Theoretical study of point defects in crystalline zircon

We present a numerical study of point defects in crystalline zircon (ZrSiO₄). Vacancies and interstitials of all the constituents of zircon have been considered. For each defect, the structure and the formation energies have been calculated. Calculations, using the supercell method, are based on the Density Functional Theory in the Local Density Approximation. Empirical potentials have also been considered for comparison with electronic structure results. We find a formation energy for the oxygen interstitial of 1.7 eV. This value is compatible with the experimental activation energy for oxygen diffusion in zircon, which proves an interstitial mechanism for the diffusion of oxygen in zircon. For all other defects the calculated formation energies lead to negligible thermal concentration at equilibrium. Received: 8 January 1999 / Revised, accepted: 14 May 1999     

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.     

Melting of albite and dehydration of brucite in H2O–NaCl fluids to 9 kbars and 700–900°C: implications for partial melting and water activities during high pressure metamorphism

 The melting reaction: albite_(solid)+ H₂O_(fluid) =albite-H₂O_(melt) has been determined in the presence of H₂O–NaCl fluids at 5 and 9.2 kbar, and results compared with those obtained in presence of H₂O–CO₂ fluids. To a good approximation, albite melts congruently at 9 kbar, indicating that the melting temperature at constant pressure is principally determined by water activity. At 5 kbar, the temperature (T)- mole fraction (X _(H2O) ) melting relations in the two systems are almost coincident. By contrast, H₂O–NaCl mixing at 9 kbar is quite non-ideal; albite melts ∼70 ^°C higher in H₂O–NaCl brines than in H₂O–CO₂ fluids for X _(H2O) =0.8 and ∼100 ^°C higher for X _(H2O) =0.5. The melting temperature of albite in H₂O–NaCl fluids of X _(H2O)=0.8 is ∼100 ^°C higher than in pure water. The P–T curves for albite melting at constant H₂O–NaCl show a temperature minimum at about 5 kbar. Water activities in H₂O–NaCl fluids calculated from these results, from new experimental data on the dehydration of brucite in presence of H₂O–NaCl fluid at 9 kbar, and from previously published experimental data, indicate a large decrease with increasing fluid pressure at pressures up to 10 kbar. Aqueous brines with dissolved chloride salt contents comparable to those of real crustal fluids provide a mechanism for reducing water activities, buffering and limiting crustal melting, and generating anhydrous mineral assemblages during deep crustal metamorphism in the granulite facies and in subduction-related metamorphism. Low water activity in high pressure-temperature metamorphic mineral assemblages is not necessarily a criterion of fluid absence or melting, but may be due to the presence of low a _(H2O) brines. Received: 17 March 1995/Accepted: 9 April 1996     

Ordering and exsolution processes in Or-rich alkali feldspar megacrysts from the Eldzhurtinskiy granite (Caucasus)

 The extremely young (2.5 Ma) I-type Eldzhurtinskiy granite complex (Central Caucasus) is uniform with respect to modal composition, major and trace element chemistries of bulk rocks and mineral phases. In contrast, it reveals two types of alkali feldspar megacrysts differing in tetrahedral Al-content (2t₁) and exsolution microtextures: 1. Alkali feldspar megacrysts (Or₇₀An₂Ab₂₈) from the top of the body consist of ideally coherent intergrowths of fine-scale regular Or- and Ab-rich lamellae. The exsolved K-feldspar host is monoclinic (2t₁=0.7), the exsolved Na-rich phase consists of Albite- and/or Pericline-twinned albite. 2. Megacrysts from greater depths have the same bulk composition, but the exsolved Ab-rich phase occurs in the form of optically visible, broad lamellae and patches of low albite. In addition, the K-rich host yields a higher degree of (Al, Si) ordering (2t₁=0.8). The evolution of the distinct types of megacrysts reflects differences in the cooling history within the upper and lower part of the granite body. The occurrence of the coherent lamellae in the megacrysts from the top of the body is attributed to exsolution under dry conditions during fast cooling, whereas coarsening of lamellae and formation of albite patches in the megacrysts from the lower part are caused by fluid-feldspar interaction. The transition zone in the body between the two types of megacrysts is sharp (in a depth interval of 100–200 m) and not related to shear zones. Received: 12 June 1995 / Accepted: 29 January 1996     

Grain boundary diffusion of oxygen,potassium and calcium in natural and hot-pressed feldspar aggregates

