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’}.     

Rare earth element and gallium diffusion in yttrium aluminum garnet

Diffusion of four rare-earth elements and gallium has been measured in yttrium aluminum garnet (YAG). Sources of diffusant were mixtures of alumina and rare-earth element oxides for REE diffusion, and mixtures of gallium and yttrium oxides for Ga diffusion. Diffusion profiles were measured with Rutherford backscattering spectrometry (RBS). For the rare-earth elements investigated, the following Arrhenius relations were obtained: D_La=6.87×10^–1 exp (–582±21 kJ mol^–1 /RT) m²s^–1 D_Nd=1.63×10^–1 exp (–567±15 kJ mol^–1 /RT) m²s^–1 D_Dy=2.70×10⁰ exp (–603±35 kJ mol^–1 /RT) m²s^–1 D_Yb=1.50×10^–2 exp (–540±26 kJ mol^–1 /RT) m²s^–1 Diffusion rates for the rare earths are quite similar, in contrast with trends noted for zircon. It is likely that these differences are a consequence of the relative ionic radii of the REE and the cations for which they substitute in the mineral lattice. For gallium, the following Arrhenius relation was determined: D_Ga=9.96×10^–6 exp (–404±19 kJ mol^–1 /RT) m²s^–1 Gallium diffuses faster than the REE in YAG and has a smaller activation energy for diffusion. These data mirror relative trends in diffusion rates for YIG, in which trivalent cations occupying tetrahedral and octahedral sites (i.e., Al, Ga, Fe) diffuse faster than trivalent cations occupying dodecahedral sites (i.e., Y and the REE), and suggest that the rate-limiting process in the diffusion-controlled regime of solid-state creep of YAG is the diffusion of yttrium. Received: 10 November 1997 / Revised; accepted: 13 March 1998     

Diffusion of lead in plagioclase and K-feldspar: an investigation using Rutherford Backscattering and Resonant Nuclear Reaction Analysis

Chemical diffusion of Pb has been measured in K-feldspar (Or₉₃) and plagioclase of 4 compositions ranging from An₂₃ to An₉₃ under anhydrous, 0.101 MPa conditions. The source of diffusant for the experiments was a mixture of PbS powder and ground feldspar of the same composition as the sample. Rutherford Backscattering (RBS) was used to measure Pb diffusion profiles. Over the temperature range 700–1050°C, the following Arrhenius relations were obtained (diffusivities in m²s^-1):Oligoclase (An₂₃): Diffusion normal to (001): log D = ( – 6.84 ± 0.59) – [(261 ± 13 kJ mol ^–1)/2.303RT]Diffusion normal to (010): log D = ( – 3.40 ± 0.50) – [(335 ± 11 kJ mol ^–1)/2.303RT]Andesine (An₄₃): Diffusion normal to (001): log D = ( – 6.73 ± 0.54) – [(266 ± 12 kJ mol ^–1)/2.303RT] Diffusion normal to (010) appears to be only slightly slower than diffusion normal to (001) in andesine.Labradorite (An₆₇): Diffusion normal to (001): log D = ( – 7.16 ± 0.61) – [(267 ± 13 kJ mol ^–1)/2.303RT] Diffusion normal to (010) is slower by 0.7 log units on average.Anorthite Diffusion normal to (010): log D = ( – 5.43 ± 0.48) – [(327 ± 11 kJ mol ^–1)/2.303RT]K-feldspar (Or₉₃): Diffusion normal to (001): log D = ( – 4.74 ± 0.52) – [(309 ± 16 kJ mol ^–1)/2.303RT] Diffusion normal to (010): log D = ( – 5.99 ± 0.51) – [(302 ± 11 kJ mol ^–1)/2.303RT]In calcic plagioclase, Pb uptake is correlated with a reduction of Ca, indicating the involvement of PbCa exchange in chemical diffusion. Decreases of Na and K concentrations in sodic plagioclase and K-feldspar, respectively, are correlated with Pb uptake and increase in Al concentration (measured by resonant nuclear reaction analysis), suggesting a coupled process for Pb exchange in these feldspars. These results have important implications for common Pb corrections and Pb isotope systematics. Pb diffusion in apatite is faster than in the investigated feldspar compositions, and Pb diffusion rates in titanite are comparable to both K-feldspar and labradorite. Given these diffusion data and typical effective diffusion radii for feldspars and accessory minerals, we may conclude that feldspars used in common Pb corrections are in general less inclined to experience diffusion-controlled Pb isotope exchange than minerals used in U-Pb dating that require a common Pb correction.     

