Deviation from Wiedemann–Franz Law for the Thermal Conductivity of Liquid Tin and Lead at Elevated Temperature

The thermal conductivities of tin and lead in solid and liquid states have been determined using a nonstationary hot wire method. Measurements on tin and lead were carried out over temperature ranges of 293 to 1473 K and 293 to 1373 K, respectively. The thermal conductivity of solid tin is 63.9±1.3 Wm^–1K^–1 at 293 K and decreases with an increase in temperature, with a value of 56.6±0.9 Wm^–1K^–1 at 473 K. For solid lead, the thermal conductivity is 36.1±0.6 Wm^–1K^–1 at 293 K, decreases with an increase in temperature, and has a value of 29.1±1.1 Wm^–1K^–1 at 573 K. The temperature dependences for solid tin and lead are in good agreement with those estimated from the Wiedemann–Franz law using electrical conductivity values. The thermal conductivities of liquid tin displayed a value of 25.7±1.0 Wm^–1K^–1 at 573 K, and then increased, showing a maximum value of about 30.1 Wm^–1K^–1 at 673 K. Subsequently, the thermal conductivities gradually decreased with increasing temperature and the thermal conductivity was 10.1±1.0 Wm^–1K^–1 at 1473 K. In the case of liquid lead, the same tendency, as was the case of tin, was observed. The thermal conductivities of liquid lead displayed a value of 15.4±1.2 Wm^–1K^–1 at 673 K, with a maximum value of about 15.6 Wm^–1K^–1 at 773 K and a minimum value of about 11.4±0.6 Wm^–1K^–1 at 1373 K. The temperature dependence of thermal conductivity values in both liquids is discussed from the viewpoint of the Wiedemann–Franz law. The thermal conductivities for Group 14 elements at each temperature were compared.     

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.     

Experimental study of the boundary between single-phase convection and boiling in underheated cryogenic liquids

The effect of pressure and underheating on the position of the boundary between heat-transfer regimes in liquid helium and hydrogen is investigated.Notation q heat flux - p pressure - =T_s–T underheating - T_s saturation temperature - T temperature of liquid - T=T_wa – T T_s=T_wa – T_s - T_wa temperature of heat-emitting surface - A,a, B, b, C constants - m, n indices - Nu Nusselt number - Ra Rayleigh number - thermal conductivity - coefficient of cubical expansion - kinematic viscosity - g acceleration - standard deviation Indices 01 conditions of convection-boiling transition - 02 conditions of boiling-convection transition Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 5–11, January, 1982.     

Heat capacities of the anomalous fluid phase in two-dimensional 3He

No Heading We measured heat capacities of two dimensional ³He adsorbed on graphite preplated with a ⁴He monolayer (³He/⁴He/gr) in a wide temperature (0.3 T 80 mK) and density range (1.3 7.3 nm^–2). We found that the system behaves as a normal Fermi fluid at low densities between 1.3 and 5.6 nm^–2 where the quasiparticle effective mass seems to diverge at a density for the 4/7 phase (_4/7 = 6.8 nm^–2). At higher densities but below _4/7, we observed anomalous temperature dependencies of heat capacity with two round maxima near 1 and 30 mk. With increasing density in this region, a high temperature weight of heat capacity decreases selectively leaving the 30 mK peak, while the 1 mK peak develops. This unexpected behavior can not be explained by the conventional two-phase co-existence model. Instead, we propose here that the 2D normal Fermi fluid is continuously transformed to the 4/7 Mott localized phase through a new quantum phase where a hopping of the zero-point vacancy plays an important role.PACS numbers: 75.70.Ak, 67.80.Jd, 75.10.Jm, 67.70.+n.     

Experiments on expanded liquid metals at high temperatures

The electrical resistivity of liquid tungsten was measured using electric pulse heating of the wires inside capillary tubes. Under fast heating (10 µs) or slow heating (50 µs), the wire expands and fills the inner cavity of the capillary. On the oscillogram traces of the voltage drop across the wire, one can see the phases solid, liquid, fast expansion, and then the moment when the cavity is filled with the metal. Using the voltage drop, current, and volume of the capillary cavity, one can calculate the electrical resistivity,, of the expanded metal. Tungsten densities from 7.5 to 1 g · cm^–3(3 x 10²² to 0.5 x 10²² atoms · cm^–3) were investigated at temperatures from 10 x 10³ to 14 x 10³ K. For these densities, the electrical resistivity increased from 0.5 to 5m·cm.     

