Thermochemistry of glasses and liquids in the systems CaMgSi₂O₆-CaAl₂Si₂O₈-NaAlSi₃O₈, SiO₂-CaAl₂Si₂O₈-NaAlSi₃O₈ and SiO₂-Al₂O₃-CaO-Na₂O     

A. Navrotsky  R. Hon  D.F. Weill  D.J. Henry 《Geochimica et cosmochimica acta》1980,44(10):1409-1423

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.  相似文献   

Heat capacity and entropy of low structural state plagioclases     

A. Benisek  E. Dachs  M. A. Carpenter 《Physics and Chemistry of Minerals》2013,40(2):167-173

The heat capacity of 11 different compositions of the low structural state plagioclase binary was measured between 5 and 773 K. The results are compared to those obtained from synthetic high structural state samples investigated in a previous study and obtained from a heat-treated natural sample of this study. The heat capacity of anorthite samples with slightly different order parameters shows large differences at ~500 K, where the Ibar1-Pbar1 phase transition occurs, which affects petrological calculations. At T = 298.15 K, the vibrational entropy versus composition behaviour of the low structural state plagioclases is almost ideal, in contrast to the high structural state plagioclases with positive excess vibrational entropies. At higher temperatures, the low structural state plagioclases show a negative deviation from ideal vibrational entropy composition behaviour in the Na-rich region.  相似文献   

Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation     

Ronald E. Cohen 《Physics and Chemistry of Minerals》1986,13(3):183-197

A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si₂O₆)-jadeite (NaAlSi₂O₆) and diopside-CaTs (CaAl₂SiO₆). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other. The calculations show that the random model, in which the configurational entropy is calculated as if atoms on each crystallographic site mix randomly, is appropriate as a first approximation. The excess entropy relative to the random model behaves regularly, is always negative, and becomes more negative as temperature decreases or the ordering energies increase. The excess entropy relative to the random model can be modeled reasonably well with a simple power series, or Margules-type, formulation. In contrast, the excess entropy relative to a molecular model, in which the ideal activity is assumed to be equal to some mole fraction, is irregular, can be positive or negative, and even changes in sign with variations in temperature and composition. The configurational enthalpy is positive at high temperatures, and becomes negative with decreasing temperature or increasing ordering energy. The mixing enthalpy can have non-configurational contributions, in addition to the effective short-range configurational contributions considered explicitly. The pair approximation predicts an ordering transition from C2/c to P2₁/n for CaTs and diopside-CaTs solutions at moderate to low temperatures, respectively. A field where C2/c orders to C2 is also found. A higher order approximation, different relative ordering energies, or quantitative consideration of strain contributions is required to account for the C2/c to P2/n transition in omphacites. There is no justification for molecular models, in which the configurational entropy is calculated as if endmember “molecules” were mixing in the crystal, in either concentrated or dilute solutions. Molecular models do not represent limiting ordered states for coupled solid solutions.  相似文献   

Activity-composition relations in feldspars     

S. K. Saxena  P. H. Ribbe 《Contributions to Mineralogy and Petrology》1972,37(2):131-138

Seck's (1971a) compositional data on coexisting feldspars in the Or-Ab-An ternary at 650° C and 1 kb were used to calculate the activity-composition relations in binary alkali feldspar and binary plagioclase. The energy constants in Guggenheim's expression for excess free energy of mixing are A ₀=3920 and A ₁=657 cal/mole for alkali feldspar, in excellent agreement with values obtained by Thompson and Waldbaum (1969), and 1320 and 373 cal/ mole for plagioclase. Using Orville's (1972) data from ion-exchange experiments between plagioclase and Na—Ca chloride solutions at 700° C and 2 kb, we obtained 967 cal/mole for A ₀ and 715 cal/mole for A ₁ in the plagioclase crystalline solution.Activity-composition relations for plagioclase are interpreted in terms of a continuous, random substitution of CaAl for NaSi across the high structural state plagioclase series. This interpretation is consistent with that obtained from a consideration of lattice parameters.  相似文献   

