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     

Synthetic MgGa2O4-Mg2GeO4 spinel solid solution and β-Mg3Ga2GeO8: chemistry, crystal structures, cation ordering, and comparison to Mg2GeO4 olivine

 Structural parameters and cation ordering are determined for four compositions in the synthetic MgGa₂O₄-Mg₂GeO₄ spinel solid solution (0, 8, 15 and 23 mol% Mg₂GeO₄; 1400 °C, 1 bar) and for spinelloid β-Mg₃Ga₂GeO₈ (1350 °C, 1 bar), by Rietveld refinement of room-temperature neutron diffraction data. Sample chemistry is determined by XRF and EPMA. Addition of Mg₂GeO₄ causes the cation distribution of the MgGa₂O₄ component to change from a disordered inverse distribution in end member MgGa₂O₄, ^[4]Ga = x = 0.88(3), through the random distribution, toward a normal cation distribution, x = 0.37(3), at 23 mol% Mg₂GeO₄. An increase in a_o with increasing Mg₂GeO₄ component is correlated with an increase in the amount of Mg on the tetrahedral site, through substitution of 2 Ga³⁺⇄ Mg²⁺+Ge⁴⁺. The spinel exhibits high configurational entropy, reaching 20.2 J mol⁻¹ (four oxygen basis) near the compositional upper limit of the solid solution. This stabilizes the spinel in spite of positive enthalpy of disordering over the solid solution, where ΔH _D  = αx + βx ², α = 22(3), β = −21(3) kJ mol⁻¹. This model for the cation distribution across the join suggests that the empirically determined limit of the spinel solid solution is correlated with the limit of tetrahedral ordering of Mg, after which local charge-balanced substitution is no longer maintained. Spinelloid β-Mg₃Ga₂GeO₈ has cation distribution ^M1[Mg_0.50(2)Ga_0.50(2)] ^M2[Mg_0.96(2)Ga_0.04(2)] ^M3[Mg_0.77(2) Ga_0.23(2)]₂ (Ge_0.5Ga_0.5)₂O₈ (tetrahedral site occupancies are assumed). Octahedral site size is correlated to Mg distribution, where site volume, site distortion, and Mg content follow the relation M1<M3<M2. The disordered cation distribution provides local electrical neutrality in the structure, and stabilization through increased configurational entropy (27.6 J mol⁻¹; eight oxygen basis). Comparison of the crystal structures of Mg_{1+ N} Ga_{2−2 N} Ge _N O₄ spinel, β-Mg₃Ga₂GeO₈, and Mg₂GeO₄ olivine reveals β-Mg₃Ga₂GeO₈ to be a true structural intermediate. Phase transitions across the pseudobinary are necessary to accommodate an increasing divergence of cation size and valence, with addition of Mg₂GeO₄ component. Octahedral volume increases while tetrahedral volume decreases from spinel to β-Mg₃Ga₂GeO₈ to olivine, with addition of Mg and Ge, respectively. Furthermore, M-M distances increase regularly across the join, suggesting that changes in topology reduce cation-cation repulsion. Received: 9 November 1998 / Revised, accepted: 3 August 1999     

Transformations of the stuffed cristobalites, K2MSiO4, M=Mg, Zn, Co, Cd, with temperature and composition

The effects of composition and of temperature on the orthorhombic, Pca2 ₁ to cubic, F4ˉ3m transition of the stuffed cristobalite structure are reported. A distorton index which measures the departure of the orthorhombic unit cell from a metrically cubic cell shows that at room temperature, distortion increases in the progression K₂CdSiO₄ <K₂MgSiO₄ <K₂ZnSiO₄≈K₂CoSiO₄. High temperature X-ray powder measurements document an apparently discontinuous transition to a structure of F4ˉ3m symmetry. Differential scanning calorimetry shows a sharp, reversible, first order transition to the high temperature phase at about 500–600 °C for these compounds. Measured transformation enthalpies in the range of 7 to 16 J/g correlate roughly with the distortion index. The transformation involves tetrahedral rotation to an orientationally disordered cubic structure which retains an ordered M²⁺/Si distribution. Received: 8 November 1996 / Revised, accepted: 14 October 1997     

