A finite temperature chandrasekhar model: Determining the parameters and calculation of the characteristics of degenerate dwarfs

We suggest a generalization of the standard Chandrasekhar model for degenerate dwarfs. We apply an equation of state for a degenerate ideal electron gas in the form of a Sommerfeld expansion in the parameter k _B T(r)/m ₀ c ². The radial temperature distribution T(r) is modeled taking into account the presence of the isothermal core. The model has four dimensionless parameters, two microscopic (the relativistic parameter at the stellar center x ₀ and the chemical-composition parameter ?? _e = A/Z) and two macroscopic (the dimensionless temperature T ₀ ^* = k _B T _c /m ₀ c ² and dimensionless radius ?? ₀ = R _c /R of the core, where R _c and R are the radii of the core and dwarf). We found x ₀, ?? _e , and T ₀ ^* for about 3000 DA white dwarfs, based on their masses, radii, and effective temperatures from the Sloan Digital Sky Survey Data Release 4; ?? ₀ was treated as a free parameter. The influence of temperature effects on the macroscopic characteristics is analyzed, in particular, the minimum mass and maximum radii of the stars. Based on our computed energy-radius dependence, we suggest an interpretation of the observed radius distribution for these dwarfs.     

Direct Sequential Co-simulation with Joint Probability Distributions

The practice of stochastic simulation for different environmental and earth sciences applications creates new theoretical problems that motivate the improvement of existing algorithms. In this context, we present the implementation of a new version of the direct sequential co-simulation (Co-DSS) algorithm. This new approach, titled Co-DSS with joint probability distributions, intends to solve the problem of mismatch between co-simulation results and experimental data, i.e. when the final biplot of simulated values does not respect the experimental relation known for the original data values. This situation occurs mostly in the beginning of the simulation process. To solve this issue, the new co-simulation algorithm, applied to a pair of covariates Z ₁(x) and Z ₂(x), proposes to resample Z ₂(x) from the joint distribution F(z ₁,z ₂) or, more precisely, from the conditional distribution of Z ₂(x ₀), at a location x ₀, given the previously simulated value z₁^(l)(x₀)z_{1}^{(l)}(x_{0}) (F(Z₂|Z₁=z₁^(l)(x₀)F(Z_{2}|Z_{1}=z_{1}^{(l)}(x_{0}) ). The work developed demonstrates that Co-DSS with joint probability distributions reproduces the experimental bivariate cdf and, consequently, the conditional distributions, even when the correlation coefficient between the covariates is low.     

天然Ⅱ型CaCO3矿物的发现

本文报道了天然Ⅱ型CaCO₃ 矿物。该矿物发现于海洋表层沉积物,成分与方解石、文石及六方球方解石相同,但结构完全不同,它们共同组成了天然CaCO₃ 的同质多象变体。天然Ⅱ型CaCO₃ 矿物的空间群为P21/c,单位轴长为a₀= 0.6290±0.0002 nm,b₀= 0.4934±0.0002 nm,c₀= 0.7979±0.0003nm,β= 107.571°±0.002°,Z= 4,单胞体积为0.23605±0.1749nm³;理论密度为2.82 g/cm³,实测值为2.76 g/cm³;实测硬度H= 4.天然Ⅱ型CaCO₃ 矿物是在深水环境中较高静水压力下形成的珊瑚体生物矿物。     

A statistical-mechanics model of ordering in aluminosilicate solid solutions

A statistical-thermodynamic approximation for order-disorder phase transitions in aluminosilicate solid solutions is presented. The approximation involves estimating the number of configurations with long range order parameter Q and short range order parameter σ, using an approximation to the probability that a configuration with the correct amount of long range order will also have the correct amount of short range order. This estimate is then used to give a free energy F(Q, σ, x, T), where x is the concentration of Al in the structure, and hence quantities such as T _c (x) are estimated. The predictions of the model for T _c (x) and the critical concentration x _c at which T _c falls to zero are shown to be in good agreement with the results of Monte Carlo simulations. Received: 14 May 1997 / Revised, accepted: 2 June 1997     

非等轴颗粒付林图解

非等轴颗粒付林图解由直线a=1、b=1、a=b和曲线a2b=1、ab2=1分割成10个微区,并对应于不同的e_x、e_y、e_z组合和应变类型。这些直线和曲线分别对应于特殊的e_x、e_y、e_z组合和岩石应变类型。岩石的应变类型有18种。函数a.b的表征方程有4种类型,并分别表征直线a=1/k₁和b=1/k₂所分割的4个区间。a,b表征方程的确定取决于岩石总的变形行为。此图解可用于非等轴颗粒标志体应变测量和应变类型的确定和图示,文章给出了应用实例.      

