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• 1
Electronic Resource
Springer
Pure and applied geophysics 141 (1993), S. 643-652
ISSN: 1420-9136
Keywords: High pressure ; pressure calibration ; ZnTe ; synchrotron X-ray source ; DIA type cubic anvil apparatus
Source: Springer Online Journal Archives 1860-2000
Topics: Geosciences , Physics
Notes: Abstract Pressure behavior of ZnTe at room temperature was studied using an X-ray energy dispersive method on a DIA type cubic anvil apparatus (SAM-85) at NSLS-X17B1. By using powdered polyethylene, the sample and NaCl for a pressure scale were held under quasihydrostatic conditions, which were confirmed by X-ray diffraction method. Two high-pressure phase transitions were confirmed using X-ray powder diffraction simultaneously with electrical resistance measurements. The phase transition pressures under quasihydrostatic conditions were determined to be 9.6 GPa, at which the resistance increased, and 12.0 GPa, which was the midpoint of a large resistance decrease. Errors in the pressure determinations were estimated to be less than 0.2 GPa. These pressure values may depend on grain size and anisotropic stress effects on the calibrant. From X-ray observation of ZnTe, the bulk modulus of the zinc blende structure was calculated to beK 0=51(3) GPa andK 0 ′ =3.6(0.8), and the first transition at 9.6 GPa was found to have about 9% volume change. It was consistent with an anomaly in the pressure generating curves.
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• 2
Electronic Resource
Springer
Pure and applied geophysics 146 (1996), S. 533-549
ISSN: 1420-9136
Keywords: Lower mantle ; seismic tomography ; thermoelasticiti ; composition models ; geodynamics ; shear modulus
Source: Springer Online Journal Archives 1860-2000
Topics: Geosciences , Physics
Notes: Abstract We estimate (ϖμ/ϖT) P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(ϖμ/ϖT) P | by comparing the shear modulus (μ) profile of PREM with laboratory room-temperature data of μ extrapolated to high pressures. The second approach employs a seismic tomography constraint (ϖ lnV S /ϖ lnV P ) P =1.8–2, which directly relates (ϖμ/ϖT) P with (ϖK S /ϖT) P . An average (ϖK S /ϖT) P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK S profile of PREM along several possible adiabats. Both (ϖK S /ϖT) and (ϖμ/ϖT) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (ϖμ/ϖT) P vs. (ϖK S /ϖT) P curves, which intersect at a composition similar to pyrolite with (ϖμ/ϖT) P =−0.02 to −0.035 and (ϖK S /ϖT) P =−0.015 to −0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of (ϖ lnp/ϖ lnV S ) P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of (ϖ lnV S /ϖ lnV P ) P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios (ϖ ln ϱ/ϖ lnV S ) P and (ϖ ϱ/ϖ lnV S ) P are free parameters arbitrarily adjusted to fit the tomography and geoid data.
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• 3
Electronic Resource
[s.l.] : Macmillian Magazines Ltd.
Nature 419 (2002), S. 824-826
ISSN: 1476-4687
Source: Nature Archives 1869 - 2009
Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
Notes: [Auszug] The Earth's lower mantle consists mainly of (Mg,Fe)SiO3 perovskite and (Mg,Fe)O magnesiowüstite, with the perovskite taking up at least 70 per cent of the total volume. Although the rheology of olivine, the dominant upper-mantle mineral, has been extensively studied, ...
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• 4
Electronic Resource
Copenhagen : International Union of Crystallography (IUCr)
Applied crystallography online 32 (1999), S. 218-225
ISSN: 1600-5767
Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics: Geosciences , Physics
Notes: This report discusses a new method to determine experimental pressure–volume–temperature (P–V–T) data and to correct misalignment of diffraction optics using thermoelastic equations of state of multiple phases. Analytical approaches as well as numerical approaches are presented for the technique. A number of phase combinations yield the best experimental result and the whole-pattern Rietveld and/or Le Bail refinement of diffraction patterns of multiple phases is a significant aspect of the technique. Specific examples indicate that the corrected pressure, temperature and diffraction optics are robust. Errors are estimated from the uncertainties of the measured cell dimensions. The error propagation for different experimental cases is discussed, along with the conditions and limitations of the method. This technique for P–V–T determination and the correction of diffraction optics is crucial for experiments conducted under extreme conditions of high pressure, high temperature and dynamic reactions.
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• 5
Electronic Resource
Springer
Physics and chemistry of minerals 10 (1984), S. 261-272
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract The single-crystal elastic moduli, c ij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni2SiO4 olivine: c 11=3.40(2), c 22=2.38(2), c 33=2.53(2), c 44=0.71(1), c 55=0.87(1), c 66=0.78(1), c 12=1.09(2), c 13=1.10(4), c 23=1.13(3), Ni2SiO4 spinel: c 11=3.66(3), c 44=1.06(1), c 12=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c 11〉c 33〉c 22, regardless of composition. The moduli c 55 and c 66 are approximately equal, and greater than c 44. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO4 tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of $$\bar c_{12} 〉 \; = (c_{12} + c_{13} + c_{23} )/3$$ and $$\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3$$ . When transition-metal cations are six-coordinated by oxygen $$\bar c_{12} 〉 \bar c_{44}$$ , and when alkaline-earth cations are six-coordinated $$\bar c_{44} 〉 \bar c_{12}$$ . The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni2SiO4 (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni2SiO4 are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c ij's and shear modulus of a spinel-structure silicate to be estimated from c 11 of the corresponding α phase and the bulk modulus of the γ phase.
