An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

Thermally activated flow parameters in the deformation of MgO single crystals

Strain-rate cycling methods have been used to determine the thermally activated flow parameters in the compressive deformation of MgO single crystals. Activation volumes of the order of 100b ³ have been measured for deformation below room temperature, indicating dislocation-point defect interactions as the rate controlling mechanism for hardening at these temperatures, whileV ^* values of the order of 1000b ³ have been measured at and above room temperature. This, together with the fact that the effective stress remains constant with strain at these temperatures identifies the interaction of dislocations with dislocation dipoles as the rate controlling mechanism in this temperature range. The Gibbs free energy for deformation,G, equals the activation enthalpy,H, at low temperatures and the deviation ofG fromH above room temperature may be attributed to entropy effects.     

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.     

Two-particle tunneling current in Josephson junctions

The contribution to the tunneling current of a Josephson junction from the Two-particle tunneling, to the 2nd order approximation in the barrier transparency, is investigated. Expressions for the current onset amplitudes corresponding to eV = _1,2 are given together with the full expressions for the voltage and the temperature dependencies of the two-particles current. The theory has ben developed to take also into account corrections due to depairing mechanisms, which lead to the smearing of the current singularities. Introducing a depairing parameter , which accounts for the probability of these processes, I–V curves in the voltage region of the onset of single and two particle current are obtained. It is shown that, though having the same functional dependence, spreading occurs over a voltage range of different widths. In particular, it is shown that the width of the single-particle structure is twice larger the one for the two-particle. A careful investigation of the I–V curves in the region 2 -eV is presented and some aspects of the interesting voltage region near ¦₁-₂¦ is discussed.     

A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid     

Fatigue behaviour of precipitation-hardening medium C steels containing Cu

The presence of Cu precipitates counteracts the cyclic softening present in ordinary quenched and tempered steels. This is expected to result in an increase in fatigue limit. The fatigue crack propagation rate (dc/dN) at constant K in the Cu-C steels was shown to depend on heat-treatment and carbon content. To maximize yield strength and minimize ¦da/dN¦_K for tempering at 500° C, one must choose a low C content and temper for a short time; ¦da/dN¦_K in 0.28 wt % C-1.45 wt % Cu tempered for 13 min was one-third that for 0.45 wt % C-1.45 wt% Cu tempered for 200 min. There is also an advantage in adding Cu while simultaneously lowering the Ccontent. The dc/dN data are discussed in terms of the yield strength and the energy to form a unit area of fatigue crack, U, which was measured using foil strain gauges. The quantity (¦dc/dN ¦_{K y} ² U) where _y is the cyclic yield stress, was found to be nearly constant. In the 0.28 wt % C-1.45wt % Cu alloy, short ageing times at 500° C resulted in greater resistance to initiation of cracks at notches for low Ks than long ageing times.     

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*.     

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.     

Third sound in a restricted geometry

Bergman's general treatment of third sound waves has been extended to a (restricted) parallel plate geometry. In a parallel plate geometry two independent third sound modes can propagate: a symmetric and an antisymmetric one. Calculations show that at temperatures below 1 K the antisymmetric mode carries the most important part of the temperature amplitude. Because of the relatively strong substrate influence the temperature amplitude of the symmetric mode is suppressed. The T/h versus T measurements by Laheurteet al. ¹ and of the T/h versus measurements by Elliset al. ² are explained.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Self-similar heating regime upon destruction of the surface of materials

The applicability of the dependence ^* Ka in mass transfer from the surface of heat insulating materials is experimentally demonstrated. A formula for calculating the temperature coefficient K is suggested.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 2, pp. 236–240, February, 1986.     

Excitation spectrum and the density of states for a superconducting bilayer composite

The single-particle excitation spectrum and the density of states (DOS) for a superconducting bilayer composite are calculated by solving the Bogoliubov equations. The bilayer consists of two different superconducting films in contact. The superconducting order parameters of the films ₁ and ₂ are assumed constant. For various film thicknesses the dependence of the DOS on the ratio ₁/₂ is shown. This dependence is most prominent for states with excitation energy less than ₂.     

Singular Band Behavior of the Extended Emery Model for the Superconducting Cuprates

Mean field slave-boson approximation is performed on the extended Emery model for the CuO₂ conducting plane. The model is parameterized by Cu–O charge transfer energy _pd , copper–oxygen overlap t ₀, oxygen–oxygen overlap t', and Coulomb interaction U on the copper site taken as infinite. Special emphasis is placed on the role of t in the renormalization trends of the effective band parameters _pf and t, replacing _pd and t ₀, at small doping . It is shown that small, negative t expands the range of stability of the metallic phase, changing, in the second order of the perturbation theory, the nature of the metal–insulator transition point. In the nonperturbative limit, t modifies strongly the renormalization of _pf , making it saturate at the value of 4t. Finite doping suppresses the insulating state approximately symmetrically with respect to its sign. The regime _pf 4t fits very well the ARPES spectra of Y123, Bi2212, and LSCO and also explans, in the latter case, the evolution of the FS with doping accompanied by the spectral weight-transfer from the oxygen to the resonant band.     

On mode I and mode II energy release rates of an interface crack

The opening (mode I) and sliding (mode II) components of the energy that is released during an incremental extension of an interface crack between two different elastic materials are evaluated by the Irwin's crack closure method. Each component of the energies (G _I and G _II ) is expressed in terms of the functions of the length of the incremental crack extension (a) and the real and imaginary part of the complex stress intensity factor defined by Malyshev and Salganik. It is found that values of G _I /a and G _II /a oscillate violently when a approaches zero and that, hence, in contrast with the case for homogeneous materials, each energy release rate should be defined as G _I /a and G _II /a for an actual crack growth step size.     

A micromechanics theory for the transformation toughening of two-phase ceramics

Summary Based on the principle of thermodynamic equilibrium, the condition of stress-induced phase transformation in a two-phase ceramic is established. The development makes use of the change of potential energy that was calculated with a mean-field approach. In this process the elastic heterogeneity of the constituent phases, and the shape and volume concentration of the randomly oriented metastable ellipsoidal inclusions, are fully accounted for. Both the transformation heightH of the process zone with a steadily growing crack and the fracture toughness increment K of the transforming system are derived. The derived theory is then used to address the effect of inclusion shape and elastic inhomogeneity on the transformation toughening of two-phase ceramics. By considering the metastable ellipsoidal inclusions as phase 1 and the stable matrix as phase 0, it is found that, when ₁/₀>1, flat-like discs always provide a larger transformation-height while spherical ones provide the smallest, and vice versa. As the ratio of ₁/₀ increases, the size of the process zone also increases. For the toughness increment, the results indicate that thin-disc inclusions are again the most effective toughening medium. It is further found that Poisson's ratio of the constituent phases also has a significant effect; the combination ofv ₁0.5 for the inclusions andv ₁0 for the matrix has the best enhancement for fracture toughness. But whenv ₁, the toughness increment K all approaches to an asymptotic value regardless of the values of Poisson's ratios. Some explicit solutions of toughness change for several distinctive shapes of inclusions are also derived for the first time.     

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.

     

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.