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.     

Electrical properties of BaSnO3 in substitution of antimony for tin and lanthanum for barium

Polycrystalline materials of BaSn_1–x Sb _x O_3– and Ba_1–y La _y SnO_3– were prepared. Substitutional solubilities of antimony for tin and lanthanum for barium, respectively, in BaSnO₃ were obtained to be x=0.18 for BaSn_1–x Sb _x O_3– and y<0.052 for Ba_1-y La _y SnO_3–. The X-ray photoemission spectroscopy measurements showed the valence of antimony and tin is mixed in our samples of BaSn_1–x Sb _x O_3–. At lower temperature, magnetic susceptibilities of BaSn_1–x Sb _x O_3– and Ba_1–y La _y SnO_3– satisfy the Curie law, indicating the existence of non-interacting localized electrons at the Sn⁴⁺ site, and forming a Sn⁴⁺+e^– state in these systems. By substitution of antimony and lanthanum in BaSnO₃, the conductive properties are semiconductor-like. To explain this conductive behaviour, three types of mechanism were taken into consideration.     

Thermophysical Property Measurements of Supercooled and Liquid Rhodium

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

Static recrystallization kinetics of 304 stainless steels

Static restoration mechanism during hot interrupted deformation of 304 stainless steel was studied in the temperature range from 900 to 1100°C, various strain rate from 0.05 to 5/sec and pass strain of 0.25–3 times peak strain. It was clarified that the static recrystallization was happened after 3–10 seconds at first deformation. The static restoration was depended on the pass strain, deformation temperature and strain rate and fractional softening (FS) values increased with increasing strain rate, deformation temperature and pass strain. Recystallization kinetics was explained with Avrami equation and Avrami constant was 1.113. This value was independent of deformation variables significantly. The time of 5, 50, 95% recrystallization was evaluated using such equations: t _0.05 = 2.9 × 10^{–12 –1.17 –0.94} D exp(222000 J/mol/RT), t _0.5 = 2.0 × 10^{–10 –1.56 –0.81} D exp(197000 J/mol/RT), t _0.95 = 1.9 × 10^{–8–1.63 –0.76} D exp(173000J/mol/RT). The predicted values by use of upper equations had a good agreement with a measurement.     

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.     

Phase Equilibria and Structure of Solid Solutions in the La–Co–Fe–O System at 1100°C

Phase equilibria in the La–Co–Fe–O system are studied at 1100°C in air using samples prepared by the citrate, nitrate, and conventional ceramic routes. The stability regions and structures of solid solutions in the La–Co–Fe–O system are determined by x-ray powder diffraction: LaCo_{1 – y} Fe _y O_{3 –} (0 < y 0.25, sp. gr. R c; 0.775 y< 1, sp. gr. Pbnm), Co_{1 – y} Fe _y O (0 < y 0.13, NaCl-type structure, sp. gr. Fm3m), and Fe_{3 – x} Co _x O₄ (0.84 x 1.38, sp. gr. Fd3m). The structural parameters of phase-pure solid solutions are determined by the Rietveld method. The composition dependences of lattice parameters are presented for LaCo_{1 – y} Fe _y O_{3 –} (0 < y 0.25) and Fe_{3 – x} Co _x O₄ (0.84 x 1.38). The 1100°C isotherm of the pseudoternary system La₂O₃–CoO–Fe₂O₃ in air is constructed.     

Metrological Characteristics of MN-3 Solid-Body DC Voltage Measures

Results of theoretical and experimental investigations into the statistical characteristics of the voltage instability of type MN-3 measures are presented. The capabilities of linear mathematical models of the voltage instability of solid-body measures are considered and evaluated. It is shown that MN-3 type measures maintain a relative measurement (comparison) error in the range 1·10^–8–3·10^–8 only for a measurement period t 1 h and that with t 1 day, the error increases to values in the range 5·10^–8–8·10^–8, while when t 1–3 months it increases to 5·10^–7.     

