Zr-in-rutile thermometry in HP/UHP eclogites from Western China

Four Zr-in-rutile thermometry calibrations are applied to eclogites from Western China. Here, we show that if rutile grows in equilibrium with Qtz and Zrn, and is isolated inside garnet, it preserves its Zr composition and does not undergo compositional change due to cation exchange with the host garnet. It thus preserves the composition for the P–T conditions of its formation and the growth zoning of the host garnet. For the HP/UHP metamorphic temperature, the Tomkins et al. (J Metamorph Geol 25:703–713, 2007) calibration yields temperatures that agree well with previous studies, whereas the other three calibrations (Zack et al. in Contrib Mineral Petrol 148:471–488, 2004; Watson et al. in Contrib Mineral Petrol 151:413–433, 2006; Ferry and Watson in Contrib Mineral Petrol in 154:429–437, 2007), which do not include a pressure correction, give systematically lower temperatures. Zr contents of rutile inclusions within garnet show systematic decrease from garnet core to rim. The rutile inclusions in garnet rims contain the lowest Zr content, similar to that in the matrix. Analyses confirm that the pressure plays a significant role in modifying the primary temperature dependence of the Zr content of rutile. Rutiles trapped in garnets are unable to re-equilibrate easily during retrogression, but those in the matrix can do so, providing retrograde P–T path information.     

Reply to “Oxygen isotope heterogeneity of the mantle beneath the Canary Islands: a discussion of the paper of Gurenko et al.”

The comment by Day et al. (Contrib Mineral Petrol, 2012) (1) discusses the validity of the previously obtained oxygen isotope data for El Hierro and La Palma (Canary Island) olivines, (2) questions the approach by Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) of using weakly correlated variations of δ¹⁸O_olivine values with X _px (proportion of pyroxenite-derived melt in the parental magma), and (3) provides reasons why oxygen isotope data by secondary ion mass spectrometry (SIMS) “offer sensitive means for detecting melt-crust interactions.” We respond these comments and report a new set of oxygen isotope measurements performed by SIMS and single-grain laser fluorination methods. These measurements confirm our previous data and conclusions and demonstrate the ability of the SIMS technique to analyze O isotopes in terrestrial samples with 2-sigma uncertainty better than ±0.25 ‰.     

Oxygen isotope heterogeneity of the mantle beneath the Canary Islands: a discussion of the paper of Gurenko et al.

Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) report laser-assisted fluorination (LF) and secondary ionization mass spectrometry (SIMS) ¹⁸O/¹⁶O datasets for olivine grains from the Canary Islands of Gran Canaria, Tenerife, La Gomera, La Palma and El Hierro. As with prior studies of oxygen isotopes in Canary Island lavas (e.g. Thirlwall et al. Chem Geol 135:233–262, 1997; Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010), these authors find variations in δ¹⁸O_ol (~4.6–6.0 ‰) beyond that measured for mantle peridotite olivine (Mattey et al. Earth Planet Sci Lett 128:231–241, 1994) and interpret this variation to reflect contributions from pyroxenite-peridotite mantle sources. Furthermore, Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) speculate that δ¹⁸O_ol values for La Palma olivine grains measured by LF (Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) may be biased to low values due to the presence of altered silicate, possibly serpentine. The range in δ¹⁸O_ol values for Canary Island lavas are of importance for constraining their origin. Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) took a subset (39 SIMS analyses from 13 grains from a single El Hierro lava; EH4) of a more extensive dataset (321 SIMS analyses from 110 grains from 16 Canary Island lavas) to suggest that δ¹⁸O_ol is weakly correlated (R ² = 0.291) with the parameter used by Gurenko et al. (Earth Planet Sci Lett 277:514–524, 2009) to describe the estimated weight fraction of pyroxenite-derived melt (Xpx). With this relationship, end-member δ¹⁸O values for HIMU-peridotite (δ¹⁸O = 5.3 ± 0.3 ‰) and depleted pyroxenite (δ¹⁸O = 5.9 ± 0.3 ‰) were defined. Although the model proposed by Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) implicates similar pyroxenite-peridotite mantle sources to those proposed by Day et al. (Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) and Day and Hilton (Earth Planet Sci Lett 305:226–234, 2011), there are significant differences in the predicted δ¹⁸O values of end member components in the two models. In particular, Day et al. (Geochim Cosmochim Acta 74:6565–6589, 2010) proposed a mantle source for La Palma lavas with low-δ¹⁸O (<5 ‰), rather than higher-δ¹⁸O (c.f. the HIMU-peridotite composition of Gurenko et al. in Contrib Mineral Petrol 162:349–363, 2011). Here we question the approach of using weakly correlated variations in δ¹⁸O_ol and the Xpx parameter to define mantle source oxygen isotope compositions, and provide examples of why this approach appears flawed. We also provide reasons why the LF datasets previously published for Canary Island lavas remain robust and discuss why LF and SIMS data may provide complementary information on oxygen isotope variations in ocean island basalts (OIB), despite unresolved small-scale uncertainties associated with both techniques.     

