EXPERIMENT AL STUDIES

A MODEL OF PHASE RELATIONS IN THE SYSTEM Mg0-Si02-H 20-C02 AND PREDICTION OF THE

COMPOSITIONS OF LIQUIDS COEXISTING WITH FORSTERITE AND ENSTATI TE

David E. El lis and Peter J . Wy l lie

Department of Geophysical Sciences , University of Chicago, Chicago , Illinois 60637

Abstract . A comprehensive model has been developed for the system MgO-Si02-HzO-C02 on the basis of experimental studies , Schreinemaker ' s rules , a nd thermodynamic data . The assemblage forster ite pl us ensta t ite is predicted t o melt in the presence o f vapor of any H20/C02 ratio at low pressures , i n the presence of vapor whose HzO/C02 ratio is buffered by the presence of magnesite at intermediate pr essures, a nd at a vapor-absent eutect ic with brucite and magneRite a t high pressures . The composition of t he liquid at the solidus for a bulk composition of forsteri te plus enstatite plus a small amount of volatiles with a 3/1 H20/C02 ratio changes from enstatite-q uartz norma tive a t 20 kbar, t o peri­clase- for ster ite normative at 50 kbar, to forsterite-enstat i te no r ma tive at 90 kbar and greater pres sures . Forster ite cannot coexist with H20-C02 vapor at pressures greater tha n 90 kbar . Thus all melting in the earth ' s mantle at hi gher pressures must be vapor- absent .

I n troduction

In the Proceedings of the First I n ternat i onal Kimberlite Conference Eggler (1975) repor t ed on experimental stud ies in the system Mg0-Si 02-H20-C02 at 20 kbar and Mysen and Boettcher (1975) disc ussed experimental r esults on t he effects of H20 and COz on the melting of peridot i te at 20 kbar . We have combined their contributions with other phase equilibrium studies ~o construct a model of phase equilibria in the system Mg0-Si0 2-Hz0-C02 at pressur es up to 100 kbar, where the relationships des cribed at 20 kbar are r epla ced by more complex phase equilibria involving stable hydrat es a nd carbonat es . The model outlined here is descr ibed in detail in the papers of Ellis and Wyllie (1978a , b , c) . The sal i ent f ea tu res of phase relations in t he ternary systems Mg0-H20-C02 , Mg0-Si0 2-co2, and Mg0-Si0 2-H20 will be d i scussed , fol lowed by a summary of the quat ernary phase r elations and the processes o f melting a nd crystal lization.

The System MgO-H20- C02

The phase r el ations of brucite in the system MgO-HzO are analogous t o those determi ned by Huang a nd Wyllie (1976) for magnesite in the system MgO-COz (see Figure 1) . The position of the r eaction

Brucite + Periclase + H20 (1)

has been predicted on th e basis of the experi­mental stud ies of Walter et al. (1962), Ba rnes and Ernst (1963), and Irving et al. (1977), thermochemical data, and water fugacities pre­dicted by th e modified Redlich- Kwong equation of s t ate (Holloway, 1977 ) . We estimate that reactio n 1 maintains a posi tive P-T slope until brucite melts a t the invariant poin t (MC), at which brucite, periclase , liquid , and vapor coexist . The invariant point (MC) i s located near 58 kbar and 1310°c . At pressures gr ea ter than or equal to t hat of po i n t I, where the reaction

Magnesi t e + Brucite + Periclase + Vapor (2)

mee t s the sol i dus, bruc i te and magnesite melt t oge t her at a eutectic. The melting model de­r ived by Brad l ey (1962) for the system Ca (OH) 2-CaC03 has been used to pred i ct that the com­position of the eu t ectic liqui d is 73 mo l e percent Mg(OH)z plus 27 mole percen t MgC03 . At temperatu r es bel ow the solidus the compos ition of vapor coexis ting with magnesite-bearing assem­blages is buffe r ed.