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• 6
Electronic Resource
Springer
Physics and chemistry of minerals 3 (1978), S. 133-144
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract The nine elastic constants of andalusite and sillimanite have been determined, using the technique of Brillouin scattering. They are, in megabars, for andalusite: c 11=2.334, c 22=2.890, c 33=3.801, c 44=0.995, c 55=0.878, c 66=1.123, c 23=0.977, c 13=1.162, c 12=0.814; for sillimanite: c 11=2.873, c 22=2.319, c 33=3.884, c 44=1.224, c 55=0.807, c 66=0.893, c 23=1.586, c 13=0.834, c 12=0.947. Both structures are characterized by chains of edge-linked coordination octahedra extending parallel to the crystallographic c direction, cross-linked by polyhedra of lower coordination. In each structure the stiffness measured parallel to c is greater than that measured normal to c. The shear moduli can be directly correlated with the relative rigidity of the cross-linking structures.
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• 7
Electronic Resource
Springer
Physics and chemistry of minerals 13 (1986), S. 360-370
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract A modified rigid-ion model is developed based on coordination polyhedra as the fundamental modelling units in a crystal structure. A crystal structure is represented by its constituent coordination polyhedra that are treated as three-dimensional elastic continua. Elastic moduli, experimentally determined or otherwise assumed, are ascribed to these coordination polyhedra. Finite element analysis is applied to retrieve the interatomic force information implicit in the elastic moduli of these polyhedra. The polyhedral approach provides a framework to model noncentral and many-body forces in a conventional lattice calculation because the elastic moduli contain much information on the nature of static interatomic forces within a crystal structure. The polyhedral model of the single-crystal elastic moduli of forsterite compares very well with the observed data; the average deviation of the calculated elastic moduli from the measured elastic moduli is within 6 percent.
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• 8
Electronic Resource
Springer
Physics and chemistry of minerals 16 (1989), S. 360-364
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract The adiabatic single-crystal elastic moduli of a beryllium silicate (phenacite: Be2SiO4, trigonal, have been determined at atmospheric pressure and 22° C by Brillouin spectroscopy. The elastic stiffness moduli in gigapascals are: C 11=341.9 C 33=391.0 C 44=91.4 C 66= 96.9 C 12=148.0 C 13=136.0 C 14= 0.1 C 15= 3.5 Overall, the elastic stiffness moduli for phenacite parallel and perpendicular to the c axis are comparable (i.e., it is almost cubic in its elastic “signature”). The elastic moduli can be rationalized in terms of division of the structure into two types of coordination polyhedra (1Si+2Be) with slightly different stiffnesses, which are linked to form a three dimensional framework. Values of the isothermal bulk modulus and the linear compressibilities, as determined from hydrostatic compression experiments of Hazen and Au (1986), are in good agreement with those obtained here. Combining the two studies indicates a low pressure derivative of the bulk modulus for phenacite.
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• 9
Electronic Resource
Springer
Physics and chemistry of minerals 18 (1991), S. 294-301
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract High-temperature X-ray diffraction studies of SrZrO3 and BaZrO3 perovskites have been carried out to 1200° C. The diffraction patterns are analyzed with Rietveld method so as to refine the unit cell dimensions. The volumetric thermal expansion coefficient are observed to be 2.98*10-5K-1 for orthorhombic Pbnm phase, 3.24*10-5K-1 for orthorhombic Cmcm phase, 3.75*10-5K-1 for tetragonal I4/mcm phase of SrZrO3 perovskite, and 2.06*10-5K-1 for cubic Pm3m phase of BaZrO3 perovskite, respectively. The linear thermal expansion coefficients of SrZrO3 perovskite show considerable anisotropy of α a 〉α c 〉α b for orthorhombic Pbnm phase, which reflect the decrease of distortion of the perovskite. It is demonstrated that thermal expansion of the centrosymmetrically distorted ABX3 perovskite can be empirically expressed as a combination of the changes of [B-X] bond length and tilting angle of BX6 octahedral framework. The octahedral tilting is considered to be the primary order parameter for the ferroelastic type of structural phase transitions in perovskite. Thermodynamically, the tilting induced volume change denotes the “excess volume” and the corresponding thermal expansion represents the “excess thermal expansion” for the lower symmetry phase with respect to its prototype of the cubic perovskite.
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• 10
Electronic Resource
Springer
Physics and chemistry of minerals 16 (1988), S. 42-50
ISSN: 1432-2021
Source: Springer Online Journal Archives 1860-2000
Topics: Chemistry and Pharmacology , Geosciences , Physics
Notes: Abstract The single crystal elastic moduli bear evidence of non-central or many-body forces in the simple oxides with transition-metal oxides being very distinctive from alkaline-earth oxides. These features which persist in more complicated structures such as olivine, suggest that noncentral or many-body forces are important in defining the physical properties of these compounds as well. Within the framework of a Born type static lattice model, the elastic properties of simple oxides can be described with charges which are less than the formal charge, anioncation repulsive forces, and angle-bending forces. The transition-metal oxides and alkaline-earth oxides mainly differ in the nature of the angle-bending forces, where even the sign could be different. The potentials which are derived to fit the simple oxide properties, serve very well to define the crystal structure and elastic properties of Mn, Mg, and Co silicate olivines. In the case of Mg, the predicted crystal structure and elastic properties were better predicted than a model without the angle-bending forces and one where the other potential terms were derived as to optimize the fit of the structure. In all cases, the relationship of the off-diagonal and shear moduli are well modeled by including the angle-bending forces.
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