Mg-vacant structural modules and dilution of the symmetry of hydrous wadsleyite, β-Mg2–xSiH2xO4 with 0.00≤x≤0.25

The crystal structures of the two hydrous wadsleyite crystals with formulae, Mg_1.75SiH_0.50O₄ (0.5H–β) and Mg_1.86SiH_0.28O₄ (0.3H–β) have been analyzed in this study. The single-crystal X-ray diffraction data showed that the unit cells of the 0.3H–β and the 0.5H–β are metrically monoclinic with a slight distortion from the orthorhombic cell but their intensity distributions conform to the orthorhombic symmetry within the limit of experimental errors. The Fourier and the difference Fourier syntheses were calculated. Small but significant Fourier peaks were found at the site, Si2, in a normally vacant tetrahedral void adjacent to Mg3 site as reported for the monoclinic hydrous wadsleyite by Smyth et al.. From the comparison of the hydrous and anhydrous wadsleyite structures, the Mg-vacant structural modules were found to be the building units for the structure of hydrous wadsleyite. The dilution of symmetry from orthorhombic to monoclinic in the hydrous wadsleyite structure is interpreted qualitatively due to lack of mirror perpendicular to the a axis in the module. The mode of arrangement of the Mg-vacant structural modules interprets the symmetry and hydrogen content of the hydrous wadsleyite and gives the structural relationship between hydrous wadsleyite and hydrous ringwoodite. Received: 8 May 1998 / Revised, accepted: 3 October 1998     

Structured diffuse scattering, displacive flexibility and polymorphism in Ba-hexacelsian

 The results of a temperature-dependent electron diffraction study of the low frequency modes of distortion of Ba-hexacelsian and their relationship to the α-β polymorphic phase transition therein are presented. Cs- and Rb-doped Ba-hexacelsian specimens are also investigated. An extremely strong and characteristic diffuse intensity distribution in the form of polarized sheets of diffuse intensity perpendicular to the <1 1 0> directions is found for the high temperature polymorph and the doped specimens. The diffuse distribution appears to result from coupled tetrahedral rotation of <1 1 0> columns of corner-connected (Al,Si)O₄ tetrahedra about the [0 0 1] axis (uncorrelated from column to column as a result of the positioning of the rotation axes). Received: 25 January 1999 / Revised, accepted: 13 July 1999     

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.     

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     

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.     

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     

Elasticity of CaIrO<Subscript>3</Subscript> with perovskite and post-perovskite structure

Compression behaviors of CaIrO₃ with perovskite (Pv) and post-perovskite (pPv) structures have been investigated up to 31.0(1.0) and 35.3(1) GPa at room temperature, respectively, in a diamond-anvil cell with hydrostatic pressure media. CaIrO₃ Pv and pPv phases were compressed with the axial compressibility of β _a > β _c > β _b and β _b > β _a > β _c, respectively and no phase transition was observed in both phases up to the highest pressure in the present study. The order of axial compressibility for pPv phase is consistent with the crystallographic consideration for layer structured materials and previous experimental results. On the other hand, Pv phase shows anomalous compression behavior in b axis, which exhibit constant or slightly expanded above 13 GPa, although the applied pressure remained hydrostatic. Volume difference between Pv and pPv phases was gradually decreased with increasing pressure and this is consistent with the results of theoretical study based on the ab initio calculation. Present results, combined with theoretical study, suggest that these complicate compression behaviors in CaIrO₃ under high pressure might be caused by the partially filled electron of Ir⁴⁺. Special attention must be paid in case of using CaIrO₃ as analog materials to MgSiO₃, although CaIrO₃ exhibits interesting physical properties under high pressure.     

