Effect of melt composition on the partitioning of trace elements between titanite and silicate melt

Isobaric and isothermal experiments were performed to investigate the effect of melt composition on the partitioning of trace elements between titanite (CaTiSiO₅) and a range of different silicate melts. Titanite-melt partition coefficients for 18 trace elements were determined by secondary ion mass spectrometry (SIMS) analyses of experimental run products. The partition coefficients for the rare earth elements and for Th, Nb, and Ta reveal a strong influence of melt composition on partition coefficients, whereas partition coefficients for other studied monovalent, divalent and most quadrivalent (i.e., Zr, Hf) cations are not significantly affected by melt composition. The present data show that the influence of melt composition may not be neglected when modelling trace element partitioning.It is argued that it is mainly the change of coordination number and the regularity of the coordination space of trace elements in the melt structure that controls partition coefficients in our experiments. Furthermore, our data also show that the substitution mechanism by which trace elements are incorporated into titanite crystals may be of additional importance in this context.     

Thermal expansion and high-temperature P21/c–C2/c phase transition in clinopyroxene-type LiFeGe2O6 and comparison to NaFe(Si,Ge)2O6

A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) Å, β = 108.844(6)°, V = 442.75(16) ų, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the $(\bar{1}\,0\,1) A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) ?, β = 108.844(6)°, V = 442.75(16) ?³, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the ([`1] 0 1)(\bar{1}\,0\,1) plane, mostly along [0 1 0], and pure shear in the (0 1 0) plane due to the decrease of β. From comparison with silicate analogues, the germanate clinopyroxenes are more expansible, while the P2₁/c expands more than the C2/c phase. The evolution of Q ² (calculated as the normalized intensity of b-type reflections) with T in the framework of the Landau theory has been done using a standard expression for a first order phase transition. We observe a jump of Q ₀² = 0.538(2) at T _tr, with T _c of 481(7) K, b/a = −2,290 K, and c/a = 3,192 K, and thus far from being tri-critical point. A closely related composition (LiFe³⁺Si₂O₆) shows an equivalent phase transition at 228 K, which is very close to the tri-critical point and 561 K cooler. This result indicates that a change in the composition of tetrahedral sites can have dramatic effects on the P2₁/c ↔ C2/c displacive phase transition in clinopyroxenes. The major changes observed in the evolution of the crystal structure with T are observed in the M2 polyhedron, with a volume decrease by ca. 13.3%, compared to ca. 1.3% observed in the M1 polyhedron. The tetrahedra behave as rigid units with neither a significant change of volume at T > T _tr (<1‰), nor a change of tilting of the basal plane. No change in coordination is observed at T > T _tr in the M2 polyhedron, which remains sixfold coordinated although a strong deformation of this polyhedron is observed. This deformation is related to a strong change by 51.4° at T _tr of the kinking angle (O3–O3–O3 angle) of the B-chain of tetrahedra, which switches from O-rotated to S-rotated [from 143.3(5)° to 194.7(6)°]. The A-chain is S-rotated at T < T _tr [206.8(5)° at 703 K] and extends by 12° at the transition.     

Graben width controlling syn-rift sedimentation: the Palaeogene southern Upper Rhine Graben as an example

Eocene to Early Oligocene syn-rift deposits of the southern Upper Rhine Graben (URG) accumulated in restricted environments. Sedimentation was controlled by local clastic supply from the graben flanks, as well as by strong intra-basinal variations in accommodation space due to differential tectonic subsidence, that in turn led to pronounced lateral variations in depositional environment. Three large-scale cycles of intensified evaporite sedimentation were interrupted by temporary changes towards brackish or freshwater conditions. They form three major base level cycles that can be traced throughout the basin, each of them representing a stratigraphic sub-unit. A relatively constant amount of horizontal extension (ΔL) in the range of 4–5 km has been estimated for the URG from numerous cross-sections. The width of the rift (L _f ), however, varies between 35 and more than 60 km, resulting in a variable crustal stretching factor between the bounding masterfaults. Apart from block tilting, tectonic subsidence was, therefore, largely controlled by changes in the initial rift width (L ₀). The along-strike variations of the graben width are responsible for the development of a deep, trough-like evaporite basin (Potash Basin) in the narrowest part of the southern URG, adjacent to shallow areas in the wider parts of the rift such as the Colmar Swell in the north and the Rhine Bresse Transfer Zone that delimits the URG to the south. Under a constant amount of extension, the along-strike variation in rift width is the principal factor controlling depo-centre development in extensional basins.     

Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation

The transport of chemically reactive solutes (e.g. surfactants, CO₂ or dissolved minerals) is of fundamental importance to a wide range of applications in oil and gas reservoirs such as enhanced oil recovery and mineral scale formation. In this work, we investigate exponential time integrators, in conjunction with an upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs. We model sub-grid fluctuations in transport velocities and uncertainty in the reaction term by writing the advection–dispersion–reaction equation as a stochastic partial differential equation with multiplicative noise. The exponential integrators are based on the variation of constants solution and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing the finite volume discretisation, the use of real Léja point or the Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. For the deterministic system, we investigate two exponential time integrators, the second-order accurate exponential Euler midpoint (EEM) scheme and exponential time differencing of order one (ETD1). All our numerical examples demonstrate that our methods can compete in terms of efficiency and accuracy compared with standard first-order semi-implicit time integrators when solving (stochastic) partial differential equations that model mixing and chemical reactions in 3D heterogeneous porous media. Our results suggest that exponential time integrators such as the ETD1 and EEM schemes could be applied to typical 3D reservoir models comprising tens to hundreds of thousands unknowns.     

Lower crustal melting and the role of open-system processes in the genesis of syn-orogenic quartz diorite–granite–leucogranite associations: constraints from Sr–Nd–O isotopes from the Bandombaai Complex, Namibia

The Bandombaai Complex (southern Kaoko Belt, Namibia) consists of three main intrusive rock types including metaluminous hornblende- and sphene-bearing quartz diorites, allanite-bearing granodiorites and granites, and peraluminous garnet- and muscovite-bearing leucogranites. Intrusion of the quartz diorites is constrained by a U–Pb zircon age of 540±3 Ma.

Quartz diorites, granodiorites and granites display heterogeneous initial Nd- and O isotope compositions (_{Nd (540 Ma)}=−6.3 to −19.8; δ¹⁸O=9.0–11.6‰) but rather low and uniform initial Sr isotope compositions (⁸⁷Sr/⁸⁶Sr_initial=0.70794–0.70982). Two leucogranites and one aplite have higher initial ⁸⁷Sr/⁸⁶Sr ratios (0.70828–0.71559), but similar initial _Nd (−11.9 to −15.8) and oxygen isotope values (10.5–12.9‰). The geochemical and isotopic characteristics of the Bandombaai Complex are distinct from other granitoids of the Kaoko Belt and the Central Zone of the Damara orogen. Our study suggests that the quartz diorites of the Bandombaai Complex are generated by melting of heterogeneous mafic lower crust. Based on a comparison with results from amphibolite-dehydration melting experiments, a lower crustal garnet- and amphibole-bearing metabasalt, probably enriched in K₂O, is a likely source rock for the quartz diorites. The granodiorites/granites show low Rb/Sr (<0.6) ratios and are probably generated by partial melting of meta-igneous (intermediate) lower crustal sources by amphibole-dehydration melting. Most of the leucogranites display higher Rb/Sr ratios (>1) and are most likely generated by biotite-dehydration melting of heterogeneous felsic lower crust. All segments of the lower crust underwent partial melting during the Pan-African orogeny at a time (540 Ma) when the middle crust of the central Damara orogen also underwent high T, medium P regional metamorphism and melting. Geochemical and isotope data from the Bandombaai Complex suggest that the Pan-African orogeny in this part of the orogen was not a major crust-forming episode. Instead, even the most primitive rock types of the region, the quartz diorites, represent recycled lower crustal material.     

Garnet and spinel in fertile and depleted mantle: insights from thermodynamic modelling

We performed thermodynamic calculations based on model and natural peridotitic compositions at pressure and temperature conditions relevant to the Earth’s upper mantle, using well-established free energy minimization techniques. The model is consistent with the available experimental data in Cr-bearing peridotitic systems and can therefore be used to predict phase relations and mineral compositions in a wide range of realistic mantle compositions. The generated phase diagrams for six different bulk compositions, representative of fertile, depleted and ultra-depleted peridotitic mantle, shown that the garnet + spinel stability field is always broad at low temperatures and progressively narrows with increasing temperatures. In lithospheric sections with hot geotherms (ca. 60 mW/m²), garnet coexists with spinel across an interval of 10–15 km, at ca. 50–70 km depths. In colder, cratonic, lithospheric sections (e.g. along a 40 mW/m² geotherm), the width of the garnet–spinel transition strongly depends on bulk composition: In fertile mantle, spinel can coexist with garnet to about 120 km depth, while in an ultra-depleted harzburgitic mantle, it can be stable to over 180 km depth. The formation of chromian spinel inclusions in diamonds is restricted to pressures between 4.0 and 6.0 GPa. The modes of spinel decrease rapidly to less than 1 vol % when it coexists with garnet; hence, spinel grains can be easily overlooked during the petrographical characterization of small mantle xenoliths. The very Cr-rich nature of many spinels from xenoliths and diamonds from cratonic settings may be simply a consequence of their low modes in high-pressure assemblages; thus, their composition does not necessarily imply an extremely refractory composition of the source rock. The model also shows that large Ca and Cr variations in lherzolitic garnets in equilibrium with spinel can be explained by variations of pressure and temperature along a continental geotherm and do not necessarily imply variations of bulk composition. The slope of the Cr# [i.e. Cr/(Cr + Al)mol] isopleths in garnet in equilibrium with spinel changes significantly at high temperatures, posing serious limitations to the applicability of empirical geobarometric methods calibrated on cratonic mantle xenoliths in hotter, off-craton, lithospheric mantle sections.     

The reaction MgCr2O4 + SiO2 = Cr2O3 + MgSiO3 and the free energy of formation of magnesiochromite (MgCr2O4)

Low-temperature heat capacity measurements for MgCr₂O₄ have only been performed down to 52 K, and the commonly quoted third-law entropy at 298 K (106 J K⁻¹ mol⁻¹) was obtained by empirical extrapolation of these measurements to 0 K without considering the magnetic or electronic ordering contributions to the entropy. Subsequent magnetic measurements at low temperature reveal that the Néel temperature, at which magnetic ordering of the Cr³⁺ ions in MgCr₂O₄ occurs, is at ∼15 K. Hence a substantial contribution to the entropy of MgCr₂O₄ has been missed. We have determined the position of the near-univariant reaction MgCr₂O₄+SiO₂=MgSiO₃+Cr₂O₃. The reaction, which has a small positive slope in P-T space, has been bracketed at 100 K intervals between 1273 and 1773 K by reversal experiments. The reaction is extremely sluggish, and lengthy run times with a flux (H₂O, BaO-B₂O₃ or K₂O-B₂O₃) are needed to produce tight reversal brackets. The results, combined with assessed thermodynamic data for Cr₂O₃, MgSiO₃ and SiO₂, give the entropy and enthalpy of formation of MgCr₂O₄ spinel. As expected, our experimental results are not in good agreement with the presently available thermodynamic data. We obtain Δ _f H ^∘ ₂₉₈=−1759.2±1.5 kJ mol⁻¹ and S ^∘ ₂₉₈=122.1±1.0 J K⁻¹ mol⁻¹ for MgCr₂O₄. This entropy is some 16 J K⁻¹ mol⁻¹ more than the calorimetrically determined value, and implies a value for the magnetic entropy of MgCr₂O₄ consistent with an effective spin quantum number (S') for Cr³⁺ of 1/2 rather than the theoretical 3/2, indicating, as in other spinels, spin quenching. Received: 9 May 1997 / Accepted: 28 July 1997