Spectroscopic properties of Cr-doped melilite crystals

 Four kinds of Cr-droped melilite crystals, Ca₂MgSi₂O₇ (akermanite), CaAl₂SiO₇ (gehlenite), CaGa₂SiO₇ (Ga-gehlenite) and CaGa₂GeO₇ (GaGe-gehlenite), with different sizes of the sites for Cr ions to substitute, were grown in series, using both the CZ and FZ techniques. Although Cr⁴⁺ is regarded as a major species in melilites, the existence of Cr⁶⁺ in gehlenite is also suggested from the change in absorption spectra by annealing, and the dependence of distribution coefficient of Cr ions on growth atmosphere. Spectral peak shifts are not obvious if the host crystal field is altered in melilites, because the local environment of the sites for Cr ion is possibly changed by reforming the packing features of the host lattice. Received February 7, 1996 / Revised, accepted September 20, 1996     

Plastic deformation of garnets: systematics and implications for the rheology of the mantle transition zone

Plastic properties of materials with garnet structure have been studied under wide temperature conditions, ranging from room temperature to 95% of the melting temperatures, using uniaxial compression and hot microhardness tests. Garnets studied include single crystals of oxide garnets (Y₃Al₅O₁₂, Gd₃Ga₅O₁₂ and Y₃Fe₅O₁₂) and silicate garnets (various solid solutions, including grossular, almandine, andradite, pyrope, spessartine and uvarovite). Both uniaxial compression and hot hardness tests indicate that there is a general trend in the plasticity of garnets when the data are compared at normalized conditions (T/T_m andσ/μ), and that the resistance to plastic deformation in garnets is significantly higher than most of the other minerals in the Earth's mantle. Based on both stress-dip tests and microstructural observations, it is proposed that the creep strength of garnet is largely controlled by the resistance to dislocation glide rather than by recovery processes. This conclusion is consistent with the high Peierls stress inferred from the hot hardness tests. The high Peierls stress in garnets is, presumably, due to the large unit cell (i.e., long Burgers vectors) and/or the bcc packing, which are common to all garnets. We postulate, therefore, that the present results can be applied to the strength of high-pressure garnet (majorite) and suggest that garnet-rich layers in the Earth, such as subducted oceanic crust in the transition zone or a possibly garnet-rich (bottom part of the) transition zone, will be considerably stronger than surrounding regions.     

Fate of carbonates within oceanic plates subducted to the lower mantle, and a possible mechanism of diamond formation

We report on high-pressure and high-temperature experiments involving carbonates and silicates at 30–80 GPa and 1,600–3,200 K, corresponding to depths within the Earth of approximately 800–2,200 km. The experiments are intended to represent the decomposition process of carbonates contained within oceanic plates subducted into the lower mantle. In basaltic composition, CaCO₃ (calcite and aragonite), the major carbonate phase in marine sediments, is altered into MgCO₃ (magnesite) via reactions with Mg-bearing silicates under conditions that are 200–300°C colder than the mantle geotherm. With increasing temperature and pressure, the magnesite decomposes into an assemblage of CO₂ + perovskite via reactions with SiO₂. Magnesite is not the only host phase for subducted carbon—solid CO₂ also carries carbon in the lower mantle. Furthermore, CO₂ itself breaks down to diamond and oxygen under geotherm conditions over 70 GPa, which might imply a possible mechanism for diamond formation in the lower mantle.     

Intensity of radiation reflected by a vertically inhomogeneous medium through multiple scattering

To facilitate the computation of the radiative intensity reflected, upon multiple scattering, by a vertically inhomogeneous medium, an implicit formula for integrating the invariant imbedding equation for Fourier-decomposed reflection function is derived starting with the formal solution: the height variations of the single-scattering albedo and the phase function characterizing the degree of inhomogeneity are thereby approximated by piece-wise, but continuous, linear functions of optical height , while the reflection function is approximated by a piece-wise quadratic polynomial in over each integration step. Using these approximations, the integration involved in the formal solution is then carried out analytically, yielding a correctortype formula for finding the reflection function at each step of . It is expected that this formula is capable of handling general cases of inhomogeneous media where both single-scattering albedo and phase function are allowed to vary continuously with height.Similar, but explicit expressions are also derived for the single and the second-order scattering solutions, with which the higher-order Fourier terms of reflection function are to be approximated, thereby enabling us to avoid the iterative process.     

Growth and sedimentation of dust grains in the primordial solar nebula

Of the formation processes in the solar system, the process of growth and sedimentation of dust grains in the primordial solar nebula is investigated for a region near the Earth's orbit. The growth equation for dust grains, which are sinking as well as being in thermal motion, is solved numerically in the wide mass range between 10^?12 and 10⁶ g. Any turbulent motions in the nebula are assumed to have already decayed when the sedimentation begins. The numerical simulation shows that the growth and sedimentation proceed faster than was found by Kusaka et al. (1970) but in accordance with the estimate of Safronov (1969) owing to a cooperative interaction of the growth and the sedimentation; that is, at about 3 × 10³ years after the beginning of the growth and sedimentation a dust layer, composed of centimeter-sized grains, is formed at the equator of the solar nebula. Furthermore, the mass density of dust grains floating in the outer layers of the nebula is found to be of the order of 10^?5 after 10⁵ years compared with that before the sedimentation. From these results, it can be estimated that at about 5 × 10³ years after the beginning of sedimentation the dust layer breaks up owing to the onset of gravitational instability.     

A direct numerical approach to the Chandrasekhar'sH-functions for arbitrary characteristic functions

The purpose of this paper is to present a numerical technique to directly compute the Chandrasekhar'sH ()-function for anisotropic scattering in terms of the roots of the characteristic equations as well as the quadrature points of a certain degreen employed to approximate the definite integral involved in the basic equation. The principal feature of the algorithm proposed here is a compact computer code to enumerate _n C _m combinations ofn distinct integers {1,...,n} takenm at a time. With these quantities available, the coefficients of the polynomial equation of the characteristics equation can be readily computed for any given characteristic function, so that a standard technique such as the Laguerre method can be applied to find all the roots.It is shown that the results obtained for some representativeH()-functions using the present technique with relatively low-order formula (e.g.,n=7) are sufficiently accurate for all practical purposes.