Hot degenerate dwarfs in a two-phase model

The characteristics of degenerate dwarfs-core radius, mass, and energy, thickness of their outer layers-are calculated based on a mechanical-equilibrium equation in a five-parameter, two-phase compositemodel with an isothermal core and a non-degenerate outer region. An accurate equation of state for the partially degenerate, ideal, relativistic electron gas of the core is used together with a polytropic approximation for the outer layers. The model parameters are determined using the known masses, radii, and luminosities of observed DA white dwarfs. A region where dwarfs can exist is identified in a plot of core temperature vs. the relativity parameter at the center of the star, and the dependence of the core temperature on the effective temperature of the photosphere is constructed.     

A thermodynamic model of Fe–Cr spinels

A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe₃O₄–FeCr₂O₄ spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe_1-x²⁺ Fe_x³⁺)[Fe_x²⁺Fe_2-2y-x³⁺Cr_2y]O₄, and their thermodynamic properties depend strongly on Fe²⁺–Cr³⁺ cation mixing. Mixing of Fe²⁺–Fe³⁺ and Fe³⁺–Cr³⁺ can be accepted as ideal. If Fe²⁺, Fe³⁺ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is –RT ln(x²/((1–x)(2–2y–x)))= G₁₃^* + (1–2x)W₁₃+y(W₁₄–W₁₃–W₃₄) where G₁₃^* is the difference between the Gibbs energy of inverse and normal magnetite, W_ij is a Margules parameter of cation mixing and G₁₃^*, J/mol =–23,000+13.4 T, W₁₄=36 kJ/mol, W₁₃=W₃₄=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe₃O₄–FeCr₂O₄ spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.     

Interatomic potentials for CaCO3 polymorphs (calcite and aragonite), fitted to elastic and vibrational data

Calcite and aragonite have been modeled using rigid-ion, two-body Born-type potentials, supplemented by O-C-O angular terms inside the CO₃ groups. A shell model has also been developed for calcite. Atomic charges, repulsive parameters and force constants have been optimized to reproduce the equilibrium crystal structures, the elastic constants and the Raman and infrared vibrational frequencies. The rigid-ion potential RIM (atomic charges:z _O= -0.995e,z _C = 0.985e,z _Ca = 2.0e) fitted to calcite properties is able to account for those of aragonite as well. Experimental unit-cell edges, elastic constants, internal and lattice frequencies are reproduced with average relative errors of 2.1, 5.5, 2.4, 15.1% for calcite and of 0.2, 19.4, 2.5, 11.8% for aragonite, respectively. The RIM potential is suitable for thermodynamic and phase diagram simulations in the CaCO₃ system, and is discussed and compared to other potentials.     

Britvinite, Pb15Mg9(Si10O28)(BO3)4(CO3)2(OH)12O2, a new mineral species from Långban, Sweden

