From geometry to dynamics of microstructure: using boundary lengths to quantify boundary misorientations and anisotropy

The microstructure of a quartzite experimentally deformed and partially recrystallised at 900 °C, 1.2 GPa confining pressure and strain rate 10⁻⁶/s was investigated using orientation contrast and electron backscatter diffraction (EBSD). Boundaries between misoriented domains (grains or subgrains) were determined by image analysis of orientation contrast images. In each domain, EBSD measurements gave the complete quartz lattice orientation and enabled calculation of misorientation angles across every domain boundary. Results are analysed in terms of the boundary density, which for any range of misorientations is the boundary length for that range divided by image area. This allows a more direct comparison of misorientation statistics between different parts of a sample than does a treatment in terms of boundary number.The strain in the quartzite sample is heterogeneous. A 100×150 μm low-strain partially recrystallised subarea C was compared with a high-strain completely recrystallised subarea E. The density of high-angle (>10°) boundaries in E is roughly double that in C, reflecting the greater degree of recrystallisation. Low-angle boundaries in C and E are produced by subgrain rotation. In the low-angle range 0–10° boundary densities in both C and E show an exponential decrease with increasing misorientation. The densities scale with exp(−θ/λ) where λ is approximately 2° in C and 1° in E; in other words, E has a comparative dearth of boundaries in the 8–10° range. We explain this dearth in terms of mobile high-angle boundaries sweeping through and consuming low-angle boundaries as the latter increase misorientation through time. In E, the density of high-angle boundaries is larger than in C, so this sweeping would have been more efficient and could explain the relative paucity of 8–10° boundaries.The boundary density can be generalised to a directional property that gives the degree of anisotropy of the boundary network and its preferred orientation. Despite the imposed strain, the analysed samples show that boundaries are not, on average, strongly aligned. This is a function of the strong sinuosity of high-angle boundaries, caused by grain boundary migration. Low-angle boundaries might be expected, on average, to be aligned in relation to imposed strain but this is not found.Boundary densities and their generalisation in terms of directional properties provide objective measures of microstructure. In this study the patterns they show are interpreted in terms of combined subgrain rotation and migration recrystallisation, but it may be that other microstructural processes give distinctive patterns when analysed in this fashion.     

Numerical simulation of a South China Sea typhoon Leo (1999)

Summary ?A South China Sea typhoon, Leo (1999), was simulated using the Penn State/NCAR mesoscale model MM5 with the Betts-Miller convective parameterization scheme (BMEX). The simulation had two nested domains with resolutions at 54 and 18 km, and the forecast duration was 36 hours. The model was quite successful in predicting the track, the rapid deepening, the central pressure, and the maximum wind speed of typhoon Leo as verified with reports from the Hong Kong Observatory (HKO). The structure of the eye, the eye wall, and the spiral convective cloud band simulated in the model are found to be comparable to corresponding features identified in satellite images for the storm, and also with those reported by other authors. A trajectory analysis was performed. Three kinds of trajectory were found: (1) spirally rising trajectories near the eye wall; (2) spirally rising/descending trajectories in the convective/cloud free belt; (3) straight and fast rising trajectories in a heavy convection zone along one of the cloud bands on the periphery of the tropical cyclone. Both the HKO and the U.S. Joint Typhoon Warning Center (JTWC) reported the rapid deepening of Leo started around 00 UTC 29 April. In the model, the eye was first formed in the lower troposphere, and it extended to the upper troposphere within a few hours. We speculate that the spin-up of cyclonic rotation in the low-level eye enhanced the positive vorticity along the low-level eye wall. The positive vorticity was then transported to the upper troposphere by convection, leading to an extension and growth of the eye into the upper troposphere. To examine the impact of convective parameterization scheme (CPS) on the simulation, the Grell scheme (GLEX) was also tested. The GLEX predicted a weaker typhoon with a wilder eye that extended not as high up in the upper troposphere as BMEX. The different structures of the eye between the BMEX and GLEX suggest that the mesoscale features of the eye are dependent on the convection. In other words, the vertical and horizontal distribution of convective heating is essential to the development and structure of the eye. Received December 18, 2001; accepted May 7, 2002 Published online: March 20, 2003     

Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

Control‐volume mixed finite element methods

A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large‐scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control‐volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular (i.e., distorted logically rectangular) block‐centered quadrilateral grids. The control‐volume formulation of Darcy’s law can be viewed as a discretization into element‐sized “tanks” with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block‐by‐block conservation in the usual mixed discretization of the mass‐conservation equation. Numerical results in two dimensions show second‐order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.     

