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Silicon bulk diffusion rates were determined in a fine-grained (1.2 μm diameter) natural quartz aggregate (novaculite) from Hot Springs, AR. The diffusion experiments were done at 600–800°C and 150 MPa confining pressure (hydrothermal) and at 800–1100°C and 1 atm (in a stream of dry N2). The technique employed an isotopic tracer (30Si) and standard step-scan analysis using an ion microprobe (SIMS). The temperature dependence of silicon bulk diffusion in the novaculite is described by the Arrhenius parameters: D0, bulk=3.7×10−10 m2/s and Q=137 ±18 kJ/mol, and D0, bulk=6.2×10−9 m2/s and Q=178 ±38 kJ/mol for the hydrothermal and dry experiments, respectively. At 800°C, the silicon bulk diffusion rate at 150 MPa, hydrothermal is about a factor of 10 greater than at 1 atm, dry. For an assumed effective grain boundary width of 2 nm, the silicon grain boundary diffusion rates in novaculite are a factor of two to three less than oxygen diffusion rates for similar hydrothermal conditions, and more than 12 orders of magnitude greater than anhydrous silicon volume diffusion rates extrapolated to the temperature of these experiments. The results of this study provide valuable constraints on the role of diffusion-accommodated deformation in quartz-rich rocks.

Silicon diffusion rates were determined in fine-grained (∼4.5 µm) hot-pressed forsterite aggregates at 900° to 1200°C and 0.1 MPa using a 30Si-tracer and standard SIMS analysis. There is no measurable difference in diffusion rates between samples buffered by excess MgO or SiO2, nor samples run in dry N2 or H2/CO2. The results yield the Arrhenius parameters D0, bulk = 5.4 × 10−9 m²/sec and Q = 203±36 kJ/mol. At 1200°C, the grain boundary diffusion rate of 30Si is similar to 26Mg (Si ∼10 times greater), ∼10² less than Fe, and ∼105 less than O. In addition, the 30Si grain boundary diffusion rate is ∼109 greater than the Si volume diffusion rate and indicates that diffusional transport of Si in forsterite aggregates is dominated by grain boundaries.

Oxygen grain boundary diffusion rates were experimentally determined in natural (Solnhofen limestone) and hot-pressed calcite aggregates at 300 to 500°C and 100 MPa water pressure. The Solnhofen limestone was 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. The synthetic calcite aggregates were formed by hot isostatic pressing of an intimate mixture of 1–2 μm calcite grains plus 5 wt% 0.3 μm alumina grains at 700°C and 200 MPa for 3–10 days. Values for the product of the grain boundary diffusion coefficient ( D ′) and the effective grain boundary diffusion width ( δ ) were determined from 18 O concentration profiles measured with an ion microprobe. There is no measurable difference between D ′ δ values obtained for pre-annealed Solnhofen samples and hot-pressed calcite aggregates; the temperature dependence for oxygen grain boundary diffusion at 100 MPa is described by the Arrhenius parameters D 0 ′ δ =3.8×10 −14 m 3 /s and Q =127±17 kJ/mol. Comparison of the results of this study with previously published data show that the rate of oxygen grain boundary diffusion in calcite aggregates is four to five orders of magnitude greater than that of volume diffusion in calcite single crystals, and the activation energy is less. Grain boundary diffusion of oxygen in calcite aggregates is five to six orders of magnitude greater than that of calcium, when the latter is extrapolated to the temperature range of this study. In addition, oxygen grain boundary diffusion rates in calcite aggregates are about a factor of 4–10 and ∼100 times greater than that in feldspar and quartz aggregates, respectively, under similar experimental conditions.

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.

The growth rates of enstatite rims produced by reaction of Fo92 and SiO2 were determined at 250–1500 MPa and 900–1100°C for a wide range of water contents. Growth rates were also determined for forsterite rims between MgO and Mg2Si2O6 and between MgO and SiO2. Rim growth rates are parabolic indicating diffusion-controlled growth of the polycrystalline rims which are composed of ˜ 2 μm diameter grains. Rim growth rates were used to calculate the product of the grain boundary diffusion coefficient (D'A) times the effective grain boundary thickness (δ) assuming in turn that MgO, SiO2, and Mg2Si−1 are the diffusing components (coupled diffusion of a cation and oxygen or interdiffusion of Mg and Si). The values for D'MgOδ, D' , and D' for enstatite at 1000°C and 700 MPa confining pressure with about 0.1 wt % water are about five times larger than the corresponding D'Aδ values for samples initially vacuum dried at 250°C. Most of the increase in D'Aδ occurs with the first 0.1 wt % water. The activation energy for diffusion through the enstatite rims (1100–950°C) is 162 ± 30 kJ/mole. The diffusion rate through enstatite rims is essentially unchanged for confining pressures from 210–1400 MPa, but the nucleation rate is greatly reduced at low confining pressure (for ≤ 1.0 wt % water present) and limits the conditions at which rim growth can be measured. The corresponding values for D'Aδ through forsterite rims are essentially identical for the two forsterite-producing reactions when 0.1 wt % water is added and similar to the D'Aδ values for enstatite at the same conditions. The D'Aδ values for forsterite are ˜ 28 times larger for samples starting with 0.1 wt % water compared to samples that were first vacuum dried. Thus water enhances these grain boundary diffusion rates by a factor of 5–30 depending on the mineralogy, but the total range in D'Aδ is only slightly more than an order of magnitude for as wide a range of water contents as expected for most crustal conditions.

