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.     

Microwave surface resistance of epitaxial YBa2Cu3O7 thin films at 18.7 GHz measured by a dielectric resonator technique

We used a dielectric resonator technique for highly sensitive measurements of the temperature dependence of the microwave surface resistanceR _s of 1×1 cm² superconducting films at 18.7 GHz. It consists of a sapphire disc positioned on the film under investigation within a copper cavity which is acting as a radiation shield. In the TE₀₁ oscillation mode the highly reproducible quality factor of about 10⁵ results in a sensitivity of ±50 forR _s measurements. The temperature dependence ofR _s can be measured up to values as high as 1 . We have investigated several YBa₂Cu₃O₇ thin films prepared by high oxygen pressure d.c. sputtering on LaAlO₃ and NdGaO₃. Our best films exhibit a pronounced nonlinear behavior of the d.c. resistivity(T) with(300K)/(100K) values of about 3.7. Those films show, besides the initial fall-off just belowT _c , a further strong decrease ofR _s at low temperatures. This was observed both at 18.7 GHz and 87 GHz, as measured by a conventional cavity end plate replacement technique. ForTT_c/2 these films exhibit an exp (–T _c/T) dependence ofR _s with-values around 0.4. These observations may be explained by a superconducting energy gap with 2/kT _c0.8 for charge carriers localized in the CuO chains for YBa₂Cu₃O₇.     

A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials

Summary The problem of heat conduction of thermoelastic cylindrical medium composed of two different materials is considered. The problem is solved in the framework of the generalized thermoelasticity theory with one relaxation time. The solution is obtained in the Laplace transform domain using the potential function approach. Numerical inversion formula is used to obtain the corresponding solutions in the physical domain.Notation T _i absolute temperature - _irr radial component of the stress tensor - _i transverse component of the stress tensor - _izz axial component of the stress tensor - u radial component of displacement vector - _i density - k _i thermal conductivity - t time - _i , _i Lamè's constants - _i coefficient of linear thermal expansion - c _i specific heat for constant strain - _i = (3 _i +2 _i ) _i T ₀ reference temperature chosen such that |(T-T ₀)/T ₀|1 - _i relaxation time - r, ,z cylindrical coordinates - r ₁,r ₂ nondimensional inner and outer radii respectively - f ₁(t),f ₂(t) inner and outer surrounding temperatures - q _i heat flux where - i=1, 2 for inner and outer media, respectively With 5 Figures     

ΔK ol level effects on fatigue crack propagation

In order to determine the effects of K _ol level on fatigue life, a single peak load was applied at distinct K levels of 7.8×10.3 and 9.8×10³ p.s.i. in^1/2. Here the K _ol level was defined to be a K level at which overload was applied. Three different overload ratios of 1.5, 2.0, and 2.5 were used to determine the overload ratio effect on the recovery factor. The result showed that the recovery factor, Z, was linearly related to K as Z = qK+Z _o, where q was a function of overload ratio. The value of q decreased as the overload ratio increased in a given K _ol level and seemed to be an important factor as well as retardation cycles in determining the fatigue life. For the same overload ratio, specimens that underwent overload at a smaller K _ol level showed more improved fatigue life.Nomenclature a Crack length - a ^* Overload affected zone size - B Specimen thickness - (da/dN)_ca Crack growth rate due to constant amplitude fatigue load - (da/dN)_ol Crack growth rate after overload is applied - E Young's modulus - K Stress intensity factor - K _min Minimum stress intensity factor - K _max Maximum stress intensity factor - K _ol K level at which overload is applied - N Number of cycles - N _D Number of delayed cycles - N _f Number of cycles needed for a specimen to be completely fractured - r _p Assumed plastic zone size - S Load - _ys Yield stress - W Width - Z Recovery factor     

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.     

Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Specific heat measurements of intercalation compounds M x TiS2 (M=3d transition metals) using ac calorimetry technique

Specific heats of 3d transition metal intercalates of 1T-CdI₂-type TiS₂, M _x TiS₂ (M=V, Cr, Mn, Fe, Co, and Ni; 0x1), have been measured in the temperature range 1.6–300 K using an ac calorimetry technique. The electronic specific heat coefficient (2–100 mJ/mole K²) and the Debye temperature _D (240–430 K) are found to depend on the guest 3d metals and their concentrations. All the intercalates show anomalous specific heat at low temperatures following an – lnT dependence ( and are constants), as found in dilute alloys.     

Simultaneous ac Susceptibility and Specific Heat Measurements of YBCO Ceramics

Simultaneous ac magnetic susceptibility and specific heat studies of YBCO ceramics permitted the correct correlation of the corresponding critical temperatures. The midpoint of the real component () and the maximum of the imaginary component () of ac susceptibility curves confirmed the T _c = 92 K critical temperature value determined by dc resistance measurements. The specific heat maximum's temperature (T _cc 93.6 K)—-taken as the calorimetric critical one—fell between T _c and T* (the pseudogap onset temperature). We suggest that T _cc signals the appearance of the first localized coherent pairs, while the temperature T _c marks their percolation. The existence of two different critical temperature values confirms the coexistence of partial coherent and coherent electron pairing phenomena in the region below T _cc of the superconducting phase diagram.     

Precipitate strengthening mechanisms in magnesium zinc alloy single crystals

The mechanical behaviour of Mg-5.1 wt % Zn alloy single crystals was studied in the 4.2 to 300° K temperature range. Quenched crystals have activation energies and volumes best associated with the cutting of small clusters of Zn atoms by dislocations. Fully hardened crystals contain fine ₁ and occasional ₂ precipitates with an average ₁ interparticle spacing of 330 to 660 Å. Strengthening in these crystals is mainly ascribed to the cutting of ₁ particles by dislocations. In the overaged condition ₁, ₂ and equilibrium particles are present and lead to a considerable temperature-dependence unusual for an overaged condition. Analysis of this temperature-dependence suggests that below 77° K the relatively easy cutting of ₁ particles by dislocations takes place in addition to the cutting of ₂ and particles. Above 77° K the difficult cutting of ₂ and particles alone controls the deformation, ₁ being more easily cut with the aid of thermal fluctuations.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

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 critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

A simple model to explain the geometry dependence of J−Δa-curves

Very different patterns of geometry effects may occur if in a bend type specimen the ligament length is increased at constant specimen thickness. These geometry effects can be explained by a model of the total crack growth resistance R which is defined as the sum of the non-reversible energy which must be put into a body to produce an increment of crack area. The relationship between R and the commonly used J–a-curves is worked out. The model shows that a wider-lower pattern, i.e. the case where an increase of the ligament length causes a flatter J–a-curve, appears for fracture under lefm conditions or for contained yielding where R is independent of the geometry. A wider-no effect or a wider-higher pattern may be observed if the crack extension occurs at the plastic limit load and if either plane strain or plane stress conditions prevail.     

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.     

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.     

Singular Band Behavior of the Extended Emery Model for the Superconducting Cuprates

Mean field slave-boson approximation is performed on the extended Emery model for the CuO₂ conducting plane. The model is parameterized by Cu–O charge transfer energy _pd , copper–oxygen overlap t ₀, oxygen–oxygen overlap t', and Coulomb interaction U on the copper site taken as infinite. Special emphasis is placed on the role of t in the renormalization trends of the effective band parameters _pf and t, replacing _pd and t ₀, at small doping . It is shown that small, negative t expands the range of stability of the metallic phase, changing, in the second order of the perturbation theory, the nature of the metal–insulator transition point. In the nonperturbative limit, t modifies strongly the renormalization of _pf , making it saturate at the value of 4t. Finite doping suppresses the insulating state approximately symmetrically with respect to its sign. The regime _pf 4t fits very well the ARPES spectra of Y123, Bi2212, and LSCO and also explans, in the latter case, the evolution of the FS with doping accompanied by the spectral weight-transfer from the oxygen to the resonant band.     

