The system Mg2SiO4MgOH2O at high pressures and temperatures — Possible hydrous magnesian silicates in the mantle transition zone

The system Mg₂SiO₄MgOH₂O was investigated at pressures between 85 and 160 kbar and at temperatures between 750 and 1200°C. In runs for a gel with Mg/Si ratio of 3 and with 4.0 wt.-percent H₂O, a dense hydrous magnesian silicate, denoted phase B by Ringwood and Major, was found at pressures from about 100 kbar to at least 160 kbar in the whole temperature range studied. In the following table the crystallographic parameters and chemical formula of phase B, determined in this study, are compared with those of the other dense hydrous silicates in Mg₂SiO₄MgOH₂O.

     

2.

Interionic repulsive force and compressibility of ions     

Yoshiaki Ida 《Physics of the Earth and Planetary Interiors》1976,13(2):97-104

The compressibility of an individual ion is examined, in comparison with a known set of data for the alkali halides. A simple extrapolation of ionic radius to high pressure is not acceptable, because the pressure derivative of ionic radius changes for different salts. According to the classical concept of an elastic ion, the repulsive potential energy between the ions i and j is specified by the nature of each ion as:

$\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{) exp[}\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{? r)}\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{)}\text{]}$

as a function of the interionic distance r. In this expression, q_i and ρ_i are the ionic radius and ionic compressibility, respectively, in a suitably modified meaning. Such a form of the repulsive potential fits well to the data of lattice constants and bulk moduli. The parameters q_i and ρ_i are evaluated for alkali and halogen ions, and an anion turns out to be much more compressible than a cation. The present treatment may be usefully applied to the minerals in the Earth's mantle, which contain only a few major ions.     

3.

High temperature creep of an orthorhombic perovskite—YAlO3     

《Physics of the Earth and Planetary Interiors》1999,110(1-2):51-69

     

4.

Field observations of hydrodynamic conditions and suspended particulate matter in the southern North Sea     

《Continental Shelf Research》1998,18(11):1215-1233

     

5.

Hydraulic exponents M and N for gravity flow pipes     

《Advances in water resources》1998,21(3):185-191

     

6.

General relationships among sound speeds: II. Theory and discussion     

T.J. Shankland  D.H. Chung 《Physics of the Earth and Planetary Interiors》1974,8(2):121-129

The dependence of bulk sound speed V_φ upon mean atomic weight $\text{m}$ and density ρ can be expressed in a single equation:

$\text{V}{}_{\mathrm{\phi }}\text{=Bρ}{}^{\mathrm{\lambda }}\text{(}\text{m}{}_0\text{m}{}^{\mathrm{<mtext>[</mtext><mtext>1</mtext><mtext>2</mtext><mtext>+\lambda (1?c)]</mtext>}}\text{(}\text{km/sec}\text{)}$

Here B is an empirically determined “universal” parameter equal to 1.42, $\text{m}{}_0\text{= 20.2}$, a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to $\text{γ ?}\text{1}\text{3}$ where γ is a Grüneisen parameter. The constant c = (? ln V_M/? ln $\text{m}\text{)}{}_{\mathrm{X}}$, where V_M is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use c_Fe = 0.14 for Fe²⁺Mg²⁺ and GeSi substitutions and c_Ca ? 1.3 for CaMg 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 V_M^?4.     

7.

AVO-A response of an anisotropic half-space bounded by a dipping surface for P–P,P–SV and P–SH data     

《Journal of Applied Geophysics》2001,46(1):1-29

     

8.

Anelastic degradation of acoustic pulses in rock     

M.T. Gladwin  F.D. Stacey 《Physics of the Earth and Planetary Interiors》1974,8(4):332-336

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:

$\text{τ=τ}{}_0\text{+C}\text{∫}\text{)}\text{T}\text{Q}{}^{\mathrm{?1}}\text{d}\text{t}$

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.     

9.

On the relationship between meteor height and ambipolar diffusion     

《Journal of Atmospheric and Solar》2004,66(11):899-906

     

10.

