Showing papers in "Journal of Applied Physics in 1963"
TL;DR: In this article, a formula for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film was derived for a rectangular barrier with and without image forces, where the true image potential was considered and compared to the approximate parabolic solution derived by Holm and Kirschstein.
Abstract: A formula is derived for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film. The formula is applied to a rectangular barrier with and without image forces. In the image force problem, the true image potential is considered and compared to the approximate parabolic solution derived by Holm and Kirschstein. The anomalies associated with Holm's expression for the intermediate voltage characteristic are resolved. The effect of the dielectric constant of the insulating film is discussed in detail, and it is shown that this constant affects the temperature dependence of the J‐V characteristic of a tunnel junction.
3,727 citations
TL;DR: In this article, the authors discussed the mechanism of creep in polycrystalline alumina based on the differences between the lattice and boundary diffusion models and showed that the boundary diffusion model is more stable than lattice diffusion model, while the grain size dependence and the numerical constant are greater.
Abstract: The creep rate (ė) predicted by the boundary diffusion (Db) model is ė≃150σDbWΩ/(GS)3kT, where σ is the stress, W is the boundary width, (GS) is the average grain size, and Ω is vacancy volume. The stress dependence is the same as the lattice diffusion model, given by C. Herring, while the grain size dependence and the numerical constant are greater for boundary diffusion. Discussion of the mechanism of creep in polycrystalline alumina is based on the differences between the lattice and boundary diffusion models.
2,050 citations
TL;DR: In this article, the stability of the shape of a phase boundary enclosing a particle whose growth during a phase transformation is regulated by the diffusion of material or the flow of heat is studied.
Abstract: THE purpose of this paper is to study the stability of the shape of a phase boundary enclosing a particle whose growth during a phase transformation is regulated by the diffusion of material or the flow of heat. The principal approximations used are (1) the neglect of crystallographic factors such as elastic strain energy or anisotropy of interface properties, (2) the description of the thermal or diffusion fields by Laplace’s equation (the frequently satisfied conditions for the latter approximation to be valid are discussed explicitly), and (3) the assumption of local equilibrium at each element of interface. The question of stability is studied by introducing a perturbation in the original interface shape and determining whether this perturbation will grow or decay. The method is fundamental in the sense that the velocity of each element of interface is calculated from the basic heat flow or diffusion boundary conditions; no ad hoc principles are employed
1,687 citations
TL;DR: In this paper, a method for finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region was given, and the solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x-ray absorption coefficient in two dimensions, (2) the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter, and (3) a variable density of matter with constant chemical composition, using the energy loss
Abstract: A method is given of finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region. The solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x‐ray absorption coefficient in two dimensions; (2) the determination of the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter; and (3) the determination of a variable density of matter with constant chemical composition, using the energy loss of charged particles in the matter.
1,409 citations
TL;DR: In this paper, it was shown that alloys near the stoichiometric TiNi composition undergo transformation into the related phases Ti2Ni and TiNi3 at low temperatures, and the main factors controlling these phase transformations are alloy composition, temperature, and mode of plastic deformation.
Abstract: X‐ray diffraction and dilation studies have shown that alloys near the stoichiometric TiNi composition undergo transformation into the related phases Ti2Ni and TiNi3 at low temperatures. The main factors controlling these phase transformations are alloy composition, temperature, and mode of plastic deformation. In plastic deformation, tensile or compressive stressing produced separate and unlike decomposition phases; this finding was dramatically demonstrated by unique temperature‐sensitive dimensional changes in plastically deformed specimens. Changes of large magnitude in vibration damping have also been noted and appear related to variations in the phase equilibria of the system.
998 citations
TL;DR: In this paper, the growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time-dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa.
Abstract: The growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time‐dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa. The equations are solved in closed form for an arbitrary input pulse and an arbitrary initial distribution of inverted population. The solutions are discussed in detail for the particular cases of a square pulse and a Lorentzian pulse, both with a uniform initial population inversion.
893 citations
TL;DR: In this article, the theory of the electric tunnel effect has been extended to asymmetric junctions, i.e., junctions having electrodes of different materials, and it is found that the J-V characteristic is polarity-dependent.
Abstract: The theory of the electric tunnel effect has been extended to asymmetric junctions—i.e., junctions having electrodes of different materials. It is found that the J—V characteristic is polarity‐dependent. At lower voltages, the greater current flows when the electrode of lower work function is positively biased, in agreement with observations on junctions having one aluminum electrode. At higher voltages, there is a change in direction of rectification; i.e., greater current flows when the electrode of lower work function is negatively biased. This effect has also been experimentally observed.
871 citations
TL;DR: In this article, the origins of fibrous crystal habits in the absence of appreciable temperature gradients and profuse non-crystallographic branching are explained, and it is shown that a plane crystal face cannot grow without suffering an instability of profile.
