Zr diffusion in titanite

Chemical diffusion of Zr under anhydrous, pO₂-buffered conditions has been measured in natural titanite. The source of diffusant was either zircon powder or a ZrO₂–Al₂O₃–titanite mixture. Experiments were run in sealed silica glass capsules with solid buffers (to buffer at NNO or QFM). Rutherford Backscattering Spectrometry (RBS) was used to measure diffusion profiles. The following Arrhenius parameters were obtained for Zr diffusion parallel to c over the temperature range 753–1,100°C under NNO-buffered conditions: D _Zr = 5.33 × 10⁻⁷ exp(−325 ± 30 kJ mol⁻¹/RT) m² s⁻¹ Diffusivities are similar for experiments buffered at QFM. These data suggest that titanite should be moderately retentive of Zr chemical signatures, with diffusivities slower than those for O and Pb in titanite, but faster than those for Sr and the REE. When applied in evaluation of the relative robustness of the recently developed Zr-in-titanite geothermometer (Hayden and Watson, Abstract, 16th V.M. Goldschmidt Conference 2006), these findings suggest that Zr concentrations in titanite will be less likely to be affected by later thermal disturbance than the geothermometer based on Zr concentrations in rutile (Zack et al. in Contrib Mineral Petrol 148:471–488, 2004; Watson et al. in Contrib Mineral. Petrol, 2006), but much less resistant to diffusional alteration subsequent to crystallization than the Ti-in-Zircon geothermometer (Watson and Harrison in Science 308:841–844, 2005).     

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’}.     

Pb diffusion in rutile

Diffusion of Pb was measured in natural and synthetic rutile under dry, 1 atmosphere conditions, using mixtures of Pb titanate or Pb sulfide and TiO₂ as the sources of diffusant. Pb depth profiles were then measured with Rutherford Backscattering Spectrometry (RBS). Over the temperature range 700–1100 °C, the following Arrhenius relation was obtained for the synthetic rutile: D=3.9 × 10⁻¹⁰exp(−250 ± 12 kJ mol⁻¹/RT) m²s⁻¹. Results for diffusion in natural and synthetic rutile were quite similar, despite significant differences in trace element compositions. Mean closure temperatures calculated from the diffusion parameters are around 600 °C for rutile grains of ∼100 μm size. This is about 100 °C higher than rutile closure temperature determinations from past field-based studies, suggesting that rutile is more resistant to Pb loss through volume diffusion than previously thought. Received: 28 June 1999 / Accepted: 29 December 1999     

Iron Diffusion in Single-Crystal Diopside

 Iron tracer diffusion experiments in diopside have been performed using natural and synthetic single crystals of diopside, and stable iron tracers enriched in ⁵⁴Fe, at temperatures in the range 950–1100 °C, total pressure 1 atm, for times up to 29 days. Iron isotope diffusion profiles were determined with an ion microprobe. For experiments performed at log pO₂ = −13, in directions parallel to the c axis and the b axis of two natural, low iron (Fe ∼ 1.8 at %) diopsides, the data obey a single Arrhenius relationship of the form D = 6.22_−5.9 ^+49.6×10⁻¹⁵ exp(−161.5 ± 35.0 kJ mol⁻¹/RT) m² s⁻¹. A single datum for iron diffusion in iron-free, single-crystal diopside at 1050 °C, is approximately 1 order of magnitude slower than in the natural crystals. The pO₂ dependence of iron diffusion in natural crystals at 1050 °C (power exponent = 0.229 ± 0.036) indicates a vacancy mechanism; this is consistent with the results of unpublished atomistic simulation studies. There is no evidence of anisotropy for iron diffusion in diopside. Received: 16 March 1999 / Accepted: 10 April 2000     

