A search for evolutionary period variations of Cepheids using the Harvard plates: V396 Cyg

We obtained 503 photographic brightness estimates for the long-period classical Cepheid V396 Cyg (P = 33.3 days) from the plates of the Harvard Observatory and the Sternberg Astronomical Institute (SAI). Combined with published photoelectric observations, these data were used to plot an O-C diagram covering a time interval of 108 years. The O-C diagram is parabolic in shape, enabling the first determination of quadratic light elements and calculation of the evolutionary rate of decrease of the period, dP/dt = 14.1(±0.8) s per year (log(?/P) = ?6.35), in agreement with theoretical computations for the second crossing of the instability strip. The available data, reduced using the method introduced by Eddington and Plakidis, demonstrate the presence of small random period fluctuations that do not distort the evolutionary changes of the O-C residuals.     

A search for evolutionary period variations of Cepheids using the Harvard plate stacks: FF Aql

Photographic plates of the Harvard Observatory stacks have been used to obtain 1261 brightness estimates for the low-amplitude Cepheid FF Aql (P = 4.47 days). Combined with published visual, photoelectric, and CCD observations, these data enable the construction of an O-C diagram spanning 122 years. The resulting O-C diagram is parabola-shaped, enabling the determination of quadratic brightness elements for the first time. The evolutionary rate of increase of the period, dP/dt = 0.072 ± 0.011 s/year, is in agreement with theoretical computations for the third crossing of the instability strip. The available data, reduced using the technique of by Eddington and Plakidis, reveal the presence of small, random period fluctuations, ? = 0.0061^d ± 0.0044^d, that do not distort the evolutionary trend of the O-C residuals.     

The drift model for AXPs and SGRs in the light of new observtional data

The latest observational data are analyzed to investigate their consistency with two known models for anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs): the magnetar and drift models. The results of spectral measurements disagree with the predictions of theories that assume the presence of super-strong magnetic fields on AXPs and SGRs and associated processes for the generation of electron-positron plasma in the upper layers of the neutron-star magnetosphere. We present arguments against the use of magnetic-dipole braking for these objects. The rotational periods P, period derivatives dP/dt, and magnetic fields B of known AXPs and SGRs are calculated for the drift model. The mean values of these parameters in the sample used are 〈P〉 = 108 ms and 〈log B _s [G]〉 = 12.08. Overall, the measured profiles, polarizations, and spectra can be brought into agreement with the drift model.     

Multiplicity and apsidal motion in the eclipsing binary EQ Boo

We present the first estimates of the relative and absolute parameters of the eclipsing binary EQ Boo based on a light-curve analysis (P = 5.43^d, V = 8.8 ^m ). This star is simultaneously Component A of the visual binary ADS 9422 (spectral types F7V + G0V; separation of the components 1.3″; magnitude difference 0.7 ^m ). The derived disagreement between the components’ physical parameters and the assumption that they have the same age can be removed if there is a fourth, late-type star in the system. This is also able to explain the observed anomaly in the behavior of the O-C residuals at times of minima.     

The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W ₁₀, since the broadening of the observed pulses due to the transition to the full width W ₀ and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β ₁ are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β ₁〉 = 18° at λ = 10 cm and 〈β ₁〉 = 14° at λ = 20 cm). The angle β ₂ is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β ₂ at 10 cm is found to be 〈β ₂〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β ₂〉 = 52.1° ifC < 0. We find at 20 cm 〈β ₂〉 = 33.9° ifC > 0 and 〈β2〉 = 54.1° ifC < 0. The values at the two wavelengths are equal within the errors, and close to the β ₂ value obtained earlier at 30 cm (〈β ₂〉 = 36.4° if C >0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β ₂〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P ^−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P ^−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.     

Features of discrete VLF emissions observed at Gulmarg,India during the magnetic storm of 6–7 March, 1986

During the analysis of archived VLF data from Indian low latitude ground stations, some discrete VLF emissions recorded at the low latitude ground station Gulmarg (geomagnetic latitude 24°26′N; geomagnetic longitude 147°09′E, L = 1.28) during moderate magnetic storm activity (Σ K _P ⁻ = 32, K _P index varies from 4 to 6 during the observation period) on 6/7 March, 1986 are presented in this paper. The dynamic spectra of these discrete VLF emissions were observed along with tweeks and its harmonics, which is interesting and complex to explain. In most of the events the harmonic frequency of tweeks correlates with the starting frequency of harmonics of discrete emissions. In order to explain the observed features of discrete VLF emissions, we propose cyclotron resonance interaction between whistler mode wave and energetic electrons of inner radiation belt as possible generation mechanism. An attempt is also made to determine parallel energy, anisotropy and wave growth relevant to the generation process of VLF emissions.     

