Dynamic recrystallization of wet synthetic polycrystalline halite: dependence of grain size distribution on flow stress, temperature and strain

It is often observed that dynamic recrystallization results in a recrystallized grain size distribution with a mean grain size that is inversely related to the flow stress. However, it is still open to discussion if theoretical models that underpin recrystallized grain size–stress relations offer a satisfactorily microphysical basis. The temperature dependence of recrystallized grain size, predicted by most of these models, is rarely observed, possibly because it is usually not systematically investigated. In this study, samples of wet halite containing >10 ppm water (by weight) were deformed in axial compression at 50 MPa confining pressure. The evolution of the recrystallized grain size distribution with strain was investigated using experiments achieving natural strains of 0.07, 0.12 and 0.25 at a strain rate of 5×10⁻⁷ s⁻¹ and a temperature of 125 °C. The stress and temperature dependence of recrystallized grain size was systematically investigated using experiments achieving fixed strains of 0.29–0.46 (and one to a strain of 0.68) at constant strain rates of 5×10⁻⁷–1×10⁻⁴ s⁻¹ and temperatures of 75–240 °C, yielding stresses of 7–22 MPa. The microstructures and full grain size distributions of all samples were analyzed. The results showed that deformation occurred by a combination of dislocation creep and solution-precipitation creep. Dynamic recrystallization occurred in all samples and was dominated by fluid assisted grain boundary migration. During deformation, grain boundary migration results in a competition between grain growth due to the removal of grains with high internal strain energy and grain size reduction due to grain dissection (i.e. moving boundaries that crosscut or consume parts of neighbouring grains). At steady state, grain growth and grain size reduction processes balance, yielding constant flow stress and recrystallized grain size that is inversely related to stress and temperature. Evaluation of the recrystallized grain size data against the different models for the development of mean steady state recrystallized grain size revealed that the data are best described by a model based on the hypothesis that recrystallized grain size organizes itself in the boundary between the (grain size sensitive) solution-precipitation and (grain size insensitive) dislocation creep fields. Application of a piezometer, calibrated using the recrystallized grain size data, to natural halite rock revealed that paleostresses can vary significantly with temperature (up to a factor of 2.5 for T=50–200 °C) and that the existing temperature independent recrystallized grain size–stress piezometer may significantly underestimate flow stresses in natural halite rock.     

Volume and grain boundary diffusion of calcium in natural and hot-pressed calcite aggregates

 Calcium self-diffusion rates in natural calcite single crystals were experimentally determined at 700 to 900° C and 0.1 MPa in a stream of CO₂. Diffusion coefficients (D) were determined from ⁴²Ca concentration profiles measured with an ion microprobe. The Arrhenius parameters yield an activation energy (Q)=382±37 kJ/mol and pre-exponential factor (D₀)=0.13 m²/s, and there is no measurable anisotropy. Calcium grain boundary diffusion rates were experimentally determined in natural (Solnhofen) limestone and hot-pressed calcite aggregates at 650° to 850° C and 0.1 to 100 MPa pressure. The Solnhofen limestone was first pre-annealed for 24 h at 700° C and 100 MPa confining pressure under anhydrous conditions to produce an equilibrium microstructure for the diffusion experiments. Values for the product of the grain boundary diffusion coefficient (D′) and the effective grain boundary diffusion width (δ) were determined from ⁴²Ca concentration profiles measured with an ion microprobe. The results show that there is no measurable difference between D′δ values obtained for pre-annealed Solnhofen samples at 0.1 and 100 MPa or between hot-pressed calcite aggregates and pre-annealed Solnhofen samples. The temperature dependence for calcium grain boundary diffusion in Solnhofen samples annealed at 0.1 MPa is described by the Arrhenius parameters D^′ ₀δ=1.5×10⁻⁹ m³/s and Q=267±47 kJ/mol. Comparison of the results of this study with previously published data show that calcium is the slowest volume diffusing species in calcite. The calcium diffusivities measured in this study place constraints on several geological processes that involve diffusive mass transfer including diffusion-accommodated mechanisms in the deformation of calcite rocks. Received: 19 December 1994/Accepted: 30 June 1995     

Compositional zoning of calcite in a high-pressure metamorphic calc-schist: clues to heterogeneous grain-scale fluid distribution during exhumation

