Strong ground motion attenuation in Aswan area, Egypt

Recent and paleo seismicity indicate that moderate seismic activity is relatively large for Aswan area. This is a warning on the possibility of occurrence of earthquakes in the future too. No strong motion records are available in Aswan area for engineers to rely upon. Consequently, the seismological modeling is an alternative approach till sufficient instrumental records around Aswan become available. In the present study, we have developed new ground motion attenuation relationship for events spanning 4.0?≤? M _w?≤?7.0 and distance to the surface projection of the fault up to 100 km for Aswan based on a statistically simulated seismological model. We generated suites of ground motion time histories using stochastic technique. The ground motion attenuation relation describes the dependence of the strength of the ground motions on the earthquake magnitude and distance from the earthquake. The proposed equation for peak ground acceleration (PGA) for the bed rock is in the form of: $ {\mathbf{log}}{\text{ }}\left( {{\mathbf{PGA}}/{\mathbf{gal}}} \right){\text{ }} = {\mathbf{1}}.{\mathbf{24}} + {\mathbf{0}}.{\mathbf{358}}{M_{\mathbf{w}}} - {\text{ }}{\mathbf{log}}\left( {\mathbf{R}} \right){\text{ }}-{\text{ }}{\mathbf{0}}.{\mathbf{008}}{\text{ }}{\mathbf{R}}{\text{ }} + {\text{ }}{\mathbf{0}}.{\mathbf{22}}{\text{ }}{\mathbf{P}} $ . Where PGA is the peak ground acceleration in gal (cm/s²); M_w, its moment magnitude; R is the closest distance between the rupture projection and the site of interest; and the factor P is a dummy variable. It is observed that attenuation of strong motion in Aswan is correlated with those used before in Egypt.     

Crystal field and covalency of octahedral chromium in natural [8](Mg1?xCax) 3[6] (Al0.67Cr0.33)2Si3O12 garnets from upper mantle rocks

In the course of a thorough study of the influences of the second coordination sphere on the crystal field parameters of the 3d ^N -ions and the character of 3d ^N –O bonds in oxygen based minerals, 19 natural Cr³⁺-bearing (Mg,Ca)-garnets from upper mantle rocks were analysed and studied by electronic absorption spectroscopy, EAS. The garnets had compositions with populations of the ^[8] X-sites by 0.881 ± 0.053 (Ca + Mg) and changing Ca-fractions in the range 0.020 ≤ w _Ca[8] ≤ 0.745, while the ^[6] Y-site fraction was constant with x _Cr³⁺ _[6] = 0.335 ± 0.023. The garnets had colours from deeply violet-red for low Ca-contents (up to x _Ca = 0.28), grey with 0.28 ≤ x _Ca ≤ 0.4 and green with 0.4 ≤ x _Ca. The crystal field parameter of octahedral Cr³⁺ 10Dq decreases strongly on increasing Ca-fraction from 17,850 cm⁻¹ at x _Ca[8] = 0.020 to 16,580 cm⁻¹ at x _Ca[8] = 0.745. The data could be fit with two model which do statistically not differ: (1) two linear functions with a discontinuity close to x _Ca[8] ≈ 0.3,

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.     

The reversed alumina contents of orthopyroxene in equilibrium with spinel and forsterite in the system MgO-Al2O3-SiO2

