Craze intersections in biaxially-stressed polystyrene

Crazes are produced on two orthogonal planes in both thin film and macroscopic samples of polystyrene by sequentially applying two orthogonal tensile strains ₁ and ₂. Although many crazes produced by the second strain ₂ (secondary crazes) are stopped when they meet a primary craze, some intersections occur. The fraction of craze meetings resulting in intersection increases from 20% at ₁= ₂=3% to 55% at ₁= ₂=5%; intersections also occur preferentially in thin regions of primary crazes. The craze fibril structure in the intersection has a much lower fibril volume fraction, v _f, than either of the two crazes from which it formed. The fibril volume fraction in the intersection is approximately given by the product of the fibril volume fractions of the two crazes, in agreement with a prediction based on the surface drawing mechanism of craze thickening. At higher strain levels the v _fs of the intersections are lower, leading to higher fibril stresses and enhanced fibril fracture; an increasing fraction of intersections breaks down to form large voids at these higher strain levels. Fractography of macroscopic samples containing intersecting crazes demonstrates that voids formed at the intersections can act as nuclei for cracks causing premature fracture of the material.     

Theory of superconductivity. II. Excited Cooper pairs. Why does sodium remain normal down to 0 K?

Based on a generalized BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between electron (1) and hole (2) Cooper pairs are differentiated, the thermodynamic properties of a type-I superconductor below the critical temperatureT _c are investigated. An expression for the ground-state energy,W-W ₀, relative to the unperturbed Bloch system is obtained:W-W ₀=–1/4[N ₁(0) ₁ ² +N ₂(0) ₂ ² ], whereN _j(0) represent the electron and hole densities of states at the Fermi energy _F, and _j are the solutions of the simultaneous equations, with _D denoting the Debye frequency. The usual BCS formulas are obtained in the limits: (all)V _jl=V₀,N ₁(0) =N ₂(0). Any excitations generated through the BCS interaction Hamiltonian containingV _jl must involve Cooper pairs of antiparallel spins and nearly opposite momenta. The nonzero momentum orexcited Cooper pairs belowT _c are shown to have an excitation energy band minimum lower than the quasi-electrons, which were regarded as the elementary excitations in the original BCS theory. The energy gap _g(T) defined relative to excited and zero-momentum Cooper pairs (whenV _jl>0) decreases from _g(0) to 0 as the temperatureT is raised from 0 toT _c. If electrons only are available as in a monovalent metal like sodium (V ₁₂=0), the energy constant ₁ is finite but the energy gap vanishes identically for allT. In agreement with the BCS theory, the present theory predicts that a pure nonmagnetic metal in any dimensions should have a Cooper-pair ground state whose energy is lower than that of the Bloch ground state. Additionally it predicts that a monovalent metal should remain normal down to 0K, and that there should be no strictly one-dimensional superconductor.     

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.     

Study on the applicability of the Friedel relation with dislocation velocity-stress exponent

It was investigated at 77–178 K whether the Friedel relation is appropriate for the interaction between a dislocation and the impurity in KCl:Mg²⁺ (0.035 mol% in the melt) single crystal. This was carried out by fitting of m ₌₀ to the temperature versus dislocation velocity-effective stress exponent, m ^*, curves with respect to the two models: one is the Fleischer's model taking account of the Friedel relation and the other the Fleischer's model. The former model is termed the F-F. m ₌₀ is the m value at zero strain. m is a dislocation velocity-applied stress exponent. The m ^* for the F-F was examined from m ^* = 2F ₀ b(T _c/T)^1/2 – 1/(3kT _c)where F ₀ is the force acted on the dislocation at 0 K, b is the magnitude of the Burgers vector, k is the Boltzmann's constant and T _c is the critical temperature T, at which the effective stress due to the impurities is zero. As a result, it was found that the m ₌₀ values tend to increase with decreasing temperature and further approach to the m ^* for the Fleischer's model in contrast to the F-F. That is, the interaction between a dislocation and the impurity in the specimen could be approximated to the Fleischer's model rather than to the F-F. Similar result was also deduced on the basis of the data analyzed in terms of strain-rate sensitivity versus stress decrement due to oscillation. Consequently, it was considered that the Friedel relation is inappropriate for the specimen within the temperature range.     

Mixed convection boundary-layer on a vertical cylinder embedded in a saturated porous medium

Summary The mixed convection boundary layer on a vertical circular cylinder embedded in a saturated porous medium is considered. It is found that the flow depends on the parameter =R _a /P _e whereR _a andP _e are the Rayleigh number and Peclet number respectively. gives the ratio of the velocity scale for free convection to that for the forced convection. When is small the solution is, to a first approximation, obtained by a known heat conduction problem. The flow near the leading edge is considered and it is shown that a solution is possible only for ₀, ₀–1.354, and that a stable finite-difference solution away from the leading edge can be obtained only if –1; with <–1 there is a region of reversed flow near the cylinder. The finite-difference scheme is unable to give a satisfactory solution at very large distances from the leading edge, and to overcome this difficulty a simple approximate solution is developed. This solution shows that at large distances along the cyclinder, forced convection eventually becomes the dominant mechanism for heat transfer. This is also confirmed by an asymptotic solution of the full boundarylayer problem.Nomenclature a radius of cylinder - g acceleration of gravity - K permeability of the porous medium - N _u non-dimensional Nusselt number - r radial coordinate - non-dimensionalr=r/a - R _a Rayleigh number=(g T)Ka/ - P _e Peclet number=U ₀ a/ - T temperature - T _w temperature of the cylinder (constant) - T ₀ temperature of the ambient fluid (constant) - T temperature difference=T _w –T ₀ - u Darcy's law velocity in thex direction - U ₀ velocity of the outer flow - v Darcy's law velocity in ther-direction - x coordinate measuring distance along the cylinder - X non-dimensionalx,=x(aP _e )^–1 - equivalent thermal diffusivity - coefficient of thermal expansion - ratio of free to forced convection=R _a /P _e - viscosity of the convective fluid - density of the ambient fluid - non-dimensional temperature - stream function With 2 Figures     

Thermal boundary conductance between the U2D2 solid and B superfluid phases of3He

We present the first measurement of the thermal boundary conductance, 1/R _B , between the U2D2 spin ordered solid and theB superfluid phases of³He. We find that 1/R _B is exceedingly high, roughly seven orders of magnitude greater than that between sintered silver powder and liquid³He. ForT<0.56 mK, 1/R _B appeared to be thermally activated, i.e. 1/R _B exp(–/k _B T), with =4.5(±0.5) mK, close to the superfluid gap energy. We also present a theory involving magnon-quasiparticle coupling as a model to explain the experimental observations.     

Dielectric Permittivity of Eight Gases Measured with Cross Capacitors

A four-ring, toroidal cross capacitor was used to measure accurately the relative dielectric permittivity (p,T) of He, Ar, N₂, O₂, CH₄, C₂H₆, C₃H₈, and CO₂. ( is often called the dielectric constant.) The data are in the range from 0 to 50°C and, in many cases, extend up to 7 MPa. The accurate measurement of (p,T) required a good understanding of the deformation of the gas-filled capacitors with applied pressure. This understanding was tested in two ways. First, the experimental values of (p,T) for helium were compared with theoretical values. The average difference was within the noise, _expt– _theory=(–0.05±0.21)×10^–6, demonstrating that the four-ring cross capacitor deformed as predicted. Second, (p,T) of argon was measured simultaneously on three isotherms using two capacitors: the four-ring capacitor, and a 16-rod cross capacitor made using different materials and a different geometry. The results for the two capacitors are completely consistent, within the specifications of the capacitance bridge. There was a small inconsistency that was equivalent to 1×10^–6 of the measured capacitances, or, for argon, 3×10^–5 A , where A is the zero-density limit of the molar polarizability (–1)/[(+2)].     

Microdeformation in partially compatible blends of poly(styrene-acrylonitrile) and polycarbonate

Dilute 3-component 1-phase solutions in methylene chloride of poly(styrene-acrylonitrile) PSAN and polycarbonate PC are used to cast phase separated thin films. Films of pure PSAN, pure PC and five intermediate compositions are examined. The films are bonded to copper grids and strained at a constant rate of 4.1 × 10^–6sec^–1. The median tensile strain _v for void formation is determined using an optical microscope and the regions surrounding the voids are examined by TEM. At room temperature and slow strain rates both PSAN and PC plastically deform by shear yielding. For pure PSAN _v was found to be 0.13 whereas for PC _v exceeds 0.23. The addition of the more ductile polymer PC to PSAN at weight fractionsx forx 0.4 decreases _v. In this case voids form in crazes at the boundaries between the PC-rich inclusion and the PSAN-rich matrix. When the PC content is increased tox = 0.8, _v approaches 0.23. The effect of physical ageing (annealing belowT _g the glass transition temperature) on the mode of plastic deformation was also examined over the same compositional range. Physical ageing was found to suppress shear deformation and favour crazing in PSAN and PSAN-rich phases. Because crazes are more susceptible to breakdown than DZ's (shear deformation zones), physical ageing results in a marked decrease in _v. The breakdown statistics of these phase separated partially compatible blends was found to follow a Weibull distribution in strain from which two parameters may be extracted: the Weibull modulus and _w the Weibull scale parameter. is a measure of the breadth of distribution of void initiation and _w is a measure of the median strain to void formation in the films. The behaviour of _w was found to approximately mirror _v. The Weibull modulus appears to be primarily controlled by the matrix phase.     

The Accuracy of Dielectric Measurements in a Cylindrical Cavity H01p Resonator

The error of measurements of the dielectric parameters and tan in a cylindrical cavity resonator supporting the H _01p mode by varying the length of the resonator at a constant resonance frequency is considered. The errors in measuring and tanare investigated numerically as a function of the electric thickness of the sample being investigated and its permittivity .     

Strengthening mechanisms in Elgiloy

The effects of cold-working and age-hardening on the microstructure of Elgiloy (composition in wt %, 40 Co, 20 Cr, 15 Ni, 7 Mo, 2 Mn, 0.1 C, balance Fe) have been established. 36% and 72% cold reduction of the solution treated (ST) alloy (f c c) produced a network of thin f c c deformation twins and h c p-martensite platelets. The subsequent age-hardening of the cold-worked strip noted at 500° C was attributed to the formation of additional e-phase (via the _{f c c h c p} transformation), whereas the ST condition did not harden significantly at this temperature. In contrast, ageing the ST condition at 800° C for periods >1000 h caused an increase in hardness due to the formation of a coarse Mo-Co-Cr intermetallic compound together with a smaller amount of M₂₃C₆ carbide, while age softening of the cold-worked strip occurred at this temperature as a result of recovery and dissolution of the deformation induced-phase.     

A method of determining liquid water and ice in thermophysical tests on porous materials

A method is described for quantitative determination of liquid water and ice based on the sharp difference between the time characteristics of water and heat transport.Notation dielectric constant - ₀ density of dry material - u moisture content - l thickness - relative error - v_i volume proportion of phase i Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 889–893, May, 1981.     

Thermal conductivity of argon and argon-neon mixtures at high temperature

The thermal conductivity of neon and argon-neon mixtures is studied in the temperature range 400–1500°K. This is the first recording of such data above 793°K.Notation T_g true temperature drop in gas layer °K - ¯T temperature, °K, Q, effective thermal flux, W - Q_t, Qr thermal flux transmitted by thermal conductivity and radiation, respectively, W - T_sh correction for temperature shift, % - thermal conductivity of gas mixture, W/m·°K - x_i a molar concentration of neon - _i, _i, _ij, _ij potential function parameters for inter molecular interaction of homogeneous and inhomogeneous molecules - slope of exponential repulsion term Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 848–856, November, 1977.     

Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites

When a matrix crack encounters a fibre that is inclined relative to the direction of crack opening, geometry requires that the fibre flex is bridging between the crack faces. Conversely, the degree of flexing is a function of the crack face separation, as well as of (1) the compliance of the supporting matrix, (2) the crossing angle, (3) the bundle size, and (4) the shear coupling of the fibre to the matrix. At some crack face separation the stress level in the fibre bundle will cause it to fail. Other bundles, differing in size and orientation, will fail at other values of the crack separation. Such bridging contributes significantly to the resistance of the composite to crack propagation and to ultimate failure. The stress on the composite needed to produce a given crack face separation is inferred by analysing the forces and displacements involved. The resulting model computes stress versus crack-opening behaviour, ultimate strengths, and works of failure. Although the crack is assumed to be planar and to extend indefinitely, the model should also be applicable to finite cracks.Glossary of Symbols a radius of fibre bundle - C 2 _f /aE _f - ^* critical failure strain of fibre bundle - _b bending strain in outer fibre of a bundle - _c background strain in composite - _f axial strain in fibre - _s strain in fibre bundle due to fibre stretching = _f - () strain in composite far from crack - E Young's modulus of fibre bundle - E _c Young's modulus of composite - E _f Young's modulus of fibre - E _m Young's modulus of matrix - f() number density per unit area of fibres crossing crack plane in interval to + d - F total force exerted by fibre bundle normal to crack plane - F _s component of fibre stretching force normal to crack plane - F _b component of bending force normal to crack plane - G _m shear modulus of matrix - h crack face opening relative to crack mid-point - h _m matrix contraction contribution to h - h _f fibre deformation contribution to h - h _max crack opening at which bridging stress is a maximum - I moment of inertia of fibre bundle - k fibre stress decay constant in non-slip region - k ₀ force constant characterizing an elastic foundation (see Equation 7) - L exposed length of bridging fibre bundle (see Equation 1a) - L _f half-length of a discontinuous fibre - m, n parameters characterizing degree of misalignment - N number of bundles intersecting a unit area of crack plane - P _b bending force normal to bundle axis at crack midpoint - P _s stretching force parallel to bundle axis in crack opening - Q() distribution function describing the degree of misalignment - s _f fibre axial tensile stress - s _f ^* fibre tensile failure stress - S stress supported by totality of bridging fibre bundles - S _max maximum value of bridging stress - v fibre displacement relative to matrix - v elongation of fibre in crack bridging region - u _coh non-slip contribution to fibre elongation - U fibre elongation due to crack bridging - v overall volume fraction of fibres - v _f volume fraction of bundles - v _m volume fraction matrix between bundles - w transverse deflection of bundle at the crack mid-point - x distance along fibre axis, origin defined by context - X distance between the end of discontinuous fibre and the crack face - X ^* threshold (minimum) value of X that results in fibre failure instead of complete fibre pullout - y displacement of fibre normal to its undeflected axis - Z() area fraction angular weighting function - tensile strain in fibre relative to applied background strain - ^* critical value of to cause fibre/matrix debonding - angle at which a fibre bundle crosses the crack plane - (k ₀/4EI)^1/4, a parameter in cantilever beam analysis - v_m Poisson's ratio of matrix - L (see Equation 9) - shear stress - _* interlaminar shear strength of bundle - _d fibre/matrix interfacial shear strength - _f frictional shear slippage stress at bundle/matrix interface - angular deviation of fibre bundle from mean orientation of all bundles - angle between symmetry axis and crack plane     

Fatigue properties of pure metals

The report considers the stress fatigue limit _D, the fatigue to tensile strength ratio _D/R_m, and the deformation fatigue limit _D of pure metals. For FCC and some HCP metals there exists a linear correlation between fatigue limit and tensile strength. The fatigue limit and the fatigue ratio _D/R_m depend upon the homologous temperature. The fatigue ratios of BCC metals are higher than the fatigue ratios of other metals at room temperature as is also true for metals with nearly the same homologous temperature. The deformation fatigue limit decreases rapidly when T_h - 0.5 and T_h 1. When T_h = 1 then _D = 0, _D = 0 and _D/R_m = 0. The deformation fatigue limits of metals belonging to the same subgroup of the periodic element system and having, similar homologous temperatures at room temperature are very similar.