The System Mg0-Si02-H20

The topology for the sys t em Mg0-Si02-H20 shown i n Figure 2 was derived on the basis of numerous s t udies o f subsolidus r eactions , (especially those of Bowen and Tutt l e (1949), Chernosky (1976) , Evans et al . (1976), Greenwood (1963, 1971) , Johannes (1968), Kita harn et a l. (1966), and Scarfe a nd Wyllie (1967)), and from studies

31 3

.... 0 .n

• X

Q) .... :::i U'I U'I Q) ....

Q

100

90

80

70

60

50

40

30

20

10

0 1000 1200 1400 1600 1800 2000

Temperature oc Figure 1 . P-T ne t for t he system MgO-H 20-C02 . Abbreviations used in Figures a r e Pe = MgO, Br= Mg(OH) 2, MC= MgC0 3, Q = Si0 2, En= MgSi03 , Fo = Mg2Si04 , L = liquid , V =mixed H20- C0z vapor , H20 = pure HzO vapor , COz = pur e COz vapor .

of melting r elations i n this sys tem a nd related sys t ems (by Eggler (19 75) , Hod ges (1973), Kushiro e t al . (1968), Mysen and Boettcher (1975a,b), and Nakumur a and Kushiro ( 1974)) . The subsolidus reac t ions 1 and

Brucite + Enstati t e -+ Fors t eri t e + H20 (3)

i ntersect the soli dus r espectively at t he i n­va r iant poin t (En,Q) at abou t 45 kbar a nd 1250°c, and t he i nvarian t point (Pe , Q) at about 1200°C a nd 90 kbar . The work of Yamamoto and Aki mo t o (1977) indicates that t he hydrous magnesium silica t es , parti cularly hydroxyl-c linohumit e , are not stable at the temperature of the solidus in t his system , and thus need not be considered. We assume that th e hydrous melting reac t ions maintain a slight nega t ive slope throughout the range o f pressure consider ed . Near the solid us fors t er ite plus ens t atite coex i s t with water vapor a t low pressures a nd with b r ucite at high pressu r es . At high t empera tures wate r is dis­solved in the s i licate liquid coexisting with forsterite plus enstatite . If suff i cien t HzO is availa ble a t pressures greater than 90 kbar, al l for sterite wil l r eac t to for m enstatite plus b r uc i te. The assemblage forsterite plus ensta ti te can not coexist with H20 a t pressures great er than t hat of t he invariant point (Pe , Q).

The System MgO-S i 02- C02

The phase equilibria of this sys t em were modeled by Wyllie a nd Huang (1976). The sub-

314

solidu s and melting reac t ions i nvolving magnesite in t he system Mg0-Si0 2-C02 t ake place at h i gher t empera tures and l ower pressur es than the analogous r eactions i nvolving brucit e in the system Mg0-Si0 2- H20 . The solidus has a pos itive P-T slope above 25 kbar . Near t he solidus of thi s system , fors t erite plus ensta tite coexist with co2 vapo r at low pressure , with magnesite at high pressure , and wi th silica te liquid s conta i ning d i ssolved C02 at temperatur es above t he solidus . In analogy t o the system Mg0-Si0 2-H20, C0 2 may exist as a vapor at high pressur es only if all fors terite has been reacted to ensta t ite plus magnesite .

Th e System Mg0-Si02-H20- C02

A model for the system Mg0-Si02- H20-C02 has been derived f r om the ter na r y sys tems descr i bed above. Those r eactions which i nvolve the assem­blage forsterite pl us e nstatit e are shown in Fi gur e 4. The assemb l age for sterite plus enstatite may coexist wit h a vapor phase onl y in t he low P-T region enclosed by heavy lines . The compositio n of the vapor phase in the univariant reac t ion

Magnesite+For steri t e+Vapor-+ Ens t a tite+Liquid ( 4)

is buffered by t he intersection of t he divariant subsolidus r eac t ion s urface

Magnes i te + Enstatite -> Fors terite + Vapo r (5)

wi t h the solidus surface . P-T-XCOz calc ul ations

for reaction 5 show that the vapor pr esent at the solidus must be r ich i n H20 at all pressures signifi cantly great er than that of the invariant point labeled A i n Figur e 4 . At pressur es

100

90

80

70

.... 0

60 ~

~ 50

" "' "' 40 Q)

a: 30

20

10

0 1000 1200 1400 1600 1800 2000

Temperatu r·e °C

Figure 2 . P-T net for the system Mg0-Si02-H20 ·

r !

grea t er than 90 kbar forsterite is not stable in the presence of vapor of any composition . Forsterite will react with vapor t o form ens ta­t i te plus magnesite plus brucite until either the vapor or the forsterite is consumed .