Rayleigh linewidth in4He near the gas-liquid critical point

Spectra of Rayleigh-scattered light in⁴He near the gas-liquid critical point have been measured, using a photon correlation method. Fitting the obtained relaxation times to Kawasaki's expression with background modification, we have obtained along the critical isochore the correlation length =(3.6±0.78)^{–0.534±0.046} Å and the high-frequency shear viscosity *=21.5±3.6 µP. * has been revealed to be in good agreement with the regular part of the viscosity _r=21±2µP. The singular part of the thermal diffusivity has been determined to beD _Ts =(4.9±2.7)×10^{–5–0.543±0.046} cm²/sec along the critical isochore.     

Zr surface diffusion in tetragonal yttria stabilized zirconia

The value for surface diffusivity of Zr tetragonal ZrO₂–3mol% Y₂O₃ has been calculated from measurements of surface area reduction and pore growth in powder compacts during sintering. The surface diffusivity thereby obtained can be described by D =5.52×10⁵ exp[–531(kJ mol^-1)/RT] m²/s, which is in reasonable agreement with values calculated by prior researchers from direct TEM observation of neck growth between touching particles.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Non-isothermal crystallization and isothermal transformation kinetics of the Ni68.5Cr14.5P17 metallic glass

Non-isothermal crystallization of the Ni_68.5Cr_14.5P₁₇ alloy is characterized by differential scanning calorimetry (DSC) and X-ray techniques. Transformation occurs in two stages at peak temperatures 622±1 and 692±1 K (at 20 K min^–1), with H ₁=1.50+0.1 kJ mol^–1 and H ₂=3.0±0.1 kJ mol^–1. Precipitation of a nickel phase occurs in the first stage and a (NiCr)₃ P phase is formed during the second stage. An approach to the isothermal kinetics of the two crystallization events is derived within the frame work of the Johnson-Mehl-Avrami theory.     

Ideal elastic,anelastic and viscoelastic deformation of a metallic glass

The elastic, viscoelastic and anelastic components of the homogeneous strain response of the metallic glass Pd₈₂Si₁₈ to an applied stress have been examined. The elastic response is fully reversible, instantaneous and linear. The measured elastic modulus, E, and temperature dependence, d(ln E)/dT, are 84±8 GPa and (–3.2±0.6) × 10^–4 C^–1, respectively. The viscoelastic flow is non-recoverable and, if the configuration remains constant, is characterized by a constant strain rate. This strain rate varies linearly with the stress, gtr, in the low stress regime ( < 300 MPa), becoming non-linear for higher stresses. For isoconfigurational flow, the strain rate has an Arrhenius-type temperature dependence with an activation energy of - 200 ± 15 kJ mol^–1, independent of stress and thermal history. The magnitude of the strain rate is strongly dependent on the degree of structural relaxation and therefore on thermal history. During isothermal annealing the viscoelastic strain rate varies inversely with time. The anelastic response is a transient that, at 500 K, contributes to the flow for approximately fifty hours after a stress increase and is fully recovered upon stress reduction. A spectrum of exponential decays is required to model this flow component. The anelastic strain, _A, varies linearly with the magnitude of the stress change, , over the entire stress range tested: _A/gDA=(8.0±0.8)× 10^–6 MPa^–1.     

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.     

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.     

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.     

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

Self-diffusion and the isotope-mass-effect in stearic acid single crystals

Self-diffusion parallel to the molecular axis in melt-grown crystals of the monoclinic c form of stearic acid has been examined in the temperature range 320 to 340 K using the radiotracer serial-sectioning technique. The results are best described by an expression of the form D=4×10³³ exp (–314±4 kJ mol^–1/RT) m²sec^–1. The value of the preexponential factor and activation energy are similar, relatively, to those obtained previously for other organic solids and are consistent with self-diffusion by a vacancy mechanism. Isotope-mass-effect measurements yielded mass factors E _ab=fK=0.3±0.04. For vacancy migration in a simple monoclinic lattice f _v0.6, thus K0.5. This is not an unreasonable value of K. It is argued however that values of f for vacancy diffusion in such anisotropic lattices as stearic acid could be significantly lower than expected.     

Oxidation of an Al2O3-γAlON ceramic composite

The oxidation of dispersed aluminium oxynitride particles in an alumina matrix has been studied. The kinetics law of this reaction is linear and the activation energy is 420±40 kJ mol^–1 (100±10 kcal mo^–1). A-alumina layer is formed and leads to-alumina above 1200° C. The-alumina formation produces surface compressive stresses, and thus the mechanical properties ( _f, HV) are improved. We have proved that the formation of-alumina in the Al₂O₃-AION composite can lead to the best properties for this ceramic. A-alumina layer has a very interesting effect on the wear resistance of this material.     

