Structural stabilities, electronic and optical properties of CaF2 under high pressure: A first-principles study

The structural stabilities, electronic and optical properties, the pressure-induced metallization for CaF₂ have been studied by using the density functional theory calculations. The ground phase is predicted to transform into Pnma structure at 8.1 GPa, which is well consistent with the experimental findings. Above 278 GPa, Pnma-CaF₂ transform into P6₃/mmc phase. The calculated structural data for and pnma phases are in very good agreement with experimental values. The electronic band structures show that Pnma and P6₃/mmc phases of CaF₂ are insulators at the transition pressure. Upon further compression, the band gap of P6₃/mmc decreases with pressure, and CaF₂ is predicted to undergo metallization around 2250 GPa. The possible reason for the metallization was discussed. All CaF₂ polymorphs have ionic character between Ca–F bond with the analysis of the charge–density distribution and density of states.     

Critical Field and Shubnikov-de Haas Oscillations of κ-(BEDT-TTF)2Cu(NCS)2under Pressure

We have used a novel experimental method to study the crossover of an anisotropic superconductor from a possible Pauli limited superconducting state to a vortex limited superconducting state by applying pressure. The new apparatus combined a tuned tank circuit with a nonmetallic diamond anvil cell to measure the change in critical field with angle in -(BEDT-TTF)₂Cu(NCS)₂ at pressures up to 1.75 kbar and at temperatures down to 70 mK. The critical fields (in the perpendicular or parallel orientation to the conducting planes) have been found to decrease by more than 90% within less than 2 kbar of pressure. In the parallel orientation, at 1.75 kbar, we have seen a clear change from the ambient pressure behavior of the critical field with temperature at low temperatures. Up to P=1.75 kbar, the H_c2 phase diagram is in good agreement with the theoretical prediction for weakly coupled layered superconductors. We have also succeeded in measuring oscillations in the resistivity of the normal state at higher magnetic field which could be used to find the effective quasi-particle mass. The -orbit Shubnikov-de Haas frequency was found to increase at a rate of 44T/kbar. Our experiment opens the possibility for further investigations of the effective mass with pressure, especially because the setup is suitable for pulsed fields as well.     

Pressure dependence of T c for lead

The superconducting transition temperature T _c for Pb has been determined as a function of hydrostatic pressure up to 26 kbar. T _c is found to more closely follow a linear pressure dependence, with T _c/P = –(3.61 ± 0.05)× 10^–5K/bar, than a linear volume dependence, as previously reported. The volume dependence of the electron-phonon parameter derived from these measurements, d(ln )/d(ln V) = 4.2 ± 0.1, is in good agreement with theoretical calculations by Ott and Sorbello and by Carbotte and Vashishta. The variation of for larger volume changes is discussed.Supported by the Australian Research Grant Committee.     

Calculation of the band structure and superconductivity in the hexagonal close-packed phase of silicon

We report a calculation of the band structure and superconductivity of silicon in the hexagonal close-packed phase under pressure. The effect of pressure on the band structure is obtained by means of the linear muffin-tin orbital method. The superconducting transition temperatureT _c is calculated using the formulas of Allen and Dynes¹ as well as those of McMillan². It is found that the value ofT _c increases with pressure up to 74.3 GPa. The increase inT _c is attributed to the continuous s d electron transfer under pressure. The calculated values ofT _c are compared with the available experimental data. Further, Heine's fifth power law³ has been tested from thed-band widths obtained from the band-structure results.     

Thermal conductivity of five normal alkanes in the temperature range 283–373 k at pressures up to 250 MPa

Experimental data on the thermal conductivity of five liquid n-alkanes-hexane, heptane, octane, decane, and dodecane-are presented in the temperature range from 283 to 373 K at pressures up to 250 MPa or the freezing pressures. The measurements were performed on an absolute basis by an automated transient hot-wire apparatus. The uncertainty of the reported data is estimated to be within ±1%. The thermal conductivity of each alkane decreases almost linearly with rising temperature at a constant pressure and increases with increasing pressure at a constant temperature. Both the temperature coefficient of the thermal conductivity ¦(/T) _p¦ and the pressure coefficient (/P) _T decrease with increasing carbon number of alkanes. The experimental results were correlated with temperature and pressure by a similar expression to the Tait equation. It is also found that both the dense hard-sphere model presented by Menashe et al. and the modified significant structure theory proposed by Prabhuram and Saksena provide good representations of the present experimental results.     

