Pressure and temperature dependence of the single crystal elastic moduli of the cubic perovskite KMgF3

The elastic moduli (c) of single crystal KMgF₃ have been determined by the ultrasonic pulse superposition technique as a function of temperature from T=298?550 K, and as a function of pressure from P=1 bar?2.5 kbar. Room temperature values of the elastic moduli and their temperature derivatives are consistent with Reshchikova's (1969) values. Comparison with the data for SrTiO₃ indicates that, for most of the moduli, 1/c(?c/?T) _P and (?c/?P) _T are very similar for the fluoride-oxide analogue pair, KMgF₃-SrTiO₃. Values of (?c/?P) _T for KMgF₃ are calculated from a simple central force model using parameters determined for KF and are in good agreement with the measured values. The bulk sound velocity-mean atomic weight relationship, v _ф M ^1/2=constant, is well obeyed by the fluoroperovskites; comparison with the perovskite oxide data on a log-log plot of v _ф versus M leads to a value of 70% for the relative effective charge of the oxides with respect to the fluorides.     

Pressure dependence of the elastic constants of nonmetamict zircon

The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C ₁₁=10.78, C ₃₃=5.88, C ₄₄=0.99, C ₆₆=?0.31, C ₁₂=3.24, C ₁₃=6.20. The anomalous negative behaviour of C ₆₆ versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK _S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ?_D, and the high temperature limit of the Grüneisen parameter, γ_Ht, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Grüneisen parameter, γ_th, calculated from the thermal expansion, heat capacity, and compressibility data.     

The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4

The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe₂SiO₄, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: V_p = 6.67 km/s; V_s = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)_T = 5.2; (?μ/?P)_T=1.5;(?K/?T)_P= ?0.030 GPa/K;and,(?/?T)_P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg₂SiO₄, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C _ij for which i=j) values, and generally higher for the off-diagonal (C _ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.     

Pressure and temperature dependence of cation distribution in Mg-Mn olivine

Synthetic (Mg_0.51, Mn_0.49)₂SiO₄ olivine samples are heat-treated at three different pressures; 0, 8 and 12 GPa, all at the same temperature (～500° C). X-ray structure analyses on these single crystals are made in order to see the pressure effect on cation distribution. The intersite distribution coefficient of Mg and Mn in M1 and M2 sites, K _D = (Mn/Mg) _M1/(Mn/Mg) _M2, of these samples are 0.192 (0 GPa), 0.246 (8 GPa) and 0.281 (12 GPa), indicating cationic disordering with pressure. The small differences of cell dimensions between these samples are determined by powder X-ray diffraction. Cell dimensions b and c decrease, whereas a increases with pressure of equilibration. Cell volume decreases with pressure as a result of a large contraction of the b cell dimension. The effect of pressure on the free energy of the cation exchange reaction is evaluated by the observed relation between the cell volume and the site occupancy numbers. The magnitude of the pressure effect on cation distribution is only a fifth of that predicted from the observed change in volume combined with thermodynamic theory. This phenomenon is attributed to nonideality in this solid solution, and nonideal parameters are required to describe cation distribution determined in the present and previous experiments. We use a five-parameter equation to specify the cationic equilibrium on the basic of thermodynamic theory. It includes one energy parameter of ideal mixing, two parameters for nonideal effects, one volume parameter, and one thermal parameter originated from the lattice vibrational energy. The present data combined with some of the existing data are used to determine the five parameters, and the cation distribution in Mg-Mn olivine is described as a function of temperature, pressure, and composition. The basic framework of describing the cationic behavior in olivine-type mineral is worked out, although the result is preliminary: each of the determined parameters is not accurate enough to enable us to make a reliable prediction.     

Pressure and composition dependence of the electrical conductivity of iron-rich synthetic olivines to 200 kbar

The objectives of this study of olivines are, to calibrate the variation of electrical conductivity with pressure, up to 200 kbar in a diamond-anvil cell, and to determine how this is influenced by chemical composition. Experimentally, we have found that the variation of the electrical conductivity of three synthetic olivines containing 50, 75 and 100 mole percent of fayalite, is an exponential function of pressure P, closely represented at room temperature by:σ_xP=σ_x·exp ·(B _x·P) where x is the iron content of the olivine, σ _x the extrapolated value of conductivity at normal pressure and B _x the slope of the regression line in semi-logarithmic coordinates. It is thus possible to express the temperature dependence of conductivity through the Boltzmann relationship:σ_xPT= σ_αT· exp ·(-H*/RT)=σ_xT·exp ·[-(E*+PV _* ^x )/RT] where H* is the activation enthalpy, E* the activation energy and V _x ^* the activation volume. At constant temperature V _* ^x =B _x·RT and is approximately equal to 0,6 cm³/mole at 295 K. On the other hand, we have found that σ_xT is an exponential function of x and thus, B _x and of course V _x ^* are linear functions. The experimental procedure is described and the results discussed.     

