High-pressure phase transformations in the MgFe2O4 and Fe2O3–MgSiO3 systems

 The crystal structure of MgFe₂O₄ was investigated by in situ X-ray diffraction at high pressure, using YAG laser annealing in a diamond anvil cell. Magnesioferrite undergoes a phase transformation at about 25 GPa, which leads to a CaMn₂O₄-type polymorph about 8% denser, as determined using Rietveld analysis. The consequences of the occurrence of this dense MgFe₂O₄ form on the high-pressure phase transformations in the (MgSi)_0.75(Fe^III)_0.5O₃ system were investigated. After laser annealing at about 20 GPa, we observe decomposition to two phases: stishovite and a spinel-derived structure with orthorhombic symmetry and probably intermediate composition between MgFe₂O₄ and Mg₂SiO₄. At pressures above 35 GPa, we observe recombination of these products to a single phase with Pbnm perovskite structure. We thus conclude for the formation of Mg₃Fe₂Si₃O₁₂ perovskite. Received: 27 March 2000 / Accepted: 1 October 2000     

The charge-density distribution, its multipole refinement and the antiferromagnetic structure of dioptase, Cu6[Si6O18]·6H2O

 The chemical bonding in the ring silicate mineral dioptase is investigated on the basis of accurate single-crystal X-ray diffraction data. A multipole model is used in the refinements. Static deformation electron density is mapped for the silicon tetrahedron, Cu-octahedron and water molecule in different sections. The silicon tetrahedron exhibits peaks resulting from σ-bonds between Si–sp³ hybrid orbitals and O–p orbitals. The excess density is located on bonds between the Si atom and bridge (in ring) O(1)-, O(1′)-oxygens and across the interior of the Si–O–Si angle. In the Jahn-Teller distorted Cu octahedron, in addition to peaks which result from single Cu–O σ-bonds, there are peaks which are due to 3d electrons. The analysis of crystal-field influence on the Cu charge distribution is made using the tetragonal D _{4 d} approximation for the low-symmetry (C1) Cu octahedron. The calculation of the occupancies of the 3d atomic orbitals shows that the Cu non-bonding orbitals are most populated (˜20%) and the bonding orbitals least populated (14%), as is typical for the Jahn-Teller octahedron. The effective atomic charge on the Cu atom in dioptase determined from the multipoles is +1.23e: closer to the Cu⁺¹ than to the Cu⁺² state. The charge on the Si atom has a value +1.17e, which is in the range typical for Si atoms already determined by this method. The accumulation of density on bridge oxygens and across the interior of the Si–O–Si angle may be explained by additional strain in the bond with the decrease of the Si–O–Si angle in dioptase to 132°. The same effect was found earlier in coesite. A single-crystal neutron diffraction study shows that dioptase becomes antiferromagnetic below a Néel temperature of 15.9(1) K, in contrast to the previously reported specific heat anomaly at 21 K. The magnetic propagation vector is (0, 0, 3/2) on the hexagonal triple cell or (1/2, 1/2, 1/2) in rhombohedral indices. The relation between the antiferromagnetic and the charge-density models for dioptase is discussed. The less occupied Cu d _x2−y2 orbitals are responsible for the magnetic properties. These lie in the Cu–O squares, which are approximately perpendicular to c _hex, but which are alternately inclined to it by a small angle. The magnetic moments of 0.59(1)μ _B on the Cu ions in the same level are ordered ferromagnetically, but between ions in alternate levels the coupling is antiferromagnet. Within experimental error the magnetic moments are perpendicular to the square planes, which make an angle ±13(3)° to the triad axis. Received: 8 June 2001 / Accepted: 10 January 2002     

Displacive phase transitions in C-centred clinopyroxenes: spodumene, LiScSi2O6 and ZnSiO3