Cordierite as an indicator of thermodynamic conditions of petrogenesis

A refined thermodynamic model of H₂O and CO₂ bearing cordierite based on recent data on volatile incorporation into cordierite (Thompson et al. in Contrib Mineral Petrol 142:107–118, 2001; Harley and Carrington in J Petrol 42:1595–1620, 2001) reflects non-ideality of channel H₂O and CO₂ mixing. The dependence of cordierite H₂O and CO₂ contents on P, T and equilibrium fluid composition has been calculated for the range 600–800°C and 200–800 MPa. It has been used for establishing thermodynamic conditions of cordierite formation and the following retrograde P–T paths of cordierite rocks from many localities. Estimates of the H₂O and CO₂ activities have shown that cordierites in granites, pegmatites and high-pressure granulites were formed in fluid-saturated conditions and wide range of H₂O/CO₂ relations. Very low cordierite H₂O contents in many migmatites may be caused not only by fluid-undersaturated conditions at rock formation and H₂O leakage on retrograde P–T paths but also by the presence of additional volatile components like CH₄ and N₂. The pressure dependence of cordierite-bearing mineral equilibria on fluid H₂O/CO₂ relations has been evaluated.     

Heat capacity,entropy and phase equilibria of stishovite

The low-temperature heat capacity (C _P) of stishovite (SiO₂) synthesized with a multi-anvil device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system (PPMS) and around ambient temperature using a differential scanning calorimeter (DSC). The entropy of stishovite at standard temperature and pressure calculated from DSC-corrected PPMS data is 24.94 J mol⁻¹ K⁻¹, which is considerably smaller (by 2.86 J mol⁻¹ K⁻¹) than that determined from adiabatic calorimetry (Holm et al. in Geochimica et Cosmochimica Acta 31:2289–2307, 1967) and about 4% larger than the recently reported value (Akaogi et al. in Am Mineral 96:1325–1330, 2011). The coesite–stishovite phase transition boundary calculated using the newly determined entropy value of stishovite agrees reasonably well with the previous experimental results by Zhang et al. (Phys Chem Miner 23:1–10, 1996). The calculated phase boundary of kyanite decomposition reaction is most comparable with the experimental study by Irifune et al. (Earth Planet Sci Lett 77:245–256, 1995) at low temperatures around 1,400 K, and the calculated slope in this temperature range is mostly consistent with that determined by in situ X-ray diffraction experiments (Ono et al. in Am Mineral 92:1624–1629, 2007).     