Equilibrium alumina contents of orthopyroxene coexisting with spinel and forsterite in the system MgO-Al₂O₃-SiO₂ have been reversed at 15 different P-T conditions, in the range 1,030–1,600° C and 10–28 kbar. The present data and three reversals of Danckwerth and Newton (1978) have been modeled assuming an ideal pyroxene solid solution with components Mg₂Si₂O₆ (En) and MgAl₂SiO₆ (MgTs), to yield the following equilibrium condition (J, bar, K): $$\begin{gathered} RT{\text{ln(}}X_{{\text{MgTs}}} {\text{/}}X_{{\text{En}}} {\text{) + 29,190}} - {\text{13}}{\text{.42 }}T + 0.18{\text{ }}T + 0.18{\text{ }}T^{1.5} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [0.013 + 3.34 \times 10^{ - 5} (T - 298) - 6.6 \times 10^{ - 7} P]P. \hfill \\ \end{gathered} $$ The data of Perkins et al. (1981) for the equilibrium of orthopyroxene with pyrope have been similarly fitted with the result: $$\begin{gathered} - RT{\text{ln(}}X_{{\text{MgTs}}} \cdot X_{{\text{En}}} {\text{) + 5,510}} - 88.91{\text{ }}T + 19{\text{ }}T^{1.2} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [ - 0.832 - 8.78{\text{ }} \times {\text{ 10}}^{ - {\text{5}}} (T - 298) + 16.6{\text{ }} \times {\text{ 10}}^{ - 7} P]{\text{ }}P. \hfill \\ \end{gathered} $$ The new parameters are in excellent agreement with measured thermochemical data and give the following properties of the Mg-Tschermak endmember: $$H_{f,970}^0 = - 4.77{\text{ kJ/mol, }}S_{298}^0 = 129.44{\text{ J/mol}} \cdot {\text{K,}}$$ and $$V_{298,1}^0 = 58.88{\text{ cm}}^{\text{3}} .$$ The assemblage orthopyroxene+spinel+olivine can be used as a geothermometer for spinel lherzolites, subject to a choice of thermodynamic mixing models for multicomponent orthopyroxene and spinel. An ideal two-site mixing model for pyroxene and Sack's (1982) expressions for spinel activities provide, with the present experimental calibration, a geothermometer which yields temperatures of 800° C to 1,350° C for various alpine peridotites and 850° C to 1,130° C for various volcanic inclusions of upper mantle origin.     

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.     

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.     

Garnet-clinopyroxene geothermometer

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.     

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.     

Phase relationships in granulitic metapelites from the Ivrea-Verbano zone (Northern Italy)

Paragneisses of the Ivrea-Verbano zone exhibit over a horizontal distance of 5 km mineralogical changes indicative of the transition from amphibolite to granulite facies metamorphism. The most obvious change is the progressive replacement of biotite by garnet via the reaction: a $${\text{Biotite + sillimanite + quartz }} \to {\text{ Garnet + K - feldspar + H}}_{\text{2}} {\text{O}}$$ which results in a systematic increase in the modal ratio g = (garnet)/(garnet + biotite) with increasing grade. The systematic variations in garnet and biotite contents of metapelites are also reflected by the compositions of these phases, both of which become more magnesian with increasing metamorphic grade. The pressure of metamorphism has been estimated from the Ca₃Al₂Si₃O₁₂ contents of garnets coexisting with plagioclase, sillimanite and quartz. These phases are related by the equilibrium: b $$\begin{gathered} 3 CaAl_2 {\text{Si}}_{\text{2}} {\text{O}}_{\text{8}} \rightleftharpoons Ca_3 Al_2 {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} + 2 Al_2 {\text{SiO}}_{\text{5}} + {\text{SiO}}_{\text{2}} \hfill \\ plagioclase garnet sillimanite quartz \hfill \\ \end{gathered} $$ which has been applied to these rocks using the available data on the mixing properties of plagioclase and garnet solid solutions. Temperature and f _{H 2O} estimates have been made in a similar way using thermodynamic data on the biotite-garnet reaction (a) and the approximate solidus temperatures of paragneisses. Amphibolite to granulite facies metamorphism in the Ivrea-Verbano zone took place in the P-T ranges 9–11 kb and 700–820 °C. The differences in temperature and pressure of metamorphism between g= 0 and g = 1 (5 kms horizontal distance) were less than 50° C and approximately 1 kb. Retrogression and re-equilibration of garnets and biotites in the metapelites extended to temperatures more than 50° C below and pressures more than 1.5 kb below the peak of metamorphism, the degree of retrogression increasing with decreasing grade of the metamorphic “peak”. The pressure and temperature of the peak of metamorphism are not inconsistent with the hypothesis that the Ivrea-Verbano zone is a slice of upthrusted lower crust from the crust-mantle transition region, although it appears that the thermal gradient was too low for the zone to represent a near-vertical section through the crust. The most reasonable explanation of the granulite facies metamorphism is that it arose through intrusion of mafic rocks into a region already undergoing recrystallisation under amphibolite facies conditions.     