The influence of residual gas pressure on the thermal conductivity of microsphere insulations

Experimental results of investigations of the heat exchange by residual gas in microsphere insulations are presented. The results of measurements of microsphere effective thermal conductivity versus residual gas (N₂) pressure in the pressure range of 10^–3–10⁵ Pa are also given. A sample of self-pumping microsphere insulation was prepared and its thermal parameters were tested. In comparison to the standard microsphere insulation, the self-pumping insulation yielded lower thermal conductivity results over the entire pressure range. The stability of its thermal parameters as a result of considerable gas input into the insulation volume is discussed. Measurements of temperature and pressure distributions inside the microsphere layer were performed. Plots of temperature and pressure gradients inside the layer of the microsphere insulation are presented.Nomenclature d _m Mean value of the microsphere diameter - k Apparent thermal conductivity coefficient - ¯k Average thermal conductivity coefficient - k _c Component of the heat transfer by conduction - k _g Modified gas thermal conductivity under atmospheric pressure - k _r Component of the heat transfer by radiation - k _s Thermal conductivity of the sphere material - k _gc Component of the heat conduction by gas - k _go Gas thermal conductivity under atmospheric pressure - k _gr Sphere effective conductivity - k _ss Component of the heat conduction by the solid state - K 1–(k _g/k _gr) - Kn Knudsen number - ¯L Mean free path of gas molecules - m 1–_s; porosity - m Empty volume of a single sphere - p Residual gas pressure - ¯p Average pressure - p _g Pressure measured by gauge - p ₀ Residual gas pressure above the insulation bed - r Radial coordinate - T Temperature - T _c Temperature of the cold calorimeter wall - T _g Temperature of the pressure gauge - T _H Temperature of the hot calorimeter wall - T _i Gas temperature inside the bed - T _y Constant dependent on the sort of gas - v Volume - Accommodation coefficient - Density - _a Local distance between surfaces - _s Solid fraction - Constant dependent on the sort of gas - Time measured from the initiation of insulation cooling     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

Thermal conductivity of gaseous fluorocarbon refrigerants R 12, R 13, R 22, and R 23, under pressure

The thermal conductivity of four gaseous fluorocarbon refrigerants has been measured by a vertical coaxial cylinder apparatus on a relative basis. The fluorocarbon refrigerants used and the ranges of temperature and pressure covered are as follows: R 12 (Dichlorodifluoromethane CCl₂F₂): 298.15–393.15 K, 0.1–4.28 MPa R 13 (Chlorotrifluoromethane CClF₃): 283.15–373.15 K, 0.1–6.96 MPa R 22 (Chlorodifluoromethane CHClF₂): 298.15–393.15 K, 0.1–5.76 MPa R 23 (Trifluoromethane CHF₃): 283.15–373.15 K, 0.1–6.96 MPaThe apparatus was calibrated using Ar, N₂, and CO₂ as the standard gases. The uncertainty of the experimental data is estimated to be within 2%, except in the critical region. The behavior of the thermal conductivity for these fluorocarbons is quite similar; thermal conductivity increases with increasing pressure. The temperature coefficient of thermal conductivity at constant pressure, (/T) _p , is positive at low pressures and becomes negative at high pressures. Therefore, the thermal conductivity isotherms of each refrigerant intersect each other in a specific range of pressure. A steep enhancement of thermal conductivity is observed near the critical point. The experimental results are statistically analyzed and the thermal conductivities are expressed as functions of temperature and pressure and of temperature and density.     

