Thermophysical Properties of Low-Density Pure Alkanes and Their Binary Mixtures Calculated by Means of an (n-6) Lennard-Jones Temperature-Dependent Potential

Self-consistent calculations of interaction pVT-virial coefficients B ₁₂(T), viscosities η _mix (T), and diffusion coefficients D ₁₂(T) of binary mixtures of the alkanes C _n H_{2n + 2} (n < 6) are presented. This study is based on the recently developed model of the (n-6) Lennard-Jones temperature-dependent potential (LJTDP) and uses already obtained potential parameters of the pure alkanes as input data. The well-known and simple Lorentz-Berthelot (LB) and the more laborate Tang-Toennies (TT) mixing rules are applied to the potential parameters of the pure alkanes in order to determine those of the mixtures. The new Hohm–Zarkova–Damyanova (HZD) mixing rule, which is an extension of the TT-mixing rule, is also considered. The HZD takes into account that for the LJTDP model, in general, the repulsive parameter is an independent variable whose value n ≠ 12. As in a recent examination of binary mixtures of globular molecules, the LB-mixing rule is superior to TT- and HZD-mixing rules when calculating equilibrium properties such as B ₁₂(T). For the transport properties η _mix (T) and D ₁₂(T), the new mixing rule performs slightly better.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Second-Order Derivatives of the Gibbs Energy for Liquid Mixtures of Alcohol + Heptane at Pressures up to 100 MPa

Second-order thermodynamic derivative properties, such as isobaric thermal molar expansions, isothermal and adiabatic molar compressibilities, and isochoric molar heat capacities of (ethanol, decan-1-ol, 2-methyl-2-butanol) +  heptane mixtures at pressures up to 100 MPa and in the temperature range from 293.15 K to 318.15 K were derived from experimental speed-of-sound u(T, p), density ρ(T, p = 0.1 MPa), and isobaric heat-capacity C _p (T, p = 0.1 MPa) data using appropriate thermodynamic relations. Excess values for the given properties were calculated according to the criterion of thermodynamic ideality of a mixture (Douhéret et al., Chem. Phys. Chem. 2, 148 (2001)), i.e., assuming that the chemical potential of component i in the ideal liquid mixture is equal to the chemical potential of component i in the mixture of perfect gases. The deviations from ideality for the mixtures under test have been explained in terms of the self-association of alcohols in solution which produces a strong departure from random mixing, the change in the non-specific interactions during mixing, and the packing effects.     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

Measurements of thermophysical properties of molten silicon by a high-temperature electrostatic levitator

Several thermophysical properties of molten silicon measured by the high-temperature electrostatic levitator at JPL are presented. They are density, constant-pressure specific heat capacity, hemispherical total emissivity, and surface tension. Over the temperature range investigated (1350<T _m<1825 K), the measured liquid density (in g·cm⁻³) can be expressed by a quadratic function,p(T)=p _m−1.69×10⁻⁴(T−T _m)−1.75×10⁻⁷(T−T _m)² withT _m andp _m being 1687 K and 2.56 g·cm⁻³, respectively. The hemispherical total emissivity of molten silicon at the melting temperature was determined to be 0.18, and the constant-pressure specific heat was evaluated as a function of temperature. The surface tension (in 10⁻³ N·m⁻¹) of molten silicon over a similar temperature range can be expressed by σ(T)=875–0.22(T−T _m). Invited paper presented at the Fourth Asian Thermophysical Properties Conference, September 5–8, 1995, Tokyo, Japan.     

He4 State Equation Below 0.8 K

This work develops the Helmholtz potential A(ρ, T) for He⁴ below 0.8 K. Superfluid terms, related to temperature and momentum gradients, are neglected with negligible loss of accuracy in the derived state properties (specific heats, first sound velocity, expansivity, compressibility, etc.). Retained terms are directly related to a bulk fluid compressibility plus phonon and roton excitations in this quantum fluid. The bulk fluid compressibility is found from the empirical equation c₁³ ≈ c₁₀³ + b; P, where c₁ is the velocity of first sound, P is the pressure, and c₁₀ and b are constants; this empirical equation is found to apply also to other helium temperature ranges and to other fluids. The phonon excitations lead to a single temperature-dependent term in A(ρ ,T) up to 0.3 K, with only two more terms added up to 0.8 K. The roton potential, negligible below about 0.3 K, is a single term first derived 60 years ago but little used in more recent work. The final A(ρ ,T) is shown to fit available experimental specific heat data to about ±2% or better. The magnitude of the pressure-independent Gruneisen parameter below 0.3 K is typical of highly compressed normal liquids. Extension of the equation above 0.8 K is hampered by lack of data between 0.8 and 1.2 K     

