Molecular dynamics study of structural changes in berlinite

Fractional coordinates and anisotropic temperature factors of atoms in berlinite, AlPO₄ with the quartz topology, were successfully simulated in a molecular dynamics simulation (MDS) at high temperatures. Time-dependent and time-averaged atomic order parameters were analyzed in detail with the aid of spectral densities calculated from trajectory data. These parameters show characteristic behavior of the order-disorder regime for a structure change, where atoms spend most of the time oscillating around the ₁-sites (or ₂-sites) in the low temperature α-phase, but oscillate over both sites in the higher temperature α-phase and the β-phase. In the spectral density functions calculated for atom order parameters, a nearly zero-frequency excitation, which is accompanied by the emergence of large-scale ₁ and ₂ clusters, appears at the Γ point of the Brillouin zone below the transition point T _o, and increases in intensity up to T _o. A low-lying optic branch along Γ-M, which is strongly temperature dependent in the small q-region, is another characteristic of the spectral density functions for the β phase. The spectrum at Γ continuously reduces its frequency from 0.6 THz at temperatures far above T _o to nearly 0 THz at temperatures approaching T _o from above. The dynamical behavior in β berlinite rapidly but continuously changes from that in less oscillatory clusters in the vicinity of T _o to that in the typical β phase at temperatures departing from T _o. Received: 10 August 1998 / Revised, accepted: 18 February 1999     

Experimental investigation of the α-β transformation of San Carlos olivine single crystal

Single crystalline San Carlos olivine (1 mm cube) was transformed to (Mg,Fe)₂SiO₄β-phase at 13.5–15 GPa, 1030–1330 °C for 0–600 min using a multi-anvil high pressure apparatus. The α-β transformation occurred by incoherent surface nucleation and interface-controlled growth and recovered partially transformed samples showed sharply defined reaction rim. The growth rate of the β-phase rim significantly decreased with time and the growth eventually ceased. TEM observations revealed that many dislocations were created in both the relict olivine just near the α-β interface and the β-phase in the rim, which show evidence for deformation caused by interfacial stresses associated with the misfit elastic strain of the transformation. The observed tangled dislocation texture in β-phase suggested that the β-phase rim was hardened and relaxation of the interfacial stress was retarded. This probably caused a localized pressure drop in the relict olivine and decreased the growth rate. Time-dependent growth rates of β-phase is possibly controlled by the rheology of β-phase, which must be considered for the prediction of the olivine metastability in the subducting slabs. Received: 24 January 1997 / Revised, accepted: 24 July 1998     

Occurrence of highly abundant bacterial hopanoids in Dajiuhu peatland, central China

Based on gas chromatography and gas chromatography-mass spectrometry analyses, an amazing amount of hopanoids was detected in the peat deposits in the Dajiuhu National Wetland Park in central China. The hopanoids identified included hopanes (C₂₇-C₃₁ αβ, C₂₇-C₃₂ ββ, C₂₉ βα), hopenes (hop-22(29)-ene, 22,29,30-trinorhop-17(21)-ene, hop-17(21)-ene, hop-13(18)-ene, etc.), hopanoic acids (C₃₁-C₃₄ ββ, C₃₂-C₃₃ βα, C₃₂ αβ), hopanols (C₃₂ ββ and αβ) and hopanone (22,29,30-trinorhop-21-one). C₃₁ αβ-22R hopane was found to be the dominant hopanoid, more abundant than individual nalkanes derived from higher plants. These hopanoids, exclusive of some hopenes, are proposed to be primarily from bacteria. The dominant C₃₁ αβ-22R hopane in young sediments, without any thermal maturation, might be formed through microbial epimerization under acidic conditions in the peatland as suggested before, or directly from aerobic bacteria. This finding highlights the importance of microbes in the formation of peatland as well as in the reconstruction of paleoenvironments.     

Defect structure of the low temperature α-cristobalite phase and the cristobalite ⇆ tridymite transformation in (Si-Ge)O2

Using minimum exposure techniques, it is feasible to perform high resolution electron microscopy on the α-cristobalite phase of (Si_0.9 Ge_0.1)O₂, which is extremely radiation sensitive. Such images reveal atomic scale information of twins and tridymite-like stacking faults on (1 1 1)_β planes, as well as of domain boundaries resulting from the β→α transition. Polytype structures are formed in certain cases. Morphological features suggest that the phase transformation cristobalite → tridymite proceeds by means of a zonal dislocation mediated synchro-shear process on (1 1 1)_β planes; the geometry of this process is analyzed. Received: 13 June 1999 / Accepted: 30 October 1999     

Wavelength-dispersive x-ray fluorescence spectrometric determination of tantalum in columbite-tantalite using TaKα and an LiF 420 analysing crystal

The paper proposes a simple, accurate, precise, and rapid method for determining the high atomic number (Z) major-element, tantalum (Z = 73), in the rare mineral, columbite [(Fe,Mn) (Nb,Ta)₂O₆] — tantalite [(Fe,Mn) (Ta,Nb)₂O₆], by wavelength-dispersive x-ray fluorescence spectrometry (WDXRFS). The other major-element in columbite-tantalite is the lower atomic number niobium (Z = 41). The method uses the characteristic radiation, TaKα, and an LiF 420 analysing crystal, to overcome the problems associated with the serious x-ray spectral-line interference of the secondorder NbKα and NbKβ with the first-order TaLα1 and TaLβ1 respectively.     

Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T ₀|⁻ⁿ , where T is temperature and T ₀ is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K ₁ = (C ₁₁ +C ₁₂ +C ₁₃)/3 and K ₃ = (C ₃₃ +2C ₁₃)/3 decrease rapidly toward the transition, whereas, shear moduli C ₄₄, C _S1 = (C ₁₁ +C ₃₃ -2C ₁₃)/4 and C _S3 = (C ₁₁ -C ₁₂)/2 = C ₆₆ decrease only slightly. The shear modulus C _S3 = C ₆₆ increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.     

The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001     

EPR study of coordination of Ag and Pb cations in BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> crystals and barium borate glasses

It is shown the possibility to determine the coordination of paramagnetic ions in disordered solid structures, e.g., in barium borate glasses. For this purpose the electron paramagnetic resonance (EPR) method was used to study α-and β-BaB₂O₄ crystals and glasses of 45·BaO × 55·B₂O₃ and 40·BaO × 60·B₂O₃ (mol%) composition activated by Ag⁺ and Pb²⁺ ions. After the samples were exposed to X-rays at 77 K, different EPR centers were observed in them. In α-and β-BaB₂O₄ crystals and glasses the EPR centers Ag²⁺, Ag⁰, Pb⁺, Pb³⁺, and hole centers of O⁻ type were studied. The EPR parameters of these centers and their arrangement in crystal structure were determined. It is shown that Pb³⁺ ions in β-BaB₂O₄ crystals occupy Ba²⁺ position in an irregular polyhedron from the eight oxygen, whereas in α-BaB₂O₄ crystals they occupy Bа₂ position in a sixfold coordination. Pb⁺ ions in α-BaB₂O₄ crystals occupy Bа₁ position in a ninefold coordination from oxygen. In barium borate glasses, Pb³⁺ ions were studied in coordination polyhedron from six oxygen atoms and in a polyhedron from nine to ten oxygen atoms. It is assumed that the established difference in the structural position of Pb³⁺ ions in glasses is due to their previous incorporation in associative cation–anion complexes (AC) and “free” structure-forming cations (FC). Computer simulations have been performed to analyze the stability of specific associative complexes and to compare their bond lengths with experimental data.     

Negative thermal expansion in beta-quartz

Computer modelling and theoretical analysis are used to explain the nearly zero and slightly negative coefficients of thermal expansion in β-quartz well above the α-β phase transition temperature. Quartz was selected for study as an archetypal material with a framework structure of stiff units, namely SiO₄ tetrahedra, linked through shared oxygen atoms as very flexible hinges. The contributions of the soft mode, the Vallade mode, the TA_z phonon branch and the phonon spectrum as a whole are discussed in detail. The results fully support and illustrate a recent theory of the negative contribution to thermal expansion in framework structures. It is a geometrical effect due to the rotation of the tetrahedral units, folding together as they vibrate. The very rapid increase in the lattice parameters for about 20 K above the transition temperature is well accounted for within quasiharmonic theory, and is therefore not evidence for critical fluctuations or fluctuating patches of α ₊, α ₋ structure. Received August 14 1997 / Revised, accepted January 26 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     

High-temperature structure and dynamics of coesite (SiO<Subscript>2</Subscript>) from numerical simulations

The 1-bar structure and properties of the high-pressure SiO₂ polymorph coesite have been simulated by lattice and molecular dynamics up to 1600 and 2100 K, respectively. In agreement with available experimental data, the monoclinic structure was found metastable (with respect to cristobalite or SiO₂ liquid) up to the highest temperatures investigated. Thermal expansion of coesite is small because of restricted rotations of SiO₄ tetrahedra. Above about 1000 K, the structure of coesite becomes dynamically disordered and similar to those reported for the -phases of quartz and cristobalite. Disorder sets smoothly, however, in contrast to its abrupt onset in quartz and cristobalite, which have – transitions. The radial distribution functions for all bond distances indicate that order then prevails only for the nearest neighbors whereas the angle distributions widen markedly so that the monoclinic form of coesite with an Si–O–Si angle of 180° is only a time-averaged structure.     

