Heat capacity of hydrous trachybasalt from Mt Etna: comparison with CaAl<Subscript>2</Subscript>Si<Subscript>2</Subscript>O<Subscript>8</Subscript> (An)–CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript> (Di) as basaltic proxy compositions

The specific heat capacity (C _p) of six variably hydrated (~3.5 wt% H₂O) iron-bearing Etna trachybasaltic glasses and liquids has been measured using differential scanning calorimetry from room temperature across the glass transition region. These data are compared to heat capacity measurements on thirteen melt compositions in the iron-free anorthite (An)–diopside (Di) system over a similar range of H₂O contents. These data extend considerably the published C _p measurements for hydrous melts and glasses. The results for the Etna trachybasalts show nonlinear variations in, both, the heat capacity of the glass at the onset of the glass transition (i.e., C _p ^g ) and the fully relaxed liquid (i.e., C _p ^l ) with increasing H₂O content. Similarly, the “configurational heat capacity” (i.e., C _p ^c  = C _p ^l  ? C _p ^g ) varies nonlinearly with H₂O content. The An–Di hydrous compositions investigated show similar trends, with C _p values varying as a function of melt composition and H₂O content. The results show that values in hydrous C _p ^g , C _p ^l and C _p ^c in the depolymerized glasses and liquids are substantially different from those observed for more polymerized hydrous albitic, leucogranitic, trachytic and phonolitic multicomponent compositions previously investigated. Polymerized melts have lower C _p ^l and C _p ^c and higher C _p ^g with respect to more depolymerized compositions. The covariation between C _p values and the degree of polymerization in glasses and melts is well described in terms of SM_hydrous and NBO/T _hydrous. Values of C _p ^c increase sharply with increasing depolymerization up to SM_hydrous ~ 30–35 mol% (NBO/T _hydrous ~ 0.5) and then stabilize to an almost constant value. The partial molar heat capacity of H₂O for both glasses (\( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{g}} \)) and liquids (\( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \)) appears to be independent of composition and, assuming ideal mixing, we obtain a value for \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \) of 79 J mol^?1 K^?1. However, we note that a range of values for \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \) (i.e., ~78–87 J mol^?1 K^?1) proposed by previous workers will reproduce the extended data to within experimental uncertainty. Our analysis suggests that more data are required in order to ascribe a compositional dependence (i.e., nonideal mixing) to \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \).     

The mass of the compact object in the X-ray binary 4U 1700-37

The results of a systematic analysis of master radial-velocity curves for the X-ray binary 4U 1700-37 are presented. The dependence of the mass of the X-ray component on the mass of the optical component is derived in a Roche model based on a fit of the master radial-velocity curve. The parameters of the optical star are used to estimate the mass of the compact object in three ways. The masses derived based on information about the surface gravity of the optical companion and various observational data are 2.25 _?0.24 ^+0.23 M_⊙ and 2.14 _?0.56 ^+0.50 M_⊙. The masses based on the radius of the optical star, 21.9R_⊙, are 1.76 _?0.21 ^+0.20 M_⊙ and 1.65 _?0.56 ^+0.78 M_⊙. The mass of the optical component derived from the mass-luminosity relation for X-ray binaries, 27.4M_⊙, yields masses for the compact object of 1.41 _?0.08 ⁺ M_⊙ and 1.35 _?0.18 ^+0.18 M_⊙.     

Influence of the <Emphasis Type="Italic">X</Emphasis>-site composition on tourmaline’s crystal structure: investigation of synthetic K-dravite,dravite, oxy-uvite,and magnesio-foitite using SREF and Raman spectroscopy