Plagioclase buoyancy in oceanic basalts: Chemical effects     

Don Elthon 《Geochimica et cosmochimica acta》1984,48(4):753-768

Certain petrological features of oceanic volcanic and plutonic rocks are not completely consistent with previously proposed models of crystal fractionation or magma mixing. For example, Sr is often higher in the differentiated basalts of a suite of aphyric rocks than in the relatively primitive basalts even though the differentiated basalts have apparently been produced by crystallization of large amounts of plagioclase with olivine and clinopyroxene. Additionally, oceanic basalts and gabbroic rocks often contain plagioclase crystals in excess of the appropriate cotectic proportions. Certain differentiated oceanic basaltic glasses and aphyric rocks crystallize plagioclase as the liquidus mineral, which would seem inconsistent with the strongly cotectic nature of the olivine + plagioclase + liquid surface.It is proposed here that plagioclase in mid-ocean ridge magma chambers separates from the basaltic liquid that it crystallizes in at a slower rate than does co-crystallizing olivine or pyroxene. Magma mixing in which a portion of the plagioclase remains suspended in the liquid during crystallization results in much more complex liquid lines of descent in mixed magmas and appears to resolve the apparent discrepancies noted above.  相似文献   

A thermochemical calculation of the pyroxene saturation surface in the system diopside-albite-anorthite     

R Hon  D.J Henry  A Navrotsky  D.F Weill 《Geochimica et cosmochimica acta》1981,45(2):157-161

The pyroxene saturation surface in the system diopside-albite-anorthite may be calculated to ±10°C from thermochemical data over most of its composition range. The thermochemical data used are the experimentally determined enthalpies of mixing of the ternary liquids and the enthalpy of fusion of diopside. These are combined with a mixing model for the configurational entropy in the melt and the activity of CaMgSi₂O₆ in the clinopyroxene, which is less than unity due to departures from CaMgSi₂O₆ stoichiometry. The ‘two-lattice’ melt model appears to work satisfactorily throughout the pyroxene primary phase field but probably needs modification at more anorthite-rich compositions.  相似文献   

Variation of viscosity with temperature and composition in the plagioclase system     

W. Hummel  J. Arndt 《Contributions to Mineralogy and Petrology》1985,90(1):83-92

The viscosities of supercooled melts of 13 different plagioclase compositions have been measured in the range 10¹³–10⁸ dPas with a micro-penetration viscometer. Application of the most common empirical and theoretical viscosity-temperature models to the present data and plagioclase viscosity data available from the literature showed that the configurational entropy theory represents the best approach. Using this theory together with an entropy of mixing term evaluated from a modified two-lattice mixing model, the viscosities of intermediate plagioclase compositions have been calculated as a function of temperature and anorthite content solely from the appropriate data of the end members albite and anorthite. The agreement between experimental and calculated viscosity data is excellent.Dedicated to Professor Wolf von Engelhardt on the occasion of his 75th birthday  相似文献   

Bias in topographic thresholds for gully heads   总被引：1，自引：0，他引：1  

Rossi  M.  Torri  D.  Santi  E. 《Natural Hazards》2015,77(1):51-63

Inter-event time series of seismic activities of Sumatra region with magnitude (m _b  ≥ 4.8) and period spanning over 1973–2012 has been analyzed using the techniques of nonlinear dynamics. The earthquake data were collected from the USGS Web catalog. The rank order statistics of inter-event time series reveal mixed response with distinct breaks in slope suggesting that earthquake dynamics in this region are unstable, but “self-organized.” Comparison of return maps of the data with random, stochastic, and chaotic time records shows quasi-deterministic behavior. We assessed the dimensionality of earthquake-generating mechanism using a nonlinear predictor technique on two-dimensional phase portrait constructed by recurrence time series. The nonlinear forecasting analysis suggests that the earthquake processes in the Sumatra region evolve on a non-random low-dimensional chaotic plane. Further, second-order Kolmogorov entropy “K2” analysis revealed a coherent time structure, indicating quasi-deterministic dynamical pattern. Our result is consistent with “self-organized” processes determined by the internal dynamics, where impulsively derived interdependencies cascade through the tectonic stress generated by plate movement. However, we do not preclude the triggering role of other external processes on the coupled underlying system.  相似文献   

Thermochemical study of glasses in the system NaAlSi₃O₈-KAlSi₃O₈-Si₄O₈ and the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈     

Richard L. Hervig  Alexandra Navrotsky 《Geochimica et cosmochimica acta》1984,48(3):513-522

