Dielectric Dispersion in Yttrium and Erbium Formate Dihydrate Crystals

The dielectric properties of Y(HCOO)₃ · 2H₂O and Er(HCOO)₃ · 2H₂O are studied. The frequency dependences (0.01 Hz to 20 kHz) of the real () and imaginary () parts of dielectric permittivity ( = – i) are shown to follow a fractal scaling law for the dielectric response of solids. In the tan versus temperature curves, a number of maxima are revealed in a narrow temperature range. The experimental data are used to evaluate the activation energies of relaxation processes. The observed anomalies are assumed to be associated with changes in the dynamics of protons in hydrogen bonds.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of β-silicon nitride ceramic

Ultrasonic wave velocity measurements have been used to determine the elastic stiffness moduli and related elastic properties of high-purity, dense -Si₃N₄ ceramic samples as functions of temperature in the range 150–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Due to its covalently bonded, rigid structural framework -Si₃N₄ is an elastically stiff material; the elastic stiffness moduli of the ceramic at 295 K are: C _L = 396 GPa, = 119 GPa, B ^S = 238 GPa, E = 306 GPa, Poisson's ratio = 0.285. The longitudinal elastic stiffness C _L increases with decreasing temperature and shows a knee at about 235 K; the decrease in slope below the knee indicates mode softening. The shear elastic stiffness shows mode softening which results in a plateau centred at about 235 K and an anomalous decrease with further reduction in temperature. The hydrostatic-pressure derivatives of elastic stiffnesses at 295 K are (C _L/P) _P=0 = 4.5 ± 0.1, (B ^S/P) _P=0 = 4.3 ± 0.1 and (/P) _P=0 = 0.17 ± 0.02 (pressure < 0.12 GPa). An interesting feature of the nonlinear acoustic behaviour of this ceramic is that, in the pressure range above 0.12 GPa, the values obtained for (/P) _P=0 and the shear mode Grüneisen parameter (_S) are small and negative, indicating acoustic-mode softening under these higher pressures. Both the anomalous temperature and pressure dependences of the shear elastic stiffness indicate incipient lattice shear instability. The shear _S(=0.005) is much smaller than the longitudinal _L(=1.18) accounting for the thermal Grüneisen parameter ^th(=1.09): since the acoustic Debye temperature _D(=923 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic -Si₃N₄.     

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.     

The microstructure developments and electrical properties of calcium-modified barium titanate ceramics

The microstructure and electrical behaviour of calcium-modified BaTiO₃ ceramics of compositions (a) (Ba_1-x Ca _x )TiO₃, (b) Ba(Ti_1-x Ca _x )O_3-x and (c) (Ba_1-x/2Ca _x/2) (Ti_1-x/2Ca _x/2) O3_3-x/2 have been investigated. These characteristics are observed to vary systematically with the cationic ratio, = (Ba + Ca)/Ti, rather than the amount (x-value) and sites that Ca²⁺ ions are supposed to occupy. A large uniform grain microstructure and normal dielectric behaviour are obtained for 1.01 samples (groups I and II), whereas an ultra-fine grain microstructure and diffuse phase transformation (DPT) characteristics are observed for 1.08 samples (groups III). The latter is proposed to be the suppression of tetragonal to cubic transformation due to the formation of second phase. When the sintering atmosphere is changed from air to H₂/N₂ mixture, the electrical resistivity decreases and dielectric loss increases tremendously for = 0.99 samples (groups I), whereas the high electrical resistivity and low dielectric loss characteristics are preserved for 1.01 samples (groups II and III). The mechanism by which the cationic ratio improves the resistance of the materials to a reducing atmosphere is proposed to be the formation of hexagonal BaTiO_3- phase which consumes the oxygen vacancies generated.     

Effect of Grain Size on the Modulus of Elasticity and Strength of Synthetic Graphites

The effect of the grain size of the filler on the mechanical properties (compressive, bending, and tensile strength and modulus of elasticity) of synthetic graphite is analyzed using data for commercial structural graphites. As the mean particle size of the filler (_av) decreases from 3000 to 1 m, the modulus of elasticity increases, on the average, from 10 to 15 GPa, and the compressive, bending, and tensile strength increases by about one order of magnitude. The Griffith equation is used to evaluate the size of defects that initiate fracture (c _c) in different types of graphites. It is shown that the factors determining the critical defect size depend on the particle size of the filler. For _av > 150 m, c _c is comparable to _av or _max. In the range 30 < _av < 150 m, c _c is equal to or greater than _max. In graphites with _av < 30 m, c _c far exceeds _max and, presumably, corresponds to the particle size of the molding powder.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

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.     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

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.     