Britvinite, a new mineral species, has been found in manganese ore at the Långban deposit, Bergslagen ore district, Filipstad, Värmland County, Sweden. Calcite, barytocalcite, brucite, cerussite, and hausmannite are associated minerals. Britvinite occurs as pale yellow to colorless transparent plates with a white streak up to 0.2 × 0.5 × 0.5 mm in size, which are flat parallel to {001}; the luster is adamantine. Thin lamellae are flexible, whereas thick ones are brittle; the Mohs hardness is 3. The cleavage is eminent parallel to {001}. The calculated density is 5.51 g/cm³. In the infrared spectrum of the new mineral, the bands of (OH)?, (CO₃)^2?, and (BO₃)^3? are recorded, whereas those corresponding to water molecules are absent. Britvinite is optically biaxial and negative, α = 1.896(2), β = 1.903(2), γ = 1.903(2), 2Vmeas = 20(10), Z≈c. Dispersion is strong, r<v. The chemical composition (electron microprobe; H₂O determined with the Alimarin method, CO₂, with selective sorption) is (wt %) 7.95 MgO, 71.92 PbO, 0.41 Al₂O₃, 12.77 SiO₂, 2.2 H₂O, 2.1 CO₂, 2.67 B₂O₃ (calculated on the basis of structural data); total 100.02. The empirical formula calculated on the basis of 59 anions (O + OH) (Z = 1) is as follows: Pb_14.75Mg_9.03Si_9.73Al_0.37O_30.76(BO₃)_3.51(CO₃)_2.18(OH)_11.7. The simplified formula (Z = 2) is Pb_{7 + x} Mg_4.5(Si₅O₁₄)(BO₃)₂(CO₃)(OH,O)₇ (x < 0.5). The crystal structure of britvinite has been studied on a single crystal at 173 K; R = 0.0547. The new mineral is triclinic, space group P $ \bar 1 Britvinite, a new mineral species, has been found in manganese ore at the L?ngban deposit, Bergslagen ore district, Filipstad, V?rmland County, Sweden. Calcite, barytocalcite, brucite, cerussite, and hausmannite are associated minerals. Britvinite occurs as pale yellow to colorless transparent plates with a white streak up to 0.2 × 0.5 × 0.5 mm in size, which are flat parallel to {001}; the luster is adamantine. Thin lamellae are flexible, whereas thick ones are brittle; the Mohs hardness is 3. The cleavage is eminent parallel to {001}. The calculated density is 5.51 g/cm³. In the infrared spectrum of the new mineral, the bands of (OH)−, (CO₃)²⁻, and (BO₃)³⁻ are recorded, whereas those corresponding to water molecules are absent. Britvinite is optically biaxial and negative, α = 1.896(2), β = 1.903(2), γ = 1.903(2), 2Vmeas = 20(10), Z≈c. Dispersion is strong, r<v. The chemical composition (electron microprobe; H₂O determined with the Alimarin method, CO₂, with selective sorption) is (wt %) 7.95 MgO, 71.92 PbO, 0.41 Al₂O₃, 12.77 SiO₂, 2.2 H₂O, 2.1 CO₂, 2.67 B₂O₃ (calculated on the basis of structural data); total 100.02. The empirical formula calculated on the basis of 59 anions (O + OH) (Z = 1) is as follows: Pb_14.75Mg_9.03Si_9.73Al_0.37O_30.76(BO₃)_3.51(CO₃)_2.18(OH)_11.7. The simplified formula (Z = 2) is Pb_{7 + x} Mg_4.5(Si₅O₁₄)(BO₃)₂(CO₃)(OH,O)₇ (x < 0.5). The crystal structure of britvinite has been studied on a single crystal at 173 K; R = 0.0547. The new mineral is triclinic, space group P ; the unit-cell dimensions are a = 9.3409(8), b = 9.3597(7), c = 18.8333(14) ?, α = 80.365(6)°, β = 75.816(6)°, γ = 59.870(5)°, V = 1378.74(19) ?³. The structure consists of alternating TOT stacks (containing octahedral brucite-like and discontinuous tetrahedral (Si₅O₁₄)_∞∞ layers) and multilayered [Pb_7.1(OH)_3.6(CO₃)(BO₃)_1.75(SiO₄)_0.25]_∞∞ blocks. The strongest reflections in the X-ray powder diffraction pattern [d, ? (I, %)(hkl)] are 18.1(100)(001), 3.39(30)(12, 14, 015), 3.02(90)(006, 130, 106, 20, 11), 2.698(70)(332, 134, 030, 1), 2.275(30)(008, 420, 424), 1.867(30)(446, 239, 2.1.10, 18), 1.766(40)(151, 31, 10, 453, 542, 512, 42), 1.519(40)(0.0.12). The mineral has been named in honor of Sergei Nikolaevich Britvin (b. 1965), a Russian mineralogist. The type material of britvinite is deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow. The registration number is 3458/1. Original Russian Text ? N.V. Chukanov, O.V. Yakubovich, I.V. Pekov, D.I. Belakovsky, W. Massa, 2007, published in Zapiski Rossiiskogo Mineralogicheskogo Obshchestva, 2007, Pt CXXXVI, No. 6, pp. 18–25. The new mineral britvinite and its name were accepted by the Commission on New Minerals and Mineral Names, Russian Mineralogical Society, June 7, 2006, and approved by the Commission on New Minerals and Mineral Names, International Mineralogical Association, October 17, 2006.     

