Polar constituents isolated from Green River oil shale

This paper interprets the mass spectrometric, i.r. absorption and NMR data for 22 compounds obtained from a polar fraction of Green River shale. The major constituents analyzed are believed to be of the following compositional types: C_nH_2nO (cyclohexanols and chain isoprenoid ketones), C_nH_2n?10O (tetralones and indanones), C_nH_2n?7N (tetrahydroquinolines), C_nH_2n?11N (quinolines), C_nH_2n?1NO (alkoxypyrrolines), C_nH_2n?5NO₂ (maleimides), C_nH_2n?8 (tetralins), C_nH_2n?12 (naphthalenes) and C_nH_2n?14 (benzylbenzenes). This work expands the present information about nitrogen, oxygen and aromatic constituents indigenous to Green River shale.     

External seismic stability of vertical geosynthetic-reinforced soil walls using pseudo-static method

Analysis of external stability of vertical geosynthetic-reinforced soil (GRS) walls is very important in the seismic prone zone. The scope of this paper is to obtain required minimum reinforcement length, L _min, for external seismic stability of vertical GRS walls by pseudo-static limit equilibrium method. Then, L _min can be calculated to resist sliding, eccentricity, and bearing capacity failure modes. The parameters considered include both horizontal and vertical seismic coefficients (k _h and k _v ), surcharge load (q), wall height (H) and the properties of retained backfill, GRS, and foundation soil. Results show that L _min against sliding failure mode, L _min,S , increases more quickly than that against the other two failure modes with the increase in k _h , q, or unit weight of retained backfill, γ _b , while L _min,S decreases more quickly than that against the other two failure modes with increase in friction angle of retained backfill, ? _b , or unit weight of GRS, γ _r . For the different failure modes, the effect of k _v on L _min is not identical with the change of k _h , and in addition, L _min/H will tend to remain unchanged with the increase in H. In general, L _min against bearing capacity failure mode, L _min,BC, is larger than L _min against the other two failure modes. However, L _min,BC will be less than L _min against eccentricity failure mode, L _min,E , for k _h exceeding 0.35, or friction angle of foundation soil, ? _f , exceeding 37°, and L _min,BC will also be less than L _min,S for friction angle of GRS, ? _r , being no more than 26°.     

The effective stochastization time in stellar systems

Stochastization in stellar systems is analyzed in the framework of the paradigm of Krylov and Gurzadyan-Savvidi. The use of a Holtsmark distribution for the random forces with a Rastorguev-Sementsov cutoff confirms that τ _e /τ _c ∝ N ^1/5, where τ _c is the crossing time, τ _e is the effective stochastization time, and N is the number of stars. More oblate systems evolve more rapidly, and rotation slows stochastization. The need for a cutoff does not arise if a Petrovskaya distribution is adopted for the random forces (although applying a cutoff does not change the results). In this case, τ _e /τ _c varies with N approximately as N ^0.3. It is found theoretically that τ _e /τ _c ∝ N ^1/3/(lnN)^1/2 for large N. Thus, the evolutionary scale found is close to that proposed earlier by Genkin.     

Stratigraphy and palaeoenvironment of the Lower-“middle” Oligocene units in the northern part of the Western Taurides (İncesu area,Isparta, Turkey)