Calcite in former aragonite–dolomite-bearing calc-schists from the ultrahigh-pressure metamorphic (UHPM) oceanic complex at Lago di Cignana, Valtournanche, Italy, preserved different kinds of zoning patterns at calcite grain and phase boundaries. These patterns are interpreted in terms of lattice diffusion and interfacial mass transport linked with a heterogeneous distribution of fluid and its response to a changing state of stress. The succession of events that occurred during exhumation is as follows: As the rocks entered the calcite stability field at T=530–550 °C, P ca. 1.2 GPa, aragonite occurring in the matrix and as inclusions in poikilitic garnet was completely transformed to calcite. Combined evidence from microstructures and digital element distribution maps (Mn-, Mg-, Fe- and Ca–Kα radiation intensity patterns) indicates that transformation rates have been much higher than rates of compositional equilibration of calcite (involving resorption of dolomite and grain boundary transport of Mg, Fe and Ca). This rendered the phase transformation an isochemical process. During subsequent cooling to T ca. 490 °C (where lattice diffusion effectively closed), grains of matrix calcite have developed diffusion-zoned rims, a few hundred micrometres thick, with Mg and Fe increasing and Ca decreasing towards the phase boundary. Composition profiles across concentrically zoned, large grains in geometrically simple surroundings can be successfully modelled with an error function describing diffusion into a semi-infinite medium from a source of constant composition. The diffusion rims in matrix calcite are continuous with quartz, phengite, paragonite and dolomite in the matrix. This points to an effective mass transport on phase boundaries over a distance of several hundred micrometres, if matrix dolomite has supplied the Mg and Fe needed for incorporation in calcite. In contrast, diffusion rims are lacking at calcite–calcite and most calcite–garnet boundaries, implying that only very minor mass transport has occurred on these interfaces over the same T–t interval. From available grain boundary diffusion data and experimentally determined fluid–solid grain boundary structures, inferred large differences in transport rates can be best explained by the discontinuous distribution of aqueous fluid along grain/phase boundaries. Observed patterns of diffusion zoning indicate that fluid was distributed not only along grain-edge channels, but spread out along most calcite–white mica and calcite–quartz two-grain junctions. On the other hand, the inferred non-wetting of calcite grain boundaries in carbonate-rich domains is compatible with fluid–calcite–calcite dihedral angles >60° determined by Holness and Graham (1995) for a wide range of fluid compositions under the P–T conditions of interest. Whereas differential stress has been very low at the stage of diffusion zoning (T > 490 °C), it increased as the rocks were cooling below 440 °C (at 0.3–0.5 GPa). Dislocation creep and the concomitant increase of strain energy in matrix calcite induced migration recrystallisation of high-angle grain boundaries. For that stage, the compositional microstructure of recrystallised calcite grain boundary domains indicates significant mass transport along calcite two-grain junctions, which at the established low temperatures is likely to have been accomplished by ionic diffusion within a hydrous grain boundary fluid film (“dynamic wetting” of migrating grain boundaries). Received: 10 January 2000 / Accepted: 10 April 2000     

THERIA_G: a software program to numerically model prograde garnet growth

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure–temperature–time (P–T–t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P–T–t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P–T–t trajectory. The results of garnet growth simulation can be used to infer the P–T–t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Diffusion-controlled growth of albite and pyroxene reaction rims

The growth rates of albite and pyroxene (enstatite + diopside + spinel) reaction rims were measured at 1000°C and ˜700 MPa and found to be parabolic indicating diffusion-controlled growth. The parabolic rate constants for the pyroxene (+ spinel) rims in samples with 0.5 wt% H₂O added or initially vacuum dried at 25°C and 250°C are 1.68 ± 0.09, 0.54 ± 0.05 and 0.25 ± 0.06 μm²/h, respectively. The values for albite rim growth in samples initially dried at 60°C and with 0.1 wt% H₂O added are 0.25 ± 0.04 and 0.33 ± 0.03 μm²/h, respectively. The latter values were used to derive the product of the grain boundary diffusion coefficient D′_A, where A = SiO₂, NaAlO₂, or NaAlSi₋₁, and the grain boundary thickness δ in albite. The calculated D′_SIO2δ in the albite aggregate for the situations of two different water contents are about 9.9 × 10⁻²³ and 1.4 × 10⁻²² m³ s⁻¹, respectively. Both the rate constants and the calculated D′_Aδ demonstrate that the effect of water content on the grain boundary diffusion rate in monomineralic albite and polymineralic pyroxene (+ spinel) aggregates is small, consistent with recent studies of monomineralic enstatite and forsterite rims. Received: 1 July 1995 / Accepted: 1 August 1996     