Raman spectra of hydrous γ -Mg2SiO4 at various pressures and temperatures

 One well-defined OH Raman band at 3651 ± 1 cm⁻¹ and one weak feature near 3700 ± 5 cm⁻¹ are recognized for the hydrous γ-phase of Mg₂SiO₄. Like the hydrous β-phase, the H₂O content in the γ-phase shifts most of the corresponding silicate modes towards lower frequencies. Variations in Raman spectra of the hydrous γ-phase were investigated up to about 200 kbar at room temperature and in the range 81–873 K at atmospheric pressure. Unlike the anhydrous γ-phase, which remains intact up to at least 873 K, the hydrous γ-phase sometimes converts to a defective forsterite structure above 800 K. Although the hydrous γ-phase remains intact up to at least 800 K, Raman signals of the OH bands disappear completely above 423 K. The Raman frequency of the well-defined OH band decreases linearly with increasing temperature between 81 and 423 K. In the region of the silicate vibrations, the Raman frequencies of the two most intense bands increase nonlinearly with increasing pressure, and decrease with increasing temperature. The frequencies for all other weak bands, however, decreased linearly with increasing temperature. The latter most likely reflects the larger scatter of the data for the weak bands. Received: 27 April 2001 / Accepted: 12 September 2001     

Crystal orbital contributions to the pyrrhotite valence band with XPS evidence for weak Fe–Fe π bond formation

 Synchrotron excited X-ray photoelectron spectra (SXPS) of hexagonal pyrrhotite reveal three distinct Fe 3d-derived photopeaks within its outer valence band. The t _2gα band (majority spin) is centered at about 2.5 eV, the e _g α band at about 1.0 eV and the t _2gβ (minority spin) contribution at about 0.25 eV. From these data the ligand field splitting energy is 1.5 (±0.2) eV and the majority spin pairing energy is 2.25 (±0.2) eV. These are the first such XPS measurements for this mineral. S 3p-derived bonding and non-bonding bands are identified, with the former centred at about 6.5 eV and the latter near 4.5 eV. The XPS results are remarkably consistent with SCF-Xα scattered wave molecular orbital calculations. Although the calculations and the collected spectra are consistent, they differ from a recent interpretation of the pyrrhotite valence band. An explanation for the discrepant results is provided. Auger resonant enhancement of Fe 3d photopeaks at 60 eV photon energy results in the t _2gα emission (at 2.5 eV) being strongly enhanced and broader than the t _2gβ emission (0.25 eV). The explanation of these observations requires the presence of weak Fe–Fe π and π^* crystal (molecular) orbitals located near 2.5 eV, and separated by no more than about 0.5 eV. The π-bonded crystal orbitals are derived from weak mixing of adjacent Fe t _2g atomic orbitals along the c crystallographic axis. Received: 15 June 2000 / Accepted: 11 June 2001     

Thermophysical properties of the α–β–γ polymorphs of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>: a computational study

Thermophysical properties of the various polymorphs (i.e. α-, β- and γ) of Mg₂SiO₄ were computed with the CRYSTAL06 code within the framework of CO-LCAO-GTF approach by using the hybrid B3LYP density functional method. Potential wells were calculated through a symmetry preserving, variable cell-shape structure relaxation procedure. Vibrational frequencies were computed at the long-wavelength limit corresponding to the center of the Brillouin zone (k → 0). Thermodynamic properties were estimated through a semiclassical approach that combines B3LYP vibrational frequencies for optic modes and the Kieffer’s model for the dispersion relation of acoustic modes. All computed values except volume (i.e. electronic energy, zero point energy, optical vibrational modes, thermal corrections to internal energy, standard state enthalpy and Gibbs free energy of reaction, bulk modulus and its P and T derivatives, entropy, C _V, C _P) are consistent with available experimental data and/or reasonable estimates. Volumes are slightly overestimated relative to those determined directly by X-ray diffraction. A set of optimized volumetric properties that are consistent with the other semiclassical properties of the phases α, β and γ have been derived by optimization procedure such that the calculated boundaries for the α/β and β/γ equilibria have the best overall agreement with the experimental data for these transitions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

High-temperature phase transitions and elasticity of silica polymorphs

The single-crystal acoustic velocities of α- and β-quartz were measured by Brillouin spectroscopy to a maximum temperature >1,500°C at room pressure. From these velocities, the single-crystal elastic moduli were calculated up to 1,050°C, exceeding the temperature range of previous measurements by 350°C for the elastic moduli and by 710°C for acoustic velocities. The ordinary refractive index (n _o) of α- and β-quartz was measured from room temperature to 800°C. In the temperature interval from ∼950 to 1,000°C a subtle change in the temperature derivative of the longitudinal acoustic velocity was observed in platelet geometry for all measured directions. The high-temperature acoustic velocity data may indicate the presence of a second phase, presumably β-cristobalite, that nucleates below 1,000°C.

Structural defects and polymorphic transformations in quartz

The influence of structural defects on the polymorphic transformations in quartz was studied by electron paramagnetic resonance and electron microscopy. It was established that the kinetics of the accumulation of the clusters of the β-phase depends on isomorphic impurities in quartz. It was confirmed that germanium ions and vacancies in quartz participate in the formation of the clusters. Obtained results allow the assumption that the amount of germanium required to preserve clusters increases with increasing temperature and vice versa. An explanation is presented for experimentally observed decomposition of clusters during artificial heating of some quartz samples. It was found that the clusters of the β-phase are autonomous units, i.e. may exist independently of host crystalline structure of quartz. The possible mechanism of influence of Ge impurity on the temperature of α-β-transition in quarts is discussed.