New Zr–Hf Geothermometer for Magmatic Zircons

A geothermometer equation \(T = \frac{{1531}} {{\ln K_d + 0.883}}\), where \(K_{\dot d} = \frac{{X_{Zr}^S X_{Hf}^m }} {{X_{Zr}^m X_{Hf}^s }}\) [X _j ⁱ is the concentration (in ppm) of component i in phase j] is the Zr and Hf distribution coefficient between melt and zircon, and T is temperature in K, was derived by thermodynamic processing of literature experimental data on Zr and Hf distribution between acid melts (m) and zircon (s) and on the solubility of zircon and hafnon in the melts with variable silica content. In calculations with this equations, we assumed the Zr concentration in zircon to be constant: 480000 ppm. It is shown that the commonly observed increase in Hf concentration from the cores to margins of magmatic zircon crystals is caused by the fractional crystallization of zircon. For differentiated acid magmatic series, the initial crystallization temperature of zircon in the least silicic cumulates should be evaluated using the cores of large zircon grains with the highest Zr/Hf ratio. Application of the geothermometer for mafic and intermediate rocks may be hampered due to simultaneous crystallization of zircon with some other ore and mafic minerals relatively enriched in Zr and Hf. The newly derived geothermometer has some advantages over other indicators of the crystallization temperature of magmatic zircon based on the zircon saturation index (Watson and Harrison, 1983; Boehnke et al., 2013) and on Ti concentration in this mineral (Ferry and Watson, 2007) as it does not depend on the major-oxide melt composition and on the accuracy of the estimated SiO₂ and TiO₂ activities in the melts. Calculations of the Zr and Hf fractionation trends in the course of zircon crystallization in granitoid melts allow one to evaluate the temperature at which more evolved melt portions were segregated.     

Experimental study of fluorine and chlorine contents in mica (biotite) and their partitioning between mica,phonolite melt,and fluid

This paper reports the results of a study of the composition of mica (biotite) crystallizing in the system of phonolite melt-Cl- and F-bearing aqueous fluid at T ～ 850°C, P = 200 MPa, and \(f_{O_2 } \) = Ni-NiO, as well as data on F and Cl partitioning between coexisting phases. It was established that Cl content in mica is significantly lower than in phonolite melt and, especially, in fluid. Fluorine shows a different behavior in this system: its content in mica is always higher than in phonolite melt but lower than in fluid. The mica-melt partition coefficients of Cl and F also behave differently. The Cl partition coefficient gradually increases from 0.17 to 0.33 with increasing Cl content in the system, whereas the partition coefficient of F sharply decreases from 3.0 to 1.0 with increasing total F content. The apparent partition coefficients of F between biotite and groundmass (melt) in various magmatic rocks are usually significantly higher than the experimental values. It was supposed that the higher ^Bt/glassD_F values in natural samples could be related to the influence of later oxidation reactions, reequilibration of biotite at continuously decreasing \(f_{H_2 O} \)/f _HF ratio, and an increase in this coefficients with decreasing total F content in the system.     

Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas

Bubbles grow in decompressing magmas by simple expansion and by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate elements and isotopes (or isotopologues) of dissolved components. This raises the possibility that the character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the absence of equilibrium vapor/melt isotopic fractionation. Recent experiments have confirmed the existence of an isotope mass effect on diffusion of the volatile element Cl in silicate melt [Fortin et al. (Isotopic fractionation of chlorine during chemical diffusion in a dacitic melt and its implications for isotope behavior during bubble growth (abstract), 2016 Fall AGU Meeting, 2016)], so there is a clear need to understand the efficacy of diffusive fractionation during bubble growth. In this study, numerical models of diffusion and mass redistribution during bubble growth were implemented for both “passive” volatiles—those whose concentrations are generally well below saturation levels—and “active” volatiles such as CO₂ and H₂O, whose elevated concentrations and limited solubilities are the cause of bubble nucleation and growth. Both diffusive and convective bubble-growth scenarios were explored. The magnitude of the isotope mass effect on passive volatiles partitioned into bubbles growing at a constant rate R in a static system depends upon R/D _L, K _d and D _H/D _L (K _d = bubble/melt partition coefficient; D _H/D _L = diffusivity ratio of the heavy and light isotopes). During convective bubble growth, the presence of a discrete (physical) melt boundary layer against the growing bubble (of width x _BL) simplifies outcomes because it leads to the quick onset of steady-state fractionation during growth, the magnitude of which depends mainly upon R?x _BL/D _L and D _H/D _L (bubble/melt fractionation is maximized at R?x _BL/D _L ≈0.1). Constant R is unrealistic for most real systems, so other scenarios were explored by including the solubility and EOS of an “active” volatile (e.g., CO₂) in the numerical simulations. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble. For volatile species whose isotope mass effects on diffusion have been measured (Cl, Li), predicted isotope fractionation in the exsolved vapor can be as large as ?4‰ for Cl and ?25‰ for Li.     

Genesis of the Paleoproterozoic Rare-Metal Granites of the Katugin Massif

We studied the petrography, mineralogy, and geochemistry of the Paleoproterozoic (2.06 Ga) granites of the Katugin massif (Stanovoy suture zone), which hosts the combined rare-metal Katugin deposit. Three groups of granites were distinguished: (1) biotite (Bt) and biotite–riebeckite (Bt–Rbk) granites of the western block of the massif; (2) biotite–arfvedsonite (Bt–Arf) granites of the eastern block; and (3) arfvedsonite (Arf), aegirine–arfvedsonite (Aeg–Arf), and aegirine (Aeg) granites of the eastern block. The Bt and Bt–Rbk granites of the first group are mainly metaluminous and peraluminous rocks with rather high CaO contents and the minimum F contents among the granites described here. It was suggested that the granites of this group could be derived from a source dominated by crustal rocks with a small addition of mantle materials. These granites probably crystallized from a metaluminous–peraluminous melt with elevated CaO and moderate F contents. Melts of such compositions are least favorable for the crystallization of ore minerals. The Bt–Arf granites of the second group are mainly peralkaline and show high contents of CaO and Y and low contents of Na₂O and F. A mixed mantle–crust source was proposed for the Bt–Arf granites. The initial melt of the Bt–Arf granites could have a peralkaline composition with elevated CaO content and moderate to high F content. The Arf, Aeg–Arf, and Aeg granites of the third group are enriched in ore mineral and were classified as peralkaline granites with very low CaO contents, elevated Na2O and F contents, and usually very high contents of Zr, Hf, Nb, and Ta. Based on the geochemical and isotopic data, it was supposed that the source of the granites of the third group could be derivatives of basaltic magmas produced in an OIB-type source with a minor addition of crustal material to the magma generation zone. It was suggested that the primary melt of this granite group could be a peralkaline CaO-poor and F-rich silicic melt, which is most favorable for the crystallization of ore minerals. Based on the analysis of the geochemical characteristics of the three granite groups and their relationships within the Katugin massif, a qualitative model of its formation was proposed. According to this model, the Bt and Bt–Rbk granites of the western block crystallized first, followed by the Bt–Arf granites of the eastern block and, eventually, the Arf, Aeg–Arf, and Aeg granites enriched in ore minerals.     

