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1.
Richard J. Lisle 《Mathematical Geosciences》1988,20(7):879-890
An approximating form for coarse water-worn clasts based on the superellipsoid is proposed. The sectional outlines of pebbles from Gower (Wales) beaches approximate superellipses described by this equation in rectangular coordinates $$\frac{{x^p }}{{a^p }} + \frac{{x^p }}{{b^p }} = 1$$ wherea andb are principal semi-axes. For AB planes of the pebbles,p is close to 2, but in AC sections,p averages about 2.6. The measured volumes of pebbles are poor approximations to the previously proposed ellipsoidal model of pebble form. Instead, volumes are shown to accord with a three-dimensional form consisting of a superellipsoid of revolution, i.e., a solid of revolution produced by rotating a superellipse about one of its principal axes. 相似文献
2.
The following equation is proposed in this paper to estimate the crustal growth rate of the North China Platform on the basis
of mass equilibrium between the crust and the mantle:
相似文献
3.
Paola Comodi Marcello Mellini Pier Francesco Zanazzi 《Physics and Chemistry of Minerals》1992,18(8):483-490
The response of magnesiochloritoid to pressure has been studied by single crystal X-ray diffraction in a diamond anvil cell, using crystals with composition Mg1.3Fe0.7Al4Si2O10(OH)4. The unit cell parameters decrease from a = 9.434 (3), b = 5.452 (2), c = 18.136 (5) Å, β = 101.42° (2) (1 bar pressure) to a = 9.370 (7), b = 5.419 (5), c = 17.88 (1) Å, β = 101.5° (1) (42 kbar pressure), following a slightly anisotropic compression pattern (linear compressibilities parallel to unit cell edges: β a = 1.85, β b = 1.74, βc = 3.05 × 10?4 kbar?1) with a bulk modulus of 1480 kbar. Perpendicular to c, the most compressible direction, the crystal structure (space group C2/c) consists of two kinds of alternating octahedral layers connected via isolated SiO4 tetrahedra. With increasing pressure the slightly wavy layer [Mg1.3Fe0.7AlO2(OH)4] tends to flatten. Furthermore, the octahedra in this layer, with all cations underbonded, are more compressible than the octahedra in the (A13O8) layer with slightly overbonded aluminum. Comparison between high-pressure and high-temperature data yields the following equations: $$\begin{gathered} a_{P,T} = 9.434{\text{ }}{\AA} - 174 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 9 \cdot 10^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ b_{P,T} = 5.452{\text{ }}{\AA} - 95 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 5 \cdot 65 \cdot 10^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ c_{P,T} = 18.136{\text{ }}{\AA} - 549 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 16 \cdot 2^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ \end{gathered} $$ with P in kbar and T in °C. These equations indicate that the unit cell and bond geometry of magnesiochloritoid at formation conditions do not differ greatly from those at the outcrop conditions, e.g. the calculated unitcell volume is 917.3 Å3 at P = 16 kbar and T=500 °C, whereas the observed volume at room conditions is 914.4 Å3. In addition, they show that the specific gravity increases from formation at depth to outcrop at surface conditions. 相似文献
4.
Oxygen isotope fractionation between rutile and water 总被引:1,自引:0,他引:1
Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows:
5.
The data of Reed (1983) are analysed to produce the following empirical equations for the amplitude p 0 (overall fluctuation) in Pascals of the air pressure wave associated with a volcanic eruption of volume V km3 or a nuclear explosion of strength M Mt: Here s is the distance from the source in km. $$\begin{gathered} \log _{10} p_0 = 4.44 + \log _{10} V - 0.84\log _{10} s \hfill \\ {\text{ }} = 3.44 + \log _{10} M - 0.84\log _{10} s. \hfill \\ \end{gathered} $$ Garrett's (1970) theory is examined on the generation of water level fluctuations by an air pressure wave crossing a water depth discontinuity such as a continental shelf. The total amplitude of the ocean wave is determined to be where c 2 1 = gh 1, c 2 2 = gh 2, g is acceleration of gravity, h 1 and h 2 are the water depths on the ocean and shore side of the depth discontinuity, c is the speed of propagation of the air pressure wave, and ? is the water density. $$B = \left[ {\frac{{c_2^2 }}{{c^2 - c_2^2 }} + \frac{{c^2 (c_1 - c_2 )}}{{(c - c_1 )(c^2 - c_2^2 )}}} \right]\frac{{p_0 }}{{g\varrho }}$$ It is calculated that a 10 km3 eruption at Mount St. Augustine would cause a 460 Pa air pressure wave and a discernible water level fluctuation at Vancouver Island of several cm amplitude. 相似文献
6.
Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO3 and Mg2SiO4 melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ25Mg values in the MgSiO3 and Mg2SiO4 melts were 0.141?±?0.004 and 0.143?±?0.003‰ more positive than in their respective vapors. The corresponding δ26Mg values were 0.270?±?0.008 and 0.274?±?0.006‰ more positive than in vapors, respectively. The general \(\alpha - T\) equations describing the equilibrium Mg α in MgSiO3 and Mg2SiO4 melt–vapor systems were: \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\) and \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\), respectively, where m is the mass of light isotope 24Mg and m′ is the mass of the heavier isotope, 25Mg or 26Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution. 相似文献
7.
Bernd Wruck Ekhard K. H. Salje Ann Graeme-Barber 《Physics and Chemistry of Minerals》1991,17(8):700-710
The kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Q od occur. The variations of Q od are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Q od can be well described by the rate law: $$\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}$$ with the excess Gibbs energy G and G a 0 = 433.8 kJ/mol, ?= -27.4 kJ/mol, γ = 1.687 · 1014 h ?1. Under wet conditions, two processes were found which occur simultaneously. Firstly, some material renucleated with the equilibrium degree of order. Secondly, the bulk of the material transformed following the same rate law as under dry conditions but with the reduced activation energy G a 0 = 332.0 kJ/mol and ? = -43.0 kJ/ mol, γ = 1.047 · 1013 h?1. The applicability of the kinetic theory is discussed and some ideas for the analysis of geological observations are evolved. 相似文献
8.
An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene 总被引:1,自引:0,他引:1
Simon L. Harley 《Contributions to Mineralogy and Petrology》1984,86(4):359-373
The partitioning of Fe and Mg between garnet and aluminous orthopyroxene has been experimentally investigated in the pressure-temperature range 5–30 kbar and 800–1,200° C in the FeO-MgO-Al2O3-SiO2 (FMAS) and CaO-FeO-MgO-Al2O3-SiO2 (CFMAS) systems. Within the errors of the experimental data, orthopyroxene can be regarded as macroscopically ideal. The effects of Calcium on Fe-Mg partitioning between garnet and orthopyroxene can be attributed to non-ideal Ca-Mg interactions in the garnet, described by the interaction term:W CaMg ga -W CaFe ga =1,400±500 cal/mol site. Reduction of the experimental data, combined with molar volume data for the end-member phases, permits the calibration of a geothermometer which is applicable to garnet peridotites and granulites: $$T(^\circ C) = \left\{ {\frac{{3,740 + 1,400X_{gr}^{ga} + 22.86P(kb)}}{{R\ln K_D + 1.96}}} \right\} - 273$$ with $$K_D = {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } \mathord{\left/ {\vphantom {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}$$ and $$X_{gr}^{ga} = (Ca/Ca + Mg + Fe)^{ga} .$$ The accuracy and precision of this geothermometer are limited by largerelative errors in the experimental and natural-rock data and by the modest absolute variation inK D with temperature. Nevertheless, the geothermometer is shown to yield reasonable temperature estimates for a variety of natural samples. 相似文献
9.
Andreas K. Kronenberg Richard A. Yund Bruno J. Giletti 《Physics and Chemistry of Minerals》1984,11(3):101-112
The diffusion rates of carbon and oxygen in two calcite crystals of different Mn contents have been studied between 500° and 800° C in a CO2-H2O atmosphere (P CO 2=1?5 bars, P H2O=0.02?24 bars) labeled with 13C and 18O. Isotope concentration gradients within annealed specimens were measured using a secondary ion microprobe by depth profiling parallel and perpendicular to the c axis. Despite the anisotropic structure of calcite, the diffusion of carbon and oxygen are both very nearly isotropic. Least-squares fitting of the carbon data to an Arrhenius relation gives an activation energy of 87±2 kcal/mole, with D 0 terms dependent only slightly upon direction:
10.
