A new Jurassic cow shark (Chondrichthyes,Hexanchiformes) with comments on Jurassic hexanchiform systematics

A new taxon, ?Crassodontidanus gen. nov. of Hexanchiformes (cow sharks) from the Jurassic of Germany is described. It is characterized by peculiar teeth combining apomorphic (serrated mesial cutting edge of the main cusp) and plesiomorphic features (deep root with convex mesial and distal margins in labial and lingual views; protruding lingual root bulge). This character combination readily distinguishes members of the new taxon from all other known extant (Heptranchias, Hexanchus, Notorynchus) and extinct (?Gladioserratus, ?Notidanodon, ?Notidanoides, ?Pachyhexanchus, ?Paraheptranchias, ?Weltonia) hexanchiforms. Currently, two species, ?C. serratus (type species; Late Jurassic, Late Kimmeridgian of Nusplingen, South Germany) and ?C. wiedenrothi (Early Jurassic, Early Pliensbachian of Gretenberg (Hanover), North Germany) are assigned to this taxon. ?Crassodontidanus gen. nov. is member of ?Crassonotidae fam. nov. and sister to ?Notidanoides Maisey, 1986 and ?Pachyhexanchus Cappetta, 1990. We consider ?Notidanus amalthei Oppel, 1854 from the Pliensbachian of South Germany, ?Notidanus insignis Seguenza, 1887 from the Oxfordian of Sicily (Italy) and ?Notidanus wagneri Agassiz, 1843 from the Early Tithonian of Solnhofen (South Germany) nomina dubia and nomina nuda, respectively. The family ?Crassonotidae comprises plesiomorphic hexanchiforms ranging from the Sinemurian (Early Jurassic) to the Hauterivian (Early Cretaceous).     

Experimental anatexis and genesis of migmatites: A reply

Recentlyvon Platen applied the results of his laboratory experiments to a migmatite studied byHärme. Some comments are presented upon that re-interpretation.     

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

The phonon dispersion and thermodynamic properties of pyrope (\(\hbox {Mg}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}\)) and grossular (\(\hbox {Ca}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}\) ) have been computed by using an ab initio quantum mechanical approach, an all-electron variational Gaussian-type basis set and the B3LYP hybrid functional, as implemented in the Crystal program. Dispersion effects in the phonon bands have been simulated by using supercells of increasing size, containing 80, 160, 320, 640, 1280 and 2160 atoms, corresponding to 1, 2, 4, 8, 16 and 27 \(\mathbf {k}\) points in the first Brillouin zone. Phonon band structures, density of states and corresponding inelastic neutron scattering spectra are reported. Full convergence of the various thermodynamic properties, in particular entropy (S) and specific heat at constant volume (\(C_\mathrm{{V}}\)), with the number of \(\mathbf {k}\) points is achieved with 27 \(\mathbf {k}\) points. The very regular behavior of the S(T) and \(C_\mathrm{{V}}(T)\) curves as a function of the number of \(\mathbf {k}\) points, determined by high numerical stability of the code, permits extrapolation to an infinite number of \(\mathbf {k}\) points. The limiting value differs from the 27-\(\mathbf {k}\) case by only 0.40 % at 100 K for S (the difference decreasing to 0.11 % at 1000 K) and by 0.29 % (0.05 % at 1000 K) for \(C_\mathrm{{V}}\). The agreement with the experimental data is rather satisfactory. We also address the problem of the relative entropy of pyrope and grossular, a still debated question. Our lattice dynamical calculations correctly describe the larger entropy of pyrope than grossular by taking into account merely vibrational contributions and without invoking “static disorder” of the Mg ions in dodecahedral sites. However, as the computed entropy difference is found to be larger than the experimental one by a factor of 2–3, present calculations cannot exclude possible thermally induced structural changes, which could lead to further conformational contributions to the entropy.     