Hydrogen defects in adularia from Kristallina, Switzerland (Or90.2 Ab8.7 An0.0 Cs1.1) have been investigated by examining their vibrational modes in the infrared and near-infrared, and by measuring rates of hydrogen loss and hydrogen gain at elevated temperatures. Principal absorption bands exhibited by adularia at wavenumbers of 362 and 345.5 mm^(−1) (corresponding to O-H stretching modes) are strongly dichroic, with maximum and minimum absorptivities measured for vibrations α (E at 5° to a) and β (E at 5° to c^∗), respectively, whereas bands at 328 and 309 mm^(−1) are more nearly isotropic. Similarly, near-infrared bands at 525 and 513 mm^(−1) (associated with combination H-OH bend, O-H stretch modes) exhibit maximum peak heights for α while a lesser band at 475 mm^(−1) appears to be nearly isotropic. Comparison of fundamental and combination band intensities reveal that molecular water is the predominant hydrogen-bearing species, consistent with previous results for microcline and orthoclase crystals in which H_2O substitutes for K. However, differences in magnitude of fundamental and combination band polarizations suggest multiple defect sites or potentially a secondary population of hydroxyl defects. Rates at which these defects can be eliminated from samples annealed in air at temperatures T from 500° to 900°C are much faster than those predicted by oxygen mobilities, yielding diffusivities of D[/_s]=6.2x10^(-4)exp ( -l72 ± 15[^(kJ)/mol))/RT indistinguishable from those reported for proton interstitials in quartz. Dissociation of stationary molecular water defects to mobile proton interstitials which leave crystal interiors requires that oxygen defects are left behind. Hydrogen defects can be added to adularia crystals annealed at elevated water pressures (corresponding to H_2O fugacities of 412 and 1710 MPa and H_2 fugacities up to 174 MPa), again at rates that exceed oxygen mobilities. In addition, significant redistribution amongst sites is suggested by changes in band character and polarization. Neither Fe nor other multivalent impurities are sufficiently abundant to accommodate local charge balance upon the loss or gain of protons and other mechanisms of internal adjustment are required.

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.

Interphase boundary diffusion rates of oxygen and potassium in fine-grained K-feldspar/ quartz aggregates were determined experimentally at 450–700°C and 100 MPa (hydrothermal). The starting materials were hot-pressed and crystallized using equal weights of natural quartz fragments and orthoclase (KAlSi 3 O 8 ) composition glass. The technique employed isotopic tracers ( 18 O, 41 K) in an aqueous solution surrounding the sample, and depth profiling using an ion microprobe (SIMS). From the depth profiles, the product of the average boundary diffusion coefficient ( D ′) and average effective boundary width (δ) was calculated using numerical solutions to the appropriate diffusion equation. Potassium and oxygen profiles measured in the same samples are different, confirming a diffusional transport mechanism. Potassium diffusion in the K-feldspar/quartz aggregate has a greater activation energy than oxygen (218 vs. 75 kJ/mol), and the Arrhenius relations cross at ∼600°C. The D ′ δ values in the K-feldspar/quartz aggregates are about a factor of four greater than both oxygen and potassium D ′ δ values previously determined in monomineralic K-feldspar aggregates, and a factor of 20–40 greater than oxygen D ′ δ values in monomineralic quartz aggregates. The Arrhenius relations show the activation energies for both oxygen and potassium are similar for the K-feldspar/quartz and monomineralic K-feldspar aggregates, and significantly lower for oxygen in K-feldspar/quartz versus monomineralic quartz aggregates.

Eshelby's theory is used to calculate the elastic strain energy associated with coherent homogeneous nucleation for the olivine-spinel transformation. Incorporating the elastic strain energy, the activation energy, ΔG ∗ , for homogeneous nucleation is estimated using a quasi-Newton's method, a finite-difference gradient, and assuming an orientation-independent interfacial energy. For the limiting case of coherent, homogeneous nucleation and interface-controlled growth, the overall transformation rate along a relatively cold subducting slab (approximately 500°C at 400 km depth) is calculated for various nucleation rates (theoretical) and previously published growth rates (experimental). The result indicates that the transformation rate assuming coherent, homogeneous nucleation and interface-controlled growth may be comparable with that for grain boundary nucleation and interface-controlled growth in a relatively cold subducting slab. The large transformation strain energy and stresses can be greatly relaxed by plastic deformation of the olivine matrix. In a cold subducting slab, the deformation of olivine around a growing spinel grain or cluster of grains probably proceeds by the mechanism of low-temperature plasticity (dislocation glide). Under the influence of externally applied differential stresses, the interaction between the residual stresses around individual spinel inclusions may cause the formation of a through-going fault and initiate deep-focus earthquakes.

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

Magnesium grain boundary diffusion rates in forsterite aggregates have been experimentally determined from 1000° to 1300°C and 0.1 MPa to 10 GPa. The samples are fine-grained (mean linear intercept of 4.3 μm) hot-pressed aggregates. The technique employs a 26Mg-enriched surface layer and depth profiling using an ion microprobe. Values of the product of the grain boundary diffusion coefficient (D′) and the effective grain boundary width (δ) were calculated using appropriate analytical solutions to the grain boundary diffusion equation of Whipple (1954). The Arrhenius parameters for the 0.1 MPa data for samples annealed in H2 + CO2 and CO + CO2 gas mixtures are D0′δ = 2.1 × 10−10 and 7.7 × 10−10 m3/s and Q = 343 ± 27 and 376 ± 47 kJ/mol, respectively. The reproducibility of D′δ measurements is a factor of 2. A determination of D′ independent of δ yields a calculated effective grain boundary width of ∼3 nm, similar to the physical grain boundary width of 1–3 nm estimated from high-resolution transmission electron microscopy observations. The data indicate a very low pressure dependence for magnesium grain boundary diffusion in forsterite with an apparent activation volume for grain boundary diffusion of ≤∼1 cm3/mol at 1100°C. The results of this study provide information concerning diffusion creep in solid state deformation of forsterite aggregates over a broad range of pressures and temperatures.