Formation of dome and basin structures: Results from scaled experiments using non-linear rock analogues

Dome and basin folds are structures with circular or slightly elongate outcrop patterns, which can form during single- and polyphase deformation in various tectonic settings. We used power-law viscous rock analogues to simulate single-phase dome-and-basin folding of rocks undergoing dislocation creep. The viscosity ratio between a single competent layer and incompetent matrix was 5, and the stress exponent of both materials was 7. The samples underwent layer-parallel shortening under bulk pure constriction.Increasing initial layer thickness resulted in a decrease in the number of domes and basins and an increase in amplitude, A, arc-length, L, wavelength, λ, and layer thickness, H_f. Samples deformed incrementally show progressive development of domes and basins until a strain of e_Y=Z = −30% is attained. During the dome-and-basin formation the layer thickened permanently, while A, L, and λ increased. A dominant wavelength was not attained. The normalized amplitude (A/λ) increased almost linearly reaching a maximum of 0.12 at e_Y=Z = −30%. During the last increment of shortening (e_Y=Z = −30 to −40%) the domes and basins did not further grow, but were overprinted by a second generation of non-cylindrical folds. Most of the geometrical parameters of the previously formed domes and basins behaved stable or decreased during this phase. The normalized arc-length (L/H_f) of domes and basins is significantly higher than that of 2D cylindrical folds. For this reason, the normalized arc length can probably be used to identify domes and basins in the field, even if these structures are not fully exposed in 3D.     

Fivegite K4Ca2[AlSi7O17(O2 ? xOHx)][(H2O)2 ? xOH]Cl: A new mineral species from the Khibiny alkaline pluton of the Kola Peninsula in Russia

A new mineral fivegite has been identified in a high-potassium hyperalkaline pegmatite at Mt. Rasvumchorr in the Khibiny alkaline complex of the Kola Peninsula in Russia. This mineral is a product of the hydrothermal alteration of delhayelite (homoaxial pseudomorphs after its crystals up to 2 × 3 × 10 cm in size). Hydrodelhayelite, pectolite, and kalborsite are products of fivegite alteration. The associated minerals are aegirine, potassic feldspar, nepheline, sodalite, magnesiumastrophyllite, lamprophyllite, lomonosovite, shcherbakovite, natisite, lovozerite, tisinalite, ershovite, megacyclite, shlykovite, cryptophyllite, etc. Areas of pure unaltered fivegite are up to 2 mm in width. The mineral is transparent and colorless; its luster is vitreous to pearly. Its Cleavage is perfect (100) and distinct (010). Its Mohs hardness is 4, D(meas) = 2.42(2), and D(calc) = 2.449 g/cm³. Fivegite is optically biaxial positive: α 1.540(1), β 1.542(2), γ 1.544(2), and 2V(meas) 60(10)°. Its orientation is X = a, y = c, and Z = b. Its IR spectrum is given. Its chemical composition (wt %; electron microprobe, H₂O determined by selective sorption) is as follows: 1.44 Na₂O, 19.56 K₂O, 14.01 CaO, 0.13 SrO, 0.03 MnO, 0.14 Fe₂O₃, 6.12 Al₂O₃, 50.68 SiO₂, 0.15 SO₃, 0.14 F, 3.52 Cl, 4.59 H₂O; −O = −0.85(Cl,F)2; total 99.66. The empirical formula based on (Si + Al + Fe) = 8 is H_4.22K_3.44Na_0.39Ca_2.07Sr_0.01Fe_0.01Al_1.00Si_6.99O_21.15F_0.06Cl_0.82(SO₄)_0.02. The simplified formula is K₄Ca₂[AlSi₇O₁₇(O_{2 − x} OH _x ][(H₂O)_{2 − x} OH _x ]Cl (X = 0−2). Fivegite is orthorhombic: Pm2₁ n, a = 24.335(2), b = 7.0375(5), c = 6.5400(6) ?, V = 1120.0(2) ?³, and Z = 2. The strongest reflections of the X-ray powder pattern are as follows (d, ?, (I, %), [hkl]): 3.517(38) [020], 3.239(28) [102], 3.072(100) [121, 701], 3.040(46) [420, 800, 302], 2.943 (47) [112], 2.983(53) [121], 2.880 (24) [212, 402], 1.759(30) [040, 12.2.0]. The crystal structure was studied using a single crystal: R _hkl = 0.0585. The base of fivegite structure is delhayelite-like two-layer terahedral blocks [(Al,Si)₄Si₁₂O₃₄(O_{4 − x} OH _x )] linked by Ca octahedral chains. K⁺ and Cl⁻ are localized in zeolite-like channels within the terahedral blocks, whereas H₂O and OH occur between the blocks. The mineral is named in memory of the Russian geological and mining engineer Mikhail Pavlovich Fiveg (1899–1986), the pioneering explorer of the Khibiny apatite deposits. The type specimen is deposited at the Fersman Mineralogical Museum of the Russian Academy of Sciences in Moscow. The series of transformations is discussed: delhayelite K₄Na₂Ca₂[AlSi₇O₁₉]F₂Cl—fivegite K₄Ca₂[AlSi₇O₁₇(O_{2 − x} OH _x ]Cl—hydrodelhayelite KCa₂[AlSi₇O₁₇(OH)₂](H₂O)_{6 − x} .     