 Grain boundary diffusion rates of oxygen, potassium and calcium in fine-grained feldspar aggregates were determined experimentally. The starting materials were a natural albite rock from the Tanco pegmatite and aggregates hot-pressed from fragments of Amelia albite or Ab, Or and An composition glasses. The technique employed isotopic tracers (¹⁸O, ⁴¹K, ⁴²Ca) either evaporated onto the surface or in an aqueous solution surrounding the sample, and depth profiling using an ion microprobe (SIMS). From the depth profiles, the product of the grain boundary diffusion coefficient (D′) and effective boundary width (δ) was calculated using numerical solutions to the appropriate diffusion equation. The experimental reproducibility of D′δ is a factor of 3. A separate determination of D′ independent of δ yields an effective grain boundary width of ∼3 nm, consistent with high resolution TEM observations of a physical grain boundary width <5 nm. Oxygen (as molecular water) grain boundary diffusion rates were determined in the Ab and Or aggregates at 450°–800° C and 100 MPa (hydrothermal), potassium rates in Or aggregates at 450°–700° C both at 0.1 MPa (in air) and at 100 MPa (hydrothermal), and calcium rates in An aggregates at 700°–1100° C and 0.1 MPa (in air). Oxygen grain boundary diffusion rates are similar in all three of the Ab aggregates and in the Or aggregate. Potassium and oxygen depth profiles measured in the same samples yield different D′δ values, confirming a diffusional transport mechanism. Potassium diffusion in the Or aggregate has a greater activation energy (216 vs 78 kJ/mol) than oxygen, and the Arrhenius relations cross at ∼625° C. Potassium D′δ values in Or aggregates are about a factor of five greater in hydrothermal experiments at 100 MPa than in experiments at 0.1 MPa in air. Calcium grain boundary diffusion rates in An aggregates are 4 to 5 orders of magnitude slower than potassium in Or and have a greater (291 kJ/mol) activation energy. This suggests that differences in formal charge and/or size of diffusing species may play an important role in their relative grain boundary diffusion rates. Received: 24 December 1993 / Accepted: 16 June 1994     

Calcium self-diffusion in diopside at high temperature: implications for transport properties

We have investigated ⁴⁴Ca self-diffusion in natural diopside single crystals (containing ∼2 atomic % Fe) at temperatures up to 1320 °C (i.e. 30 °C below the nominal melting point). Oxygen fugacity was controlled by gaseous mixtures. Diffusion profiles ranging from ∼50 to 500 nm were analysed by Rutherford Back-Scattering Spectrometry (RBS). The present results are complementary to previous studies, and show that in both synthetic (Fe-poor) and natural (Fe-rich) diopside, there are two different diffusion regimes for Ca with a transition at ∼1230±15 °C. Below this temperature diffusion is characterised by an activation enthalpy of ∼284±10 kJ/mol, while at higher temperatures it increases up to ∼1006±75 kJ/mol. These regimes are proposed to be respectively extrinsic and intrinsic. For the intrinsic regime Ca self-diffusion may involve Ca-Frenkel point defects. These are pairs of a vacancy on a M₂ site and a calcium cation on an interstitial (normally unoccupied) site. The concentration of such point defects depends only on temperature, and it is especially important at very high temperatures. The activation enthalpy for intrinsic diffusion may represent the half defect formation enthalpy plus the migration enthalpy for movement through interstitial sites. For the extrinsic regime we propose Ca self-diffusion to involve extrinsic interstitial point defects with concentration proportional to ()^{–0.19±0.03}. We suggest that for both regimes, Ca diffusion involves the well known M₃ sites in the octahedral layers, as well as sites in the tetrahedral layers, that we call M_4. These sites are especially convenient to explain the observed isotropic diffusion. Increasing concentration of Ca-Frenkel point defects may be related to the onset of premelting, which affects the thermodynamic properties of Fe-“free” diopside above 1250 °C. In the light of the present results, premelting is also expected to occur in natural Fe-bearing diopside and it could strongly influence its thermodynamic and transport properties. Subsequently, in deep upper mantle conditions (T≈1250 °C–1300 °C) where premelting could occur, diffusional cation exchanges with surrounding phases and diffusion controlled creep might be facilitated. Finally, our diffusion data support a previous suggestion that electrical conductivity may be electronic rather than ionic. Received: 17 December 1997 / Revised, accepted: 17 April 1998     

Computer simulation of defect structure in sillimanite and mullites

 Defect structure and the defect formation in mullites and sillimanites have been investigated using computer simulation techniques. From point defect chemistry and computer simulations, oxygen vacancies are identified as the majority defect responsible for oxygen transport in mullite. The defect formation energies are between 3 and 4 eV. Using supercell calculation methods, the random structure is identified to be stable in mullites, whereas the ordered structure can be confirmed to be more stable in sillimanite. An energy of 0.7–1.0 eV for the association of oxygen vacancies with cations is estimated. Received: 11 May 2001 / Accepted: 12 December 2001     

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.     