Rare earth element diffusion in a natural pyrope single crystal at 2.8 GPa

Volume diffusion rates of Ce, Sm, Dy, and Yb have been measured in a natural pyrope-rich garnet single crystal (Py₇₁Alm₁₆Gr₁₃) at a pressure of 2.8 GPa and temperatures of 1,200-1,450 °C. Pieces of a single gem-quality pyrope megacryst were polished, coated with a thin layer of polycrystalline REE oxide, then annealed in a piston cylinder device for times between 2.6 and 90 h. Diffusion profiles in the annealed samples were measured by SIMS depth profiling. The dependence of diffusion rates on temperature can be described by the following Arrhenius equations (diffusion coefficients in m²/s): % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0d % Xdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9 % pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca % qabeaadaabauaaaOqaauaabeqaeeaaaaqaaiGbcYgaSjabc+gaVjab % cEgaNnaaBaaaleaacqaIXaqmcqaIWaamaeqaaOGaemiraq0aaSbaaS % qaaiabbMfazjabbkgaIbqabaGccqGH9aqpcqGGOaakcqGHsislcqaI % 3aWncqGGUaGlcqaI3aWncqaIZaWmcqGHXcqScqaIWaamcqGGUaGlcq % aI5aqocqaI3aWncqGGPaqkcqGHsisldaqadaqaaiabiodaZiabisda % 0iabiodaZiabgglaXkabiodaZiabicdaWiaaysW7cqqGRbWAcqqGkb % GscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2aaWbaaSqabeaacqqGTaql % cqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUaGlcqaIZaWmcqaIWaamcq % aIZaWmcqWGsbGucqWGubavaiaawIcacaGLPaaaaeaacyGGSbaBcqGG % VbWBcqGGNbWzdaWgaaWcbaGaeGymaeJaeGimaadabeaakiabdseaen % aaBaaaleaacqqGebarcqqG5bqEaeqaaOGaeyypa0JaeiikaGIaeyOe % I0IaeGyoaKJaeiOla4IaeGimaaJaeGinaqJaeyySaeRaeGimaaJaei % Ola4IaeGyoaKJaeG4naCJaeiykaKIaeyOeI0YaaeWaaeaacqaIZaWm % cqaIWaamcqaIYaGmcqGHXcqScqaIZaWmcqaIWaamcaaMe8Uaee4AaS % MaeeOsaOKaaGjbVlabb2gaTjabb+gaVjabbYgaSnaaCaaaleqabaGa % eeyla0IaeeymaedaaOGaei4la8IaeGOmaiJaeiOla4IaeG4mamJaeG % imaaJaeG4mamJaemOuaiLaemivaqfacaGLOaGaayzkaaaabaGagiiB % aWMaei4Ba8Maei4zaC2aaSbaaSqaaiabigdaXiabicdaWaqabaGccq % WGebardaWgaaWcbaGaee4uamLaeeyBa0gabeaakiabg2da9iabcIca % OiabgkHiTiabiMda5iabc6caUiabikdaYiabigdaXiabgglaXkabic % daWiabc6caUiabiMda5iabiEda3iabcMcaPiabgkHiTmaabmaabaGa % eG4mamJaeGimaaJaeGimaaJaeyySaeRaeG4mamJaeGimaaJaaGjbVl % abbUgaRjabbQeakjaaysW7cqqGTbqBcqqGVbWBcqqGSbaBdaahaaWc % beqaaiabb2caTiabbgdaXaaakiabc+caViabikdaYiabc6caUiabio % daZiabicdaWiabiodaZiabdkfasjabdsfaubGaayjkaiaawMcaaaqa % aiGbcYgaSjabc+gaVjabcEgaNnaaBaaaleaacqaIXaqmcqaIWaamae % qaaOGaemiraq0aaSbaaSqaaiabboeadjabbwgaLbqabaGccqGH9aqp % cqGGOaakcqGHsislcqaI5aqocqGGUaGlcqaI3aWncqaI0aancqGHXc % qScqaIYaGmcqGGUaGlcqaI4aaocqaI0aancqGGPaqkcqGHsisldaqa % daqaaiabikdaYiabiIda4iabisda0iabgglaXkabiMda5iabigdaXi % aaysW7cqqGRbWAcqqGkbGscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2a % aWbaaSqabeaacqqGTaqlcqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUa % GlcqaIZaWmcqaIWaamcqaIZaWmcqWGsbGucqWGubavaiaawIcacaGL % Paaaaaaaaa!0C76!