Experimental data are used to model the transformation rate of polycrystalline aragonite (grain diameter ∼80 μm) to calcite. Optimized values for nucleation and growth rates were obtained by numerically fitting the overall transformation rates from 280° to 380°C and 0.10 MPa to an expression for a grain-boundary-nucleated and interface-controlled transformation. The nucleation rate is ∼4–5 orders of magnitude faster than for calcite nucleated within aragonite grains, and the growing in rate is slower below 300°C than for calcite growing in aragonite single crystals. The activation enthalpy for growth in polycrystalline aggregate is ∼247kJ/mol compared to 163 kJ/mol for growth in single crystals. Permanent deformation of the phases limits the elastic strain energy due to the ∼7% volume change and reduces the coherency of the calcite/aragonite interace. Theoretical expressions are used to extrapolate the data for nucleation and growth to other temperatures, and data from 0.10 to 400 MPa are used to evaluate the effect of pressure on the grain-boundary nucleation rate. Because of permanent deformation of the phases, the effective strain energy for nucleation is ≤0.55 kJ/mol, which is less than a quarter of the value for purely elastic deformation. These data are used to predict the percent transformation for various P-T-t paths; without heating during uplift partial preservation of aragonite in dry blueschist facies rocks can occur if the calcite stability field is entered at ∼235° C, and the kinetic data are also consistent with published P-T-t paths which include heating during uplift. The predicted percent transformation is relatively insensitive to variations in the initial grain size of the aragonite, but strongly dependent on the effective strain energy.

The rate of compositional and isotopic exchange between minerals may be enhanced significantly if the rock is deformed simultaneously. The enhanced exchange rate may result from a reduction in grain size (shorter distance for volume diffusion), dissolution and growth of grains by diffusion creep (pressure solution), or the movement of high-angle grain boundaries through strained grains during recrystallization in the dislocation creep regime. The migration of high-angle grain boundaries provides high diffusivity paths for the rapid exchange of components during recrystallization. The operation of the latter process has been demonstrated by deforming aggregates consisting of two plagioclases (An1 and An79) at 900°C, 1 GPa confining pressure, and a strain rate of ∼2x10-6s-1. The polygonal, recrystallized grains were analyzed using an analytical transmission electron microscope and have a variable but often intermediate composition. At the conditions of these experiments, the volume interdiffusion rate of NaSi/CaAl is too slow to produce any observable chemical change, and microstructural-chemical relations indicate that the contribution from diffusion creep was insignificant except for initially fine-grained (2–10 μm) aggregates. These results indicate that strain-induced recrystallization can be an effective mechanism for enhancing the kinetics of metamorphic reactions and for resetting the isotope systematics of minerals such as feldspars, pyroxenes, and amphiboles.

Grain boundary diffusion measurements using fine-grained, natural, monomineralic aggregates offer several distinct advantages over techniques previously employed. Pure quartz aggregates (Arkansas novaculite), with 1.2 and 4.9 μm diameter grains, were annealed at 450–800°C and 100 MPa confining pressure in 18O-enriched water. Profiles of 18O(18O + 16O) with depth from the surface were measured using an ion microprobe, and data were collected from an area 68 μm in diameter in order to obtain a well-averaged value for many grain boundaries. Using graphical solutions appropriate to the boundary conditions employed, the product of the average grain boundary diffusion coefficient (D′) and effective boundary width (δ) is obtained and is independent of the grain size, geometry, and grain boundary tortuosity. Arrhenius parameters for the 1.2 and 4.9 μm grain size samples are: D′0δ = 2.6 and 3.4 × 10−17 m3/sec, and Q = 27 ± 1 and 26 ± 3 kcal/mol, respectively. Measured values of D′δ were about three times greater for the 4.9 μm aggregate, although this might be due in part to thermal cracking while going to temperature. The activation energy of both samples, ~ 27 kcal/mol ( 113 kJ/mol), is significantly less than that for volume diffusion of oxygen in quartz, but greater than that for ionic diffusion in a static fluid. Measured D′δ values are within the range of most previous estimates. For a representative effective grain boundary width of 1 nm, the oxygen grain boundary diffusion coefficients are 4 to 6 orders of magnitude greater than oxygen volume diffusion coefficients in quartz single crystals, and ~6 orders of magnitude less than ionic diffusion coefficients in a static fluid, over the temperature range of the experiments.

Oxygen self-diffusion coefficients (D) were determined in single crystals of Brazilian quartz by measuring 18O concentration profiles with an ion microprobe. In the α-quartz field at 450–590°C and 100-MPa confining pressure, for diffusion parallel to c, the Arrhenius relation is described by the parameters D0 = 2.9 · 10−5 m2 s−1 and Q = 243 ± 17 kJ (g-at. O)−1. The diffusion rate was also measured in β-quartz from 5- to 350-MPa confining pressure and at 700°C as a function of water, hydrogen and oxygen fugacities as well as for different proton activities. There is a good correlation of D with water fugacity, no correlation with oxygen nor hydrogen fugacities, and no correlation with proton activity over the range for which this parameter could be fixed independent of the water fugacity, The available evidence suggests that the oxygen-bearing species responsible for the rapid transport of oxygen under hydrothermal conditions is molecular water. The rate controlling step for oxygen diffusion may be either the rate of migration of water molecules, or the rate of oxygen exchange between the water molecules and the quartz structure.