Solubility of alumina in orthopyroxene plus spinel as a geobarometer in complex systems. Applications to spinel-bearing alpine-type peridotites

The addition of Fe and Cr to the simple system MgO-SiO₂-Al₂O₃ markedly affects the activities of phases involved in the equilibrium

Temperature coefficients of elastic constants of single crystal MgO between 80 and 1,300 K

Elastic constants of single crystal MgO have been measured by the rectangular parallelepiped resonance (RPR) method at temperatures between 80 and 1,300 K. Elastic constants C _ij (Mbar=10³ kbar) and their temperature coefficients (kbar/K) are: $$\begin{gathered} {\text{ }}C_{{\text{11}}} {\text{ }}C_{{\text{12}}} {\text{ }}C_{{\text{44}}} {\text{ }}K_s {\text{ }}C_s \hfill \\ C_{ij} {\text{ 300 K 2}}{\text{.966 0}}{\text{.959 1}}{\text{.562 1}}{\text{.628 1}}{\text{.004}} \hfill \\ \partial C_{ij} {\text{/}}\partial T{\text{100 K }} - {\text{0}}{\text{.259 0}}{\text{.013 }} - {\text{0}}{\text{.072 }} - {\text{0}}{\text{.078 }} - {\text{0}}{\text{.136}} \hfill \\ {\text{ 300K }} - {\text{0}}{\text{.596 0}}{\text{.068 }} - {\text{0}}{\text{.122 }} - {\text{0}}{\text{.153 }} - {\text{0}}{\text{.332}} \hfill \\ {\text{ 800 K }} - {\text{0}}{\text{.619 0}}{\text{.009 }} - {\text{0}}{\text{.152 }} - {\text{0}}{\text{.200 }} - {\text{0}}{\text{.314}} \hfill \\ {\text{ 1,300 K }} - {\text{0}}{\text{.598 0}}{\text{.036 }} - {\text{0}}{\text{.130 }} - {\text{0}}{\text{.223 }} - {\text{0}}{\text{.218}} \hfill \\ \end{gathered} $$ By combining the present results with the previous data on the thermal expansivity and specific heat, the thermodynamic properties of magnesium oxide are presented and discussed. The elastic parameters of MgO at very high temperatures in the earth's lower mantle are also clarified.     

Statistical mechanics of coupled solid solutions in the dilute limit

A statistical mechanical analysis of the limiting laws for coupled solid solutions shows that the random model, in which the configurational entropy is calculated as if atoms mix randomly on each crystallographic site, is correct as a first approximation. In coupled solid solutions, since atoms of different valence substitute on the same sites, significant short-range order which reduces the entropy can be expected. A first-order correction is rigorously obtained for the entropy in dilute binary short-range ordered coupled solid solutions: $$\bar S^{{\text{XS}}} {\text{/R = }}Q\left( {{\text{e}}^{--H_{\text{A}} /{\text{R}}T} \left( {\frac{{H_{\text{A}} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_2^a N_4^b ,$$ where Q is the number of positions an associated cation pair can assume per formula unit, H _A is the association energy per formula unit, and N ₂ ^a and N ₄ ^b are the site occupancy fractions for atoms 2 and 4 that are dilute on sites a and b. S ^XS is the configurational entropy minus the random model entropy. Aluminous pyroxenes on the joints diopside-jadeite and diopside-CaTs are examined as examples. A generalization for dilute multiple component solutions, including possible long-range ordering variations is given by: $$\frac{{\bar S^{{\text{XS}}} }}{{\text{R}}}{\text{ = }}\sum\limits_i {\sum\limits_j {\sum\limits_k {Q_i } } \left( {{\text{e}}^{--H_{\text{A}}^{j{\text{ }}k{\text{, }}i} /{\text{R}}T} \left( {\frac{{H_{\text{A}}^{j{\text{ }}k{\text{, }}i} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_j^l N_k^m ,} $$ where i labels each crystallographically distinct pair, j and k label atomic species, l and m label crystallographic sites, and the N's are site occupancy fractions for the solute atoms. A total association model is examined as well as the partial association and random models. Real solution behavior must lie between the total association model and the random model. Molecular models in which the ideal activity is proportional to a mole fraction, which in itself is not always unambiguously defined, do not lie in this range and furthermore have no physical justification.     

