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1.
By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) d K/ / K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of d K/d P proposed by Birch (1939) and Bullen (1949). (2) dln TM/dln ρ = ( γCV ? 1)/( is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and CV the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for CV = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if . However, it is shown that , which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ～ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory. 相似文献
2.
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
3.
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 Fe 2+Mg 2+ 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
4.
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
5.
The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xj's are the properties of the end-members j ( j = pyrope, almandine, spessartine, grossular and andradite). The Xj's are determined for density ρ, bulk modulus K, and shear moduli Cs = ( C11 ? C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are: | Almandine | Pyrope | Spessartine | Grossular | Andradite | | 1.779 ± 0.008 | 1.730 ± 0.009 | 1.742 ± 0.009 | 1.691 ± 0.008 | 1.379 ± 0.017 | | 0.981 ± 0.004 | 0.925 ± 0.004 | 0.964 ± 0.004 | 1.106 ± 0.004 | 0.979 ± 0.007 | | 0.958 ± 0.005 | 0.919 ± 0.005 | 0.937 ± 0.005 | 1.017 ± 0.006 | 0.827 ± 0.010 | 相似文献
6.
The melting curve of perovskite MgSiO 3 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 MgSiO 3 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 MgOFeOSiO 2 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
7.
Ultrasonic data for the velocities of the ilmenites MgTiO 3 and CoTiO 3 have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed in a piston-cylinder apparatus at pressures up to 30 kbar. Titanate and germanate ilmenites define divergent isostructural trends on a Birch diagram of bulk sound velocity ( υφ) vs. density (ρ). On a υφ vs. mean atomic weight ( ) diagram, however, all of the ilmenite consistent with a single . Elasticity systematics for isostructural sequences are used to e the bulk modulus (2.09 Mbar) and bulk sound velocity (7.4 km/sec) of MgSiO 3-elmenite. 相似文献
8.
Recent experiments on the olivine-spinel phase transformation in Ni 2SiO 4 have provided the following fundamental results: (1) the interphase structural orientation relationships with between the olivine and spinel phases upon transformation; and (2) the growth of 300 μm spinel single crystal from single crystals of olivine. In the light of these observations, transformation mechanisms proposed have been compared. We conclude that neither a nucleation and growth model nor a martensite model is verified by the experimental results. The former model lacks consistency in terms of the interphase relationships, and the latter cannot offer a dislocation-multiplication mechanism for the growth process. 相似文献
9.
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
10.
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
13.
An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q( ω) and of Young's modulus E( ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10 ?5.The Q?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?( t) = ?u · [1 + 3.7 · q · {(1 + 50 t) 0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to E( ω) is related to Q( ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation indicative of grain boundary diffusion or superplasticity. At higher stresses a power law typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity ηf and Q of the form: are derived, where α ～ 0.25, n is the power of σ, and D is a constant. 相似文献
14.
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, k 0 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 cm 3 mol ?1. 相似文献
15.
Tin dioxide (SnO 2) in the rutile structure as starting material has been found to transform to the orthorhombic α-PbO 2 structure (S.G. P bcn) at about 155 kbar and 1000–1400°C when compressed in a diamond-anvil cell and heated by irradiation with a YAG laser. The lattice parameters at room temperature and 1 bar are for the orthorhombic form of SnO 2, which is 1.5% more dense than the rutile form. Crystal-chemical arguments suggest that stishovite (SiO 2) may also transform to the α-PbO 2 structure at elevated pressure and temperature with an increase in zero-pressure density of about 2–3%. Mineral assemblages containing the orthorhombic SiO 2 are unstable relative to those containing the perovskite MgSiO 3 under lower-mantle conditions. 相似文献
16.
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
17.
Pressure-induced phase transformations in each of the rutile-structured difluorides (NiF 2, MgF 2, CoF 2, ZnF 2, FeF 2 and MnF 2) exhibit unique behavior; however, a general trend is found in the major structural changes: rutile phase → “distorted fluorite” phase → post-“distorted fluorite” phase with volume changes of about 5–10%. For a given phase transformation sequence found commonly in two or more difluorides, the phase transformation pressure is related inversely to the unit cell volume and thus inversely to the mean cation-anion bond length. The relationship in oxides (SnO 2, TiO 2 and GeO 2) is much less systematic. It is therefore not possible to predict without uncertainty the post-stishovite phases in the lower mantle.Velocity-density systematics in the difluorides and oxides are governed, to a large extent, by cationic radius. The pressure dependence of shear elastic constant CS = ( C11 ? C12)/2 is negative in all of the nine difluorides and oxides. However, the CS mode does not vanish at the initial phase transformation pressure; rather, the ratios of are 0.10 and 0.04 to 0.10 for transitions of rutile → orthorhombic and of rutile → “distorted fluorite”, respectively, and are in agreement with the approach of Demarest et al. 相似文献
19.
A comprehensive analysis has been made of analog and digital recordings of eigenvibration ground motion obtained following four great earthquakes; August 1976 (Philippines), August 1977 (Indonesia), September 1979 (West Irian), and December 1979 (Colombia). The time series (ranging in length from ～28 to ～140 h) are assumed to be linear combinations of damped harmonics in the presence of noise. Tables are calculated from values of the four parameters: Θ, used in describing eigenvibrations, period of oscillation, amplitude, damping factor Q, and phase together with their statistical uncertainties (53 spheroidal modes, , and 13 torsional modes, ). The estimation procedures are by the methods of complex demodulation and non-linear regression that specifically incorporate into the basic model the decaying aspect of the oscillations. These methods, extended to simultaneous estimations of groups of modes, help to eliminate measurement error and measurement bias from estimations of Θ. The result is that overtone modes very near in frequency to fundamental modes can, under certain conditions, be resolved through a non-linear regression technique, although parameter uncertainties are underestimated in general.Of the time series analyzed, 17 were from a northern California regional network of ultra-long period seismographs at Berkeley (three components), Jamestown (vertical component), and Whiskeytown (vertical component) following the four listed earthquakes. The other 7 time series were recorded digitally by the worldwide IDA network following the 1977 Indonesian earthquake. Weighted regional and worldwide averages were made for period and Q of each eigenvibration mode.From the theoretical viewpoint, comparisons of measured period, Q, amplitude, and phase for all modes analyzed led to five conclusions. First, there are no detectable systematic shifts in period, Q, or phase of eigenvibrations within a region whose dimensions are less than a wavelength. Second, though not conclusive, there may be slight systematic shifts in period (<0.65 s) and relative amplitudes within the California regional network due to different source positions and mechanisms. Differences in Q values are not statistically significant. Third, even though differences in period obtained worldwide were as great as 1.33 s (≈0.33%), differences between Q values (as great as 20%) for the same mode were not significant. The conclusion is that the damping characteristics of singlet eigenfunctions are not observed to be significantly different. Fourth, the assumption that a multiplet behaves as a single oscillation is valid from at least through . Fifth, no systematic pattern emerged for the shift of eigenperiod as a function of order / or posit on the Earth. 相似文献
20.
Interdiffusion experiments were performed between Fe 3O 4 (single crystal) and Fe 2.8Ti 0.2O 4 (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
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