Calculation of the UV Absorption Spectra of As(III) Oxo- and Thio- Acids and Anions in Aqueous Solution and of PF3 in the Gas-phase

Changes in the UV spectra of As(OH)₃ solutions with variations in pH and temperature have recently been used to determine the temperature dependence of the pK_a of the acid. In previous studies I used quantum mechanical techniques to study changes in structure and vibrational spectra as a function of pH for arsenites and thioarsenites. I previously calculated UV spectra for ``molecular' minerals, like realgar As₄S₄. Here I use a number of different quantum mechanical methods, both Hartree-Fock and density functional theory based, to calculate the UV spectra for both a related simple well-characterized gas-phase molecule PF₃ and for As(OH)₃ and As(SH)₃ and their conjugate anions and some neutral and anionic oligomers in aqueous solution. For the monomeric species small numbers of water molecules have been explicitly included, in a supermolecule or microsolvation approach. I find that UV absorption energies accurate to a few tenths of an eV can be obtained both for gas- phase PF₃ and for neutral arsenious acid in aqueous solution, for which the UV absorption maximum is calculated to occur around 6.5 eV, consistent with experiment. Accurate calculation of the UV energies for arsenite anions in aqueous solution is much more difficult, since basis set size and solvation effects are considerably larger than for the neutral molecules, but fairly reliable results can still be obtained. Deprotonation is found to reduce the lowest calculated UV transition energy by about half an eV. Oligomerization also reduces the lowest calculated UV energy by at least half an eV. Replacement of one or all the –OH groups by –SH groups reduces the lowest calculated UV energies by about 2 eV. UV excitation energies have been calculated for oligomeric species as large as As₃E₃(EH)₃ and As₄E₆, where E = O, S, and may be useful for identifying such species in solution.     

Crystal field transitions in Co2[Al4Si5]O18 cordierite and CoAl2O4 spinel determined by neutron spectroscopy

Inelastic magnetic neutron scattering has been used to determine the energy of the ⁴ A ₂→⁴ T ₂ transition in CoAl₂O₄ spinel and the δ₁ transition in Co₂[Al₄Si₅]O₁₈ cordierite. The observed crystal field splitting in Co-spinel is 485 meV (3900 cm⁻¹), which corresponds to a crystal field stabilization energy of 56.2 kJmol⁻¹. The transition energy of the δ₁ transition in Co-cordierite has been determined to be 21 meV (170 cm⁻¹). The present data demonstrate that magnetic neutron scattering can be used to measure crystal field transitions at energies of interest in the study of 3d-containing silicates. It may be used to measure transition energies when the use of optical spectroscopy is inappropriate. Received: 30 January 1997 / Accepted: 5 July 1997     

Interlayer proton transfer in brucite under pressure by polarized IR spectroscopy to 5.3 GPa

In order to investigate the behaviour of proton in brucite under pressure, polarized IR absorption spectra and polarized absorbance distributions of (001) and (110) oriented single crystal of brucite under high pressure were measured by Fourier transform polarized infrared microspectroscopy with diamond anvil cell. A pressure-induced absorption peak at 3645 cm⁻¹ observed under pressures over 2.9 GPa was confirmed to be due to a secondarily formed OH dipole. Polarized absorbance distribution measured under pressure of (110) suggests that the secondary OH dipole is oriented 136.0° to c-axis under 5.3 GPa. Isotropic absorbance distribution of (001) suggests that the secondary OH dipole is disorderly trifurcated. Abrupt onset of the secondary peak and its reverse pleochroism suggest that the process of secondary OH dipole formation is due to proton transfer between layers in brucite. The calculated orientation of the secondary OH dipole consistent with the O-H···O′ angle revealed by neutron diffraction supports the existence of proton transfer along H···O′. The secondary OH dipole implies a new site of proton in brucite under pressure. Received: 6 March 1997 / Revised, accepted: 9 June 1997     