Vanadium magnetite–melt oxybarometry of natural,silicic magmas: a comparison of various oxybarometers and thermometers

To test a recently developed oxybarometer for silicic magmas based on partitioning of vanadium between magnetite and silicate melt, a comprehensive oxybarometry and thermometry study on 22 natural rhyolites to dacites was conducted. Investigated samples were either vitrophyres or holocrystalline rocks in which part of the mineral and melt assemblage was preserved only as inclusions within phenocrysts. Utilized methods include vanadium magnetite–melt oxybarometry, Fe–Ti oxide thermometry and -oxybarometry, zircon saturation thermometry, and two-feldspar thermometry, with all analyses conducted by laser-ablation ICP–MS. Based on the number of analyses, the reproducibility of the results and the certainty of contemporaneity of the analyzed minerals and silicate melts the samples were grouped into three classes of reliability. In the most reliable (n = 5) and medium reliable (n = 10) samples, all fO₂ values determined via vanadium magnetite–melt oxybarometry agree within 0.5 log units with the fO₂ values determined via Fe–Ti oxide oxybarometry, except for two samples of the medium reliable group. In the least reliable samples (n = 7), most of which show evidence for magma mixing, calculated fO₂ values agree within 0.75 log units. Comparison of three different thermometers reveals that temperatures obtained via zircon saturation thermometry agree within the limits of uncertainty with those obtained via two-feldspar thermometry in most cases, whereas temperatures obtained via Fe–Ti oxide thermometry commonly deviate by ≥50 °C due to large uncertainties associated with the Fe–Ti oxide model at T-fO₂ conditions typical of most silicic magmas. Another outcome of this study is that magma mixing is a common but easily overlooked phenomenon in silicic volcanic rocks, which means that great care has to be taken in the application and interpretation of thermometers and oxybarometers.     

Petrogenesis of the Late Jurassic peraluminous biotite granites and muscovite-bearing granites in SE China: geochronological,elemental and Sr–Nd–O–Hf isotopic constraints

Biotite granites and muscovite-bearing granites are dominant rock types of the widespread granites in SE China. However, their petrogenesis has been enigmatic. A combined study of zircon U–Pb dating and Lu–Hf isotopes, whole-rock element geochemistry and Sr–Nd–O isotopes was performed for three late Mesozoic granitic plutons (Xinfengjie, Jiangbei and Dabu) in central Jiangxi province, SE China. All the plutons are composed of biotite granites and muscovite-bearing granites that have been poorly investigated previously. The new data not only allow us to assess their sources and magma evolution processes, but also helps us to better understand the genetic link to the large-scale polymetallic mineralization in SE China. LA-ICP-MS zircon U–Pb dating shows that three plutons were emplaced in the Late Jurassic (159–148 Ma) and that the muscovite-bearing granites are almost contemporaneous with the biotite granites. The biotite granites have SiO₂ contents of 70.3–74.4 wt% and are weakly to strongly peraluminous with ASI from 1.00 to 1.26, and show a general decrease in ASI with increasing SiO₂. They have relatively high zircon saturation temperatures (T _Zr = 707–817 °C, most > 745 °C) and show a general decrease in T _Zr with increasing SiO₂. They have high initial ⁸⁷Sr/⁸⁶Sr ratios (0.7136 to 0.7166) and high δ¹⁸O values (9.1–12.8‰, most > 9.5‰) and clearly negative ε _Nd (T) (? 9.5 to ? 11.8) and ε _Hf (T) (in situ zircon) (? 13.1 to ? 13.5). The muscovite-bearing granites have high SiO₂ contents (74.7–78.2 wt%). They are also weakly to strongly peraluminous with ASI of 1.04–1.18 but show a general increase in ASI with increasing SiO₂. They have relatively low T _Zr (671–764 °C, most < 745 °C) and also show a general decrease in T _Zr with increasing SiO₂. The muscovite-bearing granites have high Rb (up to 810 ppm) and high (K₂O + Na₂O)/CaO (up to 270), Rb/Sr (up to 42) and Rb/Ba (up to 30) as well as low K/Rb (< 150, down to 50), Zr/Hf (< 24, down to 11) and Nb/Ta (< 6, down to 2). They show similar Nd–O–Hf isotopic compositions to the biotite granites with ε _Nd (T) of ? 8.7 to ? 12.0, δ¹⁸O of 8.7–13.0‰ (most > 9.5‰) and ε _Hf (T) (in situ zircon) of ? 11.3 to ? 13.1. Geochemical data suggest the origin of the biotite granites and muscovite-bearing granites as follows: Partial melting of Precambrian metasedimentary rocks (mainly two-mica schist) in the lower crust at temperatures of ca. 820 °C generated the melts of the less felsic biotite granites. Such primary crustal melts underwent biotite-dominant fractionation crystallization, forming the felsic biotite granites. Progressive plagioclase-dominant fractionation crystallization from the evolved biotite granites produced the more felsic muscovite-bearing granites. Thus, the biotite granites belong to the S-type whereas the muscovite-bearing granites are highly fractionated S-type granites. We further suggest that during the formation of the muscovite-bearing granites the fractional crystallization was accompanied by fluid fractionation and most likely the addition of internally derived mineralizing fluids. That is why the large-scale polymetallic mineralization is closely related to the muscovite-bearing granites rather than biotite granites in SE China. This is important to further understand the source and origin of biotite granites and muscovite-bearing granites in SE China even worldwide.     