Numerical Solution of Inverse Radiative–Conductive Transient Heat Transfer Problem in a Grey Participating Medium

The problem of simultaneous identification of the thermal conductivity Λ(T) and the asymmetry parameter g of the Henyey–Greenstein scattering phase function is under consideration. A one-dimensional configuration in a grey participating medium with respect to silica fibers for which the thermophysical and optical properties are known from the literature is accepted. To find the unknown parameters, it is assumed that the thermal conductivity Λ(T) may be represented in a base of functions {1, T, T ², . . .,T ^K } so the inverse problem can be applied to determine a set of coefficients {Λ₀, Λ₁, . . ., Λ _K ; g}. The solution of the inverse problem is based on minimization of the ordinary squared differences between the measured and model temperatures. The measured temperatures are considered known. Temperature responses measured or theoretically generated at several different distances from the heat source along an x axis of the specimen set are known as a result of the numerical solution of the transient coupled heat transfer in a grey participating medium. An implicit finite volume method (FVM) is used for handling the energy equation, while a finite difference method (FDM) is applied to find the sensitivity coefficients with respect to the unknown set of coefficients. There are free parameters in a model, so these parameters are changed during an iteration process used by the fitting procedure. The Levenberg– Marquardt fitting procedure is iteratively searching for best fit of these parameters. The source term in the governing conservation-of-energy equation taking into account absorption, emission, and scattering of radiation is calculated by means of a discrete ordinate method together with an FDM while the scattering phase function approximated by the Henyey–Greenstein function is expanded in a series of Legendre polynomials with coefficients {c _l } = (2l + 1)g ^l . The numerical procedure proposed here also allows consideration of some cases of coupled heat transfer in non-grey participating media. The inverse method may be treated, after performing a suitable validation, as an alternative method in relation to other classical measurement methods for investigation of thermophysical parameters of solid states.     

Pinning Energy of High-Tc (Bi, Pb)2Sr2Ca2Cu3Oy

The flux pinning potential energy of silver (Ag) sheathed high-T _c Bi-2223 tapes determined from measured current densities, J(T,H), is reported in this paper. Measurements of the transport current density, J, of the Ag sheathed Bi-2223 tapes were performed with an applied magnetic field directions parallel (H‖ab) and perpendicular (H‖c) to the tape’s board surface from 0 to 3 T, at temperatures from 23 to 77 K. To obtain the pinning potential energy of the Bi-2223 superconductor, an empirical scaling of J(T,H) is introduced in this study. Under the flux dynamics, the effective pinning energy, U _eff(T,H,J), can be formulated using the measured current density, J(T,H). Furthermore, the pinning potential energies, U(T,H), for both H‖ab and H‖c were quantitatively determined by the scaling of J(T,H). The two energies, U(T,H), exhibit as a function that is inversely proportional to both temperature and logarithmic magnetic field. The magnitude of U(T,H) for H‖ab is three or more times larger than that for H‖c under the considered conditions. The U(T,H) is sensitive to the temperature, but insensitive to the magnetic field. This characteristic of insensitiveness towards magnetic field is an advantage for applications on the conditions of high current density, high magnetic field, and low temperature.     

