Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

The thermal conductivity and Lorenz function of the tin-lead alloy system Sn x Pb1 − x (x = 0.85, 0.7 0.5 0.3)

The thermal conductivity and electrical resistivity of the tin-lead alloy system Sn _x Pb_{1 – x} (x = 0.85, 0.7 0.5 0.3) were measured in the temperature range 7–300 K. The thermal conductivity was analyzed at temperature T 20K, assuming 1//T+Tⁿ, where , , and n are constants. The analysis shows that n < 2, and not n 2, which would be expected for a normal pure metal. The electrical resistivities could be represented by a T ⁵ relation for temperatures up to about 60 K. The characteristic temperature _R appears to decrease with increasing weight percent of lead. The total Lorenz functions were high, indicating the presence of phonon conductivity. The phonon conductivity _g appears to vary with T, and can be represented by _g=a/Tⁿ (a > 0) and n2.Work supported by the Universiti Sains Malaysia.     

Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation of normal liquid ³He has been studied over a range of temperatures from slightly above the superfluid transition temperature, T _c, to approximately 10mK at the constant pressures of 1 and 5bar. Using longitudinal LiNbO₃ transducers, operating both on and off resonance, the experiment was performed at 15 discrete frequencies located in several broadband frequency windows, including 16–25, 60–70, and 105–111MHz. The results are compared to Landau's prediction for the attenuation of zero sound in the quantum limit, (k _B Tk _B T _F), where ₀(P,T, )= (P) T ²{1+(/2k _B T)²}. Calibration of the received zero sound signals was performed by measuring the temperature dependence of the first sound attenuation from 30 to 800mK at those same frequencies and pressures. The data are compared to previous results.     

p-Version hierarchical three dimensional curved shell element for heat conduction

This paper presents a finite element formulation for a three dimensional nine node p-version hierarchical curved shell element for heat conduction where the element temperature approximation can be of arbitrary order p , p , and p in the , and directions. This is accomplished by first, constructing one dimensional hierarchical approximation functions and the corresponding nodal variable operators for each of the three directions , and using Lagrange interpolating polynomials and then taking their products (sometimes also called tensor products). The element approximation functions as well as the nodal variables are hierarchical and therefore the element matrices and the equivalent heat vectors are hierarchical also i.e. the element properties corresponding to polynomial orders p , p , and p are a subset of those corresponding to (p +1), (p +1), and (p +1). The element formulation ensures C ⁰ continuity. The curved shell geometry is constructed in the usual way by taking the coordinates of the nodes lying on the middle surface of the element (=0) and the nodal thickness vectors. The element properties i.e. element matrices and the equivalent heat vectors are derived using weak formulation (or quadratic functional) of the three dimensional F ourier heat conduction equation and the hierarchical element temperature approximation. The element formulation is equally effective for very thin as well as extremely thick shells. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, faster rate of convergence and over all superiority of the present formulation. The h-approximation results are presented for comparison purposes.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

Magnetic properties of highly dilutedPdFex andPtFex-alloys. Part II. Susceptibility at micro- and milli-kelvin temperatures

We have measured the 16 Hz susceptibility of the giant magnetic moments induced by Fe impurities in highly dilutedPdFe_x andPtFe_x samples with 2.5 ppm x 75 ppm in a wide temperature range, 30 K T 300 mK, and at static magnetic fields 0,01 mT B 25 mT. We find spin glass freezing at Tf(X)/X0,19mK/ppm Fe forPdFe_x and the larger value 0.26 mK/ppm Fe forPtFe_x. This is the first observation of spin glass freezing inPtFe_x. In the low-temperature range T 0.5T_f(x), the susceptibilities follow — ₀ T with small zero-temperature ₀ values forPdFe_X and vanishing ₀ values forPtFe_x. In the paramagnetic high-temperature range, we find (T — )^it-1 at T 10 mK independent of x forPdFe_x, and at T 2Tf(x) dependent of x forPtFe_x with vanishing values for both systems. The data compare well to the predictions of the Thouless-Anderson-Palmer TAP approach of the Sherrington-Kirkpatrick SK model for spin glasses.     

Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Heat capacity and magnetic properties in the (PdCO y )H x -system at low temperatures

Results of heat capacity measurements on (PdCo _y )H _x (y 2.5 at %; 0 x 0.8) in the temperature range from 2 to 12 K are reported. The dependence of the coefficient of the electronic heat capacity on the Co content and on the x value is considered. For the binary alloy PdCo _y a decreasing spin wave contribution to the heat capacity (T ^3/2) is found, which agrees well with the known ferromagnetic properties of the alloy. In contrast, for the phase of (PdCo _y )H _x a contribution to the heat capacity can be separated, probably caused by the thermal excitation of magnetic clusters. The temperature dependence of this cluster contribution can be well explained by means of an Einstein function. Conclusions are drawn with regard to the intercluster interaction and to the number of atoms per cluster.     

Viscosities and Excess Molar Volumes of Binary Mixtures of Alkyl Acetates with Di-, Tri-, and Tetrachloroethane

The excess molar volume V ^E, viscosity deviation , excess viscosity ^E, and excess Gibbs energy of activation G*^E of viscous flow have been investigated from density and viscosity measurements of nine binary mixtures of methyl acetate, ethyl acetate, and amyl acetate with dichloroethane, trichloroethane, and tetrachloroethane at 303.15 K. The results were fitted to polynomials of variable degree. The viscosity data have been correlated with the equations of Grunberg and Nissan, Hind, McLaughlin, and Ubbelohde, Tamura and Kurata, Katti and Chaudhri, McAllister, Heric, and Auslaender. The results have been analyzed in terms of molecular interactions between alkyl acetates and chloroethanes.     

Low-temperature specific heat of YBa2Cu3O7, YBa2Cu3O6, Y2BaCuO5, YBa3Cu2O7, BaCuO2, and CuO

We have measured the low-temperature specific heat (1.3T20 K) and the dc magnetic susceptibility (100T250 K) of eight samples of the high-T _c superconductor Y _x Ba_3–x Cu₃O_7– (x=0.9, 1.0, 1.1) and of two samples of nonsuperconducting YBa₂Cu₃O₆₊. We have also performed specific heat measurements on the possible impurity phases: YBa₃Cu₂O₇, Y₂BaCuO₅, CuO, and BaCuO_2+x . The superconducting samples all have a nonzero, sample-dependent linear term * and an upturn inC/T at very low temperature. We show that this anomalous behavior is at least partly due to the presence of a small amount (1%) of BaCuO_2+x impurity phase in the measured samples. This is evidenced by the correlation between * and the Curie component of the susceptibility, which is proportional to the amount of paramagnetic impurities.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Non fermi liquid ground states in strongly correlated f-electron materials

Experimental efforts to characterize and develop an understanding of non Fermi liquid (NFL) behavior at low temperature in f-electron materials are reviewed for three f-electron systems: M_1–xU_xPd₃ (M = Sc, Y), U_1–xTh_xPd₂Al₃, and UCu_5–xPd_x. The emerging systematics of NFL behavior in f-electron systems, based on the present sample of nearly ten f-electron systems, is updated. Many of the f-electron systems exhibit the following temperature dependences of the electrical resistivity p, specific heat C, and magnetic susceptibility for T T₀, where T_o is a characteristic temperature: P(T) 1 –aT/T ₀, where a < 0 or > 0, C(T)/T (-1/T _o) In (T/bT ₀), and (T) 1 –c(T/T_o)^1/2. In several of the f-electron systems, the characteristic temperature T_o can be identified with the Kondo temperature T_k.     

Supercarrier Effective Mass Isotope Effect by Interband Scattering

Supercarrier effective mass isotope effect (exponent ) is investigated using a two-band model with interband pair scattering. The corresponding repulsive interaction incorporates besides the dominating electronic (Coulomb) part an electron-phonon contribution inversely proportional to the ionic mass factor. Calculations illustrating the behaviour of T _c , its isotope exponent , and with doping in La _2–x Sr _x CuO ₄ type underdoped system reflect the observed tendencies. ² Both and diminish with doping, the sign of is opposite to . A typical estimation gives || 0.2.     