Abstract: To account for spherulitic crystallization from the melt, one must explain the origins (i) of fibrous crystal habits in the absence of appreciable temperature gradients and (ii) of profuse noncrystallographic branching. Attention is drawn to properties held in common by spherulite‐forming melts of various types and, in particular, to the facts that (a) they are multicomponent systems, (b) they exhibit small coefficients of self‐diffusion, and (c) they crystallize slowly. It is shown that a consequence of these properties is that a plane crystal face cannot grow without suffering an instability of profile. Analagous instabilities lead in metal crystals to a cellular interface but, because of unusual growth kinetics, instability in spherulite‐forming melts gives rise to a drastic modification of crystal habit. Bundles of discrete fibers are formed whose widths are determined by δ = D/G, D being the coefficient of self‐diffusion and G being the growth rate. δ is generally small in these systems and commensurate with the scale of crystalline disorder in the fibers. It is this circumstance that allows noncrystallographic branching to occur.
761 citations
TL;DR: In this article, the authors present a calculation of the stresses and energies for interfaces between different crystals, where the difference between the two crystals is expressed in terms of different elastic constants and variable interfacial bondings, and the contribution of the normal forces to the interfacial energies is negligible for the approximation used.
Abstract: This paper presents a calculation of the stresses and energies for interfaces between different crystals. Only simple cases corresponding to interfacial dislocations of pure screw or edge type are treated. The difference between the two crystals is expressed in terms of different elastic constants and variable interfacial bondings. Two kinds of interfacial forces appear: tangential forces with a periodic character and normal forces. The latter are induced by different normal displacements of the two contact surfaces of the crystals due to the equal and opposite tangential interfacial forces and are accounted for by assuming a linear relation between force and relative displacement. By using a periodic parabolic model to represent the periodic potential associated with the tangential forces, it is shown that the contribution of the normal force to the interfacial energies is negligible for the approximation used. When these normal forces are neglected, the Peierls‐Nabarro representation of the interfacial ...
629 citations
TL;DR: In this article, the authors analyzed the elastic wave amplitude with respect to the characteristics of the input heat flux and the thermal and elastic properties of the body and found that the latter may be much greater than the former, as experiments have demonstrated.
Abstract: When the surface of a body is subjected to transient heating (e.g., by electron bombardment or rf absorption) elastic waves are produced as a result of surface motion due to thermal expansion. This process is analyzed, with particular emphasis on the case of an input heat flux varying harmonically with time, to relate the elastic wave amplitude to the characteristics of the input flux and the thermal and elastic properties of the body. Experiments performed with both electron impact and rf absorption verify the proportionality of the stress wave amplitude and the absorbed power density, and correlate well with the thermal and elastic properties of the heated medium. Comparison of the elastic wave stress amplitude with radiation pressure shows that the former may be much greater than the latter, as experiments have demonstrated. When a barium titanate crystal was used to detect the elastic waves produced, heating by a single 2‐μsec pulse of electrons or microwave radiation produced easily detectible signal...
626 citations
TL;DR: In this article, the interfacial energy between a crystalline film and a substrate of a different substance for the simple case in which the lattice parameters differ in one direction only, is presented.
Abstract: A calculation of the interfacial energy between a crystalline film and a crystalline substrate of a different substance for the simple case in which the lattice parameters differ in one direction only, is presented. The results are expressed in terms of film thickness h, interfacial misfit η, interfacial bonding, and relative hardness of film and substrate. A parabolic interfacial potential has been used to investigate the effect of h showing that it is only a significant factor when either or both h and η are small. It is further shown that, in the minimum energy configuration of the system, the film is homogeneously strained. According to the calculations, a critical value of misfit ηc exists below which the film is strained to fit the substrate exactly and above which the required strain is an order of magnitude less than ηc. The misfit ηc is estimated to vary from as much as 13% for a ``soft'' monatomic layer which is tightly bound down to practically zero for thick films which are loosely bound. It is shown that the interfacial energy associated with an infinitely thick film as calculated with a Peierls‐Nabarro type of interfacial force, is a useful approximation for many purposes. Approximate expressions for the strains in terms of the relevant parameters are deduced from this result.
TL;DR: Improved experimental data have been obtained between 20° and 350°K for the widths and temperature shifts of the R lines in ruby as mentioned in this paper, which can be accurately described in terms of Raman scattering of Debye-model phonons.
Abstract: Improved experimental data have been obtained between 20° and 350°K for the widths and temperature shifts of the R lines in ruby. Above 77°K the results can be accurately described in terms of Raman scattering of Debye‐model phonons. There is no evidence for measurable contributions to the widths and shifts from direct processes involving emission or absorption of a single resonant phonon. Below 77°K the principal contributions are from crystal inhomogeneities.
TL;DR: In the case of a free energy function with deep minima at θ = 0 and π, such treatment leads again to a result derived previously by a method adapted from Kramers and valid when v(Vmax−Vmin)/kT is at least several times unity (v=particle volume, Vmax and Vmin=maximum and minimum free energy per unit volume, k=Boltzmann's constant, T=Kelvin te... as mentioned in this paper.
