Thermodynamic Properties of Lanthanum Chlorides

The enthalpies of atomization of LaCl, LaCl₂, and LaCl₃ are determined by measuring the vapor pressure over liquid and solid LaCl₃ and assessing the equilibrium constants of the gas-phase reactions BaCl + La = Ba + LaCl and 2BaCl + La = 2Ba + LaCl₂, using the appearance potentials of ions and the ionization potentials of the lanthanum chlorides: _at H ⁰(LaCl, 298 K) = 502.4 ± 0.5 kJ/mol, _at H ⁰(LaCl₂, 298 K) = 999.2 ± 0.8 kJ/mol, and _at H ⁰(LaCl₃, 298 K) = 1524.6 ± 2.0 kJ/mol. In addition, the enthalpies of formation of gaseous lanthanum chlorides are determined using new data on the thermodynamic functions of condensed LaCl₃ and gaseous LaCl, LaCl₂, and LaCl₃: _f H ⁰(LaCl, g, 298 K) = 48.9 ± 1.0 kJ/mol, _f H ⁰(LaCl₂, g, 298 K) = –326.6 ± 1.2 kJ/mol, and _f H ⁰(LaCl₃, g, 298 K) = –730.7 ± 2.0 kJ/mol. The ionization and appearance potentials of ions resulting from electron impact ionization of LaCl₃ are determined.     

Interaction between a dislocation and various divalent impurity in KCl single crystals for the Fleischer's model taking account of the Friedel relation

The interaction between a dislocation and the impurity in KCl : Mg²⁺ (0.035 mol% in the melt), KCl : Ca²⁺ (0.035 and 0.065 mol% in the melt) and KCl : Ba²⁺ (0.050 and 0.065 mol% in the melt) was investigated from the strain-rate cycling test during the Blaha effect measurement. This was carried out at 77–254 K. As a result, it was found that the Fleischer's model taking account of the Friedel relation seems to be suitable for KCl : Ca²⁺ and KCl : Ba²⁺. However, it was not appropriate for KCl : Mg²⁺. Furthermore, the values of T _c, H(T _c) and G ₀ were obtained for the specimens. T _c is the critical temperature at which effective stress is zero. H(T _c) and G ₀ are the enthalpy and the Gibbs free energy of activation for the breakaway of the dislocation from the impurity, respectively. H(T _c) was almost the same for the specimens except KCl : Mg²⁺. G ₀ increased with increasing the divalent cation size. In addition, the tetragonality around the divalent ion-positive ion vacancy pair was estimated on the basis of G ₀ for the each specimen.     

Pressure of the Saturated Vapor of Nickel at High Temperatures

Two series of measurements of the saturated vapor pressure of crystalline and liquid nickel are carried out in the temperature range of 1270–1896 K using the integral version of the effusion method and Knudsen mass spectrometry. The enthalpy of sublimation of Ni at 0 K is calculated from the measurement results in accordance with the second _s H ₀ ⁰(II) and the third _s H ₀ ⁰(III) laws of thermodynamics. Good agreement between the vapor pressure values, determined by different methods under different experimental conditions, makes possible their joint treatment for crystalline and liquid nickel and leads one to recommend the value of _s H ₀ ⁰ = 425.3 ± 2.0 kJ/mol. The results obtained are compared with the available data of other authors.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

New equations for enthalpy of vaporization from the triple point to the critical point

Two new equations are proposed for the enthalpy of vaporization from the triple point to the critical point. One of these equations containing four parameters is exceptionally good for fitting the data. The other equation containing three parameters is quite adequate for fitting the data but it is exceptionally suited for interpolation when the data do not cover the entire range. These equations have been tested using the enthalpy of vaporization of water from the triple point to the critical point and are compared with other equations.Nomenclature T _c Critical temperature, K - T _t Triple point, K - T _x Any particular temperature, K - T _r Reduced temperature - P _r Reduced pressure - R Gas constant - P Vapor pressure - X (T _c–T)/T _c - Y (T _c–T)/T - X _x (T _c–T)/(T _c–T _x) - X _t (T _c–T)/(T _c–T _t) - H _vt Enthalpy of vaporization at the triple point, kJ · mol^–1 - H _vx Enthalpy of vaporization at any temperature x, kJ · mol^–1 - Z _v Compressibilty factor of the saturated vapor - Z ₁ Compressibilty factor of the saturated liquid Relative deviation = 100[H_v(obs)–H_v(cal)]/H_v(obsd) Standard deviation = { [H _v(obs)–H _v(cal)]²/(No. points — No. parameters)}^0.5     

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

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

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

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.     

Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges

The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*= _–L ^L [1–(z)/]dz, where (z) is the pair potential of the junction, is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than besides the BCS peak atE=; forE> there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.     

ESR line broadening in Cr3+/MgO at liquid helium temperatures

Line broadening has been observed at 9 GHz in the ESR absorption spectrum of Cr³⁺ in MgO in the liquid helium temperature range, for a range of Cr³⁺ concentrations from 800 7400 ppm. The broadened linewidths at 4.2 K are about two times larger than those at 77 K and depend on polar angle. The lineshapes are Gaussian, in contrast to the Lorentzian lineshape between 293 and 77 K. The broadening is interpreted by the combined effects of strain, due to the charge misfit of Cr³⁺ and the host cation, and temperature which causes both exchange striction and departure from the cubic symmetry to a lower symmetry. Analysis of the linewidth data gives D=(5.25±0.40)×10^–4 cm^–1 and confirms that the total linewidth, H _t, is given by H _t=H ₀+(2D/g) cos _H where H ₀ is the linewidth independent of concentration, temperature and polar angle, _H.     

Thermodynamic considerations of metal halide vapour complexes

Certain metal halide vapour complexes of the type ABX _m+n increase the equilibrium vapour concentration of one or both of the component salts in the binary system (AXm/BX_n). Such enhancement depends upon the free energy of complex formation, the saturated vapour pressure of the complexing salt and the melt activities, in a manner formulated here by means of a thermodynamic scheme. Certain trends in the periodic table are established.Nomenclature enhancement term=p ⁰ K _a - enhancement term=P ⁰ K _a - F enhancement - p partial vapour pressure (atm) - p ⁰ saturated vapour pressure of monomer (atm) - P ⁰ total saturated vapour pressure exerted by a salt (atm) - vapour concentration of a species - ⁰ vapour concentration of a species above the pure salt (mol m^–3) - x cation mole fraction - H _a enthalpy of complex formation from monomers - H _b vaporization enthalpy of AX _m - H _c vaporization enthalpy of BX _n - H _d vaporization enthalpy of ABX _m+n - H _e exchange enthalpy - H _m enthalpy of mixing in liquid pool - V change in coulombic potential energy - D _b bridge bond strength - D _t end bond strength     

A correlation of ΔK th-value with the exponent,m, in the equation of fatigue crack growth for various steels

Literature (mainly in Japan) relating to fatigue-crack-growth-data at R=0 in an air environment for a wide range of steels is reviewed with particular attention to the threshold stress intensity, K _th. The collected data are analyzed in terms of the exponent, m(the slope of the linear portion of the log(da/dN)-logD relationship) by taking account of microstructure, material strength, fracture toughness and specimen thickness. The mean rate of fatigue crack growth for ductile steels in the range from the intermediate growth rate to threshold level and the relevant threshold values at R=0, K _th0, can be represented asda/dN = 1.700 × 10^-4(K103.6)^m - 10^-6andK _th0 = 103.6(5.88 × 10^-3)^1/m,where (da/dN) and K are measured by the units of mm/cycle and kgf/mm^3/2, respectively. Contrary to this, in the case of extremely brittle steels with K _IC-value below 200 kgf/mm^3/2 (the fracture occurs by the intergranular separation), the relationships are given byda/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7andK _th0 = 49.94(8.64 × 10^-3)^1/m.

