in the BASH system based on multisystems anal-ysis and on the then-existing phase-equilibrium, mineral-association, and mineral-volume data. Although there aresimilarities between Burt's topology and the one calcu-lated here, they difer substantially. The principal differ-ences arise from two sources: interpretations ofthe P-?"extent of the assemblage chrysoberyl + quartz and of theP-Zextent of euclase stability at low temperatures. In theabsence of reported natural assemblages of beryl with py-rophyllite or aluminum silicate, Burt omitted them fromhis multisystem. This omission led to the erroneous con-clusion that chrysoberyl * quartz is stable to temperaturesbelow the stability limits of the anhydrous aluminum sil-icates plus water; thus, the replacement of chrysoberyl inquartz-containing systems would be by a reaction such aschrysoberyl + quartz: beryl + kaolinite. In contrast, theexperimental results on this reaction (Fig. 3) indicate thatchrysoberyl + q\artz breaks down to give beryl + alu-minum silicate at temperatures substantially above thestability ofkaolinite and pyrophyllite and probably abovethe stability limit of euclase.
As noted above, pyrophyllite-a key mineral in the cal-culated phase relations-has not been reported with be-ryllium minerals. The association chrysoberyl + eu-clase + quartz would support Burt's model, as would anyhydrous aluminum silicate * chrysoberyl * quartz, butsuch assemblages have not been reported. In contrast, theassociation beryl + andalusite or sillimanite has been re-ported from several places, although the two always seemto be in a reaction relationship (Heinrich and Buchi, 1969;Franz and Morteani, 1984).
The paucity of the lower-temperature coexisting pairsberyl plus andalusite or sillimanite, which might be usedto argue for their incompatibility, can be explained by abulk-composition effect. Because pegmatites generally haveabundant K-feldspar, aluminum silicate assemblageswould not be expected in pegmatites for temperatures lessthan those of the reaction KAlr[AlSirO,o](OH), + SiO, :
KAlSi3Or + AlrSiOs + HrO. At higher pressures, this re-action is replaced by melting reactions (e.g., Huang andWyllie, 1974).Franz and Morteani (1984) have proposedthe formation of chrysoberyl + quartz by related meltingreactions. Other evidence given by Franz and Morteani(1984) and Heinrich and Buchi (1969) suggests thatchrysoberyl forms during a high-grade, probably progradeevent. Chrysoberyl * quartz assemblages are not associ-ated with later hydrous alteration even though they maycontain crystals of substantial size. This suggests forma-tion from high-temperature fluids such as melts. Chryso-beryl + quartz has been described by Franz and Morteani(1981) as reacting to beryl * muscovite. Although this isnot within the BASH system, it does indicate that chry-soberyl * quartz is not highly stable as indicated by thenarrowness of the muscovite + quartz field at high tem-peratures (Fig. l2).
294 BARTON: PHASE EQUILIBRIA IN THE BeO-A1'O,-SiO,-H,O SYSTEM
Many alternative assemblages to chrysoberyl * quartzare known. An important possibility is euclase + dia-spore. Sainsbury (1968) described euclase * white micaveinlets cutting diaspore * chrysoberyl replacement zonesat Lost River, Alaska. It is possible, but not clear fromhis descriptions, that euclase may also coexist with dia-spore. This association supports the thermodynamic modelthat predicts a broad stability range for this pair (Fig. I l)precluding the assemblage chrysoberyl + quartz at inter-mediate temperatures. Other reported associations, how-ever, do not prohibit chrysoberyl + qvartz at least at thehigher temperatures. The apparent lack of appropriatenatural bulk compositions precludes an unambiguous an-swer to this question.
The other significant distinction between Burt's topol-ogy and that calculated here is in his inference ofthe low-temperature breakdown of euclase to bertrandite * ka-olinite assemblages. The thermodynamic model, how-ever, suggests that bertrandite and kaolinite can coexistonly under conditions of unusually high silica activity,consistent with the natural occurrences.
Hsu (1983) reproduced a portion ofBurt's topology andindicated where the reactions that he determined fit inlhowever, neither his experimental data nor any others arecompatible with the stable existence of the invariant point
[Qz] shown in Hsu's Figure 6.The BASH phase relations proposed by Franz and Mor-
teani (1981) on the basis of their experimental resultsshare some features with Figure l0 at intermediate andhigh temperatures. The similarity results from the largestability field for beryl + alurninum silicates (both hy-drous and anhydrous) shown by Franz and Morteani incontrast to Burt (1978). There are, however, many differ-ences in the details of the topology that result from theuse by Franz and Morteani of Chatterjee's (1976) phaserelations for the ASH system.