The low-pressure stability of phase A,Mg7Si2O8(OH)6

 Phase A, Mg₇Si₂O₈(OH)₆, is a dense hydrous magnesium silicate whose importance as a host of H₂O in the Earth’s mantle is a subject of debate. We have investigated the low-pressure stability of phase A in experiments on the reaction phase A=brucite+forsterite. Experiments were conducted in piston-cylinder and multi-anvil apparatus, using mixtures of synthetic phase A, brucite and forsterite. The reaction was bracketed between 2.60 and 2.75 GPa at 500° C, between 3.25 and 3.48 GPa at 600° C and between 3.75 and 3.95 GPa at 650^° C. These pressures are much lower than observed in the synthesis experiments of Yamamoto and Akimoto (1977). At 750^° C the stability field of brucite + chondrodite was entered. The enthalpy of formation and entropy of phase A at 1 bar (10⁵ Pa), 298 K, were derived from the experimental brackets on the reaction phase A=brucite+forsterite using a modified version of the thermodynamic dataset THERMOCALC of Holland and Powell (1990), which includes a new equation of state of H₂O derived from the molecular dynamics simulations of Brodholt and Wood (1993). The data for phase A are: ΔH ^o _f =−7126±8 kJ mol^-1, S ^o=351 J K^-1 mol^-1. Incorporating these data into THERMOCALC allows the positions of other reactions involving phase A to be calculated, for example the reaction phase A + enstatite=forsterite+vapour, which limits the stability of phase A in equilibrium with enstatite. The calculated position of this reaction (753° C at 7 GPa to 937° C at 10 GPa) is in excellent agreement with the experimental brackets of Luth (1995) between 7 and 10 GPa, supporting the choice of equation of state of H₂O used in THERMOCALC. Comparison of our results with calculated P-T paths of subducting slabs (Peacock et al. 1994) suggests that, in the system MgO–SiO₂–H₂O, phase A could crystallise in compositions with Mg/Si>2 at pressures as low as 3 GPa. In less Mg rich compositions phase A could crystallise at pressures above approximately 6 GPa. Received: 3 July 1995/Accepted: 14 December 1995     

Electrical properties of opal-CT

 The electrical properties of opal-CT are validated at temperatures from 600 to 840 °C and frequencies from 5 Hz to 10 MHz. The opals are hydrothermal, containing less than 11270 ppm total of Al, Fe, Ca, Na, and K, and from 1.17 to 17.63 wt% H₂O interstitial and structural. Opal-CT shows fine crystallites, measuring from 19.4 to 22.7 μm, of an ordered tridymite-M stratification with high-cristobalite, embedded in a non-crystalline matrix. When heated to 600 °C, the non-crystalline phase devitrifies to the same stacked high-cristobalite-tridymite-M crystals. Opals containing less than 2070 ppm of cationic impurities are characterized by one single high-frequency complex impedance arc corresponding to the bulk polarization of the crystalline phase, of capacitances between 25 and 30×10⁻¹² F and resistances from 132 to 890 ohm. Opals having over 6300 ppm of cationic impurities show two superimposed high- and low-frequency complex impedance arcs. The high-frequency arc corresponds to the bulk polarization of the crystalline phase, of capacitance between 8 and 15.7×10⁻¹² F and resistance from 14 to 236 ohm, less than the capacitance of 0.25 to 0.53×10⁻⁹ F and resistance from 26 to 360 ohm of the non-crystalline minor intergranular material represented by the low-frequency impedance arc. The electric module shows one single vertex, ascribed to the bulk polarization of the crystalline phase. The conductivities are from 10⁻⁷ to 10⁻⁴ ohm⁻¹cm⁻¹, in the range of poor ionic conductors, essentially constant below 1.8 kHz, rapidly increasing at higher frequencies, due to ionic and electronic charge carriers. The activation energy changes between 0.905 and 1.003 eV for the conduction mechanism in the crystalline phase and from 0.924 to 1.087 eV in the non-crystaline phase. X-ray diffraction and impedance spectroscopy confirm that opal-CT is a crystalline stacked sequence of tridymite-M and cristobalite-high, in a non-crystalline matrix. Received October 20, 1995/Revised, accepted June 15, 1996     