Enthalpies of solution in 2PbO · B₂O₃ at 981 K have been measured for glasses in the system albite-orthoclase-silica and along the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈. The join KAlSi₃O₈-Si₄O₈ shows zero heat of mixing similar to that found previously for NaAlSi₃O₈-Si₄O₈ glasses. Albite-orthoclase glasses show negative heats of mixing symmetric about Ab₅₀Or₅₀ (W_n = ? 2.4 ± 0.8 kcal). Negative heats of (Na, K) mixing are also found at $\text{Si}\text{(Si + Al)}\text{= 0.6.}$ Ternary excess enthalpies of mixing in the glassy system Ab-Or-4Q are positive but rarely exceed 1 kcal mol^?1.Using earlier studies of the thermodynamic properties of the crystals, the present calorimetric data and the “two-lattice” entropy model, the albite-orthoclase phase diagram is calculated in good agreement with experimental data. Attempts to calculate albite-silica and orthoclase-silica phase diagrams reveal complexities probably related to significant (but unknown) mutual solid solubility between cristobalite and alkali feldspar and to the very small heat and entropy of fusion of SiO₂.  相似文献   

Local structural heterogeneity,mixing behaviour and saturation effects in the grossular–spessartine solid solution     

U.?RodehorstEmail author  M. A.?Carpenter  T. Boffa?Ballaran  C. A.?Geiger 《Physics and Chemistry of Minerals》2004,31(7):387-404

Local structural heterogeneities in crystals of the binary grossular–spessartine solid solution have been analyzed using powder IR absorption spectroscopy. Wavenumber shifts of the highest energy Si–O stretching mode in spectra collected at room temperature are consistent with variations in Si–O bond length from structural data. They show a smaller positive deviation from linearity across the join than is seen for the grossular–pyrope and grossular–almandine binaries. The effective line widths, corr, of three selected wavenumber regions all deviate positively from linear behaviour. An empirical calibration of this excess spectroscopic property, obtained by comparison with calorimetric enthalpy of mixing data, gives an estimate for the symmetric Margules parameter of W^H_spec = 14.4(7) kJ mol^–1 in H^mix = W^H_specX_GrX_Sp. W^H_spec values derived on the same basis for four aluminosilicate garnet solid solutions analyzed by IR spectroscopy vary with V², where V represents the difference in molar volume between the end members of each binary system. Measurements of lattice parameters and IR spectra were made over a range of temperatures for seven samples with different compositions. Positive excess molar volumes of mixing at low temperature (30 K) may be larger than the excess molar volumes at room temperature. The saturation temperatures of the molar volumes show no correlation with composition, however, in contrast with what had been expected on the basis of data for the grossular–pyrope binary. Saturation temperatures for spectroscopic parameters and lattice parameters of samples with compositions Gr15Sp85 and Gr60Sp40 seem to be outliers in all experiments. It is concluded that the data hint at systematic changes in saturation temperatures across the solid solution, with implications for both the excess entropy of mixing and the excess volume of mixing, but more precise data or further sample characterization are needed to prove that this composition dependence is real in garnet solid solutions.  相似文献   

The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables     

Mark S. Ghiorso  Ian S. E. Carmichael  Mark L. Rivers  Richard O. Sack 《Contributions to Mineralogy and Petrology》1983,84(2-3):107-145

The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa₇₅, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities  相似文献   

The description of the primary textures of “Cordilleran” granitic rocks     

David N. Bryon  Michael P. Atherton  Robert H. Hunter  I. Parsons 《Contributions to Mineralogy and Petrology》1994,117(1):66-75

Variation in the primary textures of “Cordilleran” granitic rocks is described relative to three identifiable stages of the crystallisation interval; namely: (1) crystallisation in suspension; (2) growth of a touching crystal framework; (3) interstitial crystallisation. Crystals that initially grow in isolation will start to impinge and form small clusters as crystallisation proceeds and the volume of solid material increases, eventually forming a continuous interconnected crystal framework. Subsequent crystallisation involves solidification of the melt occupying the interstices of the framework, and therefore shows similarities to the way in which the porosity occludes in sedimentary systems. A case study of textural development in Cordilleran granitic rocks from the zoned Linga superunit of the Peruvian Coastal Batholith, reveals that compositional zonation from granodiorite through to syenogranite is accompanied by a systematic variation in the textures, specifically those of the three felsic phases (plagioclase, quartz and alkali feldspar). Plagioclase was the first phase to appear on the liquidus, and was joined by the other two phases as crystallisation proceeded and the melt evolved. The melt fraction at which quartz and alkali feldspar started to crystallise influenced the early growth of plagioclase, and the way in which the texture developed through each stage of the crystallisation interval. The geometry of plagioclase progressively changes from a touching framework of crystals in the granodiorite, to small aggregates or isolated crystals suspended in an equant mosaic of the other felsic phases in the syenogranite. This variation can be explained by an earlier evolution of the melt to the cotectic (i.e. at higher melt fractions) as the rocks become more acidic, and hence a greater contribution of alkali feldspar and quartz to the growth of the framework at the expense of plagioclase and the mafic phases. Textural observations are comparable to the crystallisation pathways of the felsic phases modelled in the quaternary An-Ab-Or-Qz system from the bulk compositions. All compositions lie in the plagioclase volume, and evolved to three-phase saturation on the cotectic via either the quartz/plagioclase divariant surface (granodiorites) or the alkali feldspar/plagioclase divariant surface (monzogranite and syenogranite).  相似文献   

