GEOPIIYSICAL RESEAKCH LETTERS, VOL. 22, NO. 19, PAGES 2565-2568, OCTOBER I, 1995

A note on the sensitivity of mantle convection models to composition-dependent phase relations

Craig R. Bina Department of Geological Sciences, Northwestern University, Evanston, Illinois

Mian Liu Department of Geological Sciences. University of Missouri, Columbia, Missouri

Abstract. Numesical simulations of mantle convection are inhibit mantle circulation across such phase transitions and highly sensitive to the dependence of phase relations upon that strong time-dependent instabilitiesmay be induced near pressure, temperature, and composition. Phase transitions in phase boundaries. the (relatively silica-poor) olivine components of the man- In such studies, the phase transitions are approximated tle tend, with increasing iron content, to inhibit convective by univariant phase boundaries with fixed Clapeyron slopes mass transfer between the upper and lower mantle. Those in simple wmpositions (e.g., the a -+ 0 transition in pure a w i n g in the (relatively silica-rich) non-olivine wmpo- MgzSi04). n u s , the 660 km seismic disconlinuity is repre- nents fail to inhibit (and indeed promote) such mass transfer. sented by theunivariant y + pv+mw transitioninMgzSiO4, Behavior in the real mantle must entail an interplay between whose fixed negative Clapeyron slope inhibits transport be- sucb competing effects, with the finite width of multivariant tween the upper and lower mantle. Similarly, the 410 km phase fields actiug tomitigateimpediments to flow. Attempts seismic discontinuity is represented by the &variant a - P to dirsccj corJate computed flow or temperature fields transitionin MgzSi04. whose fixed positiveClapeyron slope with models derived from physical observables should be does not inhibit transport. approached with caution, given the sensitivity ofthe former The magnitudes of sucb Clapeyron slopes, however, are to compositional heterogeneity and uncertainties in phase not necessarily constant; they may be h c t i o m of pres- relations. sure and temperature [cf. Bina and Helffrich, 19941. More-

over, the actual identity of the televanl phase iransilion, and

Introduction thus the magnitude and sign 01 the wrresponding Clapey- ron slope, may change with pressure and temperature. This The m a c e of mineralogjd phase transitions in the Was explored recently by Liu [19941, who nqted that the

E & ~ ~ [ ~ i ~ ~ ~ ~ ~ d , 19701 has long been inferred to Y + P + 7JZW transition in endmember MgzSi04 olivine impose significant constraints upon the convective dynam- is replaced by the P + pv + m w transition at high tem- ics of the interior. Early work [Richter, 1973; Schubert et peratures (Figure la). While the former Possesses a nega- al., 1975; Christensen and Yuen, 1984, 19851 demonstrated tive C1apeyron slope, so that descent of cool downwellings that the sign and mapoitude of the Clapeyron brasure- whose geoth- pass below the triple point is inhibited, the temperature) slopes of phase transitions are imponant in de- latter Possesses a zero or w&y positive Clapeyron slope

termining the extent to which the and lower (due to its greater volume decrease and more negative en- may mix or remain stably stratified. More recent studies mPY change), so that ascent of warm upwellings whose [Nakakuki et al., 1994; Solheim and Peltier, 1993, 1994: geotherms pass above the trip1e point is not inhibited. ne Tackley et al., 1993, 1994; Honda et al., 1993; Weinstein, ~*gas~-etr~ whichresults. in which the phase bound- 1992, 1993; Peltier and Solheim, 1992; Zhao et al., 1992; IVY resists the descent of subducting but ascent Liu et al., 1991; Machete1 and Weber, 19911 have suggested rising plumes, can be s e a in Fi!Pe 2a. Higher Rayleigh that, because of its negative Clapeyron slope, the dispro- serve to amplify portionation of y-spinel into magnesiowiistite and silicate Here we expand upon the work of Liu [1994], noting that

perovskite (the y - pv + m w transition) at 660 km depth phase relations depend not only upon pressure and tempera- has the potential to inhibit mantle and to induce ture but also upon composition. The identity of the relevant time-dependent instabilities so that even a stably stratified phase transitions. and thus the nature of any corresponding mantle may occasionally mix through catastrophic overturn Clapeyron slopes, are functions of chemical composition. events. We may briefly summarize such work by noting Because the mantle is a complex multiwmponeat chemical that the local body forces induced by t h d distortion of System, and because it should be characterized by varying phase boundaries with negative Clapeyron slopes tend to degrees of wm~ositional heterogeneity [e.g., Metcalfe et al.,

