Intergrowth of pyroxene and pyroxenoid; chain periodicity faults in pyroxene

Intergrowth of clinopyroxenes (augite, A) and pyroxenoids (Fe-rhodonite and pyroxferroite, Pxo) was observed by transmission electron microscopy. The following orientation relationship was found: (001)_Pxo is parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)_{\text{A}}\) and \([1\bar 10]_{Pxo}\) is parallel to [011]_A. This relationship can be explained by similarities of the structures of clinopyroxenes and pyroxenoids. It contradicts a suggestion based on structural arguments of Koto et al. (1976). Chain periodicity faults parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)\) are also observed in pure clinopyroxenes.     

Crystal structures and phase transitions in Sr2InTaO6 perovskite

The preparation and crystal structure of the double perovskite oxide Sr₂InTaO₆ are reported. This oxide has a monoclinic structure in space group P2₁/n at room temperature, where In and Ta display a rock-salt type ordering with a = 5.73356(10), b = 5.74052(10), c = 8.10905(14) Å and β = 90.022(6)°. Variable temperature neutron diffraction measurements demonstrate this displays the sequence of phase transitions $ P2_{1} /n\mathop{\longrightarrow}\limits^{{605\,^\circ {\text{C}}}}I2/m\mathop{\longrightarrow}\limits^{{705\,^\circ {\text{C}}}}I4/m\mathop{\longrightarrow}\limits^{{930\,^\circ {\text{C}}}}Fm\bar{3}m $ as a consequence of the sequential loss of tilting of the corner shared octahedra upon heating. The evolution of Sr₂InTaO₆ crystal structure upon heating is analysed and described in terms of symmetry-adapted distortion modes. The GM4+ and X3+, that are responsible for anti-phase and in-phase tilting, respectively, are highly temperature dependent, with the GM4+ mode having the largest amplitude at room temperature.     

An experimental study of Ti and Zr partitioning among zircon, rutile, and granitic melt

In order to evaluate the effect of trace and minor elements (e.g., P, Y, and the REEs) on the high-temperature solubility of Ti in zircon (zrc), we conducted 31 experiments on a series of synthetic and natural granitic compositions [enriched in TiO₂ and ZrO₂; Al/(Na + K) molar ~1.2] at a pressure of 10 kbar and temperatures of ~1,400 to 1,200 °C. Thirty of the experiments produced zircon-saturated glasses, of which 22 are also saturated in rutile (rt). In seven experiments, quenched glasses coexist with quartz (qtz). SiO₂ contents of the quenched liquids range from 68.5 to 82.3 wt% (volatile free), and water concentrations are 0.4–7.0 wt%. TiO₂ contents of the rutile-saturated quenched melts are positively correlated with run temperature. Glass ZrO₂ concentrations (0.2–1.2 wt%; volatile free) also show a broad positive correlation with run temperature and, at a given T, are strongly correlated with the parameter (Na + K + 2Ca)/(Si·Al) (all in cation fractions). Mole fraction of ZrO₂ in rutile $ \left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) $ in the quartz-saturated runs coupled with other 10-kbar qtz-saturated experimental data from the literature (total temperature range of ~1,400 to 675 °C) yields the following temperature-dependent expression: $ {\text{ln}}\left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) + {\text{ln}}\left( {a_{{{\text{SiO}}_{2} }} } \right) = 2.638(149) - 9969(190)/T({\text{K}}) $ , where silica activity $ a_{{{\text{SiO}}_{2} }} $ in either the coexisting silica polymorph or a silica-undersaturated melt is referenced to α-quartz at the P and T of each experiment and the best-fit coefficients and their uncertainties (values in parentheses) reflect uncertainties in T and $ \mathop X\nolimits_{{{\text{ZrO}}_{2} }}^{\text{rt}} $ . NanoSIMS measurements of Ti in zircon overgrowths in the experiments yield values of ~100 to 800 ppm; Ti concentrations in zircon are positively correlated with temperature. Coupled with values for $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ for each experiment, zircon Ti concentrations (ppm) can be related to temperature over the range of ~1,400 to 1,200 °C by the expression: $ \ln \left( {\text{Ti ppm}} \right)^{\text{zrc}} + \ln \left( {a_{{{\text{SiO}}_{2} }} } \right) - \ln \left( {a_{{{\text{TiO}}_{2} }} } \right) = 13.84\left( {71} \right) - 12590\left( {1124} \right)/T\left( {\text{K}} \right) $ . After accounting for differences in $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ , Ti contents of zircon from experiments run with bulk compositions based on the natural granite overlap with the concentrations measured on zircon from experiments using the synthetic bulk compositions. Coupled with data from the literature, this suggests that at T ≥ 1,100 °C, natural levels of minor and trace elements in “granitic” melts do not appear to influence the solubility of Ti in zircon. Whether this is true at magmatic temperatures of crustal hydrous silica-rich liquids (e.g., 800–700 °C) remains to be demonstrated. Finally, measured $ D_{\text{Ti}}^{{{\text{zrc}}/{\text{melt}}}} $ values (calculated on a weight basis) from the experiments presented here are 0.007–0.01, relatively independent of temperature, and broadly consistent with values determined from natural zircon and silica-rich glass pairs.     

