Dielectric properties of (Ba,Sr)O-(Sm,La)2O3-TiO2 ceramics at microwave frequencies

The dielectric properties of (Ba, Sr)O-(Sm, La)₂O₃-TiO₂ material at microwave frequencies were investigated. By varying the amount of strontium from 0–25 mol% in the 0.15(Ba_1–x Sr _x )O-0.15Sm₂O₃-0.7TiO₂ composition, it was possible to adjust the frequency temperature coefficient, _f, from –13 p.p.m. °C^–1 to + 30 p.p.m. °C^–1. When 7 mol% Sr was substituted for barium, _f=0 p.p.m. °C^–1 was obtained. TiO₂ with rutile phase (_f400 p.p.m. °C^–1) acted as a dominant element in _f variation of the 0.15(Ba_1–x Sr _x )O-0.15(Sm_1–y La _y )₂O₃-0.7TiO₂ (0x0.25, 0y0.6) system. Additionally, increasing the quantity of lanthanum substitution for samarium had a greater positive effect on _f than strontium substitution for barium. When 60 mol% La was substituted for samarium with 7mol% Sr substitution barium, _f of the system reached 95 p.p.m. °C^–1. The effect on microwave dielectric characteristics of the 0.15(Ba_0.93Sr_0.07)O-0.15Sm₂O₃-0.7TiO₂ (BSST) ceramics by varying the calcination and/or sintering conditions or doping additives, were studied. The added SnO₂ acted as a firing agent to lower the sintering temperature, and the dielectricQ(Q _d) value was improved by properly adding CdO. With 1 wt% CdO addition, the highestQ _d value of the BSST resonator, after calcination at 1100 °C/2 h and sintering at 1370 °C/4 h, reached 4180 at 4 GHz with a small _f of –4 p.p.m. °C^–1 and an _r of 80.7 was obtained.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

Dynamic Measurements of Thermal Transport Coefficients and Boundary Resistance. II.Model for 3He-Superfluid 4He Mixtures

This is the second of a three-part study of the ac response of liquid helium. We derive the temperature response function, T(), of a ³ He-superfluid ⁴ He mixture from the equations of superfluid hydrodynamics in the presence of two interfacial boundary resistances,R_b.Specifically, we consider the response T(), across a fluid layer of thickness,d, to an ac heat flux,Q(t) = Q_o exp(it).T() depends on the effective thermal conductivity, _eff , Griffin's diffusion coefficient, _o (i.e. the thermal diffusivity of ³ He impurities, D_iso in the low ³ He concentration limit) and the thermal boundary resistance, 2R_b. This analysis provides the basis for experiments to determine these parameters. Although past experiments to measure these properties have been carried out using dc and transient techniques, an ac technique offers significant noise reduction over these techniques. By sweeping the frequency, it is possible for an experimenter to clearly identify different components of the system response to the heat flux. For instance, if t is the slowest fluid thermal response time, conventional Kapitza boundary effects dominate at frequencies, 1. These calculations reveal an interesting analogy to the Piston Effect for near-critical classical fluids. In Part I of this work, we used normal liquid ⁴ He as a testing ground for developing models of ac heat transport. In Part III of this work, we will present results in which we apply this technique to measurements on dilute mixtures of ³ He in superfluid ⁴ He.     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

