Water-related defects and oxygen diffusion in albite: a computer simulation study

 Computer simulation techniques have been used to investigate the energetics of defect formation in Albite and to calculate O and (OH) migration activation energies. We find that the Na Frenkel defect has the lowest formation energy, whilst interstitials associated with impurities are the most favourable O defects. Water can be accommodated in the albite structure as both OH groups and as H₂O molecules with solution energy of 0.73 eV and 0.9 eV respectively. The activation energies for O migration is reduced by up to 50% when the O is migrating as part of an (OH) group. In addition, we find a marked diffusional anisotropy for both O and (OH) in albite. Received: 15 September 1995 / Accepted: 29 April 1996     

An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique

Diffusion rates of¹⁸O tracer in quartz ( c, 1 Kb H₂O) and Amelia albite ( 001, 2 Kb H₂O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c), ,Q=98±7 KJ mol^–1 (600–825° C, 1 Kb); Amelia albite ( 001), ,Q=85±7 KJ mol^–1, (400–600° C, 2 Kb). Measured quartz¹⁸O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted.     

Comparison of low-temperature with high-temperature diffusion of sodium in albite

Diffusion of sodium in albite from Amelia County, Virginia, was examined at high and intermediate temperatures by means of the sectioning technique and at low temperatures by means of an exchange technique. These studies indicate that diffusion is heterogeneous at low and intermediate temperatures, but goes to volume diffusion at high temperatures. Apparent diffusion coefficients of the order of magnitude of 10⁻¹⁸ cm²/sec and an activation energy of approximately 3000 cal/mole sodium are determined for the low-temperature movement. An activation energy of approximately 35 kcal/mole sodium is determined for the high-temperature movement.     

Strontium diffusion in sanidine and albite, and general comments on strontium diffusion in alkali feldspars

Strontium chemical diffusion has been measured in albite and sanidine under dry, 1 atm, and QFM buffered conditions. Strontium oxide-aluminosilicate powdered sources were used to introduce the diffusant and Rutherford Backscattering Spectroscopy (RBS) used to measure diffusion profiles. For the 1 atm experiments, the following Arrhenius relations were obtained:

Sanidine (Or₆₁), temperature range 725–1075°C, diffusion normal to (001): D=8.4 exp(−450±13 kJ mol⁻¹/RT) m²s⁻¹. Albite (Or₁), temperature range 675–1025°C, diffusion normal to (001): D=2.9 × exp(−224±11 kJ mol⁻¹/RT) m²s⁻¹.

The alkali feldspars in this and earlier work display a broad range of activation energies for Sr diffusion, which may be a consequence of the thermodynamic non-ideality of the alkali feldspar system and/or the mixed alkali effect.     

Defect properties of albite

Knowledge of the defect properties of Lunar and Mercurian minerals has recently become important, with the advent of models which attempt to explain the formation of the thin exosphere of these celestial bodies. Here, we have calculated the formation energies of sodium and oxygen vacancies in the mineral albite (NaAlSi₃O₈), as well as the Schottky defect energy for the removal of a Na₂O unit. We have employed both the supercell and Mott–Littleton approaches, using Kohn–Sham density functional theory and classical interatomic potential methods. As well as reporting the defect energies and structures, we comment upon the relative merits of the methods used.     

Cathodoluminescence of authigenic albite

Authigenic albites in carbonate rocks typically grow in a high-grade diagenetic to low-grade metamorphic environment and often show Roc-Tourné-twinning sensu Füchtbauer. Based on an investigation of four Middle to South European occurrences, they show Mn²⁺- and Fe³⁺-activated cathodoluminescence (CL), as revealed by combined high resolution spectroscopy of cathodoluminescence emission (HRS-CL), electron paramagnetic resonance (EPR), and proton-induced X-ray emission (μPIXE).     