Fast diffusion along mobile grain boundaries in calcite

Experimental measurements of grain boundary diffusion are usually conducted on static boundaries, despite the fact that grain boundaries deep in the Earth are frequently mobile. In order to explore the possible effect of boundary mobility on grain boundary diffusion rates we have measured the uptake of ⁴⁴Ca from a layer of ⁴⁴Ca-enriched calcite powder during the static recrystallization of a single crystal of calcite at 900°C. A region about 500 μm wide adjacent to the powder layer is heterogeneously enriched in ⁴⁴Ca, and complex zoning patterns, including sharp steps in composition and continuous increases and decreases in ⁴⁴Ca content, are developed. In metamorphic rocks, these would normally be interpreted in terms of changes in pressure or temperature, Rayleigh fractionation, or episodic fluid infiltration. These explanations cannot apply to our experiments, and instead the zoning patterns are interpreted as being due to variations in grain boundary migration rate. We have applied an analytical model which allows the product of grain boundary diffusion coefficient and grain boundary width (D _GB δ) to be calculated from the grain boundary migration rate and the compositional gradient away from the powder layer. The value of D _GB δ in the mobile grain boundaries is at least five orders of magnitude greater than the published value for static boundaries under the same conditions. In order to allow the scale of chemical equilibrium (and hence textural evolution) to be predicted under both experimental and geological conditions, we present quantitative diffusion-regime maps for static and mobile boundaries in calcite, using both published values and our new values for grain boundary diffusion in mobile boundaries. Enhanced diffusion in mobile boundaries has wide implications for the high temperature rheology of Earth materials, for geochronology, and for interpretations of the length- and time-scales of chemical mass-transport. Moreover, zones of anomalously high electrical conductivity in the crust and mantle could be regions undergoing recrystallization such as active shear zones, rather than regions of anomalous mineralogy, water- or melt-content as is generally suggested.     

Grain boundary diffusion of oxygen,potassium and calcium in natural and hot-pressed feldspar aggregates

 Grain boundary diffusion rates of oxygen, potassium and calcium in fine-grained feldspar aggregates were determined experimentally. The starting materials were a natural albite rock from the Tanco pegmatite and aggregates hot-pressed from fragments of Amelia albite or Ab, Or and An composition glasses. The technique employed isotopic tracers (¹⁸O, ⁴¹K, ⁴²Ca) either evaporated onto the surface or in an aqueous solution surrounding the sample, and depth profiling using an ion microprobe (SIMS). From the depth profiles, the product of the grain boundary diffusion coefficient (D′) and effective boundary width (δ) was calculated using numerical solutions to the appropriate diffusion equation. The experimental reproducibility of D′δ is a factor of 3. A separate determination of D′ independent of δ yields an effective grain boundary width of ∼3 nm, consistent with high resolution TEM observations of a physical grain boundary width <5 nm. Oxygen (as molecular water) grain boundary diffusion rates were determined in the Ab and Or aggregates at 450°–800° C and 100 MPa (hydrothermal), potassium rates in Or aggregates at 450°–700° C both at 0.1 MPa (in air) and at 100 MPa (hydrothermal), and calcium rates in An aggregates at 700°–1100° C and 0.1 MPa (in air). Oxygen grain boundary diffusion rates are similar in all three of the Ab aggregates and in the Or aggregate. Potassium and oxygen depth profiles measured in the same samples yield different D′δ values, confirming a diffusional transport mechanism. Potassium diffusion in the Or aggregate has a greater activation energy (216 vs 78 kJ/mol) than oxygen, and the Arrhenius relations cross at ∼625° C. Potassium D′δ values in Or aggregates are about a factor of five greater in hydrothermal experiments at 100 MPa than in experiments at 0.1 MPa in air. Calcium grain boundary diffusion rates in An aggregates are 4 to 5 orders of magnitude slower than potassium in Or and have a greater (291 kJ/mol) activation energy. This suggests that differences in formal charge and/or size of diffusing species may play an important role in their relative grain boundary diffusion rates. Received: 24 December 1993 / Accepted: 16 June 1994     

Growth of multilayered polycrystalline reaction rims in the MgO–SiO<Subscript>2</Subscript> system,part II: modelling

