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Volume 27, Issue 5, 01 May 1956

Apparatus for the Direct Determination of the Dynamic Bulk Modulus
View Description Hide DescriptionAn apparatus has been developed for the direct measurement of the real and imaginary parts of the dynamic bulk modulus of solid and liquidmaterials over the frequency range of 50 to 10 000 cps. Piezoelectric crystals serving as driver and detector, together with the sample and a confining liquid, are contained in a cavity small compared with the wavelength of sound at these frequencies. Static pressure is superposed to eliminate the effect of small air bubbles. The complex compliances of the sample, confining liquid, and the cavity, are additive in this region, where the compliance is pure dilatation. The dynamic compliances of several natural rubber‐sulfur mixtures were obtained in a preliminary evaluation of the behavior of the apparatus.

Interfacial Waves in Viscoelastic Media
View Description Hide DescriptionThe stability of waves on the interface of two superposed semi‐infinite layers of incompressible media is studied. The two uniform layers are of different densities and different viscoelastic properties. Gravity, Taylor acceleration, and surface tension are taken into consideration. The main problems considered are the dispersion, decay and growth of waves, and the formulation of a hydrodynamical foundation for the cohesive action of elasticity.

Gradient Dependence of the Intrinsic Viscosity of Linear Macromolecules
View Description Hide DescriptionThe decrease of intrinsic viscosity with increasing gradient was found with all linear macromolecules investigated at high enough molecular weight irrespective of the solvent. But experiments do not agree on the power of the gradient to which the deviations from the zero value are proportional. Exponents ½, 1, and 2 have been proposed to fit experimental data. The necklace model with hydrodynamicinteraction yields suitable gradient dependence of the intrinsic viscosity only if either the molecule has a nonvanishing rigidity or the anisotropy of the hydrodynamicinteraction is explicitly considered. Since the first effect decreases with increasing M, very likely most of the observed gradient dependence has to be attributed to the second one which is intrinsically connected with the statistical shape of the molecular coil and the character of the hydrodynamic forces.

Mechanical Behavior of Viscoelastic Fibers
View Description Hide DescriptionThe under‐determined equation M(F,D,dF/dt,dD/dt)=0, where F=F(t), D=D(t) are measures of force and deformation and t is time, can be transformed into a first‐order partial differential equation in F, D, ∂F/∂D, ∂F/∂t whose characteristics represent the totality of all possible force‐elongation trajectories in F, D, t space. Historically, M has seen considerable service either as a complete stress‐strain relation or an element in a distribution of such relations. A geometric interpretation of M useful in rheological studies of fibers is given. Necessary conditions are given for M to provide a satisfactory description of a fiber's mechanical behavior. An operational procedure is outlined for constructing M in the laboratory based on direct measurements instead of on a priori assumptions involving springs and dash pots. The discussion is brief and theoretical.

Hypo‐Elastic Shear
View Description Hide DescriptionPart I reproduces the lecture given at the meeting of the Society of Rheology and furnishes a nonmathematical introduction to the theory of hypo‐elasticity. Hypo‐elasticity is a smooth, simple theory of elastic response based on time rates. For small strains it agrees with the classical linear theory of elasticity. To determine stress‐strain relations for large deformation is a mathematical problem, the answer to which varies from one special case to another. Simple shear is taken as an example. Here it turns out that hypo‐elastic materials may soften or stiffen in shear, depending on the value of a dimensionless constant which has no effect when the strain is small. For bodies which soften, a theoretical prediction of ``hypo‐elastic yield'' is obtained.
Part II concerns a new special type of hypo‐elastic body in some ways more general, in other ways more special than that considered in Part I. According to this theory, yield of the von Mises type appears to follow if the stress intensity is sufficiently great. The equations of this theory are solved for the case of simple shear. It is shown that if von Mises yield occurs, hypo‐elastic yield must occur at a lesser stress. For large values of a certain parameter, von Mises yield is imaginary and only hypo‐elastic yield occurs. For moderate values of the parameter, hypo‐elastic yield appears as primary yield, with von Mises yield as secondary yield at infinite strain. For small values of the parameter, hypo‐elastic yield and von Mises yield are indistinguishable, and the stress‐strain curve is similar to the idealized forms assumed at the outset in the conventional Prandtl‐Reuss theory.