Thermal equations of state of dioctahedral micas on the join muscovite–paragonite

 Powder diffraction measurements at simultaneous high pressure and temperature on samples of 2M1 polytype of muscovite (Ms) and paragonite (Pg) were performed at the beamline ID30 of ESRF (Grenoble), using the Paris-Edinburgh cell. The bulk moduli of Ms, calculated from the least-squares fitting of V–P data on each isotherm using a second-order Birch–Murnaghan EoS, were: 57.0(6), 55.1(7), 51.1(7) and 48.9(5) GPa on the isotherms at 298, 573, 723 and 873 K, respectively. The value of (∂K _T /∂T) was −0.0146(2) GPa K⁻¹. The thermal expansion coefficient α varied from 35.7(3) × 10⁻⁶ K⁻¹ at P ambient to 20.1(3) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −3.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. The corresponding values for Pg on the isotherms at 298, 723 and 823 K were: bulk moduli 59.9(5), 55.7(6) and 53.8(7) GPa, (∂K _T /∂T) −0.0109(1) GPa K⁻¹. The thermal expansion coefficient α varied from 44.1(2) × 10⁻⁶ K⁻¹ at P ambient to 32.5(2) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −2.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. Thermoelastic coefficients showed that Pg is stiffer than Ms; Ms softens more rapidly than Pg upon heating; thermal expansion is greater and its variation with pressure is smaller in Pg than in Ms. Received: 28 January 2002 / Accepted: 5 April 2002     

Franciscan eclogite revisited: Reevaluation of the P–T evolution of tectonic blocks from Tiburon Peninsula, California, U.S.A.

Summary High-grade blocks in the Franciscan complex at Tiburon, California, record relatively low temperature eclogite-facies metamorphism and blueschist-facies overprinting. The eclogite-facies mineral assemblage contains prograde-zoned garnet + omphacite + epidote ± hornblende (katophoritic and barroisitic Ca–Na amphibole) ± glaucophane + phengite (∼3.5 Si p.f.u.) ± paragonite + rutile + quartz. The blueschist-facies mineral assemblage contains chlorite + titanite + glaucophane + epidote ± albite ± phengite (∼3.3 Si p.f.u.). Albite is not stable in the eclogite stage. New calculations based on garnet-omphacite-phengite thermobarometry and THERMOCALC average-P–T calculations yield peak eclogite-facies P–T conditions of P = 2.2–2.5 GPa and T = 550–620 °C; porphyroclastic omphacite with inclusions of garnet and paragonite yields an average-P–T of 1.8 ± 0.2 GPa at 490 ± 70 °C for the pre-peak stage. The inferred counterclockwise hairpin P–T trajectory suggests prograde eclogitization of a relatively “cold” subducting slab, and subsequent exhumation and blueschist-facies recrystallization by a decreasing geotherm. Although an epidote-garnet amphibolitic assemblage is ubiquitous in some blocks, P–T pseudosection analyses imply that the epidote-garnet amphibolitic assemblage is stable during prograde eclogite-facies metamorphism. Available geochronologic data combined with our new insight for the maximum pressure suggest an average exhumation rate of ∼5 km/Ma, as rapid as those of some ultrahigh pressure metamorphic terranes.     

In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg₃Al₂Si₃O₁₂) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) _P = −19.3(4); (∂G/∂T) _P = −10.4(2) MPa K⁻¹] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) _P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂² G/∂P∂T = [0.07(12), 0.20(14)] × 10⁻³ K⁻¹ and ∂² K _S /∂P∂T = [−0.20(24), 0.22(26)] × 10⁻³ K⁻¹, both of order 10⁻⁴ K⁻¹ and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.     