Occurrence of Superconductivity and Magnetism in Nominally Undoped LaOFeAs

Superconductivity in a LaOFeAs system is known to get introduced by F-doping (LaO_1−x F _x FeAs) even under ambient conditions and oxygen deficiency (LaO_1−x FeAs) under high pressure conditions. Hitherto unreported, superconductivity in F-free undoped LaOFeAs samples is observed and confirmed for the first time by various characterization tools–resistive ρ(T,B), magnetic M(T,B) and modulated microwave absorption (MMA) measurements. The ρ(T) at B=0 shows a clear superconducting transition with an onset at T _con∼17 K and a tail-like behavior when R goes to zero at T _c0∼8 K. In the presence of B, the superconducting transition shifts to lower T with a rate ∼−5.5 and −1.65 T/K, depending on whether the ρ(T) has dropped to 90% or 5% of its normal state value, respectively. M(T) in zero field cooling at B=10 mT shows diamagnetic downturn below at ∼12 K. At T<T _c0 the change in MMA with B shows a low field (B∼1 mT) peak, which vanishes at T>T _c0, indicating the presence of weak link superconducting networks in the sample. The sample shows a complex electrical and magnetic behavior in the normal state. For instance, ρ(T) reveals a weak SDW-like anomaly at T∼132 K along with a resistivity minimum at T _min∼78 K. M(T) also shows the presence of a magnetic anomaly at T∼130 K. Both below and above T _con, presence of an additional ferromagnetic component is observed in the isothermal M(B) loop measurements. The superconducting and normal state features of our sample are compared with other undoped and doped LaOFeAs systems reported in the literature.     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

Containerless Property Measurements of Liquid Palladium

Some thermophysical properties of liquid and supercooled palladium were measured using containerless techniques. Over the 1640–1875 K temperature interval, the density could be expressed as (T)=10.66× 10³ –0.77(T–T_m)(kg·m^–3) and the ratio between the isobaric heat capacity and the hemispherical total emissivity could be rendered as (J·mol^–1·K^–1), where T_m=1828 K. The volume expansion coefficient was also determined as 7.2 × 10^–5 K^–1.     

Isochoric Heat-Capacity Measurements for Pure Methanol in the Near-Critical and Supercritical Regions

Isochoric heat-capacity measurements for pure methanol are presented as a function of temperature at fixed densities between 136 and 750 kg·m⁻³. The measurements cover a range of temperatures from 300 to 556 K. The coverage includes the one- and two-phase regions, the coexistence curve, the near-critical, and the supercritical regions. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat-capacity measurements are estimated to be 2–3% depending on the experimental density and temperature. Temperatures at saturation, T _S(ρ), for each measured density (isochore) were measured using a quasi-static thermogram technique. The uncertainty of the phase-transition temperature measurements is 0.02 K. The critical temperature and the critical density for pure methanol were extracted from the saturated data (T _S,ρ_S) near the critical point. For one near-critical isochore (398.92 kg·m⁻³), the measurements were performed in both cooling and heating regimes to estimate the effect of thermal decomposition (chemical reaction) on the heat capacity and phase-transition properties of methanol. The measured values of C _V and saturated densities (T _S,ρ_S) for methanol were compared with values calculated from various multiparametric equations of state (EOS) (IUPAC, Bender-type, polynomial-type, and nonanalytical-type), scaling-type (crossover) EOS, and various correlations. The measured C _V data have been analyzed and interpreted in terms of extended scaling equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes ( and B ₀).     

The Activation Energy <Emphasis Type="Italic">U</Emphasis>(<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">H</Emphasis>) in Y-based Superconductors

Based on the Arrhenius equation, a method to calculate the activation energy from the resistance transition is proposed for high temperature superconductors. This method is applied to the Y-based superconductors. The activation energy is found to be U(T,H)∼(1−T/T _c )^4.8(H/H ₀)^−3.8 of YBCO crystal, and U(T,H)∼(1−T/T _c )^3.3(H/H ₀)^−2.2 of Er doped MTG YBCO crystal, respectively. With the obtained activation energy U(T,H), the lower part of the experimental curve ρ(T,H) and its derivative can be reproduced.      

Thermal conductivity, heat capacity, and compressibility of atactic poly(propylene) under high pressure

The thermal conductivity λ and the heat capacity per unit volume of atactic poly(propylene) have been measured in the temperature range 90–420 K at pressures up to 1.5 GPa using the transient hot-wire method. The bulk modulus has been measured in the range 200–295 K and up to 0.7 GPa. These data were used to calculate the volume dependence of λ,g=−[∂λ/λ)/(∂V/V)] _T , which yielded the following values for the glassy state (T<256 K at atmospheric pressure): 3.80±0.19 at 200 K, 3.74±0.19 at 225 K, 3.90±0.20 at 250 K, 3.77±0.19 at 271 K, and 3.73±0.19 at 297 K. The resultant value forg of the liquid state was 3.61±0.15 at 297 K. Values forg which are calculated at 295 K, using theoretical models of λ(T), agree to within 12% with the experimental value for the glassy state.     

