Unit-cell dimensions and tetrahedral-site ordering in synthetic gallium albite (NaGaSi3O8)

The tetrahedral-site order-disorder transformation in gallium albite (NaGaSi₃O₈) has been investigated using Rietveld structure refinement. Study of gallium-substituted albite (in contrast to pure albite [NaAlSi₃O₈]) is facilitated by a relatively rapid order-disorder transformation and the large difference in X-ray scattering efficiencies of gallium and silicon. High albite-structure NaGaSi₃O₈, grown in a Na₂WO₄ flux, was ordered by hydrothermal annealing below 820° C and dry annealing above 820° C, to avoid melting, using a load pressure of approximately 1 kbar. Equilibration of the order-disorder reaction has been verified by three independent reversals of ordering. The transformation between low gallium albite and high gallium albite occurs over the temperature range 890° C 970° C. The gallium content of the T ₁o site increases continuously with decreasing temperature. The gallium contents of the T ₁m and T ₂m sites decrease smoothly with increasing ordering while the gallium content of the T ₂o site decreases, then increases and then decreases again with decreasing temperature. Unit-cell parameters and the triclinic obliquity vary throughout the order-disorder transformation and undergo abrupt changes at 913±3° C and 937±3° C. These abrupt changes correlate with changes in the gallium content of the T ₂o site, the X and Z ordering parameters and the configurational entropy. The order-disorder transformation in gallium-aluminum albite (NaGa_0.5Al_0.5Si₃O₈) occurs in the temperature range 765° C-850° C, at a temperature intermediate to the transformation in albite (50% order at about 680±20° C) and gallium albite.     

Electronic absorption spectra of Cr3+ ions in natural clinopyroxenes

The polarized (E‖a′, E‖b and E‖c) electronic absorption spectra of five natural chromium-containing clinopyroxenes with compositions close to chromdiopside, omphacite, ureyite-jadeite (12.8% Cr₂O₃), jadeite, and spodumene (hiddenite) were studied. The polarization dependence of the intensities of the Cr³⁺ bands in the clinopyroxene spectra cannot be explained by the selection rules for the point groups C ₂ or C _2v but can be accounted for satisfactorily with the help of the higher order pseudosymmetry model, i.e. with selection rules for the point symmetry group C _3v. The trigonal axis of the pseudosymmetry crystal field forms an angle of 20.5° with the crystallographic direction c in the (010) plane. D _q increases from diopside (1542 cm^?1) through omphacite (1552 cm^?1), jadeite (1574 cm^?1) to spodumene (1592 cm^?1). The parameter B which is a measure of covalency for Cr³⁺-O bonds at M1 sites in clinopyroxene depends on the Cr³⁺ concentration and the cations at M2 sites.     

High temperature creep of single crystal gadolinium gallium garnet

High temperature creep of single crystal gadolinium gallium garnet (GGG) was studied in the temperature range of 1723–1853 K (0.86–0.94 T_m, T_m: melting temperature) and strain rate from 9 · 10^?7 s^?1 to 2 · 10^?5 s^?1. The compression tests were made along the 〈100〉 and 〈111〉 orientations. We have performed both constant strain-rate and stress-dip tests. For the 〈100〉 orientation, deformation occurs via the 〈111〉 slip systems. For the 〈111〉 orientation, both the 〈100〉 {010} and the 〈111〉 slip systems can be activated. GGG garnet is very strong under these conditions: σ/μ=(1–3)×10^?3 (σ: creep strength, μ: shear modulus). The creep behavior is characterized by a power law with stress exponent n=2.9–3.3 and high activation energies E^*=612–743 kJ/mol (E^*～45×RT_m, at zero stress which decrease with the increase of stress). Stress-dip tests suggest a small internal stress (σ_i/σ～0.62; σ_i: internal stress, σ: applied stress) compared to other materials. These results suggest that the high creep strength of GGG is mainly due to difficulty of dislocation glide rather than dislocation climb.     