Microtextural constraints on the interplay between fluid–rock reactions and deformation

Schists from two mylonitic localities in the footwall of a low-angle normal fault in the eastern Alps record different degrees of embrittlement during exhumation, depending on the extent to which fluid–rock reactions proceeded. At one site, graphitic schists preserve textural evidence for two metamorphic reactions that modified and/or fluid volume: (1) reaction between graphite and aqueous fluid that increased without changing the molar amount of fluid, and (2) replacement of titanite by rutile, calcite, and quartz. The latter reaction involved net consumption of increasingly CO₂-rich fluid. Areas where the first reaction proceeded are associated with abundant Mode I microcracks. Fluid inclusion arrays within the microcracks show that increased from ∼0.1 to 0.6 during decompression from 4.75 to 2 kbar at a reference temperature of 500°C. Titanite consumption is most pronounced within transgranular Mode I microcracks, but microcracks do not crosscut products of this reaction; fluid consumption during reaction was coeval with the end of microcracking, at least on a local scale. At the other site, graphitic schists lack small-scale Mode I cracks as well as evidence for graphite consumption during decompression. SEM imaging shows that graphite is anhedral and pitted at the first site, but occurs in clusters of euhedral grains at the second site. Mass balance calculations demonstrate that rocks with partially consumed graphite were infiltrated by an externally derived, H₂O-rich fluid that drove subsequent graphite-fluid reaction. Evidence for similar fluid infiltration is absent at the second site. Variations in the degree of reaction progress indicate that fluid pathways and deformation style were heterogeneous on the scale of millimeters to kilometers during exhumation from mid-crustal depths.     

Experimental calibration of Forsterite–Anorthite–Ca-Tschermak–Enstatite (FACE) geobarometer for mantle peridotites

The crystallization of plagioclase-bearing assemblages in mantle rocks is witness of mantle exhumation at shallow depth. Previous experimental works on peridotites have found systematic compositional variations in coexisting minerals at decreasing pressure within the plagioclase stability field. In this experimental study we present new constraints on the stability of plagioclase as a function of different Na₂O/CaO bulk ratios, and we present a new geobarometer for mantle rocks. Experiments have been performed in a single-stage piston cylinder at 5–10 kbar, 1050–1150?°C at nominally anhydrous conditions using seeded gels of peridotite compositions (Na₂O/CaO?=?0.08–0.13; X _Cr = Cr/(Cr?+?Al)?=?0.07–0.10) as starting materials. As expected, the increase of the bulk Na₂O/CaO ratio extends the plagioclase stability to higher pressure; in the studied high-Na fertile lherzolite (HNa-FLZ), the plagioclase-spinel transition occurs at 1100?°C between 9 and 10 kbar; in a fertile lherzolite (FLZ) with Na₂O/CaO?=?0.08, it occurs between 8 and 9 kbar at 1100?°C. This study provides, together with previous experimental results, a consistent database, covering a wide range of P–T conditions (3–9 kbar, 1000–1150?°C) and variable bulk compositions to be used to define and calibrate a geobarometer for plagioclase-bearing mantle rocks. The pressure sensitive equilibrium:

$$\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}^{{\text{Ol}}}}\limits_{{\text{Forsterite}}} +\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{8}}}^{{\text{Pl}}}}\limits_{{\text{Anorthite}}~} =\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{6}}}^{{\text{Cpx}}}}\limits_{{\text{Ca-Tschermak}}} +{\text{ }}\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}}^{{\text{Opx}}}}\limits_{{\text{Enstatite}}} ,$$