Part I of this contribution (Gardés et al. in Contrib Mineral Petrol, 2010) reported time- and temperature-dependent experimental growth of polycrystalline forsterite-enstatite double layers between single crystals of periclase and quartz, and enstatite single layers between forsterite and quartz. Both double and single layers displayed growth rates decreasing with time and pronounced grain coarsening. Here, a model is presented for the growth of the layers that couples grain boundary diffusion and grain coarsening to interpret the drop of the growth rates. It results that the growth of the layers is such that (Δx)² ∝ t ^1−1/n , where Δx is the layer thickness and n the grain coarsening exponent, as experimentally observed. It is shown that component transport occurs mainly by grain boundary diffusion and that the contribution of volume diffusion is negligible. Assuming a value of 1 nm for the effective grain boundary width, the following Arrhenius laws for MgO grain boundary diffusion are derived: log D _gb,0^Fo (m²/s) = −2.71 ± 1.03 and E _gb^Fo = 329 ± 30 kJ/mol in forsterite and log D _gb,0^En (m²/s) = 0.13 ± 1.31 and E _gb^En = 417 ± 38 kJ/mol in enstatite. The different activation energies are responsible for the changes in the enstatite/forsterite thickness ratio with varying temperature. We show that significant biases are introduced if grain boundary diffusion-controlled rim growth is modelled assuming constant bulk diffusivities so that differences in activation energies of more than 100 kJ/mol may arise. It is thus important to consider grain coarsening when modelling layered reaction zones because they are usually polycrystalline and controlled by grain boundary transport.     

The role of the grain boundary at chemical and isotopic fronts in marble during contact metamorphism

Carbon and oxygen isotopic profiles around a low pressure metasomatic wollastonite reaction front in a marble of the Hida metamorphic terrain, central Japan, display typical metamorphic fluid-enhanced isotopic zonations. Isotopic profiles obtained from detailed microscale analyses perpendicular to the chemical reaction front in calcite marble show that diffusion-enhanced isotopic exchange may control these profiles. Carbon and oxygen isotopic behaviour in grain boundaries is remarkably different. Oxygen isotopic troughs (¹⁸O depleted rims) around the calcite-grain boundaries are widely observed in this contact aureole, demonstrating that diffusion of oxygen in calcite grain boundary dominates over lattice diffusion in calcite. In contrast, no difference is observed in carbon isotopic profiles obtained from grain cores and rims. There is thus no specific role of the grain boundary for diffusion of carbonic species in the metamorphic fluid during transportation. Carbon chemical species such as CO₂ and CO₃ ions in metamorphic fluid migrate mainly through lattice diffusion. The carbon and oxygen isotope profiles may be modelled by diffusion into a semi-infinite medium. Empirically lattice diffusion of oxygen isotopes is almost six times faster than that of carbon isotopes, and oxygen grain-boundary diffusion is ten times faster than oxygen lattice diffusion. Oxygen isotopic results around the wollastonite vein indicate that migration of the metamorphic fluid into calcite marble was small and was parallel to the aquifer. From the stability of wollastonite and the attainment of oxygen isotopic equilibrium, we suggest that diffusion of oxygen occurred through an aqueous fluid phase. The timescale of formation of the oxygen isotopic profile around the wollastonite vein is calculated to be about 0.76 × 10⁶ years using the experimentally determined diffusion constant. Received: 14 January 1997 / Accepted: 23 April 1998     

The normal grain growth behaviour of nominally pure calcitic aggregates

The normal grain growth behaviour of four different, but all nominally pure, calcite powders (99%+ analytic grade calcite, 99.7% chalk, 99.97% crushed Iceland Spar, 99.95%+ chelometric grade calcite) has been investigated as a function of temperature (550, 600, 650, 700 °C) and confining pressure (100, 190 MPa) under both “dry” and hydrostatic (P _fluid = P _total) conditions. The initial particle size of both the analytic grade and chelometric grade calcite was about 5 μm, and that of the chalk was about 3 μm, while the experiments on the Iceland Spar were conducted on powders of three different initial particle sizes (3.4, 7.5, 38.5 μm). On each material, at each pressure/temperature condition 6 to 15 experiments, equally spaced in log time from 15 minutes to 50 days, were conducted. Under dry conditions all four materials recrystallized to aggregates which contained less than 2% porosity and which had a grain size of between 4 and 20 μm (depending on the initial particle size). Subsequently the aggregates coarsened by normal grain growth, with the kinetics of the growth process being controlled by the rate at which the grain boundaries could drag the residual pores with them as they migrated. Under nominally identical conditions both the mechanism and rates of pore drag differed greatly for the different materials, implying that this process is highly sensitive to trace solute impurity concentrations. This sensitivity renders the task of providing a systematic account of dry calcite grain growth kinetics highly problematic. Under hydrostatic conditions all the powders followed the same normal grain growth kinetics in which the growth process was rate-controlled by diffusion through the pore fluid on the grain boundaries. An activation enthalpy of 162.6 kJ mol⁻¹ and an activation volume of 34.35 cm³ mol⁻¹ was obtained for this process. Received: 23 May 1996 / Accepted: 8 July 1997     

