The thermal conductivity and Lorenz function of the tin-lead alloy system Sn x Pb1 − x (x = 0.85, 0.7 0.5 0.3)

The thermal conductivity and electrical resistivity of the tin-lead alloy system Sn _x Pb_{1 – x} (x = 0.85, 0.7 0.5 0.3) were measured in the temperature range 7–300 K. The thermal conductivity was analyzed at temperature T 20K, assuming 1//T+Tⁿ, where , , and n are constants. The analysis shows that n < 2, and not n 2, which would be expected for a normal pure metal. The electrical resistivities could be represented by a T ⁵ relation for temperatures up to about 60 K. The characteristic temperature _R appears to decrease with increasing weight percent of lead. The total Lorenz functions were high, indicating the presence of phonon conductivity. The phonon conductivity _g appears to vary with T, and can be represented by _g=a/Tⁿ (a > 0) and n2.Work supported by the Universiti Sains Malaysia.     

Specific heat near the lambda point in 4He and 3He-4He mixtures: Test of universality of the critical exponent and the amplitude ratio,and observation of the critical-tricritical crossover effect

The specific heat under saturated vapor pressure of pure ⁴He and of six ³He-⁴He mixtures up to X = 0.545 was measured in the temperature range 3 × 10^–6 <¦T-T ¦ <10^–2 K. The critical exponents and along the path = are independent of X up to X = 0.545, where (= ₃ – ₄) is the difference between chemical potentials. If we take account of higher order terms, the exponent (= ) and the amplitude ratio A /A are independent of X up to X = 0.545. The values of and A /A are –0.023 and 1.090, respectively. The critical-tricritical crossover effect was observed for X = 0.545 and the boundary of crossover region closest to the critical region was at /T = (1–2) × 10^–4, where is the distance ¦T – T ¦ along the path = . This value is in good agreement with the estimated value by Riedel et al. But, remarkably, in the case of X = 0.439 this effect was not observed.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Thermal diffusion in3He-4He mixtures near the tricritical point and λ line

It is shown that in the superfluid phase of helium mixtures, near the tricritical point, the thermal diffusion ratiok _T is positive and, both in the tricritical region and along the coexistence curve, behaves as (c/) _T,p [(T _t –T)/T _t ] ^–1 (same exponent as in the normal phase); and near the line,k _T again is positive and behaves as (c/) _T,p . In both cases, quasielastic light scattering is shown to provide a convenient means of measuring the thermal conductivity at the transition.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

Temperature effects on the properties of Ge thin films

The effects of substrate temperature (T_s) on the properties of vacuum evaporated p-type Ge thin films have been investigated for 25s<400°C. Increase in the substrate temperature improves the crystallinity and increases the grain size resulting a gradual change from amorphous to polycrystalline structure which was attained above a substrate temperature of 225°C. Low resistive (1×10^–2 ohm-cm) and high mobility (280 cm²/V·s) films were obtained at T_s=400°C. It has been observed that the conduction mechanism in polycrystalline films was dominated successively by hopping, tunneling and thermionic emission as the sample temperature was increased from 40 to 400 K. In amorphous samples, conduction was described in terms of different hopping mechanisms.     

Superfluid density near the lambda point of4He under pressure

The superfluid density in ⁴ He was determined near T from the second-sound velocity as a function of T–T and pressure. The critical exponent of the superfluid density was found to depend, even slightly, on the pressure. Furthermore, the fundamental length ₀ in the coherence length = ₀ [1–(T/T)]^–' seemed to be proportional to the mean interatomic distance. The implications of the results are also discussed.This work was partly supported by The Ito Science Foundation and by The Nishina Memorial Foundation.     