19951, we explore the sensitivity of mantle wnvection sim- Copyright 1995 by the American Geophysical Union. ulations to such wmposition-dependent variations. Compo-

sitional heterogeneity may also induce chemical buoyancy effects [Liu and Chase. 19911, such as the reversal whereby

Paper number 95GLO2546 oceanic crustal compositions become intrinsically less dense 0094-8534195195GL-02546$03 .OO thanpyrolite mantle compositions over the670-71Okmdepth

2565

2566 BWA AND LIU: PHASE RELATl :ONS W MANTLE CONVECTION

C: Pyrolite minus (MgC,,Fec,),SiO,

8 12 16 20 24 28

Pressure (GPa) Figure 1. Schematic phase diagrams for Mg2Si04 olivine (A), (Mg~.sFea.~)~SiO~ olivine (B), and pyroxene-garnet components (C). after Gasparik [I9901 and Ita and Stixrude 119921. Phases are olivine (u). modified svinel (4). cpinel (-,). perovskirc (pr ). mapesiowiisute c i r , ? ~ ), pyrox- ene (p .r ) . garnct ( ! / I ) . and ilmenite ( 1 1 ) . Broken lines dcpict highlv schematic z e o t h m lor ambient mantlc. cold down- we'u&gs, and h ~ t ~ ~ w e l l i g s .

intmal [Irifime andRingwood, 19871, but we restrict thefo- cus of this study to the effects upon convection models of changes in phasc relations.

Method and Res~~lts

To obtain our results, we have used the finite difference method to solve a numerical model formulated within the

extended Boussinesq approximation in a two-dimensional Cartesian box. employing a sheet of anomalous mass at the phase boundary to approximate the local body force induced by phase boundary distortion. The thickness of the sheet is determined by the Clapeyron slope and the lateral tem- perature contrast. To isolate phase transition effects, we have assumed an isoviscous mantle. The Rayleigh number is 1 x lo6, and adiabatic and viscous heating effects are in- cluded. Our grid is 100 by 100. givinga spatial resolutiouof 15 km vertical and 45 km horizontal. (For further details of the method, see Liu 119941.)

To investigate compositional effects, we examine the above case of pure M&SiO.+, extending it to natural mantle (Mgo.gF~.l)2SiO~ olivinecompositions. As can be seen in Figure lb, the entropy of mixing contributed by Fe solid so- lution shifts the /? and y stability fields to lower pressures. Thus, the point at which the relevant Clapeyron slope in- creasm (due to high-temperature stabilization of p at the expense of y) shifts to higher temperatures (indeed, above the solidus [Chopelaset al., 19941). Hence, bothupwellings and downwelliigs now are inhibited by the negative Clapey- ron slope, as can be seen in the results of the corresponding numerical model in Figure 2b. Higher Rayleigh numbers amplify this blocking effect.

Furthermore, we may consider the behavior of more silica-rich mantle components such as MSi03 pyroxene and M3A12Si3012 garnet (M = Mg, Fe, Ca, etc.). Phaserelations in the pyrolite components other than (Mgo,sFq,l)zSi04 olivine are depicted in Figure Ic. The relevant change in Clapeytou slope now occurs where the il + pv transition gives way to the gt - pv transition with increasing tem- perature. Again, the former transition possesses a negative Clapcyron slope, and the latter possesses a zero or weakly positive slope (due to the greater volume decrease and more negative entropy change). The point at which the the rel- evant Clapeyron slope increases, however, now occurs at significantly lower temperatures (since the large entropy of the garnet structure restricts the stability field of ilmenite to low temperatures). Hence, neither upwellings nor down- wellings are inhibited for these components, as illustrated in the results of the corresponding numerical model in Figure 2c.