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.     

Molecular composition and organic petrographic characterization of Madbi source rocks from the Kharir Oilfield of the Masila Basin (Yemen): palaeoenvironmental and maturity interpretation

The upper part of Madbi Formation organic-rich shale is considered an important regional source rock in the Masila Basin, Yemen. Ten cutting samples from this Upper Jurassic organic-rich shale were collected from wells drilled in the Kharir Oilfield, Masila Basin in order to geochemically assess the type of organic matter, thermal maturity and depositional environment conditions. Results reveal that Upper Jurassic organic-rich shale samples contain high organic matter more than 2.0 wt.% TOC and have very good to excellent hydrocarbon potential. Marine algae organic matter is the main source input for the Upper Jurassic shale sequence studied. This has been identified from organic petrographic characteristics and from the n-alkane distributions, which dominated by n-C₁₄-n-C₂₀ alkanes. This is supported by the high value of the biomarker sterane/hopane ratio that approaches unity, as well as the relatively high C₂₇ sterane concentrations. A mainly suboxic depositional environment is inferred from pr/ph ratios (1.75–2.38). This is further supported by relatively high homohopane value, which is dominated by low carbon numbers and decrease towards the C₃₅ homohopane. The concentrations of C₃₅ homohopane are very low. The depositional environment conditions are confirmed by some petrographic characteristics (e.g. palynofacies). Detailed palynofacies analysis of Madbi shales shows that the Madbi shale formation is characterised by a mix of amorphous organic matter, dinoflagellates cysts and phytoclasts, representing a suboxic, open marine setting. The Upper Jurassic marine shale sequence in the Masila Basin is thermally mature for hydrocarbon generation as indicated by biomarker thermal maturity parameters. The 22 S/22 S + 22R C₃₂ homohopane has reached equilibrium, with values range from 0.58 to 0.62 which suggest that the Upper Jurassic shales are thermally mature and that the oil window has been reached. 20 S/(20 S + 20R) and ββ/(ββ + αα) C₂₉ sterane ratios suggest a similar interpretation, as do the moretane/hopane ratio. This is supported by vitrinite reflectance data ranging from 0.74% to 0.90%Ro and thermal alteration of pollen and spore. The thermal alteration index value is around 2.6–3.0, corresponding to a palaeotemperature range of 60–120°C. These are the optimum oil-generating strata. On the basis of this study, the Madbi source rock was deposited under suboxic conditions in an open marine environment and this source rock is still within the oil window maturity range.     

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     

Comparison of the surface structure of the tetrahedral sheets of muscovite and phlogopite by AFM

 The surface structure of the tetrahedral sheet of dioctahedral mica muscovite was compared to that of the tetrahedral sheet of trioctahedral mica phlogopite using atomic force microscopy (AFM). AFM revealed distinct structural differences between the tetrahedral sheet surfaces of the two micas. The hexagonal ring in the AFM image of muscovite elongates in the [3 1 0] direction, and the groove runs perpendicular to the [3 1 0] direction. On the phlogopite surface, the hexagonal ring contracts slightly in the a axis direction, but the groove is not apparent. These results were consistent with the bulk structure data of the two micas determined by X-ray diffraction (XRD). The degree of surface relaxation was much larger in muscovite than in phlogopite. In muscovite, the interlayer K reduces the amount of tetrahedral rotation that actually occurs, since the interlayer K is too large for its hexagonal hole after full tetrahedral rotation. Thus, it is naturally expected that muscovite will show more tetrahedral rotation after removal of the interlayer K. It is also expected that muscovite will show more tilting of SiO₄ tetrahedra after cleaving, since an attractive force between the hydrogen in the OH group and the lower basal oxygen should be in operation, due to the decreased distance between them following interlayer K removal. Received: 14 March 2000 / Accepted: 29 July 2000     