The clinopyroxenes spodumene (LiAlSi₂O₆), LiScSi₂O₆ and ZnSiO₃, all with space group C2/c at ambient conditions, were studied under high pressures by single-crystal X-ray diffraction in a diamond-anvil cell. Changes in the evolution of the unit-cell parameters, optical properties and the appearance of h + k odd reflections characteristic of a primitive lattice, indicate that all three pyroxenes undergo phase transitions. The transitions are mostly displacive in character, and are non-quenchable. Transition pressures are 3.19 GPa in spodumene, ∼0.6 GPa in LiScSi₂O₆ and 1.92 GPa in ZnSiO₃. The space group of all three high-pressure phases was determined to be P2₁/c by structure refinement to single-crystal X-ray intensity data collected in the DAC. In the ZnSiO₃ clinopyroxene the intermediate P2₁/c phase further transforms to a second C2/c phase (HP-C2/c) at 4.9 GPa (confirmed by structure refinement). The volume change at this transition is about 2.6%, three times larger than in the first phase transition, and typical of the P2₁/c→ HP-C2/c phase transitions found previously in MgSiO₃, FeSiO₃, etc. These results therefore provide the first direct evidence that the HP-C2/c and the HT-C2/c structures of pyroxenes are distinct polymorphs with the same space group. The phase transition from C2/c to P2₁/c symmetry in spodumene and LiScSi₂O₆ therefore occurs because the polymorphs stable at ambient conditions are isotypic to the high-temperature C2/c phases of clinopyroxenes such as pigeonite and clinoenstatite. Received: 22 December 1999 / Accepted: 7 June 2000     

A 29Si MAS-NMR study of Cd7[Ge6Si]O21 pyroxmangite

 Synthetic (SiGe)-pyroxenoids are often observed to have superperiods. Whether or not these superperiods grow in connection with Si-Ge ordering is a fundamental question. The size difference between Ge and Si tetrahedra leads to CdGeO₃ having the pyroxmangite structure, whereas CdSiO₃ has the wollastonite structure. Consequently, considerable strain is expected for a pyroxenoid with a disordered Ge-Si distribution. A ²⁹Si MAS-NMR study of a Cd-pyroxmangite of nominal composition Cd₇[Ge₆Si]O₇ points to considerable Si clustering, probably as GeSiSiSiGe triples corresponding to the wollastonite-like units of the siebener chain. It is proposed that such ordering relieves strain within the tetrahedral chain. Residual strain is also relieved by insertion of an extra pair of GeO₄ tetrahedra into the pyroxene-like component of the siebener-chain units, leading to single neuner-chain units which terminate the superperiods. This growth pattern is cyclic. The presence of several types of superperiod may reflect similar energetics for different Ge-Si-ordering patterns within the siebener chains. Ordering of Si-rich unit cells and of unit cells having no Si is proposed as the reason for the occurrence of the superperiods in Cd-pyroxmangite. Received: 25 August 1999 / Accepted: 19 May 2000     

Diffusion in single crystal of melilite: interdiffusion of Al + Al vs. Mg + Si

Interdiffusion coefficients of Al + Al vs. Mg + Si in the gehlenite–åkermanite system of melilite were determined by coupled annealing of synthesized end-member single crystals. The observed diffusion coefficients for a couple-annealed sample vary for about 2 orders of magnitude, showing strong dependence on the gehlenite–åkermanite composition: diffusion coefficient observed at 1350 °C, for example, is 3 × 10^?13 cm² s^?1 at 5 mol% åkermanite composition (Ak₅), increases to 2 × 10^?11 cm² s^?1 at Ak₈₀, and then decreases to 1 × 10^?12 cm² s^?1 at Ak₉₅. The diffusion coefficient–temperature relation indicates high activation energy of diffusion of about 420 kJ mol^?1 for gehlenite-rich melilite. The observed diffusion coefficient–composition relation may be explained by a combination of (1) the diffusion coefficient–melting temperature relation (Flynn's rule) and (2) the feasibility of local charge compensation, which can possibly be maintained more easily in the intermediate chemical composition. The high activation energy value for gehlenitic melilite appears to correspond to the complex diffusion mechanism. The observed highly variable diffusion coefficients suggest that gehlenite–åkermanite zoning in the melilite crystals in Ca, Al-rich inclusions in the carbonaceous meteorites may provide a sensitive indicator for the thermal history of the inclusions.     

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     

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.     