A rock fall of the north Zhongtiao Shan fault and the Yongji earthquake in 793, Shanxi Province,North China

Earthquake is the main driving factor of landslides, and a large number of empirical formulas for seismic parameters have been proposed. This article studies a rock avalanche triggered by a paleoearthquake and two trial trenches in Yongji, Shanxi Province. Six quartz samples were collected from different parts on the top of the boulder, and the youngest ¹⁰Be exposure age is 1173 ± 123 years, which is considered as the occurrence time of the rock fall. The trenches excavated near the boulder infer that there was an earthquake between 2000 ± 110 and 465 ± 45 cal a bp in the north Zhongtiao Shan (NZS) fault with a maximum vertical displacement of 1.5 m and the surface rupture length (SRL) of ~35 km corresponding to a magnitude (M _S) of 6.70 ± 0.12 based on the displacement. Taking into account the occurrence time and minimum magnitude triggering the rock fall, the latest paleoearthquake revealed by trenches may be the forcing factor. Furthermore, according to historical records of Yongji, the earthquake of magnitude 6 in ad 793 is in consistency with the occurrence time and magnitude of the earthquake triggering the landslide. Therefore, the rock fall is related to the paleoearthquake revealed by the trenches, which may be the 793 Yongji earthquake.     

The geochemistry of pyroxenes from the lower layered series of the Jimberlana intrusion,Western Australia

Most of the Al³⁺ entering the pyroxenes does so by substituting for tetrahedral Si⁴⁺. This creates a charge imbalance that requires the simultaneous entry of Cr³⁺, Ti⁴⁺, Fe³⁺ or Al³⁺ into octahedral sites. Cr³⁺, because of its high crystal field stabilisation energy (CFSE), is the most important of these elements to enter the early-formed pyrosenes but it is replaced by Ti⁴⁺ later in fractionation when the Cr³⁺ content of the melt becomes depleted. The dependence of Cr³⁺ and Ti⁴⁺ on charge balance controls their partition between coexisting pyroxenes and olivines. Ca-rich pyroxene which contains more Al³⁺ than Ca-poor pyroxene also has more Ti⁴⁺ and Cr³⁺ whereas olivine, which contains negligible Al³⁺, has low Cr³⁺ and Ti⁴⁺. The Al³⁺ content of pyroxenes is influenced by changes in P, T, \(a_{{\text{SiO}}_{\text{2}} }\) and \(a_{{\text{Al}}_{\text{2}} {\text{O}}_{\text{3}} }\) of the magma and by the nature of the ion providing charge balance in the octahedral site. Of these \(a_{{\text{SiO}}_{\text{2}} }\) is dominant and variations in the Al³⁺ content of the Jimberlana pyroxenes correspond closely with the expected changes in the \(a_{{\text{SiO}}_{\text{2}} }\) of the melt. The substitution of divalent ions, such as Mn²⁺ and Ni²⁺, in the pyroxene lattice is by replacement of Fe²⁺ or Mg²⁺ in the octahedral M ₃ and M ₂ sites and is therefore independent of charge balance. If there are no size restrictions, the principal factor to be considered is the CFSE the ion receives in octahedral co-ordination. Ni²⁺, which receives a high CFSE, partitions strongly between the early-formed pyroxenes and olivines and therefore becomes depleted in the magma with fractionation. Conversely Mn²⁺, which receives zero CFSE, concentrates in the magma with fractionation and becomes a more important substitute in the later-formed pyroxenes. Its geochemical behaviour is controlled by its size. The narrow miscibility gap of the Jimberlana pyroxenes and the high En content of the Ca-poor pyroxenes at the bronzite pigeonite changeover suggest that these pyroxenes crystallised at a higher temperature than pyroxenes of comparable composition from other intrusions.     

EPR study of chromium-doped forsterite crystals: Cr3+(M1) with associated trivalent ions Al3+ and Sc3+

Electron paramagnetic resonance (EPR) study of single crystals of forsterite co-doped with chromium and scandium has revealed, apart from the known paramagnetic centers Cr³⁺(M1) and Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2) (Ryabov in Phys Chem Miner 38:177–184, 2011), a new center Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ formed by a Cr³⁺ ion substituting for Mg²⁺ at the M1 structural position with a nearest-neighbor Mg²⁺ vacancy at the M2 position and a Sc³⁺ ion presumably at the nearest-neighbor M1 position. For this center, the conventional zero-field splitting parameters D and E and the principal g values have been determined as follows: D?=?33,172(29) MHz, E?=?8,482(13) MHz, g?=?[1.9808(2), 1.9778(2), 1.9739(2)]. The center has been compared with the known ion pair Cr³⁺(M1)–Al³⁺ (Bershov et al. in Phys Chem Miner 9:95–101, 1983), for which the refined EPR data have been obtained. Based on these data, the known sharp M1″ line at 13,967?cm^?1 (with the splitting of 1.8?cm^?1), observed in low-temperature luminescence spectra of chromium-doped forsterite crystals (Glynn et al. in J Lumin 48, 49:541–544, 1991), has been ascribed to the Cr³⁺(M1)–Al³⁺ center. It has been found that the concentration of the new center increases from 0 up to 4.4?×?10¹⁵?mg^?1, whereas that of the Cr³⁺(M1) and Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2) centers quickly decreases from 7.4?×?10¹⁵?mg^?1 down to 3?×?10¹⁵?mg^?1 and from 2.7?×?10¹⁵?mg^?1 down to 0.5?×?10¹⁵?mg^?1, i.e., by a factor of 2.5 and 5.4, respectively, with an increase of the Sc content from 0 up to 0.22 wt?% (at the same Cr content 0.25 wt?%) in the melt. When the Sc content exceeds that of Cr, the concentration of the new center decreases most likely due to the formation of the Sc³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ complex instead of the Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ center. The formation of such ordered neutral complex is in agreement with the experimental results, concerning the incorporation of Sc into olivine, recently obtained by Grant and Wood (Geochim Cosmochim Acta 74:2412–2428, 2010).     

