The effect of P2O5 on the viscosity of haplogranitic liquid

The effect of P2O5 on the viscosity of a haplogranitic (K2O-Na2O-Al2O3-SiO2) liquid has been determined at 1 atm pressure in the temperature interval of 700 - 1650°C. Viscosity measurements of a haplogranite, haplogranite + 5.1 wt.% P2O5 and haplogranite + 9.5 wt.% P2O5 have been performed using the concentric cylinder and micropenetration methods. The viscosity of haplogranite liquid decreases with the addition of P2O5 at all temperatures investigated. The viscosity decrease is nonlinear, with the strongest decrease exhibited at low P2O5 concentration. The temperature-dependence of the viscosity of all the investigated liquids is Arrhenian, as is the case for P2O5 liquid. The Arrhenian activation energy is slightly lower in the P2O5-bearing liquids than in the P2O5-free haplogranite with the result that the effect of P2O5 on viscosity is a (weak) function of temperature. At temperatures corresponding to the crystallization of phosphorus-rich granitic and pegmatitic systems the addition of 1 wt.% of P2O5 decreases the viscosity 0.2 log10 units. The effect of P2O5 on haplogranitic melt viscosity is much less than that for B2O3, F2O−1 on the same melt composition (Dingwell et al., 1992 and this study). This implies that P2O5 concentration gradients in high-silica melts during, for example, phosphate mineral growth or dissolution in granitic magmas, will not significantly influence melt viscosity

The effect of F on the density of haplogranite melt

The densities and thermal expansivities of F-bearing haplogranitic glasses and liquids have been investigated using a combination of scanning calorimetry and dilatometry. F2O-1 reduces the density of haplogranitic liquids (at 750 °C) from 2.295 + 0.006 g/cm3 to 2.261 + 0.005 g/cm3 with the addition of 4.55 wt% F (0.33% per wt% of F added). The expansivities of the liquids increase with the addition of F2O-1 from 29.9 +- 3.0 x l0 -6/°C to 53.1 +- 1.4 x l0 -6/°C (at 750°C). Densities have been converted into molar volumes based on the haplogranite and F2O-1 components. The partial molar volume of F2O-1 has been calculated at 750°C to be 14.2 +- 1.3 cm3/mol in these melts. This value is close to the molar volume per O for several components of silicate melts. F and O have similar ionic and covalent radii, and thus the substitution of two F for one O yields approximately the volume change expected, assuming no secondaryc onsequencesfo r the averagec oordination number of cations. This is despite evidence from quenched melts that [6]Al exists in these compositions. F is significantly more effective (per wt% added) than B2O3 in reducing the density of haplogranitic melt. The effect of F on density reported here should complement the viscosity- reducing effect of F2O-1 on granitic melts in significantly acceleratingg ravity-driven processes of crystal-melt fractionation in F-rich igneous systems

Temperature-dependent thermal expansivities of silicate melts: The system anorthite-diopside

The temperature-dependent thermal expansivities of melts along the join anorthite-diopside have been determined on glassy and liquid samples using a combination of calorimetry, dilatometry, and Pt double bob Archimedean densitometry. Supercooled liquid volumes and molar thermal expansivities were determined using scanning calorimetric and dilatometric measurements of properties in the glass region and their behavior at the glass transition. The extraction of low-temperature liquid molar expansivities from dilatometry /calorimetry is based on an assumed equivalence of the relaxation of volume and enthalpy at the glass transition using a method developed and tested by Webb et al. (1992). This method corrects for transient effects at the glass transition which can lead to serious overestimates of liquid thermal expansivity from “peak” values. Superliquidus volumes were determined using double Pt bob Archimedean densitometry at temperatures up to 1650°C. The resulting data for liquid volumes near glass transition temperatures (810–920°C) and at superliquidus temperatures (1400–1650°C) are combined to yield thermal expansivities over the entire supercooled and stable liquid range. The molar expansivities are, in general, temperature dependent. The temperature-dependence of thermal expansivity increases from anorthite to diopside composition. The thermal expansivity of anorthite is essentially temperature independent, whereas that of diopside decreases by 50% between 800 and 1500°C, with the consequence that the thermal expansivities of the liquids in the anorthite-diopside system converge at high temperature