The petrogenesis of basic and ultrabasic alkaline rocks of western Makhtesh Ramon,Israel: geochemistry,melt and fluid inclusion study

The basic and ultrabasic alkaline rocks of western Makhtesh Ramon, Israel crop out in numerous lava flows and subvolcanic bodies. The rock suite is composed of tephrite, basanite, basanitic nephelinite, analcimite, olivine nephelinite, and melilite-olivine nephelinite and in many outcrops is represented by glass-bearing varieties. Melt and fluid inclusions have been studied in olivine, clinopyroxene, and plagioclase phenocrysts. The EP, SIMS and microthermometry methods were used for inclusion study. The geochemical data obtained on glasses of melt inclusions (major, REE, trace elements, volatiles) are compared with the data on whole-rock and groundmass glass compositions. The compositions of melt inclusions reflect the different stages of rock crystallization: the initial products of crystallization are similar to whole-rock compositions whereas final portions of melts are usually enriched in SiO₂, Al₂O₃, and alkalis, and depleted in mafic components. The data on contemporaneous melt and CO₂ inclusions were used for the evaluation of the P–T conditions of rock generation. The following parameters were obtained: tephrite: P = 6.3–7.7 kbar and T = 1,150–1,250°C; basanite: P = 6.6–9.2 kbar and T = 1,150–1,250°C; olivine and analcime-olivine nephelinite: P = 5.6–8.2 kbar and T = 1,150–1,250°C; melilite-olivine nephelinite: 4.0–5.4 kbar and T mainly between 1,150 and 1,200°C. Magma genesis was restricted to P–T conditions of spinel- and plagioclase-lherzolite fields. These data suggest the shallowest depth of magma genesis occurred in Makhtesh Ramon compared to other occurrences of Early Cretaceous magmatism at the Middle East. Differences in the degree of batch partial melting of the same source rocks best explain the diversity of the igneous suite in western Makhtesh Ramon.     

Low T heat capacity measurements and new entropy data for titanite (sphene): implications for thermobarometry of high-pressure rocks

The accepted standard state entropy of titanite (sphene) has been questioned in several recent studies, which suggested a revision from the literature value 129.3 ± 0.8 J/mol K to values in the range of 110–120 J/mol K. The heat capacity of titanite was therefore re-measured with a PPMS in the range 5 to 300 K and the standard entropy of titanite was calculated as 127.2 ± 0.2 J/mol K, much closer to the original data than the suggested revisions. Volume parameters for a modified Murgnahan equation of state: V _P,T  = V ₂₉₈° × [1 + a°(T − 298) − 20a°(T − 298)] × [1 – 4P/(K ₂₉₈ × (1 – 1.5 × 10⁻⁴ [T − 298]) + 4P)]^1/4 were fit to recent unit cell determinations at elevated pressures and temperatures, yielding the constants V ₂₉₈° = 5.568 J/bar, a° = 3.1 × 10⁻⁵ K⁻¹, and K = 1,100 kbar. The standard Gibbs free energy of formation of titanite, −2456.2 kJ/mol (∆H°_f = −2598.4 kJ/mol) was calculated from the new entropy and volume data combined with data from experimental reversals on the reaction, titanite + kyanite = anorthite + rutile. This value is 4–11 kJ/mol less negative than that obtained from experimental determinations of the enthalpy of formation, and it is slightly more negative than values given in internally consistent databases. The displacement of most calculated phase equilibria involving titanite is not large except for reactions with small ∆S. Re-calculated baric estimates for several metamorphic suites yield pressure differences on the order of 2 kbar in eclogites and 10 kbar for ultra-high pressure titanite-bearing assemblages.     

Heat capacity of wadeite-type K2Si4O9 and the pressure-induced stable decomposition of K-feldspar

The heat capacity of synthetic, stoichiometric wadeite-type K₂Si₄O₉ has been measured by DSC in the 195≤T(K)≤598 range. Near the upper temperature limit of our data, the heat capacity observed by DSC agrees with that reported by Geisinger et al. (1987) based on a vibrational model of their infrared and Raman spectroscopic data. However, with decreasing temperature, the Cp observed by DSC is progressively higher than that predicted from the vibrational model, suggesting that the standard entropy of K₂Si₄O₉ is likely to be larger than 198.9 ± 4.0 J/K · mol computed from the spectroscopic data. A fit to the DSC data gave: Cp(T) = 499.13 (±1.87) − 4.35014 · 10³(±3.489 · 10¹) · T ^−0.5, with T in K and average absolute percent deviation of 0.37%. The room-temperature compressibilities of kalsilite and leucite, hitherto unknown, have been measured as well. The data, fitted to the Murnaghan equation of state, gave K _o = 58.6 GPa, K _o ^′ = 0.1 for kalsilite and K _o = 45 GPa, K _o ^′ = 5.7 for α-leucite. Apart from the above mentioned data on the properties of the individual phases, we have also obtained reaction-reversals on four equilibria in the system K₂O-Al₂O₃-SiO₂. The Bayesian method has been used simultaneously to process the properties of 13 phases and 15 reactions between them to derive an internally consistent thermodynamic dataset for the K₂O-Al₂O₃-SiO₂ ternary. The enthalpy of formation of K₂Si₄O₉ wadeite is in perfect agreement with its revised calorimetric value, the standard entropy is 232.1 ± 10.4 J/K · mol, ∼15% higher than that implied by vibrational modeling. The phase diagram, generated from our internally consistent thermodynamic dataset, shows that for all probable P-T trajectories in the subduction regime, the stable pressure-induced decomposition of K-feldspar will produce coesite + kalsilite rather than coesite + kyanite + K₂Si₄O₉ (cf. Urakawa et al. 1994). Received: 11 June 1997 / Accepted: 2 December 1997     

