Pressure-volume-temperature behavior of fayalite based on static compression measurements at 400° C

Twenty-one energy-dispersive X-ray diffraction spectra for fayalite at 400° C constitute the basis for an elevated-temperature static compression isotherm for this important silicate mineral. A Murnaghan regression of the resulting molar volumes yields 103.8 GPa and 7.1 for the 400° C, room-pressure values of the isothermal bulk modulus (K ₀) and its first pressure derivative (K₀), respectively. When compared to the room-temperature static compression isotherm of Yagi et al. (1975), our 400° C value for K ₀ yields 5.4 ×10^–2 GPa/deg for (K/T)₀₀. When combined with literature volume data, our measurements indicate that the fayalite isochores are strongly concave toward the pressure axis [( ² T/P ² ) _v <>This is publication number 1125 of the School of Earth Sciences, Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA     

Diamagnetic anisotropies of oxide minerals

The diamagnetic anisotropy of oxide minerals is analyzed in terms of a new model, in which the anisotropy is assigned to the individual chemical bond in the [MO₆] octahedral unit of the crystal. The diamagnetic principal axis of the individual M-O bond is assumed to be parallel to the direction of the bond. The calculated anisotropy based on this model shows a good correlation with the measured diamagnetic anisotropy, , for various minerals such as talc, sericite, kaolinite of the sheetsilicate group, forsterite of the orthosilicate group, and corundum of the hematite group. The values of many diamagnetic minerals are still unknown since the measurement is difficult to perform by means of conventional methods. The magnetic grain orientation recently observed in the mineral suspensions is effective for estimating the value, when the single crystal of the mineral cannot be obtained. The observation of fieldinduced crystal oscillation in the high magnetic fields can be applied for measuring the minerals with small values of less than 5 × 10^–10 emu/cc. The chemical bond model on the diamagnetic anisotropy can be confirmed, when the compiling of data on various mineral is made by means of the above two methods.     

Pressure-volume-temperature behavior of γ-Fe2SiO4 (spinel) based on static compression measurements at 400° C

Thirteen energy-dispersive x-ray diffraction spectra for -Fe₂SiO₄ (spinel) collected in situ at 400° C and pressures to 24 GPa constitute the basis for an elevated-temperature static compression isotherm for this important high-pressure phase. A Murnaghan regression of these molar volume measurements yields 177.3 (±17.4) GPa and 5.4(±2.5) for the 400° C, room pressure values of the isothermal bulk modulus (K _{P 0}) and its first pressure derivative (K _{P 0}), respectively. When compared to the room-Tdeterminations of K _{P 0} available in the literature, our 400° C K _{P 0} yields -4.1 (±6.2)×10^-2 GPa/degree for the average value of (K/T) _{P 0} over the temperature interval 25° C<><400°>A five-parameter V(P, T) equation for -Fe₂SiO₄ based on simultaneous regression of our data combined with the elevated P-Tdata of Yagi et al. (1987) and the extrapolated thermal expansion values from Suzuki et al. (1979) yields isochores which have very little curvature [(² T/P ²) _v 0], in marked contrast to the isochores for fayalite (Plymate and Stout 1990) which exhibit pronounced negative curvature [(T/P ²) _v <0]. along=" the=">-Fe₂SiO₄ reaction boundary V_Rvaries from a minimum of approximately 8.3% at approximately 450° C to approximately 8.9% at 1200° C. Extrapolation of the fayalite and -Fe₂SiO₄ V(P, T) relationships to the temperature and pressure of the 400 km discontinuity suggests a V _R of approximately 8.4% at that depth, approximately 10% less than the 9.3% V _R at ambient conditions.     

Pressure and temperature dependence of the elastic properties of synthetic MnO

The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C _ij ^s ) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K ^s=155.1±0.8 GPa; (K^s/P)_T=4.70±0.13; and, (K ^s/T)_P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn₃O₄ inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C ₄₄ exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C ₄₄ data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition.     