Kinetics of formation of zeolite Na-A [LTA] from natural kaolinites

 The kinetics and mechanism of hydrothermal formation of zeolite A from natural kaolinites have been studied using as starting materials two international kaolinite standards (KGa-1 and KGa-2 from Georgia, USA) exhibiting a different degree of stacking disorder. Precursors utilized for the synthesis were prepared by heating the kaolinites at 800 °C. Metakaolinite was also prepared from KGa-1 by thermal activation at 600 °C. The hydrothermal syntheses were accomplished by heating the samples in NaOH solutions at temperatures between 70 and 110 °C. The kinetic experiments were performed by time-resolved synchrotron powder diffraction in isothermal mode using a transmission geometry and an Image Plate detector. The results of the kinetic analysis are interpreted in the light of the structural state of the starting kaolinite, and of the temperature of activation of the precursor material. For kaolinite activated at high temperature the nucleation and crystallization of zeolite A is essentially independent of the defect density of the original kaolinite, and the thermal history of the precursor seems to be the main controlling parameter. The formation process of zeolite A from metakaolinite materials obtained at lower activation temperatures shows significantly faster reaction rates and lower apparent activation energies. This is again interpreted in the light of the short range inhomogeneities present in metakaolinite. As the reaction proceeds metastable zeolite A transforms into hydroxy-sodalite. Received April 18, 1996 / Revised, accepted September 27, 1996     

Electrical conductivity of dry and hydrous NaAlSi<Subscript>3</Subscript>O<Subscript>8</Subscript> glasses and liquids at high pressures

We report the first study of electrical conductivities of silicate melts at very high pressures (up to 10 GPa) and temperatures (up to 2,173 K). Impedance spectroscopy was applied to dry and hydrous albite (NaAlSi₃O₈) glasses and liquids (with 0.02–5.7 wt% H₂O) at 473–1,773 K and 0.9–1.8 GPa in a piston-cylinder apparatus, using a coaxial cylindrical setup. Measurements were also taken at 473–2,173 K and 6–10 GPa in two multianvil presses, using simple plate geometry. The electrical conductivity of albite melts is found to increase with temperature and water content but to decrease with pressure. However, at 6 GPa, conductivity increases rapidly with temperature above 1,773 K, so that at temperatures beyond 2,200 K, conductivity may actually increase with pressure. Moreover, the effect of water in enhancing conductivity appears to be more pronounced at 6 GPa than at 1.8 GPa. These observations suggest that smaller fractions of partial melt than previously assumed may be sufficient to explain anomalously high conductivities, such as in the asthenosphere. For dry melt at 1.8 GPa, the activation energy at T > 1,073 K is higher than that at T < 1,073 K, and the inflection point coincides with the rheological glass transition. Upon heating at 6–10 GPa, dry albite glass often shows a conductivity depression starting from ~1,173 K (due to crystallization), followed by rapid conductivity enhancement when temperature approaches the albite liquidus. For hydrous melts at 0.9–1.8 GPa, the activation energies for conductivity at ≥1,373 K are lower than those at <973 K, with a complex transition pattern in between. Electrical conductivity and previously reported Na diffusivity in albite melt are consistent with the Nernst–Einstein relation, suggesting the dominance of Na transport for electrical conduction in albite melts.     

IR active orientation of OH bending mode in topaz

Infrared (IR) and nearinfrared (NIR) absorption spectra of hydrous and F-rich topazes were measured to assign an OH bending mode of topaz. Three absorption peaks at 1165, 3650, and 4803 cm⁻¹ are assigned to OH related absorption peaks. Since a peak at 4803 cm⁻¹ can be assigned to a combination mode of 1165 and 3650 cm⁻¹, the 1165 cm⁻¹ peak is harmonic with the 3650 cm⁻¹ peak. Polarized IR absorption spectra of (100), (010), and (001) planes of the hydrous topaz were measured to examine IR active orientation of the 1165 cm⁻¹ OH related mode. Three pleochroic distributions of the absorption peak at 1165 cm⁻¹ on (100), (010), and (001) planes indicate an active orientation of the 1165 cm⁻¹ OH related mode. The IR active orientation of the 1165 cm⁻¹ OH related mode in topaz is normal to the OH dipole. The orthogonality and harmonic combination mode indicate that the 1165 cm⁻¹ peak is OH bending mode. The active orientation of OH bending mode is polarized in the plane normal to the OH dipole. The polarization suggests that anisotropic thermal vibration of protons on the hydroxyl is maximum along the IR active orientation. Received: August 16, 1996 / Revised, accepted: April 20, 1997     

Ab initio calculations on (OH)4 defects in α-quartz

Ab initio total energy calculations based on a new optimized oxygen psuedopotential have been used to study the structures and relative energies of α-quartz, a partly (OH)₄ substituted version of the α-quartz structure, and interstitial water molecules in α-quartz. Hydrogen bonds formed from two hydroxyl groups of the (OH)₄ defects in the substituted α-quartz structure promote a stable structure for the defect α-quartz at low temperature. Comparable ab initio calculation of the energy of the interstitial water molecule in the quartz structure indicates that, energetically, the (OH)₄ defect is likely to be strongly favoured as a mode for the incorporation of water. Ab initio stress calculations confirm that the (OH)₄ defect in quartz has a large associated stress field which is likely to lead to segregation of these defects on supersaturation in wet quartz. The calculations indicate that segregation should occur in the plane (10 0) of the α-quartz structure.     

