Contrib Mineral Petrol (1998) 130: 336 345Ó Springer-Verlag 1998Martin CmõÂ ral á John D. Fitz Gerald á Ulrich H. FaulDavid H. GreenA close look at dihedral angles and melt geometryin olivine-basalt aggregates: a TEM studyReceived: 13 April 1997 / Accepted: 2 October 1997Abstract Olivine-basalt aggregates sintered at high P/Thave been used as a simplest approximation of partiallymolten upper mantle peridotite. In the past, geometry ofpartial melt in polycrystalline olivine (and other materials) has been characterised by dihedral (wetting) angleswhich depend upon surface free energy. However, sinceolivine (like most other crystalline materials) is distinctively anisotropic, the simple surface energy balancede ning the dihedral angles cos H 2 cgb 2csl is notvalid and melt geometry is more complicated than canbe expressed by a single dihedral angle value. We examine in detail melt geometry in aggregates held athigh temperature and pressure for very long times(240 612 h). We show the simple dihedral angle conceptto be invalid via transmission electron microscope images. Olivine-basalt interfaces are frequently planarcrystal faces (F-faces) which are controlled by the crystalstructure rather than the surface area minimisation usedin the simple dihedral angle concept. Nevertheless, thedihedral angles may provide useful insights in some situations. They may give a rough estimation of the wetting behaviour of a system, or be used to approximatethe melt distribution if F-faces are not present (possiblyat large grain size and very low melt fraction). Ourmeasurements, excluding F-faces, give a range of dihedral angle values from 0 to 10 which is signi cantlylower than reported previously (20 50 ). The nature of0 angles ( lms and layers up to 1 lm in thickness) isunclear but their frequency compared to dry grainboundaries depends on grain size and melt fraction (e.g.70% for grain size 43 lm and melt fraction 2%).M. CmõÂ ral (&) á J.D. Fitz Gerald á U.H. Faul á D.H. GreenResearch School of Earth Sciences,Australian National University, Canberra ACT 0200, AustraliaTel: 61-2-6249 3416, fax: 61-2-6249 5989e-mail: [email protected] responsibility: J. HoefsIntroductionSome properties of partially molten material in the upper mantle are controlled by melt distribution at thescale of individual grains (Goetze 1977). For example,melt migration by porous ow will be faster if melt- lledintergranular space is well interconnected and simple inshape than if some melt remains trapped in isolatedpockets (e.g. Faul 1997); seismic attenuation will increase if more melt resides in thin segregations betweentwo grains (e.g. Schmeling 1985); and mechanicalstrength of mantle peridotite will be lower if more grainsurfaces are wetted by melt (e.g. Hirth and Kohlstedt1995).Despite its importance, relatively little is knownabout the grain-scale melt distribution in the uppermantle. In this paper, we build on the observations ofWa and Faul (1992), by presenting an electron microscopy study of the olivine-basalt aggregates sinteredat high pressure and temperature for long times. Someimportant details of local melt geometry are describedand the signi cance of olivine surface energy anisotropyis stressed. Considerable emphasis is placed on theanalysis of dihedral angles and discussion of their relevance in determination of melt distribution.Theoretical backgroundPartially molten mantle peridotite can be viewed as anexample of polycrystalline aggregates which contain asmall fraction of liquid phase. Such aggregates havebeen extensively studied in the elds of metallurgy andceramics (e.g. Martin and Doherty 1976; Sutton andBallu 1995). Theories developed to explain the behaviour of these systems predict that, at chemical equilibrium and under hydrostatic conditions, texturalevolution is driven by the minimisation of total surfacefree energy c, the extra free energy of atoms at interfaces
337between phases and at grain boundaries1. Surface energyminimisation results in the interdependent processes ofcontinuous grain growth and redistribution of liquidinto lower energy con gurations.On the scale of individual grains, the problem of meltdistribution reduces to the examination of the stabilityof an individual solid-solid grain boundary versus thatof two solid-liquid interfaces. In the simplest case, theequilibrium shape of an isolated isotropic crystal is asphere and surface energies can be expressed by vectorsof surface tensions (Gibbs 1948). In a polycrystallineaggregate, the criterion for disappearance of grainboundary by wetting is: cgb 2csl , where cgb is the grainboundary energy and csl is the solid-liquid interfacialenergy. At the point of contact between grain boundaryand liquid, the dihedral angle H is formed and is relatedto the surface energies by cos H 2 cgb 2csl (Smith1964, p 24). In an isotropic system the dihedral angle hasa unique value fully describing the geometry of liquiddistribution. If cgb 2csl , H 0 , grain boundaries arenot stable and grain surfaces are completely wetted. If0 H 60 , solid-solid grain boundaries are stable butmelt forms an interconnected network along three- andfour-grain junctions. If H 60 , a minimum melt fraction is necessary before the melt interconnects (melt isotherwise restricted to isolated pockets at four-grainjunctions).However, the