Improved Petrological Modal Analyses from X-ray Powder Diffraction Data by use of the Rietveld Method I. Selected Igneous, Volcanic, and Metamorphic Rocks

Mineral modes have been determined for specimens of eight rocktypes from CuK X-ray powder diffraction data using the Rietveldmethod. The samples include two granites, a granodiorite, adamellite,gabbro, basalt, trachyte, and two granulite-facies metamorphicrocks. Up to eight individual mineral components have been measuredin each sample (no glassy phases were observed), with a detectionlimit of {small tilde}1 wt.%, depending on the mineral assemblage.Marked variations in grain size (i.e., granite vs. trachyte)provide no difficulties for the X-ray method. The X-ray resultscompare very favourably with (1) optical modes determined forthe medium–coarse-grained samples by point counting, (2)normative calculations obtained using locally enhanced catanormand mesonorm software, and (3) corresponding Rietveld modesdetermined, for two samples, from neutron powder data. Wheredifferences occur, these are discussed in relation to the limitationsof each of the methods. The improved accuracy of the X-ray method is due primarily tothe incorporation of the full diffraction profile in the Rietveldanalysis calculations, and the elimination of preferred orientationby collecting the data from samples packed in glass capillaries(i.e., Debye–Scherrer mode). The good agreement of theX-ray and neutron modes shows that the usual problems encounteredwith microabsorption, extinction, and sampling are of littleconcern in these rocks. The results highlight one of the majoradvantages provided by Rietveld modal analysis over the moretraditional ‘reference intensity’ X-ray methods,namely, that the crystal chemistry (and thus the calibrationconstants) of the individual phases can be adjusted dynamicallyduring each individual analysis. This not only provides moreaccurate phase abundances, but also gives important supplementaryinformation about the mineralogy of the major components.     

A Model of Magmatic Crystallization

A computer model simulating fractional crystallization at oneatmosphere pressure incorporates nine broadly-defined minerals—magnetite,olivine, hypersthene, augite, quartz, plagioclase, orthoclase,leucite, and nepheline. The crystallization temperature of eachmineral is considered to be a smooth function of the compositionof the magmatic liquid. These mineral temperature equationsare obtained by multiple linear regression analysis of informationfrom published silicate systems and rock melting experiments.The nine equations are solved for any primary liquid, withinthe broad range of common magma types, to select the crystallizingmineral or minerals. Partition ratios from published experimentsand analyses of lavas and phenocrysts permit calculation ofthe composition of the crystallizing mineral assemblage. Subtractionof a small amount of that composition from the primary liquidyields a new liquid, which may be recycled to yield a sequenceof liquids during fractional crystallization. The crystallizationmodel handles assemblages of co-precipitating minerals, andcan trace progressive saturation in new minerals, substitutionof a new mineral for an old mineral, and cessation of crystallizationof a mineral. The sequences of minerals and liquids derivedfrom a broad set of primary liquids are geologically realistic,so the model is useful in predicting phenocrysts in volcanicrocks and events during crystallization of shallow intrusions.     

A case study of warm air advection over a melting snow surface

When relatively warm, moist air moves over a snow surface, sensible heat and moisture are extracted from its lower layers and used to melt the snow. The depth of the cooled layer depends on horizontal wind speeds and the presence of high vertical wind shear. The mechanism for air mass modification appears to be turbulent mixing.     

Desert vegetation and timing of solar radiation

Timing and amount of solar radiation were examined as factors influencing the distribution of seven perennial plants on a small mountain located in the Chihuahuan Desert. Average direct beam solar radiation fluxes at differing times throughout the day and year were estimated with computer calculations. Principal components analysis was used to reduce the number of solar radiation parameters and include the maximum available information with a manageable number of variables. The remaining solar radiation parameters were compared to plant distributions using redundancy analysis and generalized additive models. Unimodal, bimodal, and monotonic responses were all found depending upon the species and solar radiation parameter. Niche separation at this location depends upon the timing as well as the amount of solar radiation.     

Polarized Radiation in Relativistic Cosmology

A method to solve the general-relativistic equation of radiative transfer for polarized light incorporating elastic COMPTON scattering is discussed. The method is based on an expansion in spin-o and spin-2 spherical harmonics.     

Simulation Study on High Energy Cosmic Electron Detection by Shower Image

Many projects have recently been carried out and proposed for observing high energy electrons since it is realized that cosmic ray electrons are very important when study-ing the dark matter particles and the acceleration mechanism of cosmic rays. An imaging calorimeter,BETS (Balloon-borne Electron Telescope with Scintillator fiber),has been de-veloped for this purpose. Using pattern analysis of the shower development,the electrons can be selected from those primary cosmic ray proton events with flux heights one-tenth that of the electrons. The Monte-Carlo simulation is indispensable for the instrument design,the sig-nal trigger and the data analysis. We present different shower simulation codes and compare the simulation results with the beam test and the flight data of BETS. We conclude that the code FLUKA2002 gives the most consistent results with the experimental data.     

Authigenic iron and titanium oxides in triassic red beds: (St. Bees Sandstone), Cumbria,Northern England

Authigenic iron and titanium oxides occur in three main textural varieties in the St. Bees Sandstone, a Triassic red bed succession in Cumbria. These are: (a) overgrowths of haematite, titaniferous haematite, anatase, and rutile which generally occur on detrital host grains of similar compositions. The overgrowths may occur as syntaxial rim cements or rhombohedral and prismatic projections and are always in optical continuity, (b) discrete crystals of anatase (including octahedrite) and haematite 10-40 μm in size occur in pore spaces, and (c) fine grained ( < 1 μm) pigmentary haematite occurs as grain coatings around detrital grains and in the interstitial matrix. The euhedral nature and pore-filling habit clearly indicate the authigenic origin of these iron- and titanium oxides. All three textural varieties are believed to have been precipitated from ground waters containing dissolved ferrous and titanium ions. These ions were derived from the intrastratal solution of detrital iron and titanium bearing grains including ferromagnesian silicates and iron-titanium oxides. The precipitation of iron oxides from migrating ground waters in the manner described here goes some way to explaining how thick, uniformly red successions can be formed.     

On the eigenvalues of kinematic α-effect dynamos

The kinematic α-effect dynamo problem is investigated in the case of an exterior perfect conductor. It is shown that certain approximate symmetries discovered in the numerical analysis of ROBERTS (1972) are exact for this case. As an illustration, an exact solution is given in a cylindrical geometry, where the equations can be written in terms of one variable. The implications for the earth's dynamo are discussed.