Al-Si ordering in Sr-feldspar SrAl2Si2O8: IR,TEM and single-crystal XRD evidences

Al-Si ordering in Sr-feldspar has been followed by isothermal annealing, starting from a disordered metastable configuration. Ordering could not be followed by changes in the spontaneous strain as cell parameters did not show significant changes with thermal treatment from 0.016 h to 452 h at T=1350° C, while, on the contrary, significant changes in IR spectra are observed. A single crystal obtained from melt (Q _od 0) has been progressively heated up to 678 h at T=1350° C and the relevant structural refinements enabled to monitor changes in degree of Al-Si order up to Q_od = 0.86. In isothermal treatment for Sr-feldspar it is observed a significantly lower Q _od than in anorthite after the same annealing time. TEM observation has shown in Sr-feldspar, also for shortest annealing, b type reflections, while in anorthite, in the same conditions, e type reflections have been observed (Carpenter 1991a). In the first stages of ordering b APDs sized 100 Å (at T=1350° C, 0.33 h) have been observed in Sr-feldspar; APD coarsening occurs with an activation energy of 120±7 kcal mol^-1, not significantly different from anorthite. The ordering process seems to be a slower process in Sr-feldspar than in anorthite, even though data from longer annealing suggest that the Q _od close to the equilibrium is the same in Sr and Ca-feldspar (Q _od = 0.86 at T=1350° C).     

Hydrostatic compression of γ-(Mg0.6, Fe0.4)2SiO4 to 50.0 GPa

The bulk modulus, K ₀, and its pressure derivative K₀, of -(Mg_0.6, Fe_0.4)₂SiO₄ have been accurately determined to 50.0 GPa under hydrostatic conditions at room temperature in a diamond cell using synchrotron radiation. Our results agree with Brillouin and ultrasonic measurements on -Mg₂SiO₄ at low pressure, indicating normal elastic behaviour in the metastable pressure range of this high pressure mineral. Our values of K ₀ and k₀ are 183.0 GPa and 5.4, respectively.     

The early Toarcian and Cenomanian-Turonian anoxic events in Europe: comparisons and contrasts

Two intervals of Mesozoic time are demonstrably of sufficient geological brevity to qualify readily for the term Anoxic Event: the earlyfalciferum Zone orexaratum Subzone of the Toarcian and theWhiteinella archaeocretacea Interval Zone that straddles the Cenomanian-Turonian boundary. Both periods of time saw regional deposition of anomalously organic-rich strata (black shales) accompanied by a positive 2 PDB carbon-isotope excursion in coeval biogenic carbonates, and significant faunal change. The duration of both events was probably less than half a million years, and both were preceded by regional erosion and possible upwelling. Coincident sea-level rise and transgression is likely. A »European view« of these events, however, spotlights some significant differences. Whereas thefalciferum-Zone organic matter is generally more concentrated and more hydrogen-rich on the palaeo-European shelf than on the Tethyan continental margins, the reverse holds true for the black shales formed during theWhiteinella archaeocretacea Interval Zone. Furthermore, the carbon-isotope composition offalciferum-Zone organic matter from both north European and Tethyan sites is anomalously negative compared to that developed in theWhiteinella archaeocretacea Interval Zone. Differing planktonic organisms may have been involved and their possible diverse ecological requirements may go some way to explaining the nature and distribution of facies deposited during these two events.

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Zusammenfassung Zwei mesozoische Abschnitte rechtfertigen die Verwendung des Begriffes »Anoxic Event«: die frühefalciferum-Zone oderexaratum-Zone des Toarcian und dieWhiteinella archaeocretacea Interval-Zone, die die Grenze Cenoman-Turon überquert. In beiden Zeitabschnitten bildeten sich regional Sedimente mit anomalem Reichtum an organischer Substanz (Schwarzschiefer), die von einem positiven über 2 PDB hinausgehenden Ausschlag bei den Kohlenstoffisotopen in gleichalten biogenen Karbonaten begleitet werden. Die Dauer der beiden Ereignisse betrug wahrscheinlich weniger als eine halbe Million Jahre und beiden ging eine Phase regionaler Erosion und möglicherweise des »Aufquellenden Tiefenwassers« voraus. Gleichzeitiger Anstieg des Meerespiegels mit Transgression ist wahrscheinlich. Die europäische Sicht dieser Ereignisse bedeutet einige signifikante Unterschiede. Diefalciferum-Zone besitzt auf dem palaeo-europäischen Shelf generell eine höhere Konzentration des organischen Materials und der Kohlenwasserstoffe als auf den Kontinentalrändern der Tethys. Das Gegenteil ist der Fall in den Schwarzschiefern, die sich während derWhiteinella archaeocretacea Interval-Zone gebildet haben. Außerdem ist die Zusammensetzung der Kohlenstoffisotopen des organischen Materials derfalciferum-Zone sowohl von Nordeuropa als auch von der Tethys unnormal negativ verglichen mit derWhiteinella archaeocretacea Interval-Zone. Die Beteiligung unterschiedlicher planktonischer Organismen und möglicherweise abweichende ökologische Bedingungen können für die Faziesverteilung während dieser zwei Ereignisse verantwortlich gemacht werden.