A combination of mechanical and microstructural results for experimentally deformed albite aggregates of 2–10 μm grain size indicates a regime of grain boundary diffusion creep that depends upon the presence of water, temperature and strain rate. At 900°C and 10−5 s−1, deformation occurs dominantly by recrystallization accommodated dislocation creep when the aggregates contain < ≈0.2 wt% water, but by grain boundary diffusion creep when the aggregates contain ≈0.9 wt% water. Experiments at other temperatures and strain rates indicate that fine-grained aggregates with added water may go directly from cataclastic flow to grain boundary diffusion creep with increasing temperature or decreasing strain rate, bypassing the field of dislocation creep. Microstructural evidence for grain boundary diffusion creep in the wet fine-grained aggregates includes the development of rectangular grains rather than polygonal grains; grain growth; a very low average dislocation density; open grain boundaries including pores and channels; and the presence of overgrowths of a different composition on grains in a two-plagioclase (An1 and An79) aggregate. Additional evidence for diffusion creep in the wet fine-grained aggregates is indicated by their similar microstructures and strengths when deformed at 600 and 1500 MPa; in contrast, dry feldspar aggregates deforming by dislocation creep show an increase in strength and a transition to semi-brittle behavior at lower confining pressures. Grain boundary diffusion creep of feldspars may be common in naturally deformed rocks, due to the ease of grain size reduction by both cataclasis and dynamic recrystallization.

Oxygen self-diffusion in adularia and albite single crystals was studied hydrothermally at 650°C from 5 to 1500 MPa confining pressure using a combination of hydrogen/oxygen buffers, a hydrogen ion buffer, and variable mole fractions of water (dilution with CO2). Diffusion coefficients (D) were determined from 18O concentration profiles measured with an ion microprobe. There is a good correlation of the D values with water fugacity but not with oxygen fugacity, hydrogen fugacity, hydrogen ion concentration, nor confining pressure over the range for which these parameters could be fixed independent of the water fugacity. Oxygen diffusion must involve the transport of an oxygen-bearing species, and the results of this study suggest that the transport species is molecular water. The rate-limiting step for oxygen diffusion could be either the rate of migration of the molecular water in the crystal or the rate of exchange of its oxygen with the feldspar structure. While protons may play a role in the mechanism of oxygen diffusion in feldspar, above the concentration supplied by pure water additional protons have no measurable effect on diffusion rates.

In order to determine the effect of crystal dislocations on quartz dissolution rates, the dissolution rates of i) synthetic quartz with a dislocation density of

High temperature oxide melt solution calorimetry was used to study the energy associated with dislocations in quartz by comparing undeformed and deformed single crystals of synthetic quartz. Samples were deformed at 698 K, 1000–1500 MPa at a strain rate of 10−5 sec−1. Two sets of calorimetric measurements were made: (i) using a Pt capsule as a container for powdered sample, and (ii) using pellets made from sample powder without any container. For the first set of measurements, the undeformed sample with a dislocation density of enthalpy is sum of heat content H 973-H 295 and enthalpy of solution in molten lead borate at 973 K of 39.22 ± 1.00 kJ mol−1, while the sample deformed in the dislocation creep regime with a dislocation density of 6 × 1010 to 1 × 1011 cm−2 gave an enthalpy of 38.59 ± 0.78 kJ mol−1. For the second set of measurements the measured enthalpy of the undeformed sample was 38.87 ± 0.31 kJ mol−1, and that of a deformed sample with a dislocation density of 3 × 1010 to 1 × 1011 cm−2 was 38.24 ± 0.58 kJ mol−1. The present study and previous theoretical calculations and estimates are consistent and suggest that the energy associated with dislocations in quartz is ∼ 0.6 ± 0.6 kJ mol−1 for a dislocation density of ∼ 1011 cm−2; a precise value is difficult to determine because of the overlapping errors. These results indicate that for geologically realistic dislocation densities, the maximum excess energy due to dislocations would be ∼ 0.5 kJ mol−1 for most minerals; the exact value would depend on the Burgers vector as well as the shear modulus.

We present new experimental data on Mg tracer diffusion in oriented single crystals of forsterite (Fo100) and San Carlos olivine (Fo92) between 1000–1300° C. The activation energies of diffusion are found to be 400 (±60) kJ/mol (≈96 kcal/mol) and 275 (±25) kJ/mol (≈65 kcal/ mol) in forsterite and San Carlos olivine, respectively, along [001] at a fO2 of 10−12 bars. There is no change in activation energy of Mg tracer diffusion within this temperature range. Mg tracer diffusion in a nominally pure forsterite is found to be anisotropic (D∥c > D∥a > D ∥b) and a function of fO2. This fO2 dependence is different from that in olivine containing Fe as a major element, which suggests that the diffusion mechanism of Mg in forsterite is different from that in Fe-bearing olivine at least over some range of fO2. The diffusion mechanism in nominally pure forsterites may involve impurities present below the limits of detection or alternately, Si or Fe3+ interstitial defects, Fe being present as impurity (ppm level) in forsterite. Pressure dependence of Mg tracer diffusivity in forsterite measured to 10 GPa in a multianvil apparatus yields an activation volume of approximately 1–3.5 cm3/ mol. It is found that presence of small amounts of hydrogen bearing species in the atmosphere during diffusion anneal (fH2 ≈ 0.2 bars, fH20 ≈ 0.24 bars) do not affect Mg tracer diffusion in forsterite within the resolution of our measurement at a total pressure of 1 bar. The observed diffusion process is shown to be extrinsic; hence extrapolation of the diffusion data to lower temperatures should not be plagued by uncertainties related to change of diffusion mechanism from intrinsic to extrinsic.