This study describes the stratigraphic and palaeoenvironmental significance of the Lower-“middle” Oligocene sediments based on the fauna from the Delikarkas? Formation and the microflora from the ?ncesu Formation of the ?ncesu area (northern part of the western Taurides, Isparta province, Turkey). In the area, the Oligocene sediments show a regressive succession, which begins with the limestones of the Delikarkas? Formation indicating marine conditions followed by conglomerates, sandstones and coaly mudstones of alluvial and fluvial (shallow marine-continental) origin. A well preserved foraminiferal assemblage including Nummulites intermedius, Nummulites vascus and Halkyardia maxima proves an Early Oligocene age for the Delikarkas? Formation. Due to palynological markers such as Boehlensipollis hohli, Slowakipollis hippophaëoides, Dicolpopollis kockelii, Magnolipollis neogenicus ssp. minor, Plicapollis pseudoexcelsus, Caryapollenites simplex and Intratriporopollenites instructus the ?ncesu Formation, which concordantly rests on the Delikarkas? Formation, may be assigned to the Early-“middle” Oligocene. From the palynomorph assemblage, three zones have been recognised according to abundance of species. Zone 1 is characterized by predominance of C. simplex and Momipites punctatus and rarely presence of tricolpate and tricolporate pollen. Zone 2 consists mainly of Inaperturopollenites dubius, Leiotriletes maxoides ssp. maximus, Verrucatosporites favus, Verrucatosporites alienus and infrequently marine dinoflagellate cysts. Zone 3 is characterized by a high percentage of ferns such as Echinatisporis?chattensis and Polypodiaceoisporites saxonicus. The presence of marine dinoflagellate cysts like Apectodinium sp. and Cleistosphaeridium sp., back-mangrove elements such as Acrostichum aureum and lepidocaryoid palms (e.g. Longapertites discordis, Longapertites punctatus and Longapertites psilatus) in the sediments of the ?ncesu Formation imply coastal or near-coastal conditions. Terrestrial palynomorphs in more inland settings were transported by running water towards the sea. Conifers are represented by poorly preserved and rare pollen grains of Pityosporites, Cathayapollis and Piceapollis which may have been transported by wind. In this study, the terrestrial climate of the ?ncesu Formation is also discussed on the basis of the Coexistence Approach method. The climate was warm at the coast (over 20 °C), as evidenced by A. aureum and lepidocaryoid palms, whereas there was a mean annual temperature of 17.2–17.4 °C must be assumed for the upland environment(s).     

Empirical models relating viscosity and tracer diffusion in magmatic silicate melts

The Adam-Gibbs equations describing relaxation in silicate melts are applied to diffusion of trace components of multicomponent liquids. The Adam-Gibbs theory is used as a starting point to derive an explicit relation between viscosity and diffusion including non-Arrhenian temperature dependence. The general form of the equation is D_iη = A_iexp{Δ(s_cE_i)/TS_c}, where D is diffusivity, η is melt viscosity, T is absolute temperature, Δ(s_cE_i) is the difference between the products of activation energies and local configurational entropies for viscous and diffusive relaxation, A_i is a constant that depends on the characteristics of the diffusing solute particles, and S_c is configurational entropy of the melt. The general equation will be impractical for most predictive purposes due to the paucity of configurational entropy data for silicate melts. Under most magmatic conditions the proposed non-Arrhenian behaviour can be neglected, allowing the general equation to be simplified to a generalized form of the Eyring equation to describe diffusion of solutes that interact weakly with the melt structure: D_iη/T = Q_iexp{ΔE_i/RT}, where Q_i and ΔE_i depend on the characteristics of the solute and the melt structure. If the diffusing solute interacts strongly with the melt structure or is a network-forming cation itself, then ΔE_i = 0, and the relation between viscosity and diffusion has the functional form of the classic Eyring and Stokes-Einstein equations; D_iη/T = Q_i. If the diffusing solute can make diffusive jumps without requiring cooperative rearrangement of the melt structure, the diffusivity is entirely decoupled from melt viscosity and should be Arrhenian, i.e., D_i = Q_iexp{B_i/T}. A dataset of 594 published diffusivities in melts ranging from the system CAS through diopside, basalt, andesite, anhydrous rhyolite, hydrous rhyolite, and peralkaline rhyolite to albite, orthoclase, and jadeite is compared with the model equations. Alkali diffusion is completely decoupled from melt viscosity but is related to melt structure. Network-modifying cations with field strength Z_i²/r between 1 and 10 interact weakly with the melt network and can be modelled with the extended form of the Eyring equation. Diffusivities of cations with high field strength have activation energies essentially equal to that of viscous flow and can be modelled with a simple reciprocal Eyring-type dependence on viscosity. The values of Q_i, ΔE_i and B_i for each cation are different and can be related to the cation charge and radius as well as the composition of the melt through the parameters Z_i²/r, M/O, and Al/(Na + K + H). I present empirical fit parameters to the model equations that permit prediction of cation diffusivities given only charge and radius of the cation and temperature, composition and viscosity of the melt, for the entire range of temperatures accessible to magmas near to or above their liquidus, for magmas ranging in composition from basalt through andesite to hydrous or anhydrous rhyolite. Pressure effects are implicitly accounted for by corrections to melt viscosity. Ninety percent of diffusivities predicted by the models are within 0.6 log units of the measured values.     