Experimental determination of the reaction paragonite=jadeite+kyanite+H2O,and internally consistent thermodynamic data for part of the system Na2O−Al2O3−SiO2−H2O,with applications to eclogites and blueschists

Hydrothermal reversal experiments have been performed on the upper pressure stability of paragonite in the temperature range 550–740 ° C. The reaction $$\begin{gathered} {\text{NaAl}}_{\text{3}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{1 0}}} ({\text{OH)}}_{\text{2}} \hfill \\ {\text{ paragonite}} \hfill \\ {\text{ = NaAlSi}}_{\text{2}} {\text{O}}_{\text{6}} + {\text{Al}}_{\text{2}} {\text{SiO}}_{\text{5}} + {\text{H}}_{\text{2}} {\text{O}} \hfill \\ {\text{ jadeite kyanite vapour}} \hfill \\ \end{gathered}$$ has been bracketed at 550 ° C, 600 ° C, 650 ° C, and 700 ° C, at pressures 24–26 kb, 24–25.5 kb, 24–25 kb, and 23–24.5 kb respectively. The reaction has a shallow negative slope (? 10 bar °C^?1) and is of geobarometric significance to the stability of the eclogite assemblage, omphacite+kyanite. The experimental brackets are thermodynamically consistent with the lower pressure reversals of Chatterjee (1970, 1972), and a set of thermodynamic data is presented which satisfies all the reversal brackets for six reactions in the system Na₂O-Al₂O₃-SiO₂-H₂O. The Modified Redlich Kwong equation for H₂O (Holloway, 1977) predicts fugacities which are too high to satisfy the reversals of this study. The P-T stabilities of important eclogite and blueschist assemblages involving omphacite, kyanite, lawsonite, Jadeite, albite, chloritoid, and almandine with paragonite have been calculated using thermodynamic data derived from this study.     

Some geobarometers involving cordierite in the FeO-Al2O3-SiO2(±H2O) system: refinements,thermodynamic calibration,and applicability in granulite facies rocks

Five geobarometers involving cordierite have been formulated for quantitative pressure sensing in high grade metapelites. The relevant reactions in the FeO-Al₂O₃-SiO₂ (±H₂O) system are based on the assemblages (A) cordierite-garnet-sillimanite-quartz, (B) cordierite-spinel-quartz, (C) cordierite-garnet-spinel-sillimanite, (D) cordierite-garnet-orthopyroxene-quartz and (E) cordierite-orthopyroxene-sillimanite-quartz. Application of the barometric formulations to a large number of granulite grade rocks indicates that the cordierite-garnet-sillimanite-quartz equilibrium is widely applicable and registers pressures which are in good agreement with the “consensus” pressure estimates. The dispersion in the computed P values, expressed as one standard deviation, is within ±1.2 kbar. The geobarometers (B) and (C) also yield pressures which are reasonable and compare well with those computed from equilibrium (A). The estimated pressures from (D) and (E), both involving orthopyroxene, are at variance with these estimates. It has been argued that the discrepancy in pressures obtained from these geobarometers stems from an inadequate knowledge of activity-composition relations and/or errors in input thermodynamic data of aluminous orthopyroxene. The convergence of pressure values estimated from the barometric formulations, especially (A), (B) and (C), implies that the present formulations are more dependable than the existing formulations and are also capable of setting limits on P values in response to varying $$\begin{gathered} {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ {\text{ = 1/3Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2/3Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 5/6SiO}}_{\text{2}} {\text{. (A)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ = FeAl}}_{\text{2}} {\text{O}}_{\text{4}} {\text{ + 5/2SiO}}_{\text{2}} {\text{. (B)}} \hfill \\ {\text{Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + FeAl}}_{\text{2}} {\text{O}}_{\text{4}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{. (C)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 3/2SiO}}_{\text{2}} .{\text{ (D)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}{}_{\text{4}}{\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ = 1/2{\text{Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} {\text{ + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 1/2SiO}}_{\text{2}} .{\text{ (E)}} \hfill \\ \end{gathered}$$ . The present communication addresses the calibration, applicability and reliability of these barometers with reference to granulite facies metapelites.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

