Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Magnetic field dependence of the density of states of YBa2Cu3O6.95: Implications for the vortex structure

The total specific heat of YBa₂Cu₃O_6.95 single crystals includes contributions from phonons and spin-1/2 particles, as well as electronic contributions. The electronic specific heat is described by a quadratic term T² in zero field and a linear term [(0)+(H)]T which is increased when a magnetic field H is applied perpendicular to the CuO₂ planes. In agreement with d-wave superconductivity, we find that _n/T_c and (H)_n(H/H_c2)^1/2, where _n is the coefficient of the normal-state linear term. The H^1/2 dependence of the density of states at the Fermi level was predicted by G. Volovik for lines of nodes in the gap: the quasiparticles which contribute to this density of states are close to the nodes in momentum space and are located outside the vortex core.     

Precipitation in Ni-Co-Al alloys

Discontinuous precipitation of the phase in Ni-Co-Al alloys has been studied in the temperature range 673 to 973 K using optical microscopy and transmission electron microscopy. Discontinuous precipitation was observed to occur in all the alloys to some degree, the extent of the precipitation decreasing with decreasing cobalt content of the alloy. Only in high cobalt alloys (greater than 38 at%) did the discontinuous transformation go to completion. The discontinuous transformation product consisted of fine straight coherent lamellae with a specific cube-cube orientation relationship to the matrix at low ageing temperatures and short times. At higher temperatures and longer times, continuous and discontinuous coarsening processes produced a coarse, less regular structure with a plate spacing ten times that of the regular structure. The overall kinetics of the discontinuous transformation were affected by the prior continuous precipitation of particles ahead of the discontinuous reaction fronts. The coarsening of these continuous particles as a function of time stopped the transformation in low cobalt alloys and continuously slowed the rate of transformation in high cobalt alloys resulting in Avrami exponents,n, less than 1. Reversion experiments and experiments on prestrained specimens yielded Avrami exponents ofn=1 lending support to the above suggestion. The major effect of cobalt in these alloys was to increase their propensity to transform discontinuously. This effect was largely due to the decrease in the rate of continuous precipitation and coarsening as a result of the increased partitioning of cobalt between and in high cobalt alloys.     

Critical light scattering in4He near the gas-liquid critical point

Scattered intensities of light were measured near the gas-liquid critical point of ⁴ He at scattering angles of 30, 60, and 90° as functions of the reduced temperature =|T–T _c |/T _c along the critical isochore (T>T _c ) and the coexistence curve (T>T _c ). The temperature range was 3×10 ^–5 <<1.5×10 ^–2 . Critical exponents and coefficients describing divergence of the generalized susceptibility and the correlation length are obtained as (T>T _c )=1.31±0.02, v(T>T _c )=0.66±0.02, ₀ (T>T _c )=4.2±0.6 Å, (T>T _c )=1.32±0.02, v(T>T _c )=0.68±0.02, _± (T>T _c )=2.6±0.7 Å, =0.06±0.06(T>T _c ), 0.05±0.05(T>T _c ), and ₀(T>T _c )/x_± (T>T _c )=3.6±0.4. It is pointed out that the quantal nature of ⁴ He has remarkable influence on the critical behavior of ⁴ He in the above-mentioned temperature region.     

Improvements in the transverse properties of composites

Fracture surface energies of initiation ( _I ^c) for a transverse fracture process in glass-reinforced epoxy composites have been measured and the results calculated by three different treatments and are compared with the average fracture surface energies ( _F ^c) for the complete fracture process.Changes in these two fracture properties are studied as a function of the volume fraction of the fibres, and the relation between the surface energies is established as a factor which determines the nature of the fracture process. When _I{sic}– _F ^c>0 a catastrophic failure is expected, whereas a controlled fracture is observed for _I ^c– _F ^c<0.     

Equation of state for compressed liquids from surface tension

A method for predicting an analytical equation of state for liquids from the surface tension and the liquid density at the freezing temperature ( ₁, ₁) as scaling constants is presented. The reference temperature. T_ref. is introduced and the product (T _ref T ₁ ^{1 2} ) is shown to be an advantageous corresponding temperature for the second virial coeflicienls. B₂(T). of spherical and molecular fluids. Thus, B₂(T) follows a promising corresponding states principle and then calculations for(T) andb(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, ( ₁, ₁) are sufficient for the determination of thermophysical properties of fluids from the freezing line up to the critical temperature. The present procedure has the advantage that it can also be used in cases whereT _c andP _c are not known or the vapor pressure is too small to allow accurate measurements. We applied the procedure to predict the density of Lennard-Jones liquids over an extensive range of temperatures and pressures. The results for liquids with a wide range of acentric factor values are within 5%.     