Oxygen grain boundary and bulk diffusion rates have been measured in a 1.2-μm grain diameter quartz aggregate (Arkansas novaculite) preannealed in wetting and nonwetting fluids to determine the effect of microstructure. Samples were preannealed at 800°C and 150 MPa confining pressure for 6 to 12 days with pure water, pure CO2, or water + NaCl (∼6 M) to produce equilibrium microstructures. The samples were then annealed at 450° to 800°C and 100 MPa confining pressure with 98% 18O-enriched water to determine the diffusion rates. Profiles of 18O/(18O+16O) with depth from the surface were measured using an ion microprobe, and the product of the grain boundary diffusion coefficient (D′) and effective boundary width (δ) or the bulk diffusion coefficient (Dbulk) determined. Compared to the starting material, the D′δ values for samples texturally equilibrated with pure CO2 (nonwetted microstructure) and pure water are about the same and about 4 times greater, respectively. Bulk diffusivities in samples preannealed with 6 M NaCl (wetted microstructure) are 4 to 5 orders of magnitude greater than the bulk diffusivities in samples preannealed with pure CO2 (nonwetted). In addition, the D'δ value for a sample texturally equilibrated first with 6 M NaCl and then with pure CO2 is about a factor of 3 greater than the value for the starting material, demonstrating that the textural equilibration process is essentially reversible. The results of this study indicate that transport rates are strongly influenced by the wetting characteristics of coexisting fluids in a polycrystalline aggregate. In nonwetted samples, changes in the effective grain boundary width or the formation of small isolated pores at triple junctions can change D′δ values. However, these effects are minor compared to the change in transport rate for samples with nonwetted versus wetted microstructures. The much faster rates for samples with a wetted microstructure are believed to be due to oxygen transport along the interconnected channels by ionic diffusion in a static fluid. The bulk diffusivities obtained for samples with a wetted microstructure are consistent with previously determined values for oxygen exchange at an igneous intrusive contact.

There is no significant difference in the diffusion profiles across albite-adularia bicrystals that were simultaneously deformed at a strain rate of 10-6S-1 and those from hydrostatic experiments at the same conditions (1500 MPa and 1000°C for 156 h). This indicates that the bulk alkali diffusion rate, which is the sum of lattice diffusion (D, 1) and dislocation pipe diffusion (Dp), is not significantly enhanced by dislocations at these conditions, and that the maximum value for the ratio of Dp/D1 is about 105. This is equal to the value previously reported for‘oxygen’diffusion in albite. If this ratio is independent of temperature, the contribution of either static (pre-deformed) or moving (syn-deformed) dislocations to the bulk diffusion rate of alkalis is probably minor at all metamorphic conditions. For Al and Si diffusion the ratio of Dp/D1 may be larger if D1 is lower. Thus a significant contribution from dislocations to bulk diffusion cannot be ruled out, especially during simultaneous deformation.

Diffusional oxygen exchange between quartz and water was studied by determining 18O profiles in the quartz using an ion microprobe. Inverse error function plots of the data are linear as required for a diffusion mechanism. One natural and two synthetic samples were used, and although they had different impurity concentrations (OH−, Na, and Al per 106 Si atoms are 7–4000, 35–835, and 67–127, respectively), the D values were the same within experimental uncertainty. Diffusion parallel to c is about 2 orders of magnitude faster than that normal to c at 700°C, and diffusion normal to the rhombohedron is intermediate. The data indicate a change in slope on an Arrhenius plot at the α-β boundary. At 100-MPa (1 kbar) water pressure the preexponential factors (Do, in square centimeters per second) and activation energies (Q, in Kilojoules per mole) for α quartz (500°–550°C) are as follows: Do = 190 and Q = 284 parallel to c, and Do = 8 × 10−2 and Q = 238 normal to the rhombohedron. For β quartz (600°–800°C), Do = 4 × 10−7 and Q = 142 parallel to c, Do = 9 × 10−7 and Q = 155 normal to the rhombohedron; and Do = 1 × 10−4 and Q = 234 normal to c. D increases with PH 2 O, and between 25 and 350 MPa log D versus logƒH 2 O has a slope of approximately 1.1. These D values are all several orders of magnitude larger than previously reported values for oxygen diffusion in water-free systems.

Grain growth rates for novaculite, flint and jasper have been determined between 1000° and 800°C and 15 to 2 kb water pressure. A pre-treatment established an equilibrium microstructure and a nearly uniform mean grain diameter ($\bar{D}_{0}$). At 1000°C and 15 kb the grain growth data are linear on a log ($\bar{D}-\bar{D}_{0}$) vs. log time plot, and there is no significant difference between the three samples although the jasper contained 5-10 vol % iron oxide. At lower pressures and temperatures the growth curves are approximately parallel to the 1000°C and 15 kb data, but growth is slower and that for jasper is slower than for the other two. The growth rate is strongly dependent on the solubility of quartz in the intergranular fluid, and the activation energy is about 11 kcal/mole. The data are used to estimate the growth rate of quartz at metamorphic conditions and to help evaluate the conditions where growth of dynamically recrystallized grains may be significant. The growth rate of calcite grains (S...