Nickenichite,a new arsenate from the Eifel,Germany

Summary Nickenichite is a new mineral found close to the village of Nickenich at the Nickenicher Sattel, Eifel, Germany. The chemical composition is Na_xCa_yCu_z(Mg, Fe, Al)₃(AsO₄)3, x 0.8, y 0.4, 0.4 and was derived by means of electron microprobe analyses and by a crystal structure investigation. The latter was determined from single-crystal X-ray data:a = 11.882(4)Å,b = 12.760(4)Å,c = 6.647(2)Å, = 112.81(2)°, space group C2/c,Z = 4;R = 0.053 andR _w = 0.033 from 984 observed data and 102 free variables. Nickenichite is structurally related to the minerals o'danielite and johillerite. The two crystallographically different octahedrally coordinated cation positionsMe = (Mg, Fe, Al) have averageMe-O distances of 2.108 Å and 2.056 Å, octahedra share edges to form zig-zag chains in ; the chains are interconnected by AsO₄ tetrahedra. In addition the compound is characterized by partially occupied Na^[4+4], Ca^[6+2] and Cu^[4] positions.

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Nickenichit, ein neues Arsenat aus der Eifel, Deutschland

Zusammenfassung Nickenichit ist ein neues Mineral, das nahe dem Ort Nickenich, am Nickenicher Sattel, Eifel, Deutschland, gefunden wurde. Die chemische Formel ist Na_xCa_yCu_z, (Mg, Fe, Al)₃(AsO₄)₃, x 0,8, y 0,4, z 0,4 und wurde mittels Elektronenstrahl-Mikrosondenanalysen und einer Kristallstrukturuntersuchung ermittelt. Letztere wurde mit Einkristall-Röntgendaten durchgeführt:a = 11,882(4) Å,b = 12,760(4) Å,c = 6,647(2) Å, = 112,81(2)°, Raumgruppe C2/c,Z = 4;R = 0,053 undR _w = 0,033 für 984 beobachtete Daten und 102 freie Variable. Nickenichit zeigt enge strukturelle Beziehungen zu den Mineralen O'Danielit und Johillerit. Die zwei kristallographisch verschiedenen oktaedrisch koordinierten KationpositionenMe = (Mg, Fe, Al) haben mittlereMe-O-Abstände von 2,108 Å und 2,056 Å, die Oktaeder werden über Kanten zu zick-zack-artigen Ketten in verknüpft, diese werden untereinander über AsO₄-Tetraeder vernetzt. Des weiteren ist die Verbindung durch partiell besetzte Na^[4+4]-, Ca^[6+2]- und Cu^[4]-Positionen charakterisiert.