Thermochemistry of sulfide liquids III: Ni-bearing liquids at 1 bar

Experiments were performed in the system O–S–Fe–Ni designed to extend our understanding of the chemistry of sulfide liquids. Results indicate that adding nickel to Fe-rich sulfide liquids in equilibrium with silicate liquids extends their stability field to much higher oxygen fugacities and lower sulfur fugacities. Increasing Ni/Fe at a given temperature and sulfur and oxygen fugacity is accompanied by a significant decrease in the oxygen content of the sulfide liquid. Results of these experiments are combined with data from the literature to calibrate an associated regular solution model for O–S–Fe–Ni liquids. This model represents a complete refit of the associated regular solution model of Kress (Contrib Mineral Petrol 139:316–325, 2000). The resulting model is combined with the olivine solution model of Hirschmann (Am Mineral 76:1232–1248, 1991) to explore the effect of variations in oxygen and sulfur fugacities on the distribution of Fe and Ni between olivine and sulfide liquid. Predicted olivine–sulfide distribution trends parallel those observed by Gaetani and Grove (Geochim Cosmochim Acta 61:1829–1846, 1997), Gaetani and Grove (Earth Planet Sci Lett 169:147–163, 1999), Brenan and Caciagli (Geochim Cosmochim Acta 64:307–320, 2000) and Brenan (Geochim Cosmochim Acta 67:2663–2681, 2003), but are systematically offset toward lower predicted Ni in the sulfide. Nevertheless our results are consistent with the assertion that low K _D ^os values in magmatic ore deposits such as the J-M Reef reflect high iron contents in the sulfides combined with relatively high oxygen fugacities.

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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.     

Low T heat capacity measurements and new entropy data for titanite (sphene): implications for thermobarometry of high-pressure rocks

The accepted standard state entropy of titanite (sphene) has been questioned in several recent studies, which suggested a revision from the literature value 129.3 ± 0.8 J/mol K to values in the range of 110–120 J/mol K. The heat capacity of titanite was therefore re-measured with a PPMS in the range 5 to 300 K and the standard entropy of titanite was calculated as 127.2 ± 0.2 J/mol K, much closer to the original data than the suggested revisions. Volume parameters for a modified Murgnahan equation of state: V _P,T  = V ₂₉₈° × [1 + a°(T − 298) − 20a°(T − 298)] × [1 – 4P/(K ₂₉₈ × (1 – 1.5 × 10⁻⁴ [T − 298]) + 4P)]^1/4 were fit to recent unit cell determinations at elevated pressures and temperatures, yielding the constants V ₂₉₈° = 5.568 J/bar, a° = 3.1 × 10⁻⁵ K⁻¹, and K = 1,100 kbar. The standard Gibbs free energy of formation of titanite, −2456.2 kJ/mol (∆H°_f = −2598.4 kJ/mol) was calculated from the new entropy and volume data combined with data from experimental reversals on the reaction, titanite + kyanite = anorthite + rutile. This value is 4–11 kJ/mol less negative than that obtained from experimental determinations of the enthalpy of formation, and it is slightly more negative than values given in internally consistent databases. The displacement of most calculated phase equilibria involving titanite is not large except for reactions with small ∆S. Re-calculated baric estimates for several metamorphic suites yield pressure differences on the order of 2 kbar in eclogites and 10 kbar for ultra-high pressure titanite-bearing assemblages.     

In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg₃Al₂Si₃O₁₂) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) _P = −19.3(4); (∂G/∂T) _P = −10.4(2) MPa K⁻¹] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) _P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂² G/∂P∂T = [0.07(12), 0.20(14)] × 10⁻³ K⁻¹ and ∂² K _S /∂P∂T = [−0.20(24), 0.22(26)] × 10⁻³ K⁻¹, both of order 10⁻⁴ K⁻¹ and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.     

Application of the Ti-in-quartz thermobarometer to rutile-free systems. Reply to: a comment on: ‘TitaniQ under pressure: the effect of pressure and temperature on the solubility of Ti in quartz’ by Thomas et al.