Diffusion of tetravalent cations in zircon

Diffusion rates for the three tetravalent cations U, Th and Hf have been measured in synthetic zircon. Diffusant sources included oxide powders and ground pre-synthesized silicates. Rutherford backscattering spectrometry (RBS) was used to measure depth profiles. Over the temperature range 1400–1650 °C, the following Arrhenius relations were obtained (diffusion coefficients in m²sec⁻¹): log D _Th = (1.936 ± 0.9820) + (− 792 ± 34 kJ mol⁻¹ /2.303 RT) log D _U = (0.212 ± 2.440) + (− 726 ± 83 kJ mol⁻¹ /2.303 RT) log D _Hf = (3.206 ± 1.592) + (− 812 ± 54 kJ mol⁻¹ /2.303 RT) The data show a systematic increase in diffusivity with decreasing ionic radius (i.e., faster diffusion rates for Hf than for U or Th), a trend also observed in our earlier study of rare earth diffusion in zircon. Diffusive fractionation may be a factor in the Lu-Hf system given the much slower diffusion rates of tetravalent cations when compared with the trivalent rare earths. The very slow diffusion rates measured for these tetravalent cations suggest that they are essentially immobile under most geologic conditions, permitting the preservation of fine-scale chemical zoning and isotopic signatures of inherited cores. Received: 12 July 1996 / Accepted: 2 December 1996     

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).     

Magnesium self-diffusion in orthoenstatite

Magnesium self-diffusion coefficients were determined experimentally for diffusion parallel to each of the three crystallographic directions in natural orthoenstatite (En₈₈Fs₁₂). Experiments were conducted at 1 atm in CO-CO₂ gas mixing furnaces, which provided oxygen fugacities equivalent to the iron-wüstite buffer. Diffusion of ²⁵Mg was induced in polished samples of oriented orthoenstatite using a film of isotopically enriched ²⁵MgO as the source material. Very short (<0.15 μm) diffusional penetration profiles were measured by ion microprobe depth profiling. The diffusion coefficients determined for four temperatures (900, 850, 800, 750 °C) provide the activation energies, E _a , and frequency factors, D _o, where D = D _o exp (−E _a /RT) for Mg self-diffusion parallel to each crystallographic direction: a-axis, E _a  = 360 ± 52 kJ/mole and D _o = 1.10 × 10⁻⁴ m²/s; b-axis, E _a  = 339 ± 77 kJ/mole and D _o = 6.93 × 10⁻⁶ m²/s and c-axis, E _a  = 265 ± 66 kJ/mole and D _o = 4.34 × 10⁻⁹ m²/s. In this temperature range, any possible anisotropy of cation diffusion is very small, however the activation energy for diffusion parallel to the c-axis (001) is the lowest and the activation energies for diffusion parallel to the a-axis (100) and b-axis (010) are higher. Application of these diffusion results to the silicate phases of the Lowicz mesosiderite meteorite provides cooling rates for the silicate portion of the meteorite (4–11 °C/100 years) that are similar, although slower, to previous estimates. These silicate cooling rates are still several orders of magnitude faster than the cooling rates (0.1 °C/10⁶ years) for the metal portions. Received: 22 January 1997 / Accepted: 2 October 1997     

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl₂O₄ spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D _Cr–Al = D ₀ exp {−(Q′ + PV*)/RT}, where D ₀ = exp{(10.3 ± 0.08) × Cr#^0.54±0.02} + (1170 ± 31.2) cm²/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm³/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.     

Oxygen diffusion in anhydrous sanidine feldspar

Oxygen exchange experiments have been performed between single crystals of sanidine feldspar and oxygen gas enriched in ¹⁸O, at temperatures in the range 869–1053 °C, total pressure 1 atmosphere, for times up to 28 days. Oxygen isotope diffusion profiles in a direction perpendicular to (001) were determined with an ion microprobe. The experimental data obey a single Arrhenius relationship of the form D = 8.4 × 10⁻¹¹ exp. (−245 ± 15 kJ mol⁻¹/RT) m²s⁻¹. The results indicate that oxygen diffusion in anhydrous sanidine feldspar is marginally slower than oxygen diffusion in anhydrous anorthite. Comparison with published atomistic simulation studies suggests that oxygen transport in feldspar is by an interstitial mechanism. Received: 17 October 1997 / Accepted: 6 July 1998     

Reversible hydration in synthetic mixite, BiCu6(OH)6(AsO4)3·nH2O (n≤3): hydration kinetics and crystal chemistry