Some binary and ternary silicate solution models     

Y. Fei  S. K. Saxena  G. Eriksson 《Contributions to Mineralogy and Petrology》1986,94(2):221-229

Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G ^ex excess free energy of mixing - H ^ex excess enthalpy of mixing - S ^ex total excess entropy of mixing - S _ex ^c configurational excess entropy of mixing - W _ij interaction energy parameter between speciesi andj - X _i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi₂O₆) - En enstatite (Mg₂Si₂O₆) - Py pyrope (MgAl_2/3SiO₄) - Gr grossular (CaAl_2/3SiO₄) - CaTs Ca-Tschermak (CaAl₂SiO₆) - Ab albite (NaAlSi₃O₈) - An anorthite (CaAl₂Si₂O₈)  相似文献   

Deep Fractionation of Clinopyroxene in the East Pacific Rise 13°N: Evidence from High MgO MORB and Melt Inclusions   总被引：1，自引：1，他引：0  

ZHANG Guoliang  ZENG Zhigang  YIN Xuebo  WANG Xiaoyuan  CHEN Daigeng 《《地质学报》英文版》2009,83(2):266-277

Mid-ocean ridge basalts (MORBs) from East Pacific Rise (EPR) 13°N are analysed for major and trace elements, both of which show a continuous evolving trend. Positive MgO–Al2O3 and negative MgO–Sc relationships manifest the cotectic crystallization of plagioclase and olivine, which exist with the presence of plagioclase and olivine phenocrysts and the absence of clinopyroxene phenocrysts. However, the fractionation of clinopyroxene is proven by the positive correlation of MgO and CaO. Thus, MORB samples are believed to show a “clinopyroxene paradox”. The highest magnesium-bearing MORB sample E13-3B (MgO=9.52%) is modelled for isobaric crystallization with COMAGMAT at different pressures. Observed CaO/Al2O3 ratios can be derived from E13-3B only by fractional crystallization at pressure >4 ±1 kbar, which necessitates clinopyroxene crystallization and is not consistent with cotectic crystallization of olivine plus plagioclase in the magma chamber (at pressure ~1 kbar). The initial compositions of the melt inclusions, which could represent potential parental magmas, are reconstructed by correcting for post-entrapment crystallization (PEC). The simulated crystallization of initial melt inclusions also produce observed CaO/Al2O3 ratios only at >4±1 kbar, in which clinopyroxene takes part in crystallization. It is suggested that MORB magmas have experienced clinopyroxene fractionation in the lower crust, in and below the Moho transition zone. The MORB magmas have experienced transition from clinopyroxene+plagioclase+olivine crystallization at >4±1 kbar to mainly olivine+plagioclase crystallization at <1 kbar, which contributes to the explanation of the “clinopyroxene paradox”.  相似文献   

Palaeo-mixing zone karst features from Palaeocene carbonates of north Spain: criteria for recognizing a potentially widespread but rarely documented diagenetic system     

《Sedimentary Geology》2001,139(3-4):205-216

Marine-meteoric mixing zone dissolution effects are a major feature of present day karst systems in carbonate platforms, yet are rarely reported in the geological record. An example is described from the upper Danian platform limestones of the Alava province, in the western Pyrenees, north Spain. This consists of several narrow zones with sponge-like porosity analogous to the “Swiss-cheese” features found in present day mixing zones. These zones are stained by Fe-oxides and overlie limestones which are irregularly dolomitized and contain disseminated pyrite. These high-porosity zones are interpreted as having developed in marine mixing zones where mixing corrosion and microbially mediated processes increased dissolution. If collapsed, ancient mixing zones could be misinterpreted as “terra-rossa” palaeosols. The main criteria to identify them as mixing zone products are their occurrence below a palaeo-meteoric phreatic zone, their association with stratified oxic and anoxic redox zones and petrographic evidence for highly variable calcite saturation states.  相似文献   