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Résumé Deux intervalles de l'ère mésozoque sont assez brefs pour être qualifiés d'événements anoxiques: la Zoneà falciferum (souszone àexaratum) du Toarcien et la Zone àWhiteinella archaeocretacea à la limite Cénomanien-Turonien. Chacun de ces deux intervalles correspond à un dépôt régional de couches anormalement riches en matières organiques (black shales), accompagné, dans des carbonates biogénétiques de même âge, d'une anomalie positive de plus de 2 PDB des isotopes du carbone. Les deux événements ont probablement été précédés par une phase d'érosion ou de condensation sédimentaire et de remontée d'eaux profondes («upwelling»). Leur durée, qui correspondait probablement à une période d'élévation du niveau des mers et de transgression, a été inférieure à 500.000 ans.A l'échelle européenne, les deux événements anoxiques se distinguent: la matière organique de la Zone àfalciferum est plus concentrée et plus riche en hydrogène sur la plateforme mésozoque nord-européenne que sur la marge téthysienne, tandis que la Zone àWhiteinella archaecocretacea montre une dispostion inverse. De plus, la composition isotopique du C dans la matière organique de la Zone àfalciferum est plus négative que celle de la Zone àWhiteinella archaeocretacea tant dans les régions nord-européennes que téthysienne. Il est possible qu'il s'agisse d'espèces différentes d'organismes planctoniques, leurs milieux écologiques différents pouvant expliquer la nature et la distribution des faciès typiques déposés pendant les deux épisodes.

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n Event ( ) : , , Whiteinella archaeocretacea, / . ( ), ( PDB 2) . , , , — . , . . , , , , , , , . , , , . , , , , .

     

β(Mg0.9, Fe0.1)2SiO4: Single crystal structure,cation distribution,and properties of coordination polyhedra

The synthesis boundaries of the phase transformation; ++ in (Mg_0.9, Fe_0.1)SiO₄, have been clarified at temperatures to 2000° C and pressures up to 20 GPa in order to synthesize single crystals of high quality. A single crystal of (Mg_0.9, Fe_0.1)₂SiO₄ was grown successfully to a size of 500 m. The crystal structure has been refined from single-crystal X-ray intensities. The ferrous ions prefer M1 and M3 sites to over the larger M2 site. The volume change of all the occupied polyhedra does not contribute to the decrease of total volume in the transformation; rather it tends to increase the bulk volume through the expansion of occupied tetrahedra. The volume reduction in the phase transformations is accounted for by unoccupied polyhedra, with the octahedra contributory 60% and the tetrahedra 40% to the V of the transition. The volume change in the transformation is caused also partly by the volume decrease of MO ₆ (25%), partly the unoccupied tetrahedra (45%) and octahedra (30%).     

Chemistry of some Pb-(Cu,Fe)-(Sb,Bi sulfosalts from France and Portugal. Implications for the crystal chemistry of lead sulfosalts in the Cu-poor part of the Pb2S2-Cu2S-Sb2S3-Bi2-Bi2S3 system