The crystal structures of synthetic K-dravite [^XK^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)], dravite [^XNa^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)], oxy-uvite [^XCa^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W O], and magnesio-foitite [^X?^Y(Mg₂Al)^ZAl ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)] are investigated by polarized Raman spectroscopy, single-crystal structure refinement (SREF), and powder X-ray diffraction. The use of compositionally simple tourmalines characterized by electron microprobe analysis facilitates the determination of site occupancy in the SREF and band assignment in the Raman spectra. The synthesized K-dravite, oxy-uvite, and magnesio-foitite have significant Mg–Al disorder between their octahedral sites indicated by their respective average 〈Y–O〉 and 〈Z–O〉 bond lengths. The Y- and Z-site compositions of oxy-uvite (^YMg_1.52Al_1.48(10) and ^ZAl_4.90Mg_1.10(15)) and magnesio-foitite (^YAl_1.62Mg_1.38(18) and ^ZAl_4.92Mg_1.08(24)) are refined from the electron densities at each site. The Mg–Al ratio of the Y and Z sites is also determined from the relative integrated peak intensities of the Raman bands in the O–H stretching vibrational range (3250–3850 cm^?1), producing values in good agreement with the SREF data. The unit cell volume of tourmaline increases from magnesio-foitite (1558.4(3) ų) to dravite (1569.5(4)–1571.7(3) ų) to oxy-uvite (1572.4(2) ų) to K-dravite (1588.1(2) ų), mainly due to lengthening of the crystallographic c-axis. The increase in the size of the X-site coordination polyhedron from dravite (Na) to K-dravite (K) is accommodated locally in the crystal structure, resulting in the shortening of the neighboring O1–H1 bond. In oxy-uvite, Ca²⁺ is locally associated with a deprotonated W (O1) site, whereas vacant X sites are neighbored by protonated W (O1) sites. Increasing the size of the X-site-occupying ion does not detectably affect bonding between the other sites; however, the higher charge of Ca and the deprotonated W (O1) site in oxy-uvite are correlated to changes in the lattice vibration Raman spectrum (100–1200 cm^?1), particularly for bands assigned to the T ₆O₁₈ ring. The Raman spectrum of magnesio-foitite shows significant deviations from those of K-dravite, dravite, and oxy-uvite in both the lattice and O–H stretching vibrational ranges (100–1200 and 3250–3850 cm^?1, respectively). The vacant X site is correlated with long- and short-range changes in the crystal structure, i.e., deformation of the T ₆O₁₈ ring and lengthening of the O1–H1 and O3–H3 bonds. However, X-site vacancies in K-dravite, dravite, and oxy-uvite result only in the lengthening of the neighboring O1–H1 bond and do not result in identifiable changes in the lattice-bonding environment.     

Effects of salt solutions on the hydro-mechanical behavior of compacted GMZ01 Bentonite

In this study, the effects of salinity of infiltrating solutions on the swelling strain, compressibility, and hydraulic conductivity of compacted GMZ01 Bentonite were investigated. After swelling under vertical load using either distilled water or NaCl solutions with concentrations of 0.1, 0.5 M, and 1 M, laboratory oedometer tests were conducted on the compacted GMZ01 Bentonite. Based on the oedometer test results, hydraulic conductivity was determined using the Casagrande’s method. Results show that the swelling strain of highly compacted GMZ01 Bentonite decreases as the concentration of NaCl solution increases. The compression index C _c ^* increases and then turns to decrease with an increase in the vertical stress or a decrease in the void ratio for different solutions, and the C _c ^* decreases as the concentration of NaCl solution increases. The secondary consolidation coefficient C _α increases linearly with the increase of the compression index C _c ^* . Furthermore, a bi-linear relationship between the swelling index C _s ^* and the secondary consolidation coefficient C _α can be characterized clearly. The hydraulic conductivity increases as the concentration of NaCl solution increases, however, this increase can be prevented if a high confining stress is applied.     

Atmospheric elemental abundances for the components of the multiple system ADS 11061. 41 Draconis

We obtained speckle interferometric and spectroscopic observations of the system 41 Dra during its periastron passage in 2001. The components’ lines are resolved in the spectral interval 3700–9200 Å. The observed wavelength dependence of the brightness difference between the components is used to estimate the B-V indices separately for each of the components: B-V = 0.511 for component a and B-V = 0.502 for component b. We derived improved effective temperatures of the components from their B-V values and hydrogen-line profiles. The observations can be described with the parameters for the components T _eff ^a = 6370 K, log g^a = 4.05 and T _eff ^b = 6410 K, log g^b = 4.20. The iron, carbon, nitrogen, and oxygen abundances in the atmospheres of the components are log N(Fe)^a = 7.55, log N(Fe)^b = 7.60, log N(C)^a = 8.52, log N(C)^b = 8.58, log N(N)^a = 8.05, log N(N)^b = 7.99, log N(O)^a = 8.73, log N(O)^b = 8.76.     

Properties of galactic disks at optical and near-IR wavelengths

We have analyzed the radial scales, central surface brightnesses, and colors of 400 disks of various types of galaxies. For nine galaxies, the brightness decrease and the central disk brightness were obtained via a two-dimensional decomposition of the U BV RI J H K photometric images into bulge and disk components. We used published disk parameters for 392 of the galaxies. The central surface brightness μ _0,i ⁰ and linear (disk) scale length h vary smoothly along the Hubble sequence of galaxies within a rather narrow interval. The disks of relatively early-type galaxies display higher central K surface brightnesses, higher central surface densities, higher central mass-to-luminosity ratios M/L(B), smaller sizes (relative to the diameter of the galaxy D ₂₅), redder integrated colors, and redder central colors. The color gradient normalized to the radius of the galaxy and the “blue” central surface brightness of the disk, μ _0,i/0(B), are both independent of the galaxy type. The radial disk scales in different photometric bands differ less in early-type than in late-type galaxies. A correlation between the central disk surface brightness and the total luminosity of the galaxy is observed. We also consider the influence of dust on the photometric parameters of the disks.     

Interpretation of the light curves of “quiescent” X-ray novae in a model with a noncollisional interaction between the flow and disk. The XTE J1118+480 system

We have analyzed the orbital light curve of the X-ray nova XTE J1118+480 in a “disk + hot line” model based on three-dimensional gas-dynamical computations of gas flows in interacting binary systems. As a result, we have been able to derive reliable parameters for the system: i = 80 _?4 ⁺⁴ degrees, _MBH = 7.1 _?0.1 ^+0.5 M_⊙, M _opt = 0.39 _?0.07 ^+0.15 M_⊙.     

Development of a technique for IR spectroscopic determination of nitrogen content and aggregation degree in diamond crystals

A technique for IR spectroscopic determination of the total nitrogen content N _S in the form of A-and B ₁-defects is suggested. It provides for the computer processing and decomposition of IR spectra into constituent bands, calculation of the total absorption band area S _N and individual areas S _A and S _B1 and their normalization with respect to the total area of the diamond intrinsic absorption S ₀, with the normalization coefficients K _S , K _A , and K _B1 being calculated. Based on the analysis of the IR spectra of 60 octahedral diamond crystals from the Mir and Yubileinaya pipes (Sakha-Yakutiya), the empirical functions N _S = 911.85 K _S ^0.9919 ppm (R ² = 0.9859), N _A = 1185.6 K _A ^1.1511 ppm (R ² = 0.8703), and N _B1 = 911.85 K _S ^0.9919 ? 1185.6 K _A ^1.1511 ppm have been defined.     

Atmospheric chemical abundances of the components of the quadruple system ADS 11061. 40 Draconis

As part of our study of the components of the hierarchic quadruple system ADS 11061, we acquired spectroscopic observations of the binary 40 Dra. Echelle spectra showing the separation of the components’ lines were obtained in the spectral range 3700–9200 Å. Effective temperatures and surface gravities were derived for the components from BV photometry and the hydrogen-line profiles. The components of the 40 Dra system have parameters close to T _eff ^a = 6420 K, log g _a = 4.17, T _eff ^b = 6300 K, and log g _b = 4.20. We find the microturbulence velocity in the component atmospheres to be V _t = 2.6 km/s. The abundances of iron, carbon, nitrogen, and oxygen in the atmospheres of both components are estimated to be log N(Fe)^a = 7.50, log N(Fe)^b = 7.46, log N(C)^a = 8.39, log N(C)^b = 8.45, log N(N)^a = 8.12, log(N)^b = 8.15, log N(O)^a = 8.77, log N(O)^b = 8.74.     