surface energy of crystalline solids isfrequently anisotropic and cannot be expressed by thesimple vector form of surface tensions. At equilibrium,an isolated crystal takes the form of a polyhedron whoseshape depends on the relative magnitude of the surfaceenergies of di erent crystal faces. The concept of anequilibrium form has been geometrically expressed bythe Wul construction (e.g. Herring 1951). Planar faces(F-faces) and sharp corners as well as smoothly curvedsurfaces can appear depending on the degree of anisotrophy. In a monomineralic aggregate, constraintsamong neighbouring growing grains prevent achievement of the complete equilibrium shape by individualcrystals. Nevertheless, if a liquid is present, particularplanes of the equilibrium shape may develop in contactwith this liquid. The wetting criterion for a contact between two grains (I and II) must be modi ed to accountfor the orientation dependence of the surface free energies: cgb cIsl cIIsl (e.g. Kim et al. 1994). The energy ofa grain boundary cgb (n,R), is a function of the surfacenormal n, and the misorientation between the twoneighbouring crystals represented by the rotation matrixR. The energy of the solid-liquid interfaces is a functionof both n and composition of the liquid phase. All surface energies depend also on temperature and pressure.There is no simple trigonometric relationship forbalancing the surface energies at triple junctions of anisotropic interfaces. The energy balance at a junction of1The term interface denotes a boundary between di erent phases(e.g. olivine-melt); the term grain boundary is used for a boundarybetween grains of the same phasethree or more grains or phases is still poorly understoodtheoretically (J. Cahn, personal communication 1997)and its analysis is a very di cult problem (see for example Cahn and Kalonji, 1994 and references therein).Ho man and Cahn (1972) and Cahn and Ho man(1974) have modi ed the surface-tension method ofGibbs for isotropic surfaces and introduced a vectormethod for anisotropic interfaces (see also Cahn andHandwerker, 1993). It can be deduced from these worksthat for highly anisotropic (fully faceted) surfaces, thedihedral angle subtended between adjoining facets is nota measure of the local surface energy balance and therelationship linking such a dihedral angle to the surfaceenergies is complex. This is also true even for less anisotropic (curved) surfaces. The simple formulacos H 2 cgb 2csl can be applied only if the crystallineanisotropy is negligible i.e. at near constant curvatureof the equilibrium shape.Previous workReturning to the materials of the Earth's upper mantle, aggregatesof olivine with a few percent of basalt, sintered above solidustemperatures, have often been used as a simple experimental approximation of the partially molten upper mantle environment (seeKohlstedt, 1992 for a review). Apparent dihedral angles have beenmeasured from scanning electron microscope (SEM) or light microscope images of melt (glass) distribution exposed on polishedsurfaces. The distribution of apparent angles has then been manipulated to obtain a single true'' dihedral angle (a methodoriginally developed by Harker and Parker 1945, reviewed byJurewicz and Jurewicz 1986) which assumes isotropic surface energy. This type of analysis has also been applied to study meltdistribution in anisotropic mineral aggregates (e.g. Laporte et al.(1997). For the olivine-basalt system, dihedral angles between 20and 50 have been reported (Wa and Bulau 1982; Riley andKohlstedt 1991; Beeman and Kohlstedt 1993; Hirth and Kohlstedt1995). Based on these analyses, a common view has been that thepartially molten upper mantle is a relatively simple system inwhich melt is totally interconnected in a network of triple junctiontubules where three olivine grains meet (e.g. von Bargen and Wa 1986).Anisotropic wetting of olivine was considered by Cooper andKohlstedt (1982) and Vaughan et al. (1982), emphasised by Bussodand Christie (1991) and more recently examined in detail by Wa and Faul (1992). The latter authors documented melt morphologydeviating signi cantly from that of the triple junction tubule network and described the presence of F-faces as a major control onthe melt distribution. Subsequently, Faul et al. (1994) showed thatat melt fractions as small as 1% and grain size about 50 lm, a largeproportion of melt occurs in elongated inclusions between twograin surfaces rather than in triple junction tubules. Vaughan et al.(1982) and Kohlstedt (1990) searched in detail for melt lms between two grain surfaces in olivine-basalt using high resolutionanalytical transmission electron microscope (TEM). No thin melt lms ( 0.2 nm) replacing grain boundaries were found in thesamples sintered at 1 GPa/1250 C/200 hours despite predictionsbased on the thermodynamics of interfaces (Hess 1994) and inanalogy with some ceramics (Clarke 1987), although Vaughan et al.(1982) did note 10 50 nm layers between a small fraction of grains.In the olivine-basalt system, grains completely separated by meltlayers have also been reported by Jin et al. (1994) and thin lms byDrury and Fitz Gerald (1996), but both are studies in deformedmaterials and involve strain energy factors additional to the surfaceenergy minimisation being considered here.