Very Large Rashba Spin–Orbit Splitting in HgTe Quantum Wells

A large Rashba spin splitting has been observed in the first conduction subband of n-type modulation doped HgTe quantum wells with an inverted band structure via an investigation of Shubnikov–de Haas oscillations as a function of gate voltage. Self-consistent Hartree calculations of the band structure based on an 8 × 8 k p model quantitatively describe the experimental results. It has been shown that the heavy-hole nature of the H1 conduction subband greatly influences the spatial distribution of electrons in the quantum well and also enhances the Rashba spin splitting at large electron densities. These are unique features of type III heterostructures in the inverted band regime. The k ³ dispersion predicted by an analytical model is a good approximation of the self-consistent Hartree calculations for small values of the in-plane wave vector k . This is in contrast to the commonly used k dispersion for the conduction subband in type I heterojunctions.     

Nonlinear dynamics of structures assembled by bolted joints

Summary The nonlinear transfer behaviour of an assembled structure such as a large lightweight space structure is caused by the nonlinear influence of structural connections. Bolted or riveted joints are the primary source of damping compared to material damping, if no special damping treatment is added to the structure. Simulation of this damping amount is very important in the design phase of a structure. Several well known lumped parameter joint models used in the past to describe the dynamic transfer behaviour of isolated joints by Coulomb friction elements are capable of describing global states of slip and stick only.The present paper investigates the influence of joints by a mixed experimental and numerical strategy. A detailed Finite Element model is established to provide understanding of different slip-stick mechanisms in the contact area. An advanced lumped parameter model is developed and identified by experimental investigations for an isolated bolted joint. This model is implemented in a Finite Element program for calculating the dynamic response of assembled structures incorporating the influence of micro- and macroslip of several bolted joints.List of symbols a acceleration - E ₀, E_t material moduli - F ₀ mass weighted excitation force - F _t tangential joint force - F generalized force - F _exc ^* excitation force - F _exc amplitude of excitation force - F _C0 spring element force - F _R0 friction element force - K _A, K_B normal stiffness - K _t tangential stiffness - L length of contact area - M _t transmitted joint torque - m _red reduced mass - p normal contact pressure - r effective radius - q generalized coordinate - z internal variable - x coordinate in the contact area - u relative displacement - u relative velocity - relative angle - friction coefficient - damping ratio - material parameter - ₀ equivalent slip limit - microslip parameter - excitation frequency Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of this 60th birthday     

An integral approach to lifting wing theory at Mach one

Summary An approach to lifting wing theory at Mach one is presented that utilizes an integral method similar to the Karman-Pohlhausen method in boundary layer theory. As in any integral method the results obtained are approximate in nature. Nonetheless, comparison with experimental data shows good agreement in cases for which experimental data are available. The method can easily be used to determine the lift on wings of finite aspect ratio and also to solve transient lifting problems. The method is demonstrated by solving for the pressure distribution on a lifting airfoil of arbitrary symmetric cross-section, the lift on a wing of rectangular planform, and the transient lift on an airfoil due to a sudden change in angle of attack. These cases were chosen to illustrate the versatility of the method and are not meant to be exhaustive of all possibilities. The computational time required to obtain numerical results is very small in all cases considered.List of symbols A parameter associated with Guderley airfoil, defined in equation (28) - AR aspect ratio - AR reduced aspect ratio=AR ^1/3( + 1)^1/3 - c chord of airfoil - C _l sectional lift coefficient - C _L lift coefficient - C _p pressure coefficient - M Mach number - p Laplace transform variable - s span of wing (in units ofc) - t time (in units ofc/U) - U free stream velocity - x streamwise coordinate (in units ofc) - x ^* distance from leading edge to sonic point (in units ofc) - y spanwise coordinate (in units ofc) - z coordinate normal to plane of wing (in units ofc) - angle of attack - y/2s - ratio of specific heats (=1.4 in all calculations) Research sponsored by the Air Force Office of Scientific Research/AFSC, United States Air Force, under Contract No. F44620-72-C-0079. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.     