Thermophysical Property Measurements of Supercooled and Liquid Rhodium

The density, the isobaric heat capacity, the surface tension, and the viscosity of liquid rhodium were measured over wide temperature ranges, including the supercooled phase, using an electrostatic levitation furnace. Over the 1820 to 2250 K temperature span, the density can be expressed as (T)=10.82×10³–0.76(T–T _m ) (kgm^–3) with T _m =2236 K, yielding a volume expansion coefficient (T)=7.0×10^–5 (K^–1). The isobaric heat capacity can be estimated as C _P (T)=32.2+1.4×10^–3(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid remains constant at 0.18 over the 1820 to 2250 K interval. The enthalpy and entropy of fusion have also been measured, respectively, as 23.0 kJmol^–1 and 10.3 Jmol^–1K^–1. In addition, the surface tension can be expressed as (T)=1.94×10³–0.30(T–T _m ) (mNm^–1) and the viscosity as (T)=0.09 exp[6.4×10⁴(RT)] (mPas) over the 1860 to 2380 K temperature range.     

Investigation of the dominant point defects in tetragonal YBa2Cu3Ox at elevated temperatures

The manner in which oxygen is incorporated into YBa₂Cu₃O _x (YBCO) at 800°C for values ofx close to 6 is shown to be in the form of neutral oxygen interstitials, O _i ^x . The experimental data on which this conclusion is based are obtained from measurements of oxygen partial pressure,P(O₂), as a function of compositionx and temperatureT (5.99x 6.35, 825T1120 K). The data are obtained by a solid-state electrochemical method. Other conclusions of this study include: (a) O _i ^x are noninteracting forx 6. (b) The stoichiometric composition of YBCO isx 6.0. (c) The reaction enthalpy of oxidation is 179 kJ/mol O₂. (d) The Fermi level changes by –0.2 eV asx increases from 6.05 to 6.35.     

Non fermi liquid ground states in strongly correlated f-electron materials

Experimental efforts to characterize and develop an understanding of non Fermi liquid (NFL) behavior at low temperature in f-electron materials are reviewed for three f-electron systems: M_1–xU_xPd₃ (M = Sc, Y), U_1–xTh_xPd₂Al₃, and UCu_5–xPd_x. The emerging systematics of NFL behavior in f-electron systems, based on the present sample of nearly ten f-electron systems, is updated. Many of the f-electron systems exhibit the following temperature dependences of the electrical resistivity p, specific heat C, and magnetic susceptibility for T T₀, where T_o is a characteristic temperature: P(T) 1 –aT/T ₀, where a < 0 or > 0, C(T)/T (-1/T _o) In (T/bT ₀), and (T) 1 –c(T/T_o)^1/2. In several of the f-electron systems, the characteristic temperature T_o can be identified with the Kondo temperature T_k.     

Critical phenomena of liquid4He in the vicinity of the upper λ point

We determinedC _p along six isobars near T in the vicinity of the upper superfluid transition point (upper point) from measurements ofC _v and (P/T) _v along six isochores.C _p was analyzed with the functionC _p =(A/)^–(1+D^–)+B for T>T, and the same function with primed coefficients for T, whereD denotes the strength of the effect of the irrelevant variable. The present work clarified the effect of the pressure (irrelevant variable) on the critical behavior of ⁴ He near T, that is, the correction term due to the irrelevant variable increases with pressure even in the small range 3×10^–3. This indicates that the pressure depresses the true critical region. The universality of the amplitude ratioA/A was confirmed even in the vicinity of the upper point by specific heat measurements. With constraints ==–0.02, ==–0.5, andB=B the pressure-independent amplitude ratiosA/A=1.088±0.007 andD/D=0.85±0.2 were obtained.AD/AD=0.93±0.2 implies that the pressure has a similar effect onC _p in the normal fluid and superfluid regions, within experimental errors.     

Field and excitation dependent ultrasonic attenuation in3He-B

Sound absorption of³He-B at 0 bar was studied at a frequency of 10 MHz. We performed pulsed experiments with different pulse lengths (4 to 15 s) and pulse powers (0.1 to 160 W) in the temperature range 0.2 < T/T_C < 2. For pulse power less than pth 50 W, and in the temperature range 0.4 to 0.8 T_c and zero field, the attenuation coefficient a decreases monotonically at about 0.2 cm^–1 per decade of power. Above pth. increases up to values of 3.5 cm^–1 and 1.9 cm^–1 at highest power for temperatures of 0.8 T_c and 0.4 T_c, respectively. At pulse power around 100 W and at the lowest temperatures, the attenuation changes within the first 200 s after the application of the pulse; also increases with increasing field. In the normal fluid decreases with increasing power. All of our observations are lacking a rigorous theoretical understanding.     