Recrystallization and peristerite formation in albite

Plagioclase in the range An₂-An₁₀ in a relatively undeformed Quartz—feldspar pegmatite is compared with similar material in a strongly deformed and recrystallized shear zone. Optical and transmission electron microscope observations and chemical data are discussed in terms of established mechanisms of strain induced recrystallization.Recrystallization occurs by the formation of subgrains from recovery, and their subsequent growth by boundary migration or coalescence by rotation. It is suggested that the recrystallization and grain growth are enhanced by a small increase in the anorthite content. Peristerite formation in the recrystallized grains is associated with the migration of high angle boundaries under upper greenschist facies conditions.     

A computational study of oxygen diffusion in olivine

Atomistic modelling techniques are used to study the rate-determining steps that limit diffusion of oxygen in forsterite. The activation energies for diffusion parallel to all three crystallographic axes by the vacancy and interstitial mechanisms are calculated. The activation energy for extrinsic vacancy diffusion is predicted to be isotropic with a barrier height of 119 kJ mol^–1. Conversely, in the interstitial case it is found to be anisotropic, with extrinsic activation energies that range between 94 and 178 kJ mol^–1. The effect of intrinsic defects and two typical impurities, iron and hydrogen, upon diffusion is also considered. We find that the migration energy is slightly higher in iron-rich fayalite compared with forsterite and that the presence of hydrogen defects will not affect the diffusion mechanism. These observations lead us to reinterpret existing experimental results on oxygen diffusion in natural olivine. We suggest that at low oxygen partial pressure the mechanism observed is a vacancy mechanism, while at high oxygen partial pressure the mechanism is interstitial. We believe that this change in mechanism is mediated by iron redox reactions. Taking this process into account, we derive activation energies in excellent agreement with those found experimentally in natural samples of olivine. The anisotropy of activation barriers and hence the change in diffusion rates with temperature could be used to distinguish between the two mechanisms in future experimental work.     

Alkali ion migration in albite and K-feldspar

As part of a study of ion migration mechanisms in feldspars, the dynamical behaviour of the alkali metal cations ions in albite and K-feldspar has been investigated using a combination of dielectric spectroscopy and atomistic computer simulation techniques. The low-frequency dielectric properties of these minerals have been studied from room temperature to 1100 K. At each temperature, the dielectric constant, conductivity and dielectric loss were determined over a range of frequencies from 100 Hz to 10 MHz. At high temperatures a distinct Debye-type relaxation in the dielectric loss spectra was observed for both albite and K-feldspar; the activation energy for these processes was determined to be 1.33 eV in both albite and K–feldspar. Atomistic simulation techniques were used to elucidate the mechanism and energetics of the cation migration processes. Mechanisms involving the conventional hopping of Na⁺ and K⁺ ions between cation sites in the (010) plane were found to give calculated energy barriers in good agreement with the experimentally determined activation energies. These results assist in understanding the nature of the processes responsible for the observed dielectric behaviour.     

The hydrothermal synthesis of low albite

Glasses on the join NaAlSi₃O₈-Na₂Si₂O₅ were devitrified hydrothermally at pressures of 1 to 10 kb and at temperatures in the range 200 to 700° C to define more adequately the physical and chemical environments which favor crystallization of the fully ordered polymorph of albite. The presence of Na₂Si₂O₅ allows the synthesis of low albite with an obliquity of 1.140° (Cu K radiation) in runs of relatively short duration. The effect of increasing total pressure and time, and of decreasing temperature and amount of water down to critical values, is to favor the synthesis of ordered albite. Excess sodium is the chemical constituent necessary for ordering to proceed at a relatively rapid rate; this rate seems to vary with the ratio aNa⁺/aH⁺, and hence with the peralkalinity of the aqueous fluid attending recrystallization. The chemical environment of recrystallization thus seems as important as temperature in determining the ultimate degree of Si-Al order attained in albite.This paper is taken from a Ph. D. dissertation submitted to the Department of Geology, Stanford University, Stanford, California.     

