High-pressure stability, structure and compressibility of Cmcm -MgAl2O4: an ab initio study

 Quantum-mechanical solid-state calculations have been performed on the highest-pressure polymorph of magnesium aluminate (CaTi₂O₄-type structure, Cmcm space group), as well as on the low-pressure (Fd3ˉm) spinel phase and on MgO and Al₂O₃. An ab initio all-electron periodic scheme with localized basis functions (Gaussian-type atomic orbitals) has been used, employing density-functional-theory Hamiltonians based on LDA and B3LYP functionals. Least-enthalpy structure optimizations in the pressure range 0 to 60 GPa have allowed us to predict: (1) the full crystal structure, the pV equation of state and the compressibility of Cmcm-MgAl₂O₄ as a function of pressure; (2) the phase diagram of the MgO–Al₂O₃–MgAl₂O₄ system (with exclusion of CaFe₂O₄-type Pmcn-MgAl₂O₄), and the equilibrium pressures for the reactions of formation/decomposition of the Fd3ˉm and Cmcm polymorphs of MgAl₂O₄ from the MgO + Al₂O₃ assemblage. Cmcm-MgAl₂O₄ is predicted to form at 39 and 57 GPa by LDA and B3LYP calculations, with K ₀=248 (K′=3.3) and 222 GPa (K′=3.8), respectively. Results are compared to experimental data, where available, and the performance of different DFT functionals is discussed. Received: 31 January 2001 / Accepted: 16 May 2001     

Correlations between 29Si, 17O and 1H NMR properties and local structures in silicates: an ab initio calculation

In order to gain insight into the correlations between ²⁹Si, ¹⁷O and ¹H NMR properties (chemical shift and quadrupolar coupling parameters) and local structures in silicates, ab initio self-consistent field Hartree-Fock molecular orbital calculations have been carried out on silicate clusters of various polymerizations and intertetrahedral (Si-O-Si) angles. These include Si(OH)₄ monomers (isolated as well as interacting), Si₂O(OH)₆ dimers (C₂ symmetry) with the Si-O-Si angle fixed at 5° intervals from 120° to 180°, Si₃O₂(OH)₈ linear trimers (C₂ symmetry) with varying Si-O-Si angles, Si₃O₃(OH)₆ three-membered rings (D₃ and C₁ symmetries), Si₄O₄(OH)₈ four-membered ring (C₄ symmetry) and Si₈O₁₂(OH)₈ octamer (D₄ symmetry). The calculated ²⁹Si, ¹⁷O and ¹H isotropic chemical shifts (δ_i ^Si, δ_i ^O and δ_i ^H) for these clusters are all close to experimental NMR data for similar local structures in crystalline silicates. The calculated ¹⁷O quadrupolar coupling constants (QCC) of the bridging oxygens (Si-O-Si) are also in good agreement with experimental data. The calculated ¹⁷O QCC of silanols (Si-O-H) are much larger than those of the bridging oxygens, but unfortunately there are no experimental data for similar groups in well-characterized crystalline phases for comparison. There is a good correlation between δ_i ^Si and the mean Si-O-Si angle for both Q ¹ and Q ², where Q ⁿ denotes Si with n other tetrahedral Si next-nearest neighbors. Both the δ _i ^O and the ¹⁷O electric field gradient asymmetry parameter, η of the bridging oxygens have been found to depend strongly on the O site symmetry, in addition to the Si-O-Si angle. On the other hand, the ¹⁷O QCC seems to be influenced little by structural parameters other than the Si-O-Si angle, and is thus expected to be the most reliable ¹⁷O NMR parameter that can be used to decipher Si-O-Si angle distribution information. Both the ¹⁷O QCC and the ²H QCC of silanols decrease with decreasing length of hydrogen bond to a second O atom (Si-O-H···O), and the δ _i ^H increase with the same parameter. Received: 18 July 1997 / Revised, accepted: 23 February 1998     

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     

High-pressure transitions and thermochemistry of MGeO3 (M=Mg, Zn and Sr) and Sr-silicates: systematics in enthalpies of formation of A2+B4+O3 perovskites

