On the resonance of acoustic waves in slightly deformed and slowly moving slabs

The stability is studied of acoustic waves generated by a time harmonic force in slabs described by: 0z1±g(x, y). By using a recently developed method, the exact solution of the Dirichlet problem is found for =0. It is shown that the solution is unstable against values of the frequency: =n,n. This is in agreement with the result already known in the literature, but found by other means. In a slightly deformed slab, 0<1, it is shown that stabilization of the resonant wave occurs at a time of order ^–. This is valid if the upper boundary is a concave surface. In case of a slab with slowly moving upper boundary, only the growth rate of the amplitude of the resonant wave is reduced. This holds for a non-oscillating motion of the upper boundary. In the case of an oscillating motion a further resonance is produced.     

The dielectric properties of glass-ceramic-on-metal substrates for microelectronics packaging

The dielectric properties of some glass-ceramic-on-metal substrates have been determined over the frequency range 500 Hz to 5 MHz using a.c. bridge techniques. The substrates consisted of cordierite-based glass-ceramics screen printed on molybdenum. For glass layers of thickness greater than 100 m both the permittivity, and the dielectric loss, , are frequency independent over this frequency range at room temperature giving the value of =6.5 and tan =8×10^–3; the room-temperature data are consistent with the universal law of dielectric response. The variation of permittivity with temperature has also been examined and, below 120 °C, the temperature coefficient [(–1) (+2)]^–1 (/T)_p, was found to be 1.3×10^–5 K^–1. The results are compared with those previously reported for Al₂O₃ and AIN substrates.     

A Method for Calculating Thermal Radiation Properties of Multilayer Films from Optical Constants

A calculation method for the incident angle dependence of the solar absorptance _S and the temperature dependence of the total hemispherical emittance _H of multilayer films is proposed. The method is based on calculation of _S and _H from optical constants in the wavelength region from 0.25 to 100 m for thin polymer films and deposited metal. In this paper we provide values of _S in the incident angle region from 0 to 90° and _H in the temperature range from 173.15 to 373.15 K for two-layer samples of aluminum-deposited polyimide film. The results obtained for _S and _H by the present method are compared with experimental results measured by both spectroscopic and calorimetric methods. The calculated results of _S and _H agree well with the experimental results.     

A model with length scales for composites with periodic structure. Steady state heat conduction problem

A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with Y-periodic coefficients (Y is a cube) is replaced with a vectorial elliptic problem of constant coefficients. The unknown fields are: the averaged distribution of temperature and the vector field which stands for perturbation of the temperature within the cells of periodicity. The recovery of temperature in the original composite is given by the approximation: 0(x)=0(x) +h ^a (x/) _a (x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for satisfies the boundary condition.     

Effects of Bonding Configuration and Structural Perfection on the Properties of Doped NaNbO -Based Solid Solutions

The effects of bonding configuration (electronegativity) and doping-produced vacancies on the properties of doped NaNbO₃-based solid solutions were studied. The results demonstrate that there is an average electronegativity of the elements involved above which the uniform distortion parameter increases and the relative dielectric permittivity ^T ₃₃/₀decreases with increasing electronegativity, as is common in other solid-solution systems. Below this value, both and ^T ₃₃/₀vary in the opposite way. An explanation for the anomalous behavior of is proposed.     

Dielectric properties of chemically vapour-deposited Si3N4

The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si₃N₄ were measured in the temperature range from room temperature to 800° C. The a.c. conductivity ( _a.c.) of the amorphous CVD-Si₃N₄ was found to be less than that of the crystalline CVD-Si₃N₄ below 500° C, but became greater than that of the crystalline CVD-Si₃N₄ over 500° C due to the contribution of d.c. conductivity ( _d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si₃N₄ are smaller than those of the crystalline CVD-Si₃N₄ in all of the temperature and frequency ranges examined. The relationships of ^n-1, (- ) ^n-1 and/(- ) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si₃N₄ were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si₃N₄ was smaller than that of the crystalline CVD-Si₃N₄.     

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.     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

---

Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

---

Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

Aligned microstructure of some particulate polymer composites obtained with an electric field

Alignment by an electric field was obtained for a variety of particles dispersed in photopolymerizable fluids. The particle shapes studied were irregular, spherical, rhombohedral, rod-like (fibres), and platelet. The sizes ranged from sub-micrometres to tens of micrometres, and the dielectric constants of the particles varied from less than that of the lquid matrix to very much greater than that of the matrix. Polymerization or hardening of the matrix was possible at room temperature, required only a few seconds, and the aligned structures obtained were able to be examined by both light and scanning electron microscopy after fracture or sectioning. Nominally equiaxed particles, containing a statistical proportion of non-equiaxed particles, could be completely aligned at 48 vol% concentration in a fluid having a viscosity of about 2.5 Pa s, but at 57 vol%, the mixture behaved as a paste, and only particle rotation and local rearrangements were possible. The rate of alignment seemed to depend generally on the magnitude of 1(a)2, where 1 is the relative dielectric constant of the liquid resin, a is the particle radius, and is the particle dipole coefficient given by (2–1)/(2+21), where 2 is the relative dielectric constant of the particles. 1(a)2 emphasizes the importance of particle size and the relative unimportance of the particle dielectric constant for alignment, except when 21. Platelets were more rapidly aligned than fibres.     