Electron microprobe analysis of Pb-Cu(Fe)-Sb-Bi sulfosalts from Bazoges and Les Chalanches (France), and Pedra Luz (Portugal), give new data about (Bi, Sb) solid-solution and incorporation of the minor elements Cu, Fe or Ag in jaskolskiite, and in izoklakeite-giessenite and kobellite-tintinaite series. Jaskolskiite from Pedra Luz has high Sb contents (from 17.9 to 20.7 wt.%), leading to the extended general formula: Cu _x Pb_2+x (Sb_1–y Bi _y )_2–x S₅, with 0.10 x 0.22 and 0.19 y 0.41. Fe-free, Bi-rich izoklakeite from Bazoges has high Ag contents (up to 2.2 wt. %), leading to the simplified formula Cu₂Pb₂₂Ag₂(Bi, Sb)₂₂S₅₇; in Les Chalanches it contains less Ag content (1.2 wt.%), but has an excess of Cu that gives the formula: Cu_2.00 (Cu_0.49Ag_1.18)_=1.67Pb_22.70(Bi_12.63Sb_8.99)_=21.62S_57.27.In tintinaite from Pedra Luz, the variation of the Fe/Cu ratio can be explained by the substitution: Cu + (Bi, Sb) Fe + Pb; Fe-free kobellite from Les Chalanches has a Cu-excess, corresponding to the formula Cu_2.81Ag_0.54Pb_9.88(Bi_10.37Sb_5.21)_=15.38S_35.09. Eclarite from the type locality, structurally related to kobellite, shows a Cu excess too. In natural samples of the kobellite homologous series, Fe is positively correlated with Pb, and its contents never exceed that of Cu. Ag substitutes for Pb, together with (Bi, Sb). Taking into account the possibility of Cu excess, but excluding formal Cu²⁺ and Fe³⁺, general formulae can be written:     

Electron paramagnetic resonance of Sc3+-stabilized CO 3 3− molecule-ion in natural calcite

Electron paramagnetic resonance (EPR) spectra of CO ₃ ^3– molecule-ions stabilized by Sc³⁺ in natural calcite were identified and studied at X-band frequencies and room temperature. The principal values of the g-tensor (g _xx= 1.9997, g _yy = 2.0030, g _zz = 1.9972) and the direction cosines of the g and A tensors for CO ₃ ^3– -Sc³⁺ center were found to be close to that for the well-known CO ₃ ^3– -Y³⁺ center. A quantitative comparison of different impurity contents in calcite samples and analysis of the intensities of forbidden transitions were used to identify Sc³⁺. An estimation of the unpaired electron spin density on the nuclei of paramagnetic centers confirms that both centers, CO ₃ ^3– -Sc³⁺ and CO ₃ ^3– -Y³⁺, have the same nature.     

31P solid-state nuclear magnetic resonance spectroscopy of aluminum phosphate minerals

This study examines the links between ³¹P solidstate NMR studies of aluminum phosphate minerals and their crystallographic structures. We found that ³¹P isotropic chemical shift values, _iso, carry little information about mineral structures. There seems to be no relation between the chemical shift anisotropy, =₃₃–₁₁ (₃₃>₂₂> ₁₁), and indicies of phosphate-tetrahedra distortion. ³¹P¹H heteronuclear magnetic dipole interactions, on the other hand, carry important information about hydrous phosphate mineral structures, information that should prove to be quite valuable in studies of phosphate adsorbed on mineral surfaces. This interaction can be measured through a variety of qualitative and quantitative experiments. It appears that spin diffusion is so rapid that subtle differences in hydrogen-bonding environments cannot be resolved.     

Lithologische Untersuchungen an den Kirchberger Sanden (Pannon C,Steirisches Becken) mit Hilfe elektronischer Datenverarbeitung

Zusammenfassung Im Zuge der lithologischen Bearbeitung eines Sandhorizontes im Pannon C der Oststeiermark (Österreich) wurden statistische Auswertungen mit Hilfe einer elektronischen Rechenanlage durchgeführt. Trendflächenanalysen lassen zum Teil Zusammenhänge zwischen der aus Schrägschichtungsmessungen festgestellten Sedimentationsrichtung (NW-SE) einerseits und den Korngrößenparametern der Sande sowie der Schwermineralführung andererseits vermuten.

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In the course of lithological researches on sands occurring in Pannonian C in the east of the Province of Styria, Austria, statistical evaluations were made by means of a computer. Trend-surface analyses partly seem to indicate the existence of correlations between the paleocurrents (NW-SE), found as a result of measurements of cross-bedding on the one hand and the size-parameters of the sands as well as the heavy mineral composition on the other hand.