Phase transitions in MgGeO₃ and ZnGeO₃ were examined up to 26 GPa and 2,073 K to determine ilmenite–perovskite transition boundaries. In both systems, the perovskite phases were converted to lithium niobate structure on release of pressure. The ilmenite–perovskite boundaries have negative slopes and are expressed as P(GPa)=38.4–0.0082T(K) and P(GPa)=27.4−0.0032T(K), respectively, for MgGeO₃ and ZnGeO₃. Enthalpies of SrGeO₃ polymorphs were measured by high-temperature calorimetry. The enthalpies of SrGeO₃ pseudowollasonite–walstromite and walstromite–perovskite transitions at 298 K were determined to be 6.0±8.6 and 48.9±5.8 kJ/mol, respectively. The calculated transition boundaries of SrGeO₃, using the measured enthalpy data, were consistent with the boundaries determined by previous high-pressure experiments. Enthalpy of formation (ΔH _f°) of SrGeO₃ perovskite from the constituent oxides at 298 K was determined to be −73.6±5.6 kJ/mol by calorimetric measurements. Thermodynamic analysis of the ilmenite–perovskite transition boundaries in MgGeO₃ and ZnGeO₃ and the boundary of formation of SrSiO₃ perovskite provided transition enthalpies that were used to estimate enthalpies of formation of the perovskites. The ΔH _f° of MgGeO₃, ZnGeO₃ and SrSiO₃ perovskites from constituent oxides were 10.2±4.5, 33.8±7.2 and −3.0±2.2 kJ/mol, respectively. The present data on enthalpies of formation of the above high-pressure perovskites were combined with published data for A²⁺B⁴⁺O₃ perovskites stable at both atmospheric and high pressures to explore the relationship between ΔH _f° and ionic radii of eightfold coordinated A²⁺ (R _A) and sixfold coordinated B⁴⁺ (R _B) cations. The results show that enthalpy of formation of A²⁺B⁴⁺O₃ perovskite increases with decreasing R _A and R _B. The relationship between the enthalpy of formation and tolerance factor ( R _o: O²⁻ radius) is not straightforward; however, a linear relationship was found between the enthalpy of formation and the sum of squares of deviations of A²⁺ and B⁴⁺ radii from ideal sizes in the perovskite structure. A diagram showing enthalpy of formation of perovskite as a function of A²⁺ and B⁴⁺ radii indicates a systematic change with equienthalpy curves. These relationships of ΔH _f° with R _A and R _B can be used to estimate enthalpies of formation of perovskites, which have not yet been synthesized.     

The enthalpy of transformation of Ca(OH)2-I (portlandite) to Ca(OH)2-II (EuI2 structure) by low-temperature DSC

 Thermodynamic properties of high-pressure minerals that are not recoverable from synthesis experiments by conventional quenching methods (“unquenchable” phases) usually are calculated from equation of state data and phase diagram topologies. The present study shows that, with cryogenic methods of recovery and sample treatment, phases with a suitable decomposition rate can be made accessible to direct thermodynamic measurements. A set of samples of Ca(OH)₂-II has been synthesized in a multianvil device and subsequently recovered by cooling the high-pressure assembly with liquid nitrogen. Upon heating from liquid nitrogen to room temperature, the material transformed back to Ca(OH)₂-I. The heat effect of this backtransformation was measured by differential scanning calorimetry. A commercial differential scanning calorimeter (Netzsch DSC 404), modified to allow sample loading at liquid nitrogen temperature was used to heat the material from −150 to +200 °C at rates varying between 5 and 15 °C min⁻¹. The transformation started around −50 °C very gradually, and peaked at about 0 °C. To obtain a baseline correction, each sample was scanned under exactly the same conditions after the backtransformation was complete. Because of the relative sluggishness, onset and offset temperatures were not well defined as compared to fast (e.g., melting) reactions. To aid in integration, the resulting signals were successfully fitted using a generic asymmetric peak model. The enthalpy of backtransformation was determined to be ΔH =−10.37 ± 0.50 kJ mol⁻¹. From previous in situ X-ray diffraction experiments, the location of the direct transformation in P-T space has been constrained to 5.7 ± 0.4 GPa at 500 °C (Kunz et al. 1996). With the reaction volume known from the same study, and assuming that ΔC _p of the transformation remains negligible between the conditions of our measurements and 500 °C, our result gives an estimate of the entropy of transition and the P-T slope of the reaction curve. To a first approximation, the values ΔS = −16.00 ± 0.65 J(mol · K)⁻¹ and dP/dT = 0.0040 ± 0.0002 GPa/K have been determined. These results need to be refined by equation of state data for Ca(OH)₂-II. Received: 30 December 1999 / Accepted: 10 April 2000     