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Résumé La littérature, principalement japonaise, relative aux données sur la propagation des fissures de fatigue pour R=0 dans un environnement d'air et pour une large catégorie d'aciers fait l'objet d'une revue avec une attention particulière pour l'intensité de contrainte de seuil, K _th. Les données collectées sont analysées en terme de l'éxposant m (qui représente la pente de la portion linéaire de la relation log(da/dN)-log K, en tenant compte de la microstructure, de la résistance du matériau, de la ténacité à la rupture et de l'épaisseur de l'éprouvette. La vitesse moyenne de propagation d'une fissure de fatigue dans le cas des aciers ductiles dans la fourchette entre la vitesse intermédiaire de fissuration et le niveau critique, et les valeurs correspondantes de seuil à R=0, K _th0 peuvent être représentées par la relation:da/dN = 1.700 × 10^-4(K103.6)^m - 10^-6etK _th0 = 103.6(5.88 × 10^-3)^1/m,où (da/dN) et K sont mesurés en unités de mm/cycle et en kgf/mm^3/2 respectivement. En contraste, dans le cas d'aciers extrèmement fragiles avec des valeurs K _IC en dessous de 200 kgf/mm^3/2 (la rupture se produit par une séparation intergranulaire), ces relations sont données par:da/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7etK _th0 = 49.94(8.64 × 10^-3)^1/m.

     

Microstructural evolution and calorimetric evaluation of non-equilibrium states in rapidly solidified Al-Mn-Co ternary alloys

Evolutionary structures were observed in as-melt spun ribbons of Al-3.5Mn-0.8Co, Al-3.5Mn-1.3Co, Al-3.5Mn-2Co, Al-5Mn-0.8Co and Al-5Mn-2Co alloys. The evolutionary structures contained two zones, zone A and zone B, at the chilled and unchilled sides, respectively. A banded structure was observed between the two zones as a transitional region in the Al-3.5Mn-1.3Co alloy. The enthalpy differences, H _O ^ne , between a non-equilibrium state in as-melt spun ribbons and the equilibrium state in fully annealed ribbons of the Al-Mn-Co alloys were evaluated using data obtained by differential scanning calorimetry (DSC) measurements. The values of H _O ^ne for Al-Mn-Co alloys are lower than those for Al-Mn binary alloys. H _O ^ne corresponds to a decrease in Gibbs free energy, G, which is stored in a solidified solid during rapid solidification. The formation of the banded structure is interpreted on the basis of an analysis of the distribution of H _O ^ne or the fluctuation in G, which should oscillate in order to correspond with a gradual reduction of cooling ability for the constrained solidification by the substrate.     

Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Ordered state of one-dimensional antiferromagnetic superconductors in the presence of a homogeneous magnetic field

Assuming a one-dimensional electron band and examining the free energy difference F (=F _S–F _N) for an antiferromagnetic superconductor in the presence of a homogeneous magnetic field H₀, it is shown that (i) for temperatureT=0, the spatially varying order parameter _Q (having the same period as the antiferromagnetic fieldH _Q) and the BCS order parameter coexist when |–H _QH ₀<+H _Q (here, the pairing coupling constant for _Q is assumed small), and (ii) forT near the second-order phase transition temperature the coexistence of _Q and is always realized whenH ₀0.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.On leave of absence from Physics Department, Tohoku University, Sendai, Japan.     

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.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

A new formulation of Gor'kov's theory of clean type II superconductors

From Gor'kov's theory a functional for the free energy of the flux line lattice is derived which depends explicitly on the potentials andA. It may be interpreted as an extension of the Ginzburg-Landau functional to arbitrary temperatures. For periodic || ² andH=rotA, the functional is a rapidly converging series, of which often the main term (corresponding to the Brandt-Pesch-Tewordt approximation) plus a correction term depending on the lattice structure suffices. From the cutoff series all previously known results for the special casesT T _c ,B H _c2 ,orB 0 are reproduced by minimization with respect to || ² andH.     

Applicability of FMR for crystallization studies in metallic glasses

It has been shown theoretically that the peak-to-peak ferromagnetic resonance (FMR) line-width (H _pp) should be proportional to the volume fraction (f) of the crystalline phase formed during annealing in ferromagnetic glasses. However, in the case of zero-magnetostrictive cobalt-based glasses (=0), H _pp should remain constant due to very low values of anisotropy. In Co₆₈Fe₄Mo₁Si₁₇B₁₀ glass (=0), H _pp has been found to remain unaffected upon progressive crystallization. In Fe₆₅Cr₈B₂₇ glass, H _pp has been found to be linearly proportional tof. Using this dependence, the activation energy of crystallization (E _a) has been calculated. The value ofE _a obtained from the FMR technique (248 kJ mol^–1) agrees quite well with those from DTA studies using Kissinger's or Ozawa's technique.