An empirical estimate of the diffusion rate of oxygen in diopside

The intracrystalline diffusion rate of oxygen in diopside was constrained based on natural isotopic variations from a granulite facies marble from Cascade Slide, Adirondacks (New York, USA). The oxygen isotope compositions of the diopsides, measured as a function of grain size, are nearly constant (20.9 ± 0.3‰ vs. SMOW) over the entire measured size range (0.3–3.2 mm diameter). The δ¹⁸O values of the cores of calcite grains are 23.0‰. Temperature estimates based on the Δ¹⁸O(calcite-diopside) are 800d?C, in agreement with the highest previous thermometric estimates for these rocks. The lack of isotopic variation in the diopsides as a function of grain size requires that the oxygen intracrystalline diffusion rate in diopside from the Adirondack samples was very slow. The maximum diffusion rates (D_800d?C parallel to the c-axis) were calculated with an infinite reservoir model (IRM) and a finite reservoir model (FRM) that incorporates mineral modal abundances and initial isotopic variations. For an assumed activation energy (Q) = 100 kJ/mol, the IRM diffusion rate estimate of 1.6 times 10^-20cm²/s is two orders of magnitude faster than from the FRM; at Q=500kJ/mol, the D_800d?C estimate for both methods is c. 5.6 times 10^-20 cm²/s. The present results require that a hydrothermal fluid significantly enhances the diffusion rate of oxygen in diopside if previous data are correct. The δ¹⁸O(SMOW) and δ¹³C(PDB) values of the calcite, measured in situ with a CO₂ laser, are 22.9 ± 0.3, 0.1±0.3‰ in the grain cores, 22.1 ±0.3, 0.2 ±0.1‰ at the grain boundaries and 21.7 ±0.4, -0.6±0.1‰ abutting diopside grains. The δ¹⁸O and δ¹³δC values measured conventionally are: crystal cores, 22.96, -0.95‰; abutting diopside grains, 22.38, -0.93‰; bulk, 22.79, -0.95%. Use of the bulk δ¹⁸O(calcite) values for thermometry yields unreasonably high temperatures. The lower δ¹⁸O values at the calcite grain boundaries are not due to retrograde diffusional exchange with the diopside, they are thought to be a result of a late retrograde fluid infiltration.     

Triclinic elastic constants for low albite

The full set of elastic constants for plagioclase end-member phase albite (NaAlSi₃O₈) is reported for the first time. Velocities of surface acoustic waves (both Rayleigh and pseudo-surface waves) were measured using impulsively stimulated light scattering on polished surfaces having six different orientations (three normal to the Cartesian axes and three lying on diagonals). Data were inverted and results tested using several non-linear optimization techniques. Compliance moduli determined under hydrostatic compression provided additional constraints and reduced covariance in the reported constants. The Cartesian coordinate system associated with the constants (using the unit cell) has the y-axis parallel to the crystal b axis, the x-axis parallel to a* (perpendicular to b and c) and the z-axis consistent with a right-handed coordinate system. The values of the moduli C₁₁, C₁₂, C₁₃, C₁₄, C₁₅, C₁₆, C₂₂, C₂₃, C₂₄, C₂₅, C₂₆, C₃₃, C₃₄, C₃₅, C₃₆, C₄₄, C₄₅, C₄₆, C₅₅, C₅₆, C₆₆ and their 2σ uncertainties (in parentheses) are, respectively, 69.1(0.6), 34.0(0.7), 30.8(0.5), 5.1(0.1), −2.4(0.1), −0.9(0.1), 183.5(2.7), 5.5(2.2), −3.9(0.5), −7.7(0.7), −5.8(0.7), 179.5(2.3), −8.7(0.4), 7.1(0.6), −9.8(0.6), 24.9(0.1), −2.4(0.1), −7.2(0.1), 26.8 (0.2), 0.5(0.1), 33.5(0.2). These constants differ significantly from the previously reported pseudo-monoclinic constants that were based on velocity measurements on polysynthetic twinned crystal aggregates. Differences are consistent with systematic errors in the earlier study associated with sparse data and the presence of cracks and other imperfections.     