 The presence of zeolitic water, with a reversible hydration behaviour, was determined by structural and kinetic studies on synthetic mixite BiCu₆(OH)₆(AsO₄)₃·nH₂O (n≤3). X-ray diffraction and infrared-spectroscopic investigations were performed on single crystals. Isothermal thermogravimetric experiments were carried out to determine the reaction kinetics of the de- and rehydration processes. The single-crystal structure refinement of a fully hydrated crystal yielded five partially occupied Ow positions (Ow=oxygen atom of a H₂O molecule) within the tube-like channels of the hexagonal [BiCu₆(OH)₆(AsO₄)₃] framework. For the partially dehydrated form, with n≈1, at least two of these sites were found to be occupied significantly. In addition, the structural investigations allowed two different intra-framework hydrogen bonds to be distinguished that are independent of the extra-framework water distribution and are responsible for the stability of the self-supporting framework. The kinetic analysis of the rate data in the 298–343K temperature range shows that the dehydration behaviour obeys a diffusion-controlled reaction mechanism with an empirical activation energy of E _a ^dehyd=54±4 kJ mol^–1. A two-stage process controls rehydration of which the individual steps were attributed to an initial surface-controlled (E _a ^hyd-I=6±1 kJ mol^–1) and subsequent diffusion-controlled reaction mechanism (E _a ^hyd-II=12±1 kJ mol^–1). The estimated hydration enthalpy of 42±5 kJ mol^–1 supports the distribution model of molecular water within the channels based on a purely hydrogen-bonded network. Received June 26, 1996 / Revised, accepted November 11, 1996     

Mg–Fe interdiffusion rates in wadsleyite and the diffusivity jump at the 410-km discontinuity

Mg–Fe interdiffusion rates have been measured in wadsleyite aggregates at 16.0–17.0 GPa and 1230–1530 °C by the diffusion couple method. Oxygen fugacity was controlled using the NNO buffer, and water contents of wadsleyite were measured by infrared spectroscopy. Measured asymmetric diffusion profiles, analyzed using the Boltzmann–Matano equation, indicate that the diffusion rate increases with increasing iron concentration and decreasing grain size. In the case of wadsleyite containing 50–90 weight ppm H₂O, the Mg–Fe interdiffusion coefficients at compositions of Mg/(Mg + Fe)=0.95 in the coarse-grained region (about 60 m) and 0.90 in the fine-grained region (about 6 m) were determined to be a D_Xmg = 0.95 (m² s^–1)=1.24 × 10^–9 exp[–172 (kJ mol^–1)/RT] and D_Xmg = 0.90 (m² s^–1)=1.77 × 10^–9 exp[–143 (kJ mol^–1)/RT], respectively. Grain-boundary diffusion rates were estimated to be about 4 orders of magnitude faster than the volume diffusion rate. Grain-boundary diffusion dominates when the grain size is less than a few tens of microns. Results for the nominally dry diffusion couple in the present study are roughly consistent with previous studies, taking into account differences in pressure and grain size, although water contents of samples were not clear in previous studies. We observed that the diffusivity is enhanced by about 1 order of magnitude in wadsleyite containing 300–2100 wt. ppm H₂O at 1230 °C, which is almost identical to the enhancement associated with a 300 °C increase in temperature. It is still not conclusive that a jump in diffusivity exists between olivine and wadsleyite because water contents of olivine in previous diffusion studies and effects of water on the olivine diffusivity are uncertain.     

Heat capacity and thermodynamic properties of GdPO<Subscript>4</Subscript> in the temperature range 0–1600 K

The heat capacity of gadolinium orthophosphate (GdPO₄) measured in the temperature range 11.15–344.11 K by adiabatic calorimetry and available literature data were used to calculate its thermodynamic functions at 0–1600 K. At 298.15 K, these functions are as follows: C _p ⁰(298.15 K) = 101.85 ± 0.05 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 123.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)–H ⁰(0) = 17.250 ± 0.012 kJ mol⁻¹, and Φ ⁰(298.15 K) = 65.97 ± 0.18 J K⁻¹ mol⁻¹ The calculated Gibbs free energy of formation from the elements of GdPO₄ is Δ _f G ⁰ (298.15 K) = −1844.3 ± 4.7 kJ mol⁻¹.     

Uphill diffusion,zero-flux planes and transient chemical solitary waves in garnet

Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol⁻¹ at 1 bar and frequency factors D_o equal to 2.37 × 10⁻⁶, −4.46 × 10⁻¹⁶, −1.31 × 10⁻⁵, 9.85 × 10⁻¹⁵ m² s⁻¹ for [(D)\tilde]_FeFe^Ca \tilde{D}_{FeFe}^{Ca} , [(D)\tilde]_FeMg^Ca \tilde{D}_{FeMg}^{Ca} , [(D)\tilde]_MgFe^Ca \tilde{D}_{MgFe}^{Ca} , [(D)\tilde]_MgMg^Ca \tilde{D}_{MgMg}^{Ca} , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.     