Electrical conductivity of NaCl-bearing aqueous fluids to 600 °C and 1 GPa

The electrical conductivity of aqueous fluids containing 0.01, 0.1, and 1 M NaCl was measured in an externally heated diamond cell to 600 °C and 1 GPa. These measurements therefore more than double the pressure range of previous data and extend it to higher NaCl concentrations relevant for crustal and mantle fluids. Electrical conductivity was generally found to increase with pressure and fluid salinity. The conductivity increase observed upon variation of NaCl concentration from 0.1 to 1 M was smaller than from 0.01 to 0.1 M, which reflects the reduced degree of dissociation at high NaCl concentration. Measured conductivities can be reproduced (R ² = 0.96) by a numerical model with log \(\sigma\) = ?1.7060– 93.78/T + 0.8075 log c + 3.0781 log \(\rho\) + log \(\varLambda\) ₀(T, \(\rho\)), where \(\sigma\) is the conductivity in S m^?1, T is temperature in K, c is NaCl concentration in wt%, \(\rho\) is the density of pure water (in g/cm³) at given pressure and temperature, and \(\varLambda\) ₀ (T, \(\rho\)) is the molar conductivity of NaCl in water at infinite dilution (in S cm² mol^?1), \(\varLambda\) ₀ = 1573–1212 \(\rho\) + 537 062/T–208 122 721/T ². This model allows accurate predictions of the conductivity of saline fluids throughout most of the crust and upper mantle; it should not be used at temperatures below 100 °C. In general, the data show that already a very small fraction of NaCl-bearing aqueous fluid in the deep crust is sufficient to enhance bulk conductivities to values that would be expected for a high degree of partial melting. Accordingly, aqueous fluids may be distinguished from hydrous melts by comparing magnetotelluric and seismic data. H₂O–NaCl fluids may enhance electrical conductivities in the deep crust with little disturbance of v _p or v _p/v _s ratios. However, at the high temperatures in the mantle wedge above subduction zones, the conductivity of hydrous basaltic melts and saline aqueous fluids is rather similar, so that distinguishing these two phases from conductivity data alone is difficult. Observed conductivities in forearc regions, where temperatures are too low to allow melting, may be accounted for by not more than 1 wt% of an aqueous fluid with 5 wt% NaCl, if this fluid forms a continuous film or fills interconnected tubes.     

Droninoite,Ni<Subscript>3</Subscript>Fe<Superscript>3+</Superscript>Cl(OH)<Subscript>8</Subscript> · 2H<Subscript>2</Subscript>O,a new hydrotalcite-group mineral species from the weathered Dronino meteorite

A new mineral, droninoite, was found in a fragment of a weathered Dronino iron meteorite (which fell near the village of Dronino, Kasimov district, Ryazan oblast, Russia) as dark green to brown fine-grained (the size of single grains is not larger than 1 μm) segregations up to 0.15 × 1 × 1 mm in size associated with taenite, violarite, troilite, chromite, goethite, lepidocrocite, nickelbischofite, and amorphous Fe³⁺ hydroxides. The mineral was named after its type locality. Aggregates of droninoite are earthy and soft; the Mohs hardness is 1–1.5. The calculated density is 2.857 g/cm³. Under a microscope, droninoite is dark gray-green and nonpleochroic. The mean (cooperative for fine-grained aggregate) refractive index is 1.72(1). The IR spectrum indicates the absence of S O ₄ ^2? and C O ₃ ^2? anions. Chemical composition (electron microprobe, partition of total iron into Fe²⁺ and Fe³⁺ made on the basis of the ratio (Ni + Fe²⁺): Fe³⁺ = 3: 1; water is calculated from the difference) is as follows, wt %: 36.45 NiO, 12.15 FeO, 17.55 Fe₂O₃, 23.78 H₂O, 13.01 Cl, ?O=Cl₂ ?2.94, total is 100.00. The empirical formula (Z = 6) is Ni_2.16Fe _0.75 ²⁺ Fe _0.97 ³⁺ Cl_1.62(OH)_7.10 · 2.28H₂O. The simplified formula is Ni₃Fe³⁺Cl(OH)₈ · 2H₂O. Droninoite is trigonal, space group R \(\bar 3\) m, R3m, or R32; a = 6.206(2), c = 46.184(18) Å; V = 1540.4(8) ų. The strong reflections in the X-ray powder diffraction pattern [d, Å (I, %) (hkl)] are 7.76(100)(006), 3.88(40)(0.0.12), 2.64(25)(202, 024), 2.32(20)(0.2.10), 1.965(0.2.16). The holotype specimen is deposited at the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow, registration number 3676/1.     