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_⊙.     

Competing effects of crystal chemistry and silicate melt composition on trace element behavior in magmatic systems: insights from crystal/silicate melt partitioning of the REE,HFSE, Sn,In, Ga,Ba, Pt and Rh

We present new partition coefficients for the REE, HFSE, Sn, In, Ga, Ba, Pt and Rh between clinopyroxene, olivine and basaltic melt as a function of crystal chemistry and melt composition at temperatures of 1190–1300 °C and 1-bar pressure. Two components, namely \(\mathrm {Al_2O_3}\) and \(\mathrm {Na_2O}\), were chosen to be investigated since they are known to affect the structure of silicate melts and especially clinopyroxene crystal chemistry. The amount of \(^{[4]}\mathrm{Al}\) in clinopyroxene will result in an increase of \(D_i^\mathrm{{cpx/melt}}\) even after applying a correction factor to account for the effect of melt polymerization. Moreover, the positive correlation between \(^{[4]}\mathrm{Al}\) and \(D_i^\mathrm{{cpx/melt}}\) is not restricted to the REE, but also applies for Sn, Ga, In, and Ba. The addition of up to 2.6 wt% \(\mathrm {Na_2O}\) to the silicate melt universally increases the \(D_i^\mathrm{{cpx/melt}}\) without any concomitant change in crystal chemistry or a significant effect in melt polymerization. This compositional effect is likely due to the ability of Na to break REE–Al complexes in the melt. Our results emphasize the importance of considering all variables that affect the behavior of trace elements in magmatic systems before applying the lattice strain model and derive meaningful results for the changes in the parameters of the crystallographic sites.     

Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the I\bar 1 \leftrightarrow P\bar 1 phase transition in anorthite

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T _c ^* =510 K. The spontaneous strain couples to the order parameter Q° as x _i∝S _xQ ⁱ Q°² with S _xQ ¹ =4.166×10^?3, S _xQ ² =0.771×10^?3, S _xQ ³ =?7.223×10^?3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T _c ^* , S _xQ ⁱ and β is predicted for Al/Si disordered anorthite.     

Reappraisal of the metamorphic facies concept

Eskola's concept of metamorphic facies, now 50 years old, is reappraised in the light of current knowledge and usage among petrologists. Facies should be defined solely in terms of observable geologic criteria. LikeEskola, we continue to view each facies as a set of mineral assemblages that approximate equilibrium within a definite range of temperature; but this is inference and must be excluded from the definition of facies. Mutual boundaries between facies are transitional. Division into subfacies has proved unacceptable to many writers, and has led to confusion in the physical interpretation of metamorphic parageneses. We propose henceforth not to recognize subfacies. Eleven facies are recognized in this paper, and their terminology has been adapted as nearly as possible to current general usage:

1. A.
   Low-pressure facies commonly but not exclusively of contact metamorphism. In order of increasing temperature:

   1. (1)
      Albite-epidote-hornfels.     
      
      

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_⊙.     