The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W ₁₀, since the broadening of the observed pulses due to the transition to the full width W ₀ and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β ₁ are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β ₁〉 = 18° at λ = 10 cm and 〈β ₁〉 = 14° at λ = 20 cm). The angle β ₂ is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β ₂ at 10 cm is found to be 〈β ₂〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β ₂〉 = 52.1° ifC < 0. We find at 20 cm 〈β ₂〉 = 33.9° ifC > 0 and 〈β2〉 = 54.1° ifC < 0. The values at the two wavelengths are equal within the errors, and close to the β ₂ value obtained earlier at 30 cm (〈β ₂〉 = 36.4° if C >0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β ₂〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P ^−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P ^−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.     

Potassium coordination in trioctahedral micas investigated by K-edge XANES spectroscopy

Summary Fine-grained homogeneous powder samples of thirteen trioctahedral micas, mostly intermediate members of the phlogopite – annite solid solution series, and samples close to the phlogopite, fluor-phlogopite and tetra-ferriphlogopite end members have been examined at the potassium K-edge by X-ray absorption fine structure spectroscopy. The interlayer K⁺ cation is in a coordination that is certainly lower than 12, in contrast to what is expected from the ideal hexagonal symmetry model of the mica structure, and approaches – but it does not reach – coordination 6, as it should be when the effective ligands are the three nearest outer bridging oxygens of two facing upper and lower tetrahedral sheets. The observed range of coordinations implies that only some of the three inner bridging oxygen atoms in each sheet are involved, thus leading to 6±(1 … 6) effective configurations depending on the composition of the individual mica terms. The effective coordination number was found to vary continuously with composition from 11 to 7 and to be related to the tetrahedral rotation angle (α) according to two different linear relationships for the phlogopite – annite series (Fe²⁺Mg₋₁ exchange vector, involving the octahedral sheet only) and the phlogopite – tetra-ferriphlogopite series (Fe³⁺Al₋₁ vector, involving the tetrahedral sheet), respectively. Substitutions affecting either the A cation in the interlayer or the X anion in the octahedral sheet also affect the observed trends. In particular, the latter substitution effect is best seen in two near end member phlogopites, where the fluorine to hydroxyl substitution (F⁻ (OH)⁻₋₁ exchange vector), which greatly changes the α tetrahedral rotation angle is, reflected in the experimental K XANES spectra by modifying not only the energy but also the intensities of most multiple scattering features.     

Variation of infrared absorption spectra in the system Bi2Al4−x Fe x O9 (x = 0–4), structurally related to mullite

The crystal structure of Bi₂Al_4−x Fe _x O₉ compounds (x = 0–4) has striking similarities with the crystal structure of mullite. A complete substitution of Al by Fe³⁺ in both octahedral and tetrahedral sites is a particular structural feature. The infrared (IR) spectra of the Bi₂M₄O₉ compounds (M = Al, Fe³⁺) are characterised by three band groups with band maxima in the 900–800, 800–600 and 600–400 cm⁻¹ region. Based on the spectroscopic results obtained from mullite-type phases, the present study focuses on the composition-dependent analysis of the 900–800 cm⁻¹ band group, which is assigned to Al(Fe³⁺)–O stretching vibrations of the corner-sharing MO₄ tetrahedra. The Bi₂Al₄O₉ and Bi₂Fe₄O₉ endmembers display single bands with maxima centred at 922 and 812 cm⁻¹, respectively. Intermediate Bi₂Al_4−x Fe _x O₉ compounds exhibit a distinct splitting into three relatively sharp bands, which is interpreted in terms of ordering effects within the tetrahedral pairs. Thereby the high-energy component band of the band triplet relates to Al–O–Al conjunctions and the low-energy component band to Fe–O–Fe conjunctions. The intermediate band is assigned to stretching vibrations of Al–O–Fe or Fe–O–Al configurations of the corner-sharing tetrahedral pairs. Bands in the 800–600 cm⁻¹ range are assigned to low-energy stretching vibrations of the MO₄ tetrahedra and to M–O–M bending vibrations of the tetrahedral pairs. Absorptions in the 600–400 cm⁻¹ range are essentially determined by M–O stretching modes of the M cations in octahedral coordination.     