The temperature maximum on the solidus surf ace, shown in Figure 4 as a dashed line , is the locus of isobaric thermal maxima on the reaction

Forsterite + Enstatite +Vapor~ Liquid . (6)

It does not exis t at pr essures below 35 kbar . The t emperature maximum or iginates in the system MgO-Si02-C02 when the rapidl y increasing solu­bility of C02 in the silicate liquid which coexists with forsterite and enstatite , asso­cia t ed with the intersection of the subsolidus r eactio n 5 with the solidus, causes a r apid decrease in the temperature of reaction 6 . The therma l maximum on the solidus surface which corr esponds t o t he for sterite-vapor join then begins to migrate away from t he C02 edge of the MgO-Si02- H20-C02 sys t em with increasing pr essure. Associated with the thermal maximum on the forste r ite-vapor solidus there is a thermal ridge on the vapor-saturated liquidus surface . The fors t erite-ensta tit e boundary on the vapor­saturated l iquidus surface traverses t his ridge passing thr ough a the rmal maximum that chemo­graphic relations s how must be located between t he fors t erite-vapor and t he enstatite-vapor JOlns . As t he liquidus ridge retreats from the side forsterite-C02 with increasing pressur e the

60

50

~ 40 0

..0

.:.:;

~ ::::> en en ~

0....

30

20

10

0 1200 1400 1600 1800 2000

Temperature °C Figure 3 . P-T net showing vapor-present uni­varia nt reactions in the sys tem Mg0-Si0 2- c02 (Wyllie and Huang, 1976).

100

90

80 8r+.En+.L,. Fo+V

70

60 .... 0

.D 50 -"'

CV Xco2 -=0.2 :; 40 Cf) Cf) , , CV , , .... ~

, a.. 30 , ,

, ,~ MC En , , o, Fo

20

10

0 1000 1200 1400 1600 1800

Temperature °C

Figure 4 . Partial P-T net for the system MgO­Si02-H20-C02. Only reactions involving the assemblage fors terite plus enstatite a r e shown . Vapor may coexi st with for sterite plus enstatite only in the P- T region enc l osed by the heavy lines. The heavy dashed line shows the posi tion of the thermal maximum on reaction 6.

thermal maximum on the forsterite- ens t atite field boundary and the coexisting vapo r phase becomes richer in H20 .

In the presence of mixed H20-C02 vapor all vapor-present reactions shown in Figure 4 become divariant rather than univariant. Thus the pair of reactions

Enstatit e + H20 ~ For sterite + Liquid

and

Forsterite + Ensta t i t e + C02 ~ Liquid

s hown i n Figure 4 simply represent the two ex­treme ends of one divariant surface i n this system. In order t o illustrate how quickly the vapor present along each divariant surface be­comes water-rich, the contour for XC0

2 = 0 . 2 on

three in tersecting d ivarian t surfaces has been plotted i n Figure 4 .