Testing and evaluation of strength and deformation behaviour of jointed rocks

The objective of the paper is to derive the strength and modulus properties of rockmass as a function of intact rock strength and joint factor. The joint factor reflects the combined effect of joint frequency, joint inclination and joint strength. A study for the strength and deformation characteristics of jointed rock is done by conducting standard laboratory tests on cylindrical specimens of plaster of Paris after introducing artificial joints. The specimens having one to four joints at different inclinations which vary from 0° to 90° were tested at different confining conditions. The test results were examined to understand the effect of joint frequency and joint inclination on the strength and deformation behaviour of rock mass. Empirical correlations were developed for prediction of the uniaxial compressive strength and elastic modulus of jointed rocks. Results are compared with the earlier work on jointed specimens covering a wide variety of rocks. So, knowing the intact rock properties and the joint factor, the jointed rock properties can be estimated. These relations can be used for developing an equivalent continuum model for rock mass for handling boundary value problems. A failure criterion as proposed by Ramamurthy (1993 Ramamurthy, T. 1993. “Strength and modulus response of anisotropic rocks”. In Comprehensive rock engineering, Edited by: Hudson, J.A. Vol. 1, 313–329. Oxford: Pergamon Press.  [Google Scholar]) has been validated from these experimental results.     

On the nonstoichiometry and point defects of olivine

This paper presents the point-defect thermodynamics for fayalite and olivine solid solutions (Fe _x Mg_1?x )₂SiO₄. By means of thermogravimetry, the metal-to-oxygen ratio of these silicates has been determined as a function of oxygen potential, compositionx and temperature. Experiments were performed in the range of 1,000° C≦T≦1,280° C and 0.2≦x≦1.0. It is found that V _Me ^″ , Fe _Me ^· and the associate {Fe′ _Si ^′ Fe _Me ^· } are the majority defects. With this knowledge it is possible to calculate the nonstoichiometry at given temperature as a function of \(p_{O_2 } \) and \(a_{SiO_2 } \) . The cation vacancy concentration shows a \(p_{O_2 }^{1/5} \) -dependence (forx≧0.2) and increases at givenT and \(p_{O_2 } \) almost exponentially with compositionx. In the composition range studied here, the silicates show an oxygen excess, and FeO is more soluble in the olivine than SiO₂.     

Salinization of porewater in a multiple aquitard-aquifer system in Jiangsu coastal plain,China

Chemical and isotopic compositions were analyzed in porewater squeezed from a clayey aquitard in Jiangsu coastal plain, eastern China, to interpret the salinity origin, chemical evolution and water-mass mixing process. A strong geochemical fingerprint was obtained with an aligned Cl/Br ratio of 154 in the salinized aquitard porewater over a wide Cl^? concentration range (396–9,720 mg/L), indicating that porewater salinity is likely derived from a mixing with old brine with a proportion of less than 20%. Very small contributions of brine exerted limited effects on water stable isotopes. The relationships between porewater δ¹⁸O and δD indicate that shallow and intermediate porewaters could be original seawater and were subsequently diluted with modern meteoric water, whereas deep porewaters with depleted stable isotopic values were probably recharged during a cooler period and modified by evaporation and seawater infiltration. The cation–Cl relationship and mineralogy of associated strata indicate that porewater has been chemically modified by silicate weathering and ion-exchange reactions. ⁸⁷Sr/⁸⁶Sr ratios of 0.7094–0.7112 further confirm the input source of silicate minerals. Numerical simulations were used to evaluate the long-term salinity evolution of the deep porewater. The alternations of boundary conditions (i.e., the third aquifer mixed with brine at approximately 70 ka BP, followed by recharge of glacial meltwater at 20–25 ka BP, and then mixing with Holocene seawater at 7–10 ka BP) are responsible for the shift in porewater salinity. These timeframes correspond with the results of previous studies on ancient marine transgression-regression in Jiangsu coastal plain.     

Interdiffusion of NaSi—CaAl in peristerite

The ‘average’ interdiffusion coefficient ( \(\bar D\) ) for NaSi—CaAl exchange in plagioclase for the interval from An₀ to An₂₆ was estimated from experimentally determined homogenization times for peristerite exsolution lamellae. The average spacing between adjacent (unlike) lamellae is 554±77 Å. Dry heating in air at 1,100°C for 98 days produced no change in the exsolution microstructure; thus \(\bar D\) (dry)<10^?17 cm²/s. This limit is consistent with the recently reported ‘average’ \(\bar D\) (dry) values for the Huttenlocher interval (An_70–90) at this temperature. At 1.5 GPa with about 0.2 weight percent water added the ‘average’ diffusion coefficient from 1,100°C to 900°C is given by: \(\bar D\) (wet)=18 _?15 ⁺¹⁰⁸ (cm²/s) exp (?97±5 (kcal/mol)/RT), where R is the gas constant, and T is °K. This \(\bar D\) (wet) at 1,100°C is more than three orders of magnitude greater than \(\bar D\) (dry) for Na- and Ca-rich plagioclases.     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