Apsidal motion and physical parameters of the eclipsing binary system AR Cas

Using the four-channel automatic photoelectric photometer of the Sternberg Astronomical Institute’s Tien Shan Mountain Observatory, we have acquired accurate (σ_obs≈0.004^m) W BV R brightness measurements for the eclipsing binary AR Cas during selected phases before eclipse ingress and after egress, as well as at the center of minima. A joint analysis of these measurements with other published data has enabled us to derive for the first time a self-consistent set of physical and geometrical parameters for the star and the evolutionary age of its components, t=(60±3)×10⁶ years. We have found the period of the apsidal motion (U_obs=1100±160 years, \(\dot \omega _{obs} = 0^\circ .327 \pm 0^\circ .049\) years^?1) and the apsidal parameter of the primary, logk _2,1 ^obs =?2.41±0.08, with the apsidal parameter being in good agreement with current models of stellar evolution. There is an ultraviolet excess in the primary’s radiation, Δ(U?B)=?0.12^m and Δ(B?V)=?0.06^m, possibly due to a metal deficiency in the star’s atmosphere.     

Thermal equation of state of natural tourmaline at high pressure and temperature

Synchrotron-based in situ angle-dispersive X-ray diffraction experiments were conducted on a natural uvite-dominated tourmaline sample by using an external-heating diamond anvil cell at simultaneously high pressures and temperatures up to 18 GPa and 723 K, respectively. The angle-dispersive X-ray diffraction data reveal no indication of a structural phase transition over the P–T range of the current experiment in this study. The pressure–volume–temperature data were fitted by the high-temperature Birch–Murnaghan equation of state. Isothermal bulk modulus of K ₀ = 96.6 (9) GPa, pressure derivative of the bulk modulus of \(K_{0}^{\prime } = 12.5 \;(4)\), thermal expansion coefficient of α ₀ = 4.39 (27) × 10^?5 K^?1 and temperature derivative of the bulk modulus (?K/?T) _P  = ?0.009 (6) GPa K^?1 were obtained. The axial thermoelastic properties were also obtained with K _a0 = 139 (2) GPa, \(K_{a0}^{\prime }\) = 11.5 (7) and α _a0 = 1.00 (11) × 10^?5 K^?1 for the a-axis, and K _c0 = 59 (1) GPa, \(K_{c0}^{\prime }\) = 11.4 (5) and α _c0 = 2.41 (24) × 10^?5 K^?1 for the c-axis. Both of axial compression and thermal expansion exhibit large anisotropic behavior. Thermoelastic parameters of tourmaline in this study were also compared with that of the other two ring silicates of beryl and cordierite.     

Batisivite,V<Subscript>8</Subscript>Ti<Subscript>6</Subscript>[Ba(Si<Subscript>2</Subscript>O)]O<Subscript>28</Subscript>, a new mineral species from the derbylite group