Oxygen diffusion in albite has been determined by the integrating (bulk 18O) method between 750° and 450° C, for a P H2O of 2 kb. The original material has a low dislocation density (

In order to determine the effect of water on deformation in the brittle-ductile transition region of crustal rocks, experiments have been conducted on Westerly granite and a polycrystalline albite rock, comparing samples dried at 160°C for 12 h (‘dry’) and samples with about 0.2 wt% water added (‘wet’). The deformation mechanisms and style of deformation of the wet and dry samples, determined using optical and transmission electron microscopy, have been found to depend on temperature, pressure, strain rate, and strain. At 15 kb and 10−6, the added water reduces the temperature of the transition between microcracking and dislocation glide and climb by about 150–200°C for both quartz and feldspar. However, the penetration of ‘water’ into the grains is slow compared with the time of the experiments and many of the wet samples show evidence of initial microcracking and later dislocation creep. Wet samples deformed at 10 kb show less hydrolytic weakening than wet samples deformed at 15 kb. Because the deformation mechanism and strength of silicates depend so sensitively on trace amounts of water, and because the water content of experimental samples varies with temperature and pressure and thus with time, flow laws for any samples are only meaningful if the water content has been carefully controlled or characterized.

The disordering kinetics of Al/Si in albite depend on how the samples are dried, and thus on the presence of trace amounts of water. The disordering rate increases with water content and confining pressure. At 10 kb the activation energy is about 67 kcal/mole compared to about 87 kcal/mole for samples disordered in air. Simultaneous plastic deformation increases the disordering rate and the effect is most pronounced below 900° C at 10−6/s. Some albite ordering and microcline disordering experiments show similar kinetic behavior. These results are significant for interpreting the structural state and the high-temperature deformation of feldspars.

Self-diffusion of oxygen in adularia, anorthite, albite, oligoclase and labradorite has been measured by isotope exchange of oxygen between natural feldspars and hydrothermal water enriched in 18 O. The analysis consisted of measuring the 18 O/ 16 O gradient inward from the feldspar surface using an ion microprobe, and fitting a solution of the diffusion equation to the data. Depth of the sputtered hole was measured with an optical interferometer. Linear Arrhenius plots were obtained: d 0 ( cm 2 /sec ) Q ( kcal/g-atom O ) T(°C) Adularia (Or 98 ) 4.51 × 10 −8 25.6 350–700 Albite (Ab 97 , Ab 99 ) 2.31 × 10 −9 21.3 350–800 Anorthite (An 96 ) 1.39 × 10 −7 26.2 350–800 The results for two intermediate plagioclases (Ab 82.5 and Ab 35.7 ) between 550 and 800°C are similar to these, and hence all the feldspars have very similar oxygen exchange behavior. Diffusion coefficients for albite at 800°C measured normal to the (001), (010), ( 1 11), and (130) faces are the same within a factor of four. Owing to the low activation energy, there is no single “closure temperature” for exchange of oxygen. The feldspars are susceptible to diffusional exchange of oxygen in geological settings to comparatively low temperatures.

The diffusion rates of carbon and oxygen in two calcite crystals of different Mn contents have been studied between 500° and 800° C in a CO2-H2O atmosphere (PCO2=1−5 bars, PH2O=0.02−24 bars) labeled with 13C and 18O. Isotope concentration gradients within annealed specimens were measured using a secondary ion microprobe by depth profiling parallel and perpendicular to the c axis. Despite the anisotropic structure of calcite, the diffusion of carbon and oxygen are both very nearly isotropic. Least-squares fitting of the carbon data to an Arrhenius relation gives an activation energy of 87±2 kcal/mole, with D0 terms dependent only slightly upon direction: $$D_{\text{0}} {\text{(}}\parallel c{\text{) = }}\left( {9\frac{{ + 12}}{{ - 5}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ (1) , $$D_{\text{0}} {\text{(}} \bot c{\text{) = }}\left( {5\frac{{ + 6}}{{ - 3}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ (2) . These results are in close agreement with previous determinations. Results for oxygen diffusion, however, give D values much larger than those previously reported for dry conditions; at 650° to 800° C the D values are two orders of magnitude larger. The diffusion of oxygen, unlike carbon, is strongly dependent on water pressure, as well as Mn content, and does not fit an Arrhenius relation over the entire temperature range. On the basis of these observations and considerations of the defect chemistry of calcite, it is proposed that carbon migrates as a Frenkel pair. The diffusion of oxygen, however, appears to be more complicated and may depend upon several simultaneous mechanisms.

The rate of oxygen isotope exchange between adularia and 2 M KCl solution has been measured at 650°C at pressures from 125 to 4000 bar. Isotropie diffusion coefficients calculated from these data show a positive dependence on the fluid pressure. This dependence is opposite to the predicted effect of hydrostatic pressure and is attributed to the activity of ‘water’ (H2O, H+ or OH−) in the feldspar.