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     

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.     

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.     

Heat capacity and thermodynamic functions of xenotime YPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of xenotime YPO₄(c) was measured by adiabatic calorimetry at 4.78–348.07 K. Our experimental and literature data on H ⁰(T)-H ⁰(298.15 K) of Y orthophosphate were utilized to derive the C _p ⁰(T) function of xenotime at 0–1600 K, which was then used to calculate the values of thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. These functions assume the following values at 298.15 K: C _p ⁰ (298.15 K) = 99.27 ± 0.02 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 93.86 ± 0.08 J K⁻¹ mol⁻¹, H ⁰(298.15 K) − H ⁰(0) = 15.944 ± 0.005 kJ mol⁻¹, Φ⁰(298.15 K) = 40.38 ± 0.08 J K⁻¹ mol⁻¹. The value of the free energy of formation Δ _f G ⁰(YPO₄, 298.15 K) is −1867.9 ± 1.7 kJ mol⁻¹.     

Heat capacity and thermodynamic functions of pretulite ScPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of synthetic pretulite ScPO₄(c) was measured by adiabatic calorimetry within a temperature range of 12.13–345.31 K, and the temperature dependence of the pretulite heat capacity at 0–1600 K was derived from experimental and literature data on H ⁰(T)-H ⁰(298.15 K) for Sc orthophosphate. This dependence was used to calculate the values of the following thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. They have the following values at 298.15 K: C _p ⁰ (298.15 K) = 97.45 ± 0.06 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 84.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)-H ⁰(0) = 14.934 ± 0.016 kJ mol⁻¹, and Φ ⁰(298.15 K) = 34.73 ± 0.19 J K⁻¹mol⁻¹. The enthalpy of formation Δ _f H ⁰(ScPO₄, 298.15 K) = − 1893.6 ± 8.4 kJ mol⁻¹.     

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.     

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).     

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).     

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.     

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     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

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     

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     

Tracing magma mixing in granite genesis: in situ U–Pb dating and Hf-isotope analysis of zircons

In situ zircon U–Pb and Hf-isotopic data have been determined for mafic microgranular enclaves and host granitoids from the Early Cretaceous Gudaoling batholith in the Liaodong Peninsula, NE China, in order to constrain the sources and petrogenesis of granites. The zircon U–Pb age of the enclaves (120 ± 1 Ma) is identical to that of the host monzogranite (120 ± 1 Ma), establishing that the mafic and felsic magmas were coeval. The Hf isotopic composition of the enclaves [ε _Hf(t) = +4.5 to −6.2] is distinct from the host monzogranite [ε _Hf(t) = −15.1 to −25.4], indicating that both depleted mantle and crustal sources contributed to their origin. The depleted mantle component was not previously revealed by geochemical and Nd and Sr isotopic studies, showing that zircon Hf isotopic data can be a powerful geochemical tracer with the potential to provide unique petrogenetic information. Some wall-rock contamination is indicated by inherited zircons with considerably older U–Pb ages and low initial Hf isotopic compositions. Hafnium isotopic variations in Early Cretaceous zircons rule-out simple crystal–liquid fractionation or restite unmixing as the major genetic link between enclaves and host rocks. Instead, mixing of mantle-derived mafic magmas with crustal-derived felsic magmas, coupled with assimilation of wall rocks, is compatible with the data. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Early Permian plutons from the northern North China Block: constraints on continental arc evolution and convergent margin magmatism related to the Central Asian Orogenic Belt

Recent zircon dating identified several late Carboniferous to early Permian hornblende gabbro–diorite–quartz diorite–granodiorite–tonalite–granite plutons in lithological assemblages at the northern margin of the North China Block (NCB) that were previously regarded as Archaean to Palaeoproterozoic. Our geochronological results indicate that emplacement of these plutons was a continuous process during the late Carboniferous to early Permian, from 324 ± 6 to 274 ± 6 Ma, and lasted for at least 50 Ma. In this paper, the early Permian components with compositions from gabbro to granite within the intrusive complex were studied. The early Permian plutons exhibit calc-alkaline or high-K calc-alkaline, metaluminous geochemical features and highly variable SiO₂ contents. They have no significant Eu anomaly in their REE patterns, and in primitive-mantle-normalized spidergrams they display depletion in Th, U, Nb, Ta, P and Ti, and enrichment in Ba, K, Pb and Sr. The granitoid bodies within these plutons display I-type and adakitic geochemical signatures. The early Permian rocks exhibit low whole-rock initial ⁸⁷Sr/⁸⁶Sr ratios from 0.70520 to 0.70615 and have negative whole-rock ε _Nd(t) values ranging from −17.4 to −9.3 and zircon ε _Hf(t) values of −23.2 to −10.5. The gabbros exhibit higher ε _Nd(t) values from −11.1 to −9.3 and ε _Hf(t) values from −16.5 to −10.5, and one granodiorite exhibits an even lower ε _Nd(t) value of −17.4 and zircon ε _Hf(t) values of −23.2 to −15.1. Geochemical, Sr–Nd and in situ zircon Hf isotopic compositions suggest that the hornblende gabbros were derived from a metasomatized lithospheric mantle, and the diorite and quartz diorite were generated from a gabbroic magma by fractional crystallization, coupled with differential assimilation of ancient lower crustal material. The granodiorite was likely derived from partial melting of ancient lower crust with involvement of some mantle components. Involvement of both lithospheric mantle and ancient lower crust in the generation of the early Permian plutons indicates strong crust–mantle interaction in the northern NCB. Petrological associations as well as geochemical and Sr–Nd–Hf isotopic results show that the early Permian plutons were emplaced along an Andean-type active continental margin during southward subduction of the Palaeo-Asian oceanic plate beneath the NCB. Integration of our results with previously published data for late Carboniferous and late Permian to middle Triassic intrusions suggests that the continental arc on the northern margin of the NCB existed for at least 50 Ma during the late Palaeozoic, and final amalgamation of the Mongolian arc terranes with the northern NCB likely occurred during a period from ~270 to ~250 Ma, i.e, in the late Permian to earliest Triassic.     

Point defects and cation tracer diffusion in (Ti<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Fe<Subscript><Emphasis Type="Italic">1−x</Emphasis></Subscript>)<Subscript>3−δ</Subscript>O<Subscript>4</Subscript>. II. Cation tracer diffusion

 Cation tracer diffusion coefficients, D_Me ^*, for Me=Fe, Mn, Co and Ti, were measured using radioactive isotopes in the spinel solid solution (Ti _x Fe _1−x )_3−δO₄ as a function of the oxygen activity. Experiments were performed at different cationic compositions (x=0, 0.1, 0.2 and 0.3) at 1100, 1200, 1300 and 1400 °C. The oxygen activity dependence of all data for D_Me ^* at constant temperature and cationic composition can be described by equations of the type D_Me ^*=D^∘ _Me[V]. C_V·a _O2 ^2/3+D_Me[I] ^∘·a _O2 ^−2/3·D_Me[V] ^∘ and D_Me[I] ^∘ are constants and C_V is a factor of the order of unity which decreases with increasing δ. All log D_Me ^* vs. loga _O2 curves obtained for different values of x and for different temperatures go through a minimum due to a change in the type of point defects dominating the cation diffusion with oxygen activity. Cation vacancies prevail for the cation diffusion at high oxygen activities while cation interstitials become dominant at low oxygen activities. At constant values of x, D_Me[V] ^∘ decreases with increasing temperature while D_Me[I] ^∘ increases.