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With 2 Figures     

Photometric elements,apsidal motion,and the third body in the eclipsing binary V974 Cyg

We have derived the first photoelectric light curve of the eclipsing binary V974 Cyg from our own photoelectric observations. Analysis of the light curve has yielded the system’s photometric elements (r ₁ ≈ r ₂ = 0.1192, e = 0.058, L ₁ ≈ L ₂ = 0.486, and L ₃ = 0.028) and absolute parameters (M ₁ ≈ M ₂ = 2.2M _⊙, T _eff,1 ≈ T _eff,2 = 9500 K, a = 15.0R _⊙, distance d = 1.29 kpc, age log t = 8.0, t/tMS = 0.11). We have detected apsidal motion with the period U _obs = (1140 ± 170) yrs, and the presence of a third body in the system. The orbital parameters derived for the third body are P ₃ = 26.5 yrs, e ₃ = 0.78, and a ₃ sin i ₃ = 1.5 AU; and the lower limit for its mass is M ₃ > 0.58M _⊙. The observed apsidal-motion rate is higher than is expected theoretically by a factor of 1.5. The axial rotation of the system’s components is not yet synchronized with the orbital motion, probably because V974 Cyg is relatively young and detached.     

A simple geometric model of sedimentary rock to connect transfer and acoustic properties

A simple rock model is presented which reproduces the measured hydraulic and electric transport properties of sedimentary rocks and connects these properties with each other, as well as with the acoustic propagation velocities and elastic moduli. The model has four geometric parameters (average coordination number Z of the pores, average pore radius r, average distance between nearest pores d, and average throat radius δ) which can be directly determined from the measured porosity Φ, hydraulic permeability k, and cementation exponent m of the rock via simple analytic expressions. Inversion examples are presented for published sandstone data, and for cores taken from Saudi Arabian, Upper Jurassic and Permian carbonate reservoirs. For sandstone, the inversion works perfectly; for carbonates, the derived rock model shows order-of-magnitude agreement with the structure seen in thin sections. Inverting the equations, we express the transfer properties Φ, k, and m as functions of r, d, δ, and Z. Formulae are derived for the bulk density D _b, formation factor F, and P-wave velocity in terms of the proposed geometrical parameters.     

Toxic metals in Venice lagoon sediments: model,observation, and possible removal

We have modeled the distribution of nine toxic metals in the surface sediments from 163 stations in the Venice lagoon using published data. Three entrances from the Adriatic Sea control the circulation in the lagoon and divide it into three basins. We assume, for purposes of modeling, that Porto Marghera at the head of the Industrial Zone area is the single source of toxic metals in the Venice lagoon. In a standing body of lagoon water, concentration of pollutants at distancex from the source (C ₀) may be given byC=C ₀e^–kx wherek is the rate constant of dispersal. We calculatedk empirically using concentrations at the source, and those farthest from it, that is the end points of the lagoon. Averagek values (ppm/km) in the lagoon are: Zn 0.165, Cd 0.116, Hg 0.110, Cu 0.105, Co 0.072, Pb 0.058, Ni 0.008, Cr (0.011) and Fe (0.018 percent/km), and they have complex distributions. Given thek values, concentration at source (C ₀), and the distancex of any point in the lagoon from the source, we have calculated the model concentrations of the nine metals at each sampling station. Tides, currents, floor morphology, additional sources, and continued dumping perturb model distributions causing anomalies (observed minus model concentrations). Positive anomalies are found near the source, where continued dumping perturbs initial boundary conditions, and in areas of sluggish circulation. Negative anomalies are found in areas with strong currents that may flush sediments out of the lagoon. We have thus identified areas in the lagoon where higher rate of sediment removal and exchange may lessen pollution.     