Batisivite has been found as an accessory mineral in the Cr-V-bearing quartz-diopside metamorphic rocks of the Slyudyanka Complex in the southern Baikal region, Russia. A new mineral was named after the major cations in its ideal formula (Ba, Ti, Si, V). Associated minerals are quartz, Cr-V-bearing diopside and tremolite; calcite; schreyerite; berdesinskiite; ankangite; V-bearing titanite; minerals of the chromite-coulsonite, eskolaite-karelianite, dravite-vanadiumdravite, and chernykhite-roscoelite series; uraninite; Cr-bearing goldmanite; albite; barite; zircon; and unnamed U-Ti-V-Cr phases. Batisivite occurs as anhedral grains up to 0.15–0.20 mm in size, without visible cleavage and parting. The new mineral is brittle, with conchoidal fracture. Observed by the naked eye, the mineral is black and opaque, with a black streak and resinous luster. Batisivite is white in reflected light. The microhardness (VHN) is 1220–1470 kg/mm² (load is 30 g), the mean value is 1330 kg/mm². The Mohs hardness is near 7. The calculated density is 4.62 g/cm³. The new mineral is weakly anisotropic and bireflected. The measured values of reflectance are as follows (λ, nm—R _max ^′ /R _min ^′ ): 440—17.5/17.0; 460—17.3/16.7; 480—17.1/16.5; 500—17.2/16.6; 520—17.3/16.7; 540—17.4/16.8; 560—17.5/16.8; 580—17.6/16.9; 600—17.7/17.1; 620—17.7/17.1; 640—17.8/17.1; 660—17.9/17.2; 680—18.0/17.3; 700—18.1/17.4. Batisivite is triclinic, space group P \(\overline 1\); the unit-cell dimensions are: a = 7.521(1) Å, b = 7.643(1) Å, c = 9.572(1) Å, α = 110.20°(1), β = 103.34°(1), γ = 98.28°(1), V = 487.14(7) ų, Z = 1. The strongest reflections in the X-ray powder diffraction pattern [d, Å (I, %)(hkl)] are: 3.09(8)(12\(\overline 2\)); 2.84, 2.85(10)(021, 120); 2.64(8)(21\(\overline 3\)); 2.12(8)(31\(\overline 3\)); 1.785(8)(32\(\overline 4\)), 1.581(10)(24\(\overline 2\)); 1.432, 1.433(10)(322, 124). The chemical composition (electron microprobe, average of 237 point analyses, wt %) is: 0.26 Nb₂O₅, 6.16 SiO₂, 31.76 TiO₂, 1.81 Al₂O₃, 8.20 VO₂, 26.27 V₂O₃, 12.29 Cr₂O₃, 1.48 Fe₂O₃, 0.08 MgO, 11.42 BaO; the total is 99.73. The VO₂/V₂O₃ ratio has been calculated. The simplified empirical formula is (V _4.8 ³⁺ Cr_2.2V _0.7 ⁴⁺ Fe_0.3)_8.0(Ti_5.4V _0.6 ⁴⁺ )_6.0[Ba(Si_1.4Al_0.5O_0.9)]O₂₈. An alternative to the title formula could be a variety (with the diorthogroup Si₂O₇) V₈Ti₆[Ba(Si₂O₇)]O₂₂. Batisivite probably pertains to the V ₈ ³⁺ Ti ₆ ⁴⁺ [Ba(Si₂O)]O₂₈-Cr ₈ ³⁺ Ti ₆ ⁴⁺ [Ba(Si₂O)]O₂₈ solid solution series. The type material of batisivite has been deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Physical Parameters of the Eclipsing System V1176 Cas

The first high-accuracy CCDUBV RI light curves for the recently discovered eclipsing system V1176 Cas (P = 6 _. ^d 33, V = 11 _. ^m 1) have been obtained. A photometric solution for the light curves and physical characteristics of the component stars are derived. The orbital eccentricity is negligible, e = 0.009; both components have physical parameters similar to the Sun, but they are younger and may have an overabundance of metals. The orientation of the orbital ellipse and the low eccentricity make studies of the apsidal motion difficult. Nevertheless, the high accuracy of the available measurements of the timings of minima has enabled derivation of an upper limit for the rate of apsidal rotation, which agrees with a theoretical estimate of this effect.     

A Refined Model for Solid Particle Rock Erosion

A procedure for the estimation of distribution parameters of a Weibull distribution model K₁ = f(K_Ic^12/4/σ_C^23/4) for solid particle erosion, as recently suggested in Rock Mech Rock Eng, doi: 10.1007/s00603-014-0658-x, 2014, is derived. The procedure is based on examinations of elastic–plastically responding rocks (rhyolite, granite) and plastically responding rocks (limestone, schist). The types of response are quantified through SEM inspections of eroded surfaces. Quantitative numbers for the distribution parameter K₁ are calculated for 30 rock materials, which cover a wide range of mechanical properties. The ranking according to the parameter K₁ is related to qualitative rock classification schemes. A modified proposal for the erosion of schist due to solid particle impingement at normal incidence is introduced.     