Tangent modulus tensor in plasticity under finite strain

Summary The tangent modulus tensor, denoted as , plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for have been derived in Refs. [1]–[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux are addressed. Associated and non-associated models are accommodated, as is plastic incompressibility. A constitutive inequality with uniqueness implications is formulated which extends the condition for stability in the small to finite strain. Modifications of are presented which accommodate kinematic hardening. As an illustration, is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.Notation B strain displacement matrix - C=F ^T F Green strain tensor - compliance matrix - D=(L+L ^T )/2 deformation rate tensor - D fourth order tangent modulus tensor - tangent modulus tensor (second order) - d VEC(D) - e VEC() - E Eulerian pseudostrain - F, F _e ,F _p Helmholtz free energy - F=x/X deformation gradient tensor - f consistent force vector - residual function - G strain displacement matrix - h history vector - h time interval - H function arising in tangent modulus tensor - I, I ₉ identity tensor - i VEC(I) - k ₀,k ₁ parameters of yield function - K _g geometric stiffness matrix - K _T tangent stiffness matrix - k _k kinematic hardening coefficient - J Jacobian matrix - L=v/x velocity gradient tensor - m unit normal vector to yield surface - M strain-displacement matrix - N shape function matrix - n unit normal vector to deformed surface - n ₀ unit normal vector to undeformed surface - n unit normal vector to potential surface - r, R, R ₀ radial coordinate - s VEC() - S deformed surface - S ₀ undeformed surface - t time - t, t ₀ traction - t VEC() - VEC( ) - t VEC() - t _r reference stress interior to the yield surface - t t–t _r - T kinematic hardening modulus matrix - u=x–X displacement vector - U permutation matrix - v=x/t particle velocity - V deformed volume - V ₀ undeformed volume - X position vector of a given particle in the undeformed configuration - x(X,t) position vector in the deformed configuration - z, Z axial coordinate - vector of nodal displacements - =(F ^T F–I)/2 Lagrangian strain tensor - history parameter scalar - , azimuthal coordinate - elastic bulk modulus - flow rule coefficient - twisting rate coefficient - elastic shear modulus - iterate - Second Piola-Kirchhoff stress - Cauchy stress - Truesdell stress flux - deviatoric Cauchy stress - Y, Y yield function - residual function - plastic potential - X, Xe, Xp second order tangent modulus tensors in current configuration - X, Xe, Xp second order tangent modulus tensors in undeformed configuration - (.) variational operator - VEC(.) vectorization operator - TEN(.) Kronecker operator - tr(.) trace - Kronecker product     

Low-temperature specific heat of high-purity calcium

Low-temperature specific heat of high-purity calcium has been measured with an adiabatic calorimeter with a mechanical heat switch to avoid helium exchange gas errors, over the temperature range 1.1–4.2 K. The values obtained for the electronic coefficient of specific heat and the Debye temperature _D are =1.99±0.05 mJ/moleK ² and _D=250±4K.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

Deformation approach to the evaluation of the period of initiation and growth of fatigue macrocracks

We performed experimental investigation of the opening displacements of the contours of stress concentrators (notches and cracks) for various amplitudes of cyclic loading. On the basis of experimental results, we propose a new deformation parameter _t which is a function of the notch (crack) tip opening displacement , namely, _t /(+d*), where is the radius of the tip of the notch andd* is the characteristic size of the prefracture zone. It is shown that this parameter uniquely determines the number of cyclesN _l to the initiation of a fatigue macrocrack independently of the geometry of the specimens and stress concentrators in elastic and elastoplastic materials, i.e., the dependence of _t onN ₁ is a characteristic of the material. It is experimentally demonstrated that this dependence enables one to quantitatively describe the process of fatigue fracture both in the stage of initiation of macrocracks and their propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 7–21, September – October, 1995.