The transition with increasing pressure f rom vapor-present to vapor-absent mel t ing in this system is il l ustrated by a series of isobaric sections through Figure 4 . These are given in simplified form in Figure 5 . The lines shown are the isobaric traces of th e divariant

315

1700 1700 A. P 0 20 kb 8 p 0 50 kb c p ~ 90 kb

L

1500 1500 Fo +En1- L

L MC+Fo Fo En V

+En+L 1300 130 0

MC+Br+ Fo+En 1100 II 00 .+--...:....:.....:...--=----->

0 0 1.0 0.0 0 .2 5 0 0 I 0

Va por co,;tco,. H,Ol Vapor co,Aco, ·H,0) Bulk co,Aco, · H,O)

Figure S. Isobaric sec tions through the system Mg0-Si02-H20-C02 at 20, SO , and 90 kba r. The range of vapor compositions which may coexis t with forsterite plus enstatite becomes smal ler as pressur e i ncreases, until a t 90 kbar forsterite plus enstatite can no longer coexist with vapor .

surfaces discussed above. Figure SA shows that a t 20 kba r fors t erite plus enstatite may coexist with vapor of any Xco2 . At 20 kbar C02 i s relatively insolubl e in the silicate liquid, and does not l ower the melt i ng point of the assem­blage forster ite plus enstatite nearly as much as H20. Eggler (19 7S) concluded , in agreement with Mysen and Boe ttcher (197Sa,b) , that at 20 kbar the vapor -saturated liquid cha nges f r om quartz-norma tive to fo r steri te-normative as the XC02 of vapor becomes greater than 0 . 4S .

The thermal maximum s h01-m o n reaction 6 at SO kbar in Figure SB is the same as that denoted by the heavy dashed line in Fi gure 4 . The compo­sition of the vapor a t the thermal maximum c hanges rapidly from COrrich at 40 kbar to H20-rich at SO kbar . Figure SB shows that forsterite plus enstati t e cannot coexist with vapor richer in C02 than that at the isobaric invarian t point schematically illustrated, where the subsolidus carbonation r eac tion intersec t s the solidus . At t emperatures below the solidus the composition of the vapor coexisting with forsterite plus enstatite i s buffered by the s ubsolidus r eaction . At th e solidus th e compositions of both liquid and vapor are fixed . Above the sol id us the com­position of vapor coexi sting with forster ite plus enstati t e is buffered by reaction 6 , until the temper ature of t he thermal maximum on that reaction is exceeded . At highe r temperatures a l l vapor is dissolved in the l iquid.

Figure SC ill ust r ates that at 90 kbar and temperatures below the solidus all volatiles are tied up in brucite and magnesite , in the presence of forsteri t e plus enstati t e . A vapor phase is not s t able in the presence o f the assemblage fo r sterite plus ens t atite . The firs t melting takes place at a quaternar y eut ectic i nvolving forsterite , enstatite, brucite , and magnesite.

The P-T net const ruc ted for the system MgO­Si02- H20-C02 provides the i n formation necessary to construct i sobaric liquidus diagrams, and from them to es timate geome trically the compo­sit ions of liquids formed at ·the solidus . The position of the surface of liquid compositions which coexist with forsterite and enstatite is

316

p

"' ~ ~ " E ~

shown a t 20 , 40 , 70 , and 90 kbar in Figure 6 . The grea t change in the position of th i s surface is due to the incr eased solubility of C0 2 in the liquid associated wi th t he intersection of reac­tion S with the so lidus a t about 42 kbar.

The estimated compositi ons of liquids formed at the solidus at pressur es of 20, SO , and 90 kba r ar e l isted i n Table 1 . · These were es t i­mated for a bulk composition consis ting of for sterite plus enstatite plus a small amount of vola tiles with a 3/1 H20/C02 ra tio . At 20 kbar the first liquid i s estimated to be quartz­norma tive, in agreement with the conclusions of Eggler (197S) and of Mysen and Boe ttc her (197Sa , b) . However, at a pressure of SO kbar the fact t ha t magnesite coexists with fors t erite plus ens t atite at the solidus ca uses t he fi r st liquid to be highly undersatura t ed with respect to silica, in fac t periclase-forsterite normative . Th e involvement of magnesi t e in the melt ing reaction prevent s the Si02-enric hment caused at low pressures by vapor with high H20/C0 2. At 90 kbar the first l iquid coexis ting with forsterite plus enstati te is estima ted to be enstatite- forster it e nor mative . The exi stence of the quaternary eut ectic relationship between fors ter~te, ens t atite, brucite, and magnesite at pressures g r ea t er than 90 kbar r equires that the compositions o f the first l iquids will be essen­tially constant at higher pressur es, becomin g slightly riche r i n MgO with increasing pr essure .

