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.     

Zero-point motion and superfluid helium

We propose that He II exhibits macroscopic [ _P /N O(1)] quantum zero-point motion in momentum space, i.e., that a nonzero root-mean-square superfluid velocity exists even in an equilibrium superfluid system at rest. At absolute zero, using coherent states, we relate the uncertainty _P /N in the total momentumP (per particle) to the long-range-order (LRO) part of the phase gradient correlation function, which is proposed as an order parameter. The local equilibrium equation for the superfluid velocity potential derived by Biswas and Rama Rao yields, in the strict equilibrium limit, the equation determining this order parameter in terms of fluctuation correlations that remain to be determined. The order parameter is interaction dependent, nonzero atT=0 if (0)–₀V₀>0, and can vanish at some transition temperatureT when fluctuation terms become comparable to theT=0 value. (HereV _{0 0}, and (0) are the uniform parts of the potential, density, and chemical potential with shifted zero of energy, respectively.) A characteristic length (T), diverging atT=T , appears naturally, with its defining relation reducing to a macroscopic uncertainty relation ( _P /N)(0)=/2 atT=0. With certain assumptions it is shown that atT=0, LRO in the phase gradient correlation function is incompatible with off-diagonal long-range order (ODLRO) in the (r)(r) correlation function, and with nonzero condensate function.     

Spontaneous nuclear ferromagnetic ordering of in nuclei in AuIn2 Part I. Nuclear specific heat and nuclear susceptibility

We have measured the nuclear specific heat C_n and nuclear susceptibility _n of In nuclei (I=9/2, =5.5 _n) in the cubic intermetallic compound AuIn₂ (Korringa constant =0.11 Ksec) in the normal conducting state at 30K10mK and 2mTB115 mT. Our data show a positive nuclear Weiss temperature =+ 43 K and that the In nuclei undergo a nuclear ferromagnetic transition at T_c=35 K. The In nuclei experience an internal field of about 10 mT (obtained from C_n at T>T_c ). The nuclear ordering temperature T_c and the internal field increase with applied magnetic field. From the data we deduce exchange constants for the investigated system. The critical entropy reduction S(T_c)/S_max=8.6% and critical enthalpy E=0.28 RT_c are in reasonable agreement with the measured ordering temperature T_c,applying the Heisenberg model for a simple cubic I=9/2 spin system. The nuclear spin relaxation time calculated from the real and imaginary parts of _n is 10 msec at T>50 K, but drops to <1msec at T_c.This is the first observation of a spontaneous nuclear magnetic ordering transition in a not-hyperfine-enhanced metal at thermal equilibrium, i.e. at T _nuclear =T _electron .     

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.     

Saturation curve equations for normal and heavy water

Compact and precise equations are obtained for the saturation curves of normal and heavy water.Notation p saturated vapor pressure - p_c critical pressure - T absolute temperature - T_c critical temperature - =T/T_c dimensionless temperature - =1 – ; r heat of vaporization - c _p ⁰ isobaric heat capacity of vapor in ideal gas state - c_s liquid heat capacity along saturation curve - v specific volume of vapor - a _i coefficients of Eq. (1) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 894–897, May, 1981.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu : Mg ratio alloys the main phases found were , , S and T₁, while fewer T₂ and Al₇Cu₂Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T₁ precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu : Mg ratio alloy the addition of 0.2 wt % Ag resulted in the precipitation of phase simultaneously with , , S and T₁ phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed.     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

Dynamic Behavior of a Pure Fluid at and Near Its Critical Density Under Microgravity and 1g

A new sample cell allowing accurately measurable density quenches was developed for further and systematic investigation of dynamic temperature propagation, or the piston effect. Several experiments were performed under 1g and microgravity during and in preparation for the Perseus mission in 1999. The starting temperatures ranged in the one-phase state between 1 and 1000 mK above T _c, while the density varied between 0.7 _c<<1.3 _c. The method for the determination of the isentropic difference coefficients (/T)_S, (/p)_S, and (T/p)_S is explained. The coefficients are in reasonable agreement with the equation of state for SF₆, and the difference between the ground and the microgravity experiments is discussed. The advantage of the density quench method in contrast to the temperature quench method is demonstrated, particularly with regard to the influence of convection.     