Cation ordering in BaAl2Ge2O8-feldspar: implications for the phase transition in anorthite

BaAl₂Ge₂O₈-Feldspar undergoes an order-disorder phase transition I2/c↔C2/m at T _tr ≈1690 K. The thermodynamics of the Al,Ge cation ordering process is described in terms of the compressible Ising model in mean field approximation. The mean field potential predicts a first order character of the phase transition. This is compared to antiferromagnetic ordering in a two-dimensional square Ising model with NN-pair interactions and four-spin interactions on alternating squares. Calculated order parameters and short range ordering are in good agreement with the corresponding properties observed in BaAl₂Ge₂O₈-feldspar by means of X-ray diffraction, hard mode infrared spectroscopy and TEM. Using known calorimetric data a similar model is postulated for Al,Si ordering in anorthite, CaAl₂Si₂O₈, for which the derived potential describes a transition with slightly stronger first order character at T _tr ≈1928 K. Received: 30 January 1998 / Revised, accepted: 29 August 1998     

Thermal expansion and structural transformations of stuffed derivatives of quartz along the LiAlSiO4–SiO2 join: a variable-temperature powder synchrotron XRD study

 The structural behavior of stuffed derivatives of quartz within the Li_{1− x} Al_{1− x} Si_{1+ x} O₄ system (0 ≤ x ≤ 1) has been studied in the temperature range 20 to 873 K using high-resolution powder synchrotron X-ray diffraction (XRD). Rietveld analysis reveals three distinct regimes whose boundaries are defined by an Al/Si order-disorder transition at x=∼0.3 and a β–α displacive transformation at x=∼0.65. Compounds that are topologically identical to β-quartz (0 ≤ x < ∼0.65) expand within the (0 0 1) plane and contract along c with increasing temperature; however, this thermal anisotropy is significantly higher for structures within the regime 0 ≤ x < ∼0.3 than for those with compositions ∼0.3 ≤ x < ∼0.65. We attribute this disparity to a tetrahedral tilting mechanism that occurs only in the ordered structures (0 ≤ x < ∼0.3). The phases with ∼0.65 ≤ x ≤ 1 adopt the α-quartz structure at room temperature, and they display positive thermal expansion along both a and c from 20 K to their α–β transition temperatures. This behavior arises mainly from a rotation of rigid Si(Al)-tetrahedra about the <100> axes. Landau analysis provides quantitative evidence that the charge-coupled substitution of Li+Al for Si in quartz dampens the α–β transition. With increasing Li+Al content, the low-temperature modifications exhibit a marked decrease in spontaneous strain; this behavior reflects a weakening of the first-order character of the transition. In addition, we observe a linear decrease in the α–β critical temperature from 846 K to near 0 K as the Li+Al content increases from x=0 to x=∼0.5. Received: 26 June 2000 / Accepted: 1 December 2000     

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

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

Non-convergent ordering and displacive phase transition in pigeonite: in situ HT XRD study

A natural Ca-rich pigeonite (En₄₇Fs₄₃Wo₁₀), free of augite exsolution products, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2 ₁ /c (a=9.719(7) Å, b=8.947(9) Å, c=5.251(3) Å, β=108.49(5), V=433.0(6) ų), was annealed up to 1000 °C to induce a phase transition from P2 ₁ /c to C2/c symmetry. Complete single-crystal X-ray diffraction data collections were carried out in situ at 650, 750, 850 and 950 °C after the crystal had reached equilibrium for the Fe–Mg intracrystalline exchange reaction at each temperature. The variation, with increasing temperature, of lattice parameters, of intensity of hkl reflections with h + k=2n + 1 (which vanish at high temperature) and of some geometrical parameters from structure refinement, showed that the displacive phase transition P2 ₁ /c?C2/c was continuous in character. This contrasts with the first-order character for the HT phase transition in pigeonite containing significantly less calcium.     