Pressure–volume–temperature equations of state: a comparative study based on numerical simulations

 The P–V–T equation of state (EoS) models of Birch–Murnaghan, Vinet and Poirier–Tarantola have been compared with one another and discussed in the light of their ability to reproduce thermoelastic functions and parameters by means of fitting to pressure–volume–temperature data artificially generated for spinel, corundum and forsterite. Numerical simulations relying upon semi-empirical potentials, lattice dynamics and the quasiharmonic approximation have been used to generate P–V–T data. The results obtained indicate that all the P–V–T EoSs tested predict bulk modulus at ambient conditions with errors confined, at worst, within a few percent, and reproduce correctly its dependence on temperature. The derivatives of the bulk modulus versus P and PT are less satisfactorily modelled. The bulk thermal expansion is determined by EoSs within a few percent error, but the deviations increase significantly if the approximation of linear dependence of EoS on temperature is used (linearised thermal pressure model). Received: 30 January 2001 / Accepted: 16 June 2001     

High-temperature elasticity of magnesioferrite spinel

The elastic moduli of magnesioferrite spinel, MgFe₂O₄, and their temperature dependence have been determined for the first time by ultrasonic measurements on a polycrystalline specimen. The measurements were carried out at 300 MPa and to 700°C in a gas-medium high-pressure apparatus. On heating, both the elastic bulk (K _S) and shear (G) moduli decrease linearly to 350°C. By combining with extant thermal-expansion data, the values for the room-temperature K _S and G, and their temperature derivatives are as follows: K ₀ = 176.3(7) GPa, G ₀ = 80.1(2) GPa, (∂K _S/∂T) _P = −0.032(3) GPa K⁻¹ and (∂G/∂T) _P = −0.012(1) GPa K⁻¹. Between 350 and 400°C, there are abrupt increases of 1.4% in both of the elastic moduli; these closely coincide with the magnetic Curie transition that was observed by thermal analyses at about 360°C.     

Photometric elements,apsidal motion,and the third body in the eclipsing binary V974 Cyg

We have derived the first photoelectric light curve of the eclipsing binary V974 Cyg from our own photoelectric observations. Analysis of the light curve has yielded the system’s photometric elements (r ₁ ≈ r ₂ = 0.1192, e = 0.058, L ₁ ≈ L ₂ = 0.486, and L ₃ = 0.028) and absolute parameters (M ₁ ≈ M ₂ = 2.2M _⊙, T _eff,1 ≈ T _eff,2 = 9500 K, a = 15.0R _⊙, distance d = 1.29 kpc, age log t = 8.0, t/tMS = 0.11). We have detected apsidal motion with the period U _obs = (1140 ± 170) yrs, and the presence of a third body in the system. The orbital parameters derived for the third body are P ₃ = 26.5 yrs, e ₃ = 0.78, and a ₃ sin i ₃ = 1.5 AU; and the lower limit for its mass is M ₃ > 0.58M _⊙. The observed apsidal-motion rate is higher than is expected theoretically by a factor of 1.5. The axial rotation of the system’s components is not yet synchronized with the orbital motion, probably because V974 Cyg is relatively young and detached.     