Partitioning of trace elements between carbonate-silicate melts and mantle minerals: Experiment and petrological consequences

The partitioning of a number of trace elements (Ba, Nb, Zr, Y, REE, etc.) between orthopyroxene, garnet, and carbonate-silicate melt was experimentally studied using a belt apparatus at pressures of 3.5–4.2 GPa and temperatures of 1300–1500°C. The experimental products were investigated by electron microprobe analysis and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The experimental melts varied from carbonatitic (～5 wt % SiO₂) at low temperatures (1300–1350°C) to kimberlitic compositions (30 wt % SiO₂) at high temperatures (1500°C). The partition coefficients of most elements between orthopyroxene and melt (D _i ^Opx/L ) and garnet and melt (D _i ^Grt/L ) were almost independent of melt composition (temperature). The D _i ^Opx/L values ranged from <0.01 for the most incompatible Ba and light REE to 0.02–0.08 for moderately incompatible Zr, Y, and heavy REE. The D _i ^Grt/L values were approximately an order of magnitude higher, ～0.07 for light REE, 0.7 for Y, and 1.5 for Yb. The character of D _i ^Grt/L variations in the systems studied is in general similar to that established for silicate melts without volatile components. However, the differences in the behavior of moderately incompatible and compatible elements (e.g., light and heavy REE) in the experimental systems are less pronounced compared with CO₂-free systems. Considering carbonate-silicate and silicate melts as possible agents of mantle metasomatism, it can be concluded that the former can efficiently transport heavy REE, and the latter have a greater affinity for Nb, Ba, and light REE. A characteristic feature of mantle rocks enriched by carbonate-silicate melts is high Ba/La ratio coupled with relatively weakly fractionated REE distribution patterns. It was shown that the high degrees of enrichment observed in natural kimberlites can be explained by a two-stage scenario, including a preliminary invasion of carbonate-silicate melt into depleted harzburgites in the lower parts of the lithosphere and subsequent very low degree melting.     

Thermodynamic controls on element partitioning between titanomagnetite and andesitic–dacitic silicate melts

Titanomagnetite–melt partitioning of Mg, Mn, Al, Ti, Sc, V, Co, Ni, Cu, Zn, Ga, Zr, Nb, Mo, Hf and Ta was investigated experimentally as a function of oxygen fugacity (fO₂) and temperature (T) in an andesitic–dacitic bulk-chemical compositional range. In these bulk systems, at constant T, there are strong increases in the titanomagnetite–melt partitioning of the divalent cations (Mg²⁺, Mn²⁺, Co²⁺, Ni²⁺, Zn²⁺) and Cu²⁺/Cu⁺ with increasing fO₂ between 0.2 and 3.7 log units above the fayalite–magnetite–quartz buffer. This is attributed to a coupling between magnetite crystallisation and melt composition. Although melt structure has been invoked to explain the patterns of mineral–melt partitioning of divalent cations, a more rigorous justification of magnetite–melt partitioning can be derived from thermodynamic principles, which accounts for much of the supposed influence ascribed to melt structure. The presence of magnetite-rich spinel in equilibrium with melt over a range of fO₂ implies a reciprocal relationship between a(Fe²⁺O) and a(Fe³⁺O_1.5) in the melt. We show that this relationship accounts for the observed dependence of titanomagnetite–melt partitioning of divalent cations with fO₂ in magnetite-rich spinel. As a result of this, titanomagnetite–melt partitioning of divalent cations is indirectly sensitive to changes in fO₂ in silicic, but less so in mafic bulk systems.     