M. A. F. Candia Tj. Peters J. V. Valarelli 《Contributions to Mineralogy and Petrology》1975,52(4):261-266
The equilibrium constants for the reaction (2) Rhodochrosite + Quartz=Pyroxmangite+CO2 obtained are:logK(2)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(9862 \pm 102)}}{T} \hfill \\+ (15.887 \pm 0.220) + (0.1037 \pm 0.0020)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ and for the reaction (3) Rhodochrosite+Pyroxmangite=Tephroite+CO2: logK(3)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(6782 \pm 205)}}{T} \hfill \\+ (11.296 \pm 0.304) + (0.0835 \pm 0.0030)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ The present data lie within reasonable limits of error of the values calculated from previous experimental results at P tot = 2000 bars. 相似文献
11.
M. S. Ghiorso I. S. E. Carmichael L. K. Moret 《Contributions to Mineralogy and Petrology》1979,68(3):307-323
Fifty-two samples of inverted high-temperature quartz from volcanic rocks were investigated by Guinier-Jago powder diffractometry and differential scanning calorimetry (DSC). Quartz megacrysts from Clear Lake and Cinder Cone, California show a variability of ?2.5 ° K in their α-β transition temperature (T α-β). Quartz phenocrysts and quartz from crystalline rocks give a range of 0.5 ° K in T α-β. Neutron activation analysis of single crystals demonstrates that Al is the principal impurity (17–380 ppm). Its concentration is inversely correlated with T α-β. A very small variation was found in the a and c lattice parameters among the specimens of volcanic quartz studied. This variation does not correlate with Al content or transition temperature. Mean values at 22 ° C (a=4.1934±0.0004 Å, c=5.4046±0.0006 Å) are similar to those of quartz grown at low temperatures. Enthalpy of the α-β transition (ΔH α-β), obtained over 9.0 ° from DSC runs, is dependent upon sample grain size and for a crushed powder with zero hysteresis (T α-β on heating=T α-β on cooling) is 92.0 ±1.4 cal/mol. In contrast, a single piece of quartz requires ΔH α-β be 107.7±1.4 cal/mol and has a T α-β hysteresis of 1.1 ° K. Regression of published data provides equations for the variation of the molar volume (cc/mol) of quartz with v. These equations imply a ΔV α-β of 0.205±0.031 cc/- mol. Expressions are also provided for the temperature dependence of the thermal coefficient of expansion, α, the compressibility, β, and (?/gb/?T)p (which is identically -(?α/?P) T ). DSC heat capacity measurements over the range 400 to 900 ° K were fitted to extended Maier-Kelley type expressions to give: $$\begin{gathered} C_P = 10.31 + 9.116 \times 10^{ - 3} T - \frac{{1.812 \times 10^5 }}{{T^2 }} \hfill \\ - {\text{5}}{\text{.630}} \times 10^{ - 2} {\text{ }}\frac{T}{{(T - 848)}} - 0.3553\frac{T}{{(T - 848)^2 }} \hfill \\ - 0.9011\frac{T}{{\left( {T - 848} \right)^3 }} \hfill \\ (400{\text{ to 842}}^ \circ {\text{K), and}} \hfill \\ C_P = - 318.8 + 0.2532T \hfill \\ {\text{ + }}\frac{{8.687 \times 10^7 }}{{T^2 }} + 0.1603\frac{T}{{\left( {T - 848} \right)^4 }} \hfill \\ \end{gathered} $$ (851 to 900 ° K), which together with the values of ΔH α?β measured over the range 842–851° K give 7875.3 cal/mol for H900-H400. The behavior of α, β, and C p as a function of T emphasizes that structural changes which occur at the α?β transition do so over a broad temperature interval. 相似文献
12.
Paula M. Davidson John Grover Donald H. Lindsley 《Contributions to Mineralogy and Petrology》1982,80(1):88-102
Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)2Si2O6 clinopyroxene solution extends to more Ca-rich compositions than CaMgSi2O6, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by:
13.
To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni2SiO4), aggregates containing 3 vol% amorphous SiO2 have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f
o
2) from 10-1 to 105 Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law
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