Heat capacity and thermodynamic properties of andradite garnet,Ca3Fe2Si3O12, between 10 and 1000 K and revised values for ΔfGom (298.15 K) of hedenbergite and wollastonite

The heat capacity of synthetic andradite garnet (Ca₃Fe₂Si₃O₁₂) was measured between 9.6 and 365.5 K by cryogenic adiabatic calorimetry and from 340 to 990 K by differential scanning calorimetry. At 298.15 K C^o_p,m and S^o_m are 351.9 ± 0.7 and 316.4 ± 2.0 J/(mol·K), respectively.Andradite has a λ-peak in C^o_p,m with a maximum at 11.7 ± 0.2 K which is presumably associated with the antiferromagnetic ordering of the magnetic moments of the Fe³⁺ ions. The Gibbs free energy of formation, Δ_fG^o_m (298.15 K) of andradite is −5414.8 ± 5.5 kJ/mol and was obtained by combining our entropy and heat capacity data with the known breakdown of andradite to pseudowollastonite and hematite at ≈ 1410 to 1438 K. From a reexamination of the calcite + quartz = wollastonite equilibrium data we obtained Δ_fH^o_m (298.15 K) = − 1634.5 ± 1.8 kJ/mol for wollastonite.Between 300 and 1000 K the molar heat capacity of andradite can be represented by the equation C^o_p,m = 809.24 - 7.025 × 10−2T− 7.403 × 10³T−0.5 − 6.789 × 10⁵T−2. We have also used our thermochemical data for andradite to estimate the Gibbs free energy of formation of hedenbergite (CaFeSi₂O₆) for which we obtained Δ_fG^o_m (298.15 K) = −2674.3 ± 5.8 kJ/mol.     

Iron metal production in silicate melts through the direct reduction of Fe(II) by Ti(III), Cr(II), and Eu(II)

The production of metallic iron in silicate melts by the chemical reactions, 2Ti³⁺_(melt) + Fe²⁺_(melt) → 2Ti⁴⁺_(melt) + Fe⁰_(crystal)2Cr²⁺_(melt) + Fe²⁺_(melt) → 2Cr³⁺_(melt) + Fe⁰_(crystal)2Eu²⁺_(melt)+ Fe²⁺_(melt) → 2Eu³⁺_(melt) + Fe⁰_(crystal) has been demonstrated under experimental conditions in a simplified basaltic liquid, Such reactions may occur in lunar basalts and other reduced systems, and, thus, may aid in the understanding of the reduced nature of lunar basalts. The reactions were studied in a glass-forming Na-Ca-Mg-Al-silicate composition at a melt temperature of 1250°C and an imposed oxygen fugacity at the C/CO buffer (1 atm total pressure). Microtitrations of individually-doped samples were used in the quantitative assessment of their redox ratios and for the calibration of visible and near-infrared spectral absorptions. These spectral absorptions were then applied to the evaluation of the mutual redox interactions in dual-doped samples.     

Dielectric constants of apatite,epidote, vesuvianite,and zoisite,and the oxide additivity rule