Interplay of Superconductivity and Ferromagnetism in UGe<Subscript>2</Subscript>

The emergence of pressure induced superconductivity (SC) under the background of ferromagnetic state in 5f-electron based itinerant ferromagnetic superconductor UGe₂ is studied in the single band model by using a mean-field approximation. The solutions to the coupled equations of superconducting gap (Δ) and magnetization (m) are obtained using Green’s function technique and equation of motion method. It is shown that there generally exists a coexistent (Δ≠0, m≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The study of electronic specific heat (C/T), density of states, free energy, etc. are also presented. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, realized at low enough temperature. The agreement between theory and experimental results for UGe₂ is quite satisfactory.      

Coexistence of Itinerant Ferromagnetism and Superconductivity in ZrZn<Subscript>2</Subscript>

A microscopic coexistence of itinerant ferromagnetism and superconductivity is studied in a single- band homogeneous system, using an equation of motion method and Green’s function technique. Self-consistent equations for the superconducting order parameter Δ and magnetization m are derived. It is shown that there generally exists coexistent (Δ≠0 and m≠0) solutions to the coupled equations of the order parameters in the temperature range 0<T<min (T _c ,T _FM ), where T _c and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The expressions for specific heat, density of states, free energy, and critical field are also derived. The theory is applied to explain the observations in ZrZn₂. The agreement between the theory and experimental observations is quite satisfactory.      

Experimental Study of the Critical Behavior of the Isochoric Heat Capacity of Aqueous Ammonia Mixture

The isochoric heat capacity of a NH₃ + H₂O (0.2607 mole fraction of ammonia) mixture has been measured in the near- and supercritical regions. Measurements were made in the single- and two-phase regions including the coexistence curve using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. Measurements were made along 38 liquid and vapor isochores in the range from 120.03 kg · m⁻³ to 671.23 kg · m⁻³ and at temperatures from 478 K to 634 K and at pressures up to 28 MPa. Temperatures at the liquid–gas phase transition curve, T _S(ρ), for each measured density (isochore) and the critical parameters (T _C and ρ _C) for the 0.2607 NH₃ + 0.7393  H₂O mixture were obtained using the quasi-static thermograms technique. The expanded uncertainty of the heat-capacity measurements at the 95 % confidence level with a coverage factor of k = 2 is estimated to be 2 % to 3 % in the near-critical and supercritical regions, 1.0 % to 1.5 % in the liquid phase, and 3 % to 4 % in the vapor phase. Uncertainties of the density, temperature, and concentration measurements are estimated to be 0.06 %, 15mK, and 5×10⁻⁵ mole fraction, respectively. An unusual behavior of the isochoric heat capacity of the mixture was found near the maxcondetherm point (in the retrograde region). The value of the Krichevskii parameter was calculated using the critical properties data for the mixture and vapor-pressure data for the pure solvent (H₂O). The derived value of the Krichevskii parameter was used to analyze the critical behavior of the strong (C _P , K _T ) and weakly (C _V ) singular properties in terms of the principle of isomorphism of critical phenomena in binary mixtures. The values of the characteristic parameters (K ₁, K ₂), temperatures (τ ₁, τ ₂), and the characteristic density differences (Δρ ₁, Δρ ₂) were calculated for the NH₃ + H₂O mixture by using the critical-curve data.     