Study of the electron density in MgO, (Mg0.963Fe0.037)O and Cu2O by the maximum entropy method and multipole refinements: comparison between methods

 The electron densities determined by the maximum entropy method and by the multipole refinement approach are compared with each other, in terms of some topological properties according to the Bader formalism (Laplacian and eigenvalues of the Hessian matrix of the electron density at the critical points). The cases of MgO, (Mg,Fe)O and Cu₂O are examined. The best agreement is observed for the critical points along the Mg–O, (Mg,Fe)–O and Cu–O directions, whereas larger discrepancies occur at the other critical points. Plots of the electron densities generated by the maximum entropy method and the multipole formalism along the most representative crystallographic directions contribute to elucidating the comparison between approaches. Received: 3 July 2001 / Accepted: 7 March 2002     

Determination of cation distribution in (Co,Ni,Zn)2SiO4 olivine by synchrotron X-ray diffraction

 The cation distribution of Co, Ni, and Zn between the M1 and M2 sites of a synthetic olivine was determined with a single-crystal diffraction method. The crystal data are (Co_0.377Ni_0.396Zn_0.227)₂SiO₄, M _r  = 212.692, orthorhombic, Pbnm, a = 475.64(3), b = 1022.83(8), and c = 596.96(6) pm, V = 0.2904(1) nm³, Z = 4, D _x  = 4.864 g cm⁻³, and F(0 0 0) = 408.62. Lattice, positional, and thermal parameters were determined with MoKα radiation; R = 0.025 for 1487 symmetry-independent reflections with F > 4σ(F). The site occupancies of Co, Ni, and Zn were determined with synchrotron radiation employing the anomalous dispersion effect of Co and Ni. The synchrotron radiation data include two sets of intensity data collected at 161.57 and 149.81 pm, which are about 1 pm longer than Co and Ni absorption edges, respectively. The R value was 0.022 for Co K edge data with 174 independent reflections, and 0.034 for Ni K edge data with 169 reflections. The occupancies are 0.334Co + 0.539Ni + 0.127Zn in the M1 sites, and 0.420Co + 0.253Ni + 0.327Zn in the M2 sites. The compilation of the cation distributions in olivines shows that the distributions depend on ionic radii and electronegativities of constituent cations, and that the partition coefficient can be estimated from the equation: ln [(A/B)_M1/(A/B)_M2] = −0.272 (IR _A -IR _B ) + 3.65 (EN _A −EN _B ), where IR (pm) and EN are ionic radius and electronegativity, respectively. Received: 8 April 1999 / Revised, accepted: 7 September 1999     

Characterization of NH4-phlogopite (NH4) (Mg3) [AlSi3O10] (OH)2 and ND4-phlogopite (ND4) (Mg3) [AlSi3O10] (OD)2 using IR spectroscopy and Rietveld refinement of XRD spectra

 A synthesis technique is described which results in >99% pure NH₄-phlogopite (NH₄) (Mg₃) [AlSi₃O₁₀] (OH)₂ and its deuterium analogue ND₄-phlogopite (ND₄) (Mg₃) [AlSi₃O₁₀] (OD)₂. Both phases are characterised using both IR spectroscopy at 298 and 77 K as well as Rietveld refinement of their X-ray powder diffraction pattern. Both NH₄ ⁺ and ND₄ ⁺ are found to occupy the interlayer site in the phlogopite structure. Absorption bands in the IR caused by either NH₄ ⁺ or ND₄ ⁺ can be explained to a good approximation using T_d symmetry as a basis. Rietveld refinement indicates that either phlogopite synthesis contains several mica polytypes. The principle polytype is the one-layer monoclinic polytype (1M), which possesses the space group symmetry C2/m. The next most common polytype is the two-layer polytype (2M ₁ ) with space group symmetry C2/c. Minor amounts of the trigonal polytype 3T with the space group symmetry P3₁12 were found only in the synthesis run for the ND₄-phlogopite. Electron microprobe analyses indicate that NH₄-phlogopite deviates from the ideal phlogopite composition with respect to variable Si/Al and Mg/Al on both the tetrahedral and octahedral sites, respectively, due to the Tschermaks substitution ^VIMg²⁺+^IVSi⁴⁺↔^VIAl³⁺+^IVAl³⁺ and with respect to vacancies on the interlayer site due to the exchange vector ^XII(NH₄)⁺+^IVAl³⁺↔^XII□+^IVSi⁴⁺. Received: 30 August 1999 / Accepted: 2 October 2000     