The dielectric constants and dielectric loss values of 4 Ca-containing minerals were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: vesuvianitel κ′ _a=9.93 tan δ=0.006 κ′ _c=9.79 tan δ=0.005 vesuvianitel κ′ _a=10.02 tan δ=0.002 κ′ _c=9.85 tan δ=0.003 zoisite1 κ′ _a =10.49 tan δ=0.0006 κ′ _b =15.31 tan δ=0.0008 κ′ _c=9.51 tan δ=0.0008 zoisite2 κ′ _a =10.55 tan δ=0.0011 κ′ _b =15.45 tan δ=0.0013 κ′ _c=9.39 tan δ=0.0008 epidote κ′ ₁₁= 9.52 tan δ=0.0008 κ′ ₂₂=17.1 tan δ=0.0009 κ′ ₃₃= 9.37 tan δ=0.0006 fluorapatite1 κ′ _a =10.48 tan δ=0.0008 κ′ _c = 8.72 tan δ=0.0114 fluorapatite2 κ′ _a =10.40 tan δ=0.0010 κ′ _c=8.26 tan δ=0.0178 The deviation (δ) between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α _D (mineral)=∑ α _D (oxides) for vesuvianite is ～ 0.5%. The large deviations of epidote and zoisite from the additivity rule with Δ=+ 10.1 and + 11.7%, respectively, are attributed to “rattling” Ca ions. The combined effects of both a large F thermal parameter and possible F-ion conductivity in fluorapatite are believed to be responsible for Δ=+2–3%. Although variation of oxygen polarizability with oxygen molar volume (V_o) is believed to affect the total polarizabilities, the variation of V_o in these Ca minerals is too small to observe the effect.     

Hydrogen isotope fractionation between OH-bearing minerals and water

Hydrogen isotope fractionation factors between hydroxyl-bearing minerals and water were determined at temperatures ranging between 400 and 850°C. The hydrogen isotope exchange rates for the mineral-water pairs examined were very slow. In most cases it was necessary to use an interpolation method for the determination of the hydrogen isotope equilibrium fractionation factor, α_e.For the temperature range of 450–850°C the hydrogen isotope fractionation factors for the mica-water and amphibole-water systems are simply expressed as a function of temperature and the molar fractions of the six-fold coordinated cations in the crystal, regardless of mineral species, as follows: 10³ In α_{e(mineral-water)} = ? 22.4 (10⁶T^?2) + 28.2 + (2X_Al ? 4X_Mg ? 68X_Fe), where X is the molar fraction of the cations. As the equation indicates, for any specific composition of the OH-bearing minerals, the change of α_e with temperature, over the temperature range investigated, is the same for all minerals studied. Thus for any specified values of X_Al, X_Mg, and X_Fe for these minerals, the relationship between α_e and T is 10³ In α_e = αT^?2 + k. Consequently, hydrogen isotope fractionation among coexisting minerals is temperature independent and cannot be used as a hydrogen isotope geothermometer.Some exceptions to the above general observations exist for minerals such as boehmite and kaolinite. In these minerals hydrogen bonding modifies the equilibrium hydrogen isotopic fractionation between mineral and water.     

Scaling properties of corner frequencies of Kamchatka earthquakes

Scaling properties of earthquake populations bear the major information on the physics of the source process of an earthquake. To determine scaling properties, source spectra of more than 400 earthquakes of Kamchatka were determined in a frequency range 0.1–30 Hz using materials of digital registration of PET station, and characteristic frequencies of earthquakes were estimated. The range of magnitudes is 4–6.5, the range of distances is 80–220 km. To enable reduction of a spectrum to the source, attenuation properties of the medium around PET were determined beforehand. It is revealed that source spectra show several corner (characteristic) frequencies: f _c1, f _c2 and f _c3; where the spectral trend changes: from f ⁰ to f ^?1, from f ^?1 to f ^?2, and from f ^?2 to f ^?3, respectively. Although in some cases f _c1 ≈ f _c2 in agreement with the usual ω^?2 spectral model, the main part of spectra has more complicated character. For a large part of the studied earthquakes a source-controlled upper cutoff of acceleration spectrum, or corner frequency f _c3, is observed. This is an important fact, as the existence of f _c3 (source-controlled f _max) is not recognized in the bulk of the seismological literature. For f _c1, the observed scaling agrees with the usual hypothesis of similarity of the earthquake sources of different size (magnitude); it is close to f _c1 ～ M ₀ ^?1/3 , where M ₀ is seismic moment. For f _c2, scaling is close to f _c2 ～ M ₀ ^?0.17 ～ f _c1 ^0.5 , that indicates an expressed violation of similarity. For f _c3, scaling is close to f _c2 ～ M ₀ ^?0.08 ～ f _c1 ^0.25 , so that similarity is broken even sharper in this case. Hypotheses about possible causes of the observed scaling are discussed.     

