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     

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.     

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.     

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     

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     

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’}.     

Compression studies of gibbsite and its high-pressure polymorph

Various X-ray diffraction methods have been applied to study the compression behavior of gibbsite, Al(OH)₃, in diamond cells at room temperature. A phase transformation was found to take place above 3 GPa where gibbsite started to convert to its high-pressure polymorph. The high-pressure (HP) phase is quenchable and coexists with gibbsite at the ambient conditions after being unloaded. This HP phase was identified as nordstrandite based on the diffraction patterns obtained at room pressure by angle dispersive and energy dispersive methods. On the basis of this structural interpretation, the bulk modulus of the two polymorphs, i.e., gibbsite and nordstrandite, could be determined as 85 ± 5 and 70 ± 5 GPa, respectively, by fitting a Birch-Murnaghan equation to the compression data, assuming their K_o ^′ as 4. Molar volume cross-over occurs at 2 GPa, above which the molar volume of nordstrandite is smaller than that of gibbsite. The differences in the molar volume and structure between the two polymorphs are not significant, which accounts for the irreversibility of the phase transition. In gibbsite, the axial compressibility behaves as c/c _o > a/a _o > b/b _o. This is due to the fact that the dioctahedral sheets along the c-axis are held by the relatively weak hydrogen bonding, which results in the greater compressibility along this direction. In nord- strandite, the axial compressibility is b/b _o > c/c _o > a/a _o, which can also be interpreted as resulting from the the existence of hydrogen bonds along the b-axis. Received: 28 September 1998 / Revised, accepted: 22 December 1998     

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

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

Thermodynamics of hydration of Na- and K-clinoptilolite to 300 °C

The hydration state of Na- and K-exchanged clinoptilolite from Castle Creek (Idaho, U.S.A.) has been measured by a pressure titration method to 300 °C and P _H2O<30 bars. The water content of clinoptilolite can be predicted as a function of water activity and temperature with the equation: a _H2O = [exp[[−ΔH _h ^∘/nRT] + [ΔS _h ^∘/nR] − 1/nRT· [W₁ X _h + W₂ X _{h 2}]− ln(X _a/X _h)]]⁻¹ where T is degrees in Kelvin, ΔH _h ^∘ is the standard molal enthalpy of hydration, ΔS _h ^∘ is the entropy of hydration, X _h and X _a are, respectively, the mole fractions of the hydrous and anhydrous components of the solid solution, W ₁ and W ₂ are interaction parameters, n is the maximum number of moles of H₂O per formula unit (based on 12 oxygens), and R is the gas constant. This equation can be used to locate clinoptilolite-H₂O isohydrons in a _H2O-T space below the liquid-vapor equilibrium curve of water. The standard molal Gibbs free energy of hydration is −47.62 ± 5.52 kJ/mol H₂O and −5.40 ± 2.71 kJ/mol H₂O for the Na- and K-clinoptilolite, respectively. These standard-state thermodynamic properties of clinoptilolite hydration are in good agreement with previous data at low H₂O pressures. The experiments indicate that clinoptilolite progressively dehydrates with increasing temperature at pressures along the liquid-vapor equilibrium curve. Kinetic data above 150 °C show that clinoptilolite dehydration and hydration reactions are fast and reversible and that steady-state hydration states are attained in minutes. Received: 19 June 1998 / Revision, accepted 14 December 1998     

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     

An experimental investigation on diffusion of water in haplogranitic melts

  The diffusivity of water has been investigated for a haplogranitic melt of anhydrous composition Qz₂₈Ab₃₈Or₃₄ (in wt %) at temperatures of 800–1200°C and at pressures of 0.5–5.0 kbar using the diffusion couple technique. Water contents of the starting glass pairs varied between 0 and 9 wt %. Concentration-distance profiles for the different water species (molecular water and hydroxyl groups) were determined by near-infrared microspectroscopy. Because the water speciation of the melt is not quenchable (Nowak 1995; Nowak and Behrens 1995; Shen and Keppler 1995), the diffusivities of the individual species can not be evaluated directly from these profiles. Therefore, apparent chemical diffusion coefficients of water (D _water) were determined from the total water profiles using a modified Boltzmann-Matano analysis. The diffusivity of water increases linearly with water content <3 wt % but exponentially at higher water contents. The activation energy decreases from 64 ± 10 kJ/mole for 0.5 wt % water to 46 ± 5 kJ/mole for 4 wt % water but remains constant at higher water contents. A small but systematic decrease of D _water with pressure indicates an average activation volume of about 9 cm³/mole. The diffusivity (in cm²/s) can be calculated for given water content (in wt %), T (in K) and P (in kbar) by