has been empirically calibrated by least squares regression analysis of experimental data combined with Monte Carlo simulation. The result of the fit gives the following equation:

$$P=7.2( \pm 2.9)+0.0078( \pm 0.0021)T{\text{ }}+0.0022( \pm 0.0001)T{\text{ }}\ln K,$$

$${R^2}=0.93,$$

where P is expressed in kbar and T in kelvin. K is the equilibrium constant K?=?a _CaTs × a _en/a _an × a _fo, where a _CaTs, a _en, a _an and a _fo are the activities of Ca-Tschermak in clinopyroxene, enstatite in orthopyroxene, anorthite in plagioclase and forsterite in olivine. The proposed geobarometer for plagioclase peridotites, coupled to detailed microstructural and mineral chemistry investigations, represents a valuable tool to track the exhumation of the lithospheric mantle at extensional environments.

     

The system Fe-Si-O: Oxygen buffer calibrations to 1,500K

The five solid-phase oxygen buffers of the system Fe-Si-O, iron-wuestite (IW), wuestite-magnetite (WM), magnetite-hematite (MH), quartz-iron-fayalite (QIF) and fayalite-magnetite-quartz (FMQ) have been recalibrated at 1 atm pressure and temperatures from 800°–1,300° C, using a thermogravimetric gas mixing furnace. The oxygen fugacity, \(f_{{\text{O}}_{\text{2}} }\) was measured with a CaO-doped ZrO₂ electrode. Measurements were made also for wuestite solid solutions in order to determine the redox behavior of wuestites with O/Fe ratios varying from 1.05 to 1.17. For FMQ, additional determinations were carried out at 1 kb over a temperature range of 600° to 800° C, using a modified Shaw membrane. Results agree reasonably well with published data and extrapolations. The reaction parameters K, ΔG _r ^o , ΔH _r ^o , and ΔS _r ^o were calculated from the following log \(f_{{\text{O}}_{\text{2}} }\) /T relations (T in K): $$\begin{gathered} {\text{IW }}\log f_{{\text{O}}_{\text{2}} } = - 26,834.7/T + 6.471\left( { \pm 0.058} \right) \hfill \\ {\text{ }}\left( {{\text{800}} - 1,260{\text{ C}}} \right), \hfill \\ {\text{WM }}\log f_{{\text{O}}_{\text{2}} } = - 36,951.3/T + 16.092\left( { \pm 0.045} \right) \hfill \\ {\text{ }}\left( {{\text{1,000}} - 1,300{\text{ C}}} \right), \hfill \\ {\text{MH }}\log f_{{\text{O}}_{\text{2}} } = - 23,847.6/T + 13.480\left( { \pm 0.055} \right) \hfill \\ {\text{ }}\left( {{\text{1,040}} - 1,270{\text{ C}}} \right), \hfill \\ {\text{QIF }}\log f_{{\text{O}}_{\text{2}} } = - 27,517.5/T + 6.396\left( { \pm 0.049} \right) \hfill \\ {\text{ }}\left( {{\text{960}} - 1,140{\text{ C}}} \right), \hfill \\ {\text{FMQ }}\log f_{{\text{O}}_{\text{2}} } = - 24,441.9/T + 8.290\left( { \pm 0.167} \right) \hfill \\ {\text{ }}\left( {{\text{600}} - 1,140{\text{ C}}} \right). \hfill \\ \end{gathered}$$ These experimentally determined reaction parameters were combined with published 298 K data to determine the parameters G_f, H_f, and S_f for the phases wuestite, magnetite, hematite, and fayalite from 298 K to the temperatures of the experiments. The T? \(f_{{\text{O}}_{\text{2}} }\) data for wuestite solid solutions were used to obtain activities, excess free energies and Margules mixing parameters. The new data provide a more reliable, consistent and complete reference set for the interpretation of redox reactions at elevated temperatures in experiments and field settings encompassing the crust, mantle and core as well as extraterrestrial environments.     