A method for calculating fractional s-character for bonds of tetrahedral oxyanions in crystals

A method for calculating fractional s-character, f _s , for TO bonds has been devised to apply to TO₄ tetrahedral oxyanions in crystals. These f _s -values rank bond lengths with the better correlations obtained for T atoms associated with larger bond strengths and larger electronegativities. As a simple formula, it is found that 2cot²〈?〉₃ does a good job of estimating f _s where 〈?〉₃ is the triple angle average of the three angles common to a given bond.     

The relationship between apparent equilibrium temperature and closure temperature with application to oxygen isotope geospeedometry

Oxygen isotope fractionation between coexisting minerals in slowly cooled rocks conveys information about their cooling history. By using the fast grain boundary （FGB） model to simulate closed-system diffusive ex- change of oxygen isotopes between coexisting minerals, I show that the apparent equilibrium temperatures （Tae） by the mineral pair with the largest isotopic fractionation （PLIF） always lies between the closure temperatures （To） of those two minerals. Therefore, when the rate of oxygen diffusion and hence Tc for the PLIF chance to be comparable （such as in the case of quartz and magnetite）, Tae will serve as a good approximation of To regardless of variation in mineral proportions. The specialty of the PLIF in constraining Tac within their Tc range can be generalized to other stable isotope systems and element partitioning. By approximating Tc with Tac and inverting Dodson＇s equation, the cooling rate of plutonic or metamorphic rocks can be inferred.     

The crystal and magnetic structure of Li-aegirine LiFe3+Si2O6: a temperature-dependent study

Single crystals of Li-aegirine LiFe³⁺Si₂O₆ were synthesized at 1573?K and 3?GPa, and a polycrystalline sample suitable for neutron diffraction was produced by ceramic sintering at 1223?K. LiFe³⁺Si₂O₆ is monoclinic, space group C2/c, a=9.6641(2)?Å, b= 8.6612(3)?Å, c=5.2924(2)?Å, β=110.12(1)^° at 300?K as refined from powder neutron data. At 229?K Li-aegirine undergoes a phase transition from C2/c to P2₁ /c. This is indicated by strong discontinuities in the temperature variation of the lattice parameters, especially for the monoclinic angle β and by the appearance of Bragg reflections (hkl) with h+k≠2n. In the low-temperature form two non-equivalent Si-sites with 〈SiA–O〉=1.622?Å and 〈SiB–O〉=1.624?Å at 100?K are present. The bridging angles of the SiO₄ tetrahedra O3–O3–O3 are 192.55(8)° and 160.02(9)° at 100?K in the two independent tetrahedral chains in space group P2₁ /c, whereas it is 180.83(9)° at 300?K in the high-temperature C2/c phase, i.e. the chains are nearly fully expanded. Upon the phase transition the Li-coordination changes from six to five. At 100?K four Li–O bond lengths lie within 2.072(4)–2.172(3)?Å, the fifth Li–O bond length is 2.356(4)?Å, whereas the Li–O3?A bond lengths amount to 2.796(4)?Å. From ⁵⁷Fe Mössbauer spectroscopic measurements between 80 and 500?K the structural phase transition is characterized by a small discontinuity of the quadrupole splitting. Temperature-dependent neutron powder diffraction experiments show first occurrence of magnetic reflections at 16.5?K in good agreement with the point of inflection in the temperature-dependent magnetization of LiFe³⁺Si₂O₆. Distinct preordering phenomena can be observed up to 35?K. At the magnetic phase transition the unit cell parameters exhibit a pronounced magneto-striction of the lattice. Below T _N Li-aegirine shows a collinear antiferromagnetic structure. From our neutron powder diffraction experiments we extract a collinear antiferromagnetic spin arrangement within the a–c plane.     