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Zusammenfassung Der Artikel behandelt die Dauerfestigkeit _D des Ermuedungskoeffizienten _D/R_m und die Deformation _D, die der Dauerfestigkeit entspricht. Fuer kubisch flachzentrierte Metalle und einige hexagonal Metalle existiert eine lineare Korrelation zwischen Dauerfestigkeit _D and Zugfestigkeit R_m. Die Dauerfestigkeit _D und der Ermuedungskoeffizient _D/R_m koennen als Funktion der homologischen Temperatur betrachtet werden. Der Ermuedungskoeffizient der kubisch raumzentrierten Metalle ist groesser als der der anderen in Raumtemperatur. Dieses stimmt auch fuer Metalle mit aehnlichen hornologischen Temperaturen. Die Deformation _D, die der Dauerfestigkeit entspricht, faellt schnell ab, wenn T_h > 0.5 und T_h 1, Wenn T_h = 1, darn ist _D = 0, _D = 0 und _D/R_m = 0. Die Metalle, die zu derselben Gruppe des periodischen Systems der Elemente gehoeren and aehnliche homologische Temperaturen (in Raumtemperatur) besitzen, haben sehr aehnliche Werte der Deformation _D.

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Résumé L'article parle de la contrainte de la limite de fatigue _D le facteur de fatigue _D/R_m et la déformation _D correspondante à la limite de fatigue des métaux pures. Pour les métaux du système cubique aux faces centrées (c. f. c.) et quelques uns du système hexagonale (hex. c.) il existe une correlation linéare entre la limite de fatigue _D et de la résistance a la fraction R_m. La limite de fatigue _D et le facteur de fatigue _D/R_m dependent de la température homologue. Les facteurs de la fatigue des métaux du système cubique centre (c.c.) sort plus grands que ceux des autres métaux dans la température de chambre, aussi por des métaux qui ont presque la même température homologue. La déformation correspondante à la limite de fatigue tombe rapidement quand T_h > 0.5 et T_h 1. Quand T_h = 1, alors _D = 0, _D = 0 et _D/R_m = 0. Cettes déformations _D pour les métaux du même groupe du système périodique des éléments sont proches si les températures homologues dans la température de chambre sont analogues.

     

On the Bose-Einstein condensation of nonzero-momentum cooper pairs. A second-order phase transition

Based on the BCS Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperatureT _c from the high-temperature side. Nonzero-momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta aboveT _c in the bulk limit, are shown to move like independent bosons with the energy vs. momentump relation=1/2v_F , where _F represents the Fermi velocity (1/2m* _F ² _FFermi energy). The system of free Cooper pairs undergoes a phase transition of the second order with the critical temperatureT _c given byk _B T _c=1/2(²³ _F ³ n/1.20257)^1/3 wheren is the number density of Cooper pairs. The ratio of the jump of the heat capacity, C, to the maximum heat capacity,C _s, is a universal constant: C/C _s=0.60874; this number is close to the universal constant 0.588 obtained by the finite-temperature BCS theory. The physical significance of these results is discussed, referring to the well-known BCS theory, which treats the many-Cooper-pair ground state exactly and the thermodynamic state belowT _c approximately. An explanation is proposed on the question why sodium should remain normal down to 0 K, based on the band structures with the hypothesis that the supercondensate composed of zero-momentum electron and hole Cooper pairs is electrically neutral.     

Optical Spectra of Porous Silicon

The dielectric permittivity ₂, absorption coefficient, and refractive index spectra of porous silicon matrices (m-Si) are calculated for the spectral range 2.5–5 eV and porosities of 0.57, 0.66, and 0.77. The ₂ spectra of m-Si are decomposed into individual components, and their principal parameters are determined: energy position, half width, area, and intensity. Porosity is shown to have a significant effect on the strength of optical transitions in m-Si.     

