Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

Integral results for nonlinear diffusion equations

We show how to construct integral results for the multi-dimensional nonlinear diffusion equation c/t=·(D(c)c) and for some generalisations of this. For appropriate boundary conditions these become integral invariants. An application of these results to determining the large-time behaviour of some radially symmetric problems is indicated.     

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 stress dependence of superconducting parameters in pure In and Sn and in α-phase In-Sn alloys

We have measured the length change due to the transition from the super-conducting to the normal state in pure In and Sn and in In-Sn alloys. The measurements were made on single-crystal specimens. The alloys had Sn content ranging from zero to 12 at %. Crystals parallel and perpendicular to the tetragonal axis were grown at each alloy content. We find that the relative length changes l/l are very sensitive to alloy content. From l/l we have calculated the stress derivatives H _c/ and T _c / and we find that T _c / changes from +59 to –92 mK/bar for stress along the tetragonal axis, and from –9 to 46 mK/kbar for stress perpendicular to the tetragonal axis. We suggest that these large changes are due to Fermi surface topology changes upon increasing the Sn content in In.     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

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.     

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.     

Magnetically and Thermally Modulated Microwave Absorption in Y1Ba2Cu3O7–x Single Crystal near Tc

The microwave absorption R in the Y ₁ Ba ₂ Cu ₃ O _7–x single crystals was investigated near T _c 92K and in the external magnetic field 0 < H 9kOe. A modified ESR spectrometer was used in the experiment. The method of temperature modulation, along with the usual method of magnetic-field modulation, was first applied in studying of the microwave response of these crystals. Peaks in the temperature dependencies of the signals R/H and R/T observed in the vicinity of T _c were differently shaped and shifted one with respect to another. The evolution of the peaks with variation of the magnetic field and angle between H and the c-axis was traced. It has been shown that the observed difference of the temperature dependencies of the derivatives R/H and R/T occurs due to the field-induced broadening of the superconducting transition, which is inherent in the high-T _c superconductors.     

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.     

Thermal transport properties in the normal phase of dilute3He-4He mixtures

We present steady-state measurements of the thermal diffusion ratiok _T and of the heat conductivity for three dilute mixtures of³He in⁴He with concentrations 9×10^–3X(³He)5×10^–2 at saturated vapor pressure in the normal phase close to the superfluid transition. The data are compared with predictions by Dohm and Folk from the renormalization group (RG) theory. From auxiliary determinations of thermodynamic derivatives for these mixtures, we obtain the separation factor =–(k _T /T)×(/X) _T,P /(/T) _X,P above T over the range wherek _T is positive. Here is the mass density. From the transients of X(t) as a function of time, we obtain an estimation for the mass diffusion coefficientD and compare the results with predictions by Dohm and Folk and with results from other experiments.     

Diffusion-controlled evaporation of a moving droplet

The problem of the quasisteady diffusion-controlled evaporation of a droplet moving in a viscous medium is solved numerically. The relative values of the droplet radius and velocity are determined, along with the total droplet evaporation time and the mass-transfer characteristics of the droplet and the medium.Notation R droplet radius - t time - D diffusion coefficient - density - C_s mass concentration of saturated vapor - C mass concentration of vapor far from the droplet - C=(C–C)/ (C_s–C) dimensionless vapor concentration - (r, , ) spherical coordinates - Re=2RU/ Reynolds number - Sc=/D Schmidt number - Sh Sherwood number - T=tD/R² dimensionless time - C_x coefficient of fluid friction - m mass of the droplet - T total droplet evaporation time - ratio of dynamic viscosities inside and outside the droplet - Q masstransfer intensity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 739–744, October, 1980.     

Thermal conductivity of 4He vapor as a function of density

Measurements of the dependence of the thermal conductivity (T, ) of ⁴He vapor on the density are presented at 3.3 and 4.5 K. The initial dependence upon near = 0 agrees with the prediction of the modified Enskog theory; but at higher densities there are departures from the prediction. The excess thermal conductivity (T, ) – (T, 0) is independent of T within experimental error.     

Spin-glass with short-range interaction in a magnetic field

The properties of spin-glasses with nonmagnetic defects are considered in the vicinity of the transition point in a finite magnetic field, by means of a percolational approach. It is shown that the dependence of the magnetic specific heat C(h) = C(h)–C(o) or of the magnetic susceptibility M(h)/h on field and temperature allows us to define the distribution function of finite clusters with respect to their size. In addition to general formulas resulting from the scaling laws, more detailed formulas are obtained for two model distributions: (a) the Bethe lattice distribution, (b) a special model distribution with arbitrary indices.     

Thermal pressure coefficients of ethanenitrile,propanenitrile, and butanenitrile in the region 295–395 K

The thermal pressure coefficient (p/T) _v has been measured for ethanenitrile from 299 to 364 K, for propanenitrile from 295 to 377 K, and for butanenitrile from 297 to 398 K. The results are discussed in terms of the diminishing role of polarity in the alkanenitrile series and of a corresponding-states approach using gas-liquid critical properties as reduction factors. Although (p/T) _v varies unevenly with chain length, the reduced quantity shows a more regular behavior similar to that of the related quantity the cohesive energy density.     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a single-crystal Heusler structure Cu41Mn20Al39 alloy

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C (=(C11–C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44–C)=205 GPa, and BS (=C11–4C/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (C11/P)P=0, (C44/P)P=0, (C/P)P=0, (C12/P)P=0, (CL/P)P=0, and (BS/P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (CIJ/P)P=0 and (BS/P)P=0 and the acoustic-mode Grüneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (C/P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Grüneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers     

Cross-Correlated Dynamic Resistance of a Direct Current Superconducting Quantum Interference Device

This paper presents experimental data on a comparative study of a dc SQUID with voltage and current bias. We introduce a cross-correlated dynamic resistance of the device defined as a ratio R _dCV = _VC/_IV, where _VC = (V/) _A is the slope of the voltage-to-flux characteristics measured in the current bias mode and _IV = (I/) _A is the slope of the current-to-flux characteristics measured with voltage bias. It has been found that R _dCV may deviate strongly from the dynamic resistance observed in the current bias mode of operation. The intrinsic energy resolution of the SQUID remains unchanged for both modes of operation, but the current noise of the voltage biased device scales with the cross-correlated dynamic resistance. In our SQUID with the loop inductance L = 105 pH, is equal to 37 h in the white noise region at a temperature of 4.2 K.     