The influence of multiple diffraction on the space group determination of orthopyroxene,spodumene, low omphacite and pigeonite

Forbidden reflections of some pyroxenes described as having a lower symmetry than Pbca or C2/c have been examined, mainly using the detailed ψ-scanning method of the four-circle automated diffractometer. All reflections violating the systematic absences of Pbca orthopyroxene, C2/c spodumene, P2/n omphacite and P2₁/c pigeonite were found to be due to the Umweganregung process of multiple diffraction; the Umweganregung peaks observed for the ψ azimuth were indexed in terms of a four-circle geometry. Thus, the space groups of orthopyroxene, α spodumene, low omphacite and low pigeonite were confirmed to be Pbca, C2/c, P2/n and P2₁/c, respectively.     

Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO2 and AlPO4 from 31P, 27Al and 29Si NMR spectroscopy to 770 K

Nuclear magnetic resonance spectroscopic data are presented for the cristobalite polymorphs of AlPO₄ and SiO₂ from RT to 770 K, through their respective α-β transitions. The nuclear magnetic resonance (NMR) data include chemical shifts for ³¹P, ²⁷Al, and ²⁹Si, ²⁷Al quadrupole coupling parameters, and ³¹P and ²⁷Al spin-lattice relaxation rates. Also presented are electron diffraction patterns of β-cristobalite AlPO₄ that show diffuse scattering similar to that reported previously for SiO₂. For the α-phases of both AlPO₄ and SiO₂, the chemical shifts decrease approximately linearly with increasing temperature from RT to T_c and discontinuously by -2 to -3 ppm from α to β. This result is consistent with a small, continuous increase in the mean T-O-T angle (〈θ〉) of the α-phases with increasing T and an increase of 〈θ〉 by about 4° across the α-β transition for both cristobalite and its AlPO₄ analogue. Based on the ²⁹Si chemical shifts, the mean Si-O-Si angle for β-cristobalite is 152.7±1° near T_c. For AlPO₄-cristobalite, the ²⁷Al nuclear quadrupole coupling constant (C_Q) decreases approximately linearly from 1.2 MHz at RT to 0.94 MHz near T_c (493±10 K). At the α-β transition the ²⁷Al C_Q approaches zero, in agreement with the cubic average structure observed by diffraction. The satellite transitions retain a small frequency distribution above the α-β transition from electric field gradients attributed to defects. The short-range cubic symmetry of the Al-site and non-linear Al-O-P angle support a dynamically disordered model of the β-cristobalite structure. Complete averaging of the ²⁷Al quadrupole coupling in the β-phase indicates that the lifetime of any short-range ordered domains must be shorter than about 1 μs.     

Eclogites from the south Tianshan, NW China: petrological characteristic and calculated mineral equilibria in the Na2O–CaO–FeO–MgO–Al2O3–SiO2–H2O system

Eclogites from the south Tianshan, NW China are grouped into two types: glaucophane and hornblende eclogites, composed, respectively, of garnet + omphacite + glaucophane + paragonite + epidote + quartz and garnet + omphacite + hornblende (sensu lato) + paragonite + epidote + quartz, plus accessory rutile and ilmenite. These eclogites are diverse both in mineral composition and texture not only between the two types but also among the different selected samples within the glaucophane eclogite. Using thermocalc 3.1 and recent models of activity–composition relation for minerals, a P–T projection and a series of P–T pseudosections for specific samples of eclogite have been calculated in the system Na₂O–CaO–FeO–MgO–Al₂O₃–SiO₂–H₂O (NCFMASH) with quartz and water taken to be in excess. On the basis of these phase diagrams, the phase relations and P–T conditions are well delineated. The three selected samples of glaucophane eclogite AK05, AK11 and AK17 are estimated to have peak P–T conditions, respectively, of 540–550 °C at c. 16 kbar, c. 560 °C at 15–17 kbar and c. 580 °C at 15–19 kbar, and two samples of hornblende eclogite AK10 and AK30 of 610–630 °C and 17–18 kbar. Together with H₂O‐content contours in the related P–T pseudosections and textural relations, both types of eclogite are inferred to show clockwise P–T paths, with the hornblende eclogite being transformed from the glaucophane eclogite assemblage dominantly through increasing temperature.     

