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1.
Thirty-one single crystals of synthetic forsterite, Fo100, were deformed in 69 compressional creep tests in a 0.1-MPa confining atmosphere of H2 + Ar. Temperature ranged from 1753 to 2023 K and stress σ (= σ1 - σ3) from 1.5 to 37.8 MPa. Steady-state creep under these conditions follows an empirical law of the form: strain rate where A, n, and Q are constants. General characteristics of Fo100 creep — uniformity of strain, shape change as a function of orientation of σ, relative deformation resistance of different orientations — match those of natural olivine single crystals of composition Fo92. Specific constants in the flow law, however, are distinctly new: for σ oriented along [111]c (equidistant from the three principal crystallographic axes), values for Fo100 are n = 2.9 ± 0.2 and Q = 0.67 ± 0.03 MJ/mol (160 ± 7 kcal/mol). A single law covers the range 3 < σ < 30 MPa and 1753 < T < 1953 K. Steady-state deformation is preceded by a transient period of strain softening. High strain rates at σ ? 10 MPa render the transient barely resolvable; it apparently displaces the steady-state flow law by approximately ?0.5% in strain. At σ ? 7.8 MPa, the amount of strain imparted to a sample of the [101]c orientation is typically <0.1% after one hour. 相似文献
2.
High-temperature and high-pressure recovery experiments were made on experimentally deformed olivines at temperatures of 1613–1788 K and pressures of 0.1 MPa to 2.0 GPa. In the high-pressure experiments, a piston cylinder apparatus was used with BN and NaCl powder as the pressure medium, and the hydrostatic condition of the pressure was checked by test runs with low dislocation density samples. No dislocation multiplication was observed. The kinetics of the dislocation annihilation process were examined by different initial dislocation density runs and shown to be of second order, i.e. where ρ is the dislocation density, k0 is a constant, are the activation energy and volume respectively, and P, R and T are pressure, gas constant and temperature, respectively. Activation energy and volume were estimated from the temperature and pressure dependence of the dislocation annihilation rate as and , respectively.The diffusion constants relevant to the dislocation annihilation process were estimated from a theoretical relation k=αD where is the diffusion constant and α is a non-dimensional constant of ca. 300. The results agree well with the self-diffusion constant of oxygen in olivine. This suggests that the dislocation annihilation is rate-controlled by the (oxygen) diffusion-controlled dislocation climb.The mechanisms of creep in olivine and dry dunite are examined by using the experimental data of static recovery. It is suggested that the creep of dry dunite is rate-controlled by recovery at cell walls or at grain boundaries which is rate-controlled by oxygen diffusion. Creep activation volume is estimated to be 16±3 cm3 mol?1. 相似文献
3.
Interdiffusion experiments were performed between Fe3O4 (single crystal) and Fe2.8Ti0.2O4 (powder), under self-buffering conditions (temperature range 600–1034°C), and for various oxygen potentials at 1400°C. Profiles of Fe and Ti were obtained by electronprobe microanalysis, and the interdiffusion coefficient was calculated by the Boltzmann-Matano method. Low-temperature data at 3 mole% Ti could be described by . An estimate is given for the time to interdiffuse 2μm at various temperatures, and the results compared with recent experiments. 相似文献
4.
A.W. Gerhard Kunze 《Physics of the Earth and Planetary Interiors》1974,8(4):375-387
The settling trends of 318 lunar mare craters are compared with predictions of numerical finite-element models in order to determine the creep response of the upper lunar mare crust. No settling is evident in craters smaller than 5 km in diameter. Settling rates of larger craters increase as function of crater size in a manner suggesting a non-linear lunar creep response corresponding to the power law where έ is the strain rate and σ is the differential stress. However, the observed nonlinearity is probably an apparent nonlinearity resulting from the temperature induced viscosity decrease with depth due to a lunar crustal temperature gradient of 3° C/km and a creep activation energy of 20 kcal/mole. It is concluded that creep in the lunar medium is essentially Newtonian, and that the effective viscosity of the upper lunar mare crust is (1.6 ± 0.3) · 1025 poise. 相似文献
5.