Grain growth kinetics of dolomite,magnesite and calcite: a comparative study

The rates of grain growth of stoichiometric dolomite [CaMg(CO₃)₂] and magnesite (MgCO₃) have been measured at temperatures T of 700–800°C at a confining pressure P _c of 300 MPa, and compared with growth rates of calcite (CaCO₃). Dry, fine-grained aggregates of the three carbonates were synthesized from high purity powders by hot isostatic pressing (HIP); initial mean grain sizes of HIP-synthesized carbonates were 1.4, 1.1, and 17 μm, respectively, for CaMg(CO₃)₂, MgCO₃, and CaCO₃, with porosities of 2, 28, and 0.04% by volume. Grain sizes of all carbonates coarsened during subsequent isostatic annealing, with mean values reaching 3.9, 5.1, and 27 μm for CaMg(CO₃)₂, MgCO₃, and CaCO₃, respectively, in 1 week. Grain growth of dolomite is much slower than the growth rates of magnesite or calcite; assuming normal grain growth and n = 3 for all three carbonates, the rate constant K for dolomite (≃5 × 10⁻⁵ μm³/s) at T = 800°C is less than that for magnesite by a factor of ~30 and less than that for calcite by three orders of magnitude. Variations in carbonate grain growth may be affected by differences in cation composition and densities of pores at grain boundaries that decrease grain boundary mobility. However, rates of coarsening correlate best with the extent of solid solution; K is the largest for calcite with extensive Mg substitution for Ca, while K is the smallest for dolomite with negligible solid solution. Secondary phases may nucleate at advancing dolomite grain boundaries, with implications for deformation processes, rheology, and reaction kinetics of carbonates.     

Effect of grain growth on cation exchange between dunite and fluid: implications for chemical homogenization in the upper mantle

The effect of grain growth on the cation exchange between synthesized forsterite aggregates (i.e., dunite) and nickel-rich aqueous fluid was evaluated experimentally at 1.2 GPa and 1,200°C. The grain boundary (GB) migration caused nickel enrichment in the area swept by the GBs in a fashion similar to that reported for stable isotope exchange in the quartz aggregates. The progress of the grain growth resulted in an increase in the average nickel concentration in the dunites of up to ~80 times that was calculated for a system having stationary GBs. The overall diffusivity of the nickel along the wet GBs and interconnected fluid networks was found to be 6.5 × 10⁻¹⁹–6.7 × 10⁻¹⁸ m³/s, which is 4–5 orders of magnitude higher than the grain boundary diffusivity in the dry dunite. These results show that the grain growth rate is a fundamental factor in the evaluation of the time scale of chemical homogenization in the upper mantle.     

Grain growth kinetics and the effect of crystallographic anisotropy on normal grain growth of quartz

Annealing experiments on agate were performed to investigate grain growth kinetics and the effect of crystallographic anisotropy on normal grain growth of quartz. The experiments were conducted using a piston-cylinder apparatus at 700–800°C and 0.5 GPa for 0–66 h. The grain growth rate was expressed by D ⁿ −D ₀ ⁿ  = kt with k = k ₀ exp(−H*/RT) where D ₀ is the initial grain size at t = 0, with n = 4.4 ± 0.3, and H* = 191.3 ± 11.0 kJ/mol is the activation enthalpy and logk ₀  = 19.8 ± 1.4. While the grain aspect ratios are nearly constant at ~0.7 (short/long) during grain growth, the longest axis in individual grains tends to be oriented parallel to their c-axis, indicating that a primary crystal-preferred orientation of c-axis of the agate could result in the development of a weak shape-preferred orientation during grain growth.     