S iO,

co,

H20 co. H20 co,

Figure 6 . Partial i sobaric liquidus diagrams for t he sys tern Mg0-Si0rH20- C02. Heavy lines show liquidus fie l d boundaries o n the vapor­saturated liquidus surface . The s urface of liquid compositions coexisting with forsterite plus enstatite i s s t ippled . Thi s is vapor absent, but reaches the vapor-saturated l iqui dus sur face in Figures 6A , 6B , a nd 6C . As pr essure i ncreases t he volatile-rich parts of the surface become i ncreasingly silica-under satura t ed.

TABLE 1. Geome tr ically estimated compositions of first liquids coexis ting with fo r s t er ite plus ensta tite in a bulk composition

wi th an H20/C02 ratio of 3/1 .

Mo l e Percent Weight Percent Pressure MgO Si02 H20 C02

20 kbar 12 17 70

SO kbar 34 10 31

90 kbar 32 18 39

Summary

The model developed for the sys t em Mg0-Si 02-H20-C02 requires that in s uccessivel y higher pr essure ranges, three different types of mel ting processes characteriz e the melting of forsterite plus enstati t e in the presence of H20-C02 vapor .

1 18 37 45 O. x

25 38 17 15 30

11 36 31 19 14

present as vapor , or are stored in amphibole , phlogopite , and carbonate . The distribution of H20 a nd C02 among liquid crystals and vapor i n the simple sys t em MgO- Si02-H20-Si02 provides a guide for interpretation of the phase relation­ships i n the compl ex perido t ite-H20-C02 sys t em (Wyl l ie , this volume) .

(1) At l ow pr essures the melting reaction is either

Enstatite + Vapor ~ Forsterite + Liquid

Acknowledgments. Th i s research was supported by the Ear th Sciences Section, National Science Foundation, NSF Grant EAR 76-20410 .

a t low xC02

, o r

Forster ite + Enstati t e + Vapor + Liquid

a t hi gh XC02

. The compos ition of the liqu ids

produced varies from quartz-normative in the pr esence of H20 to forsterite-normative in the presence of C02 · This agrees with the conc lu­sions of Eggler (1975) a nd Mysen and Boettcher (1975a,b). At 20 kbar H20 is partitioned toward silicate liquids, a nd C02 is partitioned toward the coexis ting vapor.

(2) At pressures between 42 and 80 kba r the important melting reaction is 4 . The composition of the vapo r phase taking pa rt in this reaction is bu ffered by th e subso l idus reaction 5 . At temperatures above the solidus for the assem­blage for s t erite plus ensta tite, a therma l max­imum exists on the react i on

For sterite + Ensta tit e +Vapor + Liquid .

The XCO of th e vapor at this thermal maximum

becomes2rapidly smaller as pressure increases.

(3) At pr essures above 90 kiloba~s fors t erite plus ensta ti te me l t a t a quaternary eutec tic with brucite and magnesit e , with no vapor present . H20/C02 of the liquid i s fixed a t a bou t 3/1 by the eutectic between Mg(OH)2 and MgC03 .

The composi t ion of the fi r s t liquid formed in bul k compos itions of forsterite plus enstat it e and a small amount of volatil es wi t h a 3/1 H20/ C02 ratio changes from quart z-normat ive to peri­clase-forster i t e norma tive t o enstatite-for£terite normative as pressu r e inc r eases .

These three kinds of melting r eaction must a l so occur in peridotite , where H20 and C0 2 a re

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F. R. Boyd Henry 0. A. Meyer editors

QE t-/62 Kb Isq

Kimberlites 1q77

=oiatremes,' v. 1

and Diamonds: Their Geology,

Petrology, and aoL

Geochemistry

Proceedings of the Second International Kimberlite Conference

///

Volume 1

American Geoph ysical Union Washington, D.C. 20006 1979