High-pressure behaviour of Ca-rich C 2 /c clinopyroxenes along the join diopside-enstatite (CaMgSi2O6-Mg2Si2O6)

 An in situ high-pressure (HP) X-ray diffraction investigation of synthetic diopside and of the Ca_0.8Mg_1.2Si₂O₆ clinopyroxene (Di₈₀En₂₀) was performed up to respectively P=40.8 and 15.1 GPa, using high brilliance synchrotron radiation. The compression of the cell parameters is markedly anisotropic, with β_b ⋙ β_c > β_a > β_asinβ for any pressure range and for both diopside and Di₈₀En₂₀. The compressibility along the crystallographic axes decreases significantly with pressure and is higher in Di₈₀En₂₀ than in diopside. The β cell parameter decreases as well with pressure, at a higher rate in Di₈₀En₂₀. The cell volume decreases at almost the same rate for the two compositions, since in diopside a higher compression along a* occurs. A change in the mechanism of deformation at P higher than about 5–10 GPa is suggested for both compositions from the analysis of the strain induced by compression. In diopside at lower pressures, the deformation mainly occurs, at a similar rate, along the b axis and at a direction 145° from the c axis on the (0 1 0) plane. At higher pressures, instead, the deformation occurs mostly along the b axis. In Di₈₀En₂₀ the orientation of the strain axes is the same as in diopside. The substitution of Ca with Mg in the M2 site induces at a given pressure a higher deformation on (0 1 0) with respect to diopside, but a similar change in the compressional behaviour is found. Changes in the M2 polyhedron with pressure can explain the above compressional behaviour. A third-order Birch-Murnaghan equation of state was fit to the retrieved volumes, with K=105.1(9) GPa, K′=6.8(1) for diopside and K=107.3(1.4) GPa, K′=5.7(3) for Di₈₀En₂₀; the same equation can be applied for any pressure range. The elasticity of diopside is therefore not significantly affected by Mg substitution into the M2 site, in contrast to the significant stiffening occurring for Ca substitution into Mg-rich orthopyroxenes. Received: 3 January 2000 / Accepted: 21 May 2000     

Molecular dynamics interpretation of structural changes in quartz

 Constant temperature and constant pressure molecular dynamics (MD) simulations were applied to quartz to calculate the structural details which are indeterminable in usual X-ray structure studies. The dynamics of the structural changes was analyzed by means of time-dependent atomic displacement parameters. The Si-O bonds expand with increasing temperatures through the α- and β-phases, and atoms vibrate around the α₁- (or α₂-) sites at lower temperatures in the α-phase, and over the energy barriers between the α₁- and the α₂-sites at higher temperatures in the α- and the β-phases. The ratios of time lengths spent by atoms in the α₁- and α₂-sites determine the apparent atomic positions as obtained in usual structure studies of α-quartz. More frequent transfer of atoms over the α₁- and the α₂-sites contributes positively to the thermal expansions, whereas larger amplitudes of vibrations, which carry atoms more distantly and more frequently from the β-sites, contribute negatively. The well-known steep thermal expansion in the α-phase is attributed to the additive contribution from the expansions of the Si-O bond lengths, the widening of Si-O-Si angles, and the increase of the atomic transfer-frequency between the α₁- and the α₂-sites. The nearly zero or negative expansion in the β-phase is caused by balancing the negative to the positive effects. The MD crystal transforms to the β-phase via a transitional state, where the α- and β-structures appear alternately with time, or coexist. The slight and continuous expansions observed right after the steep rise(s) of the volume or cell dimensions up to the nearly horizontal curve(s) are attributed to the continuous changes within the transitional state. Received: 17 July 2000 / Accepted: 13 January 2001     

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