Thermophysical Properties of Molten Germanium Measured by a High-Temperature Electrostatic Levitator1

Thermophysical properties of molten germanium have been measured using the high-temperature electrostatic levitator at the Jet Propulsion Laboratory. Measured properties include the density, the thermal expansivity, the hemispherical total emissivity, the constant-pressure specific heat capacity, the surface tension, and the electrical resistivity. The measured density can be expressed by _liq=5.67×10³–0.542 (T–T _m ) kg·m^–3 from 1150 to 1400 K with T _m=1211.3 K, the volume expansion coefficient by =0.9656×10^–4 K^–1, and the hemispherical total emissivity at the melting temperature by _{T, liq}(T _m)=0.17. Assuming constant _{T, liq}(T)=0.17 in the liquid range that has been investigated, the constant-pressure specific heat was evaluated as a function of temperature. The surface tension over the same temperature range can be expressed by (T)=583–0.08(T–T _m) mN·m^–1 and the temperature dependence of the electrical resistivity, when r _liq(T _m)=60·cm is used as a reference point, can be expressed by r _{e, liq}(T)=60+1.18×10^–2(T–1211.3)·cm. The thermal conductivity, which was determined from the resistivity data using the Wiedemann–Franz–Lorenz law, is given by _liq(T )=49.43+2.90×10^–2(T–T _m) W·m^–1·K^–1.     

Non-Contact Measurements of Surface Tension and Viscosity of Niobium, Zirconium, and Titanium Using an Electrostatic Levitation Furnace

The surface tension and viscosity of liquid niobium, zirconium, and titanium have been determined by the oscillation drop technique using a vacuum electrostatic levitation furnace. These properties are reported over wide temperature ranges, covering both superheated and undercooled liquid. For niobium, the surface tension can be expressed as (T)=1.937×10³–0.199(T–T _m) (mN·m^–1) with T _m=2742 K and the viscosity as (T)=4.50–5.62×10^–3(T–T _m) (mPa·s), over the 2320 to 2915 K temperature range. Similarly, over the 1800 to 2400 K temperature range, the surface tension of zirconium is represented as (T)=1.500×10³–0.111(T–T _m) (mN·m^–1) and the viscosity as (T)=4.74–4.97 ×10^–3(T–T _m) (mPa·s) where T _m=2128 K. For titanium (T _m=1943 K), these properties can be expressed, respectively, as (T)=1.557×10³–0.156(T–T _m) (mN·m^–1) and (T)=4.42–6.67×10^–3(T–T _m) (mPa·s) over the temperature range of 1750 to 2050 K.     

Anomalous High-Temperature Properties of BaPbO3-Based Solid Solutions

The thermal expansion, thermal stability, and electrical resistivity of the Ba_{1 – x} M _x Pb_{1 + y} O_{3 +} (M = Sr, Ca; 0 x 1.0, 0 y 0.2) and Ba_{1 – x} M" _x Pb_{1 – y} M" _y O_{3 +} (M" = K, La; M" = Sc, Sb; x, y= 0.01) ceramic materials were studied between 293 and 1073 K in air. The linear thermal expansion coefficient of the ceramics was found to increase abruptly at 700 K, from (10–14) × 10^–6K^–1in the range 300–600 K to (13–18) × 10^–6K^–1in the range 800–1000 K. The electrical resistivity of the ceramics passes through a sharp maximum near 750 K, with the largest jump in resistivity at the compositions Ba_0.6Sr_0.4PbO₃and Ba_0.9Ca_0.1PbO₃. The anomaly in thermal expansion is likely associated with the rearrangement of the lead–oxygen polyhedra in the structure of the solid solutions, and the jump in resistivity is attributable to changes in the average oxidation state of Pb ions in the surface layer of the ceramics.     