Studies in the system KAlSiO4-BaAl2Si2O8-SiO2-H2O

Various members of the KAlSi₃O₈-BaAl₂Si₂O₈ feldspar series are hydrothermally synthesized. Cellparameters of these are calculated from diffractometer patterns and found to be similar to those of Gay and Roy. A variation diagram is constructed correlating Cn-content and values of Δ_FeKα(2θ₍₁₁₁₎CaF₂—2θ₍₀₀₄₎Fs_ss), which gives $${\text{Mol}}\% {\text{ Cn = 229}}{\text{.83}}\Delta {\text{2}}\theta ---{\text{190}}{\text{.81}}$$ by a least square regression fitting. Phase equilibria relation in the solidus-liquidus-region for the KAlSi₃O₈-BaAl₂Si₂O₈-H₂O system at 1000 kg/cm² are investigated. It is found to be a case of simple solid solution in a binary system, with reservations at the potassium-rich side of the system. Goranson (1938) gives a temperature of about 1000°C at 1000 kg/cm² \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) for the incongruent melting of sanidine, but the authors prefer a value around 930°C at the same \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) . Reaction products of starting materials on the join KAlSi₂O₆-BaAl₂Si₂O₈ and KAlSiO₄-BaAl₂Si₂O₈ gave no experimental hint for replacement of K⁺ by Ba⁺⁺.     

Aluminum partitioning between olivine and ultrabasic silicate liquid to 6 GPa

Trace element analyses of 1-atm and high-pressure experiments show that in komatiite and peridotite, the olivine (OL)/liquid (L) distribution coefficient for Al₂O₃ ( ) increases with pressure and temperature. Olivine in equilibrium with liquid accepts as much as 0.2 wt% Al₂O₃ in solution at 6 GPa. Convergence to equilibrium compositions at this high level is shown by cation diffusion of Al into synthetic forsterite crystals of low-Al contents in the presence of melt. Convergence to low-Al equilibrium compositions at lower P and T is shown by diffusion of Al out of synthetic forsterite with high initial Al content. Isobaric and isothermal experimental data subsets reveal that temperature and pressure variations both have real effects on . Variation in silicate melt composition has no detectable effect on within the limited range of experimentally investigated mixtures. Least-squares regression for 24 experiments, using komatiite and peridotite, performed at 1 atm to 6 GPa and 1300 to 1960°C, gives the best fit equation: Increase in with increasingly higher-pressure melting is consistent with incorporation of a spinel-like component of low molar volume into olivine, although other substitutions possibly involving more complex coupling cannot be ruled out. High P-T ultrabasic melting residues, if pristine, may be recognized by the high calculated from microprobe analyses of Al₂O₃ concentrations in residual olivines and estimated Al₂O₃ concentration in the last liquid removed. In general the low levels of Al in natural olivine from mantle xenoliths suggest that pristine residues are rarely recovered.     

H<Subscript>2</Subscript>O diffusion in peralkaline to peraluminous rhyolitic melts

The diffusion of water in a peralkaline and a peraluminous rhyolitic melt was investigated at temperatures of 714–1,493 K and pressures of 100 and 500 MPa. At temperatures below 923 K dehydration experiments were performed on glasses containing about 2 wt% H₂O _t in cold seal pressure vessels. At high temperatures diffusion couples of water-poor (<0.5 wt% H₂O _t ) and water-rich (~2 wt% H₂O _t ) melts were run in an internally heated gas pressure vessel. Argon was the pressure medium in both cases. Concentration profiles of hydrous species (OH groups and H₂O molecules) were measured along the diffusion direction using near-infrared (NIR) microspectroscopy. The bulk water diffusivity () was derived from profiles of total water () using a modified Boltzmann-Matano method as well as using fittings assuming a functional relationship between and Both methods consistently indicate that is proportional to in this range of water contents for both bulk compositions, in agreement with previous work on metaluminous rhyolite. The water diffusivity in the peraluminous melts agrees very well with data for metaluminous rhyolites implying that an excess of Al₂O₃ with respect to alkalis does not affect water diffusion. On the other hand, water diffusion is faster by roughly a factor of two in the peralkaline melt compared to the metaluminous melt. The following expression for the water diffusivity in the peralkaline rhyolite as a function of temperature and pressure was obtained by least-squares fitting:

Measurement of the turbulence in the free atmosphere above Mt. Ma\overset{\lower0.5em\hbox{danak