The premise of the Wilson et al. comment is that the Ti-in-quartz solubility calibration (Thomas et al. in Contrib Mineral Petrol 160:743–759, 2010) is fundamentally flawed. They reach this conclusion because P–T estimates using the Ti-in-quartz calibration differ from their previous interpretations for crystallization conditions of the Bishop and Oruanui rhyolites. If correct, this assertion has far-reaching implications, so a careful assessment of the Wilson et al. reasoning is warranted. Application of the Ti-in-quartz calibration as a thermobarometer in rutile-free rocks requires an estimation of TiO₂ activity in the liquid ( (liquid–rutile); referenced to rutile saturation) and an independent constraint on either P or T to obtain the crystallization temperature or pressure, respectively. The foundation of Wilson et al.’s argument is that temperature estimates obtained from Fe–Ti oxide thermometry accurately reflect crystallization conditions of quartz in the two rhyolites discussed. We maintain that our experimental approach is sound, the thermodynamic basis of the Ti-in-quartz calibration is fundamentally correct, and our experimental results are robust and reproducible. We suggest that the reason Wilson et al. obtain implausible pressure estimates is because estimates for T and they used as input values for the Ti-in-quartz calibration are demonstrably too high. Numerous studies show that Fe–Ti oxide temperature estimates of some rhyolites are substantially higher than those predicted by well-constrained phase equilibria. In this reply, we show that when reasonable input values for T and (liquid–rutile) are used, pressure estimates obtained from the Ti-in-quartz calibration are well aligned with phase equilibria and essentially identical to melt inclusion volatile saturation pressures.     

Basanite–nephelinite suite from early Kilauea: carbonated melts of phlogopite–garnet peridotite at Hawaii’s leading magmatic edge

A basanite–nephelinite glass suite from early submarine Kilauea defines a continuous compositional array marked by increasing concentrations of incompatible components with decreasing SiO₂, MgO, and Al₂O₃. Like peripheral and post-shield strongly alkalic Hawaiian localities (Clague et al. in J Volcanol Geotherm Res 151:279–307, 2006; Dixon et al. in J Pet 38:911–939, 1997), the early Kilauea basanite–nephelinite glasses are interpreted as olivine fractionation products from primary magnesian alkalic liquids. For early Kilauea, these were saturated with a garnet–phlogopite–sulfide peridotite assemblage, with elevated dissolved CO₂ contents responsible for the liquids’ distinctly low-SiO₂ concentrations. Reconstructed primitive liquids for early Kilauea and other Hawaiian strongly alkalic localities are similar to experimental 3 GPa low-degree melts of moderately carbonated garnet lherzolite, and estimated parent magma temperatures of 1,350–1,400°C (olivine–liquid geothermometry) match the ambient upper mantle geotherm shortly beneath the base of the lithosphere. The ~3 GPa source regions were too hot for stable crystalline carbonate and may have consisted of ambient upper mantle peridotite containing interstitial carbonate–silicate or carbonatitic liquid, possibly (Dixon et al. in Geochem Geophys Geosyst 9(9):Q09005, 2008), although not necessarily, from the Hawaiian mantle plume. Carbonate-enriched domains were particularly susceptible to further melting upon modest decompression during upward lithospheric flexure beneath the advancing Hawaiian Arch, or by conductive heating or upward drag by the Hawaiian mantle plume. The early Kilauea basanite–nephelinite suite has a HIMU-influenced isotopic character unlike other Hawaiian magmas (Shimizu et al. in EOS Tran Amer Geophys Union 82(47): abstr V12B-0962, 2001; Shimizu et al. in Geochim Cosmochim Acta 66(15A):710, 2002) but consistent with oceanic carbonatite involvement (Hoernle et al. in Contrib Mineral Petrol 142:520–542, 2002). It may represent the melting products of a fertile domain in the ambient upper mantle impinged upon and perturbed by the sustained plume source that feeds later shield-stage magmatism.     

Thermodynamics of mixing in diopside–jadeite,CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>, solid solution from static lattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.     