Measurements of Critical Current of Superfluid 4He through An Array of Submicron Apertures very near Tλ

Far from the lambda transition the critical flow of superfluid ⁴ He through a small orifice is determined by thermal nucleation of quantized vortices. Between 300 mK and 2 K linearly decreasing critical flow velocity has been observed earlier. As the temperature approaches T the size of the vortex core increases and becomes comparable to that of the orifice. We report here measurements of the critical mass current in this temperature range. An array of 24 3×0.17 m holes in parallel with a macroscopic parallel path and flexible-diaphragm Helmholtz resonator have been used. The temperature range explored was from 80 mK to 20 K below T. Preliminary analysis of the data shows that for a reduced temperature t=(T–T)/T1·10 ^–4 the critical current scales approximately as t ^1.25 . Closer to T the critical phase difference across the array becomes comparable to 2 and the results have to be analyzed in terms of Josephson effect. The superfluid density has been measured at the same time as the critical current.     

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.     

4He very nearT λ heated from above

We discuss the feasibility and likely results of measurements of the thermal conductivity (Q,t) of⁴He very nearT T (Q = 0) as a function of the heat currentQ and the reduced temperature t [T —T]/T by heating a sample from above and cooling it from below. Although the expansion coefficient is negative, the experiment should be possible without inducing convection in the HeI layer provided the sample length does not significantly exceed one cm. Fort 10^–7(Q 0.2 erg/s cm²), a state of self-organized criticality can be attained. For these conditions, the thermal gradient cancels the gradient inT induced by gravity, thus permitting measurements extremely close to the transition even in an Earthbound laboratory. However, the data will be only for a unique path in the Q—t plane. For 0.2 Q 0.5 erg/s cm² (10^–7t 10^–8) they will be in the range of linear response and give (0,t); for Q between about 0.5 and 10 erg/s cm² and over a temperature range of about 20 nK, the experimental path samples the regime where the conductivity is expected to be influenced by nonlinear finite-current effects. The small currents and narrow temperature range of the experiment imply that ultra-high resolution thermometry as well as very careful control of stray heat currents will be required. ForQ 10 erg/s cm² and up to very largeQ, the method can be used to determine the onset temperatureT _c (Q) of thermal resistance.     

Linear effects of the energy transfer in gases

The authors discuss the linear effects of energy transfer in a gas that can attain a steady state and the linear similarity theory based on geometric transformations preserving the distance between points.Notation L _ii ,L _ij phenomenological coefficients - x _i thermodynamic forces - I _q specific heat flux - U ^* transfer energy - T temperature - T ^* reduced temperature - thermal conductivity of the local-equilibrium gas - _* reduced thermal conductivity - k Boltzmann constant - , parameters of the intermolecular interaction potential - m molecular weight Institute of Applied Physics of the Academy of Sciences of Belarus, Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 793–798, September–October, 1995.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

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.     

Dielectric Permittivity of Eight Gases Measured with Cross Capacitors

A four-ring, toroidal cross capacitor was used to measure accurately the relative dielectric permittivity (p,T) of He, Ar, N₂, O₂, CH₄, C₂H₆, C₃H₈, and CO₂. ( is often called the dielectric constant.) The data are in the range from 0 to 50°C and, in many cases, extend up to 7 MPa. The accurate measurement of (p,T) required a good understanding of the deformation of the gas-filled capacitors with applied pressure. This understanding was tested in two ways. First, the experimental values of (p,T) for helium were compared with theoretical values. The average difference was within the noise, _expt– _theory=(–0.05±0.21)×10^–6, demonstrating that the four-ring cross capacitor deformed as predicted. Second, (p,T) of argon was measured simultaneously on three isotherms using two capacitors: the four-ring capacitor, and a 16-rod cross capacitor made using different materials and a different geometry. The results for the two capacitors are completely consistent, within the specifications of the capacitance bridge. There was a small inconsistency that was equivalent to 1×10^–6 of the measured capacitances, or, for argon, 3×10^–5 A , where A is the zero-density limit of the molar polarizability (–1)/[(+2)].     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.