On the basis of two assumptions i.e. (1) plastic and anelastic behaviour of the upper mantle can be approximated by the behaviour of the dominant mineral olivine, and (2) the behaviour of natural olivine and synthetic forsterite are similar, we have investigated the flow laws and the flow microstructures of forsterite single crystals. The results obtained between 1400–1650°C and 10–100 MPa suggest a model of climb controlled creep in which the a edge dislocations are dominant. The activation energy measured in that regime is 4.7 eV, close to that of Si self-diffusion and the flow law is , where σ is in MPa. Extrapolation of these results to the upper mantle would imply very low stresses (i.e. ?10 MPa) in the asthenosphere. However the effect of pressure and grain size are unknown and extrapolation to very low stresses is not straightforward. 相似文献
6.
Frank D. Stacey 《Physics of the Earth and Planetary Interiors》1980,22(2):89-96
By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, , can be related to the mantle-derived heat flux, . If cell size is independent of then . (If cell size varies with , then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto , gives convective stress , i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 108 years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10?8 deg y?1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 1012 W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 1020 kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core. 相似文献
7.
Measurements on acoustic pulses propagating in massive rock lead to a simple empirical relationship between the pulse rise time, τ and the time of propagation of a pulse, t: where τ0 is the initial rise time (at t = 0), Q is the anelastic parameter which may be expressed in terms of the fractional loss of energy per cycle of a sinusoidal wave, Q = 2π(ΔE/E)?1, and is assumed to be essentially independent of frequency, and C is a constant whose value we estimate experimentally to be 0.53 ± 0.04. Of the linear theories of seismic pulse attenuation, model 2 of Azimi et al. (1968) is favoured. Pulse shapes computed from equations of Futterman (1962) also give C = 0.5, but the pulse arrives earlier than in a non-attenuating medium with the same elasticity and density. Pulse shapes calculated using Strick's (1967, 1970, 1971) theory give values of C incompatible with our results. The observations suggest that a method of estimating the Q-structure of the earth from seismic pulse rise times may have a particular advantage over the spectral ratio method. 相似文献
8.
Ari Ben-Menahem 《Physics of the Earth and Planetary Interiors》1977,15(1):P10-P18
Source parameters of 27 major shallow earthquakes in the magnitude range 7.0–8.6, which occurred during 1906–1969, are used to establish dimensionless invariants involving the fault dimensions, average slip, and the rise time. It is found that these entities are expressible as simple functions of the subsonic shear Mach number (M) and the cube root of the seismic potency, . Moreover, a new principle is suggested according to which all dimensionless numbers which can be constructed from the basic fault elements are simple powers of the contraction factor with coefficients of the order unity. The laws of dynamical similarity thus found are those appropriate for subsonic rupture in which the Mach number is very close to unity and the radiation efficiency is between and . The empirical similarity laws are shown to be compatible with a source model in which the fault plane is simulated by a flexible membrane with additional restoring stiffness forces provided by an elastic medium attached to it on one side. Results suggest the possibility that earthquake rupture, together with the radiation of seismic waves, terminates at the moment that Mach 1 is reached. 相似文献
9.
Lowes (1966, 1974) has introduced the function Rn defined by are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by is the Earth's radius. We refer to Rn as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rn = RMn = RCn where the components RnM due to the main (or core) field and RnC due to the crustal field are given approximately by . The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to Rn are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the Rn for celestial bodies from average great circle power spectra of the magnetic field components. 相似文献
10.
An approximate expression is developed for the relationship between the hydraulic gradient (J), the specific discharge (q) and fluid and porous matrix properties in the case of saturated, steady and uniform (macroscopic) flow of a Newtonian liquid at high Reynolds numbers through a homogeneous anisotropic porous medium: In this expression, the tensors w(2), B(4) and C(3) denote properties of the solid matrix only. The tensors W(2), and C(3) are symmetrical; the tensor B(4) is symmetrical only in the first and last pairs of indices. It seems that no mathematical expression with a finite number of parameters exists, which can serve as a universal exact expression for the sought relationship between J and q. 相似文献
11.