Structure of Cu-bearing orthopyroxene, Mg(Cu.56,Mg.44)Si2O6, and behavior of Cu2+ in the orthopyroxene structure

Cu-bearing pyroxene, Mg(Cu.₅₆,Mg.₄₄)Si₂O₆, has been synthesized by a flux method and crystal structure refinement has been performed by single crystal X-ray diffraction. It is found that the crystal structure is orthorhombic (space group Pbca) with unit cell dimensions of a=18.221(4), b=8.890(1), c=5.2260(7)Å and the cell volume of 846.5( )3ų. In the M2-site one of the M-O bonds(M-O3B) is extremely expanded from 2.444(2) in enstatite to 2.732(2), thus the coordination polyhedron around M2-site is regarded as square pyramidal rather than square planar or octahedral. It is also found that the M1-site in the pyroxene structure is occupied almost exclusively by Mg, while the M2-site is almost evenly occupied by Mg and Cu. The observed extreme site preference shown by Cu²⁺ is unusual among the divalent cations with similar ionic sizes.     

High-pressure phase transition and behavior of protons in brucite Mg(OH)2: a high-pressure–temperature study using IR synchrotron radiation

 Infrared absorption spectra of brucite Mg (OH)₂ were measured under high pressure and high temperature from 0.1 MPa 25 °C to 16 GPa 360 °C using infrared synchrotron radiation at BL43IR of Spring-8 and a high-temperature diamond-anvil cell. Brucite originally has an absorption peak at 3700 cm⁻¹, which is due to the OH dipole at ambient pressure. Over 3 GPa, brucite shows a pressure-induced absorption peak at 3650 cm⁻¹. The pressure-induced peak can be assigned to a new OH dipole under pressure. The new peak indicates that brucite has a new proton site under pressure and undergoes a high-pressure phase transition. From observations of the pressure-induced peak under various P–T condition, a stable region of the high-pressure phase was determined. The original peak shifts to lower wavenumber at −0.25 cm⁻¹ GPa⁻¹, while the pressure-induced peak shifts at −5.1 cm⁻¹ GPa⁻¹. These negative dependences of original and pressure-induced peak shifts against pressure result from enhanced hydrogen bond by shortened O–H···O distance, and the two dependences must result from the differences of hydrogen bond types of the original and pressure-induced peaks, most likely from trifurcated and bent types, respectively. Under high pressure and high temperature, the pressure-induced peak disappears, but a broad absorption band between 3300 and 3500 cm⁻¹ was observed. The broad absorption band may suggest free proton, and the possibility of proton conduction in brucite under high pressure and temperature. Received: 16 July 2001 / Accepted: 25 December 2001     

Structure and compressibility of synthetic ZnAl2O4 (gahnite) under high-pressure conditions, from synchrotron X-ray powder diffraction

 The structural behavior of synthetic gahnite (ZnAl₂O₄) has been investigated by X-ray powder diffraction at high pressure (0–43 GPa) and room temperature, on the ID9 beamline at ESRF. The equation of state of gahnite has been derived using the models of Birch–Murnaghan, Vinet and Poirier–Tarantola, and the results have been mutually compared (the elastic bulk modulus and its derivatives versus P determined by the third-order Birch–Murnaghan equation of state are K ₀=201.7(±0.9) GPa, K ^′ ₀=7.62(±0.09) and K ^″ ₀=−0.1022 GPa⁻¹ (implied value). The compressibilities of the tetrahedral and octahedral bond lengths [0.00188(8) and 0.00142(5) GPa⁻¹ at P=0, respectively], and the␣polyhedral volume compressibilities of the four-␣and␣sixfold coordination sites [0.0057(2) and 0.0041(2) GPa⁻¹ at P=0, respectively] are discussed. Received: 15 January 2001 / Accepted: 23 April 2001     