Enthalpy of formation of CaSi2O5, a quenched high-pressure phase with pentacoordinate silicon

 The monoclinic titanite-like high-pressure form of calcium disilicate has been synthesized and quenched to ambient conditions to form the triclinic low-pressure phase containing silicon in four-, five- and sixfold coordination. The enthalpy of formation of the quench product has been measured by high-temperature oxide melt calorimetry. The value obtained from samples from a series of several synthesis experiments is ΔH _f = (−26.32 ± 4.27) kJ mol⁻¹ for the formation from the component oxides, or ΔH _f  = (−2482.81 ± 4.59) kJ mol⁻¹ for the formation from the elements. The result is identical within experimental error to available estimates, although the previously predicted energy difference between the monoclinic and triclinic phases could not be verified. Received: 16 February 2000 / Accepted: 14 July 2000     

Temperature evolution between 50 K and 320 K of the thermal expansion tensor of gypsum derived from neutron powder diffraction data

The unit cell parameters, extracted from Rietveld analysis of neutron powder diffraction data collected between 4.2 K and 320 K, have been used to calculate the temperature evolution of the thermal expansion tensor for gypsum for 50 ≤ T ≤ 320 K. At 300 K the magnitudes of the principal axes are α ₁₁  = 1.2(6) × 10⁻⁶ K⁻¹, α ₂₂  = 36.82(1) × 10⁻⁶ K⁻¹ and α ₃₃  = 25.1(5) × 10⁻⁶ K⁻¹. The maximum axis, α ₂₂ , is parallel to b, and using Institution of Radio Engineers (IRE) convention for the tensor orthonormal basis, the axes α ₁₁ and α ₃₃ have directions equal to (−0.979, 0, 0.201) and (0.201, 0, 0.979) respectively. The orientation and temperature dependent behaviour of the thermal expansion tensor is related to the crystal structure in the I2/a setting. Received 12 February 1998 / Revised, accepted 19 October 1998     

Behavior of epidote at high pressure and high temperature: a powder diffraction study up to 10 GPa and 1,200 K

The thermo-elastic behavior of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 458.8(1)ų, K _T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K _T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a ₀ = 8.8877(7) Å, K _T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b ₀ = 5.6271(7) Å, K _T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c ₀ = 10.1527(7) Å, K _T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K _T0(a):K _T0(b):K _T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, β_P(°) = β_P0 −0.0286(9)P +0.00134(9)P ² (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α₀ + α₁ T ^−1/2. The refined parameters for epidote are: α₀ = 5.1(2) × 10⁻⁵ K⁻¹ and α₁ = −5.1(6) × 10⁻⁴ K^1/2 for the unit-cell volume, α₀(a) = 1.21(7) × 10⁻⁵ K⁻¹ and α₁(a) = −1.2(2) × 10⁻⁴ K^1/2 for the a-axis, α₀(b) = 1.88(7) × 10⁻⁵ K⁻¹ and α₁(b) = −1.7(2) × 10⁻⁴ K^1/2 for the b-axis, and α₀(c) = 2.14(9) × 10⁻⁵ K⁻¹ and α₁(c) = −2.0(2) × 10⁻⁴ K^1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α₀(a): α₀(b): α₀(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with β_T(°) = β_T0 + 2.5(1) × 10⁻⁴ T + 1.3(7) × 10⁻⁸ T ². A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.     

Structural thermal behavior of paragonite and its dehydroxylate: a high-temperature single-crystal study