Modelling of the thermal dependence of structural and elastic properties of calcite, CaCO3

A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO₃; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10^?6K^?1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10^?4K^?1 is obtained.     

Pressure solution in sandstones: influence of clays and dependence on temperature and stress

The enhancement of dissolution of quartz under the influence of clays has been recognized in sandstones for many years. It is well known that a grain of quartz in contact with a clay flake dissolves faster than when in contact with another grain of quartz. This phenomenon promotes silica transfer during the diagenesis of sandstones and is responsible of deformation and porosity variations. Here we make an attempt to explain the process of this rock deformation using a pressure solution mechanism.

The model of water film diffusion assumes that matter is dissolved inside the contact between two grains. The resulting solutes are transported to the pore fluid through diffusion along an adsorbed water film. Between two micas, this trapped film is thicker than between two grains of quartz. As a consequence diffusion is easier and the rate of pressure solution faster.

Experiments on pressure solution show that diffusion controls the mechanism at great depth whereas a model based on natural mica indentation indicates that kinetics is the limiting process through the precipitation rate of quartz at low depth, thus temperature is a crucial parameter. There should be a transition between thermally controlled rate and diffusion limited evolution.     

Dynamic recrystallization of wet synthetic polycrystalline halite: dependence of grain size distribution on flow stress, temperature and strain

It is often observed that dynamic recrystallization results in a recrystallized grain size distribution with a mean grain size that is inversely related to the flow stress. However, it is still open to discussion if theoretical models that underpin recrystallized grain size–stress relations offer a satisfactorily microphysical basis. The temperature dependence of recrystallized grain size, predicted by most of these models, is rarely observed, possibly because it is usually not systematically investigated. In this study, samples of wet halite containing >10 ppm water (by weight) were deformed in axial compression at 50 MPa confining pressure. The evolution of the recrystallized grain size distribution with strain was investigated using experiments achieving natural strains of 0.07, 0.12 and 0.25 at a strain rate of 5×10⁻⁷ s⁻¹ and a temperature of 125 °C. The stress and temperature dependence of recrystallized grain size was systematically investigated using experiments achieving fixed strains of 0.29–0.46 (and one to a strain of 0.68) at constant strain rates of 5×10⁻⁷–1×10⁻⁴ s⁻¹ and temperatures of 75–240 °C, yielding stresses of 7–22 MPa. The microstructures and full grain size distributions of all samples were analyzed. The results showed that deformation occurred by a combination of dislocation creep and solution-precipitation creep. Dynamic recrystallization occurred in all samples and was dominated by fluid assisted grain boundary migration. During deformation, grain boundary migration results in a competition between grain growth due to the removal of grains with high internal strain energy and grain size reduction due to grain dissection (i.e. moving boundaries that crosscut or consume parts of neighbouring grains). At steady state, grain growth and grain size reduction processes balance, yielding constant flow stress and recrystallized grain size that is inversely related to stress and temperature. Evaluation of the recrystallized grain size data against the different models for the development of mean steady state recrystallized grain size revealed that the data are best described by a model based on the hypothesis that recrystallized grain size organizes itself in the boundary between the (grain size sensitive) solution-precipitation and (grain size insensitive) dislocation creep fields. Application of a piezometer, calibrated using the recrystallized grain size data, to natural halite rock revealed that paleostresses can vary significantly with temperature (up to a factor of 2.5 for T=50–200 °C) and that the existing temperature independent recrystallized grain size–stress piezometer may significantly underestimate flow stresses in natural halite rock.     