Contribution to the biostratigraphy of the Lower Cretaceous in eastern Serbia: Upper Hauterivian Orbitolinidae from the Kamenica 1 section,Kurilovo anticline

Upper Hauterivian deposits in the Kurilovo area, Kamenica 1 section, NE of Niš, are described based of abundant and diverse orbitolinids. So far, the interval was assigned to the Barremian–Aptian on the geological map. Such a new age assignment results from the first detailed study carried out on the orbitolinid fauna contained in the Lower Cretaceous (upper Hauterivian) shallow-water limestones of eastern Serbia. The upper Hauterivian is documented on the basis of two key stratigraphic markers, specifically Valserina primitiva and Paleodictyoconus beckerae.In addition to these late Hauterivian index fossils, the studied section bears orbitolinids having a larger stratigraphic distribution: Cribellopsis neoelongata, Cribellopsis thieuloyi?, Montseciella glanensis, Orbitolinopsis debelmasi, Orbitolinopsis cf. debelmasi, Orbitolinopsis sp., Paleodictyoconus cuvillieri, Paleodictyoconus cf. cuvillieri, Paleodictyoconus cf. beckerae, Paleodictyoconus cf. actinostoma, Paleodictyoconus sp., Paracoskinolina? jourdanensis, Paracoskinolina cf. hispanica, Urgonina alpillensis, Valserina sp. The microfossil assemblage includes other foraminifers such as Charentia cuvillieri, Mayncina bulgarica, Nautiloculina cretacea, Pfenderina globosa, Pseudocyclammina cf. lituus, Pseudolituonella gavonensis, Ammobaculites sp., Bolivinopsis sp., abundant trocholinids, various miliolids, other foraminifers and sparse algae which will be presented separately.     

The electronic structure and absorption spectrum of MnO 6 9− octahedra in manganian andalusite

The energy levels of MnO ₆ ^9? clusters, with D _4h approximated and C _2v actual symmetry of the M ₁ site of Mn³⁺-bearing andalusite, are calculated using the multiple scattering method. The energies of the electronic d-d transition of Mn³⁺ in the clusters with D _4h symmetry are calculated to be 6,000–7,000 cm^?1 (⁵ B _1g → ⁵ A _1g ), ～18,000 cm^?1 (⁵ B _1g → ⁵ B _2g ) and ～19,000 cm^?1 (⁵ B _1g → ⁵ E _g ). Apart from a splitting of the ⁵ E _g -level into two levels separated by 300–350 cm^?1, no significant changes of these transition energies are noted for the corresponding cluster with C _2v symmetry. The calculated transition energies give a good fit to the structure of the optical absorption spectra of Mn³⁺-bearing andalusites and support recent assignments of the major absorption bands observed in these spectra.     

Are S–C structures,duplexes and conjugate shear zones different manifestations of the same scale-invariant phenomenon?

By measuring S spacing, C spacing and the S–C angle (α) in deformed rocks, this paper investigates the geometry of previously published examples of S–C and S–C-like structures on a scale range between micrometres and several hundred kilometres. The results indicate that common S–C fabrics of thin-section, hand-specimen and outcrop scale, and conjugate fault/mylonite zones of map scale define a simple function C_spacing=2S_spacing, which depicts a scale-invariant geometry over ten orders of magnitude. Logarithmic plots of cumulative frequency suggest that the S–C fractal set (D=0.13) is restricted to the scale range between 600–800 μm and 1 km where genuine S–C structures, characterized by antithetic shear on the S planes, can be formed. Below 600–800 μm, grain scale processes seem to influence the development of S–C structures. Above the upper limit (1 km), only S–C-like structures with duplex kinematics (synthetic shear on S planes) occur. The S–C and S–C–C′ fractals are envisaged as self-similar structures where the foliations work as both S or C planes, depending on which scale is considered.     