An estimate of the probability of capture of a binary star by a supermassive black hole     

G. N. Dremova  V. V. Dremov  A. V. Tutukov 《Astronomy Reports》2016,60(8):695-701

A simple model for the dynamics of stars located in a sphere with a radius of one-tenth of the central parsec, designed to enable estimation of the probability of capture in the close vicinity (r < 10^?3 pc) of a supermassive black hole (SMBH) is presented. In the case of binary stars, such a capture with a high probability results in the formation of a hyper-velocity star. The population of stars in a sphere of radius <0.1 pc is calculated based on data for the Galactic rotation curve. To simulate the distortion of initially circular orbits of stars, these are subjected to a series of random shock encounters (“kicks”), whose net effect is to “push” these binary systems into the region of potential formation of hyper-velocity stars. The mean crossing time of the border of the close vicinity of the SMBH (r < 10^?3 pc) by the stellar orbit can be used to estimate the probability that a binary system is captured, followed by the possible ejection of a hyper-velocity star.  相似文献   

Enthalpies in (Na,Ca)- and (K,Ca)-feldspar binaries: a high-temperature solution calorimetric study     

A.?BenisekEmail author  H.?Kroll  L.?Cemi?  V.?Kohl  U.?Breit  B.?Heying 《Contributions to Mineralogy and Petrology》2003,145(1):119-129

A series of high structural state plagioclases (Ab-An) was crystallized from glasses. By exchanging Na for K in KCl melts, metastable K-plagioclases (Or-An) were prepared which possess the same structural state as the starting plagioclases. Both series were investigated at 980 K by lead borate solution calorimetry. Continuing the ideas of Carpenter and McConnell (1984) and Carpenter (1992a), the results can be interpreted as follows. In the high plagioclase series, the enthalpies of solution, jH_sol, reflect the schemes of Al,Si ordering: (1) analbite-like (C2/m) ordering in the An-poor region 0hX_AnА.2, (2) high albite-like (C1¥) ordering in intermediate plagioclases, and (3) anorthite-like (I1¥) ordering in the An-rich region 0.7AnБ. In regions 1 and 2, jH_sol decreases as a function of X_An, but increases in region 3 as a consequence of the C1¥MI1¥ ordering reaction. Therefore, it is not a mixing effect but a compositionally restricted ordering effect which causes the excess enthalpies, jH^ex, to be positive in the plagioclase binary as a whole. Neglecting the existence of phase transitions at X_An=0.2 and X_An=0.7, jH^ex can be approximated by a two-parameter Margules model yielding W^H_AnAb=14Dž kJ/mol and W^H_AbAn=40Dž kJ/mol. jH_sol values of I1¥ plagioclases (X_An>0.7) can be "corrected" for the C1¥MI1¥ ordering effect (Carpenter 1992a). When combining the corrected values with the jH_sol data which were actually measured on the C1¥ plagioclases (X_An<0.7), negative excess enthalpies are generated in the plagioclase binary. This may be expected when C1¥ ordering occurs relative to topochemically monoclinic reference states of analbite and hypothetical anorthite devoid of I1¥ order. The solution experiments on the K-plagioclases resulted in similar characteristics as those found for the plagioclases. However, in addition to the ordering effects observed in the plagioclase binary, volume mismatch effects contribute to jH^ex in the K-plagioclase series. jH^ex can be represented by a Margules model with W^H_AnOr=60ᆞ kJ/mol and W^H_OrAn=91ᆢ kJ/mol when the phase transitions at X_An=0.2 and X_An=0.7 are again neglected. The contribution of the volume mismatch effect to jH^ex is considerable, as appears from the large difference between the K-plagioclase and the plagioclase Margules parameters. Their difference corresponds to a practically symmetrical dependence of jH^ex_volmism on composition, with W^H_volmism=48ᆡ kJ/mol.  相似文献   

Light-curve syntheses for close binary systems: Modeling spiral waves in an elliptical disk around a white dwarf     