Flow Patterns in Glacier Ice
View Description Hide DescriptionThe mass of ice varies along the length of a glacier because of the accumulation of snow in its upper regions and the ablation of ice in the lower regions. This mass change brings about variable speeds of flow and complex streamlines. General equations are derived using a type of plug flow for ice for the following: (1) glaciers of constant arbitrarily shaped cross sections, arbitrary rates of ablation and accumulation, and arbitrary variations of the longitudinal velocity across the glacier; and (2) glaciers of rectangular cross section with varying widths and depths, arbitrary velocity profiles, and arbitrary rates of ablation and accumulation. Streamlines are calculated for five typical cases by using these general equations. The calculated flow behavior is in agreement with the known behavior of glaciers.

Fracture in the Extrusion of Amorphous Polymers through Capillaries
View Description Hide DescriptionIn the extrusion of an amorphous, un‐cross‐linked polymer through a capillary, there is a critical stress at and beyond which the emerging stream becomes irregular in shape. This effect appears to originate in the approach to the capillary rather than within the capillary. Tearing or fracture of the molten polymer appears to occur in this region.

Theory of Deformation of a Porous Viscoelastic Anisotropic Solid
View Description Hide DescriptionEquations are established for the deformation of a viscoelastic porous solid containing a viscous fluid under the most general assumptions of anisotropy. The particular cases of transverse and complete isotropy are discussed. General solutions are also developed for the equations in the isotropic case. As an example the problem of the settlement of a loaded column is treated. The second–order effect of the change of permeability with deformation is also discussed.

Viscometric Analysis of Dispersions at Small Shear Stresses
View Description Hide DescriptionThe flow behavior of certain dispersions at small shear stresses has been studied in a rotational viscometer. Criteria which were used in analyzing the dispersions are the relative viscosity and its temperature dependence, the ratio of viscosities at infinite and zero shear, sedimentation rates, and the existence of a critical volume concentration for the occurrence of non‐Newtonian behavior.
 REGULAR ARTICLES


Technique for Making Surface Replicas from Comparatively Small Objects
View Description Hide DescriptionA simple replica technique for making surface replicas from small objects is described and illustrated with electron micrographs taken from replicas prepared by these techniques from glass fibers of 8μ diam and 36 grit Al_{2}O_{3} grains.

Resolution of the Atomic Structure of a Metal Surface by the Field Ion Microscope
View Description Hide DescriptionA formula for the resolution of the field ion microscope is derived by considering that most of the ions originate from rebounding molecules after random elastic collision with the surface. Cooling the tip with solid N_{2} or liquid H_{2} in order to obtain a large accommodation coefficient drastically reduces the lateral velocity of the ions in a helium operated microscope. As a result the potential resolution for a tip of radius 1000 A is improved to 1.5 A. Photographs show the individual atoms of a tungsten surface. The actual resolution is sufficient to resolve neighboring atoms with 2.74 A separation.

Problem of Intense Surface Heating of a Slab Accompanied by Change of Phase
View Description Hide DescriptionIn an attempt to bound the problem, steady‐state solutions are obtained for the speed of surface recession (melting) and the internal temperature history of a slab which uniformly absorbs heat on one face at a large caloric rate. The solutions are found to be sensitive to assumptions that must be made regarding both the thickness attained by the layer of molten matter produced during the heat pulse and the mechanisms (e.g., air drag, evaporation) that control this thickness.

Effect of Dispersion and Geometric Intensity Factors on X‐Ray Back‐Reflection Line Profiles
View Description Hide DescriptionAt high diffraction angles the rapid variation of dispersion causes the center of gravity of the observed diffraction‐line distribution of intensity versus 2τ to be displaced away from the Bragg angle τ_{ m } corresponding to the mean value of the convolution of the distribution of lengths ρ of reciprocal‐lattice vectors hkl with the distribution of x‐ray wavelengths λ. The displacement has been calculated for the case of measurements both on individual Kα components and on unresolved Kα doublets. In a probable example of the latter case, with CuKα radiation, the displacement at 2τ=160° corresponds to a relative error in spacing measurement of 1 part in 10^{4} and increases rapidly with increasing 2τ. The simple procedure is recommended of replotting the observed intensities against a scale of sine τ. The mean of the replotted distribution corresponds very closely to τ_{ m }.