The dielectric properties of aluminium nitride substrates for microelectronics packaging

The dielectric behaviour of sintered polycrystalline aluminium nitride substrates has been examined over the frequency range 500 Hz to 10 MHz and correlated with composition and microstructure. For pure, white AlN at 20 ° C both the permittivity () and dielectric loss () are frequency independent giving = 9.2±0.05 and tan = (2.1±0.1) × 10^–3. The permittivity is less than for pure alumina substrates ( = 10.2) but tan compares favourably, with that (1.4 × 10^–3) of alumina, which though used more widely has a thermal conductivity some eight times less than that of AlN. The addition of impurities, particularly iron, to give opaque black AlN causes large, frequency dependent increases in ; at 500 Hz the loss is seven times that of pure white AlN and is two times greater above 100 kHz. The temperature coefficient of permittivity [( – 1)( + 2)]^–1 [/T]_p between –180 and +180 ° C for pure white AlN is 1.05×10^–5 K^–1 which is similar to the value of 9×10^–6 K^–1 for pure Al₂O₃. For impure black AlN the coefficient below 20 ° C is the same but above 20 ° C there is a rapid, non-linear increase of with temperature. Below 180 ° C for pure white AlN and 20 ° C for impure black AlN the values of temperature coefficient are frequency independent at least up to 200 kHz.     

Phase transitions and high-temperature crystal chemistry of polymorphous modifications of Cs<Subscript>2</Subscript>(UO<Subscript>2</Subscript>)<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)

Phase transitions and thermal deformations of - and -Cs₂(UO₂)₂(MoO₄)₃ were studied by high-temperature X-ray diffraction analysis. In heating of -Cs₂(UO₂)₂(MoO₄)₃ to 625 ± 25°C, the reconstructive phase transition proceeds. -Cs₂(UO₂)₂(MoO₄)₃ is stable up to 700 ±25°C. The thermal expansion of both phases is sharply anisotropic: ₁₁ = 10 × 10^–6, ₂₂ = 33 × 10^–6, ₃₃ = 10 × 10^–6, _V = 53 × 10^–6 deg^–1 for -Cs(UO₂)₂(MoO₄)₃ and ₁₁ = 13 × 10^–6, ₃₃ = 3 × 10^–6, _V = 31 × 10^–6 deg^–1 for -Cs₂ (UO₂)₂ (MoO₄)₃. The anisotropy of thermal expansion is explained by features of the crystal structure of the compounds.Translated from Radiokhimiya, Vol. 46, No. 5, 2004, pp. 405–407.Original Russian Text Copyright © 2004 by Nazarchuk, Krivovichev, Filatov.     

Sintering Behavior of Hot-Pressed Ca–αSialon Ceramics

On the basis of phase relationships in the Ca–Si–Al–O–N system, a Ca––sialon ceramic was synthesized using the hot-pressing technique. The reaction sequences and densifications of the Ca––sialon vs. firing temperatures have been characterized in detail. The present experiments reveal a reaction sequence as follows: at 1250°C the reactant mixture started to soften, at 1300°C a gehlenite phase was produced, at 1500°C the gehlenite phase was resolved into a liquid phase and a Ca––sialon started to form, and at 1600°C the formation of Ca––sialon was complete. The product was stable and almost entirely single phase Ca––sialon. Accompanying to the above sequences, densification also proceeded via a liquid-phase sintering, particle rearrangement, solution–reprecipitation, and grain growth process. In the final microstructure elongated grains of Ca––sialon were obtained, improving the fracture toughness of this Ca––sialon ceramic.     

A new parameter for describing the structure bifurcation in two-phase alloys containing coherent particles

The so-called bifurcation diagrams for precipitate particles in nickel-based alloys were obtained by calculating the energy state for a pair of particles on the basis of the bifurcation theory. Based on the bifurcation diagrams, we have proposed a new parameter for describing the two-phase structure containing coherent particles. The parameter is defined as the mean particle radius at the intersection of the energy ridge and the line ofR=–0.5 orR=0.5 in the bifurcation diagram (R(r –r )/(r +r ), wherer andr are the radii of and ), and is symbolized by¯r ^* _±0.5. Because the energy state of the paired and is maximum at¯r ^* _±0.5 whenR=±0.5,¯r ^* _±0.5 is just like the watershed and hence we have termed it structureshed. This parameter successfully describes the effects of elastic energy as well as surface energy on the microstructural changes during coarsening of precipitate particles.