T. S. Khruzina 《Astronomy Reports》2005,49(10):783-800

We present an algorithm for synthesizing the light curve of a close binary consisting of a normal star (a red dwarf that fills its Roche lobe) and a spherical star (a white dwarf). The spherical component is surrounded by an elliptical accretion disk with a complex shape: it is geometrically thin near the spherical star and geometrically thick at the edge of the disk. An additional complication is presented by the presence of a one-or two-armed spiral pattern at the inner surface of the disk. The maximum height of the spiral arm above the disk surface is located at ～9 R _d , and the height decreases exponentially as the arm approaches the inner regions of the disk. Shielding of the inner hot parts of the disk by the crests of the spirals results in the formation of “steps” in out-of-eclipse parts of the orbital light curves. The algorithm takes into account the presence of a “hot line” by the lateral surface of the disk, making it possible to model binary systems in both quiescence and outburst. In the latter case, the hot line degenerates into a small bulge at the outer lateral surface of the disk, which can be considered an analog of a hot spot. The algorithm was applied to the orbital light curve of the cataclysmic binary IP Peg during its October 30, 2000, outburst. To explain the variations of the out-of-eclipse brightness of the system during the outburst, it is necessary to include the presence of a one-armed spiral wave at the inner surface of the disk, close to the periastron of the elliptical disk. We have obtained the parameters of IP Peg during the outburst for various models of the system.  相似文献   

Analysis of geological events     

K. L. Burns 《Mathematical Geosciences》1975,7(4):295-321

Geological events, such as emplacement of granite or growth of slaty cleavage, may be ordered into a sequence by two methods. One is to assign each event a place in a time scale, such as years before the present, which amounts to assigning events an age designation from the set of real numbers. In ordering such a list, the algebra of real numbers applies. A second method is to determine the time relations of events in pairs, such as a fold is of type (S1, S2) or granite intrudes conglomerate. These binary relations between events may be used to order events into a sequence using the transitive properties of the relation “older than.” It is shown, however, that the binary relations between events do not follow the familiar rules for the algebra of real or integral numbers and it is necessary to erect a new system of relations called the “algebra of events.” The fundamental relation is “older than or equivalent to” and this may be used to define the relations “older than”, “younger than”, “equivalent to”, “incomparable to”, and “covers.” The essential difference from the algebra of integers is that the reflexive relation (“equal to”) is replaced by two such relations (“equivalent to” and “incomparable to”) in the algebra of events. A number of binary relations between events may be assembled into an event matrix which is basically a truth table for the relation “older than.” This may be ordered and stacked by operations termed ORDER and STACK. The relationship of each event to every other event may be determined by simple inspection of an ordered, stacked matrix, and from this a geological history may be assembled. If there are contradictions in the field data, ordering into a proper sequence is impossible and may be detected. If there are ambiguities in the field data, there are several different orders that are proper sequences so that the event matrix may be ordered. However, the ambiguities occur as voids in the stacked matrix.  相似文献   

Atomistic computer modeling of the local structure and mixing properties of a grossular-uvarovite solid solution     

N. N. Eremin  R. A. Talis  A. E. Grechanovskii  V. S. Urusov 《Moscow University Geology Bulletin》2013,68(2):72-78

An original methodology for the atomistic computer modeling of solid solutions was applied for the study of the mixing properties and local structure of the grossular-uvarovite, i.e., Ca₃Al₂[SiO₄]₃ Ca₃Cr₂][SiO₄]₃, garnet series. The parameters of the interatomic potentials for end members of this series were optimized using experimental data on their structural, elastic, and thermodynamic characteristics. The optimized model of the potentials allowed us to describe the elastic, structural, and thermodynamic characteristics of grossular and uvarovite and estimate the energy of point defects in these crystal structures. Calculations of the mixing properties and local structure for seven different compositions of the solid solution were carried out on a “Chebyshev” supercomputer (Moscow State University) in a 2 × 2 × 4 supercell of the garnet-type structure containing 2560 atoms. Mixing properties, such as the enthalpy of mixing, parameters of interaction, excess mixing volume, deviation of bulk modulus from additivity, and the vibrational and configuration contribution to the entropy of mixing, were determined. This allowed us to estimate the stability field for the grossular-uvarovite solid solution. Histograms of the interatomic distances M-O (M = Ca, Al, Cr, Si) and O-O in supercells were plotted and the parameters of relaxation and changes of the CrO₆ and AlO₆ octahedron volumes were estimated. The data of the simulation are quite consistent with the experimental data on this system and supplement it significantly.  相似文献