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Résumé L'exploitation statistique de recherches lithologiques d'un horizon sableux au pannonien C à l'est de la Styrie (Autriche) fut réalisée à l'aide d'une calculatrice électronique. En analysant des surfaces d'équation polynomiale nous supposons des corrélations entre la direction de transport (constatée par des mesures de la stratification entrecroisée: NW-SE) et les paramètres granulométriques des sables ainsi que la contenance en minéraux lourds.

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() . (- — ), .

     

Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes

The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, , consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log₁₀ units of time above . In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; _S = _S/G (where _S is the shear relaxation time, G is the shear modulus at infinite frequency and _S is the zero frequency shear viscosity). The value of G known for SiO₂ and several other silicate glasses. The shear modulus, G , and the bulk modulus, K , are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to _S, G may be considered a constant (independent of composition and temperature) and the value of _S, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from ²⁹Si NMR studies.     

Mg tracer diffusion in synthetic forsterite and San Carlos olivine as a function of P,T and fO2

We present new experimental data on Mg tracer diffusion in oriented single crystals of forsterite (Fo₁₀₀) and San Carlos olivine (Fo₉₂) between 1000–1300° C. The activation energies of diffusion are found to be 400 (±60) kJ/mol (96 kcal/mol) and 275 (±25) kJ/mol (65 kcal/ mol) in forsterite and San Carlos olivine, respectively, along [001] at a fO₂ of 10^–12 bars. There is no change in activation energy of Mg tracer diffusion within this temperature range. Mg tracer diffusion in a nominally pure forsterite is found to be anisotropic (D_c > D_a > D _b) and a function of fO₂. This fO₂ dependence is different from that in olivine containing Fe as a major element, which suggests that the diffusion mechanism of Mg in forsterite is different from that in Fe-bearing olivine at least over some range of fO₂. The diffusion mechanism in nominally pure forsterites may involve impurities present below the limits of detection or alternately, Si or Fe³⁺ interstitial defects, Fe being present as impurity (ppm level) in forsterite. Pressure dependence of Mg tracer diffusivity in forsterite measured to 10 GPa in a multianvil apparatus yields an activation volume of approximately 1–3.5 cm³/ mol. It is found that presence of small amounts of hydrogen bearing species in the atmosphere during diffusion anneal (f_H2 0.2 bars, f_H20 0.24 bars) do not affect Mg tracer diffusion in forsterite within the resolution of our measurement at a total pressure of 1 bar. The observed diffusion process is shown to be extrinsic; hence extrapolation of the diffusion data to lower temperatures should not be plagued by uncertainties related to change of diffusion mechanism from intrinsic to extrinsic.     

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

A materials failure relation of accelerating creep as empirical description of damage accumulation

A general materials failure relation, , describes accelerating creep of materials with rate coefficients andA, by relating rates of deformation, , to changes in deformation rate, (Voight, 1988). Time of failure can be extrapolated from inverse rate versus time data, and andA may be derived to permit one to calculate the failure time. The method is of value for quantitative hazard assessments.Mechanisms leading to damage accumulation during accelerating creep include creep fracture by stress corrosion and power law lattice deformation. These mechanisms are examined here as phenomenologically related to the materials failure relation. Apparently, both mechanisms favour , where is the parameter of the materials failure relation controlling the sensitivity to accelerating activity. For pure shear governed by power law creep of powerp, under constant load, =2.0 andA=p. Stress corrosion is widely described by Charles' equation, relating crack velocity to stress intensity during subcritical crack growth by the stress corrosion indexn. The relationship betweenn and is given by =(2n–2)/n.     