Stellar scintillations were measured at Mt. Ma $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ danak during 42 nights in 1998–1999 in order to estimate the contribution of the free atmosphere to the seeing. The atmosphere above 1–2 km provides a median seeing of _boxclose_boxclose 390\mathop .\limits^{'} 39 , which is about one-third of the total seeing ( 0\mathop .^" 700\mathop .\limits^{'} 70 ). The characteristic altitudes of turbulent layers are from 3 to 11 km above the summit, and the appearance of layers at altitudes of 3–4 km is accompanied by a degradation of the free-atmosphere seeing. The median isoplanatic angle is q₀ = 2\mathop .^" 30\theta _0 = 2\mathop .\limits^{'} 30 (λ=500 nm, at the zenith). This is the first time that such data have been obtained for Ma $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ danak. The instruments used for these measurements—a modified four-channel photometer and a prototype of a double-aperture scintillation sensor—are described in detail. The data reduction was based on accurate corrections for photon-counting statistics and the use of theoretical weighting functions relating scintillation indices to the altitudes and intensities of turbulent layers. Simultaneous or quasi-simultaneous measurements of scintillation indices using apertures of different sizes having significantly different weighting functions enable estimation of the altitude and intensity of the equivalent turbulent layer. Despite the simplicity of this one-layer model, it provides fairly robust estimates of the integrated parameters of the real free atmosphere.     

Carbon and oxygen diffusion in calcite: Effects of Mn content and P H2O

The diffusion rates of carbon and oxygen in two calcite crystals of different Mn contents have been studied between 500° and 800° C in a CO₂-H₂O atmosphere (P _{CO 2}=1?5 bars, P _H2_O=0.02?24 bars) labeled with ¹³C and ¹⁸O. Isotope concentration gradients within annealed specimens were measured using a secondary ion microprobe by depth profiling parallel and perpendicular to the c axis. Despite the anisotropic structure of calcite, the diffusion of carbon and oxygen are both very nearly isotropic. Least-squares fitting of the carbon data to an Arrhenius relation gives an activation energy of 87±2 kcal/mole, with D ₀ terms dependent only slightly upon direction: 1 $$D_{\text{0}} {\text{(}}\parallel c{\text{) = }}\left( {9\frac{{ + 12}}{{ - 5}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ , 2 $$D_{\text{0}} {\text{(}} \bot c{\text{) = }}\left( {5\frac{{ + 6}}{{ - 3}}} \right){\text{x10}}^{\text{2}} cm^2 /s$$ . These results are in close agreement with previous determinations. Results for oxygen diffusion, however, give D values much larger than those previously reported for dry conditions; at 650° to 800° C the D values are two orders of magnitude larger. The diffusion of oxygen, unlike carbon, is strongly dependent on water pressure, as well as Mn content, and does not fit an Arrhenius relation over the entire temperature range. On the basis of these observations and considerations of the defect chemistry of calcite, it is proposed that carbon migrates as a Frenkel pair. The diffusion of oxygen, however, appears to be more complicated and may depend upon several simultaneous mechanisms.     

Effect of solar flare on the equatorial electrojet in eastern Brazil region

The effect of solar flare, sudden commencement of magnetic storm and of the disturbances ring current on the equatorial electrojet in the Eastern Brazil region, where the ground magnetic declination is as large as \(20^{^{\circ }}\hbox {W}\) is studied based on geomagnetic data with one minute resolution from Bacabal during November–December 1990. It is shown that the mean diurnal vector of the horizontal field was aligned along \(2{^{\circ }}\hbox {E}\) of north at Huancayo and \(30{^{\circ }}\hbox {W}\) of north at Bacabal during the month of December 1990. Number of solar flares that occurred on 30 December 1990 indicated the direction of solar flare related \(\Delta H\) vector to be aligned along \(5{^{\circ }}\hbox {E}\) of north at Huancayo and \(28{^{\circ }}\hbox {W}\) of north at Bacabal. This is expected as the solar flare effects are due to the enhanced conductivity in the ionosphere. The SC at 2230 UT on 26 November 1990 produced a positive impulse in \(\Delta X\) and negative impulse in \(\Delta Y\) at Bacabal with \(\Delta H\) vector aligned along \(27{^{\circ }}\hbox {W}\) of north. At Huancayo the \(\Delta H\) vector associated with SC is aligned along \(8{^{\circ }}\hbox {E}\) of north, few degrees east to the alignment of the diurnal vector of H. The magnetic storm that followed the SC had a minimum Dst index of –150 nT. The corresponding storm time disturbance in \(\Delta X\) at Huancayo as well as at Bacabal were about –250 nT but \(\Delta Y\) at Bacabal was about +70 nT and very small at Huancayo, that give the alignment of the H vector due to ring current about \(16{^{\circ }}\hbox {W}\) of north at Bacabal and almost along N–S at Huancayo. Thus alignment of the \(\Delta H\) vector due to ring current at Bacabal is \(14{^{\circ }}\hbox {E}\) of the mean direction of \(\Delta H\) vector during December 1990. This is consistent with the direction of ring current dependent on the dipole declination at the ring current altitude which is about \(5{^{\circ }}\hbox {W}\) of north over Bacabal and the deviation of declination due to the ring current during disturbed period given by the angle (\(\psi \)-D).     