The ‘average’ interdiffusion coefficient ( $$\bar D$$ ) for NaSi—CaAl exchange in plagioclase for the interval from An0 to An26 was estimated from experimentally determined homogenization times for peristerite exsolution lamellae. The average spacing between adjacent (unlike) lamellae is 554±77 A. Dry heating in air at 1,100°C for 98 days produced no change in the exsolution microstructure; thus $$\bar D$$ (dry)

The Storm King granite at Bear Mountain, New York contains coarse alkali feldspar mesoperthite. The microstructure of these perthites grades continuously from lamellae to isolated blebs. The K rich phase in all samples has a nerely constant composition (Or97Ab3), but the Na-rich phase ranges from An3.8 (lamellae) to An21 (blebs). It is suggested that the more calcium-rich feldspars exsolved at a higher temperature and thus experienced a longer time at higher temperature, during which the microstructure became more bleby or spherical in response to minimization of the interfacial energy. Lack of perfect correlation of the microstructure with bulk composition, as well as variation in the Al/Si ordering, may be due to additional factors, of which water activity or concentration is the most likely.

The deformation behavior of quartz and feldspar has been studied in Westerly granite deformed dry at a constant strain rate of 10−6/s, confining pressures of 1.5–15 kbar, and temperatures of 25°–1000°C. Samples deformed at lower temperatures and pressures show throughgoing faults; those deformed at intermediate conditions show a combination of grain-scale faults and plastic deformation; and those deformed at higher temperatures and pressures show plastic deformation with no faults of any scale. On a grain scale the deformation is inhomogeneous at all conditions because of the polyphase nature of the material. Detailed petrographic and transmission electron microscope (TEM) observations have been made of the deformed specimens. The fault gouge consists of very fine grained material which verges on being amorphous, but no evidence of melt was seen. In the regions away from fault zones, there is a transition from dominantly microcracking to dominantly dislocation glide and climb; this transition is primarily a function of temperature. Dislocation motion is thermally activated and is probably almost unaffected by pressure over the range investigated. Thus at low temperature the strain rate that can be produced by dislocation motion is limited, and the difference between this and the imposed strain rate must occur by microcracking. The way in which the microcracking accomplishes the deformation depends on pressure. At low pressures (

Sintered aggregates composed of quartz, albite, and microcline of two different grain sizes (2–10 and 10–50 μm), each with two different melt contents (

Average values for NaSi-CaAl interdiffusion in the compositional interval from An0 to An26 have been determined at 1000°C by the method of lamellar homogenization. At 1500 MPa confining pressure (P), increases 1 order of magnitude (5.0×10−21 to 4.0×10−20 m2/s) for 4 orders of magnitude increase in hydrogen fugacity (0.029, Mn3O4-Mn2O3 buffer, to 197 MPa, FeO-Fe3O4 buffer). At constant hydrogen fugacity (fH2), increases rapidly at low pressure and becomes nearly independent of P above 1000 MPa. (For fH2 = 0.1 MPa, = 2.8 × 10−22 m2/s at P = 0.1 MPa, 5.0 × 10−21 at P = 500, 1.3×10−20 at P = 1000, and 1.4×10−20 at P = 1500). The dependence of on increasing pressure, when a hydrogen-related species is present, is believed to be due to an increase in the concentration of the structural defect associated with increase in the hydrogen impurity. In most crustal igneous rocks, which are internally buffered near quartz-fayalite-magnetite, the dependence of on fH2 is relatively minor compared to the effect of confining pressure.

In order to test the effect of ‘water‧ at high pressure on the rate of dislocation climb in quartz, we have performed annealing experiments on portions of a quartzite sample previously deformed at 700°C, 10−5 sec−1, and 1500 MPa which had a high dislocation density but few subgrain boundaries. Portions of the deformed sample were annealed at 1500 MPa and 800°C for 1 and 4 days; samples with 0.17 wt % water added have a lower average dislocation density and a greater number of subgrain boundaries than those without water added. Annealing at 800°C for 4 days at 1500 MPa after vacuum drying at 800°C, or at 550 MPa with 0.17 wt % water added, produces no significant change in the dislocation microstructure. These results indicate that: (1) the presence of a water-related defect in quartz accomplishes hydrolytic weakening by making the climb of dislocations easier, thus increasing the rate of recovery at a given imposed strain rate, and (2) for laboratory times this weakening requires a pressure >550 MPa.

The miscibility gap between FeS (troilite) and Fe1−xS (pyrrhotite) below 140°C has been confirmed. Troilite is restricted to essentially stoichiometric FeS, and the composition of pyrrhotite in equilibrium with troilite can be expressed by the relation ln ( C − 48.00) = 9.4±0.4 −(3.6±0.2 × 10 3 ) T , where C is the composition of pyrrhotite in atomic percent iron and T is ok.

A maximum microline-low albite of 33 mole percent Or was prepared by alkali ion exchange at 1000° C and subsequently annealed in air at lower temperatures. The exsolution microstructure produced in these samples was studied by transmission electron microscopy. At or above 600° C the compositional difference of the coherent lamellae increases rapidly and reaches a maximum, corresponding to the coherent solvus, within a few days. The lamellar spacing (λ) increases more slowly and the coarsening rate is given by λ=λ0+kt 1/3; where t is annealing time, k is a constant for a given temperature, and λ0 is the lamellar spacing obtained by extrapolation to zero annealing time. λ0 is 65 A at 600° C and ca. 200 A at 700° C. The latter is near the maximum temperature at which exsolution is observed. The nonzero value of λ0 and its increase with increasing temperature is evidence that the exsolution occurs by a spinodal mechanism. Data for the coarsening kinetics at other temperatures should be useful for estimating the thermal history of cryptoperthites with coherent lamellae.