The hole distribution in cuprate chains

The electronic structure of the prototypical corner-sharing Sr₂CuO₃ linear chain compound is investigated by combining several theoretical and experimental techniques. Band structure calculations within the local density approximation and using a local orbital basis provided the relevant orbitals and the transfer integrals for a four-band extended Hubbard pd-model, which was treated by means of exact diagonalization and of quantum Monte Carlo calculations for finite chain clusters. The band structure values of the transfer integrals t _pd exceed the corresponding values for layered cuprates. Enhanced values of the intersite Coulomb interaction, V _pd = 2 ... 2.5 eV, and a difference between the onsite energies of side and chain oxygen _pp = 0.5 ... 0.75 eV are deduced from the comparison of the model studies with the intensities of polarization dependent x-ray absorption spectra. The latter reflect the hole distribution over the oxygen sites.     

Ultrasonic determination of the elastic and nonlinear acoustic properties of transition-metal carbide ceramics: TiC and TaC

Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic transition-metal carbides TiC and TaC as functions of temperature in the range 135–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The carbon concentration of each ceramic has been determined using an oxidation method: the carbon-to-metal atomic ratios are both 0.98. In general, the values determined for the adiabatic bulk modulus (B ^S), shear stiffness (), Young's modulus (E), Poisson's ratio () and acoustic Debye temperature (_D) for the TiC and TaC ceramics agree well with the experimental values determined previously. The temperature dependences of the longitudinal stiffness (C _L) and shear stiffness measured for both ceramics show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. Both the bulk and Young's moduli of the ceramics increase with decreasing temperature and do not show any unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic pressure derivatives of elastic stiffnesses and the acoustic-mode Grüneisen parameters. The values determined at 295 K for the hydrostatic pressure derivatives (C _L/P)_{P = 0}, (/P)_{P = 0} and (B ^S/P)_{P = 0} for TiC and TaC ceramics are positive and typical for a stiff solid. The adiabatic bulk modulus B ^S and its hydrostatic pressure derivative (B ^S/P)_{P = 0} of TiC are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (_L), shear (_S) and mean (^el) acoustic-mode Grüneisen parameters of TiC and TaC ceramics are positive: the zone-centre acoustic phonons stiffen under pressure. The shear _S is much smaller than the longitudinal _L. The relatively larger values estimated for the thermal Grüneisen parameter ^th in comparison to ^el for the TiC and TaC ceramics indicate that the optical phonons have larger Grüneisen parameters. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiC and TaC.     

Magnetic thermometry to below one millikelvin with lanthanum-diluted cerium magnesium nitrate

Measurements are presented of the pressure and magnetic temperature coordinates of the phase diagram of liquid ³He using a powdered Ce_0.05La_0.95 magnesium nitrate thermometer in the shape of a right circular cylinder with diameter equal to height. The lowest magnetic temperature observed with the thermometer is 0.41 mK. The magnetic temperature of the intersection of the second-order line with the melting curve is 2.625 mK, and the critical temperature at zero pressure is 1.055 mK. The difference between T _c ^* and T _AB ^* extrapolated to melting pressure is 0.57 mK, in excellent agreement with the difference T _A-T_B found from measurements along the melting curve. The present data are compared with the La Jolla provisional absolute scale based on noise thermometry and zero sound. We make the assumption that the absolute temperature T and the present magnetic temperature T ^* are related by T = T ^* + and use the resultant scale to reanalyze a variety of experimental results that had been given in terms of the La Jolla provisional scale.Work supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

Viscosity of aqueous solutions of 1,2-ethanediol and 1,2-propanediol under high pressures

New experimental data on the viscosity of aqueous solutions of 1,2-ethanediol (ethylene glycol) and 1,2-propanediol (propylene glycol) are presented at 298 and 323 K under pressures up to 120 MPa. The measurements were performed by a falling-cylinder viscometer on a relative basis with an uncertainty of less than ±2%. The viscosity of these aqueous solutions at a constant temperature and pressure increases monotonously with increasing concentrations of diols (glycols) and is slightly lower than the mole fraction average value at each composition. The viscosity also increases almost linearly with pressure at a constant temperature and composition. The pressure coefficient of the viscosity, (/P)_T,x, increases with decreasing temperature and increasing concentrations of diols. The experimental results are correlated with pressure, density, and composition by several empirical equations.     