Fitting matrix-valued variogram models by simultaneous diagonalization (Part I: Theory)

Suppose that ¯(x₁),...,¯Z(x_n). are observations of vector-valued random function ¯(x). In the isotropic situation, the sample variogram γ^*(h) for a given lag h is $$\bar \gamma ^ * (h) = \frac{1}{{2N(h)}}\mathop \sum \limits_{s(h)} (\overline Z (x_1 ) - \overline Z (x_1 )) \overline {(Z} (x_1 ) - \overline Z (x_1 ))^T $$ where s(h) is a set of paired points with distance h and N(h) is the number of pairs in s(h).. For a selection of lags h₁, h₂, .... h_k such that N (h₁) > O. we obtain a ktuple of (semi) positive definite matrices $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ . We want to determine an orthonormal matrix B which simultaneously diagonalizes the $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ or nearly diagonalizes them in the sense that the sum of squares of offdiagonal elements is small compared to the sum of squares of diagonal elements. If such a B exists, we linearly transform $\overline Z (x)$ by $\overline Y (x) = B\overline Z (x)$ . Then, the resulting vector function $\overline Y (x)$ has less spatial correlation among its components than $\overline Z (x)$ does. The components of $\overline Y (x)$ with little contribution to the variogram structure may be dropped, and small crossvariograms fitted by straightlines. Variogram models obtained by this scheme preserve the negative definiteness property of variograms (in the matrix-valued function sense). A simplified analysis and computation in cokriging can be carried out. The principles of this scheme arc presented in this paper.     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

Wolf-Rayet stars and relativistic objects: Distinctions between the mass distributions in close binary systems

The observed properties of Wolf-Rayet stars and relativistic objects in close binary systems are analyzed. The final masses M _CO ^f for the carbon-oxygen cores of WR stars in WR + O binaries are calculated taking into account the radial loss of matter via stellar wind, which depends on the mass of the star. The analysis includes new data on the clumpy structure of WR winds, which appreciably decreases the required mass-loss rates $\dot M_{WR}$ for the WR stars. The masses M _CO ^f lie in the range (1–2)M _⊙–(20–44)M _⊙ and have a continuous distribution. The masses of the relativistic objects M _x are 1–20M _⊙ and have a bimodal distribution: the mean masses for neutron stars and black holes are 1.35 ± 0.15M _⊙ and 8–10M _⊙, respectively, with a gap from 2–4M _⊙ in which no neutron stars or black holes are observed in close binaries. The mean final CO-core mass is $\overline M _{CO}^f = 7.4 - 10.3M_ \odot$ , close to the mean mass for the black holes. This suggests that it is not only the mass of the progenitor that determines the nature of the relativistic object, but other parameters as well-rotation, magnetic field, etc. One SB1R Wolf-Rayet binary and 11 suspected WR + C binaries that may have low-mass companions (main-sequence or subgiant M-A stars) are identified; these could be the progenitors of low-mass X-ray binaries with neutron stars and black holes.     

High-temperature 29Si MAS NMR spectroscopy of anorthite (CaAl2Si2O8) and its P\bar 1-I\bar 1structural phase transition

We present ²⁹Si MAS NMR data for a well-ordered natural anorthite, obtained in situ at temperatures of from 25 to 500° C, which follow the changes in the aluminosilicate framework through the P $\bar 1$ -I $\bar 1$ structural phase transition. Pairs of peaks due to sites offset by approximately 1/2 [111] converge through the P $\bar 1$ phase and only four peaks are present above about 241° C. The variation of the peak positions with temperature and correlations based on structural data for the P $\bar 1$ and I $\bar 1$ phases allow assignment of all the MAS-NMR peaks to crystallographic sites. A Landau-type analysis gives an expression that relates the separation of pairs of con verging peaks to the local order parameter for the P $\bar 1$ -I $\bar 1$ transition, from which we determine its temperature dependence. Data for the best-constrained set of peak positions give for the order parameter critical exponent β = 0.27±0.04, consistent with previous results indicating that the P $\bar 1$ -I $\bar 1$ transition in pure anorthite is tricritical. No significant change in the ²⁹Si spin-lattice relaxation rate occurs across the P $\bar 1$ -I $\bar 1$ transition.