Noncontact Measurements of Thermophysical Properties of Molybdenum at High Temperatures

Four thermophysical properties of both solid and liquid molybdenum, namely, the density, the thermal expansion coefficient, the constant-pressure heat capacity, and the hemispherical total emissivity, are reported. These thermophysical properties were measured over a wide temperature range, including the undercooled state, using an electrostatic levitation furnace developed by the National Space Development Agency of Japan. Over the 2500 to 3000 K temperature span, the density of the liquid can be expressed as _L(T)=9.10×10³–0.60(T–T _m) (kg·m^–3), with T _m=2896 K, yielding a volume expansion coefficient _L(T)=6.6×10^–5 (K^–1). Similarly, over the 2170 to 2890 K temperature range, the density of the solid can be expressed as _S(T)=9.49×10³–0.50(T–T _m), giving a volume expansion coefficient _S(T)=5.3×10^–5. The constant pressure heat capacity of the liquid phase could be estimated as C _PL(T)=34.2+1.13×10^–3(T–T _m) (J·mol^–1·K^–1) if the hemispherical total emissivity of the liquid phase remained constant at 0.21 over the temperature interval. Over the 2050 to 2890 K temperature span, the hemispherical total emissivity of the solid phase could be expressed as _TS(T)=0.29+9.86×10^–5(T–T _m). The latent heat of fusion has also been measured as 33.6 kJ·mol^–1.     

Hot hardness of (Fe,Cr)3C and (Fe,Cr)7C3 carbides

Hot hardness was measured on the primary carbides, (Fe, Cr)₃C and (Fe, Cr)₇C₃, in unidirectionally solidified iron-carbon-chromium hypereutectic alloys with chromium more than 4.8 wt %. The hardness-temperature relation was represented by two Ito-Shishokin formulae,H _v =A(— BT), and thus was drawn by two lines on a semilogarithmic graph. The inflection temperature where the two lines intersected was found at 730 to 860 K for (Fe, Cr)₃C carbide containing 0 to 14 wt % Cr, increasing with an increase in the chromium concentration in the carbide, and at about 910 K for (Fe, Cr)₇C₃ carbide containing 36 to 76 wt % Cr. With increasing chromium concentration in each carbide, the hardness of the carbide increased and the thermal softening coefficients decreased. The effect of chromium on the hardness, the inflection temperature and the thermal softening coefficients was more pronounced for (Fe, Cr)₃C carbide than for (Fe, Cr)₇C₃ carbide. Each of the thermal softening coefficients,B ₁(T<T _t),B ₂(T>T _t), the inflection temperature,T _t, room-temperature hardness,H _v(T _RT), and the hardness atT _t,H _v(T _t), related linearly to the chromium concentration in the carbides, and hence the hot hardness of the carbides could be expressed as functions of temperature and chromium concentration in the carbides. The relationships betweenH _v(T _RT) andH _v(T _t) and between the thermal softening coefficient,B ₂, and the activation energy for creep,Q _c(kJ mol^–1), were represented by the following equations:H _v(T _t)0.7H _v(T _RT),B ₂=1.26/Q _c.     

Extraction of Critical Current Density and Flux Creep Exponent in the Magnetic Superconductor Ru-1212 Using the ac Magnetic Susceptibility Measurements

The ac susceptibility data was employed to extract the temperature dependence of the critical current density, J _c(T), as well as the variation of flux-creep exponent n(T,H _ac) with temperature and ac field amplitude in bulk samples of polycrystalline magnetic superconductor RuSr₂GdCu₂O₈ (Ru-1212). The critical state models and the collective flux-creep approximation model were successfully accounted to describe such behavior below the transition temperature. The calculated values of n(T,H) are well fitted to a power law of the following form: n(T,H)=n ₀(H)T ^−s(H), where s is field dependent exponent whose values varied from −2.4, −1.01 for field amplitudes ranging from 0.5 G and 3.8 G. The power law describing the frequency dependence of χ′ is found to be consistent with the results of the current-dependent effective activation energy of the form U(J)=U ₀ln (J _c/J). Additionally, the dependence of the current density is found to scale according as: J _c(T)=J _c0(1−T/T _c) ⁿ , where the exponent n values varied from 1.05 to 1.25. Such dependence is an indication of intergrain coupling that could be ascribed in terms of superconductor–insulator–superconductor junctions. The derived temperature dependence of J _c(T) is in good agreement with the data obtained from the measurements using the traditional “loss-maximum” approach. Furthermore, the flux-creep effect increased with increasing both ac fields and temperatures except at about 15–25 K below the onset of T _c, where a slowing down of the flux creep was observed.