Direct current electrical conductivity of gamma ferric oxide

The study of the direct current electrical conductivity, , of freshly prepared -Fe₂O₃ and that of a sample stored for seven days in static air suggests that -Fe₂O₃ adsorbs oxygen and water from the atmosphere. From infra-red spectra it is deduced that the absorbed water in -Fe₂O₃ is present as the physically adsorbed water and as lattice water. The adsorbed oxygen and physically adsorbed water are removed by heating to 100 C, while the lattice water remains in -Fe₂O₃ even up to 280 C. The removal of lattice water is associated with a decomposition during which some of the hydrogen formed occupies the vacancy sites. This suggested formation of the hydrogen ferrite phase is based on the kink in the log against T ^–1 curve observed at 177 C. This kink is very well resolved for a sample equilibrated at 100 C in normal atmosphere, and the measurements of above 100 C of this sample are done in an N₂ atmosphere. The suggestion that the hydrogen ferrite phase is formed has been substantiated by comparison of the X-ray diffraction patterns of -Fe₂O₃ heated under the different atmospheres. From the log against T ^–1 plot for a sample heated under a nitrogen atmosphere the activation energy is small (< 0.05 eV) up to 215 C, and it is comparatively large (0.95 eV) above 215 C. These results suggest a hopping mechanism for the direct current electrical conductivity of -Fe₂O₃. This suggestion has been substantiated by data of the temperature variation of Seebeck voltage.     

The fracture energy of a glass fibre composite

The fracture energy of a glass fibre-polyester composite has been measured by work of fracture ( _f) measurements on bending beams, and by linear elastic fracture mechanics analyses ( _i) of the bending beams and edge-notched tensile plates. It was found that for the bend specimens _i< _f. The work of fracture, _f, displayed a strain rate dependence, but there was no such dependence of _i. It is postulated that _i is determined by a debonding mechanism while _f is the sum of a debonding mechanism plus a pull-out contribution. The edge-notched tensile plate experiments showed that _i obtained from thick plates was less than that obtained from side-grooved plates, and that in each case there was a dependence of _i on crack size.     

Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Attenuation of first sound has been measured in ⁴He under saturated vapor pressure near the lambda temperature T at frequencies /2 ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function (, ) = ^1+y F(), where = ₀^–x and = T/T – 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ^x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.Based on a Ph.D dissertation submitted by K. Tozaki to the University of Tokyo (1977).     

Equation of State for Molten Alkali Metals from Surface Tension. Part II

This work presents a new method for predicting the equation of state for molten alkali metals, based on statistical–mechanical perturbation theory from two scaling constants that are available from measurements at ordinary pressures and temperatures. The scaling constants are the surface tension and the liquid density at the boiling temperature (_b, _b). Also, a reference temperature, T _Ref, is presented at which the product (T _Ref T _b ^1/2 ) is an advantageous corresponding temperature for the second virial coefficient, B ₂(T). The virial coefficient of alkali metals cannot be expected to obey a law of corresponding states for normal fluids, because two singlet and triplet potentials are involved. The free parameter of the Ihm–Song–Mason equation of state compensates for the uncertainties in B ₂(T). The vapor pressure of molten alkali metals at low temperatures is very low and the experimental data for B ₂(T) of these metals are scarce. Therefore, an equation of state for alkali metals from the surface tension and liquid density at boiling temperature (_b, _b) is a suitable choice. The results, the density of Li through Cs from the melting point up to several hundred degrees above the boiling temperature, are within 5%.     

The effective surface energy of brittle materials

The effective surface energy of four brittle materials, alumina, poly(methylmethacrylate), glass, and graphite, is calculated from load/deflection curves of notched bars deformed in three-point bending. Two of the methods, which are commonly used in fracture mechanics studies,viz the modified Griffith treatment and the compliance analysis method, are concerned with the effective surface energy at the initiation of fracture, _I . The third method, the work of fracture test, is concerned with the mean effective surface energy over the whole fracture process, _F . The two estimates of _I give consistent values, and there is no systematic variation of _I with notch depth. Values of _F decrease with increasing notch depth as the fracture process becomes more controlled. For alumina _{I F} . For PMMA and glass _I > _F because of a multiplicity of crack sources during fracture initiation. For graphite _I < _F because of subsidiary cracking as fracture proceeds.     

Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

Equation of State for Complex Liquid Mixtures from Surface Tension

The present work shows a successful extension of previous studies to molecular liquids for which the second virial coefficients are not known. Recent advances in the statistical mechanical theory of equilibrium fluids can be used to obtain an equation of state (EOS) for compressed normal liquids and molten alkali metals. Three temperature-dependent quantities are needed to use the EOS: the second virial coefficient, B(T), an effective van der Waals covolume, b(T), and a scaling factor, (T). The second virial coefficients are calculated from a correlation that uses the surface tension, _tr, and the liquid density at the triple point. Calculation of (T) and b(T) follows by scaling. Thus, thermodynamic consistency is achieved by use of two scaling parameters (_tr, _tr). The correlations embrace the temperature range T _tr<T<T _c and can be used in a predictive mode. The remaining constant parameter is best found empirically from _tr data for pure dense liquids. The equation of state is tested on 42 liquid mixtures The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T _tr to T _c.     

The fracture energy of carbon-fibre reinforced glass

The fracture energy of carbon-fibre reinforced glass has been measured by the work of fracture technique, using specimens of varied geometry, Meaningful material properties were obtained only when crack propagation was controlled throughout failure. The work of fracture ( _F) depended on strain-rate and fibre volume fraction, and was typically 3 kJm^–2 for a 40 vol % specimen. Variations of work of fracture due to strain-rates have been related to the microstructure of the fracture surfaces and estimates have been obtained of the fibre-matrix interfacial shear stress during pull-out. Approximate estimates have been made of the fracture initiation energy ( _I) by fracture mechanics analyses, _I was less than _F and no strain-rate sensitivity was detected. An attempt has been made to explain _I in terms of the initial rate of release of strain energy during fibre fracture.     

Pseudogap Behavior in the Electronic Specific Heat of La2−xSrxCuO4

In La214, the electronic specific heat coefficient (=C _el /T) is gradually suppressed with lowering T below a certain temperature T* (> T _c ), where the in-plane resistivity and magnetic susceptibility also tend to be suppressed slightly. Temperature T*, increasing with lowering x, is in qualitative agreement with the mean field T _c (T _co ), estimated from the superconducting gap amplitude 2 _o at T T _c , as the onset temperature T* of a pseudogap in Bi2212. The gradual suppression of below T _co implies that a pseudogap will also open up below T _co in La214 as in Bi2212. In underdoped samples, whose pseudogap-like behaviors in C _el(T) become marked, the anomaly of C _el around T _c is rather different from the BCS expectation.     

A high-resolution-electron-microscopy study of a γ/γ′-α directionally solidified eutectic alloy

The microstructure of a /- directionally solidified (DS) eutectic alloy with a nominal composition of Ni-30.26Mo-6.08Al-1.43V (wt%) was investigated by means of high-resolution electron microscopy (HREM) and analytical electron microscopy. The -fibres exhibited a typical morphology with a rectangular cross-section and they displayed the Bain orientation relationship (OR) with the / matrix; that is, [001][001] and (110)(010). Misfit dislocations and lattice strain fields existed at the / interface for different habit planes; that is, (110)(010) and (100)(110) were analysed. EDAX (Energy dispersive X-ray) analysis showed that the composition of the -phase was approximately Ni₄(Mo, Al, V); it contained 90° rotational domains of Ni₃(Mo, Al, V) with a DO₂₂ structure and Ni₂(Mo, Al, V) with a Pt₂Mo structure.     

Electronic specific heat of La2−xSrxCu1−yMyO4(M=Ga,Zn): Impurity effects on a D-wave superconductor

The electronic specific heat C_el was studied in Ga- and Zn-doped La_2–xSr_xCuO₄ (0.16x0.22) at T10K. Partial substitution of Ga or Zn for Cu suppresses T_c and revives the T-linear electronic specific heat, T, markedly. The (y)/n vs T_c/T_c0 relation for Zn-doped samples with x0.2 is in good agreement with the theoretical one for resonant impurity scattering in a d-wave superconductor, while those for Ga-doped samples and for Zn-doped samples with x 0.2 deviate slightly from the theoretical curve. The deviation will be discussed in relation to changes in the magnetic properties of 3d electrons.     

Viscoelastic and rheological behavior of concentrated colloidal suspensions

Molecular approaches are discussed to the density (), viscoeleastic (), and rheological () behavior of the viscosity(,,) of concentrated colloidal suspensions with 0.3 < < 0.6, where, is the volume fraction, the applied frequency, and ; the shear rate. These theories are based on the calculation of the pair distribution functionP ₂(r,,), wherer is the relative position of a pair of colloidal particles. The linear viscoelastic behavior(,,=0) follows from an equation forP ₂(r,,) derived from the Smoluchowski equation for small, generalized to large by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The rheological behavior(,,=0) follows from an equation forP ₂(r,) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity^hs(,) which yields the colloidal one(,) by the scaling relation(,) ₀=^hs(,) _B, where ₀ is the solvent viscosity. _B is the dilute hard-sphere (Boltzmann ) viscosity and the's are appropriately scaled,(,) and(,) agree well with experiment. A unified theore for(,,) is clearly needed and pursued.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994. Boulder, Colorado, U.S.A.     

Ultrasonic study of the elastic and nonlinear acoustic properties of ceramic aluminum nitride

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of aluminum nitride (AlN) ceramic samples as functions of temperature in the range 100–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Aluminum nitride is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C _L), shear stiffness (), adiabatic bulk modulus (B ^S), Young's modulus (E) and Poisson's ratio () are 373 GPa, 130 GPa, 200 GPa, 320 GPa and 0.234, respectively. The temperature dependences of C _L and B ^S show normal behaviour and can be approximated by the conventional model for vibrational anharmonicity. 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 are 4.7 ± 0.1, 0.22 ± 0.03 and 4.4 ± 0.15, respectively. The adiabatic bulk modulus B ^S and its hydrostatic-pressure derivative (B ^S/P) _P=0 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 AlN are positive: the zone-centre acoustic phonons stiffen under pressure. The shear _S (=0.006) is much smaller than the longitudinal _L (=1.09) accounting for the low thermal Gr¨neisen parameter ^th (=0.65) obtained for this ceramic: since the acoustic Debye temperature _D (=980 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic AlN.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.