A partial molar volume for B 2 O 3 in haplogranitic melt

The densitiesa nd thermal expansivitieso f boron-bearingh aplogranitic glassesa nd Iiquids have been determined using a combination of scanning .florimetry and dilatomelry. B2O3 reduces the density of haplogranitic liquids (at 750'C) from 2.295 t 0.006 g cm-r to 2.237 + 0.005 g cm-3 wirh the addition of 8.92 wt. Vo 82o,. These densities have been converted into molar volumes in the binary system haplogranite - BrO3. The partial molar volume of 8203, calculated from a linear fit to the data at 750oC, is ,10.30 + 0.77 cmr mole-r in these melts. This value compares with a molar volume of pure B2O3 at this temperature of M.36 x. 0.22 cm3 mole-l (Napolitano et ol. 1965), indicating a negative excess volume of mixing along the haplogranite - B2O3 join. In comparison, at l3moc, the addition ot Na2O to B2O3 reduces the panial molar volume of B2O3 from 46.6 to 32.3 cm3 mole-r ar 45 molego Na2O (Riebling 1966).T he densityr esultsr eported here, along with the viscosity-reducinge ffect of B2O3o n granitic melts (Dingwell et al, 1992),s hould both significantlya cceleratep rocesseso f crystal-melt fractionation and facilitate the evolution of extremely fractionated igneous systems

Determination of silicate liquid thermal expansivity using dilatometry and calorimetry

A method for the determination of relaxed silicate liquid molar volume and expansivity at temperatures just above the glass transition is discussed. The method involves the comparison of heat capacity and molar expansivity in the glass transition region. Glassy and liquid heat-capacity data are obtained using differential scanning calorimetry, and glassy thermal expansion data are obtained using scanning dilatometry. The molar expansivity of the liquid is calculated by a fictive temperature normalization of the relaxation behavior of both the heat capacity and the molar expansivity in the glass transition region, with the normalized heat capacity curve being used to extend the dilatometric data into the liquid temperature range. This comparison is based upon the assumed equivalence of the parameters describing the relaxation of volume and enthalpy. The molar expansivity of relaxed sodium trisilicate (Na2Si3O7) has been determined in this manner at temperatures above the glass transition temperature. This low-temperature determination of liquid molar expansivity has been tested against high-temperature liquid expansivity data obtained from high temperature Pt double bob Archimedean buoyancy measurements. The low-temperature molar expansivity (26.43±0.83xl0~4 cm3 mole"lßC_1 at 540°C) determined in this manner agrees within error with the high-temperature molar expansivity (23.29±1.39xl0~4 cm3 mole^ºC1 at 1400°C). This dilatometric/calorimetric method of liquid molar expansivity determination greatly increases the temperature range accessible for thermal expansion measurements. A weighted linear fit to the combined low and high temperature volume data gives a molar expansivity of 23.0010.25x10^ cm3 mole^ºC"1. The volume-temperature relationship thus derived reproduces the measured volumes from both dilatometry and densitometry with a RMSD value of 0.033 cm3 mole"1 or 0.14%. This represents a substantial increase in precision, which is especially important for liquids whose high liquidus temperatures restrict the temperature range accessible to liquid volume determinations

A volume temperature relationship for liquid GeO2 and some geophysically relevant derived parameters for network liquids

The thermal expansivity of liquid GeO2 at temperatures just above the glass transition has been obtained using a combination of scanning calorimetry and dilatometry. The calorimetric and dilatometric curves of c p and dV/dT are normalized to the temperature derivative of fictive temperature versus temperature using the method of Webb et al. (1992). This normalization, based on the equivalence of relaxation parameters for volume and enthalpy, allows the completion of the dilatometric trace across the glass transition to yield liquid expansivity and volume. The values of liquid volume and expansivity obtained in this study are combined with high temperature densitometry determinations of the liquid volume of GeO2 by Sekiya et al. (1980) to yield a temperature-volume relation for GeO2 melt from 660 to 1400 °C. Liquid GeO2 shows a strongly temperature-dependent liquid molar expansivity, decreasing from 20.27 × 10–4 cm3 mol–1°C–1 to 1.97 × 10–4cm3 mol–1 °C–1 with increasing temperature. The coefficient of volume thermal expansion ( v ) decreases from 76.33 × 10–6 °C–1 to 2.46 × 10–6 °C–1 with increasing temperature. A qualitatively similar volume-temperature relationship, with v decreasing from 335 × 10–6 °C–1 to 33 × 10–6 °C–1 with increasing temperature, has been observed previously in liquid B2O3. The determination of the glass transition temperature, liquid volume, liquid and glassy expansivities and heat capacities in this study, combined with compressibility data for glassy and liquid GeO2 from the literature (Soga 1969; Kurkjian et al. 1972; Scarfe et al. 1987) allows the calculation of the Prigogine-Defay ratio (), c p -c v and the thermal Grüneisen parameter ( th) for GeO2. From available data on liquid SiO2 it is concluded that liquid GeO2 is not a good analog for the low pressure properties of liquid SiO2