High-pressure phase transformations and compressions of ilmenite and rutile,I. Experimental results     

Lin-Gun Liu 《Physics of the Earth and Planetary Interiors》1975,10(2):167-176

Natural ilmenite (Fe,Mg)TiO₃ has been found to transform to the perovskite structure and then to disproportionate into its component oxides, (Fe,Mg)O plus a cubic phase of TiO₂, at loading pressures of 140 and 250 kbar respectively, and at temperatures of 1,400 to 1,800°C. Samples were compressed in a diamond-anvil press and heated by irradiation with a YAG laser. The lattice parameters of the perovskite phase of (Fe,Mg)TiO₃ at room temperature and 1 bar are $\text{a}{}_0\text{= 4.471 ± 0.004, b}{}_0\text{= 5.753 ± 0.005,}\text{and}\text{c}{}_0\text{= 7.429 ± 0.006}\text{A}\text{?}$ with 4 molecules per cell. The zero-pressure volume change is 8.0% for the ilmenite-perovskite transition, 13.3% for the perovskite-mixed-oxides transition, and 20.2% for the ilmenite-mixed-oxides transition. The cubic phase of TiO₂ can be indexed on the basis of space group Fm3m with $\text{Z = 4}\text{and}\text{a}{}_0\text{= 4.455 ± 0.008}\text{A}\text{?}$ at room temperature and 1 bar, which corresponds to a decrease in zero-pressure volume of 29.2% for the rutile-cubic-phase transition. An isentropic bulk modulus at zero pressure of 5.75 ± 0.30 Mbar and a pressure derivative greater than 8 were calculated for the high-pressure cubic phase. The calculated bulk modulus for the mixture of (Fe,Mg)O and cubic TiO₂ is 2.48 ± 0.25 Mbar. All the phase transformations, the calculated lattice parameters, and the bulk moduli observed in this study are in good agreement with published shock-Hugoniot data for ilmenite and rutile.     

11.

A note on the orientation of the macrodispersion tensor in partially saturated heterogeneous porous formations     

《Advances in water resources》1998,21(1):63-70

     

12.

A statistical comparison of the outflow of N+2, NO+ and O+2 molecular ions with that of atomic O+ ions using Polar/TIMAS observations     

《Journal of Atmospheric and Solar》2000,62(6):477-483

     

13.

Investigation into the spatial and temporal coherence of ionospheric outflow on January 9–12, 1997     

《Journal of Atmospheric and Solar》2002,64(15):1659-1666

     

14.

Tests of predicted downstream transport of clasts in turbulent flow     

《Advances in water resources》2003,26(11):1205-1211

     

15.

Strontium, oxygen, and hydrogen isotope geochemistry of hydrothermally altered and weathered rocks in DSDP Hole 504B, Costa Rica Rift     

Hodaka Kawahata  Minoru Kusakabe  Yoshiko Kikuchi 《Earth and Planetary Science Letters》1987,85(4)

DSDP Hole 504B was drilled into 6 Ma crust, about 200 km south of the Costa Rica Rift, Galapagos Spreading Center, penetrating 1.35 km into a section that can be divided into four zones—Zone I: oxic submarine weathering; Zone II: anoxic alteration; Zones III and IV: hydrothermal alteration to greenschist facies. In Zone III there is intense veining of pillow basalts. Zone IV consists of altered sheeted dikes. Isotopic geochemical signatures in relation to the alteration zones are recorded in Hole 504B, as follows:

Phase	Composition	Space group	Cell parameters				Density (g cm?3)
			$\text{a}$	$\text{b}$	$\text{c}$	β
			(Å)	(Å)	(Å)	(°)
Chondrodite	Mg5Si2O10H2	$\text{P2}{}_1\text{/c}$	7.914	4.752	10.350	108.71	3.06
Clinohumite	Mg9Si4O18H2	$\text{P2}{}_1\text{/c}$	13.695	4.747	10.284	100.64	3.14
Phase A	Mg7Si2O14H6	$\text{P6}{}_3$	7.860		9.573		2.96
Phase B	Mg23Si8O42H6	$\text{P2}{}_1\text{/c}$	10.600	14.098	10.092	104.05	3.32

Zone	Depth(m)	Average87Sr/86Sr	Average δ18O (%o)	Average δD (%o)
I	275–550	0.7032	7.3	−63
II	550–890	0.7029	6.5	−45
III	890–1050	0.7035	5.6	−31
IV	1050–1350	0.7032	5.5	−36

Full-size table

Interionic repulsive force and compressibility of ions

The compressibility of an individual ion is examined, in comparison with a known set of data for the alkali halides. A simple extrapolation of ionic radius to high pressure is not acceptable, because the pressure derivative of ionic radius changes for different salts. According to the classical concept of an elastic ion, the repulsive potential energy between the ions i and j is specified by the nature of each ion as:

$\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{) exp[}\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{? r)}\text{(ρ}{}_{\mathrm{i}}\text{+ ρ}{}_{\mathrm{j}}\text{)}\text{]}$

as a function of the interionic distance r. In this expression, q_i and ρ_i are the ionic radius and ionic compressibility, respectively, in a suitably modified meaning. Such a form of the repulsive potential fits well to the data of lattice constants and bulk moduli. The parameters q_i and ρ_i are evaluated for alkali and halogen ions, and an anion turns out to be much more compressible than a cation. The present treatment may be usefully applied to the minerals in the Earth's mantle, which contain only a few major ions.     