338ExperimentsFrom a set of long-duration experiments, samples that displayedsteady experimental conditions (P/T) have been selected for microstructural study. The compositions of the samples and experimental details are given in Table 1 and Table 2 respectively.The starting materials were natural olivine from mantle xenoliths collected from either Mt. Porndon in Victoria or San Carlos inArizona, and a synthetic basalt glass. Crushed olivine grains ofroughly 0.5 mm grain size were hand-picked and ground to powders. Di erent grain size fractions were obtained by sieving. Thebasalt parent mixes were prepared from high purity oxides andcarbonates ground under acetone and red at 1000 C for 10 h.Fayalite was added prior to regrinding and melting into glass. Finally the basaltic glass was ground to ne-grained ( 5 lm) powder.Oven dried ( 48 h at 200 C) mixtures of olivine and basaltpowders (up to 2 wt%) were sintered at conditions above the solidus in a 13 mm solid-media piston cylinder apparatus. The experimental temperatures were controlled using type B (Pt94/Rh6 Pt70/Rh30) thermocouples. The experimental cell assemblies werecomposed of NaCl (outermost) and Pyrex glass sleeves enclosing agraphite heater, and vertical spacers made of pyrophyllite or 60%dense pure MgO. The sample capsules were made of high puritygraphite sealed in Pt tube for the 1 GPa runs and Ni70/Fe30 alloyfor the 0.3 GPa run2. Although the experiments were quenched at arate initially exceeding 300 C/s, it is possible that some quenchgrowth of olivine occurred. However, we searched for characteristicquench features without success, so we conclude that the quenchinghas no critical e ect on the microstructure (see Faul 1997 andreferences therein for a more detailed discussion of the quenchovergrowth).The basalt composition was based on the results of a meltingexperiment on Hawaiian Pyrolite (Green and Ringwood 1967) at1200 C and 0.3 GPa (ANU#C49/1995, unpublished data). Although originally designed for 0.3 GPa runs, this composition hasbeen found satisfactory also for 1 GPa melt distribution experiments. At 1 GPa the basalt reacts with olivine (Jaques and Green1980) and crystallises a minor ( 1%) amount of small subhedralcrystals of orthopyroxene in samples OB17, OB31 and OB32. NoTable 1 Composition of starting materials (EDS analysis; wt%).(MP olivine from Mt. Porndon, Victoria, used in OB17, OB31,OB32, SC olivine San Carlos, Arizona, used in SD2). Syntheticbasalt (unpublished data) is a partial melt of Hawaiian pyrolite.While there is a mild reaction between the phases during the experiments, the basaltic character of the melt remains unchangedOlivine MPOlivine 9.49A complementary function of the 300 MPa run was to test thiscapsule material for experiments in a gas-media deformation apparatus where graphite cannot be used. According to O'Neill andWall (1987) the Ni70/Fe30 alloy is in equilibrium with mantleolivine at the upper mantle conditionssigni cant di erences between composition of the pre-run andpost-run olivine have been detected. Although fully quantitativeanalyses of the post-run basalt (glass) have