The anomalous thermal boundary resistance in superfluid4He near Tλ

The anomalous thermal boundary resistance R of superfluid⁴He near the lambda point T was studied in a cell with parallel copper faces and with various fluid layer thicknesses. The study was made as a function of the heat current Q and reduced temperature (T — T)/T = . In all cases, R tends to a maximum value R_itmax at T = T. This value is independent of Q, and is reproducible for various experiments. This contrasts with the regular boundary resistance which can vary considerably between successive experiments. Near T, the limiting slope dR/d¦¦ is found to be proportional to Q^–1, and this leads to a scaled representation of the data. This analysis is extended to data of similar experiments with gold plated copper surfaces by Duncan and Ahlers and by Zhong et al. The measurements of R over the whole range of¦¦ where it is observable are discussed and compared with previous experiments.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Nonequilibrium contributions to the electric response of dirty superconductors

Comparison of the measured microwave response in the presence of a dc current in narrow films of tin nearT _c with the results from microscopic theory shows good agreement. Nonequilibrium effects become important when the frequency becomes of the order of the inverse inelastic relaxation time _E ^–1 (k _B T _c ³ / _D ² ) (_D is the Debye temperature) even if remains well below the gap frequency ₀(T)/.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Thermal Expansion and Isothermal Compressibility of TlIn1 – xNdxSe2 (0 ≤ x≤ 0.08) Crystals

The thermal expansion coefficient () and isothermal compressibility ( _T ) of TlIn_{1 – x} Nd _x Se₂(0 x 0.08) crystals were measured between 77 and 400 K. In the range 77–160 K, both and _T increase with temperature, the increase in being much steeper. At higher temperatures, and _T change very little. The observed composition dependences of and _T are interpreted in terms of energy-band structure.     

Pressure dependence of the melting and α-β phase transition temperatures of carbon monoxide

The pressure dependences of the melting temperatureT _m and crystallographic phase transition temperatureT of carbon monoxide have been measured as a function of hydrostatic pressure to 1.75 kbar by using associated changes in the nuclear spin-spin relaxation timeT ₂ of¹³C as an indicator of the transitions. From the Clausius-Clapeyron equation the volume increments at zero pressure are deduced to beV _m =2.50±0.07 andV =0.92±0.02 cm³/mole. The CO phase diagram is compared with that of N₂.Research performed with support from National Science Foundation Grant DMR75-20161 and under auspices of U.S. ERDA.Visiting Professor of Physics, University of Florida, 1975–6.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Pressure dependence of T c for lead

The superconducting transition temperature T _c for Pb has been determined as a function of hydrostatic pressure up to 26 kbar. T _c is found to more closely follow a linear pressure dependence, with T _c/P = –(3.61 ± 0.05)× 10^–5K/bar, than a linear volume dependence, as previously reported. The volume dependence of the electron-phonon parameter derived from these measurements, d(ln )/d(ln V) = 4.2 ± 0.1, is in good agreement with theoretical calculations by Ott and Sorbello and by Carbotte and Vashishta. The variation of for larger volume changes is discussed.Supported by the Australian Research Grant Committee.     

The Impact of Nuclear Magnetism on Superconductivity in a Metal with Nuclear Electric Quadrupole Splitting: Indium

We report the first investigation of the impact of nuclear magnetism on superconductivity in the tetragonal metal indium. We have measured the superconducting critical field B_c(T) and in its vicinity the nuclear magnetic heat capacity at ultralow temperatures, 170 KT200 mK. We compare the measured quantities with calculations which consider the nuclear magnetic Zeeman and the dominating nuclear electric quadrupole interaction in indium. The heat capacity data support the occurence of a positive sign of the electrical field gradient at nuclear sites and in consequence the existence of a nuclear low spin ground state. Surprisingly, at lowest investigated temperatures, 170 KT1 mK, the reduction of the critical field B_c(T) clearly exceeds the size of the calculated magnetization ₀ M(B_c, T) which is limited by the nuclear low spin ground state. In all other materials the interplay of nuclear magnetism and superconductivity has been studied so far (Al, AuAl ₂ , AuIn ₂ , Rh, and Sn), the bare nuclear magnetization appeared as an upper limit of the reduction of the critical field.     

Radiofrequency size-effect measurements of the electron scattering frequency in cadmium

Precise parallel- and tilted-field radiofrequency size-effect measurements of the temperature dependence of the electron scattering frequency v(T) have been made on symmetric orbits on the first-, second-, and third-band Fermi surface sheets in samples with normals 11\-20 and 10\-10. The limiting point measurements on the third-band lens near 0001 provide the clearest evidence for a T ² contribution to v(T) that is the right order of magnitude for electron-electron scattering in cadmium. In parallel field measurements on orbits on the first and second bands (including a broken orbit) we find v(T) T ² + T ³. On these orbits the values for are 5–20 times larger than for the limiting point and other orbits on the third band. The temperature dependence of v(T\> 2 K) on extremal, limiting point, and open orbits on the second- and third-band Fermi surface sheets can be well accounted for by a simple plane wave model for electron-phonon intersheet scattering. This contribution to v(T) turns on approximately as exp (–T _t /T) above T _t /10, where T _t is the minimum gap temperature on the orbit for intersheet scattering by quasi-transversely polarized phonons. The fitted gap temperatures as well as the other parameters of the plane wave model agree well with the known dimensions of the Fermi surface of cadmium. While clear evidence is lacking, we note that this intersheet scattering model can also be used to explain the large T ² coefficients obtained for the first- and second-band orbits, where, in fact, one has gap temperatures T _t smaller than 1 K.Supported by the Fonds National Suisse de la Recherche Scientifique.