Study of the paramagnetic-antiferromagnetic transition and the γ → ε martensitic transformation in Fe-Mn alloys

The paramagnetic-antiferromagnetic transition and the martensitic transformation of Fe-Mn (Mn 15–32 wt%) alloys have been investigated by resistivity, dilatometry and X-ray diffraction (XRD). The results show that paramagnetic-antiferromagnetic transition increases the resistivity and the volume of alloys, whereas the martensitic transformation reduces the resistivity and volume of alloys. The A _f that was determined by the dilatometric method is not the temperature that martensites in the Fe-Mn alloys have reverse transformed to austenites completely. Mn additions reduce M _s, increase T _N and the lattice parameter of austenite in the Fe-Mn alloys. Both the antiferromagnetic transition and the martensitic transformation lead to an increase in the lattice parameter of austenite. The lattice parameters both above T _N and below T _N decrease linearly with temperature. The lattice parameter below M _s increases first and then decreases. Moreover, the (110) and (002) atomic planes in the Fe-15Mn-0.15C alloy are separated into two peaks: 2 for (002) is 44.16°, 2 for (110) is 44.47°.     

The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.     

The dielectric properties of alumina substrates for microelectronic packaging

The dielectric characterization of alumina substrate materials used in high-performance microelectronic packaging is described. These materials included both pure and impure polycrystalline substrates and, as a reference standard, pure and chromium-doped single crystals of alumina. For each material the permittivity () and dielectric loss () has been measured over a frequency range of 0.5 kHz to 10 MHz, at room temperature, and correlated with the structure and composition as determined by supplementary techniques. At room temperature the pure substrates show the frequency independence of both and , characteristic of pure single-crystal material. The permittivity (= 10.1) agrees closely with the average of the anisotropic values for the single crystal but the dielectric loss is an order of magnitude higher than in the single crystal, giving tan 1.5 × 10^–3. The impure substrates compared with the pure, show a small increase in and a marked, frequency-dependent increase in dielectric loss. Measurements have also been made in both the high- and low-temperature ranges (i.e. 20 to 600 ° C and 77 to 293 K, respectively) in order to establish the variation of permittivity with temperature and frequency. At temperatures below 200 °C the temperature coefficient of permittivity, [( –1)( + 2)]^–1 (/T) _p is about 9 × 10^–6 K^–1 for the pure materials but this increases rapidly with impurity addition.     

The role of ε-martensite in the impact toughness of an Fe-17Mn alloy

The influence of -martensite on the cryogenic toughness of an Fe-17 wt% Mn alloy was studied in this work. Alloys were tempered at various temperatures in order to systematically increase the volume fraction of -martensite. This was followed by Charpy impact testing conducted at room temperature and at–196°C. The experimental results indicated that although room-temperature toughness was not influenced by the -martensite content, the cryogenic toughness was strongly dependent on the volume fraction of -martensite. In particular, with the exception of the alloys tempered at 400 and 450°C, the impact toughness consistently increased with -martensite content. Microstructural and fractographic evaluations using SEM and TEM suggested that the toughness improvements were attributed to the stress-induced martensite transformation. No microstructural evidence was found which could be ascribed to an effect of -martensite on the low-temperature embrittlement exhibited by Fe-Mn alloys tempered at 400–450°C.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Effect of Gamma Irradiation on the Piezoelectric Properties of K2Sr4Nb10O30–K6Li4Nb10O30 Solid Solutions

The effect of gamma irradiation on the dielectric ( ₃₃/₀, tan) and piezoelectric (d ₃₁, g ₃₁, K _p, Q _m) properties of ₂Sr₄Nb₁₀O₃₀–K₆Li₄Nb₁₀O₃₀ solid solutions (tetragonal tungsten bronze structure) was studied as a function of K₆Li₄Nb₁₀O₃₀ content. The results demonstrate that increasing the gamma dose to 9 × 10⁵ Gy reduces ₃₃/₀ and tan. With increasing Li⁺ content (filling of triangular channels), d ₃₁, g ₃₁, K _p, and Q _m increase. The results are interpreted in terms of the generation of stable defects and effective redistribution of the energy of gamma radiation over the ceramic sample.     

A study of the Bailey-Orowan equation of creep

A new method was developed to study the Bailey-Orowan equation of creep, _c=r/h, where _c is the creep rate,r is the recovery rate andh is the work-hardening coefficient. The method was to vary the strain rate,, around the creep rate, _c, and to measure the corresponding stress rate,. In a plot of stress rate against strain rate, a straight line was obtained. The slope of the straight line was equal toh, and the intersection of the straight line with the stress axis was equal to –r, as in the equation=–r+h. The creep test under a constant stress is a special case of this equation when the stress rate,, is zero. The above measurement was carried out within a very small stress variation, less than 1% of the total stress, so that the values ofr andh were not disturbed. The creep test was performed on Type 316 stainless steel. The creep rate was shown to be equal to the ratior/h, but the value ofh was approximately equal to Young's modulus at the testing temperature, rather than, as is commonly believed, to the work-hardening coefficient.     

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.     

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.     

Two phonon pair breaking in superfluid3He-B

We report on pulsed zero sound experiments in the B-phase of ³ He down to 0.6 mK. The investigated pressure and frequency range was 5 to 16 bar and 10 to 70 MHz, respectively. The dissipated energy during the sound pulses was between 0.4 to 90 nJ. The resolution in damping was about 0.1 cm ^–1 . Within the range of our experimental parameters we never observed two phonon absorption resulting from non-linear coupling of zero sound to the J =2⁺ mode. However, with pulses of single frequency a new peak structure was found at temperatures corresponding to (T) = . This behavior is attributed to pair breaking by two phonons of the same energy. The attenuation increased with increasing pulse power, but also depended on pulse duration. In addition to that, we found at all pressures and frequencies an unreproducible attenuation structure close to the position of the J=2⁺ mode.