General relationships among sound speeds: II. Theory and discussion

The dependence of bulk sound speed V_φ upon mean atomic weight $\text{m}$ and density ρ can be expressed in a single equation:

$\text{V}{}_{\mathrm{\phi }}\text{=Bρ}{}^{\mathrm{\lambda }}\text{(}\text{m}{}_0\text{m}{}^{\mathrm{<mtext>[</mtext><mtext>1</mtext><mtext>2</mtext><mtext>+\lambda (1?c)]</mtext>}}\text{(}\text{km/sec}\text{)}$

Here B is an empirically determined “universal” parameter equal to 1.42, $\text{m}{}_0\text{= 20.2}$, a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to $\text{γ ?}\text{1}\text{3}$ where γ is a Grüneisen parameter. The constant c = (? ln V_M/? ln $\text{m}\text{)}{}_{\mathrm{X}}$, where V_M is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use c_Fe = 0.14 for Fe²⁺Mg²⁺ and GeSi substitutions and c_Ca ? 1.3 for CaMg 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 V_M^?4.     

Anelastic degradation of acoustic pulses in rock

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:

$\text{τ=τ}{}_0\text{+C}\text{∫}\text{)}\text{T}\text{Q}{}^{\mathrm{?1}}\text{d}\text{t}$

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.     

High-pressure phase transformations and compressions of ilmenite and rutile,I. Experimental results

Natural ilmenite (Fe,Mg)TiO₃ has been found to transform to the perovskite structure and then to disproportionate into its component oxides, (Fe,Mg)O plus a cubic phase of TiO₂, at loading pressures of 140 and 250 kbar respectively, and at temperatures of 1,400 to 1,800°C. Samples were compressed in a diamond-anvil press and heated by irradiation with a YAG laser. The lattice parameters of the perovskite phase of (Fe,Mg)TiO₃ at room temperature and 1 bar are $\text{a}{}_0\text{= 4.471 ± 0.004, b}{}_0\text{= 5.753 ± 0.005,}\text{and}\text{c}{}_0\text{= 7.429 ± 0.006}\text{A}\text{?}$ with 4 molecules per cell. The zero-pressure volume change is 8.0% for the ilmenite-perovskite transition, 13.3% for the perovskite-mixed-oxides transition, and 20.2% for the ilmenite-mixed-oxides transition. The cubic phase of TiO₂ can be indexed on the basis of space group Fm3m with $\text{Z = 4}\text{and}\text{a}{}_0\text{= 4.455 ± 0.008}\text{A}\text{?}$ at room temperature and 1 bar, which corresponds to a decrease in zero-pressure volume of 29.2% for the rutile-cubic-phase transition. An isentropic bulk modulus at zero pressure of 5.75 ± 0.30 Mbar and a pressure derivative greater than 8 were calculated for the high-pressure cubic phase. The calculated bulk modulus for the mixture of (Fe,Mg)O and cubic TiO₂ is 2.48 ± 0.25 Mbar. All the phase transformations, the calculated lattice parameters, and the bulk moduli observed in this study are in good agreement with published shock-Hugoniot data for ilmenite and rutile.     

Strontium, oxygen, and hydrogen isotope geochemistry of hydrothermally altered and weathered rocks in DSDP Hole 504B, Costa Rica Rift

DSDP Hole 504B was drilled into 6 Ma crust, about 200 km south of the Costa Rica Rift, Galapagos Spreading Center, penetrating 1.35 km into a section that can be divided into four zones—Zone I: oxic submarine weathering; Zone II: anoxic alteration; Zones III and IV: hydrothermal alteration to greenschist facies. In Zone III there is intense veining of pillow basalts. Zone IV consists of altered sheeted dikes. Isotopic geochemical signatures in relation to the alteration zones are recorded in Hole 504B, as follows: