Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation of normal liquid ³He has been studied over a range of temperatures from slightly above the superfluid transition temperature, T _c, to approximately 10mK at the constant pressures of 1 and 5bar. Using longitudinal LiNbO₃ transducers, operating both on and off resonance, the experiment was performed at 15 discrete frequencies located in several broadband frequency windows, including 16–25, 60–70, and 105–111MHz. The results are compared to Landau's prediction for the attenuation of zero sound in the quantum limit, (k _B Tk _B T _F), where ₀(P,T, )= (P) T ²{1+(/2k _B T)²}. Calibration of the received zero sound signals was performed by measuring the temperature dependence of the first sound attenuation from 30 to 800mK at those same frequencies and pressures. The data are compared to previous results.     

Eliashberg analysis of the specific heat of Nb0.75Zr0.25

The specific heat of Nb_0.75Zr_0.25 is measured from 1.2 to 50 K in zero magnetic field. A phonon density of statesF() and a spectral electron-phonon coupling function ²()F() are fitted to the data in the normal state and in the superconducting state. The results are compared with a previous similar analysis of the specific heat of pure Nb and with published tunneling data. It is found that in Nb_0.75Zr_0.25, –*=1.13, _log=109 K, and N(0)=0.85 eV^–1 at^–1 spin^–1, compared with the figures 0.84, 146 K, and 0.85 eV^–1 at^–1 spin^–1, respectively, in pure Nb. These data confirm that the increase ofT _c upon the alloying of Nb with Zr is due to phonon softening. They further show that the electronic density of states at the Fermi level is identical in Nb and Nb_0.75Zr_0.25. Dimensionless thermodynamic ratios predicted from tunneling data are entirely confirmed, thus confirming the internal consistency of the Eliashberg theory for superconductivity.     

Synthesis of silicon nitride powder through nitrogen gas atomization

The feasibility of synthesizing silicon nitride powder utilizing reactive atomization processing was analysed. The range of times required for the flight time of particles, the cooling rate of the silicon melt, the reaction time of silicon and nitrogen, and the diffusion of nitrogen through silicon nitride layers were obtained and compared. The results of this study indicated that the production of silicon nitride powder through the reactive atomization process would be limited by diffusion of nitrogen through the nitride (ash) layer, assuming the nitride layer was coherent and the unreacted core model was a valid representation of the liquid silicon-silicon nitride system.Nomenclature k(T) reaction rate constant at temperature, T(s^–1) - k ₀ Arrhenius coefficient - E activation energy (kJ mol^–1) - R gas constant - T temperature (K) - fraction of normalized conversion of -phase in time t - fraction of normalized conversion of -phase in time t - k reaction rate constant for -phase (s^–1) - k reaction rate constant for -phase (s^–1) - k ⁱ intrinsic first-order rate constant for -phase (s^–1) - x conversion fraction of -phase in time t - x conversion fraction of -phase in time t - n reaction order for -phase = 1 - n reaction order for -phase = 0.5 - J diffusion flux (mol m^–2 s^–1) - D diffusivity, or diffusion coefficient (m² s^–1 or cm² s^–1) - dC change in concentration (mol m^–3) - dl change in distance, l (m) - A(_g) gaseous reactant A - B reactant B (may be solid or liquid) - P solid product P - b stoichiometric coefficient of reactant B - p stoichiometric coefficient of product P - t time of reaction passed (s) - time for complete reaction of a particle (s) - X _B conversion fraction - r _c core radius (m) - R _p particle radius (m) - _B molar density of reactant B (mol m^–3) - k _g mass transfer coefficient between fluid and particle (m s^–1) - C _Ag concentration of gaseous reactant A (mol m^–3) - D _e effective diffusion coefficient of gaseous reactant in ash layer (m² s^–1)     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Thermal conductivity and heat capacity of titanium hydrides

We have measured the thermal conductivity and the heat capacity C of Ti, TiH _0.82 , TiH _1.7 , and TiH ₂ at 0.35 K T 4 K. Whereas (TiH _0.82 ) and (TiH _1.7 ) are substantially smaller than (Ti), we find (TiH ₂ ) – 3 (Ti). This latter remarkable result may arise from the enhanced electronic density of states — which is shown by the heat capacity data — and from a rather large electronic mean free path in this stoichiometric compound.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

Coarsening of precipitates and dispersoids in aluminium alloy matrices: a consolidation of the available experimental data