Cation partitioning versus temperature in (Mg0.70Fe0.23)Al1.97O4 synthetic spinel by in situ neutron powder diffraction

Neutron powder diffraction experiments in the temperature range 300–1770 K were performed at BENSC, Berlin, Germany, on synthetic (Mg_0.70Fe_0.23) Al_1.97O₄. The cation partitioning over the crystallographic tetrahedral and octahedral sites was determined as a function of temperature through joint Rietveld refinements and advanced minimization techniques. The thermal expansion coefficients of the lattice parameter and inter-atomic bond lengths were also obtained from the full-profile structure refinements. The behaviour of the polyhedral bond-lengths, especially the T−O distances, and of the cell constant upon heating, clearly indicate that the interdiffusion of tetrahedral and octahedral Mg/Al cations starts at about 950 K. This result is straightforwardly supported by the direct analysis of the neutron site scattering factors: Fe always retains tetrahedral coordination at all temperatures, and the cation rearrangement is entirely due to Mg and Al diffusion. Received: 18 November 1997 / Revised, accepted: 23 August 1998     

Determination of structures of Ca2CoSi2O7, Ca2MgSi2O7, and Ca2(Mg0.55Fe0.45)Si2O7 in incommensurate and normal phases and observation of diffuse streaks at high temperature

 The structures of Ca₂CoSi₂O₇, Ca₂MgSi₂O₇, and Ca₂(Mg_0.55Fe_0.45)Si₂O₇ have been determined in the temperature range between 297 and 773 K with arbitrary intervals. The structures of the incommensurate phase of the three compounds are characterized by the presence of the six-, seven-, and eight-coordinated Ca–O polyhedra and of the bundles along the c-axes consisting of four arrays of the six-coordinated Ca–O polyhedra and an array of T¹O₄ (T¹: Co, Mg, or Mg–Fe) tetrahedra in the structures. The number of bundles in each material decreases at elevated temperatures. The incommensurate phase undergoes a phase transition into the normal phase at 493 K in Ca₂CoSi₂O₇, at 360 K in Ca₂MgSi₂O₇, and at 510 K in Ca₂(Mg_0.55Fe_0.45)Si₂O₇. The features of the structures of the normal phase are almost the same as those found in the basic structures (the averaged structures of the incommensurate structures), and this fact implies that the characteristics of the structures, such as the six-coordinated Ca–O polyhedra or fragments of the bundles, should be partially preserved at higher temperatures both in the incommensurate structures and also in the structures of the normal phase. Analyses of anisotropic displacement parameters clarified that disorder of the modulation waves is developed in the structures at higher temperatures. The evolution of a disorder in the structures was ascertained by observation of the circular diffuse streaks in the vicinity of the transition temperature between the incommensurate and normal phases. Received: 3 July 2000 / Accepted: 26 October 2000     

Thermodynamic properties of Zn(Al,Cr)2O4 spinels at high temperatures and pressures

Three Al-Cr exchange isotherms between Zn(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 900°, 1100°, and 1300° C, at a total pressure of 25 kbar. Employing data on the equation of state of corundum (Chatterjee et al. 1982), the experimental results were evaluated thermodynamically. It was found that the thermodynamic mixing properties of Zn(Al, Cr)₂O₄ spinels are best described in terms of a symmetric Margules equation. The T- and P- dependence of the Margules Parameter, W _G ^Sp , and of ΔG^* of the exchange reaction, 1/2 ZnAl₂O₄ + 1/2 Cr₂O₃ = 1/2 ZnCr₂O₄+1/2 A1₂O₃, are found to be ΔG ^*=1493?2.869·T+0.0081·P and W _G ^Sp (J/mol)=23456+0.0386·P, with T given in K and P in bar.     