Pressure dependence of melt viscosities on the join diopside-albite

The pressure dependence of melt viscosities on the join diopside-albite has been studied using falling-sphere viscometry. The five melt compositions investigated are: diopside, Ab₂₅Di₇₅, Ab₅₀Di₅₀, Ab₇₅Di₂₅ and albite. Experiments were performed at 1500° and 1600°C and at pressures of 5, 10, 15, 20 and 25 kbar. The positive and negative pressure dependence of the viscosity of diopside and albite, respectively, were confirmed. All intermediate compositions show an initial decrease in viscosity with increasing pressure; however, melt of Ab₂₅Di₇₅ composition passes through a minimum viscosity at approximately 12 kbar and 1600°C. This behavior is analogous to the variation in the viscosity of water with pressure at low temperature.

It is suggested that the three-dimensional, fully polymerized, albite structure dominates flow at low pressures. With increasing pressure, disruption of this structure and decrease in the average size of the flow units leads to domination by the diopside structure. The variation in viscosity with composition along the join at one atmosphere can be adequately modelled using the and (1965) configurational entropy model with an additional two-lattice configurational entropy of mixing term. The pressure dependence of viscosity in the diopside-albite system, however, cannot be predicted by the model, because there is an absence of information on the pressure dependence of the model parameters.

It is probable that relatively polymerized magmas (e.g. rhyolites to SiO₂-saturated basalts) show a negative pressure dependence of viscosity to depths where they originate in the lower crust or upper mantle. In contrast, the most depolymerized, naturally-occurring melts, such as strongly SiO₂-undersaturated basalts and picrites, may exhibit a viscosity minimum. The viscosity of these melts may be sufficiently high at depths within the upper mantle to inhibit their segregation, rise and eventual eruption at the surface.     

Pressure dependence of viscosity of rhyolitic melts

Viscosity of silicate melts is a critical property for understanding volcanic and igneous processes in the Earth. We investigate the pressure effect on the viscosity of rhyolitic melts using two methods: indirect viscosity inference from hydrous species reaction in melts using a piston cylinder at pressures up to 2.8 GPa and direct viscosity measurement by parallel-plate creep viscometer in an internally-heated pressure vessel at pressures up to 0.4 GPa. Comparison of viscosities of a rhyolitic melt with 0.8 wt% water at 0.4 GPa shows that both methods give consistent results. In the indirect method, viscosities of hydrous rhyolitic melts were inferred based on the kinetics of hydrous species reaction in the melt upon cooling (i.e., the equivalence of rheologically defined glass transition temperature and chemically defined apparent equilibrium temperature). The cooling experiments were carried out in a piston-cylinder apparatus using hydrous rhyolitic samples with 0.8-4 wt% water. Cooling rates of the kinetic experiments varied from 0.1 K/s to 100 K/s; hence the range of viscosity inferred from this method covers 3 orders of magnitude. The data from this method show that viscosity increases with increasing pressure from 1 GPa to 3 GPa for hydrous rhyolitic melts with water content ?0.8 wt% in the high viscosity range. We also measured viscosity of rhyolitic melt with 0.13 wt% water using the parallel-plate viscometer at pressures 0.2 and 0.4 GPa in an internally-heated pressure vessel. The data show that viscosity of rhyolitic melt with 0.13 wt% water decreases with increasing pressure. Combining our new data with literature data, we develop a viscosity model of rhyolitic melts as a function of temperature, pressure and water content.     

Pressure dependence of structural parameters of paragonite

The compressibility and structure of a 2M₁ paragonite with composition [Na_0.88K_0.10Ca_0.01Ba_0.01] [Al_1.97Ti_0.007Fe_0.01Mn_0.002Mg_0.006]Si_3.01Al_0.99O₁₀OH₂ were determined at pressures between 1 bar and 41 kbar, by single crystal X-ray diffraction using a Merrill-Bassett diamond anvil cell. Compressibility turned out to be largely anisotropic, linear compressibility coefficients parallel to the unit cell edges being β_a=3.5(1)·10^?4, β_b=3.6(1)·10^?4, β_c=8.3(3)·10^?4 kbar^?1 (β_a:β_b·β_c=1:1028:2.371). The isothermal bulk modulus, calculated as the reciprocal of the mean compressibility of the cell volume, was 650(20) kbar. The main features of the deformation mechanism resulting from structural refinements at pressures of 0.5, 25.4, 40.5 kbar were: –?variation in sheet thickness, showing that compression of the c parameter was mainly due to the interlayer thickness reduction from 3.07 Å at 0.5 kbar to 2.81 Å at 40.5 kbar; –?the compressibility of octahedra was greater than that of tetrahedra, the dimensional misfit between tetrahedral and octahedral sheets increased with P, so that tetrahedral rotation angel α increased from 15° at 0.5 kbar to 21.6° at 40.5 kbar; –?the basal surface corrugation (Δz) of the tetrahedral layer, due to the different dimensions of M1 and M2 octahedra and to the octahedral distortion, decreased with P (Δz=0.19 and 0.12 Å at 0.5 and 40.5 kbar respectively). Comparison of the new data on paragonite with those of a K-muscovite and a Na-rich muscovite (Comodi and Zanazzi 1995) revealed a clear trend toward decreasing of compressibility when Na substitutes for K atoms in the interlayer sites.     