P-V equation of state of portlandite, Ca(OH)2, from powder neutron diffraction data

 A high pressure neutron powder diffraction study of portlandite [Ca(OH)₂] has been performed at ISIS facility (U.K.); nine spectra have been collected increasing the pressure by steps, up to 10.9 GPa, by means of a Paris-Edinburgh cell installed on the POLARIS diffractometer. The tensorial formalism of the lagrangian finite strain theory and the Birch-Murnaghan equation of state have been used to determine, independently, two values of the bulk modulus of portlandite, obtaining K ₀=38.3(±1.1) GPa [linear incompressibilities: K _0a=188.4(±9.9), K _0c=64.5(±2.5) GPa] and K ₀=34.2(±1.4) GPa, respectively. The present results comply with values from previous measurements by X-ray diffraction [K ₀=37.8(±1.8) GPa] and Brillouin spectroscopy [K ₀=31.7(±2.5) GPa]. Reasonably, Ca(OH)₂ has revealed to be bulkly softer than Mg(OH)₂ [K ₀=41(±2), K _0a=313, K _0c=57 GPa]. The Ca(OH)₂ linear incompressibility values reflect the nature of forces acting to stabilize the (001) layer structure and, further, prove that the replacement Ca/Mg mainly affects the elastic properties in the (001) plane, rather than along the [001] direction. Data from a full refinement of the structure at room pressure are reported. Received January 12, 1996/Revised, accepted June 15, 1996     

Proton migration in portlandite inferred from activation energy of self-diffusion and potential energy curve of OH bond

A fundamental mechanism on the atomic level for self-diffusion in the proton layer of portlandite, Ca(OH)₂, was investigated by conducting hydrogen–deuterium (H–D) exchange diffusion experiments and by deriving potential energy curves of OH vibrations from optical absorption measurements. Synthetic single crystals of portlandite were used in H–D experiments between 250 and 450°C at 150 MPa. Arrhenius parameters for proton diffusion perpendicular to the c-axis gave a frequency factor of 1.0 × 10⁻¹⁰ m²/s and activation energy of 0.61 eV (58.5 kJ/mol). The activation energy corresponds to the height of the potential barrier between two oxygen atoms across an interlayer. The potential barrier height was also theoretically estimated using the OH potential energy curve (OH-PEC) determined by optical absorption measurements. Experimental and theoretical results suggest that the potential barrier height cannot be simply determined by overlapping two OH-PECs. The potential barrier derived theoretically was 3.11 eV. This is too high for the activation energy of the proton diffusion. It implies that the interaction between a diffusing proton and the vacancy of a proton site, and the shortening of interlayer oxygen distance by thermal vibration reduce the potential barrier.     

A theoretical study of the absorption spectra of Pb+ and Pb3+ in site K+ of microcline: application to the color of amazonite

The blue-green color of amazonite has been assigned by various authors to ions Pb⁺ (6 s)² (6 p) and/or Pb³⁺ (6 s) in site of K⁺ of microcline. Owing to the complex which forms between the ion Pb³⁺ and the lone pairs of the oxygen atoms surrounding it, the peripheral electron of Pb³⁺ passes on the levels (6 p) of the latter, which results in a great similarity of the spectra of Pb⁺ and Pb³⁺ in amazonite (the transition energies are multiplied by a factor greater than 1), whereas, in the isolated state, these spectra are completely different from one another. An analytical development of the crystal field around a site K⁺ is established. Under the effect of the crystal field, the transition ² P _1/2→² P _3/2 (6 p) is split into two double transitions. The lower transition only falls in the visible domain (1.6–1.8 eV for Pb⁺), the second in U−V. The green color would arise from the ion Pb⁺, whereas the blue one would be attributed to the ion Pb³⁺. Received: 23 January 1997 / Revised, accepted: 10 September 1997