Phosphorus distribution between potassic alkali feldspar and metaluminous haplogranitic liquid at 200 MPa (H<Subscript>2</Subscript>O): the effect of undercooling on crystal–liquid systematics

To evaluate the applicability of P₂O₅ concentration in potassic alkali feldspar as a monitor of P₂O₅ in melt for undercooled systems, crystal–melt partitioning for P was evaluated via feldspar growth experiments in P-bearing ((3 wt% P₂O₅), water-saturated haplogranitic liquids at 200 MPa, with liquidus undercoolings (ΔT) of 25, 50, 100, 200, and 300°C. Increasing undercooling in the range ΔT=25–200°C shows an evolution of crystal morphologies, from euhedral and well-filled individuals at ΔT=25–50°C to radial clusters with increasingly skeletal habit at greater undercooling. Experiments at ΔT=100–200°C also document the development of P- (up to (9 wt% P₂O₅) and Si-enriched, more alkaline boundary layers adjacent to crystals. Experiments at ΔT=300°C show an additional change in crystallization fabric in which spherulites of skeletal crystals form in open (vapor) space created by the dissolution of bulk silicate, and compositional boundary layers are not observed. We interpret the changes in reaction products at ΔT=300°C to indicate conditions below a glass transition; hence, partition coefficients were not determined for this undercooling. Values of K _d(P)^Kfs/melt from experiments at ΔT=25–200°C, calculated from pairs of crystal and immediately adjacent liquid compositions (including boundary layers at higher undercooling), are mostly in the range of 0.25–0.55 and show no effective change with increased undercooling. Essentially no change in K _d(P)^Kfs/melt with undercooling apparently stems from an interplay between boundary layer composition and a change in the substitution mechanism for P in feldspar from AlPSi₋₂, common in peraluminous to metaluminous liquids near equilibrium, to increasing proportions of ([ ],P)(M⁺,Si)₋₁ with increased undercooling. Bulk glass and liquid beyond boundary layers in experiments with significant percentages of crystallization are homogeneous, and show pronounced fractionation primarily due to the removal of an orthoclase component. Because crystallization was still in progress in experiments with ΔT≤200°C, compositional homogeneity in the bulk liquid requires extremely rapid diffusion of most haplogranite components (Na, K, and Al), apparently resulting from chemical potential gradients stemming from the removal of components from the liquid by crystal growth. Similar homogeneity and bulk fractionation in experiments with ΔT=300°C requires rapid diffusive equilibration for the alkalis even at temperatures below an apparent glass transition. Unlike the haplogranite components, P is only concentrated in liquid boundary layers (ΔT≤200°C) or low-density aqueous vapor (ΔT=300°C) adjacent to crystals. Hence, the P₂O₅ contents of melt inclusions likely are not representative of bulk melt concentrations in significantly undercooled systems (ΔT≤50–100°C).     

The initiation and linkage of surface fractures above a buried strike-slip fault: An experimental approach

Surface fractures in the overburdened sedimentary rocks, formed above a deep-seated basement fault, often provide important information about the kinematics of the underlying master fault. It has already been established that these surface fractures dynamically evolve and link one another with progressive displacement on the master fault below. In the present study, two different series of riedel-type experiments were carried out with clay analogue models under different boundary conditions viz., (i) heterogeneous simple shear of the cover rocks above a buried strike slip fault (wrench system) and (ii) heterogeneous simple shear with a component of shear-normal compression of the overburden package above a basement fault (transpressional system), to observe the initiation and linkage of surface fractures with varying T′ (where T′ = thickness of the overburden normalized with respect to the width of the master fault). In the wrench system, Riedel (R) shears were linked by principal displacement (Y) shears at early stages (shear strain of 0.8 to 1) in thin (2 < T′ < 18) models and finally (at a minimum shear strain of 1.4) gave rise to a through-going fault parallel to the basement fault without development of any other fracture. Conjugate Riedel (R′) shears develop only within the thicker (T′ > 18) clay models at a minimum shear strain of 0.7. With increasing deformation (at a minimum shear strain of 1.2) two R′ shears were joined by an R shear and finally opened up to make a sigmoidal vein with an asymmetry antithetic to the major fault-movement sense. Under transpression, the results were similar to that of heterogeneous simple shear for layers 2 < T′ < 15. In layers of intermediate thickness (15 < T′ < 25) early formed high angle R shears were cross cut by low angle R shears (at a minimum shear strain of 0.5 and shortening of 0.028) and “Riedel-within-Riedel” shears were formed within thick (T′ > 25) models (at minimum shear strain of 0.7 and shortening of 0.1), with marked angularity of secondary fault zone with the master fault at depth.     