Interfacial energies for quartz and albite in pelitic schist

Interfacial energies of quartz/quartz (qz/qz), albite/albite (ab/ab), and quartz/albite (qz/ab) boundaries in low-grade pelitic schist were determined based on measured values of dihedral angles. Three kinds of microstructures were investigated, and the interfacial energies were obtained in two independent ways. (1) Relative values of interfacial energy were calculated from dihedral angles formed at quartz and albite triple junctions. (2) Subgrain boundary energy was calculated using the Read-Shockley theory for a boundary connected to an intergranular pore. Dihedral angles formed at the corners of intergranular pores were measured. From the interfacial tension balance equation, the value of the qz/qz grain boundary energy was then obtained. (3) Dihedral angles formed at intersections of either pericline or albite twin boundaries with either ab/ab or qz/ab boundaries were measured. The twin boundary energy was calculated based on a previously derived equation using Landau potential, twin wall thickness, and critical temperature for a phase transition in albite. With a modified interfacial tension balance equation for a twin boundary fixed to a facet orientation, the interfacial energies of ab/ab and qz/ab boundaries were obtained. Energies obtained by methods of (2) and (3) are in good agreement. The interfacial energies for qz/qz, ab/ab, and qz/ab boundaries obtained in this study are 270뀶, 300끞, and 250끀 mJ/m², respectively.     

On the theory of Al,Si ordering in albite

Calculations of the equilibrium distribution of Al, Si in the albite framework based on quasi-chemical theories of order, disorder transformations (Yang 1945; Yang and Li 1947; Li 1949) were made for a two-dimensional framework model. The ordering is caused by the energy of Al, Si interchange between sites of different crystal-chemical types and the energy of nearest neighbour interaction. By taking into account the decrease in the energy of interchange between sites with increasing disordering and with increasing temperature, and by examining different relationships for site-to-site interchange energy and the nearest neighbour interaction, it is possible to understand the basic characteristics of the transformation from low (essentially ordered) to high (essentially disordered) albite as revealed by experiment. These characteristics are: (1) abrupt variation of the equilibrium degree of order within a narrow temperature range and possible first order phase transformation for the transition from low-albite to high-albite, (2) hysteresis of the synthetic high albite transformation path and of the low albite hydrothermal “annealing” path, (3) presence of a temperature range where high albite is stable and has a continually changing equilibrium degree of order.     

Diffusion-controlled growth of albite and pyroxene reaction rims

The growth rates of albite and pyroxene (enstatite + diopside + spinel) reaction rims were measured at 1000°C and ˜700 MPa and found to be parabolic indicating diffusion-controlled growth. The parabolic rate constants for the pyroxene (+ spinel) rims in samples with 0.5 wt% H₂O added or initially vacuum dried at 25°C and 250°C are 1.68 ± 0.09, 0.54 ± 0.05 and 0.25 ± 0.06 μm²/h, respectively. The values for albite rim growth in samples initially dried at 60°C and with 0.1 wt% H₂O added are 0.25 ± 0.04 and 0.33 ± 0.03 μm²/h, respectively. The latter values were used to derive the product of the grain boundary diffusion coefficient D′_A, where A = SiO₂, NaAlO₂, or NaAlSi₋₁, and the grain boundary thickness δ in albite. The calculated D′_SIO2δ in the albite aggregate for the situations of two different water contents are about 9.9 × 10⁻²³ and 1.4 × 10⁻²² m³ s⁻¹, respectively. Both the rate constants and the calculated D′_Aδ demonstrate that the effect of water content on the grain boundary diffusion rate in monomineralic albite and polymineralic pyroxene (+ spinel) aggregates is small, consistent with recent studies of monomineralic enstatite and forsterite rims. Received: 1 July 1995 / Accepted: 1 August 1996     