Malcolm G. McLeod 《Physics of the Earth and Planetary Interiors》1980,23(2):P1-P4
An essentially arbitrary function V(θ, λ) defined on the surface of a sphere can be expressed in terms of spherical harmonics where the Pnm are the seminormalized associated Legendre polynomials used in geomagnetism, normalized so that The angular brackets denote an average over the sphere. The class of functions V(θ, λ) under consideration is that normally of interest in physics and engineering. If we consider an ensemble of all possible orientations of our coordinate system relative to the sphere, then the coefficients gnm and hnm will be functions of the particular coordinate system orientation, but where for any orientation of the coordinate system (Sn is invariant under rotation of the coordinate system). The averages are over all orientations of the system relative to the sphere. It is also shown that 〈gmnglp〉 = 〈hmnhlp〉 = 0 for l ≠ m or p ≠ n and 〈gmnhlp〉 = 0 fro all n, m, p, l. 相似文献
12.
Eiji Ohtani 《Physics of the Earth and Planetary Interiors》1983,33(1):12-25
The melting curve of perovskite MgSiO3 and the liquidus and solidus curves of the lower mantle were estimated from thermodynamic data and the results of experiments on phase changes and melting in silicates.The initial slope of the melting curve of perovskite MgSiO3 was obtained as at 23 GPa. The melting curve of perovskite was expressed by the Kraut-Kennedy equation as , where Tm?2900 K and P?23 GPa; and by the Simon equation, .The liquidus curve of the lower mantle was estimated as (perovskite) and this gives the liquidus temperature Tliq=7000 ±500 K at the mantle-core boundary. The solidus curve of the lower mantle was also estimated by extrapolating the solidus curve of dry peridotite using the slope of the solidus curve of magnesiowüstite at high pressures. The solidus temperature is ～ 5000 K at the base of the lower mantle. If the temperature distribution of the mantle was 1.5 times higher than that given by the present geotherm in the early stage of the Earth's history, partial melting would have proceeded into the deep interior of the lower mantle.Estimation of the density of melts in the MgOFeOSiO2 system for lower mantle conditions indicates that the initial melt formed by partial fusion of the lower mantle would be denser than the residual solid because of high concentration of iron into the melt. Thus, the melt generated in the lower mantle would tend to move downward toward the mantle-core boundary. This downward transportation of the melt in the lower mantle might have affected the chemistry of the lower mantle, such as in the D″ layer, and the distribution of the radioactive elements between mantle and core. 相似文献
13.
The dependence of bulk sound speed Vφ upon mean atomic weight and density ρ can be expressed in a single equation: Here B is an empirically determined “universal” parameter equal to 1.42, , a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to where γ is a Grüneisen parameter. The constant c = (? ln VM/? ln , where VM is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use cFe = 0.14 for Fe2+Mg2+ and GeSi substitutions and cCa ? 1.3 for CaMg substitutional series. With these values it is pos to deduce from the above equation Birch's law, its modifications introduced by Simmons to account for Ca-bearing minerals, variations in the seismic equation of state observed by D.L. Anderson, and the apparent proportionality of bulk modulus K to VM?4. 相似文献
14.
Loren Shure Kathy Whaler David Gubbins Bruce Hobbs 《Physics of the Earth and Planetary Interiors》1983,32(2):114-131
Slow changes in the magnetic field are believed to originate in the core of the Earth. Interpretation of these changes requires knowledge both of the vertical component of the field and of its rate of change at the core-mantle boundary (CMB). While various spherical harmonic models show some agreement for the field at the CMB, those for secular variation (SV) do not. SV models depend heavily on annual means at relatively few and poorly distributed magnetic observatories. In this paper, the SV at the CMB is modelled by fitting 15-year differences in the annual means of the X, Y and Z components (from 1959 to 1974). The model is made unique by imposing the constraint that be a minimum, using the method of Shure et al. (1982). If SV is attributed to motions of core fluid, then this model will yield, in some sense, the slowest core motions. The null space is determined by the distribution of observations, and therefore, to be consistent, only those observatories have been retained which recorded almost continuously throughout the interval 1959–1974.The method allows misfit between the model and the observations. The best value for the misfit can be derived from estimates of errors in the data, or alternatively, because larger misfit leads to smoother models (i.e., smaller ), the best value can be estimated subjectively from the final appearance of the model. Both procedures have their counterparts in the conventional spherical harmonic expansion approach, when smoothing is achieved by lowering the truncation level. The new proposal made in this paper is to use objective criteria for determining the misfit, based on the assumption that diffusion is negligible, in which event all integrals will vanish when Si is a region on the CMB bounded by a contour of zero vertical component of field. For the 1965 definitive model which is adopted here, and for most other contemporary models, there are six such areas, giving five independent integrals (the integrals over the six regions must sum to zero if ? · B = 0). Tabulating these integrals for various choices of the misfit gives minimum values near 2 nT y?1. It is impossible to achieve this good a fit to the data using a reasonable model derived by truncating the spherical harmonic expansion. The value 2 nT y?1 corresponds to errors of ～ 20 nT in individual annual means, which is rather larger than expected from the scatter in the data. 相似文献
15.