Devonian volcanics in the Voronezh Crystalline Massif,East European Platform: Evolution of the melts and characteristics of crustal contamination

The rift system of the Dnieper–Donets trough (DDT) is the largest magmatic area in the East European Platform. Basalts of the Voronezh Crystalline Massif (VCM) are spatially constrained to the eastern shoulder of DDT and occur far away (at a distance of 150–200 km) from the rift axis. The rocks are hosted in the Paleoproterozoic Vorontsovskii terrane and are grouped in a few fields within an area of 200 × 100 km. Basalts at most of the fields were erupted at the boundary between mid- and late Frasnian time in the Late Devonian and can be studied exclusively in core material recovered by boreholes. Newly obtained mineralogical, geochemical, and isotopic-geochemical data show that the Devonian volcanic rocks in VCM are tholeiites (Bas) and basaltic andesites/andesites (ABas). The geological section was examined most exhaustively in the Novokhopersk area (Borehole 175). The bottom of the vertical section is made up of basaltic andesites and andesites (ABas) (thickness 34 m), which rest on an eroded surface of late Frasnian sandstones. The rocks are overlain by a thin (8 m thick) tholeiite sheet (Bas2), which gives way to ABas (13 m) upsection. The top portion of the vertical section is composed of tholeiites with petrography and geochemical evidence of crustal contamination (Bas1) (apparent thickness 5 m). Geochemical parameters of Bas (mg# 42–52 at SiO₂ 47–51 wt %) are typical of continental tholeiites. The rocks have (⁸⁷Sr/⁸⁶Sr)₀ = 0.7043–0.7048 and ε_Nd(372) = 2.1–3.5. ABas (mg# 28–31 at SiO₂ 52–60 wt %) are enriched in Y (48 ppm), and possess Nb/Nb* = 0.7–0.8 and high Zn/Cu = 1.9–2.3. The rocks have (⁸⁷Sr/⁸⁶Sr)₀ = 0.7034–0.7048 and Nd–ε_Nd(372) = 0.1. Some portions of Bas melts assimilated the upper crustal material, which was similar to Paleoproterozoic granites, and ABas are contaminated in the lower crust with derivatives of Early Cambrian alkaline mafic melts. Petrographic data and simulations of fractional crystallization show that olivine and high-Mg clinopyroxene were the first to crystallize from the melt. After this, clinopyroxene and plagioclase simultaneously crystallized at temperatures from 1070 to 1020°C in Bas and at 1040–900°C at f _O2 below QFM + 1 in ABas. The source of ABas was likely a network of hornblendite or amphibole pyroxenite veins in peridotite in the lithospheric mantle or amphibolized peridotite cumulate in an underplating zone; and Bas were derived from spinel peridotites of an asthenospheric diapir. The setting of the basalts relative to the DDT axis and the asymmetric zoning of magmatism in DDT (with kimberlites and other deep rocks constrained to the western shoulder and tholeiites occurring in the axial part of the rift and its eastern shoulder) can be explained by the model of an asymmetric rift structure with a translithospheric detachment gently dipping beneath VCM.     