Li diffusion in zircon

Diffusion of Li under anhydrous conditions at 1 atm and under fluid-present elevated pressure (1.0–1.2 GPa) conditions has been measured in natural zircon. The source of diffusant for 1-atm experiments was ground natural spodumene, which was sealed under vacuum in silica glass capsules with polished slabs of zircon. An experiment using a Dy-bearing source was also conducted to evaluate possible rate-limiting effects on Li diffusion of slow-diffusing REE⁺³ that might provide charge balance. Diffusion experiments performed in the presence of H₂O–CO₂ fluid were run in a piston–cylinder apparatus, using a source consisting of a powdered mixture of spodumene, quartz and zircon with oxalic acid added to produce H₂O–CO₂ fluid. Nuclear reaction analysis (NRA) with the resonant nuclear reaction ⁷Li(p,γ)⁸Be was used to measure diffusion profiles for the experiments. The following Arrhenius parameters were obtained for Li diffusion normal to the c-axis over the temperature range 703–1.151°C at 1 atm for experiments run with the spodumene source:

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.     

Cation diffusion in aluminosilicate garnets: experimental determination in pyrope-almandine diffusion couples

Diffusion couples made from homogeneous gem quality natural pyrope and almandine garnets were annealed within graphite capsules under anhydrous conditions at 22–40 kbar, 1057–1400 °C in a piston-cylinder apparatus. The concentration profiles that developed in each couple were modeled to retrieve the self diffusion coefficients [D(I)] of the divalent cations Fe, Mg, Mn and Ca. Because of their usually low concentrations and lack of sufficient compositional change across the interface of the diffusion couples, only a few reliable data can be obtained for D(Ca) and D(Mn) from these experiments. However, nine sets of D(Fe) and D(Mg) data were retrieved in the above P-T range, and cast in the form of Arrhenian relation, D=D ₀exp{−[Q(1 bar)+PΔV ⁺]/RT}. The values of the activation energy (Q) and activation volume (ΔV ⁺) depend on whether f _O2 is constrained by graphite in the system C-O or held constant. For the first case, we have for Fe:Q(1 bar)=65,532±10,111 cal/mol, D ₀=3.50 (±2.30)×10⁻⁵ cm²/s, ΔV ⁺=5.6(±2.9) cm³/mol, and for Mg:Q(1 bar)=60,760±8,257 cal/mol, D ₀=4.66 (±2.48)×10⁻⁵ cm²/s, ΔV ⁺=5.3(±3.0) cm³/mol. Here the ΔV ⁺ values have been taken from Chakraborty and Ganguly (1992). For the condition of constant f _O2, the Q values are ∼9 kcal lower and ΔV ⁺ values are ∼4.9 cm³/mol larger than the above values. Lower temperature extrapolation of the Arrhenian relation for D(Mg) is in good agreement with the Mg tracer diffusion data (D ^* _Mg) of Chakraborty and Rubie (1996) and Cygan and Lasaga (1985) at 1 bar, 750–900 °C, when all data are normalized to the same pressure and to f _O2 defined by graphite in the system C-O. The D ^* _Mg data of Schwandt et al. (1995), on the other hand, are lower by more than an order of magnitude than the low temperature extrapolation of the present data, when all data are normalized to the same pressure and to f _O2 defined by the graphite buffer. Comparison of the D(Fe), D(Mg) and D(Mn) data in the pyrope-almandine diffusion couple with those in the spessartine-almandine diffusion couple of Chakraborty and Ganguly (1992) shows that the self diffusion of Fe and Mn are significantly enhanced with the increase in Mn/Mg ratio; the enhancement effect on D(Mg) is, however, relatively small. Proper application of the self diffusion data to calculate interdiffusion coefficient or D matrix elements for the purpose of modeling of diffusion processes in natural garnets must take into account these compositional effects on D(I) along with the effects of thermodynamic nonideality, f _O2, and pressure. Received: 8 May 1997 / Accepted: 2 October 1997     

Thermodynamic functions of eskolaite Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>(c) at 0–1800 K