Adsorption kinetics of chromium(III) removal from aqueous solutions using natural red earth

Laboratory-scale-simulated experiments were carried out using Cr(III) solutions to identify the Cr(III) retention behavior of natural red earth (NRE), a natural soil available in the northwestern coastal belt of Sri Lanka. The effects of solution pH, initial Cr(III) concentration and the contact time were examined. The NRE showed almost 100 % Cr(III) adsorption within the first 90 min. [initial [Cr(III)] = 0.0092–0.192 mM; initial pH 4.0–9.0]. At pH 2 (298 K), when particle size ranged from 125 to 180 μm the Cr(III) adsorption data were modeled according to Langmuir convention assuming site homogeneity. The pH-dependent Cr(III) adsorption data were quantified by diffused layer model assuming following reaction stoichiometries: $$ \begin{aligned} 2\, {>}{\text{AlOH}}_{{({\text{s}})}} + {\text{ Cr }}\left( {\text{OH}} \right)_{{ 2\,({\text{aq}})}}^{ + } \, \to \, \left( { {>}{\text{AlO}}} \right)_{ 2} {\text{Cr}}_{{({\text{s}})}}^{ + } + {\text{ 2H}}_{ 2} {\text{O}} \quad {\text{log K 15}}. 5 6\\ 2\, {>}{\text{FeOH}}_{{({\text{s}})}} + {\text{ Cr}}\left( {\text{OH}} \right)_{{ 2\,({\text{aq}})}}^{ + } \, \to \, \left( { {>}{\text{FeO}}} \right)_{ 2} {\text{Cr}}_{{({\text{s}})}}^{ + } + {\text{ 2H}}_{ 2} {\text{O}}\quad {\text{log K 5}}.0 8.\\ \end{aligned} $$ The present data showed that NRE can effectively be used to mitigate Cr(III) from aqueous solutions and this method is found to be simple, effective, economical and environmentally benign.     

The variation of tetrahedral bond lengths in sodic plagioclase feldspars

Multiple linear regression analysis has been applied to the geometric and chemical variables in sodic plagioclases in order to determine their relative effects on individual T-O bond lengths in the Al_1+xSi_3?xO₈ tetrahedral framework. Using data from crystal structure analyses of low and high albite, An₁₆ and An₂₈, and assuming that low albite is completely ordered, 1 $$\begin{gathered} {\text{T}} - {\text{O = 1}}{\text{.568}} + {\text{[(0}}{\text{.122) x (Al content of the T site)]}} \hfill \\ {\text{ }} - {\text{[(0}}{\text{.037) x (}}\Delta {\text{{\rm A}l}}_{{\text{br}}} )] + [0.063){\text{ x }}(\Sigma {\text{[}}q{\text{/(Na,Ca}} - {\text{O)}}^{\text{2}} ])] \hfill \\ {\text{ }} + {\text{[(0}}{\text{.029) x (}} - {\text{1/cosT}} - {\text{O}} - {\text{T)]}} \hfill \\ \end{gathered}$$ where the Al content of a particular tetrahedral (T) site can be estimated from empirically-derived determinative curves, where Δ Al_br is a linkage factor to account for the Al content of adjacent tetrahedral sites, where the formal charge on the (Na_1?xCa_x) atom is q=1+x, and where T-O-T is the inter-tetrahedral angle involving the T-O bond. For sodic plagioclases it is essential to know only the anorthite content and the 2Θ₁₃₁-2Θ_1¯31 spacing (CuK _α radiation) in order to determine the independent variables in this equation and thus to evaluate the individual T-O distances. The 64 individual T-O distances predicted for the four sodic plagioclases by this equation agree well with the observed T-O bond lengths (σ=0.004 Å; r=0.994), and the method has been used by way of example to rationalize the T-O bond lengths in analcime (cf. Ferraris, Jones and Yerkess, 1972).     

