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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.

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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.

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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     

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.     

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.     

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.     

The Possibility of Reproducing the Units of Complex Permittivity at High Frequencies

The results of theoretical investigations of the reproduction of the units of the components of complex permittivity and by a method based on the use of the wave properties of a coaxial line are presented. The errors in reproducing and are analyzed.     

Heat exchange in two-phase flow about a surface located in a rectangular channel

Similitude equations are obtained on the basis of the principle of superposition of separate effects to calculate heat exchange between surfaces with complexshaped cross sections located in a rectangular channel during their cooling by a two-phase flow.Notation T, q temperature and heat flux - T_w mean surface temperature - I, R current and electrical resistance - V volume of the material - , , anda heat-transfer coefficients, thermal conductivity, and linear expansion of the material - relative functions - =_m; ^* = _m ^{* *} _s ^* ; temperature factor - X relative weight content of liquid phase Indices w surface - f incoming flow - v volume - m two-phase flow - angle of attack - s shape of surface - * pertains to surface with swirl vanes Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 780–786, May, 1980.     

A method of joint determination of the effective coefficients of horizontal mixing of large particles and of external heat exchange in an organized fluidized bed

A method is proposed for the joint determination of the coefficients of horizontal particle diffusion and external heat exchange in a stagnant fluidized bed.Notation c_f, c_s, c_n specific heat capacities of gas, particles, and nozzle material, respectively, at constant pressure - D effective coefficient of particle diffusion horizontally (coefficient of horizontal thermal diffusivity of the bed) - d equivalent particle diameter - d_t tube diameter - H₀, H heights of bed at gas filtration velocities u₀ and u, respectively - H_a height of active section - l width of bed - L tube length - l _o width of heating chamber - N number of partition intervals - p=H/H₀ expansion of bed - s_n surface area of nozzle per unit volume of bed - S_h, S_v horizontal and vertical spacings between tubes - t_c, t₀, t_s, t_n, t_w initial temperature of heating chamber, entrance temperature of gas, particle temperature, nozzle temperature, and temperature of apparatus walls, respectively - u₀, u velocity of start of fluidization and gas filtration velocity - y horizontal coordinate - ^*, coefficient of external heat exchange between bed and walls of apparatus and nozzle - ₁, ₁, ₂, ... coefficients in (4) - thickness of tube wall - _b bubble concentration in bed - ₀ porosity of emulsion phase of bed - _n porosity of nozzle - =(t_s – t₀)/(t_c – t₀) dimensionless relative temperature of particles - _n coefficient of thermal conductivity of nozzle material - f, _s, _n densities of gas, particles, and nozzle material, respectively - _be=_s(1 – ₀) (1 – _b) average density of bed - time - _max time of onset of temperature maximum at a selected point of the bed - R =l _o/l Fourier number - Pe = ₁ l ²/D Péclet number - Bi = /_n Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 457–464, September, 1981.     

The dielectric constant in liquid and solid4He

We report precision measurements of the dielectric constant of liquid and solid ⁴ He at constant density as a function of temperature in the range0.1 K. For these measurements a capacitance bridge was used, the stability of which permitted a reproducibility of / 6×10^–9 in the dielectric constant. We find that the polarizabilityp, defined by the Clausius-Mosotti equation, is a weak function of temperature. This dependence onT at the low-temperature end diminishes as the density of ⁴ He is decreased to that at saturated vapor pressure. We also describe briefly attempts at measuring the change of at the superfluid transition in ⁴ He and during the melting process, all corrected to conditions of constant volume, and upper limits for these changes are given. Finally, we present measurements of in liquid ⁴ He at saturated vapor pressure between 0.15 and 1.3 K, from which we deduce the change in density. The results are compared with recent data obtained with a microwave cavity method and good agreement is found. Further comparisons are made with Van Degrift's results at 4 MHz and also with other recent data above 0.7 K.Research supported by a grant from the National Science Foundation.     

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.