Phase relations between Ca3Fe 2 3 +Si3O12-Fe 3 2 +Fe 2 3 +Si3O12 garnet and CaFeSi2O6-Fe2Si2O6 pyroxene solid solutions

Editorial responsibility: J. Hoefs     

Simulation of structural phase transition in NaNO3 and CaCO3

 The order-disorder phase transitions in NaNO₃ and CaCO₃ are simulated by molecular dynamics. The simulations are based on the potentials calculated from the Gordon–Kim modified electron gas formalism extended to molecular ions. We successfully reproduced the transition temperature T _c and the abnormally large c axis thermal expansion observed in experiment. The phase transitions in NaNO₃ and CaCO₃ were found to be initiated by ±60 and ±180° reorientation of the NO₃ and CO₃ ions about the c axis. The orientations of NO₃ and CO₃ ions are continuous with six preferred calcite-type orientations above the phase-transition temperature. Received: 30 January 2001 / Accepted: 11 May 2001     

Electronic and magnetic structure of vivianite: cluster molecular orbital calculations

The electronic and magnetic structure of the octahydrophosphate vivianite, Fe₃(PO₄)₂·8H₂O, has been investigated by cluster molecular orbital calculations in local spin density approximation. Optical and Mössbauer spectra are well reproduced by the calculations, and the differences between the two iron sites can be correlated with differences in the geometrical structure of the first coordination sphere. The spin structure within the crystallographic ac plane is derived and explained on the basis of different superexchange pathways via edges of the phosphate tetrahedra. The calculations demonstrate that quite large clusters (up to 118 atoms) are necessary to arrive at reliable results.     

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     

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     

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     

LiFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and NaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> at low temperatures: an infrared spectroscopic study

 Synthetic aegirine LiFeSi₂O₆ and NaFeSi₂O₆ were characterized using infrared spectroscopy in the frequency range 50–2000 cm⁻¹, and at temperatures between 20 and 300 K. For the C2/c phase of LiFeSi₂O₆, 25 of the 27 predicted infrared bands and 26 of 30 predicted Raman bands are recorded at room temperature. NaFeSi₂O₆ (with symmetry C2/c) shows 25 infrared and 26 Raman bands. On cooling, the C2/c–P2₁/c structural phase transition of LiFeSi₂O₆ is characterized by the appearance of 13 additional recorded peaks. This observation indicates the enlargement of the unit cell at the transition point. The appearance of an extra band near 688 cm⁻¹ in the monoclinic P2₁/c phase, which is due to the Si–O–Si vibration in the Si₂O₆ chains, indicates that there are two non-equivalent Si sites with different Si–O bond lengths. Most significant spectral changes appear in the far-infrared region, where Li–O and Fe–O vibrations are mainly located. Infrared bands between 300 and 330 cm⁻¹ show unusually dramatic changes at temperatures far below the transition. Compared with the infrared data of NaFeSi₂O₆ measured at low temperatures, the change in LiFeSi₂O₆ is interpreted as the consequence of mode crossing in the frequency region. A generalized Landau theory was used to analyze the order parameter of the C2/c–P2₁/c phase transition, and the results suggest that the transition is close to tricritical. Received: 21 January 2002 / Accepted: 22 July 2002     

The study of the kinetics and the mechanism of dehydroxylation in muscovite by ESR on Fe3+

 Dehydroxylation of muscovite in the form of small lamellae at 923 <T <1173 K was studied by Electron Spin Resonance (ESR) on Fe³⁺. The kinetics of the process has been established to be described by the model of continuous nucleation on the large surface planes of the small plates. Determined by experimental data the rate constant of the process k is shown to be that of dehydroxylation itself. The activation energy obtained by data at T<1100 K is 97.5 KJ·mol⁻¹. The nonlinear dependence of ln(k) on 1/T is explained by the theory of transitions induced by the fluctuative preparation of a potential barrier as a result of thermal oscillations of ions in the lattice. At high temperatures the potential curve of the hydroxyl's proton is transformed so that it can overcome the barrier from one potential well to the other (from one hydroxyl site to the adjacent one). Such transformations of the curve can be caused by the oscillations of large structural clusters (∼1·10⁻²² kg) with the frequency ∼4.5·10¹² s⁻¹. Received: 3 August 1995 / Accepted: 13 April 1997