Shear heating by translational brittle reverse faulting along a single,sharp and straight fault plane

Shear heating by reverse faulting on a sharp straight fault plane is modelled. Increase in temperature (T _i ) of faulted hangingwall and footwall blocks by frictional/shear heating for planar rough reverse faults is proportional to the coefficient of friction (μ), density and thickness of the hangingwall block (ρ). T _i increases as movement progresses with time. Thermal conductivity (K _i ) and thermal diffusivity (\(k_{\mathrm {i}}^{\prime }\)) of faulted blocks govern T _i but they do not bear simple relation. T _i is significant only near the fault plane. If the lithology is dry and faulting brings adjacent hangingwall and footwall blocks of the same lithology in contact, those blocks undergo the same rate of increase in shear heating per unit area per unit time.     

CO<Subscript>2</Subscript> content of andesitic melts at graphite-saturated upper mantle conditions with implications for redox state of oceanic basalt source regions and remobilization of reduced carbon from subducted eclogite

We have performed experiments to determine the effects of pressure, temperature and oxygen fugacity on the CO₂ contents in nominally anhydrous andesitic melts at graphite saturation. The andesite composition was specifically chosen to match a low-degree partial melt composition that is generated from MORB-like eclogite in the convective, oceanic upper mantle. Experiments were performed at 1–3 GPa, 1375–1550?°C, and fO₂ of FMQ ?3.2 to FMQ ?2.3 and the resulting experimental glasses were analyzed for CO₂ and H₂O contents using FTIR and SIMS. Experimental results were used to develop a thermodynamic model to predict CO₂ content of nominally anhydrous andesitic melts at graphite saturation. Fitting of experimental data returned thermodynamic parameters for dissolution of CO₂ as molecular CO₂: ln(K ⁰) = ?21.79?±?0.04, ΔV ⁰?=?32.91?±?0.65 cm³mol^?1, ΔH ⁰?=?107?±?21 kJ mol^?1, and dissolution of CO₂ as CO₃ ^2?: ln(K ⁰ ) = ?21.38?±?0.08, ΔV ⁰?=?30.66?±?1.33 cm³ mol^?1, ΔH ⁰?=?42?±?37 kJ mol^?1, where K ⁰ is the equilibrium constant at some reference pressure and temperature, ΔV ⁰ is the volume change of reaction, and ΔH ⁰ is the enthalpy change of reaction. The thermodynamic model was used along with trace element partition coefficients to calculate the CO₂ contents and CO₂/Nb ratios resulting from the mixing of a depleted MORB and the partial melt of a graphite-saturated eclogite. Comparison with natural MORB and OIB data suggests that the CO₂ contents and CO₂/Nb ratios of CO₂-enriched oceanic basalts cannot be produced by mixing with partial melts of graphite-saturated eclogite. Instead, they must be produced by melting of a source containing carbonate. This result places a lower bound on the oxygen fugacity for the source region of these CO₂-enriched basalts, and suggests that fO₂ measurements made on cratonic xenoliths may not be applicable to the convecting upper mantle. CO₂-depleted basalts, on the other hand, are consistent with mixing between depleted MORB and partial melts of a graphite-saturated eclogite. Furthermore, calculations suggest that eclogite can remain saturated in graphite in the convecting upper mantle, acting as a reservoir for C.     

Physicochemical model for the crystallization of rocks of the calc-alkaline series

The Al-rich region of the CaO-MgO-Al₂O₃-SiO₂ system was experimentally studied at pressures of 1.0–2.8 GPa and temperatures of 1300–1535°C. The slopes of the lines of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx + Ga + Cor + Sp and the compositions of the phases involved in these reactions are determined. The results are utilized in the topological analysis of the aluminous region of the CaO-MgO-Al₂O₃-SiO₂ system. On this basis, the principal structure of the phase diagram is analyzed, and a phase diagram is constructed for the junction region of the quaternary system and the CaO-Al₂O₃-SiO₂ ternary system. A continuous series of the monovariant eutectic: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx + (Ga) + An + Sp, L = Cpx + Cor + (Ga) + An, L = An + Ga + Cpx + Ky and L = Ga + Cpx + Ky + Qz is examined within the pressure range from atmospheric to 3.0 GPa and higher. Analogous “telescoped” eutectic series are of fundamental character for interpreting the evolution of magmatic melts. A physicochemical model is suggested for the evolution of magmatic melts that produce rocks of the calc-alkaline series, with this model underlain by the fact that a change in the composition of magmatic melt at a pressure decrease should correspond to the minimum melting temperatures, i.e., to melts in the fundamental series of eutectic reactions. The comparison of our physicochemical model and rocks of the calc-alkaline series shows that the compositions of rocks of the calc-alkaline series are close to the compositions determined for the eutectic equilibria, and the mineralogical composition of xenoliths and megacrysts in volcanic and dike varieties of the rocks are similar to the subsolidus phases of the established fundamental eutectic system.     