Mössbauer study of a California desert celadonite and its pedogenically-related smectite

Celadonite from the northwestern Mojave Desert area of California was examined by detailed Mössbauer spectroscopy at temperatures from 10 K to 400 K. In addition to the predominant Fe³⁺ doublet with isomer shift 0.4 mm s^–1 and quadrupole splitting 0.4 mm s^–1, another Fe³⁺ doublet with 0.4, 1.2 mm/s and two Fe²⁺ doublets with 1.1, 1.7, 2.7 mm s^–1 at 300 K were distinguished. The minor Fe³⁺ component is ascribed to dehydroxylated surface sites. Most of the remaining Fe(90%) is M2 cis-OH octahedral in an ordered M⁺–M²⁺ array. However, about 10% is M1 trans-OH Fe²⁺. Isomer shift vs. T gives Debye temperatures of 570 K for Fe³⁺ in M2 and 380 K for both Fe²⁺ sites, indicating greater vibrational freedom for Fe²⁺. Quadrupole splitting vs. T for Fe²⁺ gives a valence electronic energy splitting of 760 cm^–1 between the ground and first excited state for M2. The M1 sites have a more drastic variation in vs. T which indicates not only a lower first excited state but a rhombic distortion at these sites. A proposed explanation is a neighboring M2 site vacancy. The soil clay formed from this celadonite, which is mostly Fe-rich smectite, was also studied by Mössbauer spectroscopy. About half the Fe²⁺ has been oxidized in the clay, but the isomer shifts and quadrupole splittings are essentially the same as in the original celadonite. A texture orientation in the clay absorber was detected by measuring the absorber at 55° to the source radiation. This texture effect produces asymmetric doublets in the usual 90° measurement.     

Static compression and H disorder in brucite,Mg(OH)2, to 11 GPa: a powder neutron diffraction study

Neutron diffraction data suitable for Rietveld refinements were collected on a powder sample of synthetic Mg(OH)₂ by the Polaris time-of-flight spectrometer (ISIS spallation source, U.K.) at 10^-4 7.8(3) and 10.9(6) GPa. The Paris-Edinburgh high-pressure cell with WC anvils was used. Pressure calibration and equation-ofstate results were attained by separate runs with an NaCl internal standard. Interpolation of p(V) data by the fourth-order Birch-Murnaghan e.o.s. yields K ₀=41(2) GPa, K₀=4(2) and K₀=1.1(9) GPa^-1. The bulk modulus obtained is smaller than previously reported results. Rietveld refinements (R _prof =1.45% and 2.02% at 10^-4 and 10.9 GPa) show that H lies on the threefold axis (1/3, 2/3, z) up to 10.9 GPa, where a model with H disordered in (x, 2x, z) can be refined. In the latter case, a hydrogen bond with O-H=0.902(7), H..O=2.026(8) Å and <>=145.9 (7)° is observed. Differences with previous results for deuterated brucite are discussed. The onset of H disorder, and a jump of the c/a ratio vs. pressure at 6–7 GPa, may be related to a second-order phase transition consistent with recently reported Raman spectroscopic results.     

The α-β phase transition in cristobalite,SiO2

Cristobalite, a high temperature phase of silica, SiO₂, undergoes a (metastable) first-order phase transition from a cubic, , to a tetragonal, P4₃2₁2 (or P4₁2₁2), structure at around 220° C. The cubic C9-type structure for -cristobalite (Wyckoff 1925) is improbable because of two stereochemically unfavorable features: a 180° Si-O-Si angle and an Si-O bond length of 1.54 Å, whereas the corresponding values in tetragonal -cristobalite are 146° and 1.609 Å respectively. The structure of the -phase is still controversial. To resolve this problem, a symmetry analysis of the (or P4₁2₁2) transition in cristobalite has been carried out based on the Landau formalism and projection operator methods. The starting point is the ideal cubic ( ) C9-type structure with the unit cell dimension a (7.432 Å) slightly larger than the known a dimension (7.195 Å at 205° C) of -cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 Å. The six-component order parameter driving the phase transition transforms according to the X₄ representation. The transition mechanism essentially involves a simultaneous translation and rotation of the silicate tetrahedra coupled along 110. A Landau free-energy expression is given as well as a listing of the three types of domains expected in -cristobalite from the transition. These domains are: (i) transformation twins from a loss of 3-fold axes, (ii) enantiomorphous twins from a loss of the inversion center, and (iii) antiphase domains from a loss of translation vectors 1/2 110 (FP). These domains are macroscopic and static in -cristobalite, and microscopic and dynamic in -cristobalite. The order parameter , couples with the strain components as ², which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the -phase. Hence, the - cristobalite transition is a fluctuation-induced first-order transition and the -phase is a dynamic average of -type domains.