Experimental data on the coarsening of precipitates and dispersoids in aluminium-based matrices are reviewed. Available data are tabulated as K=(r ³–r ₀ ³ )/t where r ₀ is the initial particle radius and r is its value after time t at temperature T, and then plotted as log (KT) against 1/T for consolidation and assessment. The considerable body of data for -A₃Li in Li-containing alloys is well represented by K=(K ₀/T) exp (–Q/RT) with K ₀=(1.3 _–0.5 ^+3.0 ) × 10^–13m³Ks^–1 and Q=115±4kJ mol^–1. The relatively limited data for and in Cucontaining alloys are representable by the same relationship with K ₀4 × 10^–8 and — 4 × 10^–10 m³ Ks^–1, respectively, and Q — 140 kJ mol^–1. Available data for coarsening of L1₂ ^– Al₃(Zr, V) and related phases in Zr-containing alloys and of Al₁₂Fe₃Si and related phases in Al-Fe based alloys indicate (i) rates of coarsening at 375 to 475 °C (0.7 to 0.8T_m) five to eight orders of magnitude less than would be expected for , and in this temperature range, and (ii) high activation energies of 300 and 180 kJ mol^–1, respectively.     

The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Gas absorptivity in a complete spectrum

Necessary conditions are established for the validity of the Hottel formulas for the absorptivity relative to black radiation. The formulas are used in describing the absorption of a badly mixed medium and for nonblack incident radiation.Notation x ray path in mat - p, P partial and total pressure - P_eff effective broadening pressure - T, T₀ gas and wall temperatures, °K - T_*, T_i selected temperature values - T_c weighted-mean temperature - a₀ absorptivity of the gas for black radiation - a same for a flux with nonblack spectrum - emissivity - m, u, n, , power exponents - i _0j Planck function for the center of the band, cm · W/m² · sr - I_j incident flux intensity at the center of the band j, cm · W/m² · sr - I integrated incident flux intensity, W/m² · sr - A_j integral absorption (equivalent width) of band f, cm^–1 - _j mean absorption in the band - wave number, cm_–1 - ₀ position of the band center - _j width parameter - _effj effective width - _j total width of the band j, cm^–1 - D_j mean transmissivity in the band j - S integrated line intensity, cm–1/mat - d, b spacing between lines and their half-width, cm–1 - S_j integrated intensity of the band j - L Landenburg and Reiche functions - spectral absorption coefficient, mat_–1 - (T) dimensionless function - c_i dimensionless number - R_*, R_c general notation for parameters averaged over the band and for T_c - E Elsasser function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 802–808, May, 1971.     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Thermal conductivity of ethane from 290 to 600 K at pressures up to 700 bar,including the critical region

The paper presents thermal conductivity measurements of ethane over the temperature range of 290–600 K at pressures to 700 bar including the critical region with maximum uncertainty of 0.7 to 3% obtained with a transient line source instrument. A correlation of the data is presented and used to prepare tables of recommended values that are accurate to within 2.5% in the experimental range except near saturation, and in the critical region, where the anomalous thermal conductivity values are predicted to within 5%.Nomenclature a _k , b _ij , b _k , c _i Parameters of the regression model, k=0 to n, i=0 to m, j=0 to n - P Pressure, (MPa or bar) - Q _l Heat flux per unit length (mW · m^–1) - t Time, s - T Temperature, K - T _cr Critical temperature, K - T _r Reduced temperature = T/T _cr - T _w Temperature rise of wire between times t ₁ and t ₂ K - T ^* Reduced temperature difference (T–T _cr)/T _cr - Thermal conductivity, mW · m^–1 · K^–1 - ₁ Thermal conductivity at 1 bar, mW · m^–1 · K^–1 - _bg Background thermal conductivity, mW · m^–1 · K^–1 - _cr Thermal conductivity anomaly, mW · m^–1 · K^–1 - _e Excess thermal conductivity, mW · m^–1 · K^–1 - Density, g · cm^–3 - _cr Critical density, g · cm^–3 - _r Reduced density, = / _cr - ^* Reduced density difference =(- _cr)/ _cr     

The boundary-layer effect on the crack tip field in mechanism-based strain gradient plasticity

The theory of mechanism-based strain gradient (MSG) plasticity involves two material length parameters, namely the intrinsic material length land the mesoscale cell size l , which are on the order of a few microns and 0.1 m, respectively. Prior studies suggest that l has essentially no effect on the macroscopic quantities, but it may affect the local stress distribution. We demonstrate in this paper that there is a boundary layer effect associated with l in MSG plasticity, and the thickness of the boundary layer is on the order of   l ² big/l. By neglecting this boundary layer effect, a stress-dominated asymptotic field around a crack tip in MSG plasticity is obtained. This asymptotic field is valid at a distance to the crack tip between l and l(i.e., from 0.1 m to a few microns). The stress in this asymptotic field has an approximate singularity of r ^–2/3, which is more singular than not only the HRR field in classical plasticity but also the classical elastic Kfield (r ^–1/2). The stress level in this asymptotic field is two to three times higher than the HRR field, which provides an alternative mechanism for cleavage fracture in ductile materials observed in experiments.     