On a nonlinear stefan problem arising in the continuous casting of steel

Summary The continuous casting process employed in the steel industry is a many faceted big industrial problem which has given rise to many sub-problems. Here, we examine the problem involving the determination of the solid-liquid steel interface and we develop and extend a previously proposed model, which incorporates heat transfer through two layers of solid and liquid mould powder and the interface between the solid powder and the mould wall. The problem simplifies to the classical Stefan problem except that the condition on the boundary is nonlinear. Integral formulation procedures are used to establish the normalized pseudo steady state temperature as an upper bound to the normalized actual temperature. The pseudo steady state approximation yields an upper bound on the interface position, which an independent numerical enthalpy scheme confirms to be an extremely accurate approximation for the parameter values occurring in practice. The present work is important since it provides a simple method for the prediction of the solid-liquid steel interface and a bounding procedure which can be used to validate other estimates.List of symbols D flux thickness atz ^*=0 - H enthalpy - L latent heat of steel - M the half thickness of the cast steel - Q heat flux - R interface thermal contact resistance - S _m ^* melting temperature of steel - T ^* temperature - T normalized temperature - T _m ^* melting temperature of mould powder - T ^* temperature of cooling water - T _w ^* temperature on mould wall - T _u ^* temperature of solid flux on its interface with mould wall - T ₀ ^* temperature on casting surfaceT ^*(0,z ^*) - U casting speed - X ^*(z ^*) physical coordinate of the steel phase change boundary - X(z) non-dimensional coordinate of the steel phase change boundary - c specific heat of steel - h(z ^*) thickness of liquid flux layer - k thermal conductivity of steel - ks thermal conductivity of solid flux layer - k _l thermal conductivity of liquid flux layer - m surface heat transfer coefficient - s(z ^*) thickness of solid flux layer - t time - , , positive constants given by (3.2) - constant given by (3.5) - coefficient of linear thermal expansion of steel - angle shown in Figure 2 - positive constant defined by (M-D)/2 - (z) positive parameter - (z ^*) amount of contraction of steel - density - (z) positive parameter used in (5.7) and (5.8)     

Surface nucleation and cellular growth kinetics of cordierite glass ceramics containing 3 mol % Y2O3-ZrO2

Cordierite-based glass ceramics of the 2MgO2Al₂O₃5SiO₂ composition with t-ZrO₂ (3 mol% Y₂O₃-ZrO₂) and P₂O₅ addition, was heat-treated isothermally and isochronically for crystallization studies. Major crystalline phases incurred by the heat treatment were t-ZrO₂ and -cordierite. Surface nucleation predominated when edge and corner nucleation in these samples were suppressed regardless of their radii of curvature. Crystallization began with the formation of -quartz S.S. and its transformation to -cordierite was followed by prolonged heating. Cellular growth of -cordierite on the surface of the quenched glass plates, gave a linear kinetics. The activation energy for cellular growth was 410 kJ mol^–1.     

Nonmonotonic Temperature Dependence of the Thermal Hall Angle of a YBa2Cu3O6.95 Single Crystal

We have performed high-resolution measurements of the magnetic field (0 TB9 T) and temperature (10 KT<140 K) dependence of the longitudinal and transverse Hall thermal conductivity of a twinned YBa₂Cu₃O_6.95 single crystal. We have used and compared two recently published methods to extract the thermal Hall angle _H(T, B). Our results indicate that cot(_H) varies quite accurately as T⁴ in the intermediate temperature range 0.3c. It shows a well defined minimum at T_m20 K which resembles that observed in the c-axis microwave conductivity. The electronic part of the longitudinal and the transverse thermal conductivity show the scaling behavior for transport properties predicted for d-wave superconductors in the temperature range 18 KT30 K.     

A study of mechanical configuration optimisation in micro-systems

This paper shows that there are three main categories of factors that make the optimum mechanical design of micro-systems different from macro-systems: scale effects, a limited range of materials, and a limited range of production processes. The combined effect of these factors can make the optimum configuration of a micro-system potentially very different from that of the same system on a macro-scale. In particular, the use of flexible elements for hinges is much more feasible and desirable on a micro-scale.Notation a acceleration (m/s²) - A cross-sectional area (m²) - B magnetic flux [wb/m²] - b width [m] - C constant - d depth [m] - D drag [N] - E Young's modulus [N/m²] - E*= - f resonant frequency [Hz] - F _D drive force [N] - F _E electrostatic pulling force [N] - F emmisivity function - F _G geometric view factor - g gravitational constant [m/s²] - h _c convention heat transfer coefficient [W/m²K] - h height [m] - i current [A] - I _A second moment of area [m⁴] - I _I moment of inertia [kg m²] - J polar second moment of area [m⁴] - k stiffness [N/m] - K thermal conductivity [W/m K] - l length [m] - m mass [kg] - M moment [N m] - P load [N] - P _H Hertz contact pressure [N/m²] - P _C cylinder pressure [N/m²] - q heat transfer rate [W] - R, r radius [m] - Re Reynolds number - T, t temperature [K] - T _A atomic friction torque [N m] - T _D drive torque [N m] - T _F Coulomb friction torque [N m] - T _I inertial resistive torque [N m] - u velocity [m/s] - mean velocity [m/s] - V volume [m³] - V _e voltage [V] - x distance between electrodes [m] - y maximum distance to neutral axis [m] - angular acceleration [rad/s²] - _d thermal diffusivity [1/K] - rolling friction factor - P pressure difference [N/m²] - ₀ dialectric constant [F/m] - strain - dynamic viscosity [Pa s] - scale factor - _S coefficient of sliding friction - _R coefficient of rolling friction - _{1, 2} Poisson's ratio - density (kg/m³) - temperature rise [°C] - _B bending stress [N/m²] - _y yield strength [N/m²] - shear stress [N/m²] - reliability constant     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