Effects of melt viscosity and silica activity on the rate and mechanism of quartz dissolution in melts of the CMAS and CAS systems

The dissolution rate of quartz in melts of the CMAS and CAS systems at 1,600°C and 1.5 GPa is a function of both the silica activity of the melt and its viscosity. In melts with low silica activity quartz dissolves more quickly than in higher aSiO₂ melts regardless of viscosity. For melts with equal aSiO₂, dissolution is faster in the low viscosity melt. Quartz dissolution is controlled by interface kinetics in three of the four melts used in this study for times much greater than predicted by the model of Zhang et al. (in Contrib Mineral Petrol 102:492–513 1989). One melt which was previously shown to adhere to the predicted behaviour at lower temperature shows a significant activation time at higher temperature. All the dissolution data indicate that there are likely to be three distinct domains of dissolution behaviour, although the details of why a particular melt falls in any one domain require further study. Although the current database is small, the relationship between quartz solubility and the dissolution constant indicate that solubility may be a useful parameter for predicting dissolution rates, particularly if silica activity and melt viscosity are also known.     

Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg systems

We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D ₀ exp{–[Q _1bar + (P–1)ΔV ⁺]/RT} for D _Mg^* and D _Fe^*: Mg: Q _1bar = 228.3 ± 20.3 kJ/mol, D ₀ = 2.72 (±4.52) × 10⁻¹⁰ m²/s, Fe: Q _1bar = 226.9 ± 18.6 kJ/mol, D ₀ = 1.64 (±2.54) × 10⁻¹⁰ m²/s. ΔV ⁺ values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).     

Double carbonate breakdown reactions at high pressures: an experimental study in the system CaO–MgO–FeO–MnO–CO2

The pressure–temperature conditions of the reactions of the double carbonates CaM(CO₃)₂, where M = Mg (dolomite), Fe (ankerite) and Mn (kutnohorite), to MCO₃ plus CaCO₃ (aragonite) have been investigated at 5–8 GPa, 600–1,100°C, using multi-anvil apparatus. The reaction dolomite = magnesite + aragonite is in good agreement with the results of Sato and Katsura (Earth Planet Sci 184:529–534, 2001), but in poor agreement with the results of Luth (Contrib Mineral Petrol 141:222–232, 2001). The dolomite is partially disordered at 620°C, and fully disordered at 1,100°C. All ankerite and kutnohorite samples, including the synthetic starting materials, are disordered. The P–T slopes of the three reactions increase in the order M = Mg, Fe, Mn. The shallower slope for the reaction involving magnesite is due partly to its having a higher compressibility than expected from unit-cell volume considerations. At low pressures there is a preference for partitioning into the double carbonate of Mg > Fe > Mn. At high pressures the partitioning preference is reversed. Using the measured reaction positions, the P–T conditions at which dolomite solid solutions will break down on increasing P and T in subduction zones can be estimated.     

Ca–Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients

We have experimentally determined the tracer diffusion coefficients (D*) of ⁴⁴Ca and ²⁶Mg in a natural diopside (~Di₉₆) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O₂) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(²⁶Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m²/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm³/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.     

Insights into the high-pressure behavior of kaolinite from infrared spectroscopy and quantum-mechanical calculations

The high-pressure behavior of Keokuk kaolinite has been studied to 9.5 GPa by infrared spectroscopy using synchrotron radiation. The kaolinite-I → kaolinite-II and kaolinite-II → kaolinite-III transformations have clear spectroscopic expression, with discontinuities coinciding with the transformation pressures bracketed by X-ray diffraction (Welch and Crichton in Am Mineral 95:651–654, 2010). The experimental spectra have been interpreted from band assignments derived from density functional theory for the structures of kaolinite-II and kaolinite-III, using as starting models the ab initio structures reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) and unit-cell parameters from Welch and Crichton (Am Mineral 95:651–654, 2010). The relaxed theoretical structures are very similar to those reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) in their theoretical investigation of kaolinite polytypes at high pressure. The vibrational spectra calculated from the quantum-mechanical analysis allow band assignments of the IR spectra to be made and provide insights into the behavior of different OH environments in the two high-pressure polytypes. The single perpendicular-interlayer OH group of kaolinite-III has a distinctive spectroscopic signature that is diagnostic of this polytype (ν = 3,595 cm⁻¹ at 9.5 GPa) and is sensitive to the compression/expansion of the interlayer space. This OH group also has a distinctive signature in the calculated spectra. The spectra collected on decompression are those of kaolinite-III and persist largely unchanged to 4.6 GPa, except for a continuous blue shift of the 3,595 cm⁻¹ band to 3,613 cm⁻¹. Finally, kaolinite-I is recovered at 0.6 GPa, confirming the kaolinite-III → kaolinite-I transformation previously observed by X-ray diffraction, and the irreversibility of the kaolinite-II → kaolinite-III transformation. The ambient spectra collected at the start and finish of the experiment are those of kaolinite-I, and start/finish band frequencies agree to within 6 cm⁻¹.     