The distribution of Fe and Mg between olivine and lunar basaltic liquids

We have examined the Fe and Mg distribution between coexisting olivine and lunar basaltic liquids produced by equilibrium partial melting of natural lunar samples. In agreement with the findings of Roeder and Emslie (Contrib. Mineral. Petrol. 29, 275–289) on terrestrial compositions, the logarithms of the conventional distribution coefficients, K_ol-L^Fe and K_ol-L^Fe-Mg, are nearly linear functions of inverse temperature; and the exchange coefficient, K_D = K_ol-L^Fe-Mg, is nearly independent of temperature and composition within a given magma group. There are, however, small but significant differences in conventional and exchange distribution coefficients from one magma group to another, e.g. low-Ti vs high-Ti lunar basalts. It is possible to achieve slightly greater precision for the inverse temperature functions by including terms approximating silica activity in the conventional distribution coefficients. The term ($\text{2Si}\text{O}\text{)}{}_{\mathrm{L}}$ is apparently the best simple approximation for silica activity in olivine-saturated liquids based upon data for Fe, Mg, Mn, Ca, Ti and Cr. Pressure has noticeable effects upon Fe and Mg distribution between olivine and liquid only above 5 kbar.The excellent linear correlation of the logarithms of the distribution coefficients with inverse temperature allows calculation of approximate values of $\text{Δ}\text{H}\text{?}{}^0$ for the reactions : 2MgO_L + SiO_2LaiMg₂SiO_4ol and 2FeO_L + SiO_2LaiFe₂SiO_4ol. Values obtained, approx ?26 kcal/mole, are comparable with values of the heats of fusion of forsterite and fayalite calculated by Bradley (Am. J. Sci.260, 550–554) and measured by Orr (J. Am. Chem. Soc. 75, 528–529).The exchange distribution coefficient for Fe and Mg, K_D, is sensitive to large changes in liquid chemistry. Although K_D is explicitly independent of silica activity, K_D apparently changes with silica concentration. This change is a reflection of changes in the mixing properties of Fe and Mg in liquids with different chemistry and hence structure. Regular solution theory predicts that as the mixing properties of an element in a solution change, the most radical changes in activity coefficients occur in the range of dilute concentrations. Therefore, the distribution coefficients for trace elements will also be dependent upon large changes in liquid chemistry, even if corrections for silica and other liquid component activities are applied.     

The relationship of elasticity and crystal structure in andalusite and sillimanite

The nine elastic constants of andalusite and sillimanite have been determined, using the technique of Brillouin scattering. They are, in megabars, for andalusite: c ₁₁=2.334, c ₂₂=2.890, c ₃₃=3.801, c ₄₄=0.995, c ₅₅=0.878, c ₆₆=1.123, c ₂₃=0.977, c ₁₃=1.162, c ₁₂=0.814; for sillimanite: c ₁₁=2.873, c ₂₂=2.319, c ₃₃=3.884, c ₄₄=1.224, c ₅₅=0.807, c ₆₆=0.893, c ₂₃=1.586, c ₁₃=0.834, c ₁₂=0.947. Both structures are characterized by chains of edge-linked coordination octahedra extending parallel to the crystallographic c direction, cross-linked by polyhedra of lower coordination. In each structure the stiffness measured parallel to c is greater than that measured normal to c. The shear moduli can be directly correlated with the relative rigidity of the cross-linking structures.     

Partitioning of Ru, Rh, Pd, Re, Ir, and Au between Cr-bearing spinel, olivine, pyroxene and silicate melts

A series of high temperature experiments was undertaken to study partitioning of several highly siderophile elements (HSE; Ru, Rh, Pd, Re, Os, Ir, Pt and Au) between Cr-rich spinel, olivine, pyroxene and silicate melt. Runs were carried out on a Hawaiian ankaramite, a synthetic eucrite basalt, and a DiAn eutectic melt, at one bar, 19 kbar, and 20 kbar, respectively, in the temperature range of 1200 to 1300°C, at oxygen fugacities between the nickel-nickel oxide (NNO) and hematite-magnetite (HM) oxygen buffers. High oxygen fugacities were used to suppress the formation of HSE-rich “nuggets” in the silicate melts. The resulting oxide and silicate crystals (<100 μm) were analyzed using both SIMS and LA-ICP-MS, with a spatial resolution of 15 to 50 μm. Rhenium, Au and Pd were all found to be incompatible in Cr-rich spinel (D_Re^sp/melt = 0.0012-0.21, D_Au^sp/melt = 0.076, D_Pd^sp/melt = 0.14), whereas Rh, Ru and Ir were all found to be highly compatible (D_Rh^sp/melt = 41-530, D_Ru^sp/melt = 76-1143, D_Ir^sp/melt = 5-22000). Rhenium, Pd, Au and Ru were all found to be incompatible in olivine (D_Re^oliv/melt = 0.017-0.073, D_Pd^oliv/melt = 0.12, D_Au^oliv/melt = 0.12, D_Ru^oliv/melt = 0.23), Re is incompatible in orthopyroxene and clinopyroxene (D_Re^opx/melt = 0.013, D_Re^cpx/melt = 0.18-0.21), and Pt is compatible in clinopyroxene (D_Pt^cpx/melt = 1.5). The results are compared to and combined with previous work on HSE partitioning among spinel-structured oxides, and applied to some natural magmatic suites to demonstrate consistency.     

Magnetic interactions possessing point group symmetry and their application to ruby

By utilizing the magnetic interactions possessingC _3v symmetry, the author has deduced the general expressions for theg-factors, zero-field splitting and effective magnetic moment of the ground singlet orbital state in d³-complex. For ruby (Al₂O₃: Cr³⁺) the results are in good agreement with experiments: theoretical values:g _‖ =1.9835;g _⊥=1.9876; 2D=?0.3731 cm^?1;μ _‖ =3.857β;μ _⊥=3.861β; experimental values:g _‖ =1.9840±0.006,g _⊥=1.9867±0.0006, 2D=?0.3831±0.0002 cm^?1,μ=3.8?3.9β.     

Polarized electronic absorption spectra of 3d3-configurated tetravalent manganese in octahedral fields of Mn(SeO3)2

Polarized optical absorption spectra of Mn(IV) in octahedral crystal fields of Mn(SeO₃)₂ have been studied by means of microscope-spectrometry in the range 40000-4000 cm^?1 and at temperatures between 113 K and 293 K. Intense charge-transfer absorptions (linear absorption coefficient α ? 30000 cm^?1) completely mask the d-d transitions in the UV and VIS region above ≈23000 cm^?1. The optical electronegativity χ _opt of Mn(IV) in Mn(SeO₃)₂ is estimated to be 2.7. In accordance with the d ₃ configuration of tetravalent manganese three d-d bands observed at ambient temperatures at 13250, 14137 (α≈50 cm^?1) and ≈18500 cm^?1 (α≈500–800 cm^?1) are assigned to the spin forbidden ⁴ A _2g →² E _g and ⁴ A _2g →² T _1g transitions as well as to the first spin allowed ⁴ A _2g →⁴ T ^2g transition, respectively. These assignments allow the calculation of the following ligand field parameters: Dq ≈ 1850 cm^?1, B ₅₅ = 869 cm^?1 (β ₅₅ = 0.82), and C = 2346 cm^?1 (293 K).     

Stretch in shear zones: implications for section balancing

The stretch, S, of a line in a zone of general shear deformation is given by S = Wsinθ /sinθ', where the shear zone's final to initial width ratio is W and the line's inclination to the zone boundary is θ before deformation and θ' after. For the special cases of simple shear and pure shear, S = sinθ / sinθ', and S² = sin 2θ / sin 2θ', respectively. Fisher's and Sorby's formulae may be combined in a form appropriate to general shear strain, γ = cotθ' - Rcotθ, where R is the axial ratio of the irrotational component of deformation and γ is the shear strain; for simple shear and pure shear the equation reduces to γ = cotθ' - cotθ, and tanθ = Rtanθ, respectively. These relationships may be used to estimate strain in exposed faulted strata, or to restrict the possible geometries of inferred fault ramps in balanced geological cross-sections.