Ab initio Hartree–Fock study and charge density analysis of beryl (Al4Be6Si12O36)

 An ab initio Hartree–Fock calculation on beryl structure has been performed and the wave function has been used for an analysis of the electron density. The equilibrium geometry, determined by minimizing the energy with respect to cell parameters and fractional coordinates, is in good agreement with structural experimental measurements; small differences in length between the various Si–O bonds of the structure are well reproduced by the calculation. The two non-equivalent oxygen atoms (O1 and O2) of beryl show different electron distributions. In particular, the valence shell charge concentration (VSCC) of O1 (the bridge between two Si ions) has a torus-like shape, showing a bulge on the external side of the Si–O–Si angle and a thinning on the internal side of it; by contrast O2 has two lone pairs which are approximately located on the line for O2, normal to the plane passing, on average, through the atoms O2, Si, Be and Al. The electron density of each oxygen is strongly polarized toward the Si ions and much less polarized towards the other cations. Such features of the VSCC of the oxygens can be recast in terms of the valence bond theory, to explain the observed differences in bond lengths. By calculating the potential inside the channels of the beryl structure, predictions could be made about the positions occupied by alkali cations, which are often found in natural minerals belonging to the beryl group: results agree in general with experimental findings, but foresee a shift of such cations off the central positions located on the six fold symmetry axis. Additionally, calculations of position and orientation of H₂O inside the channel, in the alkali-free beryl, locate the molecule close to the basal plane, with the H⋯H axis parallel to [001] or oriented at 40^∘ from it. Received: 12 December 2001 / Accepted: 6 April 2002     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000     

Variation of the oxygen content and point defects in olivines, (Fe x Mg 1−x )2SiO4, 0.2 ≤ x ≤ 1.0

 The variation of the oxygen content in olivines, (Fe _x Mg_{1− x} )₂SiO₄, with 0.2 ≤ x ≤ 1.0, was investigated by thermogravimetric measurements. Mass changes occurring upon oxygen activity changes were measured as a function of oxygen activity and cationic composition at 1130 and 1200 °C. During the measurements the samples were in direct contact with gases containing CO, CO₂ and N₂ and, at a few spots at the bottom of the sample stack, also with SiO₂. By fitting experimental data of mass changes to equations derived using point defect thermodynamics, it was shown for olivines with 0.2 ≤ x ≤ 1.0 at 1130 °C and 0.2 ≤ x ≤ 0.7 at 1200 °C within the oxygen activity ranges investigated that the observed variations in the oxygen contents are compatible with cation vacancies and Fe³⁺ ions on M sites and Fe³⁺ ions on silicon sites as majority defects if it is assumed that only three types of point defects occur as majority defects. Different cases were considered, closed systems, taking into account that ξ=[Si]/([Si]+[Fe]+[Mg]) is not necessarily equal to 1/3, and olivines in equilibrium with SiO₂ or pyroxenes. The oxygen content variations observed in this study are significantly smaller than those reported previously in the literature. It is proposed that these differences are related to the dissolution of Fe into noble metal containers used as sample holders in earlier studies and/or to the presence of secondary phases. Received: 1 November 1995 / Accepted: 15 September 2002 Acknowledgements This work was supported by the Cornell Center for Materials Research (CCMR), a Materials Research Science and Engineering Center of the National Science Foundation (DMR-0079992). The authors thank Mr. Daniel M. DiPasquo and Mr. Jason A. Schick for helping in experimental work.     

Characterization of beryl (aquamarine variety) by Mössbauer spectroscopy

The Mössbauer spectra of several blue beryls have been obtained in the temperature range of 4.2–500 K. A common feature observed in all room-temperature spectra is the presence of an asymmetric Fe²⁺ doublet (ΔE _Q ?～?2.7?mm?s^?1, δ?～?1.1?mm?s^?1), with a very broad low-velocity peak. This asymmetry seems to be related to a relaxation process involving ferrous ions and water molecules in the structural channels, as suggested by Price et?al. (1976). Surprisingly, the spectrum at 500?K also shows a broad, but symmetrical, doublet, with a clear splitting of the lines indicating the presence of at least two Fe²⁺ components. The room-temperature spectrum obtained after the 500?K run shows the same features as prior to the heating. At 4.2?K the spectrum of a deep blue beryl was well fitted with four symmetrical doublets, one of which could be related to Fe²⁺ in the structural channels. Ferrous ion was also found to occupy the octahedral and tetrahedral sites, whereas ferric ion is most probably located in the octahedral site. A meaningful fit of the room-temperature spectrum, as well as an explanation for the temperature dependence of the Mössbauer spectra, are discussed. Finally, it is believed that the color in beryl will be dictated by the relative proportions of Fe³⁺ in the octahedral sites and of Fe²⁺ in the channels.     