An experimental study of Ostwald ripening of olivine and plagioclase in silicate melts: implications for the growth and size of crystals in magmas

We carried out an experimental study to characterize the kinetics of Ostwald ripening in the forsterite-basalt system and in the plagioclase (An₆₅)-andesite system. Eight experiments were done in each system to monitor the evolution of mean grain size and crystal size distribution (CSD) with time t; the experiments were performed in a 1-atmosphere quench furnace, at 1,250°C for plagioclase and 1,300°C for olivine. Very contrasted coarsening kinetics were observed in the two series. In the plagioclase series, the mean grain size increased as log(t), from ≈3 μm to only 8.7 μm in 336 h. The kinetic law in log(t) means that Ostwald ripening was rate-limited by surface nucleation at plagioclase-liquid interfaces. In the olivine series, the mean grain size increased as t ^1/3, from ≈3 μm to 23.2 μm in 496 h. A kinetic law in t ^1/3 is expected when Ostwald ripening is rate-limited either by diffusion in the liquid or by grain growth/dissolution controlled by a screw dislocation mechanism. The shape of olivine CSDs, in particular their positive skewness, indicates that grain coarsening in the olivine experiments was controlled by a screw dislocation mechanism, not by diffusion. As the degrees of undercooling ΔT (or supersaturation) involved in Ostwald ripening are essentially <1°C, the mechanisms of crystal growth identified in our experiments are expected to be those prevailing during the slow crystallisation of large magma chambers. We extrapolated our experimental data to geological time scales to estimate the effect of Ostwald ripening on the size of crystals in magmas. In the case of plagioclase, Ostwald ripening is only efficient for mean grain sizes of a few microns to 20 μm, even for a time scale of 10⁵ years. It can, however, result in a significant decrease of the number of small crystals per unit volume, and contribute to the development of convex upwards CSDs. For olivine, the mean grain size increases from 2–3 μm to ≈70 μm in 1 year and 700 μm in 10³ years; a mean grain size of 3 mm is reached in 10⁵ years. Accordingly, the rate of grain size-dependent processes, such as compaction of olivine-rich cumulates or melt extraction from partially molten peridotites, may significantly be enhanced by textural coarsening.     

Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite

The phase boundary between MnTiO₃ I (ilmenite structure) and MnTiO₃ II (lithium niobate structure) has been determined by analysis of quench products from reversal experiments in a cubic anvil apparatus at 1073–1673 K and 43–75 kbar using mixtures of MnTiO₃ I and II as starting materials. Tight brackets of the boundary give P(kbar)=121.2−0.045 T(K). Thermodynamic analysis of this boundary gives ΔH^o=5300±1000 J·mol⁻¹, ΔS^o = 1.98 ±1J·K⁻¹· mol⁻¹. The enthalpy of transformation obtained directly by transposed-temperature-drop calorimetry is 8359 ±2575 J·mol⁻¹. Possible topologies of the phase relations among the ilmenite, lithium niobate, and perovskite polymorphs are constrained using the above data and the observed (reversible with hysteresis) transformation of II to III at 298 K and 20–30 kbar (Ross et al. 1989). The observed II–III transition is likely to lie on a metastable extension of the II–III boundary into the ilmenite field. However the reversed I–II boundary, with its negative dP/ dT does represent stable equilibrium between ilmenite and lithium niobate, as opposed to the lithium niobate being a quench product of perovskite. We suggest a topology in which the perovskite occurs stably at low T and high P with a triple point (I, II, III) at or below 1073 K near 70 kbar. The I–II boundary would have a negative P-T slope while the II–III and I–III boundaries would be positive, implying that entropy decreases in the order lithium niobate, ilmenite, perovskite. The inferred positive slope of the ilmenite-perovskite transition in MnTiO₃ is different from the negative slopes in silicates and germanates. These thermochemical parameters are discussed in terms of crystal structure and lattice vibrations.     