Silicon and oxygen self diffusion in enstatite polycrystals: the Milke et al. (2001) rim growth experiments revisited

Milke et al. (Contrib Mineral Petrol 142:15–26, 2001) studied the diffusion of Si, Mg and O in synthetic polycrystalline enstatite reaction rims. The reaction rims were grown at 1,000°C and 1 GPa at the contacts between forsterite grains with normal isotopic compositions and a quartz matrix extremely enriched in ¹⁸O and ²⁹Si. The enstatite reaction rim grew from the original quartz-forsterite interface in both directions producing an inner portion, which replaced forsterite and an outer portion, which replaced quartz. Here we present new support for this statement, as the two portions of the rim are clearly distinguished based on crystal orientation mapping using electron backscatter diffraction (EBSD). Milke et al. (Contrib Mineral Petrol 142:15–26, 2001) used the formalism of LeClaire (J Appl Phys 14:351–356, 1963) to derive the coefficient of silicon grain boundary diffusion from stable isotope profiles across the reaction rims. LeClaires formalism is designed for grain boundary tracer diffusion into an infinite half space with fixed geometry. A fixed geometry is an undesired limitation in the context of rim growth. We suggest an alternative model, which accounts for simultaneous layer growth and superimposed silicon and oxygen self diffusion. The effective silicon bulk diffusivity obtained from our model is approximately equal within both portions of the enstatite reaction rim: D _Si,En ^eff =1.0–4.3×10^–16 m² s^–1. The effective oxygen diffusion is relatively slow in the inner portion of the reaction rim, D _O,En ^eff =0.8–1.4×10^–16 m² s^–1, and comparatively fast, D _O,En ^eff =5.9–11.6×10^–16 m² s^–1, in its outer portion. Microstructural evidence suggests that transient porosity and small amounts of fluid were concentrated at the quartz-enstatite interface during rim growth. This leads us to suspect that the presence of an aqueous fluid accelerated oxygen diffusion in the outer portion of the reaction rim. In contrast, silica diffusion does not appear to have been affected by the spatial variation in the availability of an aqueous fluid.

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Si diffusion in zircon

Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for experiments was a mixture of ZrO₂ and ³⁰Si-enriched SiO₂ in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. ³⁰Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant nuclear reaction ³⁰Si(p,γ)³¹P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol⁻¹/RT) m² s⁻¹ for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements [62 exp(−738 ± 61 kJ mol⁻¹/RT) m² s⁻¹]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we can rank the diffusivities of the major constituents in zircon as follows: D _Zr < D _Si << D _{O, dry} < D _{O, ‘wet’}.     

High-temperature heat capacity and thermodynamic properties for end-member titanite (CaTiSiO5)

 The heat capacity of end-member titanite and (CaTiSiO₅) glass has been measured in the range 328–938 K using differential scanning calorimetry. The data show a weak λ-shaped anomaly at 483 ± 5 K, presumably associated with the well-known low-pressure P2₁/a ⇆ A2/a transition, in good agreement with previous studies. A value of 0.196 ± 0.007 kJ mol⁻¹ for the enthalpy of the P2₁/a ⇆ A2/a transition was determined by integration of the area under the curve for a temperature interval of 438–528 K, bracketing the anomaly. The heat capacity data for end-member titanite and (CaTiSiO₅) glass can be reproduced within <1% using the derived empirical equations (temperature in K, pressure in bars):