Neutron diffraction study of the tricritical orientational order/disorder phase transition in calcite at 1260 K

Neutron powder diffraction measurements of the temperature dependence of superlattice reflections in calcite have shown that there is a continuous phase transition at 1260 K. The change in space group symmetry and the halving of the unit cell size on heating indicate that this transition is an orientational order/disorder transition. The intensities of the superlattice reflections show that the temperature dependence of the order parameter, Q, is of the form (T _c –T), where is 0.25, indicating that the transition is tricritical. The transition is accompanied by a large contraction along the c axis on cooling, defining a spontaneous strain e₃ which is related to the order parameter (and hence temperature) via e₃ Q ². No evidence for critical lowering of the value of was found. These measurements confirm that, apart from the detailed critical behaviour, the phase transition in calcite is similar to that observed in NaNO₃.     

Opening and resetting temperatures in heating geochronological systems

We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively,

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

Modified Weibull-derived spectrum for deep water significant wave height estimation

The modified Weibull spectrum is utilized to calculate the zeroth spectral moment (m_o) using Monte Carlo integration methods. Then significant wave height (H_s) is calculated using the formula This is validated with observed buoy data and numerical wave model (WAM) predicted significant wave heights. The Weibull parameters have been calculated using energy densities from observed spectra recorded by DS5 buoy (13.80° N, 82.52° E, depth 3355.48 m) by the method of maximum likelihood (MLE).The relative root mean square error (RRMS) and relative bias error criteria show that modified Weibull spectrum estimated significant wave heights are better than those predicted by WAM model. The monthly averaged observed wave power spectra for the year 2005 recorded by deep water buoy DS5 is considered in this work. The spectra exhibit bimodal sea states for several months of the year.     

A thermodynamic formulation of hydrous cordierite

A thermodynamic formulation of hydrous Mg-cordierite (Mg₂Al₄Si₅O₁₈·nH₂O) has been obtained by application of calorimetric and X-ray diffraction data for hydrous cordierite to the results of hydrothermal syntheses. The data include measurements of the molar heat capacity and enthalpy of hydration and the molar volume. The synthesis data are consistent with a thermodynamic formulation in which H₂O mixes ideally on a single crystallographic site in hydrous cordierite. The standard molar Gibbs free energy of hydration is-9.5±1.0 kJ/mol (an average of 61 syntheses). The standard molar entropy of hydration derived from this value is-108±3 J/mol-K. An equation providing the H₂O content of cordierite as a function of temperature and fugacity of H₂O is as follows (n moles of H₂O per formula unit, n<1): $$\begin{gathered}n = {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } \mathord{\left/{\vphantom {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}}} \right.\kern-\nulldelimiterspace} {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}} \hfill \\{\text{ }}\left. {\left. { - {\text{ln}}\left( {\frac{T}{{{\text{298}}{\text{.15}}}}} \right) - \left( {\frac{{298.15}}{T} - 1} \right)} \right]} \right) \hfill \\\end{gathered}$$ Application of this formulation to the breakdown reaction of Mg-cordierite to an assemblage of pyrope-sillimanite-quartz±H₂O shows that cordierite is stabilized by 3 to 3.5 kbar under H₂O-saturated conditions. The thermodynamic properties of H₂O in cordierite are similar to those of liquid water, with a standard molar enthalpy and Gibbs free energy of hydration that are the same (within experimental uncertainty) as the enthalpy and Gibbs free energy of vaporization. By contrast, most zeolites have Gibbs free energies of hydration two to four times more negative than the corresponding value for the vaporization of water.     