Non-Contact Measurements of the Thermophysical Properties of Hafnium-3 Mass% Zirconium at High Temperature

Several thermophysical properties of hafnium-3 mass % zirconium, namely the density, the thermal expansion coefficient, the constant pressure heat capacity, the hemispherical total emissivity, the surface tension and the viscosity are reported. These properties were measured over wide temperature ranges, including overheated and undercooled states, using an electrostatic levitation furnace developed by the National Space Development Agency of Japan. Over the 2220 to 2875 K temperature span, the density of the liquid can be expressed as _L (T)=1.20×10⁴–0.44(T–T _m ) (kgm^–3) with T _m =2504 K, yielding a volume expansion coefficient _L (T)=3.7×10^–5 (K^–1). Similarly, over the 1950 to 2500 K span, the density of the high temperature and undercooled solid -phase can be fitted as _S (T)=1.22×10⁴–0.41(T–T _m ), giving a volume expansion coefficient _S (T)=3.4×10^–5. The constant pressure heat capacity of the liquid phase can be estimated as C _PL (T)=33.47+7.92×10^–4(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the 2250 K to 2650 K temperature interval. Over the 1850 to 2500 K temperature span, the hemispherical total emissivity of the solid -phase can be represented as _TS (T)=0.32+4.79×10^–5(T–T _m ). The latent heat of fusion has also been measured as 15.1 kJmol^–1. In addition, the surface tension can be expressed as (T)=1.614×10³–0.100(T–T _m ) (mNm^–1) and the viscosity as h(T)=0.495 exp [48.65×10³/(RT)] (mPas) over the 2220 to 2675 K temperature range.     

Excess thermodynamic properties of mixtures of alkyl benzoates withn-heptane

The paper reportsh ^E values at 298.15 K andv ^E and values at various temperatures for binary mixtures of propyl or butyl benzoate andn-heptane. The excess Gibbs energy of viscous flow,g ^*E, and the thermodynamic activation properties were calculated from these values. The results are compared with those for similar mixtures and interpreted on the basis of the characteristic dipole-dipole interactions of alkyl esters.Nomenclature A _i Parameters in Eq. (2) - dg ^*E Gibbs free energy of viscous flow (J · mol^–l) - dg Activation free energy (kJ · mol^–1) - K Parameter in Eq. (2) - h Planck constant - h ^E Excess enthalpy (J · mol^–1) - h Activation enthalpy (kJ · mol^–1) - N Avogadro number - R Universal gas constant (J · K^–1 · mol^–1) - s Standard deviation - s Activation entropy (J · K^–1 · mol^–1) - T Temperature (K) - v Molar volume of pure component (m³ · mol^–1) - v ^E Excess volume (m³ · mol^–1) - x _i Mole fraction of componenti Greek Letters Expansion coefficient (K^–1) - Density (kg · m^–1 ) - Viscosity (mPa · s ) - Apparent excess viscosity (mPa · s)     

On the analysis of the thermal diffusivity measurement method with modulated heat input

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(t) Energy of modulation per unit surface deposited on surface x=l, W · m^–2 - Q(t) Total energy per unit surface deposited on surface x=l, W · m^–2 - q Complex energy modulation amplitude, W · m^–2 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(x, t) Modulation temperature at any distance x and at time t, K - t Time, s - x Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1     

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.     

The high-temperature thermal expansion of BiPbSrCaCuO superconductor and the oxide components (Bi2O3, PbO,CaO, CuO)

The thermal expansion of superconducting Bi_1.6Pb_0.4Sr₂Ca₂Cu₃Ox (BiPbSrCaCuO) and its oxide components Bi₂O₃, PbO, CaO and CuO have been studied by high-temperature dilatometric measurements (30–800°C). The thermal expansion coefficient for the BiPbSrCaCuO superconductor in the range 150–830°C is =6.4×10^–6K^–1. The temperature dependences of L/L of pressed Bi₂O₃ reveals sharp changes of length on heating (T ₁=712°C), and on cooling (T ₂=637°C and T ₃=577°C), caused by the phase transition monoclinic-cubic (T ₁) and by reverse transitions via a metastable phase (T ₂ and T ₃). By thermal expansion measurements of melted Bi₂O₃ it is shown that hysteresis in the forward and the reverse phase transitions may be partly caused by grain boundary effect in pressed Bi₂O₃. The thermal expansion of red PbO reveals a sharp decrease in L/L, on heating (T ₁=490°C), related with the phase transition of tetragonal (red, a=0.3962 nm, c=0.5025 nm)-orthorhombic (yellow, a=0.5489 nm, b=0.4756 nm, c=0.5895 nm). The possible causes of irreversibility of the phase transition in PbO are discussed. In the range 50–740°C the coefficient of thermal expansion of pressed Bi₂O₃ (_m=3.6 × 10^–6 and _c=16.6×10^–6K^–1 for monoclinic and cubic Bi₂O₃ respectively), the melted Bi₂O₃ (_m=7.6×10^–6 and _c=11.5×10^–6K^–1), PbO (_t=9.4×10⁶ and _or=3.3×10^–6K^–1 for tetragonal and orthorhombic PbO respectively), CaO (=6.1×10^–6K^–1) and CuO (=4.3×10^–6K^–1) are presented.     

Phase Relations in the Systems Ln1 – x Ba x CoO3 – δ(0 < x ≤ 0.66; Ln = Nd, Sm)

Data are presented on the structural and magnetic properties of Ln_{1 – x} Ba _x CoO_{3 –} (Ln = Nd, Sm; 0 < x 0.66) samples slowly cooled in air after synthesis. The composition stability limits of the intermediate phases Ln_{1 – y} Ba_{1 + y} Co₂O_{5 +} and solid solutions are determined. The magnetic phase diagram of the Nd_{1 – x} Ba _x CoO_{3 –} system is constructed.     

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.     

Non-contact measurements of thermophysical properties of niobium at high temperature

Four thermophysical properties of both solid and liquid niobium have been measured using the vacuum version of the electrostatic levitation furnace developed by the National Space Development Agency of Japan. These properties are the density, the thermal expansion coefficient, the constant pressure heat capacity, and the hemispherical total emissivity. For the first time, we report these thermophysical quantities of niobium in its solid as well as in liquid state over a wide temperature range, including the undercooled state. Over the 2340 K to 2900 K temperature span, the density of the liquid can be expressed as _L (T) = 7.95 × 10³ – 0.23 (T – T _m)(kg · m^–3) with T _m = 2742 K, yielding a volume expansion coefficient _L(T) = 2.89 × 10^–5 (K^–1). Similarly, over the 1500 K to 2740 K temperature range, the density of the solid can be expressed as _s(T) = 8.26 × 10³ – 0.14(T – T _m)(kg · m^–3), giving a volume expansion coefficient _s(T) = 1.69 × 10^–5 (K^–1). The constant pressure heat capacity of the liquid phase could be estimated as C _PL(T) = 40.6 + 1.45 × 10^–3 (T – T _m) (J · mol^–1 · K^–1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the temperature range. Over the 1500 K to 2740 K temperature span, the hemispherical total emissivity of the solid phase could be rendered as _TS(T) = 0.23 + 5.81 × 10^–5 (T – T _m). The enthalpy of fusion has also been calculated as 29.1 kJ · mol^–1.     

A study on martensitic transformation in Ti50−x/2Ni50−x/2Cu x alloys with X≤10 at%

The effect of Cu additions on the martensitic transformation sequence and temperature in Ti_50–x/2Ni_50–x/2Cu _x alloys with x: 1–10 at% are investigated by ER, DSC, X-ray and IF measurements. Experimental results show that the transformation sequence of Ti_50–x/2Ni_50–x/2Cu _x alloys with x: 1–4 at% proceeding as two-stage B2RB19 transformation on cooling and Ti_50–x/2Ni_50–x/2Cu _x alloys with x=5, 10 at% have no martensitic transformation. The addition of Cu in Ti_50–x/2Ni_50–x/2Cu _x alloys assists the formation of R-phase, a behaviour which is quite different from that in Ti₅₀Ni_50–x Cu _x alloys. Both the Ms and T _R temperatures decrease rapidly with increasing Cu addition in Ti_50–x/2Ni_50–x/2Cu _x alloys with x: 1–4 at%. It is proposed that the Cu+Ni effects on the Ms temperature in Ti_50–x/2Ni_50–x/2Cu _x alloys is similar as Cu +Ni effects in Ti₅₀Ni_50–x Cu _x alloys and as Ni effects in as-quenched Ni-rich TiNi alloys.