Ab initio quantum-mechanical modeling of pyrophyllite [Al2Si4O10(OH)2] and talc [Mg3Si4O10(OH)2] surfaces

Bulk and slab geometry optimizations and calculations of the electrostatic potential at the surface of both pyrophyllite [Al₂Si₄O₁₀(OH)₂] and talc [Mg₃Si₄O₁₀(OH)₂] were performed at Hartree–Fock and DFT level. In both pyrophyllite and talc cases, a modest (001) surface relaxation was observed, and the surface preserves the structural features of the crystal: in the case of pyrophyllite the tetrahedral and octahedral sheets are strongly distorted with respect to the ideal hexagonal symmetry (and basal oxygen are located at different heights along the direction normal to the basal plane), whereas the structure of talc deviates slightly from the ideal hexagonal symmetry (almost co-planar basal oxygen). The calculated distortions are fully consistent with those experimentally observed. Although the potentials at the surface of pyrophyllite and talc are of the same order of magnitude, large topological differences were observed, which could possibly be ascribed to the differences between the surface structures of the two minerals. Negative values of the potential are located above the basal oxygen and at the center of the tetrahedral ring; above silicon the potential is always positive. The value of the potential minimum above the center of the tetrahedral ring of pyrophyllite is ?0.05 V (at 2 Å from the surface), whereas in the case of talc the minimum is ?0.01 V, at 2.7 Å. In the case of pyrophyllite the minimum of potential above the higher basal oxygen is located at 1.1 Å and it has a value of ?1.25 V, whereas above the lower oxygen the value of the potential at the minimum is ?0.2 V, at 1.25 Å; the talc exhibits a minimum of ?0.75 V at 1.2 Å, above the basal oxygen.     

Characterisation of tobelite (NH4)Al2[AlSi3O10](OH)2 and ND4-tobelite (ND4)Al2[AlSi3O10](OD)2 using IR spectroscopy and Rietveld refinement of XRD spectra

Tobelite (NH₄) Al₂ [AlSi₃O₁₀] (OH)₂, the ammonium analogue of muscovite, and its deuterated form ND₄-tobelite (ND₄) Al₂ [AlSi₃O₁₀] (OD)₂ have been synthesised at 600?°C and 200 and 500 Mpa using a well homogenised, stoichiometric SiO₂-Al₂O₃ oxide mix with Al₂O₃ in excess of 5 mol% and a 25% NH₃ solution whose relative abundance was such that the amount of NH₄ ⁺ stoichiometrically available was in excess of 50%. Characterisation of both tobelite and ND₄-tobelite using IR-spectroscopy, Rietveld refinement of X-ray powder diffraction data, and electron microprobe analysis indicate that, similar to K⁺ in muscovite, the NH₄ ⁺ or ND₄ ⁺ molecule occupies the interlayer site. IR absorption bands caused by NH₄ ⁺ and ND₄ ⁺ can be explained, to a very good approximation, on the basis of T_d symmetry. Nevertheless, substantial line broadening and the occurrence of shoulders indicate a deviation from ideal T_d symmetry. However, even at 77?K, no discrete splitting of the degenerate states could be confirmed. The OH stretching frequencies observed for synthetic tobelite are quite similar to those for muscovite, indicating that the replacement of K⁺ by NH₄ ⁺ has no effect. The low FWHH of the OH bands indicate that the hydroxyl groups are well ordered within the structure. Rietveld refinement of tobelite and ND₄-tobelite indicates that all samples synthesised consist of the 3 different mica polytypes which are typical of muscovite – namely 1M (C2/m), 2M ₁ (C2/c) and 2M ₂ (C2/c). Tobelite and ND₄-tobelite synthesised at 500 Mpa principally contain the 1M polytype, whereas the principle polytype for ND₄-tobelite synthesised at 200 Mpa, is 2M ₂. Rietveld refinement of X-ray diffraction spectra for tobelite synthesised at 200 Mpa was problematic due to the very broad FWHH of the X-ray peaks indicating poor crystallinity. In comparision to synthetic muscovite, the cell dimensions observed for tobelite and its deuterated analogue are quite similar except for the lattice constant c. Due to the larger radius of NH₄ ⁺ or ND₄ ⁺ compared to K⁺ cation, the c-direction is expanded form 10.275 Å in muscovite to approximately 10.540 Å in tobelite and ND₄-tobelite.