Nature of the crust in Maine,USA: evidence from the Sebago batholith

 Neodymium and lead isotope and elemental data are presented for the Sebago batholith (293±2 Ma), the largest exposed granite in New England. The batholith is lithologically homogeneous, yet internally heterogeneous with respect to rare earth elements (REE) and Nd isotopic composition. Two-mica granites in the southern/central portion of the batholith (group 1) are characterized by REE patterns with uniform shapes [Ce_N/Yb_N (chondrite normalized) = 9.4–19 and Eu/Eu* (Eu anomaly) = 0.27–0.42] and ɛ _Nd(t) = −3.1 to −2.1. Peripheral two-mica granites (group 2), spatially associated with stromatic and schlieric migmatites, have a wider range of total REE contents and patterns with variable shapes (Ce_N/Yb_N = 6.1–67, Eu/Eu* = 0.20–0.46) and ɛ _Nd(t) = −5.6 to −2.8. The heterogeneous REE character of the group 2 granites records the effects of magmatic differentiation that involved monazite. Coarse-grained leucogranites and aplites have kinked REE patterns and low total REE, but have Nd isotope systematics similar to group 2 granites with ɛ _Nd(t) = −5.5 to −4.7. Rare biotite granites have steep REE patterns (Ce_N/Yb_N = 51–61, Eu/Eu* = 0.32–0.84) and ɛ _Nd(t) = −4.6 to −3.8. The two-mica granites have a restricted range in initial Pb isotopic composition (²⁰⁶Pb/²⁰⁴Pb = 18.41–18.75; ²⁰⁷Pb/²⁰⁴Pb = 15.60–15.68; ²⁰⁸Pb/²⁰⁴Pb = 38.21–38.55), requiring and old, high U/Pb (but not Th/U) source component. The Nd isotope data are consistent with magma derivation from two sources: Avalon-like crust (ɛ _Nd>−3), and Central Maine Belt metasedimentary rocks (ɛ _Nd<−4), without material input from the mantle. The variations in isotope systematics and REE patterns are inconsistent with models of disequilibrium melting which involved monazite. Received: 8 December 1995 / Accepted: 29 April 1996     

Detection of radio emission from the AXP 4U 0142+61

The detection of pulsed radio emission from the X-ray pulsar AXP 4U 0142+61 with a period of P = 8.68832935(6) s and a period derivative of $ \dot P $ \dot P = 18.713(4) × 10⁻¹³ s/s is reported. The observations were carried out on two high-sensitivity radio telescopes of the Pushchino Radio Astronomy Observatory: the Large Phased Array at 111MHz and the DKR-1000 at 40MHz.Mean pulse profiles are presented; the measured flux density is S ₁₁₁ = 30 ± 20 mJy. The estimated distance derived from the dispersion measure, 27 pc/cm³, is 1.4 kpc, and the integrated radio luminosity is L _R = 1.5 × 10²⁷ erg/cm. Comparison with X-ray data shows an appreciable difference in the pulse duration (the radio pulse is about a factor of 20 more narrow) and strong variations in the flux density.     

P-V-T equation of state of lawsonite

A pressure-volume-temperature data set has been obtained for lawsonite [CaAl₂Si₂O₇(OH)₂.H₂O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V₀ (∂V/∂P) _T . At room temperature, the derived equation of state parameters are: K ₀=124.1 (18) GPa K'₀ set to 4) and β^–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K ₀=123.9(18) GPa, (∂K/∂T)_P=–0.111(3) GPa K^–1, (∂² K/∂T ²)_P=0.28(6) 10^–3 GPa K^–2, α₀=3.1(2) 10^–5 K^–1, assuming K'₀=4. Received: 2 June 1998 / Revised, accepted: 12 Ocotber 1998     

Synchrotron powder diffraction study of phengite 3T from the Dora-Maira massif: P -V -T equation of state and petrological consequences

X-ray powder diffraction measurements have been carried out at ESRF (Grenoble, France) on the ID30 beamline to study the equation of state of 3T phengite (Dora-Maira massif, Italian western Alps) by a large volume cell up to P = 50 kbar and T = 1000 K. Several equations of state (EOS) models (the Vinet EOS, the Birch-Murnaghan EOS and its variants, a VT-polynomial expansion) have been used to interpolate the experimental data and discussed in the light of the results achieved. The thermoelastic properties of 3T phengite (bulk modulus, its derivatives versus pressure or temperature, bulk thermal expansion) have been obtained and an isochoric curve with slope P/T = 0.02 kbar/K has been calculated by means of the Vinet EOS. This slope value supports either the occurrence at the peak conditions (about 30 kbar and 1000 K) of an originally Mg/Si-richer and stiffer phengite or a non-isochoric P-T retrograde path. Received: 5 June 1998 / Revised, accepted: 12 December 1998     

Elasticity of TiO2 rutile to 1800 K

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 oK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less. Received: 19 September 1997 / Revised, accepted: 27 February 1998