Zero-point motion and superfluid helium

We propose that He II exhibits macroscopic [ _P /N O(1)] quantum zero-point motion in momentum space, i.e., that a nonzero root-mean-square superfluid velocity exists even in an equilibrium superfluid system at rest. At absolute zero, using coherent states, we relate the uncertainty _P /N in the total momentumP (per particle) to the long-range-order (LRO) part of the phase gradient correlation function, which is proposed as an order parameter. The local equilibrium equation for the superfluid velocity potential derived by Biswas and Rama Rao yields, in the strict equilibrium limit, the equation determining this order parameter in terms of fluctuation correlations that remain to be determined. The order parameter is interaction dependent, nonzero atT=0 if (0)–₀V₀>0, and can vanish at some transition temperatureT when fluctuation terms become comparable to theT=0 value. (HereV _{0 0}, and (0) are the uniform parts of the potential, density, and chemical potential with shifted zero of energy, respectively.) A characteristic length (T), diverging atT=T , appears naturally, with its defining relation reducing to a macroscopic uncertainty relation ( _P /N)(0)=/2 atT=0. With certain assumptions it is shown that atT=0, LRO in the phase gradient correlation function is incompatible with off-diagonal long-range order (ODLRO) in the (r)(r) correlation function, and with nonzero condensate function.     

Experimental confirmation of the isotopic volume effect in superconducting molybdenum by means of energy-dispersive x-ray diffration at low temperatures

Differences in the lattice constants of Mo-100 and Mo-92 have been measured by x-ray diffraction, in order to search directly for the volume effect of isotopes in a superconductor. No significant difference in the lattice constanta(Mo-100)–a(Mo-92) could be detected at 290 K, while the differences –0.0014±0.0008 and –0.0029±0.0009 Å were detected at 85.3 and 4.31 K, respectively. These values, and their temperature dependence, are considered to be theoretically reasonable. The exponent in the isotope effect defined by T_cM^- is represented thermodynamically by =–( lnT _c / lnM)–( lnT _c / lnV)(d lnV/d lnM). From the results, d lnV/d lnM is found to be –0.033±0.009 at 4.31 K. Then, the second term representing the isotopic volume effect is estimated to be about 0.09, with lnT _c / lnV2.81. The observed value of is 0.33, so that the contribution of the second term, 0.09, is 27% of the value of . It becomes quite clear that the isotopic volume effect in superconducting Mo should not be neglected.     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

Kinetic interpretation ofα- andβ-Si3N4 formation from oxide-free high-purity silicon powder

A kinetic analysis of the isothermal nitridation of high-purity oxide-free silicon powder is described. The kinetic analysis suggests that the and polymorphs of Si₃N₄ are formed by separate and parallel reaction paths. This analysis provides for the decoupling and quantitative kinetic interpretation of- and-Si₃N₄ formation reactions. Consistent with existing microstructural and thermodynamic evidence, the-forming reaction is shown to obey a first-order rate law, whereas a phase-boundary controlled rate law describes the-forming reaction. A kinetic model employing these rate laws is developed and is used to predict the/ phase ratio as a function of isothermal reaction temperature and extent of reaction. The/ phase ratios so obtained are shown to be in good agreement with experimental observations made under a variety of reaction conditions.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Thermal expansion of bitumen-mineral compositions