Franz and Morteani infer phase relations at lower tem-peratures by extrapolation of new reactions that resultfrom the intersection of their experimentally determinedreactions. These extrapolations indicate a minimum pres-sure for euclase + quartz of about 2 kbar and lead to alow-temperature topology similar to that of Burt (1978).Such graphical extrapolations are uncertain, and the pre-dictions conflict with the thermodynamic extrapolationsdone in this study on the basis of a similar, but far moreextensive set of experimental results.
Phase equilibria in more complex systems
Most beryllium minerals occur in rocks with morecomponents than those in the BASH system. The mostimportant of these additional components are the Na2O,trlrO, and CaO that form feldspars, micas, and clays.Feldspar-mica equilibria are represented in Figure 12 bythe reaction KAlSi3Os + HrO + (AlrO3): KAlr[AlSirO'o]-(OH)r, where alumina is enclosed in parentheses to em-phasize that in general it is not represented by corundum.Other components important in equilibria involving be-ryllium-aluminum silicates include Li, Mg, Mn, Fe, Zn,
P, S, and F. Additional feldspar-mica and many otherreactions could be calculated using a suitable data base(e.g., Robie et al., 1978). The topologies of the phaserelations in more complex systems have been discussedby many authors, notably Burt (197 5a, 197 5b, 1980), Ku-priyanova (1982), and Beus and Dikov (1967).
Solrn pnrnolocrc APPLTCATIoNS
A comprehensive discussion ofthe parageneses ofbe-
ryllium minerals in this system and related, more complexsystems is beyond the scope of this study. Instead, somegeneral observations on the parageneses ofberyllium min-erals will be presented in terms of the predictions of thethermodynamic model. The calculated phase relationsconstrain not only the pressures and temperatures of for-mation of beryllium-mineral assemblages, but they alsoplace useful constraints on the activities of silica and alu-mina. With few exceptions, discrete beryllium mineralsare found only in alkalic felsic igneous rocks and relatedmetasomatic rocks. The distribution of beryllium min-erals is thoroughly discussed by Vlasov (1967, Vols. IIand III) and Beus (1966) and will not be reviewed here.
Limitations on pressure and temperature
The variation in beryllium mineral assemblages frompegmatites to greisens to volcanogenic deposits (Table 9)is consistent with a trend ofgenerally decreasing pressureand temperature. The calculated phase relations in thequaternary system agree with observed assemblages asdiscussed in the last section. The paucity ofuniquely high-or low-pressure assemblages precludes the estimation ofpressure. The phase relations provide reasonable temper-ature constraints, although solid solution in beryl shouldcause large changes in the positions of beryl-bearing equi-libria.
Only euclase + phenakite + qaartz or beryllium min-erals with kyanite have nontrivial minimum pressures offormation (ca. 0.5 and 2.5 kbar, respectively, but highlyuncertain for the former). Neither of these assemblageshas been reported. The fields of the low-pressure assem-blages bertrandite + beryl, pyrophyllite * beryl, and an-dalusite + other phases are similarly uncertain.
BASH phase equilibria provide useful temperature con-straints. The assemblage chrysoberyl + quartz indicatesamphibolite- to granulite-grade conditions, except underconditions ofreduced volatile pressure. Euclase- and ber-trandite-bearing assemblages restrict maximum temper-atures to middle and lower greenschist facies, respectively.More precise estimates might be made for particular as-semblages, if solid solution in beryl is accounted for. Be-cause most beryllium minerals form in dynamic environ-ments where temperatures and possibly pressures changesubstantially during petrogenesis, the sequence of assem-blages and hence the I(-P) paths are generally ofgreaterinterest than specific temperature or pressure estimates.For example, consider the formation of pegmatites. Thesmall size ofpegrnatites requires that they cool quickly to
BARTON: PHASE EQUILIBRIA IN THE BeO-AI,O,-SiO,-H,O SYSTEM 295
the temperature of their surroundings, but subsequentlytheir conditions change quite slowly along with the hostrocks. If the pegmatitic fluids are lost fairly rapidly, thefluid-dominated crystallization processes will reflect tem,peratures only down to that of ths host at the time offormation. Therefore, the beryllium minerals (and manyothers) might be used to constrain the cooling path andplace an upper bound on the temperature ofthe host rocksat the time of emplacement.
Equilibria in more complex systems have not been cal-culated here with the exception of the K-feldspar-mus-covite reaction in Figure 12. Franz et al. (unpub. ms.)discussed the formation of beryl from phenakite in Alpineprograde regional metamorphism by several reactions,among them 2KAlr[AlSi3Oro](OH), + 3BerSiO4 +9SiOr: 2BerAlrSiuO,. + 2KAlSi3Os + 2HrO. At 6 kbar,this reaction should take place at about 420C, which is80-130'below the peak temperatures estimated from oth-er reactions in the same rocks (Franz et al., unpublishedmanuscript), but consistent with the mineral associationsin pegmatites where beryl + K-feldspar is much morecommon than phenakite * muscovite.
Limitations on activities of components
In most occurrences, textural evidence suggests that onlya single beryllium mineral is stable in a given assemblage.If more than one is present, textures commonly indicatea reaction relation. As a component present in but onephase in a given assemblage, BeO could be ignored in theconsideration of equilibria in a rock, much as other tracecomponents can be neglected (e.g., Miyashiro, 1975, p.125). A trace component (such as zirconia) that is almostalways present in the same mineral (zircon, in granites)has a limited utility as an indicator of the intensive vari-ables (e.g., I, P, chemical potentials) during petrogenesis.In contrast, the several minerals in the BASH system,which share all but one component with major phases,yield constraints on the activities ofthe major components(Al2O3, SiOr, and HrO). This is particularly important inmetasomatic rocks where there are many degrees of free-dom and where estimates of activities are needed in orderto make petrogenetic interpretations. Comparison of thetotal set of buffers to the beryllium-free buffers in FiguresI I and I 2 illustrates the superior resolution possible withberyllium minerals present. This use ofthe beryllium min-erals in metasomatic rocks is analogous to the evaluationof the activities of major components in igneous rocks(e.9., Carmichael et al., 1974).
The activity of water is the most difrcult of the threeto evaluate directly. Only chrysoberyl + quartz can beeasily interpreted with water pressure as an independentvariable; however, because other volatiles should stabilizeberyl in the same way that water does, there will still beambiguities in interpretation.
Log a"n",on. Beryllium minerals are good indicators ofsilica activities (Fig. I l) and hence can be used to interpretthe conditions and processes of formation. Beryllium-mineral parageneses in "apocarbonate" greisens and
"crossingJine" (desilicated) pegnatites (Vlasov, I 9 6 7, Vol.III) offer excellent examples. Apocarbonate greisens formby addition of fluorine, alumina, alkalis, silica, and traceelements from granites to nearby carbonate rocks. In theLost River, Alaska, beryllium deposits described by Sains-bury (1968), the earliest mineralization is replacement oflimestone by fine-grained diaspore, fluorite, and "curdy"chrysoberyl. This stage is cutby euclase-(bertrandite-)mica-fluorite veins that are in turn followed by muscovite-fluo-rite-beryl-quartz veins. This sequence can be simplyinterpreted as the consequence of the cooling and pro-gressive reaction of fluids derived from associated gre-isenized granite. Figure llC shows this path superim-posed on the l-kbar aqueous-silica phase relations. TheLost River assemblages are consistent with a path acrossthe diagram from high to low temperature and from lowto high silica activities (the activity ofquartz is unity onthe quartz saturation line). At the highest temperaturesand low silica activities, chrysoberyl + diaspore is stable;with decreasing temperature, chrysoberyl should react togive euclase and diaspore. Further decrease in tempera-ture results in the decomposition of euclase to give py-rophyllite * beryl and eventually to precipitation ofquartz.Alkalies in the fluids at Lost River were apparently con-centrated enough to give micas in place of the pure alu-minous phases at lower temperatures. The large under-saturation in silica is likely due to the retrograde solubilityof quartz at the moderate temperatures and low pressuresof formation of the deposit (Dobson, 1982; Walther andHelgeson, 1977). This would cause initially quartz-satu-rated fluids coming from the granite to go through aq\afiz-undersaturated region leading to silica-deficient assem-blages. Progressive cooling would lead to the restorationof a prograde silica solubility and eventually a concomi-tant increase in the silica content of the precipitated min-erals.
At higher pressures, the solubility ofquartz is progradeat all temperatures. Therefore, similar apocarbonate grei-sens formed at higher pressures should show more sili-cious assemblages. This appears to be the case at Mc-Cullough Butte, Eureka County, Nevada, where beryl andlate bertrandite are the predominant beryllium minerals(Barton, 1982a). At Mccullough Butte, the vein assem-blages are mostly quartz-saturated with the exception ofa quartz-free muscovite-dominated association that in turnis followed by quartz-rich muscovite-fluorite veins.
Crossing-line (desilicated) pegmatites commonly showzoning from beryl (+ quartz) in the centers to chrysoberyland/or phenakite in outer (silica-poor) parts (Beus, 1966;Vlasov, 1967). This sequence is compatible with a pathfrom high to low silica activities at relatively high tem-peratures (Fig. I l). In a few localities where beryllium-rich solutions reacted with ultramafic rocks, the silicaactivity was reduced beneath the phenakite-bromellite re-action producing bromellite (in highly magnesian assem-blages, Klementyeva,19691' Smirnov, 1977). At constanttemperature, the presence of talc + antigorite buffersaqueous silica just below the value for bromellite * phen-
296
akite (Fig. 6, Hemley et al., 1977b) consistent with theoccurrence of bromellite with talc (Klementyeva, 1969).
Log an ror. Beryllium-mineral parageneses can also pro-vide useful constraints on the activity of alumina. As dis-cussed above, alumina is generally a fixed component,that is, other components (alkalies, hydrogen ion, silica,and halogens) are generally more mobile and thus usedin conventional projections of the phase equilibria. Theadvantage, however, of treating the activity of alumina asan independent variable is that it allows direct comparisonof a variety of beryllium-mineral equilibria on the samediagram without having to draw a separate diagram foreach new set of additional components. For example, theactivity of alumina is related to conventional hydrolysisreactions (and hence hydrogen ion and alkali concentra-tions) by reactions such as the following:
BARTON: PHASE EQUILIBRIA IN THE BeO-Al,OrSiO,-H,O SYSTEM
KAlS i rOr+HrO+(A l rO3): KALIAISi3O'ol(OH), (1 1a)
As can be seen from Reaction I lc, which is the diferenceof I la and I lb, the activity of alumina is inversely relatedto (a*.)'? and proportional to (a"-)'?. Similar relationshipsexist for other hydrolysis reactions as well as for manyother kinds ofreactions (e.g., fluorination reactions).
An immediate consequence of examining such a dia-gram is an explanation for the comparative rarity of eu-clase in spite of the central role that it plays in the cal-culated phase equilibria in the BASH system. There aretwo related reasons for its rarity. First, as can be seen inFigure l2C, euclase and qtartz are stable together only atrelatively low temperatures. Because most beryllium-richassemblages are quartz saturated (most pegmatites andgreisens), the quartz + euclase reaction represents themost common upper limit. Still, euclase + quartz is stableto higher temperatures than bertrandite, yet bertranditeis much more common. The second reason for the rarityof euclase is made clear by Figure 12. Euclase requires arelatively high chemical potential of alumina, above thatat which K-feldspar is stable. In many greisens and nearlyall pegmatites the alumina contents are buffered by re-actions such as I I between the white micas, feldspars,topaz, and quarlz. Muscovite, K-feldspar, and quartz fixthe chemical potential of alumina in the beryl field overmost of the temperature range (Fig. l2). Topaz-quartz(-muscovite) assemblages which begin at the andalusite-quartz line and extend downward do likewise, althoughat high fluorine fugacities, they may buffer p^ro, to valueswithin the quartz + phenakite field. The reaction2Be,AlrSi.O,, + 4HF : 3BezSiO+ + 2AlrSiO4F, +7SiO, + 2HrO has been proposed by Burt (1975b) as anatural fluorine buffer; such assemblages, while uncom-mon, are known in pegmatites, miarolitic cavities, andsome greisens (Barton, 1982b). These relationships ex-
plain why euclase is usually found in rocks deficient inthe alkalies relative to alumina, such as hydrolytically al-tered rocks (e.g., aluminosilicate greisens). Although ex-pansion of the stability field of beryl with solid solutionmay also play a role in diminishing the stability field ofeuclase, the high H* to total alkali ratio (Reaction llc)would work against this. Consistent with this, most greisen
beryls are more nearly stoichiometric than late-stage peg-matitic beryls that formed at similar temperatures (Beus,1966).
The topology of Figure 12 illustrates the reason thatmuscovite * bertrandite + quartz is the most commonassemblage to replace beryl. Beryl + K-feldspar coolingwith fluid will react accordingly to give muscovite +phenakite or bertrandite at temperatures below 250'C atI kbar. Because the interval for phenakite is quite small,the predominant product will be bertrandite. In fact, theonly product will be bertrandite if the stability field ofberyl is expanded slightly by solid solution.