Discussion

In the above analyses. while considering the dependence of phase relations upon pressure, temperature, and compo- sition. we have consistently treated the phase transitions as occurring nodimearly over a finite depth interval (i.e., Gaus- sian depth-distributed with 2u of 15 km). Strictly speaking, since these are multivariant transitions (Fe solid solution, for example. giving rise to a 0 + y divariant field in the olivine phase diagram of Figure lb), smct thermodynamic Clapeyron slopes are undefined. Thus, we are actnally em- ploying some sort of "effective" Clapeyron slope [cf. Bina and Helffrich. 1994; Helffrich and Bina. 19941. Further- more, the broadening of phase transitions from univariant limes in simple systems to multivariant fields of finite width in multicomponent systems swes to diminish the blocking effects of boundaries with negative Clapeyron slopes [Tack- ley. 19941.

BINA AND LIU: PHASE RELATIONS IN MANTLE CONVECTION

Nondimensional Temperature Figure 2. Numerically simulated evolution of mantle t h d field for three phase diagram topologies. Phase transitions change Clapeyron slope from -4 to 0 MPa/K above 1800°C (A), 2 100" C (B), or 1350°C (C). Rayleigh number in all cases is 1 x lo6. Tick marks indicate 660 km depth. Aspect ratio is three (horizontal) to one (vertical). Images in each column are sequential snapshots of thermal field. Top panels: beginning of experiment, convection has gone through one overturn. Middle panels: after two to three overturns. Bottom panels: after four to five overturns.

While phase transitions in the (SiOz-poor) olivinecompo- transfer. M e r compositional broadening of multivariant nents of the mantle tend, with inaeasing Fe content, to inhibit transitions (by solid solution effects) should act to further convective mass transfer between upper and lower mantle, mitigate impediments to flow. Behavior in the real mantle those occuning in the (Si02-rich) non-olivine components must represent some complex balance between such compet- of the mantle fail to inhibit (and indeed enhance) such mass ing effects. We conclude that the details of computed mantle

2568 BINA AND LIU: PHASE RELATIONS IN MANTLE CONVECTION

convection simulations are highly sensitive to the details of Machetel, P., and P. Weber, Intermittent layered convection in a phase relations as functions of temperawe, and normal mantle with an endothermic phase change at 670 km. composition. Thesefore, attempts to directly correlate com- 350, 55-57, 1991.

Metcalfe, G., C.R.Bina, andJ. M. Ottino, Kinematicconsiderations puked flow or temperature with mcdcls from for mantle mixing, Geophys. Res. Len., 22,743.746.1995. physical observables (such as three-dimensionalseismicve- Nakanuki. T., H. Sato, and H. Fujimoto. Interaction of the up- locity structures) should be a p p r o d e d with caution. given welling plume with the phase and chemical boundary at the 670 the sensitivity of the former t&compositional heterogeneity km discontinuity: ~ f f & t s of temperature-dependent viscosity. and uncertainties in phase relations. Earth Planet. Sci. Lett., 121,369-384. 1994.

Pellier. W. R.. and L. P. Solheun. Mantle ohase transitions and layered chaotic convection, ~ e h ~ h y s . ~ e s . Len., 19, 321-324,

Acknowledgments. C.R.B. is grateful to Joe Engeln for pa - 1992, cious hospitality at Mizzou and to Sue Kesson for auminating Richter, F, M,, Finite convection through a phasebound. discussions. We thank Uli Christensen, Stu Weinstein, and anony- ary, ~ ~ ~ ~ h ~ ~ . J. R, A ~ ~ ~ ~ ~ . sot,, 35,265.287, 1973, mous reviewers for helpful C~mments on this and drafts ~ i n ~ ~ o o d . A. E.. Phasetransfornations and the constitution of the We acknowledge the support of the National Science Foundation mantle, phys Earth planer. ~ ~ ~ f ~ ~ . , 3,109-155,1970. EAR-9158594toC.~.B.) andtheResearchBoardoftheuniversity schube*, G., D. A. yum, and D. L. Ircotte, Role of phasetran- of Missouri (M.L.). sitions in a dvnamic mantle, Geouhys. J. R. Astron. Soc., 42,

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C. R. Bina. Depamnent of Gwlogical Sciences, Locy Hall, Northwestern Universitv. Evanston. lL 60208-2150. (e-mail: craig@earth . n w .edu)

M. Liu, Department of Gwlogical Sciences, University of Missouri, ~oLmbia , MO 652117 (email: mian@eanh.gwsc.missouri.edu)

(received April 17, 1995; revised August 4, 1995; accepted August 11,1995.)