 The lattice constants of paragonite-2M₁, NaAl₂(AlSi₃)O₁₀(OH)₂, were determined to 800 °C by the single-crystal diffraction method. Mean thermal expansion coefficients, in the range 25–600 °C, were: α_a = 1.51(8) × 10⁻⁵, α_b = 1.94(6) × 10⁻⁵, α_c = 2.15(7) ×  10⁻⁵ °C⁻¹, and α_V = 5.9(2) × 10⁻⁵ °C⁻¹. At T higher than 600 °C, cell parameters showed a change in expansion rate due to a dehydroxylation process. The structural refinements of natural paragonite, carried out at 25, 210, 450 and 600 °C, before dehydroxylation, showed that the larger thermal expansion along the c parameter was mainly due to interlayer thickness dilatation. In the 25–600 °C range, Si,Al tetrahedra remained quite unchanged, whereas the other polyhedra expanded linearly with expansion rate proportional to their volume. The polyhedron around the interlayer cation Na became more regular with temperature. Tetrahedral rotation angle α changed from 16.2 to 12.9°. The structure of the new phase, nominally NaAl₂ (AlSi₃)O₁₁, obtained as a consequence of dehydroxylation, had a cell volume 4.2% larger than that of paragonite. It was refined at room temperature and its expansion coefficients determined in the range 25–800 °C. The most significant structural difference from paragonite was the presence of Al in fivefold coordination, according to a distorted trigonal bipyramid. Results confirm the structural effects of the dehydration mechanism of micas and dioctahedral 2:1 layer silicates. By combining thermal expansion and compressibility data, the following approximate equation of state in the PTV space was obtained for paragonite: V/V ₀ = 1 + 5.9(2) × 10⁻⁵ T(°C) − 0.00153(4) P(kbar). Received: 12 July 1999 / Revised, accepted: 7 December 1999     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Kristiansenite, a new calcium–scandium–tin sorosilicate from granite pegmatite in Tørdal, Telemark, Norway

Summary Kristiansenite occurs as a late hydrothermal mineral in vugs in an amazonite pegmatite at Heftetjern, T?rdal, Telemark, Norway. Tapering crystals, rarely up to 2 mm long, are colourless, white, or slightly yellowish. The mineral has the ideal composition Ca₂ScSn(Si₂O₇)(Si₂O₆OH) and is triclinic C1 with cell parameters a = 10.028(1), b = 8.408(1), c = 13.339(2) ?, α = 90.01(1), β = 109.10(1), γ = 90.00(1)°, V = 1062.7(3) ?³ (Z = 4). It has a monoclinic cell within ∼ 0.1 ? and is polysynthetically twinned on {010} by metric merohedry. The strongest reflections in the X-ray powder pattern are [d in ?, (I _obs), (hkl)]: 5.18 (53) (1–11), 3.146 (100) (004), 3.089 (63) (−222), 2.901 (19) (221), 2.595 (34) (222), 2.142 (17) (−3–31). The Mohs’ hardness is 5?–6; D_calc. = 3.64 g/cm³; only a mean refractive index of 1.74 could be measured. Scandium enrichment in the Heftetjern pegmatite and the crystal chemistry of scandium are briefly discussed. Received April 30, 2001; accepted July 28, 2001     

Strength of single-crystal orthopyroxene under lithospheric conditions

Creep strength of oriented orthopyroxene single crystals was investigated via shear deformation experiments under lithospheric conditions [P (pressure) = 1.3 GPa and T (temperature) = 973–1,373 K]. For the A-orientation (shear direction [001] on (100) plane), the samples have transformed completely to clinoenstatite and much of the deformation occurred after transformation. In contrast, for the B-orientation (shear direction [001] on (010) plane), samples remained orthoenstatite and deformation occurred through dislocation motion in orthoenstatite. The strength of orthopyroxene with these orientations is smaller than for olivine aggregates under all experimental conditions. Flow of the B-orientation samples is described by a power-law, and the pre-exponential constant, the apparent activation energy, and the stress exponent are determined to be A = 10^−9.5 s⁻¹·MPa^−4.2, Q = 114 kJ/mol and n = 4.2. However, for the A-orientation, the results cannot be fit by a single flow law and we obtained the following: A = 10^8.9 s⁻¹·MPa^−3.0, Q = 459 kJ/mol and n = 3.0 at high temperatures (≥1,173 K), and A = 10^−27.4 s⁻¹·MPa^−14.3, Q = 296 kJ/mol and n = 14.3 at low temperatures (<1,173 K). The stress exponent for the low-temperature regime is high, suggesting that deformation involves some processes where the activation energy decreases with stress such as the Peierls mechanism. Our study shows that orthopyroxene with these orientations is significantly weaker than olivine under the lithospheric conditions suggesting that orthopyroxene may reduce the strength of the lithosphere, although the extent to which orthopyroxene weakens the lithosphere depends on its orientation and connectivity.     

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.     

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).