Measurement of Minority Carrier Lifetime in Silicon
View Description Hide DescriptionThis report discusses lifetime in silicon as measured by photoconductive decay and checked by a drift technique. The source of pulsed light, the presentation system, and other instrumentation is described. Limitations on the injection level and field are discussed, as well as the problems presented by trapping, barriers, and making contact to the crystal. Lifetime in excess of 1500 μsec in p‐type crystals and 2500 μsec in n‐type crystals has been observed at room temperature. The photoconductive decay constant (lifetime) is reported in n‐type crystals from 78° to 450°K, and in p‐type crystals from 160° to 450°K. Measurements on another p‐type crystal permitted calculation of the surface recombination velocity (∼3500 cm/sec at 300°K after grinding or etching with CP4) between 175° and 450°K.

Radioactive Isotope Study of the Dissociation of Barium Oxide under Electron Bombardment
View Description Hide DescriptionThe evolution of Ba from BaO was detected by using radioactive Ba^{140}, and the rate was measured for various electron bombardment conditions. The following results were obtained: (1) When the bombarding voltage was fixed, the rate of evolution increased linearly with the number of primary electrons, provided the temperature of the oxide remained constant. (2) The rate of evolution increased exponentially with temperature; the activation energy was about 0.7 ev. (3) The efficiency of 500 ev electrons was far less than of 150 ev electrons at constant bombarding power. (4) The efficiency was around 3.9×10^{−7} atom per primary electron at 150 ev and 710°K. A simple mechanism of the electron bombardment dissociation is proposed.

Missile Guidance by Three‐Dimensional Proportional Navigation
View Description Hide DescriptionFollowing a brief comparison of three collision‐seeking types of navigation—pure pursuit, constant‐bearing collision, and proportional navigation—the usual definition of planar proportional navigation is extended to three dimensions. Based upon a simple criterion for optimum navigation to the line‐of‐sight motion, a proper formulation is found in terms of the geodesic and normal curvatures of the missile path on the surface generated by the line of sight. By a suitable choice of a reference coordinate system, the missile‐target kinematic relationships are then linearized, assuming relatively small deviations of the missile from a collision course. Upon combining these ``geometry feedback'' equations with the equations of guidance, the missile trajectory is found to be given in terms of two independent linear differential equations of identical form and of one higher order than the missile transfer function. Typical solutions are found for some simple cases. The character of the trajectory is shown to depend on an ``effective navigation constant'' proportional to the missile navigation constant (or gain) and the ratio of missile speed to closing speed; a value of this parameter greater than two is found to be necessary to insure finite terminal missile acceleration. Two example trajectories are calculated from both the exact and the linearized trajectory equations to indicate the accuracy of the linearization.

Transient Behavior in a Ferroresonant Circuit
View Description Hide DescriptionSeveral physical systems are described approximately by Duffing's equation ,where a, b, and c are constants of the system and F and ω_{1} are constants of the applied forcing function. This is a second‐order nonlinear differential equation whose complete exact solution is unknown.
Approximate solutions for the steady‐state behavior of the systems represented by the above equation are well known. The present work investigates the transient behavior in the region of the steady‐state response. The theory developed is supported by solutions using an analog computer and by experiment with an actual electrical circuit whose behavior is approximated by the foregoing equation.

Improved Method for Plotting Reciprocal Lattice Points
View Description Hide DescriptionA chart is presented which saves computational time in analyzing diffraction photographs of crystals. The new chart, used with a standard Bernal chart, facilitates the plotting of reciprocal lattice points from spots which are observed on a single crystal x‐ray pattern made with monochromatic radiation.

Thermoelectric Power of AuCu in Nonequilibrium States
View Description Hide DescriptionMeasurements have been made of the resistivity ρ and of the thermoelectric power Q (vs Pt) of samples of AuCu in various nonequilibrium states. One set of samples was disordered by quenching from 750°C; and annealing curves were obtained at 100°, 149°, 198°, and 258°C. A second set was first ordered and then cold worked to essentially complete disorder, and annealing curves taken at 149°C and 258°C. Of the former set, the Q—ρ curves for 100° and 149°C showed a maximum at ρ≈11.5μ ohm cm while none was observed in the curves for any of the other cases. It follows from the detailed results that to specify the state of the alloy it is necessary to give, in addition to ρ and Q, at least one other quantity such as the coefficient of magnetoresistivity.