The effects of the variation of magnetic grain size on the magnetic properties of rocks have been studied throughout a reversely magnetized basaltic dyke with concentric cooling zones.Except in a few tachylites in which the magnetic mineral is a Ti-rich titanomagnetite, in the bulk of the dyke the magnetization is carried by almost pure magnetite grains. Although the percentage p of these magnetic oxides varies slightly, the large changes in the various magnetic parameters observed across the dyke are essentially attributable to large variations in the grain size of the magnetic particles.From the outer scoria region, where the magnetic grains are a mixture of single-domain (SD) and superparamagnetic (SP) grains, to the tachylite zone with finely crystallized basaltic glass containing interacting elongated SD particles, one observes an increase of both the ratio of the saturation remanent magnetization and the saturation induced magnetization Jrs/Jis, the bulk coercive force Hc, the median destructive field MDF, the intensity of the remanent magnetization Jr, and the Koenigsberger ratio Q. In the tachylites these parameters reach unusually high values, for subaerial basalts: These parameters decrease in the basalt toward the centre of the dyke where pseudo-single-domain (pseudo-SD) particles coexist together with multidomain (MD) grains. The susceptibility remains approximately constant from the inner basalt to the tachylite, but increases in the scoria up to values 10 times higher owing to the presence of SP particles. The magnetic viscosity increases also drastically toward the margin of the dyke due to an increase of the fraction of the SD particles just above the superparamagnetic threshold. 相似文献
16.
A pulse rise-time method has been used to study pulse broadening on seismograms generated by a weight drop source at distances up to 600 m. Both source and receiver were placed on glacial overburden overlying a gneiss-monzonite rock body. One of two data sets showed a significant increase in pulse rise time, τ, as a function of travel time, T. This increase, if due to anelastic attenuation in the uppermost part of the rock body, implies a Q value of 243 ± 53, assuming a linear relationship between τ and T. The data were not capable of discriminating between the models of pulse broadening of Gladwin and Stacey (τ ∞ T) and Ricker (). 相似文献
17.
The dislocation annihilation rate in experimentally deformed olivine single crystals was measured as a function of oxygen partial pressure (PO2). It was shown that the dislocation annihilation rate decreased with increasing PO2. This result is inconsistent with the reported PO2 dependence of creep rate () in single olivine crystals, thus indicating that the creep in single olivine crystals is not rate-controlled by recovery, under the experimentally investigated conditions. 相似文献
18.
19.
The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions.The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was , and for two blocks of Black gabbro it was and , respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy.Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10?3 to 10?7 m · s?1. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ～5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered.Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%.Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earth's crust are discussed. 相似文献
20.
The splitting of the [100] dislocations of forsterite Mg2SiO4 is investigated in a hard-sphere model. Glissile splittings exist in (001) and the most energetically favorable is the one that does not involve cutting of SiO4 tetrahedra: [100] screw dislocations are shown to be able to split simultaneously on (001) and (010) according to the reaction: This sessile configuration is analogous to the one found for screw dislocations of body-centered cubic metals. It accounts forthe long rectilinear sessile screw segments commonly observed, in experimentally and naturally deformed olivine. A new creep model for the upper mantle is proposed, where recovery is controlled by cross-slip of screw dislocations instead of climb of edge dislocations. The creep law, fitted on the experimental results of the literature is: (σ in bars) the activation volume for cross-slip is estimated and viscosity-depth curves are plotted. The proposed creep mechanism is grain-size independent and less non-Newtonian than the climb-controlled one; it is found to be dominant over the latter at stresses smaller than 100 bar. 相似文献