Insight into Phase Transition,Electronic, Magnetic,Mechanical, and Thermodynamic Properties of TbTe: a DFT Investigation

Theoretical investigation on TbTe for its structural, electronic, magnetic, and thermodynamic stuffs has been carried within density functional theory (DFT) as implemented in WIEN2K code. TbTe was found stable in ferromagnetic phase. The calculated ground-state parameters were found in a good agreement with the experimental data. The compound was found to have a structural stability in cubic B1 (NaCl-type structure) phase, but under the application of high pressure (at 27 GPa), it undergone to B2 (CsCl-type structure) phase of pressure. The second-order elastic constants and mechanical properties like Young’s modulus, Shear modulus, Poisson ratio, Cauchy pressure (C₁₂–C₄₄), and Pugh’s ratio (B/G) were calculated. The present calculations confirmed the ductile nature of TbTe. Further, the thermodynamic investigations have been carried using quasi-harmonic Debye approximation. We have calculated the pressure and temperature dependence of Debye temperature (??_D), bulk modulus (B), thermal expansion (α), heat capacities (C_V), and entropy (S) in the temperature range of 0 to 1000 K and pressure range of 0 to 25 GPa.     

Pressure Effect in High-Temperature Superconductors

The model of the pressure effect on the critical temperature T _c in high-temperature superconductors [11], earlier proposed by the present author and consisting in the increase of the pair wave function overlap with increase in pressure p that in its manifestations is equivalent to an increase in doping, is compared with the recent experimental data [1–4]. By making this model more precise for inhomogeneous specimens, we obtained the doping region near the optimal one where the critical temperature is independent of doping, and the pressure region where it is independent of pressure. It is shown that, as observed in [1,2], the dependence of dT _c/dp on doping in HgBa₂CuO₄₊ after excluding the influence of the specimen's inhomogeneous structure is explained satisfactorily by the model of [11]. So the introduction in [1,2] of a term in T _c proportional to p ² is unnecessary. An analogous comparison is made for YBa₂Cu₃O_6+y .     

Pressure Effect in High-Temperature Superconductors and Fullerides

The explanation for the pressure effect in high-temperature superconductors and fullerides is offered. Besides the dependence of the pressure derivative of the critical temperature T _c on doping, the direct dependence of T _c on pressure and the universal dependence of the relative change of T _c ^max–T _c with pressure are obtained for high-temperature superconductors. The unity of the model of the pressure effect in high-temperature superconductors and fullerides is justified. The dependence of T _c on the lattice constant and the connection between the pressure effect and the chemical pressure effect in fullerides are discussed.     

Superconductivity in bulk A15 Nb3Si under pressure

We have determined the effect of hydrostatic pressureP on the superconducting transition temperatureT _c of bulk, A15 Nb₃Si. For 0P20 kbar (2 GPa),T _c decrease linearly with increasing pressure at a rate T _c/P=–2.67×10^–5 K/bar. From an estimate of T _c/P obtained using recent band structure calculations for the density-of-electronic-states change as a function of lattice parameter in Nb₃Si, we conclude that the pressure dependence of the electron-phonon interaction primarily determines T _c/P.Work performed under the auspices of the U.S. DOE.     

The volume change at the superconducting transition of lead and aluminum

The volume change at the magnetic field-induced transition from the super-conducting to the normal state has been measured on single crystals of lead and aluminum between 0.3 K andT _c. From these data we have deduced the pressure dependence of the critical fieldH _c, of the critical temperatureT _c, and of the electronic specific heat coefficient . In lead, the results are in good agreement with theoretical calculations by Carbotte, where strong coupling effects are taken into account. We find ln / lnV=3.1±0.8, whereV is the volume. The measurements on aluminum giving ln / lnV=3±4 are consistent with results derived from thermal expansion experiments.This work was in part financially supported by the Schweizerischer Nationalfonds.