Greisenization of a muscovite-biotite albite granite of northern Portugal

Greisenization of a muscovite-biotite albite granite of Alijó-Sanfins, northern Portugal, is studied for both major and trace elements. The principal tin-tungsten mineralization of the region is connected with this granite and the greisenization is accompanied by an increase in Cl, F, W, Nb, Sn, Pb and Rb. Cassiterite is the main carrier of Sn. Muscovite is the concentrator of Cl and F. The muscovite of the greisenized granite contains more Cl, F, W and Nb than the muscovite of the parental granite, but the former contains less Sn. Sn content of the muscovite of the greisenized granite is higher than that of the biotite of the parental granite; W content is similar or higher.When the greisenization is accompanied by albitization, the oxides and trace elements behave in a similar way to that found only with greisenization, except that there is a decrease of Ni and Rb. Li, Zr, Sr, Ba and Rb decrease as albitization increases.     

Moon—An albite depleted giant Skaergaard?

The chemical composition of 2188 terrestrial igneous rocks ranging from ultrabasic to granitic composition was analyzed statistically using the method of factor analysis (principal components). The resultant first and second factors were: $$\begin{gathered} {\text{ }}F_1 = 0.933{\text{ Na}}_{\text{2}} {\text{O + 0}}{\text{.143 SiO}}_{\text{2}} + 0.206{\text{ K}}_{\text{2}} {\text{O}} - 0.346{\text{ CaO}} - 0.263{\text{ MgO}} - \hfill \\ .203{\text{ FeO}} \pm \cdot \cdot \cdot \hfill \\ {\text{ }}F_2 = 0.979{\text{ Al}}_{\text{2}} {\text{O}}_{\text{3}} - 0.269{\text{ MgO}} - 0.151{\text{ SiO}}_{\text{2}} - 0.112{\text{ FeO}} \pm \cdot \cdot \cdot \hfill \\ \end{gathered} $$ where oxides are in weight percent. A plot of the first factor against the second results in a useful igneous variation diagram. When the compositions of the 2188 terrestrial rocks and 604 lunar rocks are plotted on this diagram, the two groups of rocks are clearly separated within an albite-anorthite-forsterite-fayalite-quartz polygon. None of the terrestrial differentiation trends are significant for lunar rocks. The major difference in the chemistry of lunar and terrestrial rocks lies in the former being albite poor. Removal of most of the albite from the compositions of terrestrial layered intrusives such as the Skaergaard results in an excellent match between the compositions of the two groups of rocks. Albite subtracted compositions of Skaergaard rocks in particular cover the entire range of chemical variation in the lunar rocks. The statistical results prompt us to speculate further on the similarity of the moon and Skaergaard. We note that the average composition of the moon (Wanke et al., 1974) is similar to the albite subtracted composition of the Skaergaard magma. The lunar crust and a significant part of the lunar interior may match the albite subtracted and somewhat Mg enriched Skaergaard magma.     

Analbite → monalbite transition in a heat treated twinned amelia albite

Amelia albite annealed at > 1080 °C for 3200 hrs by Duba and Piwinskii (1974) shows very fine twin lamellae (～1 μm) after the albite law, suggesting that it once underwent transformation into monalbite. A fragment of this specimen was investigated at 27 °C, 300 °C, 550 °C, 800 °C and 930 °C using the high-temperature precession technique. As the temperature increases, the splitting angle of c ^*-axes (likewise c ^*-axes) of two twin individuals continues to decrease. The photographs taken at 930 °C show that these two splitting angles have converged to 0^o, indicating completion of the transformation into monalbite. The transition point we observe supports the results of MacKenzie (1952) (920±20 °C) and Grundy et al. (1967) (930 °C) rather than those of Sueno et al. (1973) and Prewitt et al. (1974) (> 1080 °C); the discrepancy is most likely due to the differences in the degree of Al-Si disorder of the samples used in the experiments.