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.     

Logarithmic density range and the percentage of stars in the cores of various subsystems of the globular clusters M56, M12, NGC 6535, NGC 6171, NGC 5466, and M92

Lower limits for the percentages of stars with various luminosities in the cores of six globular clusters are derived using stellar spatial density distributions f(r) to deep limiting B magnitudes obtained earlier. For NGC 6535 and NGC 5466, the logarithmic density range and Kholopov parameters D_f and D_r are also determined. These two parameters are correlated with the mean masses of stars of various subsystems and the total mass (number) of stars in the cluster.     

Analytical expressions for three-phase generalized relative permeabilities in water- and oil-wet capillary tubes

We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K _{i j,r} , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K _{i j,r} reduce to a set of nine scalar quantities, K _{i j,r} . Our results show that K _{i j,r} of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K _{i j,r} of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K _{i j,r} with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases.     

Dependence of the absorption-line profiles and radial-velocity curve of the optical star in an X-ray binary on the orbital inclination and component-mass ratio

Theoretical absorption-line profiles and radial-velocity curves for tidally deformed optical stars in X-ray binary systems are calculated assuming LTE. The variations in the profile shapes and radial-velocity curve of the optical star are analyzed as a function of the orbital inclination of the X-ray binary system. The dependence of the shape of the radial-velocity curve on the orbital inclination i increases with decreasing component-mass ratio q = m _x /m _v . The integrated line profiles and radial-velocity curves of the optical star are calculated for the Cyg X-1 binary, which are then used to estimate the orbital inclination and mass of the relativistic object: i < 43° andm _x = 8.2–12.8 M_⊙. These estimates are in good agreement with earlier results of fitting the radial-velocity curve of Cyg X-1 using a simpler model (i < 45°, m _x = 9.0–13.2 M_⊙).     

Simulation of the geochemical structure of the Ioko-Dovyren layered intrusion,northwestern Baikal area

The processes of differentiation in the magmatic chamber of the Ioko-Dovyren layered dunite-troctolite-gabbro-gabbronorite massif were simulated using the COMAGMAT-3.5 software package, which is based on the convection-accumulation model for the crystallization of magmatic intrusions. The initial magma composition was assumed to be equal to the weighted mean composition of the rocks composing the intrusion (wt %: 43.92 SiO₂, 9.72 Al₂O₃, 10.53 FeO, 27.88 MgO, 6.99 CaO, 0.59 Na₂O, 0.07 K₂O, and 0.11 TiO₂). The results obtained by simulating the crystallization of this composition within a pressure range of 0–10 kbar indicate that the crystallization sequence determined for the rocks Ol + Chr → Ol+ Pl+ Chr → Ol + Pl+ CPx → ± Ol + Pl+ CPx + LowCaPx in an anhydrous system takes place under pressures of 0–2 kbar. A series of simulations for a system closed with respect to oxygen yielded estimates for the phase and chemical composition of the emplaced magma and the parameters of the optimum model, which reproduces accurately enough the geochemical structure of the Ioko-Dovyren intrusion: the naturally occurring distributions of minerals and components in its vertical section. The correlation coefficients between the concentrations of oxides determined in the rocks and calculated within the model are \(r_{MgO,Al_2 O_3 ,CaO} \) ≥ 0.9 and \(r_{FeO,SiO_2 ,Na_2 O} \) ≥ 0.6. The simulated phase composition of the magma during its emplacement corresponded to melt + olivine (Fo ₈₉). The crystallinity of the parental magma was determined to have been equal to approximately 40 vol % at an assumed cumulus density of 90% near the lower contact and 70% near the upper one. The temperature of the magma during its emplacement was close to 1340°C at a pressure of 1 kbar. In the model, plagioclase and clinopyroxene appear on the liquidus at T?1255°C at T?1210°C, respectively, and the crystallization sequence of cumulus minerals corresponds to that observed in nature. The liquid phase (melt) of the parental magma during its emplacement had the following composition (wt %): 45.95 SiO₂, 15.93 Al₂ O₃, 14.49 MgO, 10.88 FeO, 11.46 CaO, 0.97 Na₂O, 0.11 K₂O, and 0.18 TiO₂. Our results confirm the plausibility of the hypothesis that the inner structure of the Ioko-Dovyren intrusion was formed by the emplacement and differentiation of a single magma portion with no less than 40 vol % crystallinity.     