Optimal choice of descent steps in gradient methods of solution of inverse heat-conduction problems

Modifications are proposed for the methods of steepest descent and conjugate gradients for the solution of multiparameter inverse problems in heat conduction.Notation A, B, L linear operators - u element of the solution space U - f exact initial data - f error in the initial data - value of the error in the initial data - A^–1 inverse operator - u^(k)() k-th derivative of the function u - _i() polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - J(g) discrepancy functional - J'g gradient of the discrepancy functional - _n ⁱ depth of descent with respect to the i-th component of the antigradient of the discrepancy in the n-th iteration - _m length of the observation interval Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 264–269, August, 1980.     

Intergranular structure in dental amalgams

The existence of an intergranular precipitate that provides a structural basis of creep, intergranular corrosion and thermal instability in dental amalgams has been in dispute. Also in dispute is a related matter concerning the solid solubility of Sn in ₁. Both these aspects have been examined in this differential scanning calorimetry (DSC) study using the following materials: (a) a conventional ₂–containing amalgam, (b) six ₂–free amalgams, and (c) a series of ₁ specimens with up to 4 wt% Sn. It has been observed that the solid solubility of Sn in ₁ is about 1.0 wt%. Above this Sn concentration, an intergranular precipitate, identified as the ₂ phase of the SnHg system, appears in ₁. This phase is characterized by a low melting temperature (90°C). The existence of this phase in the conventional dental amalgam has been confirmed. It has been observed further that the ₂–free dental amalgams, depending on their nature and Hg contents, may contain ₂ either as a transient or a permanent phase.     

Electrical conductivity in hot-pressed nitrogen ceramics

The a.c. and d.c. electrical conductivities of some hot-pressed polycrystalline nitrogen ceramics have been measured between 400 and 1000° C. The materials examined were Si₃N₄, 5.0% MgO/Si₃N₄ and two sialons, Si_(6–z) · Al _z · O _z · N_(8–z) having z 3.2 and z 4.0 respectively. The electrical behaviour of all the materials showed similar general features. The d.c. conductivities were about 10^{–10 –1} cm^–1 at 400° C and rose to between 10^–6 and 10^{–5 –1} cm^–1 at 1000° C. The a.c. Data, taken over the frequency range 15 Hz to 5 kHz showed that below about 500° C the a.c. conductivity ( _a.c.) varied with frequency as _a.c. ^s where 0.7 _d.c.) agreed well with the relation _d.c. = A exp(–B/T ^1/4). Above 700° C both the a.c. and d.c. conductivities followed log T ^–1. Hall effect and thermoelectric power measurements enabled the Hall mobility to be estimated as less than 10^–4 cm² V^–1 sec^–1 at 400° C and showed that the materials were all p-type below 900° C and n-type above 900° C. The electrical properties of all four materials are consistent with the presence of a glassy phase.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Dependence of the flux flow viscosity coefficient on the Ginzburg-Landau parameter κ in superconducting indium films

The flux flow viscosity coefficient b ^–1 (in units of ₀ H _{c n} ^–1 c ^–2) of vacuum-deposited indium thin films with low values (1.0–2.8) is measured at temperatures between 0.5T _cand 0.98T _cin the weak magnetic field region. At each temperature, b ^–1 decreases as increases for larger than 1.7. The decrease of b ^–1 with increasing is more rapid as the temperature increases. From an analysis of the present results as well as the existing data on intermediate- and high- superconducting alloys, the relation between b ^–1 and is established over a wide range of . The dependence of b ^–1 on is qualitatively explained by taking into account the contribution of the normal electron dissipation to the viscosity coefficient in the Bardeen-Stephen model.Financial support provided by the Fonds National Suisse de la Recherche Scientifique.On leave from the Department of Electronic Engineering, Faculty of Engineering, Kyushu Industrial University, Fukuoka, Japan.     

Mutual Friction in Superfluid 4He Near the λ-Line

We present experimental results for the thermal resistivity of superfluid ⁴He along several isobars between saturated vapor pressure and the melting pressure. The measurements are for the temperature range 1–T _c(q)/T <t<2×10^–5 and the heat-flux range 3<q<70 W/cm². Here t1–T/T , T is the transition temperature in the limit of zero q, and T _c is the transition temperature at finite q. The data suggest that the resistivity has an incipient singularity at T which can be described by the power law =(t/t ₀)^–(m+) where t ₀=(q/q ₀) ^x . However, the singularity is supplanted by the transition to a more highly dissipative phase at T _c(q)<T . The results suggest a mild dependence of m+ on the pressure P, but can be described quite well by m+=2.76, x=0.89, and q ₀=q _{0, 0}–q _{0, 1} P with q _{0, 0}=401Wcm^–2 and q _{0, 1}=–5.0Wcm^–2bars^–1. The results imply that the Gorter–Mellink mutual friction exponent m has a value close to 3.46 and is distinctly larger than the classical value m=3.