Paraelectric-antiferroelectric phase transition in titanite,CaTiSiO5

The paraelectric to antiferroelectric phase transition in titanite at ～500 K involves a displacement of the titanium atom from the center of the [TiO₆] octahedron in the paraelectric phase (A2/a) to an off-center position in the antiferroelectric (P2 ₁/a) phase. We have carried out a detailed single crystal high temperature x-ray diffraction study of the phase transition including structure refinements at 294, 350, 400, 430, 440, 450, 500, 600, and 700 K. The unit cell dimensions show a pronounced hysteresis effect in the 450–500 K range on heating and cooling during the first cycle along with a reduction of the transition temperature, T _c from 495 ± 5 K on heating to 445 ± 5 K on cooling. The hysteresis effect disappears on further heating and the superstructure reflections show residual intensities above T _c (445 K). An order parameter treatment of the phase transition is presented in terms of Landau theory and induced representation theory. The Ti-displacements parallel and antiparallel to a are taken as the primary order parameter η, which transforms as the Y ₂ ⁺ representation. A coupling of Y ₂ ⁺ with T ₁ ⁺ results in the linear-quadratic coupling of the spontaneous strain components, ? _ij with η. The Ti-displacements are coupled linearly to the Cadisplacements. Both sets of displacements predicted from induced representation theory are observed experimentally. The phase transition is initially driven by the soft mode at the zone boundary point Y ₂ ⁺ ; near T _c critical fluctuations set in and an order-disorder mechanism finally drives the phase transition, whereby parallel and antiparallel Ti-displacements related by [0, 1/2, 1/2] in adjacent domains are dynamically interchanged. Immediately above T _c , the high temperature (A2/a) phase is a statistical average of small dynamic antiphase domains of the low temperature (P2 ₁/a) phase. Vacancies and defects pinning the domain boundaries may drastically alter the transition behavior and affect the domain mobility.     

Al,Ge cation ordering in BaAl2Ge2O8-feldspar: monodomain ordering kinetics

The kinetics of monodomain order-disorder processes in monoclinic (I2/c) BaAl₂Ge₂O₈-feldspar have been investigated by X-ray powder diffraction, Hard Mode IR Spectroscopy, and TEM darkfield imaging on quenched samples. Compared to the behaviour predicted by the TDGL approximation ordering kinetics observed at low temperatures slow down significantly when equilibrium is approached. Such a delay is not observed in disordering experiments starting from essentially ordered cation distributions. The deviation from TDGL behaviour is interpreted in terms of partial order parameter conservation in a non-uniformly ordered phase. Modifications to the uniform TDGL rate equation are tested against the available data. An activation energy of 352 ± 28 kJ/mol is obtained for Al,Ge ordering. The mixing coefficient ξ_c ²/ξ², which describes the degree of order parameter conservation, is obtained as a function of temperature. While this coefficient vanishes in the vicinity of the transformation temperature T _tr, it saturates towards a level of ξ_c ²/ξ²≈0.4 for T→0. ξ _c ²/ξ² determines the kinetic stability of ordered clusters quenched from T≈T _tr. Received: 21 April 1999 / Revised, accepted: 19 July 1999     

Dynamic character of the primitive to body-centered phase transition in anorthite

We show from elastic neutron diffraction data that anorthite CaAl₂Si₂O₈ (An₁₀₀) undergoes a primitive to body-centered phase transition at T _c =237±1°C. The transition is reversible, and T _c is well defined. Our measurements demonstrate that the I-lattice at the high temperature phase applies to all structural elements; in other words, the time-averaged lattice is exactly body-centered and not just in the space average of An₁₀₀, as concluded earlier by other authors.     