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,

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.     

Burial metamorphism of a Cretaceous volcanic sequence west from Santiago,Chile

This report is a petrographic study of alteration phenomena in an area of 100 km² in the Coastal Range west of Santiago. The stratified sequence of the area is of Cretaceous age and belongs to the western monoclinal limb of the Andean Geosyncline. Two structural units are present, separated by an angular unconformity. The older is about 9,000 m thick, and the younger 300 m thick. The rock types are mostly altered andesitic flows and flow breccias, and keratophyric ignimbrites and lavas, with alternating marine, brackish-water and terrestrial interbeds. Stratified rocks are cut locally by acid and basic apophyses and dikes, probably feeders of their volcanic host rocks. Discordant Cretaceous granitic plutons intrude the older unit. Throughout the whole stratigraphic section there are alteration minerals, which selectively replace the primary minerals, or fill amygdules and open fractures, or form a cement in flows, dikes and sedimentary interbeds. Patterns of alteration are regular and persistent; they correlate on a large scale with stratigraphic level and on a smaller scale with position within each individual flow and situation within amygdules. The stratigraphically controlled pattern is as follows: $$\begin{gathered} 1.{\text{ Younger unit}}{\text{.}} \hfill \\ {\text{ }}\left. \begin{gathered} {\text{Lower portion: 30m: albite}}---{\text{pistacite}}---{\text{actinolite}}---{\text{chlorite}}---{\text{ }} \hfill \\ {\text{calcite}}---{\text{sphene}}---{\text{quartz}} \hfill \\ \end{gathered} \right\}{\text{greenschist facies}} \hfill \\ {\text{2}}{\text{. Older unit}}{\text{.}} \hfill \\ {\text{ }}\left. \begin{gathered} {\text{a) 0}}---{\text{1,280 m : albite}}---{\text{pumpellyite}}---{\text{prehnite}}---{\text{calcite}}---{\text{chlorite}}---{\text{ }} \hfill \\ {\text{ laumontite}} \hfill \\ {\text{b) 1,280}}---{\text{4,850 m: albite}}---{\text{adularia}}---{\text{calcite}}---{\text{prehnite}}---{\text{pumpellyite}}--- \hfill \\ {\text{pistacite}}---{\text{white mica}}---{\text{quartz}} \hfill \\ {\text{c) 4,850}}---{\text{8,110 m: albite}}---{\text{pistacite}}---{\text{quartz}}---{\text{chlorite}}---{\text{calcite}}--- \hfill \\ {\text{white mica}}---{\text{sphene}}---{\text{adularia prehnite}}---{\text{pumpellyite}} \hfill \\ \end{gathered} \right\}{\text{prehnite}}---{\text{pumpellyite facies}} \hfill \\ {\text{ d) 8,110}}---{\text{9,060 m: albite}}---{\text{pistacite}}---{\text{actinolite}}---{\text{sphene}}---{\text{calcite \} greenschist facies}} \hfill \\ \end{gathered} $$ The pattern of alteration in the older unit is comparable to that described for burial metamorphosed sequences in New Zealand and Australia. Reappearence of the greenschist facies at a higher level in the younger unit poses a problem for which several explanations are possible. The smaller scale pattern of alteration shows a persistent tendency —not without exception — for the “grade” of the alteration assemblage (as correlated with depth on the large scale) to increase: from the base of the flow (non-amygdaloidal part) upward (amygdaloidal part), and from the rim of each amygdule inward. Also recognizable on the scale of a single flow is a tendency for upward increase in: a) extent of alteration (the basal zone may be fresh andesite), and b) weight percent of Na₂O, K₂O (with complementary depletion in CaO), and of Fe₂O₃/FeO. Preliminary observations indicate that this alteration pattern persists for at least 400 km north of the area here described in rocks of similar lithology and age. It is unrelated to local granitic plutons.