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.     

Mineralogy and geochemistry of granitoids from Kinnaur region,Himachal Higher Himalaya,India: Implication on the nature of felsic magmatism in the collision tectonics

Felsic magmatism in the southern part of Himachal Higher Himalaya is constituted by Neoproterozoic granite gneiss (GGn), Early Palaeozoic granitoids (EPG) and Tertiary tourmaline-bearing leucogranite (TLg). Magnetic susceptibility values (<3 ×10^?3 SI), molar Al₂ O ₃/(CaO + Na₂ O + K ₂O) (≥1.1), mineral assemblage (bt–ms–pl–kf–qtz ± tur ± ap), and the presence of normative corundum relate these granitoids to peraluminous S-type, ilmenite series (reduced type) granites formed in a syncollisional tectonic setting. Plagioclase from GGn (An₁₀–An₃₁) and EPG (An₁₅–An₃₃) represents oligoclase to andesine and TLg (An₂–An₁₅) represents albite to oligoclase, whereas compositional ranges of K-feldspar are more-or-less similar (Or₈₈ to Or₉₅ in GGn, Or₈₆ to Or₉₇ in EPG and Or₈₇ to Or₉₄ in TLg). Biotites in GGn (Mg/Mg + Fe^t= 0.34–0.45), EPG (Mg/Mg + Fe^t= 0.27–0.47), and TLg (Mg/Mg + Fe^t= 0.25–0.30) are ferribiotites enriched in siderophyllite, which stabilised between FMQ and HM buffers and are characterised by dominant 3Fe\(\rightleftharpoons \)2Al, 3Mg\(\rightleftharpoons \)2Al substitutions typical of peraluminous (S-type), reducing felsic melts. Muscovite in GGn (Mg/Mg + Fe^t=0.58–0.66), EPG (Mg/Mg + Fe^t=0.31?0.59), and TLg (Mg/Mg + Fe^t=0.29–0.42) represent celadonite and paragonite solid solutions, and the tourmaline from EPG and TLg belongs to the schorl-elbaite series, which are characteristics of peraluminous, Li-poor, biotite-tourmaline granites. Geochemical features reveal that the GGn and EPG precursor melts were most likely derived from melting of biotite-rich metapelite and metagraywacke sources, whereas TLg melt appears to have formed from biotite-muscovite rich metapelite and metagraywacke sources. Major and trace elements modelling suggest that the GGn, EPG and TLg parental melts have experienced low degrees (～13, ～17 and ～13%, respectively) of kf–pl–bt fractionation, respectively, subsequent to partial melting. The GGn and EPG melts are the results of a pre-Himalayan, syn-collisional Pan-African felsic magmatic event, whereas the TLg is a magmatic product of Himalayan collision tectonics.