On the relationship between refractive index and density for SiO2 polymorphs

The Gladstone-Dale law (specific refraction) and the Drude law (molecular refraction) for silica polymorphs, at “sodium light” (λ _D =0.5893 μm), are derived from simple atomic properties of SiO₂ complex (atomic weight, first ionization potential). The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) v ₀ of elementary electron oscillators (in energy units, hv) is identified with the band gap E _G of a solid; on the other hand, this E _G -gap is identified with the single ionization potential \(\tilde U\) of non-free atoms. For \(\tilde U\) =E _G =10.2 eV (energy gap of quartz, see Nitsan and Shankland 1976b) the Gladstone-Dale law, or specific refraction, is (n?1)/ρ=0.208 cm³/g, where n and ρ are the refractive index and the density of medium, respectively. According to empirical data, the average value of the specific refraction of pure SiO₂ polymorphs (except stishovite-high density phase of silica) is (〈n〉?1)/ρ=0.207±0.001 (〈n〉 denotes the mean refractive index of crystal). For stishovite the Drude law (n ²?1)/ρ=0.542 cm³/g is valid under an assumption that the first ionization potential \(\tilde U\) =E _G ≈9 eV; this result is good agreement with the empirical value (〈n〉²?1)/ρ=0.536 cm³/g.     

Sodium trisilicate: A new high-pressure silicate structure (Na2Si[Si2O7])

Crystals of sodium trisilicate (Na₂Si₃O₇) have been grown in the presence of melt at 9 GPa, 1200 °C using the MA6/8 superpress at Edmonton, and the X-ray structure determined at room pressure (R=2.0%). Na₂Si₃O₇ is monoclinic with a=8.922(2) Å, b= 4.8490(5) Å, c=11.567(1) Å, β=102.64(1)° (C2/c), D _x = 3.295 g·cm^-3. Silicon occurs in both tetrahedral and octahedral coordination (^[6]Si∶^[4]Si = l∶2). The SiO₄ tetrahedra form a diorthosilicate [Si₂O₇] group and are linked by the isolated SiO₆ octahedra via shared corners into a framework of 6-membered (^[4]Si-^[4]Si-^[6]Si^[4]Si-^[4] Si-^[6]Si) and 4-membered (^[4]Si-^[6]Si-^[4]Sr-^[6]Si) rings: 〈^[6]Si-O〉=1.789 Å, 〈^[4]Si-O〉= 1.625 Å, ^[4]Si-O-^[4]Si=132.9° and the bridging oxygen is overbonded (s = 2.22). Channels parallel to b-axis and [110] accommodate Na in irregular 6-fold coordination: 〈Na-O〉 = 2.511 Å.     

The 57Fe Mössbauer parameters of pyrite and marcasite with different provenances

Eighteen pyrite and twelve marcasite samples which have different provenances have been investigated to determine the systematics of the influence of mineralogical and geological factors on the ⁵⁷Fe Mössbauer spectra at 298 K. The following results have been obtained: there is no ambiguity in distinguishing single phase pyrite from single phase marcasite by means of ⁵⁷Fe Mössbauer spectroscopy at 298 K. At 298 K the average electric quadrupole splitting, 〈ΔE_Q〉, and average isomer shift, 〈δ〉, with respect to Fe metal, are 0.6110 ± 0.0030 mm s^?1 and 0.313 ± 0.008 mm s^?1, respectively, for the 18 pyrites; 〈ΔE_Q〉 = 0.5030 ± 0.0070 mm s^?1 and 〈δ〉 = 0.2770 ± 0.0020 mm s^?1 for the 12 marcasites. At 77 K, ΔE_Q is 0.624 mm s^?1 for pyrite and 0.508 mm s^?1 for marcasite. In distinguishing pyrites from marcasites, spectra obtained at 77 K are not warranted.The Mössbauer parameters of pyrite and marcasite exhibit appreciable variations, which bear no simple relationship to the geological environment in which they occur but appear to be selectively influenced by impurities, especially arsenic, in the pyrite lattice. Quantitative and qualitative determinations of pyrite/marcasite mechanical mixtures are straightforward at 298 K and 77 K but do require least-squares computer fittings and are limited to accuracies ranging from ±5 to ±15 per cent by uncertainties in the parameter values of the pure phases. The methodology and results of this investigation are directly applicable to coals for which the presence and relative amounts of pyrite and marcasite could be of considerable genetic significance.     