Diffusive relaxation processes in liquid3He-4He mixtures. I. Normal phase

When a heat flux is switched on across a fluid binary mixture, steady state conditions for the temperature and mass concentration gradients T and c are reached via a diffusive transient process described by a series of terms modes involving characteristic times _n . These are determined by static and transport properties of the mixture, and by the boundary conditions. We present a complete mathematical solution for the relaxation process in a binary normal liquid layer of heightd and infinite diameter, and discuss in particular the role of the parameterA=k _T ² (/c) _T,P /TC _P,c coupling the mass and thermal diffusion. Herek _T is the thermal diffusion ratio, (/c) _T,P ^–1 is the concentration susceptibility, is the chemical potential difference between the components, andC _P,c is the specific heat. We present examples of special situations found in relaxation experiments. WhenA is small, the observable times (T) and (c) for temperature and concentration equilibration are different, but they tend to the same value asA increases. We present experimental results on four examples of liquid helium of different³He mole fractionX, and discuss these results on the basis of the preceding analysis. In the simple case for pure³He (i.e., in the absence of mass diffusion) we find the observed (T) to be in good agreement with that calculated from the thermal diffusivity. For all the investigated³He-⁴He mixtures, we observe (c) and (T) to be different whenA is small, a situation occurring at high enough temperatures. AsA increases with decreasingT, they become equal, as predicted. For the mixtures with mole fractionsX(³He)=0.510 and 0.603, we derive the mass diffusionD from the analysis of (c) and demonstrate that it diverges strongly with an exponent of about 1/3 in the critical region near the superfluid transition. As the tricritical point (T _t,X _t) is approached for the mixtureX=X _t0.675,D tends to zero with an exponent of roughly 0.4. These results are consistent with predictions and also with theD derived from sound attenuation data. We discuss the difficulties of the analysis in the regime close toT andT _t, with special emphasis on the situation created by the onset of a superfluid film along the wall of the cell forX=0.603 and 0.675.Work supported by grants from the National Science Foundation and the Research Corporation and by an A. P. Sloan fellowship to one of the authors (RPB).     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. I. Vapor pressure measurements and their thermodynamic analysis

Sensitive vapor pressure (P _sat) measurements of ³ He- ⁴ He mixtures by means of a low-temperature strain gauge are described over the temperature range 0.5–1.5 K and the range 0.4<X<0.85, whereX is the ³ He mole fraction in the liquid phase. The vapor pressure cell is flat, with a height of only 2 mm, in order to reduce concentration gradients near the tricritical point. The pressure-sensitive device, which resolves changes of about 5×10 ^–8 atm, is described, and its advantages over a conventional manometer system are discussed. Data taken successively on mixtures of small mole fraction difference are used to locate the phase separation boundary in theT-X plane and also the lambda line from a change in (P _sat/T) _x at these transitions. The limiting slopes (dT/dX) and (dT/dX) of the phase separation curve and the lambda line in the vicinity of their junction point, the tricritical point, are presented and compared with previous work. From the vapor pressure data, the concentration susceptibility (X/) _T,P was obtained. Here = ₃ – ₄ is the chemical potential difference of the respective isotopic components ³ He and ⁴ He. It is shown that (X/) _t diverges as the tricritical point is approached along various paths in theT-X plane, and the relevant tricritical exponents are presented. The weak divergence of (X/) _T along the lambda line predicted from the postulates of Griffiths and Wheeler could not be detected and it is believed that such divergence has to occur in a temperature interval that is far too small to be resolved with present-day techniques. Furthermore, gravity effects might well prevent observation of the weak divergence. The lambda transition is well evidenced by a distinct shoulder in a plot of (X/) _T at constantX as a function ofT. This shoulder becomes smaller and gradually gets topped by a peak asX decreases from the tricritical mole fractionX _t . From a combination of vapor pressure and calorimetric data the chemical potential difference [(X, T)- _t ] is calculated between 0.78 and 1.22 K. Here _t is the value at the tricritical point. From this tabulation the critical line and its slope (d/dT) are obtained and compared with previous values based on calorimetric experiments only and with calculations based on the excess chemical potentials ₃ ^E and ₄ ^E derived from saturated vapor pressure data.Work supported by a Grant from the National Science Foundation.     

Isochoric Heat Capacity Measurements for 2,2-Dichloro-1,1,1-Trifluoroethane (R123) at Temperatures from 167 to 341 K and 1-Chloro-1,2,2,2-Tetrafluoroethane (R124) from 94 to 341 K at Pressures to 35 MPa

Molar heat capacities at a constant volume (C _v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C ⁽²⁾ _v), saturated liquid (C or C _x ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T _tr) and the enthalpy of fusion ( _fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2 level) for C _v is estimated to be 0.7%, for C ⁽²⁾ _v it is 0.5%, and for C it is 0.7%.