Experimental study of Fe-Mg distribution between biotite and orthopyroxene at P=490 MPa

Partitioning of Mg and Fe between coexisting biotite and orthopyroxene has been experimentally determined at temperatures 700, 750 and 800° C and 490 MPa total pressure in the system KAlO₂-MgO-FeO-SiO₂-H₂O. Oxygen fugacity was controlled by the QFM buffer. Starting materials were synthetic minerals of differing Fe/(Fe+Mg) values. Run products were analyzed for partitioning of components by a microprobe. Orthopyroxene was established to be notably inhomogeneous, whereas biotite was essentially homogeneous. To establish equilibrium relations, statistical treatment of the results of each experiment in addition to the whole complex of experimental data was applied. The regression equations for isotherms of the Fe-Mg partitioning between the minerals studied have been obtained. As a result, the equation for a two-dimensional regression may be written as: $$\begin{gathered} Y = (A + A_1 t + A_2 t^2 )(X - X^4 ) + (B + B_1 t + B_1 t^2 )(X^2 - X^4 ) + \hfill \\ (C + C_1 t + C_1 t^2 )(X^3 - X^4 ) + X^4 {\text{ where }}Y = X_{{\text{Opx}}}^{{\text{Fe}}} ;{\text{ X}} = {\text{X}}_{{\text{Bi}}}^{{\text{Fe}}} ; \hfill \\ t = 1000/T,K, \hfill \\ \begin{array}{*{20}c} {A = {\text{ }}4.59398,} & {A_1 = - {\text{ }}8.29838,} & {A_2 = {\text{ }}4.97316,} \\ {B = - 11.13731,} & {B_1 = {\text{ }}28.19304,} & {B_2 = - 20.98240,} \\ {A = {\text{ }}8.25072,} & {C_1 = - 20.80485,} & {C_2 = {\text{ }}15.35967} \\ \end{array} \hfill \\ {\text{ }}\sigma = 0.0143{\text{ }} \hfill \\ \end{gathered}$$ . This equation enables extrapolation of partitioning isotherms over a wide range of temperatures.     

Theoretical calculation of equilibrium Mg isotope fractionation between silicate melt and its vapor

Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO₃ and Mg₂SiO₄ melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ²⁵Mg values in the MgSiO₃ and Mg₂SiO₄ melts were 0.141?±?0.004 and 0.143?±?0.003‰ more positive than in their respective vapors. The corresponding δ²⁶Mg values were 0.270?±?0.008 and 0.274?±?0.006‰ more positive than in vapors, respectively. The general \(\alpha - T\) equations describing the equilibrium Mg α in MgSiO₃ and Mg₂SiO₄ melt–vapor systems were: \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\) and \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\), respectively, where m is the mass of light isotope ²⁴Mg and m′ is the mass of the heavier isotope, ²⁵Mg or ²⁶Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.     

Energetics of hydration of cordierite and water barometry in cordierite-granulites

The Gibbs free energy and volume changes attendant upon hydration of cordierites in the system magnesian cordierite-water have been extracted from the published high pressure experimental data at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P _total, assuming an ideal one site model for H₂O in cordierite. Incorporating the dependence of ΔG and ΔV on temperature, which was found to be linear within the experimental conditions of 500°–1,000°C and 1–10,000 bars, the relation between the water content of cordierite and P, T and \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) has been formulated as $$\begin{gathered} X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} = \hfill \\ \frac{{f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }}{{\left[ {{\text{exp}}\frac{1}{{RT}}\left\{ {64,775 - 32.26T + G_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{1, }}T} - P\left( {9 \times 10^{ - 4} T - 0.5142} \right)} \right\}} \right] + f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }} \hfill \\ \end{gathered} $$ The equation can be used to compute H₂O in cordierites at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) <1. Our results at different P, T and partial pressure of water, assuming ideal mixing of H₂O and CO₂ in the vapour phase, are in very good agreement with the experimental data of Johannes and Schreyer (1977, 1981). Applying the formulation to determine \(X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} \) in the garnet-cordierite-sillimanite-plagioclase-quartz granulites of Finnish Lapland as a test case, good agreement with the gravimetrically determined water contents of cordierite was obtained. Pressure estimates, from a thermodynamic modelling of the Fe-cordierite — almandine — sillimanite — quartz equilibrium at \(P_{{\text{H}}_{\text{2}} {\text{O}}} = 0\) and \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P_total, for assemblages from South India, Scottish Caledonides, Daly Bay and Hara Lake areas are compatible with those derived from the garnetplagioclase-sillimanite-quartz geobarometer.