Thermodynamics of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures

The main driving force behind Al/Si ordering in tetrahedral framework aluminosilicates is nearest-neighbour Al/Al avoidance. Computer simulation is used to explore the direct consequences of such Al/Al avoidance. The main result is that the order-disorder transition temperature T _c falls dramatically as the concentration x of Al in the structure is reduced, and if the only interactions are those associated with nearest-neighbour Al/Al avoidance, T _c becomes zero for x less than some critical value x _c , where x _c =0.31 for the feldspar framework and x _c =0.34 for cordierite. Also a large degree of short range order is found above T _c . Both results differ radically from the standard Bragg-Williams model. Plots of entropy and enthalpy of ordering are given as functions of x and T, which may be used to interpret experimental data or for extrapolation into ranges of x and T inaccessible to experiment. Received: 14 May 1997 / Revised, accepted: 2 June 1997     

Ferroelastic phase transition in cryolite,Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism

Cryolite, Na₃AlF₆[ = 2Na⁺(Na_0.5 ⁺Al_0.5 ³⁺)F₃] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF₆] and [AlF₆] octahedra and the cavities are occupied by Na⁺ ions. At 295 K, it is monoclinic (α phase), space group P2 ₁/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)°, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T ₀ ～ 885 K, in contrast to a previous report that it becomes cubic at ～823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T ₀, the coordination number of the Na⁺ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF₆] group and transforms according to the Γ ₄ ⁺ irreducible representation of Immm. Coupled to the [AlF₆] rotation is a second primary order parameter corresponding to the displacement of the Na2⁺ ion in the cavity from its equilibrium position. This order parameter transforms according to the X ₃ ⁺ irreducible representation of Immm. Following Immm → P2 ₁ /n phase transition, four equivalent domains of P2 ₁/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T ₀ indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔS_trans (11.43 JK^?1 mol^?1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK^?1 mol^?1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the ²⁷Al nuclear magnetic resonance (NMR) line-shape above T ₀ (Stebbins et al. 1992).     

Temperature dependence of the polarized electronic absorption spectra of olivines. Part II—Cobalt-containing olivines

Polarized electronic absorption spectra of single crystalline Co₂[SiO₄] and (Co_0.64Mg_0.36)₂[SiO₄] (E|| a (|| Z), E || b (|| X), E || c (|| Y)) have been studied in the temperature range 293 T/K 1273. The three polarized spectra show a total of 15 bands. Five bands are caused by spin-allowed transitions in Co²⁺ ions at M1 sites which appear in all polarization directions. Seven polarization-dependent bands can be ascribed to spin-allowed transitions in Co²⁺ ions at M2 sites and three bands may be assigned to spin-forbidden transitions. The assignment of bands due to Co²⁺ ions at M1 and M2 sites has been made on the basis of transition energies and intensity ratios. Further arguments have been derived from the comparison of spectra of crystals with different cobalt content, from the analysis of the polarization dependence of the spectra, and from the evolution of band intensities with temperature.     

Empirical models relating viscosity and tracer diffusion in magmatic silicate melts