Differences in grain growth of calcite: a field-based modeling approach

Normal grain growth of calcite was investigated by combining grain size analysis of calcite across the contact aureole of the Adamello pluton, and grain growth modeling based on a thermal model of the surroundings of the pluton. In an unbiased model system, i.e., location dependent variations in temperature-time path, 2/3 and 1/3 of grain growth occurs during pro- and retrograde metamorphism at all locations, respectively. In contrast to this idealized situation, in the field example three groups can be distinguished, which are characterized by variations in their grain size versus temperature relationships: Group I occurs at low temperatures and the grain size remains constant because nano-scale second phase particles of organic origin inhibit grain growth in the calcite aggregates under these conditions. In the presence of an aqueous fluid, these second phases decay at a temperature of about 350 °C enabling the onset of grain growth in calcite. In the following growth period, fluid-enhanced group II and slower group III growth occurs. For group II a continuous and intense grain size increase with T is typical while the grain growth decreases with T for group III. None of the observed trends correlate with experimentally based grain growth kinetics, probably due to differences between nature and experiment which have not yet been investigated (e.g., porosity, second phases). Therefore, grain growth modeling was used to iteratively improve the correlation between measured and modeled grain sizes by optimizing activation energy (Q), pre-exponential factor (k₀) and grain size exponent (n). For n=2, Q of 350 kJ/mol, k₀ of 1.7×10²¹ mⁿs^–1 and Q of 35 kJ/mol, k₀ of 2.5×10^-5 mⁿs^–1 were obtained for group II and III, respectively. With respect to future work, field-data based grain growth modeling might be a promising tool for investigating the influences of secondary effects like porosity and second phases on grain growth in nature, and to unravel differences between nature and experiment.Editorial responsibility: J. Hoefs     

The high-pressure and temperature equation of state of a majorite solid solution in the system of Mg4Si4O12-Mg3Al2Si3O12

The high-pressure and temperature equation of state of majorite solid solution, Mj_0.8Py_0.2, was determined up to 23 GPa and 773 K with energy-dispersive synchrotron X-ray diffraction at high pressure and high temperature using the single- and double-stage configurations of the multianvil apparatuses, MAX80 and 90. The X-ray diffraction data of the majorite sample were analyzed using the WPPD (whole-powder-pattern decomposition) method to obtain the lattice parameters. A least-squares fitting using the third-order Birch-Murnaghan equation of state yields the isothermal bulk modulus, K _T0  = 156 GPa, its pressure derivative, K′ = 4.4(±0.3), and temperature derivative (∂K _T /∂T) _P = −1.9(±0.3)× 10⁻² GPa/K, assuming that the thermal expansion coefficient is similar to that of pyrope-almandine solid solution. Received: 5 October 1998 / Revised, accepted: 24 June 1999     

Syndeformational recrystallization – dynamic or compositionally induced?

Dynamic recrystallization in the strict sense of the term is the reconstitution of crystalline material without a change in chemical composition, driven by strain energy in the form of dislocations. Driving potentials additional to internal strain energy may contribute to the recrystallization of naturally deformed minerals, which form solid solutions such as feldspar, amphiboles and pyroxenes, if they change their composition during recrystallization. To estimate the relative importance of these driving potentials, the chemical composition of porphyroclasts and recrystallized grains of plagioclase, clinopyroxene and hornblende have been investigated in samples from a high grade shear zone of the Ivrea Zone, Italy. The plagioclases show two different recrystallization microstructures: bulging recrystallization at grain boundaries and discrete zones of recrystallized grains across porphyroclasts probably involving fracturing. Deformation took place under amphibolite facies conditions on a retrograde P,T-path. Porphyroclast and recrystallized compositions from bulging recrystallization microstructures differ only in their Or-content and yield a ΔG between mean host grain and mean recrystallized grain composition at fixed P,T-conditions of approximately 5 Joules/10⁻⁴ m³. Extreme compositional variations yield approximately 60 J/10⁻⁴m³. The increase of free energy due to dislocations calculated for common glide systems in plagioclase are on the order of 100 Joules/10⁻⁴m³ for high values of dislocation densities of 10¹⁴m⁻². Thus, the effect of chemically induced driving energies on grain boundary velocity appears small for mean compositions but may be as great as that of deformational energies for larger chemical differences. In the other type of microstructure, porphyroclasts and recrystallized grains in discrete zones differ in their anorthite content. The maximum ΔG induced by the compositional disequilibrium is on the order of 100 J/10⁻⁴m³. This maximum value is of the same magnitude as the ΔG derived from high dislocation densities of 10¹⁴ m⁻². The resulting combined ΔG is approximately twice as high as for deformational ΔG alone, and heterogeneous nucleation may become a feasible recrystallization mechanism which is evident from the microstructures. The recrystallization mechanism depends on the nature of the driving potential. Grain boundary migration (GBM) and heterogeneous nucleation can release Gibbs free energy induced by compositional disequilibrium, whereas this is not likely for subgrain rotation. Therefore, only GBM and heterogeneous nucleation may link metamorphism and deformation, so that syndeformational recrystallization may represent a transitional process ranging from dynamic recrystallization to metamorphic reaction. Received: 8 July 1996 / Accepted: 17 November 1997