ELNES spectroscopy of mixed Si coordination minerals

 Si K- and L-edge ELNES spectroscopy and multiple-scattering (MS) calculations are used to examine mixed Si coordination compounds varying in Si^VI:Si^IV ratio. As in previous studies, the edges are influenced mainly by silicon coordination (tetrahedral vs. octahedral), as supported by the MS calculations. We demonstrate two methods semi-quantitatively to extract the value of Si^VI/(Si^VI+Si^IV): (1) A linear relationship between the L_2,3-L₁ splitting and Si^VI/(Si^VI+Si^IV) is observed, (2) a fitting method based on the coaddition of reference tetrahedral and octahedral Si spectra is applied to both Si K- and L-edge ELNES spectra. Received: February 10, 1997 / Revised, accepted: May 23, 1997     

Feasibility and cost of creating an iron-phosphate coating on pyrrhotite to prevent oxidation

 Acid mine drainage (AMD) occurs when sulfide minerals are exposed to an oxidizing environment. Most of the methods for preventing AMD are either short-term or high cost solutions. Coating with iron phosphate is a new technology for the abatement of AMD. It involves treating the sulfide with a coating solution composed of H₂O₂, KH₂PO₄, and sodium acetate as a buffer agent. The H₂O₂ oxidizes the sulfide surface and produces Fe³⁺ so that iron phosphate precipitates as a coating on the sulfide surface. Experiments performed under laboratory conditions prove that an iron phosphate coating can be established on pyrrhotite surfaces with optimal concentrations of the coating solution in the range of: 0.2M/0.01M H₂O₂, 0.2M KH₂PO₄, and 0.2M sodium acetate NaAc, depending on the experimental scale. Iron phosphate coating may be a long-term solution to the problem of AMD. The method would be easy to implement; the reagent cost, however, is not low enough, although it is lower than the conventional treatment with lime. Received: 30 March 1995 · Accepted: 6 September 1995     

Stratigraphy of the upper cretaceous and lower tertiary strata in the Tethyan Himalayas of Tibet (Tingri area,China)

The 1500-m-thick marine strata of the Tethys Himalaya of the Zhepure Mountain (Tingri, Tibet) comprise the Upper Albian to Eocene and represent the sedimentary development of the passive northern continental margin of the Indian plate. Investigations of foraminifera have led to a detailed biozonation which is compared with the west Tethyan record. Five stratigraphic units can be distinguished: The Gamba group (Upper Albian - Lower Santonian) represents the development from a basin and slope to an outer-shelf environment. In the following Zhepure Shanbei formation (Lower Santonian - Middle Maastrichtian), outer-shelf deposits continue. Pebbles in the top layers point to beginning redeposition on a continental slope. Intensified redeposition continues within the Zhepure Shanpo formation (Middle Maastrichtian - Lower Paleocene). The series is capped by sandstones of the Jidula formation (Danian) deposited from a seaward prograding delta plain. The overall succession of these units represents a sea-level high at the Cenomanian/Turonian boundary followed, from the Turonian to Danian, by an overall shallowing-upward megasequence. This is followed by a final transgression — regression cycle during the Paleocene and Eocene, documented in the Zhepure Shan formation (?Upper Danian - Lutetian) and by Upper Eocene continental deposits. The section represents the narrowing and closure of the Tethys as a result of the convergence between northward-drifting India and Eurasia. The plate collision started in the Lower Maastrichtian and caused rapid changes in sedimentation patterns affected by tectonic subsidence and uplift. Stronger subsidence and deposition took place from the Middle Maastrichtian to the Lower Paleocene. The final closure of remnant Tethys in the Tingri area took place in the Lutetian.     

Site effects at a vertical accelerometer array near Paducah, Kentucky

The downhole vertical accelerometer array VSAP near Paducah, KY, consists of three-component accelerometers at the surface, the top of the McNairy Formation (−41 m), and the top of the Paleozoic bedrock (—99 m). The array is at the northern end of the Mississippi Embayment, and it was installed to verify the ground-motion modeling for the site, assuming a significant earthquake in the New Madrid Seismic Zone. Accelerograms from 4.2 and 2.0 m_b earthquakes were used to check aspects of the modeling pertaining to linear behavior of the soil column, and to review the soil column models derived by drilling and geotechnical methods and through the use of high-resolution P- and SH-wave seismic refraction in reflection techniques. Results of the study indicate that for the linear case the soil column models derived by the two techniques are equivalent, and that the most important boundary in the soil column, with respect to amplification of the ground motions, is the interface between the limestone bedrock and soil.     

Nitrogen isotope indicators of seasonal source variability to groundwater

 A nitrogen isotope study of soil water and groundwater in southern Indiana, USA, in 1991–1992 demonstrated considerable variations in nitrate degradation processes compared to an earlier investigation in 1986–1987. Although N-fertilizers were applied in May 1991, the δ¹⁵N values in soil water decreased in February 1992, indicating its delayed release into the system after substantial rainfall. The δ¹⁵N values of groundwater decreased from +12.3‰ in November 1991 to +11.3‰ in February 1992, and to +7.5‰ in March 1992. The increased residence time of nitrate in the soil resulted in increased denitrification, ammonia volatilization and plant uptake, and reduced threat to the groundwater quality. The 1986–1987 study in the area reported that excessive rainfall during the summer rapidly transported the nitrate to deeper horizons and drastically reduced volatilization and microbial reduction of nitrate, thus increasing the immediate threat to the groundwater quality in the area. The present study demonstrated that nitrogen isotopic signatures can be used to determine the effects of local soil type, rainfall, and land-use practices on the fate of nitrate in the subsurface. Received: 18 February 1997 · Accepted: 17 June 1997