The Adam-Gibbs equations describing relaxation in silicate melts are applied to diffusion of trace components of multicomponent liquids. The Adam-Gibbs theory is used as a starting point to derive an explicit relation between viscosity and diffusion including non-Arrhenian temperature dependence. The general form of the equation is D_iη = A_iexp{Δ(s_cE_i)/TS_c}, where D is diffusivity, η is melt viscosity, T is absolute temperature, Δ(s_cE_i) is the difference between the products of activation energies and local configurational entropies for viscous and diffusive relaxation, A_i is a constant that depends on the characteristics of the diffusing solute particles, and S_c is configurational entropy of the melt. The general equation will be impractical for most predictive purposes due to the paucity of configurational entropy data for silicate melts. Under most magmatic conditions the proposed non-Arrhenian behaviour can be neglected, allowing the general equation to be simplified to a generalized form of the Eyring equation to describe diffusion of solutes that interact weakly with the melt structure: D_iη/T = Q_iexp{ΔE_i/RT}, where Q_i and ΔE_i depend on the characteristics of the solute and the melt structure. If the diffusing solute interacts strongly with the melt structure or is a network-forming cation itself, then ΔE_i = 0, and the relation between viscosity and diffusion has the functional form of the classic Eyring and Stokes-Einstein equations; D_iη/T = Q_i. If the diffusing solute can make diffusive jumps without requiring cooperative rearrangement of the melt structure, the diffusivity is entirely decoupled from melt viscosity and should be Arrhenian, i.e., D_i = Q_iexp{B_i/T}. A dataset of 594 published diffusivities in melts ranging from the system CAS through diopside, basalt, andesite, anhydrous rhyolite, hydrous rhyolite, and peralkaline rhyolite to albite, orthoclase, and jadeite is compared with the model equations. Alkali diffusion is completely decoupled from melt viscosity but is related to melt structure. Network-modifying cations with field strength Z_i²/r between 1 and 10 interact weakly with the melt network and can be modelled with the extended form of the Eyring equation. Diffusivities of cations with high field strength have activation energies essentially equal to that of viscous flow and can be modelled with a simple reciprocal Eyring-type dependence on viscosity. The values of Q_i, ΔE_i and B_i for each cation are different and can be related to the cation charge and radius as well as the composition of the melt through the parameters Z_i²/r, M/O, and Al/(Na + K + H). I present empirical fit parameters to the model equations that permit prediction of cation diffusivities given only charge and radius of the cation and temperature, composition and viscosity of the melt, for the entire range of temperatures accessible to magmas near to or above their liquidus, for magmas ranging in composition from basalt through andesite to hydrous or anhydrous rhyolite. Pressure effects are implicitly accounted for by corrections to melt viscosity. Ninety percent of diffusivities predicted by the models are within 0.6 log units of the measured values.     

An experimental investigation of hydroxyl solubility in jadeite and Na-rich clinopyroxenes

The solubility and incorporation mechanisms of water in synthetic, water-saturated jadeite and Na-rich clinopyroxenes have been experimentally investigated. Infrared spectra for water-saturated jadeite synthesised from 2.0 to 10 GPa show two prominent sharp peaks at 3,373 and 3,613 cm^–1 together with several weaker features in the OH-stretching region, indicating that there are at least 5 distinct modes of hydrogen incorporation in the structure. Water solubility in pure jadeite reaches a maximum of about 450 ppm by weight at 2 GPa and slowly decreases with increasing pressure to about 100 ppm at 10 GPa. Solubility can be described by the function c_OH=A f_H2O^0.5 exp (–PV_Solid/RT), where c_OH is water solubility in ppm H₂O by weight, A is 7.144 ppm/bar^0.5, f_H2O is water fugacity, and V_Solid=8.019 cm³/mol is the volume change of the clinopyroxene upon incorporation of OH. Jadeite provides a good model for understanding hydrogen incorporation mechanisms in more complex omphacite compositions. Assignment of absorption bands in IR spectra verifies the importance of cation vacancies on the M2 site in providing mechanisms for hydrogen incorporation. However, results also suggest that substitution of lower valency cations onto the M1 site may also be important. Solid solution of jadeite with diopside and in particular, with Ca-Eskola component leads to a drastic increase of water solubility, and the bulk composition has a more important effect on the capacity of omphacite to store water than pressure and temperature. Omphacite is expected to be the major carrier of water in a subducted eclogite after the breakdown of hydrous minerals.Editorial responsibility: W. Schreyer