Pressure dependence of hydroxyl solubility in coesite

 The solubility of hydroxyl in coesite was investigated in multianvil experiments performed at 1200 °C over the nominal pressure range 5–10 GPa, at an f _O2 close to the Ni-NiO buffer. The starting material for each experiment was a cylinder of pure silica glass plus talc, which dehydrates at high P and T to provide a source of water and hydrogen (plus enstatite and excess SiO₂). Fourier-transform infrared (FTIR) spectra of the recovered coesite crystals show five sharp bands at 3606, 3573, 3523, 3459, and 3299 cm⁻¹, indicative of structurally bonded hydrogen (hydroxyl). The concentration of hydrogen increases with pressure from 285 H/10⁶ Si (at 5 GPa) to 1415 H/10⁶ Si (at 10 GPa). Assuming a model of incorporation by (4H)_Si defects, the data are fit well by the equation C _OH=Af ² _H2<\INF>Oexp(−PΔV/RT), with A=4.38 H/10⁶ Si/GPa, and ΔV=20.6 × 10⁻⁶ m³ mol⁻¹. An alternative model entailing association of hydrogen with cation substitution can also be used to fit the data. These results show that the solubility of hydroxyl in coesite is approximately an order of magnitude lower than in olivines and pyroxenes, but comparable to that in pyropic garnet. However, FTIR investigations on a variety of ultrahigh pressure metamorphic rocks have failed in all cases to detect the presence of water or hydrogen in coesite, indicating either that it grew in dry environments or lost its hydrogen during partial transformation to quartz. On the other hand, micro-FTIR investigations of quartz crystals replacing coesite show that they contain varying amounts of H₂O. These results support the hypothesis that preservation of coesite is not necessarily linked to fast exhumation rates but is crucially dependent on limited fluid infiltration during exhumation. Received: 23 August 1999 / Accepted: 10 April 2000     

Pressure dependence of color of natural uvarovite: the barochromic effect

The electronic absorption spectra of natural uvarovite containing 62 mole% of the Cr³⁺ end-member were studied at pressures between 10⁻⁴ and ca. 13 GPa using DAC techniques combined with microscope spectrometric device. With increasing pressure, a barochromic effect with change from green to red color of the garnet specimen was observed. This change could be interpreted on the basis of the spectra and the data points derived in an ICE color card. The evaluation of crystal field data from the spectra showed that 10Dq of chromium increases on pressure while the Racah parameter B, and thus the nature of the chemical bond of Cr–O does not change significantly.     

Pressure dependence of the speciation of dissolved water in rhyolitic melts

Water speciation in rhyolitic melts with dissolved water ranging from 0.8 to 4 wt% under high pressure was investigated. Samples were heated in a piston-cylinder apparatus at 624-1027 K and 0.94-2.83 GPa for sufficient time to equilibrate hydrous species (molecular H₂O and hydroxyl group, H₂O_m + O ? 2OH) in the melts and then quenched roughly isobarically. The concentrations of both hydrous species in the quenched glasses were measured with Fourier transform infrared (FTIR) spectroscopy. For the samples with total water content less than 2.7 wt%, the equilibrium constant (K) is independent of total H₂O concentration. Incorporating samples with higher water contents, the equilibrium constant depends on total H₂O content, and a regular solution model is used to describe the dependence. K changes with pressure nonmonotonically for samples with a given water content at a given temperature. The equilibrium constant does not change much from ambient pressure to 1 GPa, but it increases significantly from 1 to 3 GPa. In other words, more molecular H₂O reacts to form hydroxyl groups as pressure increases from 1 GPa, which is consistent with breakage of tetrahedral aluminosilicate units due to compression of the melt induced by high pressure. The effect of 1.9 GPa (from 0.94 to 2.83 GPa) on the equilibrium constant at 873 K is equivalent to a temperature effect of 49 K (from 873 K to 922 K) at 0.94 GPa. The results can be used to evaluate the role of speciation in water diffusion, to estimate the apparent equilibrium temperature, and to infer viscosity of hydrous rhyolitic melts under high pressure.     