Dielectric Properties of Melt-Grown Cd1 – xZnxTe Crystals

The real (") and imaginary (") parts of the complex dielectric permittivity of Cd_{1 – x} Zn _x Te (x= 0.1–0.2) crystals are measured as a function of temperature and frequency. The "-vs.-temperature data show a maximum, and " rises rapidly at about the same temperature. This behavior is interpreted in terms of compositional fluctuations, structural defects, and the associated internal electric fields.     

Frequency-Dependent Bulk Viscosity in One- And Two-Component Near-Critical Fluids

We assume isomorphism between near-critical fluids and Ising spin systems to calculate the critical anomaly of transport coefficients. As an example we present a very simple and general expression for the frequency-dependent bulk viscosity *() in one- and two-component fluids near the critical point. It reads is a universal complex function, c is the zero-frequency sound velocity, c _c is its critical value, and is the order parameter relaxation rate. We also examine macroscopic adiabatic relaxations of pressure, temperature, and density after stepwise changes of pressure or density. Such measurements give information on the time correlation function of the diagonal part of the stress, which relaxes anomalously slowly near the critical point.     

Dielectric properties of chemically treated wood

Dielectric properties along the grain for absolutely dried untreated and seven kinds of chemically treated Sitka spruce (Picea sitchensis Carr.) woods were measured. Cole-Cole's circular arc law was applied to the results of the relaxation due to the motions of methylol groups. The following changes were caused by chemical treatments. In polyethylene glycol (PEG) impregnation, the distribution of relaxation times became very narrow, the generalized relaxation time (_m) was considerably decreased, and the relaxation magnitude (₀ – ) was slightly increased. In acetylation, the distribution of relaxation times became very broad, _m was considerably increased, and (₀ – ) was remarkably decreased. In propylene oxide treatment, the distribution of relaxation times became slightly narrow and _m was decreased. _m was slightly decreased in formalization, phenol-formaldehyde (PF) resin treatment and wood methyl methacrylate (MMA) composite. (₀ – ) was decreased in formalization and PF-resin treatment and was hardly changed in wood-MMA composite and heat treatment. The distribution of relaxation times was almost unchanged in formalization, PF-resin treatment, wood-MMA composite and heat treatment.     

Shear viscosity of the binary liquid mixture 3-methylpentane + nitroethane near the consolute point

Shear viscosity measurements of a mixture of 3-methylpentane and nitroethane at the critical concentration are presented in the temperature range 0.005 KT–T _c13.93 K, where T _c is the consolute or critical temperature. The data agree with earlier measurements.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Conditions for existence of exact solutions of the problem of a fusing wedge

A well-defined condition, determining the values of the aperture angles of a fusing wedge, is presented for exact solutions of the single-phase problem of a fusing wedge that were obtained earlier and are written for these values. The critical orientation of the fusing wedge to the axis of fusion when the written solution degenerates is indicated.Notation , , _n , _n , _n A ₁,A ₂,B auxiliary variables - P _n ,Q _n ,S _n ,T _n polynomials - k, m, n, i natural numbers - , _k angles between the normals to the surfaces forming the fusing wedge - z the axis in a Cartesian coordinate system - U temperature at points of the body infinitely remote from the fusing boundary Voronezh Institute of Technology, Voronezh, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 750–753, June, 1994.     

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.     

Thermodynamic properties of iron doped beta″-alumina by e.m.f. measurements with beta-alumina electrolytes

Thermodynamic studies of the non-stoichiometric iron doped beta-alumina (ID) phase were carried out by electrochemical measurements coupled with coulometric titration using the cell Na_liq/Li-alumina/ID. Hot pressing and glass sealing techniques were developed and employed to obtain a suitable and stable Li-alumina/ID interface. The equilibrium e.m.f. of the cell was determined as a function of sodium concentration over the temperature range 444 to 523 K. The range of sodium concentrations over which the ID phase is stable was also determined. The relative partial molar thermodynamic quantities of sodium, , , and in ID alumina as a function of sodium concentration were obtained from cell e.m.f. data.     

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.