Crystal structure and chemical formula of schmiederite,Pb2Cu2(OH)4(SeO3)(SeO4), with a comparison to linarite,PbCu(OH)2(SO4)

Summary Based on a X-ray structure analysis it was proved that the mineral schmiederite contains both selenite and selenate groups [a = 9.922(3)Å,b = 5.712(2)Å,c = 9.396(3)Å, = 101.96(3)°, space group P2₁/m,Z = 2 {Pb₂Cu₂(OH)₄(SeO₃)(SeO₄)},R _w = 0.055 for 1131 reflections up to sin / = 0.65 Å^–1]. The crystal structure is closely related to that of linarite [a = 9.701(2) Å,b = 5.650(2) Å,c= 4.690(2)Å, = 102.65(2)°, space group P2₁/m,Z = 2 {PbCu(OH)₂(SO₄)},R _w = 0.034 for 1991 reflections up to sin / = 1.0 Å^–1].The Pb atom in linarite and the Pb(1) atom in schmiederite have each three Pb-O bonds < 2.45 Å with trigonal pyramidal arranged ligands; the Pb(2) atom in schmiederite has only one such near O atom. The Cu atoms are approximately square planar coordinated by hydroxil groups. In addition two further O atoms complete the coordination figure to a strongly distorted octahedron. All the anion groups have the usual geometry.

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Kristallstruktur und chemische Formel von Schmiederit, Pb₂Cu₂(OH)₄(SeO₃)(SeO₄), mit einem Vergleich zu Linarit, PbCu(OH)₂(SO₄)

Zusammenfassung Basierend auf einer Röntgen-Strukturuntersuchung konnte das Vorliegen von Selenit-und Selenatgruppen im Mineral Schmiederit belegt werden [a=9,922(3) Å,b = 5,712(2) Å,c = 9,396(3) Å, = 101,96(3)°, Raumgruppe P2₁/m,Z=2 {Pb₂Cu₂(OH)₄(SeO₃)(SeO₄)},R _w = 0,055 für 1131 Reflexe bis sin /, = 0,65 Å^–1]. Die Kristallstruktur weist enge Beziehungen zu jener des Linarits auf [a = 9,701(2) Å,b = 5,650(2) Å,c = 4,690(2) Å, = 102,65(2)°, Raumgruppe P2₁/m,Z=2 {PbCu(OH)₂(SO₄)},R _w = 0,034 für 1991 Reflexe bis sin / = 1,0 Å^–1].Das Pb-Atom im Linarit sowie das Pb(1)-Atom im Schmiederit haben jeweils drei Pb-O-Bindungen <,45 Å, wobei die Liganden trigonal pyramidal angeordnet sind; das Pb(2)-Atom im Schmiederit hat hingegen nur ein derart nahes O-Atom. Die Cu-Atome sind etwa quatratisch planar von Hydroxilgruppen koordiniert; zwei weitere O-Atome ergänzen die Koordinationsfigur zur einem stark verzerrten Oktaeder. Die Aniongruppen haben die üblichen Dimensionen.

     

Bearing capacity of foundations on rock mass using the method of characteristics

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors N_σ0 and N_σ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.     

The mass of the compact object in the low-mass X-ray binary 2S 0921-630

We interpret the observed radial-velocity curve of the optical star in the low-mass X-ray binary 2S 0921-630 using a Roche model, taking into account the X-ray heating of the optical star and screening of X-rays coming from the relativistic object by the accretion disk. Consequences of possible anisotropy of the X-ray radiation are considered. We obtain relations between the masses of the optical and compact (X-ray) components, m _v and m _x , for orbital inclinations i = 60°, 75°, and 90°. Including X-ray heating enabled us to reduce the compact object’s mass by ～0.5–1 M _⊙, compared to the case with no heating. Based on the K0III spectral type of the optical component (with a probable mass of m _v ? 2.9 M _⊙), we concluded that m _x ? 2.45?2.55 M _⊙ (for i = 75°?90°). If the K0III star has lost a substantial part of its mass as a result of mass exchange, as in the V404 Cyg and GRS 1905+105 systems, and its mass is m _v ? 0.65?0.75 M _⊙, the compact object’s mass is close to the standard mass of a neutron star, m _x ? 1.4 M _⊙ (for i = 75°?90°). Thus, it is probable that the X-ray source in the 2S 0921-630 binary is an accreting neutron star.