The heat capacity of eskolaite Cr₂O₃(c) was determined by adiabatic vacuum calorimetry at 11.99–355.83 K and by differential calorimetry at 320–480 K. Experimental data of the authors and data compiled from the literature were applied to calculate the heat capacity, entropy, and the enthalpy change of Cr₂O₃ within the temperature range of 0–1800 K. These functions have the following values at 298.15 K: C _p ⁰ (298.15) = 121.5 ± 0.2 J K⁻¹mol⁻¹, S ⁰(298.15) = 80.95 ± 0.14 J K⁻¹mol⁻¹, and H ⁰(298.15)-H ⁰(0) = 15.30±0.02 kJ mol⁻¹. Data were obtained on the transitions from the antiferromagnetic to paramagnetic states at 228–457 K; it was determined that this transition has the following parameters: Neel temperature T _N = 307 K, Δ _tr S = 6.11 ± 0.12 J K⁻¹mol⁻¹ and δ _tr H = 1.87 ± 0.04 kJ mol⁻¹.     

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     

Rare-earth elements as source indicators of Pan-African granites from Obudu Plateau,Southeastern Nigeria

The rare-earth element （REE） concentrations of representative granite samples from the southeast of the Obudu Plateau, Nigeria, were analyzed with an attempt to determine the signatures of their source, evolutionary history and tectonic setting. Results indicated that the granites have high absolute REE concentrations （190×10^-6-1191×10^-6; av.=549×10^-6） with the chondrite-normalized REE patterns characterized by steep negative slopes and prominent to slight or no negative Eu anomalies. All the samples are also characterized by high and variable concentrations of the LREE （151×10^-6-1169×10^-6; av.= 466×10^-6）, while the HREE show low abundance （4×10^-6-107×10^-6; av.=28×10^-6）. These are consistent with the variable levels of REE fractionation, and differentiation of the granites. This is further supported by the range of REE contents, the chondrite-normalized patterns and the ratios of LaN/YbN （2.30-343.37）, CeN/YbN （5.94-716.87）, LaN/SmN （3.14-11.68） and TbN/YbN （0.58-1.65）. The general parallelism of the REE patterns, suggest that all the granites were comagmatic in origin, while the high Eu/Eu＊ ratios （0.085-2.807; av.=0.9398） indicate high fo2 at the source. Similarly, irregular variations in LaN/YbN, CeN/YbN and Eu/Eu＊ ratios and REE abundances among the samples suggest behaviors that are related to mantle and crustal sources.     

Diffusion of dissolved SiO2 in H2O at 1 GPa, with implications for mass transport in the crust and upper mantle

Cation diffusion rates at 690 ± 30 °C have been calculated by inverse modelling of observed manganese (Mn) zonation profiles in 40 garnets from two kyanite-bearing metapelite samples from the High Himalayan Crystalline Series, Zanskar, northwest India. Knowledge of the initial growth profile of Mn in garnet is a pre-requisite for this technique. Following previous workers we model Mn partitioning into growing garnet in terms of a Rayleigh fractionation process, and demonstrate that the Mn_{garnet:whole rock} partition coefficient is 60–100. Three-dimensional zonation profiles were obtained by successively grinding and polishing ∼1 cm slabs of each sample at 0.1–0.2 mm intervals and analysing the garnets at each stage, thus ensuring that core sections were measured. The diffusion model assumes that garnet has a spherical geometry and behaves as a closed system, and simulates diffusive modification of the hypothetical Mn Rayleigh growth profile for each garnet. The derived measure of the time-integrated diffusion history for each garnet is then combined with radiometric and field-relation constraints for the duration of the Himalayan metamorphic event to calculate cation diffusion rates. The average cation interdiffusion rate calculated for garnets in the two samples examined is (6 ± 3.2) × 10⁻²³ m²s⁻¹. This interdiffusion rate pertains to a temperature of 690 ± 30 °C, which is 0.97 × T _PEAK, the peak temperature conditions experienced by the samples estimated using standard thermobarometric techniques. Garnet compositions are P_y2–17Alm_65–77Gro_6–16Sp_1–17. These new diffusion data are consistent with, and more precise than, existing high-temperature (>1000 °C) experimentally determined diffusion data, although some uncertainties remain difficult to constrain. Qualitative comparison between diffusively modified Mn growth profiles in garnets from the Scottish Dalradian and the Himalayan garnets suggests that the duration of metamorphism affecting the Dalradian garnets was 10–20 times longer than that endured by the Himalayan garnets. Received: 5 June 1996 / Accepted: 29 January 1997