During partial melting, trace elements are distributed between solid (mineral) phases and melts according to their mineral-melt partition coefficient (D^{Mineral / Melt}), defined as the ratio of element concentration in the solid to that in the melt. Partition coefficients are thermodynamic variables that vary with pressure (P), temperature (T) and phase composition (X). Knowledge of variations in mineral-melt partition coefficients as a function of P, T, and mineral and melt composition is therefore of great value in the interpretation and modelling of mantle melting processes. Only when appropriate mineral-melt partition coefficients are obtained can trace element concentrations in the products of melting (e.g., magmatic rocks formed beneath ocean ridges, oceanic islands, or island arcs) be used as tracers of igneous processes in the melt source region.

In this thesis, a rigorous predictive model is developed for trace element partitioning between garnet and anhydrous silicate melt as a function of P, T and X, based on a combination of high-pressure, high-temperature partitioning experiments, lattice static computer simulations, and thermodynamic analysis of published garnet-melt partitioning data.

Garnets are cubic minerals in space group Ia @3bar d, with general structure formula X₃Y₂Z₃O₁₂ (e.g. Geller 1967, Novak and Gibbs 1971). The positions of the X, Y and Z cations are fixed by symmetry. The structure, illustrated in Figure 1.1 (after Merli et al. 1995), can be described as a corner-sharing network of alternating YO₆ octahedra and ZO₄ tetrahedra (Novak and Gibbs 1971). The cavities within this framework form XO₈ triangular dodecahedra (‘distorted cubes’, illustrated in Figure 2.2 for pyrope, Mg₃Al₂Si₃O₁₂).

Figure 1.1. The garnet structure. Alternating isolated tetrahedra (black) and octahedra (dark grey) form a three-dimensional corner-sharing network, with the resulting cavities forming triangular dodecahedra (light grey). After Merli et al. (1995).

Figure 1.2. Detail of the pyrope X-site. Divalent cation X = Mg²⁺ surrounded by 8 oxygens forming distorted cube. Mg-O bond lengths (taken from Smyth and Bish 1988) are 2.343 Å (for O1-O4) and 2.197 Å (for O5-O8).

Most natural garnets are complex solid solutions, mostly due to partial substitutions at the X-site, i.e. between the end-members pyrope [Py, Mg₃Al₂Si₃O₁₂], almandine [Alm, Fe₃Al₂Si₃O₁₂], spessartine [Spes, Mn₃Al₂Si₃O₁₂] and grossular [Gr, Ca₃Al₂Si₃O₁₂]. Many geochemically important trace elements (REE, Y, U, Th) enter the dodecahedral X-sites, while HFSE (Zr, Hf, Nb, Ta) substitute mainly onto the smaller Y-site.

Garnet forms 5-10 wt% of peridotitic rocks at pressures between 2.8 and 10 GPa. At lower pressure, it is transformed into spinel (e.g. Robinson and Wood 1998). In pyroxenite and eclogite, the percentages of garnets are significantly higher (30-50%) and garnet stability extends to shallower levels (e.g. Hirschmann and Stolper 1996). At pressures above 10 GPa, increasing amounts of pyroxene dissolve into garnet, forming garnet-majorite solid solutions (e.g. Ringwood 1991). Majoritic garnet is the second most abundant mineral in the mantle at depths between 400 and 670 km. Finally, at pressures between 22.5 and 24 GPa majoritic garnet breaks down into Ca-perovskite and a (Mg,Fe,Al) perovskite component that dissolves into Mg-perovskite already present at that depth (Wood 2000).

The role of garnet in the generation of mid-ocean ridge and ocean island basalts (MORB and OIB) is controversial. Rare earth element (REE) concentrations in basalt appear to require the presence of at least some garnet in the source of MORB and OIB (e.g. McKenzie and O’Nions 1991; Johnson et al. 1990; Frey et al. 1993; Shen and Forsyth 1995), as do U-Th and Lu-Hf isotope systematics (e.g. Salters and Hart 1989; LaTourrette et al. 1993; Bourdon et al. 1996; Blichert-Toft et al. 1999; Stracke et al. 1999). If this apparent garnet signature is imparted by garnets in peridotite, anhydrous melting beneath mid-ocean ridges is required to start at pressures > 2.8 GPa (Robinson and Wood 1998). This in turn implies high mantle temperatures, which would lead to crustal thicknesses in excess of those observed. Alternatively, the garnet signature could be imparted on melts by partial melting of garnet-bearing mantle heterogeneities (pyroxenites and / or eclogites) at PT conditions that differ significantly from those applicable to melting of peridotite (e.g. Hirschmann and Stolper 1996).

Accurate tests of these hypotheses are impaired by our incomplete knowledge of garnet-melt partition coefficients under the PTX conditions of interest. Excluding the experiments described in this thesis, of the 102 experimental garnet-melt partitioning data sets published to date, 61 contain > 3% water, and 17 are for garnets at pressures > 15 GPa which probably do not play a role in present-day mantle melting. Of the remaining 24 data sets, 11 deal with a maximum of three trace elements. Therefore only 13 garnet-melt trace element partitioning experiments (Hauri et al. 1994; Rocholl et al. 1996; Withers 1997; Johnson 1998; Salters and Longhi 1999) are available at present to describe anhydrous melting in the upper mantle in the presence of garnet. This thesis aims to provide a predictive model that can fill this gap in knowledge and is extendable to the whole range of pressures and temperatures relevant to mantle melting.

Chapter 2 describes results of a series of isobaric, near-isothermal garnet-melt partitioning experiments in the simple system CaO-MgO-Al₂O₃-SiO₂ (CMAS), aimed at isolating the effect of garnet pyrope-grossular content on partition coefficients. In Chapter 3, additional experiments in the system FCMAS (FeO-CMAS) are discussed and the role of the almandine component in determining partition coefficients is elucidated. The results of Chapters 2 and 3 are combined into a model that predicts crystal-chemical controls on garnet-melt partitioning for the REE, Y and Sc in natural systems. In Chapters 4 and 5, the energetics of trace element incorporation into garnets is discussed by means of computer simulations of perfect and defective garnet lattices. Results from the simulations are compared to the experimental data from Chapters 2 and 3, to obtain a detailed understanding at the atomistic level of the controlling factors in garnet-melt partitioning. Chapter 4 focuses on end-member garnets, while Chapter 5 is devoted to trace element incorporation into pyrope-grossular solid solutions. In Chapter 6 a fully predictive thermodynamic model of garnet-melt partitioning for the REE, Y and Sc is developed. Finally, in Chapter 7 a brief summary is provided of the key results of this project. Chapters 2-6 and Appendix 1 have either been published, are in press, or in review, and are presented in the form of research papers. This has resulted in some unavoidable overlap between chapters, especially in the introduction and methods sections.