The article presents the results of investigations of the thermal expansion of bitumen-mineral compositions and their components of different origin, carried out with newly developed dilatometers.Notation P_c index of the property of the composition - P_m, P_n, P_i indices of the properties of the components of the composition - V_m, V_n, V_i volumes of the components of the compositions - V_c volume of the composition - V_f volume of the filler - V_b volume of the bituminous binder - V_p volume of pores - _c, _f, _b thermal coefficients of volume expansion of composition, filler, and bituminous binder - K_b, K_f volumetric moduli of elasticity of bituminous binder and filler - G_b shear modulus of bituminous binder - T _g ^b , T _g ^c glass-transition temperatures of bituminous binder and composition - T ₁ ^b , T_2/b temperatures of beginning and end of the glass transition of bitumen - T ₁ ^c , T ₂ ^c temperatures of beginning and end of the glass transition of composition - T _F ^c fluidity temperature of the composition - _f, _b linear thermal expansion coefficients of filler and bituminous binder - _1e, _2e, _3e linear thermal expansion coefficients of composition at temperatures above T _F ^c , in the interval T _F ^c -T _g ^c , and below T _g ^c , respectively, found experimentally - _1t ^M , _2t ^M , _3t ^M the same, found theoretically by the equation for a mixture - _1t ^c , _2t ^c , _3t ^c the same, found theoretically by Kerner's equation - k₂, k₃ coefficients taking into account the effect of the filler surface on the thermal expansion of the bituminous binder in the temperature interval T_F/c-T_g/c and below T _g ^c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 886–893, November, 1979.     

Absorption Spectrum of ZnO Precipitates in ZnSe

The absorption spectrum of ZnO precipitates in ZnSe saturated with oxygen is studied in the spectral range 500–2000 cm^–1 and is shown to correlate with the transmission spectrum of single-crystal ZnO. Saturation of ZnSe with oxygen in the course of growth leads to ZnO precipitation during cooling. The precipitates give rise to narrow absorption bands in the range 5.8–7.1 m, which correlate with the components of the multiphonon absorption spectrum of ZnO, formed by combinations of LO and TO phonons. The 2LO mode defines the long-wavelength transmission edge of ZnO. In addition, the spectrum shows strong absorptions due to the LO + TO(10.2 m) and 2TO (11.3 and 12.7 m) modes. The possible role of SeO₂ is discussed. It is suggested that ZnO with a high carrier concentration may act as a gray filter in the spectral range 2–9 m.     

Equation of state of a3He-4He mixture near its liquid-vapor critical point

Measurements of the pressure coefficient (P/T)_,x are reported for a ³ He- ⁴ He mixture with a mole fractionX=0.805 of ³ He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval–0.50.5 and over the temperature range–0.1 t0.1, where =(– _c )/ _c andt=(T-T _c )/T _c ,with _c andT _c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (P/T)_,x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT _c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT _c closer than1 mK, (P/T)_,x along the critical isochore appears to be discontinuous atT _c ,while for the isochore / _c 0.92, (P/T)_,x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (P/T)_,x from the scaling equation of state proposed by Leung and Griffiths for ³ He- ⁴ He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (P/T)_,x along the critical isochore show excellent agreement with theory.Work supported by a grant from the National Science Foundation. A report of this work has been presented at the Washington Meeting of the APS [Bull. Am. Phys. Soc. 20, 618 (1975)].     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

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.     

Structure and Magnetism of the Composite Crystal Ca0.824CuO2

We have studied the magnetic state from a viewpoint of crystallographic features of the 1-D chain compound Ca_0.824CuO₂. A possible spin-hole arrangement in the magnetically coexisting state was determined by analyzing the local structural distortion in the CuO₂ chain by means of a modulated-crystal-structure analysis. The essential periodic sequence expected is (: up- and down-spin, : hole), which can be regarded as a kind of spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain.