Rainer Abart

Enhanced mass transfer through short-circuit diffusion: Growth of garnet reaction rims at eclogite facies conditions

Abstract In the Monte Rosa area, Northern Italy, the assemblage garnet + phengite + quartz was formed in polymetamorphic metapelites from pre-existing biotite and plagioclase during an eclogite-facies Alpine metamorphic overprint. While phengite nucleated within plagioclase, garnet formed 10 to 20 μm wide continuous rims along the original biotite-plagioclase interphase boundaries. Garnet formation involved diffusion of Ca-, Fe-, and Mg-bearing species across the growing rims. The garnet rims show an overall asymmetric compositional zoning and distinct nanometer scale chemical patterns across grain boundaries within the garnet polycrystal. The compositional patterns resulted from the interplay of diffusion along grain and interphase boundaries and volume diffusion. Individual garnet crystals are separated by low-angle grain boundaries, which are predominantly oriented perpendicular to the reaction rim giving rise to an overall palisade microstructure. Grain boundaries contain arrays of closely spaced channels about 2 nm wide, which are filled with an amorphous phase. These channels represent direct links between the garnet-biotite and garnet-plagioclase reaction fronts and provide pathways for fast diffusion. From numerical simulation of the observed chemical patterns, diffusion of Ca and Fe is inferred to have been 5.6 orders of magnitude faster within grain boundaries than through the interior of garnet grains. Although the amorphous grain boundary phase only takes up a small fraction (2.5 per mil) of the total volume of the garnet polycrystal, short-circuit diffusion along grain boundaries contributed substantially to material transfer across the growing garnet rim. Despite the presence of fast pathways, bulk diffusion was too slow to allow for chemical equilibration of the phases involved in garnet rim formation, even on a micrometer scale. Relying on published garnet volume diffusion data, Dgb (where gb = grain boundary), is estimated to be on the order of 10-(19.20) m2/s at the estimated reaction conditions of 650 °C and 12.5 kbar, where DCagb is slower than DFegb by a factor of ten.

THERMODYNAMIC MODEL FOR DIFFUSION CONTROLLED REACTION RIM GROWTH IN A BINARY SYSTEM : APPLICATION TO THE FORSTERITE-ENSTATITE-QUARTZ SYSTEM

We present a thermodynamic model for diffusion controlled growth of a reaction rim of phase γ between the phases α and β in a two component system. We investigate the case, where the reactant phase α has planar, cylindrical and spherical geometry and is embedded in a matrix of phase β. We find that for non planar geometry and for the general case, where the molar volumes of the reactant phases are different, the rim growth rate depends on the matrix-inclusion arrangement. The model is applied to growth of enstatite reaction rims that form at quartz-forsterite interfaces. Two different geometrical setups are considered, namely a spherical grain of forsterite in a quartz matrix and a spherical quartz grain in a forsterite matrix. The enstatite rims are polycrystalline and transfer of the MgO and SiO2 components across the growing rim occurs by a combination of volume− and grain boundary diffusion. For enstatite rims that were grown at experimental conditions of 1000°C and 1 GPa (Milke and others, 2008) bulk mass transfer may be described by effective diffusion coefficients in the range of 1.8 · 10−17m2s−1 ≤ DSiO2 ≤ 1.1 · 10−16m2s−1 and 2.7 · 10−17m2s−1 ≤ DMgO ≤ 1.6 · 10−16m2s−1.

Exsolution by spinodal decomposition II: Perthite formation during slow cooling of anatexites from Ngoronghoro, Tanzania

Perthites in slowly cooled granulite facies rocks from the Ngoronghoro structure (Tanzania) show complex microstructures reflecting several stages of exsolution and coarsening. Mesoperthites with an integrated bulk composition of Or26.5Ab71An2.5 are comprised of lamellar intergrowth of 5 to 10 μm wide orthoclase-rich and albite-rich lamellae. Spindle perthites with a bulk composition of Or67Ab31.5An1.5 are comprised of 2 to 10 μm wide and several 10s of μm long albite-rich spindles in an orthoclase-rich host. In the mesoperthite primary exsolution occurred by spinodal decomposition, whereas the spindle perthite formed by a nucleation and growth mechanism. The interfaces between the exsolved phases are generally incoherent. Unmixing and coarsening of the mesoperthite is discussed in the light of non-linear uphill diffusion. The microstructure evolution and successive chemical separation of the exsolved phases during cooling are modeled based on Cahn-Hilliard theory. We find that coarsening primarily occurs during the first 20 °C to 30 °C of cooling after the homogeneous precursor feldspar has entered the coherent spinodal. The extent of coarsening and the characteristic size of the exsolved phases depend on the cooling rate over this temperature interval. For geologically relevant cooling rates on the order of 5°C/Ma to 50 °C/Ma the compositions of the exsolved phases develop along the solvus down to about 480 °C to 530 °C and are “frozen in” only at lower temperatures. The compositions that are finally preserved in the orthoclase-rich and in the albite-rich phases depend on cooling rate over this temperature interval. Both the characteristic lamella width of the mesoperthite as well as the compositions of the exsolved phases indicate slow cooling at ≤ 5 °C/Ma during the coarsening stage and down to about 450 °C. During later stages of the cooling history the albite-rich phase of the mesoperthite exsolved about the peristerite gap, and the orthoclase-rich host of the spindle perthite exsolved a second generation of coherent albite-rich spindles. The incoherent phase boundaries of the primary perthite microstructures served as passageways for fluids during late stage deuteric alteration, which lead to secondary coarsening in the mesoperthite and to alteration of the albite-rich precipitates in the spindle perthite. Finally, both types of perthites were replaced by coarse grained patch perthite during deuteric alteration.

TiO2 exsolution from garnet by open-system precipitation: evidence from crystallographic and shape preferred orientation of rutile inclusions

We investigated rutile needles with a clear shape preferred orientation in garnet from (ultra) high-pressure metapelites from the Kimi Complex of the Greek Rhodope by electron microprobe, electron backscatter diffraction and TEM techniques. A definite though complex crystallographic orientation relationship between the garnet host and rutile was identified in that Rt[001] is either parallel to Grt<111> or describes cones with opening angle 27.6° around Grt<111>. Each Rt[001] small circle representing a cone on the pole figure displays six maxima in the density plots. This evidence together with microchemical observations in TEM, when compared to various possible mechanisms of formation, corroborates a precipitate origin. A review of exchange vectors for Ti substitution in garnet indicates that rutile formation from garnet cannot occur in a closed system. It requires that components are exchanged between the garnet interior and the rock matrix by solid-state diffusion, a process we refer to as “open-system precipitation” (OSP). The kinetically most feasible reaction of this type will dominate the overall process. The perhaps most efficient reaction involves internal oxidation of Fe2+ to Fe3+ and transfer from the dodecahedral to the octahedral site just vacated by

In Situ Observations of Phase Transitions in Metastable Nickel (Carbide)/Carbon Nanocomposites

{\text{Ti}}^{ 4+ }: 6\,{\text{M}}^{ 2+ }_{ 3} {\text{TiAl}}\left[ {{\text{AlSi}}_{ 2} } \right]{\text{O}}_{ 1 2} + 6\,{\text{M}}^{ 2+ }_{ 2, 5} {\text{TiAlSi}}_{ 3} {\text{O}}_{ 1 2} = 10\,{\text{M}}^{ 2+ }_{ 3.0} {\text{Al}}_{ 1. 8} {\text{Fe}}_{0. 2} {\text{Si}}_{ 3} {\text{O}}_{ 1 2} + {\text{M}}^{2+} + 2 {\text{e}}^{-} + 1 2\,{\text{TiO}}_{ 2} .

Thermodynamic Model For Reaction Rim Growth: Interface Reaction and Diffusion Control

OSP is likely to occur at conditions where the transition of natural systems to open-system behaviour becomes apparent, as in the granulite and high-temperature eclogite facies.

Thermodynamic model for growth of reaction rims with lamellar microstructure

Abstract Reaction layer growth between two chemically different solids may be controlled by polycrystalline diffusion kinetics in the growing phase. The kinetics depend on the interplay between volume and grain boundary diffusion. Using spinel formation between single crystals of periclase and sapphire as an example, we quantify the effects of an applied mechanical stress on the bulk-transport properties of the reaction layer. The rate of spinel growth increases fourfold when stress normal to the reaction interface increases from 3 to 30 MPa due to stress-induced changes in grain boundary structure. At low applied stress, low-index (i.e., Σ3) “coincidence site lattice” grain boundaries with slow diffusion coefficients dominate, related to epitactic growth of spinel on sapphire. Increasing stress triggers epitactic growth of spinel on periclase, and causes sapphire-grown spinel grains to rotate out of epitaxy, and grain boundaries with fast diffusion coefficients dominate. This effect outweighs the hitherto emphasized influence of grain size on the bulk transport properties of polycrystals.

Hydration of periclase at 350 ∘C to 620 ∘C and 200 MPa: experimental calibration of reaction rate

Nanocomposite thin films comprised of metastable metal carbides in a carbon matrix have a wide variety of applications ranging from hard coatings to magnetics and energy storage and conversion. While their deposition using nonequilibrium techniques is established, the understanding of the dynamic evolution of such metastable nanocomposites under thermal equilibrium conditions at elevated temperatures during processing and during device operation remains limited. Here, we investigate sputter-deposited nanocomposites of metastable nickel carbide (Ni3C) nanocrystals in an amorphous carbon (a-C) matrix during thermal postdeposition processing via complementary in situ X-ray diffractometry, in situ Raman spectroscopy, and in situ X-ray photoelectron spectroscopy. At low annealing temperatures (300 °C) we observe isothermal Ni3C decomposition into face-centered-cubic Ni and amorphous carbon, however, without changes to the initial finely structured nanocomposite morphology. Only for higher temperatures (400–800 °C) Ni-catalyzed isothermal graphitization of the amorphous carbon matrix sets in, which we link to bulk-diffusion-mediated phase separation of the nanocomposite into coarser Ni and graphite grains. Upon natural cooling, only minimal precipitation of additional carbon from the Ni is observed, showing that even for highly carbon saturated systems precipitation upon cooling can be kinetically quenched. Our findings demonstrate that phase transformations of the filler and morphology modifications of the nanocomposite can be decoupled, which is advantageous from a manufacturing perspective. Our in situ study also identifies the high carbon content of the Ni filler crystallites at all stages of processing as the key hallmark feature of such metal–carbon nanocomposites that governs their entire thermal evolution. In a wider context, we also discuss our findings with regard to the much debated potential role of metastable Ni3C as a catalyst phase in graphene and carbon nanotube growth.