Because the chemical potentials of the alkalis vary in-versely with that of alumina in quartz * mica or feldsparassemblages, the variations described here may equallywell be thought of as due to variations in alkalinity (withalumina as an inert component). The absence of chryso-beryl and the relative abundance of bertrandite, phen-
akite, and the alkali-beryllium silicates in peralkalinegranites and syenites (cf., Beus, 1966; Vlasov , 1967 , Yol.II) reflect the low intrinsic chemical potentials of aluminain these rocks. In peralkaline rocks, alumina-undersatu-rated minerals such as acmite and riebeckite require thatthe alumina activities be significantly below that of theK-feldspar-muscovite buffer (Reaction I l). Alumina-buffering reactions involving peralkaline minerals will bebelow the stability fields of euclase and chrysoberyl and,especially in the absence ofquartz, will be below the sta-bility field of beryl, thus rationalizing the observed abun-dance of the aluminum-free beryllium silicates in peral-kaline rocks.
SuPrlrlnY
The thermodynamic properties of behoite, bertrandite,beryl, chrysoberyl, euclase, and phenakite have been eval-uated from a combination of new phase-equilibrium, ca-lorimetric, and volumetric measurements along with datafrom the literature. Of 86 data sets containing over 1000observations, only one set does not fit the model or havegood reasons for being discarded. The resulting internallyconsistent thermodynamic model is compatible with nat-ural assemblages in the BASH system and provides asuitable basis for the prediction ofequilibria in more com-plex systems.
Beryllium minerals in the BASH system provide limitson the temperatures and activities of silica and aluminaduring formation. Beryl has a broad stability range, con-sistent with its natural abundance. The stability of berylis significantly enhanced by incorporation of volatilespecies and alkalis. The effect ofvolatile incorporation is
modeled as a simple volumetric interaction. This modelworks well for beryl and appears reasonable for cordierite,although it results in a somewhat poorer fit than the other,more elaborate models proposed for cordierite. Solutionof nonvolatile species in beryl is also inferred to have amajor efect on equilibria involving beryl.
Occurrences of the BASH minerals provide broad con-straints on temperature, but no independent pressure con-straints. Chrysoberyl + quartz is restricted to high tem-peratures except when Po",o ( P,oo,. Euclase-bearingassemblages replace aluminous beryl-bearing assemblagesin the 300-500oC range. Stoichiometric beryl breaks downin the presence ofwater about 100"C lower, although al-kali-rich beryls will persist to lower temperatures. Theresults of this study indicate that bertrandite and behoiteare stable only below 260"Cin agreement with the limitednatural data, although the results of Hsu (1983) suggestthat bertrandite is stable to 350.C.
Because beryllium minerals most commonly occur sin-gly in metasomatic rocks, perhaps their most useful pet-rologic attribute is as indicators ofthe activities ofsilicaand alumina. For example, the beryllium minerals permita much finer discrimination of the activities of silica inapocarbonate greisens and desilicated pegmatites thanwould be possible from the phases of the major elementsalone. Similarly, the beryllium minerals provide addi-tional constraints on the activities of alumina in greisens.Euclase, for example, is stable only at elevated aluminaactivities, indicating environments where the alkalis haveunusually low activities either as a consequence of acidmetasomatism (as in aluminosilicate greisens), or unusu-ally low initial alkali contents and high aluminum mo-bility (as in apocarbonate greisens).
Additional studies that might help resolve problemsfound here are an improved determination of Reaction4, more data on equilibria below 400t (solubility exper-iments might work best), direct beryl hydration measure-ments, evaluation of the effect of solid solution on berylstability (perhaps by displacement of Reaction 1), andinvestigation of the occurrence of critical natural assem-blages such as chrysoberyl + quartz * euclase or eu-clase * andalusite.
AcxNowlnncMENTS
It is a pleasure to acknowledge helpful reviews by D. M. Burt,W. A. Dollase, W. G. Ernst, and R. C. Ewing on this paper, andby J. R. Goldsmith, P. B. Moore, R. C. Newton, and P. J. Wyllieon an earlier version. Many other people contributed helpfuldiscussions or assistance on various aspects of this project in-cluding P. B. Barton, Jr., J. L. Haas, Jr., H. T. Haselton, J. J.Hemley, D. M. Jenkins, W. Moloznik, D. Perkins III, G. R.Robinson, Jr., P. Toulmin III, and W. J. Ullman. R. C. Allerprovided the facilities for and help with the silica analyses. Theexperimental work was supported by NSF grant EAR78-13675to J. R. Goldsmith. Support for the thermodynamic modelingwas obtained from EAR84-08388 to M. D. Barton. While astudent, I was supported by a National Science Foundation Grad-uate Fellowship and by a McCormick Fellowship from the Uni-versity of Chicago.
297
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