Equation of state of synthetic qandilite Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript> at ambient temperature

Using a diamond-anvil cell and synchrotron X-ray diffraction, the compressional behavior of a synthetic qandilite Mg_2.00(1)Ti_1.00(1)O₄ has been investigated up to about 14.9 GPa at 300 K. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yield an isothermal bulk modulus (K _T0) of 175(5) GPa, with its first derivative \(K_{T0}^{{\prime }}\) attaining 3.5(7). If \(K_{T0}^{{\prime }}\) is fixed as 4, the K _T0 value is 172(1) GPa. This value is substantially larger than the value of the adiabatic bulk modulus (K _S0) previously determined by an ultrasonic pulse echo method (152(7) GPa; Liebermann et al. in Geophys J Int 50:553–586, 1977), but in general agreement with the K _T0 empirically estimated on the basis of crystal chemical systematics (169 GPa; Hazen and Yang in Am Miner 84:1956–1960, 1999). Compared to the K _T0 values of the ulvöspinel (Fe₂TiO₄; ~148(4) GPa with \(K_{T0}^{{\prime }} = 4\)) and the ringwoodite solid solutions along the Mg₂SiO₄–Fe₂SiO₄ join, our finding suggests that the substitution of Mg²⁺ for Fe²⁺ on the T sites of the 4–2 spinels can have more significant effect on the K _T0 than that on the M sites.     

Simulation of molecular mass distributions and evaluation of O<Superscript>2−</Superscript> concentrations in polymerized silicate melts

A new statistical model is proposed for the molecular mass distributions (MMD) of polymerized anions in silicate melts. The model is based on the known distribution of Q ⁿ species in the MeO-Me₂O-SiO₂ system. In this model, chain and ring complexes are regarded as a random series of Q ⁿ structons with various concentrations of bridging bonds (1 ≤ n ≤ 4, Q ⁰ corresponds to SiO ₄ ^4? ). This approach makes it possible to estimate the probability of formation of various ensembles of polymer species corresponding to the general formula (Si _i O_3i+1?j )^2(i+1?j)?, where i is the size of the ion, and j is the cyclization number of intrachain bonds. The statistical model is utilized in the STRUCTON computer model, which makes use of the Monte Carlo method and is intended for the calculation of the composition and proportions of polyanions at a specified degree of polymerization of silicate melts (STRUCTON, version 1.2; 2007). Using this program, we simulated 1200 MMD for polyanions in the range of 0.52 ≤ p ≤98, where p is the fraction of nonbridging bonds in the silicon-oxygen matrix. The average number of types of anions in this range was determined to increase from three (SiO ₄ ^4? , Si₂O ₇ ^6? , and Si₃O ₁₀ ^8? ) to 153, and their average size increases from 1 to 7.2. A special option of the STRUCTON program combines MMD reconstructions in silicate melts with the formalism of the Toop-Samis model, which enables the calculation of the mole fraction of the O^2? ion relative to all anions in melts of specified composition. It is demonstrated that, with regard for the distribution and average size of anion complexes, the concentration of the O^2? ion in the MeO-SiO₂ system is characterized by two extrema: a minimum at 40–45 mol % SiO₂, which corresponds to the initial stages of the gelenization of the polycondensated silicate matrix, and a maximum, which is predicted for the range of 60–80 mol % SiO₂.     

Photometric elements and apsidal motion of the eclipsing binary ES Lac

We have obtained high-accuracy photoelectric measurements of ES Lac, an eclipsing binary with an elliptical orbit (B9III + B9III; P = 4.459^d, e = 0.198) in 1985–2004 at the Sternberg Astronomical Institute’s Tien Shan High-Altitude Observatory. Our detailed analysis of the 19-year uniform series of measurements has yielded the first photometric elements for this system, as well as a self-consistent set of physical and geometrical parameters for the binary. The virtually identical components (M ₁ = M ₂ = 3.0 M _⊙; R ₁ = R ₂ = 4.12 R _⊙) are appreciably separated from the main sequence, and are located on the giant branch: their age is t = (3.5 ± 0.2) × 10⁸ yrs. An analysis of our observations together with previously published times of minima has enabled a considerable refinement of the period of the apsidal motion, U = 355 ± 20 years, and a first determination of the apsidal parameter reflecting the radial density distributions for the components stars: k ₂ ^obs = 0.00213(18). This value is in a good agreement with the value expected theoretically for current evolutionary models of such stars: k ₂ ^th = 0.00257(15).