The effect of B2O3 on the viscosity of haplogranitic liquids

The effect of B2O3 on the viscosity of a haplogranitic liquid (KrO-Na,O-AlrOr-SiO,) has been determined at I atm pressure in the temperature interval of 600-1600 °C. Viscosity measurementso f a haplogranite, haplogranite + 4.35 wt% B2O3 and haplogranite + 8.92 wt% B2O3 have been performed using the concentric cylinder and micropenetration methods. The viscosity of a B-enriched natural rhyolite obsidian, macusanite from Macusani, Peru, has also been determined. The viscosity of haplogranite liquid decreases with the addition of B2O3 at all temperatures investigated. The viscosity decrease is nonlinear, with the strongestd ecreasee xhibited at low B2O3 concentration. The temperature dependence of the viscosity of all the investigated liquids is Arrhenian, in strong contrast to the case for B2O3 Iiquid. The Arrhenian activation energy is much lower in the B2O3-bearing liquids than in the B2O3-free haplogranite, with the result that the effect of B2O3 on viscosity is a strong function of temperature. At temperatures corresponding to the crystallization of B-rich granitic and pegmatitic systems the addition of I wt% of B2O3 decreases the viscosity 2 orders of magnitude. The macusanite liquid exhibits a reduced viscosity compared with B-free rhyolite that is consistent with the synthetic liquid systematics. B must be considered as a fluxing agent in B-rich granitic and pegmatitlc systems

Non-linear properties of supercooled liquids in the system Na2O---SiO2

The physical properties, viscosity, density, heat capacity and thermal expansivity, of relaxed supercooled liquids in the temperature range just above the glass transition have been determined for ten compositions along the compositional binary Na2O---SiO2, in the range of 2–45 mole% Na2O, by a combination of scanning calorimetry, dilatometry and micropenetration viscometry. The viscosity, density, heat capacity and thermal expansivity in the glassy state have also been determined. The heat capacities illustrate a linear composition dependence for the glassy state and a smooth but strongly non-linear composition dependence for the supercooled liquid state. The thermal expansivities were determined by dilatometry up to the glass transition and, by a normalized comparison of relaxation behavior in the glass transition interval, to temperatures 50°C above the glass transition. The expansivity is a linear function of the molar composition in the glass but a strongly non-linear function of molar composition in the supercooled liquid. The viscosity data just above the glass transition temperature, combined with data from high temperature using the concentric cylinder method, illustrate that the composition dependence of viscosity is strongly non-linear and exhibits an inflection as a function of composition. The glass transition temperature, taken as the peak temperature of the calorimetric measurements, is not in general an isokom in this system. The data for these property determinations in the Na2O---SiO2 system provide much improved constraints on the partial molar properties of SiO2 liquid and partial molar properties of the SiO2 component in silicate melts. The complex behavior of the transport properties, i.e. the glass transition temperature and the viscosity, point to complexities in viscous flow beyond that of simple binary mixing of the Na2O and SiO2 components

The role of the cortical occipital spike in photosensitive epilepsy

Chapters one to three are an introduction to photosensitive epilepsy, electroencephalography (EEG) and the magnocellular and parvocellular visual pathways. Photoparoxysmal response (PPR) are strongly associated with photosensitive epilepsy. Chapters four to nine investigated whether occipital spikes were associated with PPR and hence with photosensitive epilepsy. The chapters investigated whether the response types showed similar dependence on stimulus characteristics using EEG. Chapters four and five found that occipital spikes and PPR showed different dependence on colour and luminance contrast. The differences were consistent with the magnocellular pathway mediating occipital spikes and the pavocellular pathway mediating PPR. The study in chapter eight found that monocular occlusion had a significantly greater effect on PPR than on occipital spikes, which is further evidence against an association between the two types of response. Chapters six and seven showed that occipital spikes and PPR had similar optimum spatial and temporal frequencies. Chapter nine showed that both response types could be generated via stimulation of the periphery of the retina. However, these three chapters are not strong evidence of an association, as the results do not contradict the theory that the responses are generated via different pathways. The magnocellular and pavocellular pathways have similar optimum temporal and spatial frequencies and both are present in the periphery. In chapter ten, magnetoencephalography was used to estimate the source of activity underlying the components of the VEP and occipital spike. Changes in the amplitude and latency in the components of the normal VEP are associated with epilepsy. However, the source underlying the occipital spikes was not related to that underlying the components of the VEP so this is also removed as a source of evidence for an association between occipital spikes and photosensitive epilepsy

Isospectral deformations of closed Riemannian manifolds with different scalar curvature

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.Comment: amstex, 10 pages, no figure