Non-linear temperature dependence of liquid volumes in the system albite-anorthite-diopside

The temperature-dependent thermal expansivities of glasses and liquids in the ternary albite-anorthite-diopside have been determined using a combination of calorimetry, dilatometry and Pt and Ir double bob Archimedean densitometry. Supercooled liquid volumes and molar thermal expansivities were determined across the glass transition using a combination of scanning calorimetry and dilatometry, based upon the equivalence of relaxation of volume and enthalpy in the vicinity of the glass transition. Superliquidus volumes were determined using double Pt bob Archimedean densitometry at temperatures up to 1,650°C and double Ir bob densitometry at 1,800°C. Experimental access to liquid volumes near the glass transition temperatures (680–920°C) and at superliquidus temperatures (1,400–1,800°C) for these compositions results in the observation of a nonlinear temperature dependence of molar volume, i.e., temperature-dependent thermal expansivities. The diopside composition wxhibits the largest temperature dependence of thermal expansivity, decreasing by 50% between 800 and 1,500°C. Linear extrapolation of the high-temperature volume data of diopside to 810°C would result in a 3% overestimation of the molar voltime. The temperature dependence of the molar volume of anorthite is approximately linear. The thermal expansivities of the liquids in the albite-anorthite-diopside system appear to converge at high temperature. This study uses a combination of methods that allows interpolation rather than extrapolation of the extant melt-volume data into the petrologically meaningful (subliquidus) temperature range.     

The extrapolation of elastic moduli to high pressure and temperature

The elastic constants of a crystal under stress, defined as the second derivative of the crystal free energy with respect to strain, require a correction related to the static pressure at non-zero pressures. The corrections required for the elastic constants calculated by the free energy minimisation code PARAPOCS are described and tested by comparison with the elastic constants calculated numerically by applying small stresses in the appropriate orientations to simulated crystals of fluorite, forsterite, α-quartz and albite. The corrected elastic constants are then used to investigate the extrapolation of the bulk and shear moduli (and hence also the seismic wave velocities V _p and V _s) of β-spinel and forsterite to upper mantle pressures. A Murnaghan equation, thirdorder Eulerian finite strain equation, second order polynomial equation and a logistic equation were all fitted to the simulated bulk and shear moduli between 0 and 3 GPa pressure. The parameters derived for these equations are used to extrapolate the bulk and shear moduli to 14 GPa and the results are compared to the simulated high pressure moduli. Over this pressure range, the second order polynomial provides the best extrapolation of the bulk modulus, but the use of the logistic equation results in the best extrapolation of the shear modulus.     

The elastic properties of the lithosphere beneath Scotian basin

To assess the possibility that the North Atlantic Ocean may subduct at Scotian basin east of Canada, we investigate the present compensation state of this deep basin. A Fourier domain analysis of the bathymetry, depth to basement and observed gravity anomalies over the oceanic area east of Nova Scotia indicates that the basin is not isostatically compensated. Moreover, the analysis emphasizes that in addition to the sediments, density perturbations exist beneath the basin. The load produced by the sediments and these density perturbations must have been supported by the lithosphere. We simulate the flexure of the lithosphere under this load by that of a thin elastic plate overlying an inviscid interior. It is shown that a plate with a uniform rigidity does not adequately represent the lithosphere beneath the basin as well as the oceanic lithosphere far from the basin, rather the rigidity of the lithosphere directly beneath the basin is about one to two orders of magnitude smaller than elsewhere. We relate this weakening to the thermal blanketing effects of the thick sediments and the fact that the lithosphere has a temperature-dependent rheology. We suggest that this weak zone would have a controlling effect on the reactivation of normal faults at the hinge zone of the basin, that were formed during the break-up of Africa and North America and were locked in the early stages after the break-up. The weak zone would facilitate reactivation of the faults if tensional stresses were produced by possible reorientation of the spreading direction of the North Atlantic Ocean in the future. The reactivation of the faults would create a free boundary condition at the hinge zone, allowing further bending of the lithosphere beneath the basin and juxtaposition of this lithosphere to the mantle beneath the continent. This may provide a favorable situation for initiation of slow subduction due to subsequent compressional forces.