The theories of exsolution kinetics are reviewed. The three principal exsolution mechanisms are continuous, discontinuous (cellular), and spinodal decomposition. The continuous and discontinuous mechanisms are both initiated by a classical nucleation event, but the latter involves the formation of a duplex cell. The growth of this cell may be limited only by boundary diffusion and hence occurs at a faster rate than growth limited by volume diffusion. Alternately, growth may be limited by the interface mobility. Spinodal decomposition involves a different type of fluctuation and the conditions for spinodal decomposition are severely limited by the strain energy (coherent spinodal). The theories of isothermal and continuous cooling transformation kinetics are reviewed and the limitation of these theories are considered. The influence of factors such as impurities, imperfections, degree of super-saturation, and pressure (dry and hydrothermal) on transformation kinetics is emphasized. Suggestions are made concerning the general and specific application of these concepts to exsolution reactions in minerals.

The rate of potassium self-diffusion in pure microcline was measured between 600° and 800° C using K40 as a tracer. Transport of K40 by processes other than volume diffusion was insignificant or minimal. Isotropic diffusion coefficients were calculated assuming spherical grains. The data are well fit by the Arrhenius relation and yield a pre-exponential factor (D0) of 133.8 cm2/sec and an activation energy (Q) of 70 kcal/mole. Similar experiments on the self-diffusion of Na22 in a pure low-albite (exchanged microcline) yield D0 of 2.31×10−6 cm2/sec and Q of approximately 19 kcal/mole for the temperature interval from 200° to 600° C. The large difference in these activation energies suggests that the atomic mechanisms for sodium and potassium diffusion are different.

The yield strengths of nominally dry Westerly granite, Enfield aplite, and Hale albite rock show a positive pressure dependence at temperatures of 250 to 800° C, over the range of pressures of 5 to 15 kbar, for deformation at a constant strain rate of 3 x 10-6/sec. However, at 900° C all three rock types show an inversion of this pressure dependence, and samples deformed at higher pressures have lower yield strengths. For quartzites this inversion of the pressure dependence occurs at a somewhat lower temperature, roughly 750° C. Optical and transmission electron microscope (TEM) observations indicate that for the lower temperature samples which have a positive pressure dependence of their yield strength, dislocation mobility is limited and microcracking has contributed to the deformation. For the higher temperature samples which have a negative pressure dependence of their yield strength, through-going faults occur at 5 kbar but not at 10 or 15 kbar. In addition, there appears to be evidence of more recovery in the higher pressure samples. This inversion of the pressure dependence of the yield strength may result from a pressure dependence of hydrolytic weakening. The critical weakening temperature is known to depend on the water concentration within the crystal structure, and it appears that the equilibrium concentration of water within the structure, as well as the rate of exchange, may increase with increasing pressure. If so, then 900° C may be above the weakening temperature for quartz and feldspar for the amount of water which is made soluble in the crystal structure (and which diffuses in from the grain boundaries) by 1 5 kbar confining pressure, but below the weakening temperature for the amount of water which is made soluble in the structure by 5 kbar confining pressure., La limite élastique macroscopique du granite de Westerly, de l'aplite d'Enfield et de l'albitite de Haie, nominalement secs, augmente avec la pression entre 5 et 15 kbar pour des températures de 250 à 800° C et une vitesse de déformation constante de 3 x 10-6 s-1. Cependant à 900° C, ces trois roches exhibaient une dépendance en pression de la limite élastique en sens inverse et les specimens déformés à haute pression ont une limite élastique plus faible. Pour les quartzites, cette inversion de la dépendance en pression se produit à une température légèrement inférieure voisine de 750° C. Les observations en microscopie électronique par transmission révèlent que la microfissuration a contribué à la déformation des échantillons à basse température qui ont une limite élastique croissante avec la pression. Pour les échantillons déformés à haute température dont la limite élastique décroît lorsque la pression augmente, la microfissuration se produit à 5 kbar mais pas à 10 ou 15 kbar. Cette inversion de la dépendance en pression de la limite élastique peut résulter d'une dépendance en pression de l'adoucissement hydrolytique. On sait que la température critique d'adoucissement dépend de la concentration en eau dans le cristal et il semble que la solubilité de l'eau dans la structure ainsi que la cinétique de dissolution augmente avec la pression. Si tel est le cas, 900° C peut être supérieur à la température d'adoucissement du quartz et du feldspath pour la quantité d'eau qui peut entrer en solution à partir des joints de grains à une pression de confinement de 15 kbar mais inférieur à la température d'adoucissement pour la quantité d'eau qui peut entrer en solution à une pression de confinement de 5 kbar., Tullis Jan, Shelton Glen L., Yund Richard A. Pressure dependence of rock strength : implications for hydrolytic weakening. In: Bulletin de Minéralogie, volume 102, 2-3, 1979. Mécanismes de déformation des minéraux et des roches.

The coherent solvus and coherent spinodal for sanidine-high albite are reasonably well known from experimental studies. These relations together with experimental coarsening rates can be used to interpret the thermal histories of rapidly cooled cryptoperthites which are characterized by a coherent, lamellar microstructure. The lamellar spacing (λ) is largely dependent on the rate of cooling during the first 70°C after the sample has crossed the coherent spinodal; the compositional difference of the lamellae (∆C) is more dependent on the lower temperature history of these cryptoperthites.

Feldspar aggregates experimentally deformed in the dislocation creep regime undergo dynamic recrystallization because recovery is difficult due to the limited climb of dislocations. Recrystallizing aggregates have a lower strength because of the cyclic production of small, strain-free grains, and they develop a strong preferred orientation, consistent with that observed in mylonites. Thus, recrystallization-accommodated dislocation creep may be responsible for the grain-size reduction and strain softening that lead to the formation of many mylonites and ductile shear zones.