A MEG study of the olivine and spinel forms of Mg2SiO4

In this paper we present a theoretical investigation of the structures and relative stability of the olivine and spinel phases of Mg₂SiO₄. We use both a purely ionic model, based on the Modified Electron Gas (MEG) model of intermolecular forces, and a bond polarization model, developed for low pressure silica phases, to investigate the role of covalency in these compounds. The standard MEG ionic model gives adequate structural results for the two phases but incorrectly predicts the spinel phase to be more stable at zero pressure. This is mainly because the ionic modeling of Mg₂SiO₄ only accounts for 95 percent of the lattice energy. The remainder can be attributed to covalency and many-body effects. An extension of the MEG ionic model using “many-body” pair potentials corrects the phase stability error, but predicts structures which are in poorer agreement with experiment than the standard ionic approach. In addition, calculations using these many-body pair potentials can only account for 10 percent of the missing lattice energy. This model predicts an olivine-spinel phase transition of 8 GPa, below the experimental value of 20 GPa. Therefore, in order to understand more fully the stability of these structures we must consider polarization. A two-shell bond polarization model enhances the stability of both structures, with the olivine structure being stabilized more. This model predicts a phase transition at about 80 GPa, well above the observed value. Also, the olivine and spinel structures calculated with this approach are in poorer agreement with experiment than the ionic model. Therefore, based on our investigations, to properly model covalency in Mg₂SiO₄, a treatment more sophisticated than the two-shell model is needed.     

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

What has seismic missed?

The relative efficiencies of alternative geometric patterns of both discrete borehole and continuous grid line search have been extensively discussed in the mathematical geology literature. However, an equally important problem has received virtually no attention: How to use a sample of properties of geologic anomalies detected by grid line search of a region to estimate systematically both the number and size distribution of geologic anomalies missed by the search. We show how estimation methods developed in the sample survey design literature can be adapted to this problem, and we apply these methods to data describing 94 anomalies identified by a seismic reconnaissance survey.     

Depositional mechanics of turbulent nuées ardentes (surges) from their grain sizes

The ability of turbulent nuées ardentes (surges) to transport coarse pyroclasts has been questioned on the basis that settling velocities of coarse fragments in the deposits are much too high for them to have been supported by turbulence in a dilute gas suspension. A computer model is used to evaluate the settling velocity of pyroclasts in suspensions of varying concentration and temperature. Since suspension of grains in low-concentration surges occurs if the shear velocity exceeds the settling velocity, the shear velocities related to the 16th and 84th percentiles, and the mean of the grain-size distribution are compared in surge deposits of the Vulsini, with the shear velocity necessary to move the coarsest grain on the bed surface (the Shields criterion). The results show that the settling velocities do not vary significantly in gaseous suspensions having volume concentrations lower than 15%, and that an increase in concentration to 25% is not sufficient to decrease the settling velocity of the coarser fraction, if it represents flow shear velocity. It is shown that the settling velocity of the mean grain size (M _z ) best depicts the shear velocity of a dilute turbulent suspension. Applying the results to the May 1902 paroxysmal nuées ardentes of Mount Pelée shows that the estimated mean velocities are well within the observed velocities, and sufficient to support all the clasts in dilute, turbulent suspensions.     

Simulation of pebble abrasion on coastal benches by transgressive waves

Tumbler simulations of abrasion processes affecting rocks on basaltic marine benches have clarified the effects of mass and volume of rock fragments on their rate of wear. Several experiments indicate that rate of basalt wear increases with mass in the interval 1 g to 8 g, but is not related to volume of fragments abraded in seawater. Relatively small quantities of rock flour suspended in the immersant seawater substantially reduced the rate of basalt wear. Basalt and calcareous beachrock responded differently in systems with both rock types tumbling together. Examination of the cuttings from these low-energy encounters suggests that abrasion on elevated benches along exposed seacoasts reduces virtually all clastic material to particles of silt size or smaller, producing essentially no sand.     

The oceans and the physics of the Earth

The Earth is the only terrestrial planet to have seas, by which it is covered to the extent of seventy percent. The oceans determine the climate of the Earth and it is through them that life and civilization have evolved, but they also have major influence on physical processes in the solid Earth. Tidal friction leads to the Earth's spin slowing down with a consequent recession of the Moon from the Earth, while the presence of the oceans controls the tectonic evolution of the Earth through the formation of oceanic crust, the erosion of land and the accumulation of sediment, the formation of mountains and the establishment of isostatic balance.     

Provincialism and correlations between some properties of vitrinites

Optical and chemical properties for hand-picked samples of vitrinite from a number of British coalfields are correlated and the correlations compared with previously published data. The form of the relationship found for the properties of British vitrinites is generally similar to that exhibited by a number of other sets of analyses, but some significant differences also exist in several of the correlations. For maximum reflectance as a function of carbon content, the present data indicate that at medium and low ranks, maximum reflectance is lower than the level suggested by most previous studies. The relationships of volatile-matter yield to reflectance and carbon content suggest that at low ranks, volatile-matter yield is strongly dependent upon the nature of the coalification history of the vitrinite. Furthermore, these correlations are likely to show provincialism, in that correlations which hold for one coalfield may not be representative of the relationship in other coalfields. Similarly, major differences in relationships involving bireflectance are associated with the tectonic setting at the time of effective coalification. The data presented here indicate that for low-rank coals at least, correlations between properties of vitrinites must take account of provincialism if they are to be sufficiently reliable to be useful. The measurement of a number of rank-sensitive variables can yield additional information about rank, as compared with the use of a single rank-sensitive variable.