High-resolution measurements of the heat capacity of MnBr2·4H2O near its Néel temperature

The heat capacityC _P of the antiferromagnet MnBr₂ ·4H₂O has been measured for polycrystalline and single-crystal samples nearT _N(2.123 K) with temperature resolution of 1×10^–6 K. Similar rounding of the lambda anomaly is found in both cases. For |1 –T/T _N| 10^–1 all data can be well fitted by assuming the samples to consist of many independent subsystems obeying the same power laws but with a Gaussian distribution ofT _N's having a width of 1.1×10^–3 K. ForT>T _N, we findC _P ^–0.12, essentially as predicted for three-dimensional Ising models in the critical region. ForT<T _N and 10^–3 10^–1,C _P ln , which approximates Ising model behavior in this interval but is not expected to be valid for 10^–4. ForT>T _N and 2.5×10^–1, C_P agrees well with predictions for the classical Heisenberg model. This crossover at 10^–1 is consistent with the known anisotropy of the salt and with present theory. The data forT>T _N in the interval 10^–4 10^–3, while not in the range of obvious rounding, appear to be strongly influenced by the mechanism responsible for that rounding.Work supported by the National Science Foundation and the Office of Naval Research. Based on a thesis submitted by L.W.K. to Carnegie-Mellon University in partial fulfillment of the requirements for the Ph.D. degree. A preliminary account of this work was presented at the Atlantic City meeting of the American Physical Society, March 1972 [Bull. Am. Phys. Soc. 17, 299 (1972)].     

The Static Dielectric Constant of Liquid Water Between 274 and 418 K Near the Saturated Vapor Pressure

The complex dielectric constant (relative electric permittivity) of liquid water was redetermined in the temperature range 0°C<;t<145°C at pressures less than 440 kPa. In this work, _r was deduced from measurements of the resonant frequencies f of a novel, re-entrant, two-mode, radio-frequency resonator. The frequencies ranged from 23 to 84 MHz and were well within the low-frequency limit for because (2f _max)²<5×10^–5 where _max=1.8×10^–11 s is the maximum relaxation time of water under the conditions studied. The data for for two water samples differing in conductivity by a factor of 3.6 and for the two resonant modes differing in frequency by a factor of 2.6 were simultaneously fit by the polynomial function (t)=87.9144–0.404399t+9.58726×10^–4 t ²–1.32802×10^–6 t ³ with a remarkably small residual standard deviation of 0.0055. The present data are consistent with previously published data; however, they are more precise and internally consistent. The present apparatus was also tested with cyclohexane and yielded the values (t)=2.0551–0.00156t for 20°C<t<30°C, in excellent agreement with previously published values.     

A Monte Carlo Study of Disorder in the High Pressure Mixed Crystal N2-Ar

In order to obtain a better notion of the experimental results in our laboratory, Monte Carlo calculations have been performed of the N ₂-Ar crystal on the N ₂-rich side, in the p-T region where the and phases exist in pure N ₂. Considering the enthalpy, the system prefers the Ar atoms to be located on the sphere positions. The * phase is present for mixtures down to but is most likely metastable. The *-* transition shifts to lower temperatures with decreasing . The 2 ^nd order transition within the phase continues to exist to even smaller . In contrast to the * -* transition, the transition temperature for the 2 ^nd order transition does not shift to lower temperatures. For a mixture of it is within 5 K from the pure 2 ^nd order transition at a pressure of 7.0 GPa.     

Binary Diffusion Coefficients of Acetone in Carbon Dioxide at 308.2 and 313.2 K in the Pressure Range from 7.9 to 40 MPa

Binary diffusion coefficients of acetone in carbon dioxide were measured by the Taylor dispersion method at 308.2 K and 7.9 to 40 MPa and at 313.2 K and 8.0 to 37 MPa. The D ₁₂ values obtained from the response curves by the method of fitting in the time domain were more accurate than those obtained by the moment method. At pressures lower than about 8.3 MPa at 308.2 K or 9.1 MPa at 313.2 K, the accuracy in the D ₁₂ values was found to decrease significantly with decreasing pressure by examining (peak area)×u _{a, cal}, the values of S ₁₀, the fitting error , and u _{a, cal}/u _{a, exp} as a function of pressure. The D ₁₂ values at pressures higher than 8.3 MPa at 308.2 K or 9.1 MPa at 313.2 K were well represented with the Schmidt number correlation. The D ₁₂ data with larger fitting errors (>0.01) showed larger deviations from the values predicted by this correlation.