Interlaminar Fracture Toughness of CF/PEI and GF/PEI Composites at Elevated Temperatures

An experimental study has been conducted to assess temperature effects on mode-I and mode-II interlaminar fracture toughness of carbon fibre/polyetherimide (CF/PEI) and glass fibre/polyetherimide (GF/PEI) thermoplastic composites. Mode-I double cantilever beam (DCB) and mode-II end notched flexure (ENF) tests were carried out in a temperature range from 25 to 130°C. For both composite systems, the initiation toughness, G _IC,ini and G _IIC,ini, of mode-I and mode-II interlaminar fracture decreased with an increase in temperature, while the propagation toughness, G _IC,prop and G _IIC,prop, displayed a reverse trend. Three main mechanisms were identified to contribute to the interlaminar fracture toughness, namely matrix deformation, fibre/matrix interfacial failure and fibre bridging during the delamination process. At delamination initiation, the weakened fibre/matrix interface at elevated temperatures plays an overriding role with the delamination growth initiating at the fibre/matrix interface, rather than from a blunt crack tip introduced by the insert film, leading to low values of G _IC,ini and G _IIC,ini. On the other hand, during delamination propagation, enhanced matrix deformation at elevated temperatures and fibre bridging promoted by weakened fibre/matrix interface result in greater G _IC,prop values. Meanwhile enhanced matrix toughness and ductility at elevated temperatures also increase the stability of mode-II crack growth.     

Upper critical and irreversibility fields in selectively doped YBa2Cu3O7

The electrical resistivity of (Y_1–xPr_x)Ba₂Cu₃O_7–gd and YBa₂(Cu_1–xZn_x)₃O_7– thin films and (Y_1–x. Tb_x)Ba₂Cu₃O_7– thin films and single crystals has been measured as a function of 0xx_crit, 2KT300K and OTH20T. The samples were oriented withc-axis parallel to applied fields. Upper critical field H_c2 and irreversibility field H_irr values have been determined from these measurements. Increased Tb doping appears to shift H_irr to higher temperatures. This coupled with observed twin peaks in magnetization measurements reflects an enhancement of flux pinning. Unlike Tb which does not appear to alterT _c , Pr and Zn doping of this system tends to depress bothT _c and the slope of the mean field normal phase-mixed phase boundary line (dH _c2/dT).     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

Effect of the LIII Absorption Edge of Uranium on Chemical Shifts of the Lβ1 Line of Uranium in UO2+x

The effect of intraatomic absorption of the L₁ X-ray emission line of uranium was studied. To eliminate the effect of the L _{I I I} absorption edge on the chemical shift () of the L₁ line, the dependence of L₁ on the oxygen index x in oxide systems of variable composition UO_{2 + x} was determined indirectly. It was shown that, in the absence of the effect of the L _{I I I} absorption edge, the dependence of L₁ on x is ordinary and, as in the case of other hard emission lines of the uranium L series, can be described by a second-order polynomial. The abnormal dependence of L₁ on x is explained.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Physicochemical Properties of R1 – xBaxMnO3 ± δ(R = Rare Earth) Solid Solutions

Nd_{1 – x} Ba _x MnO_{3 ±} (0.1 x 0.5) and R_0.7Ba_0.3MnO_{3 ±} (R = La, Pr, Sm, Eu) solid solutions were prepared from nitrate mixtures by solid-state reactions in air and were characterized by x-ray diffraction and thermogravimetry. The oxygen content of the solid solutions was determined by iodometric titration. The materials were found to have a nearly perfect oxygen stoichiometry ( 0). As shown by pH measurements, the solid solutions have a high water resistance (extent of water degradation no larger than 0.1%). The dissociation of the Nd_{1 – x} Ba _x MnO_{3 ±} (0.2 x 0.4) solid solutions was studied as a function of temperature and oxygen partial pressure (–10 log(Po ₂/Pa) 1.4) by a special TG technique.