Abstract: A statistical ensemble of particles, with moment orientations (θ, φ), can be represented by a surface density W (θ, φ, t) of points on the unit sphere. The corresponding surface density J satisfies a continuity equation ∂W/∂t=−∇·J. With no thermal agitation, J=WṀ/Ms, where M is the vector magnetization (| M | = const = Ms); its rate of change Ṁ is assumed to be given by Gilbert's equation. To include thermal agitation, we may add to J a diffusion term −k′∇W; this gives directly the ``Fokker‐Planck'' equation of a previous, more laborious calculation. When ∂/∂φ=0, the equation simplifies and can be replaced by a minimization problem, susceptible to approximate treatment. In the case of a free‐energy function with deep minima at θ=0 and π, such treatment leads again to a result derived previously by a method adapted from Kramers and valid when v(Vmax−Vmin)/kT is at least several times unity (v=particle volume, Vmax and Vmin=maximum and minimum free energy per unit volume, k=Boltzmann's constant, T=Kelvin te...
TL;DR: In this paper, the coercive force and remanence of essentially spherical iron and iron-cobalt alloy particles with diameters from 20 to 3000 A have been measured at 4°, 76°, and 207°K and compared to the theoretically predicted behavior.
Abstract: The coercive force and remanence of essentially spherical iron and iron‐cobalt alloy particles with diameters from 20 to 3000 A have been measured at 4°, 76°, and 207°K and compared to the theoretically predicted behavior. The remanence shows a broad, plateau‐like maximum while the coercive force has a rather sharp maximum. The maximum of the coercive force occurs at a much larger particle diameter than the maximum of the remanence. It is shown that these essential characteristics follow from the theory. Deviations from theory are seen in the smaller size range and can be accounted for by the distribution of particle sizes. A general treatment of the coercive force of mixtures of thermally stable, high coercive force particles with superparamagnetic and multidomain particles is given.
TL;DR: In this article, the authors analyzed the flash technique for measuring thermal diffusivity for the case of a cylindrical-shaped specimen of radius r0 and thickness a to determine the effects of radiation at high temperatures, finite duration of the heat pulse, and the feasibility of low temperature measurements.
Abstract: The flash technique for measuring thermal diffusivity is analyzed for the case of a cylindrical‐shaped specimen of radius r0 and thickness a to determine the effects of radiation at high temperatures, finite duration of the heat pulse, and the feasibility of low temperature measurements. It is found that the flash diffusivity method is useful in two complementary limits: (1) pulse time τ short compared to the characteristic thermal response time tc, (2) τ/tc of the order 1 to 10. The former case corresponds to the original description of Parker, Jenkins, and Abbott, while the latter case is suitable at very low temperatures. Moreover, it is shown that there is an optimum specimen thickness a for a given material and pulse time τ, in the sense that a higher temperature can be reached before any corrections have to be made to the Parker et al. analysis.
TL;DR: In this paper, the authors considered an idealized bed in which centers are randomly situated without restricting the spheres to nonoverlapping locations, and derived the upper bound for the effective diffusion coefficient as φD0/[1−½lnφ], where D0 is the actual diffusion coefficient in a fluid which fills the void regions of the bed and φ is the void fraction.
Abstract: Recent calculations by Prager of upper bounds for the effective diffusion coefficient (or conductivity) in porous media, in terms of certain statistical parameters of the random geometry, are reformulated so as to apply specifically to a bed of spherical particles. The calculations are simplified by considering an idealized bed in which centers are randomly situated without restricting the spheres to nonoverlapping locations. The result, applicable to randomly overlapping spheres of either uniform or nonuniform sizes, gives the upper bound for the effective diffusion coefficient as φD0/[1−½lnφ], where D0 is the actual diffusion coefficient in a fluid which fills the void regions of the bed and φ is the void fraction. This result is compared with experimental results of various investigators for nonoverlapping spheres and also with Hashin and Shtrikman's expression for the best upper bound that can be calculated without taking the statistics of a particular random geometry into account.
TL;DR: In this paper, an expression for the differential capacitance of a metal contact to a semiconductor in which the bulk free carrier density is degenerate or near degenerate is derived.
Abstract: An expression is derived for the differential capacitance of a metal contact to a semiconductor in which the bulk free carrier density is degenerate or near degenerate. A significant correction to the nondegenerate theory may be required for accurate measurement of the barrier height.
TL;DR: In this article, the solubilities of helium, nitrogen, oxygen, argon, methane, carbon dioxide, and ethane in glassy amorphous and crystalline polyethylene terephthalate have been studied by time-lag and/or static sorption methods.
Abstract: The solubilities of helium, nitrogen, oxygen, argon, methane, carbon dioxide, and ethane in glassy amorphous and crystalline polyethylene terephthalate have been studied by time‐lag and/or static sorption methods. Solubilities of all the gases but ethane were also determined in the rubbery crystalline polymer. The only deviations from Henry's law were displayed by ethane at 25°C and carbon dioxide at 25° and 40° C in the glassy polymer. Correlation of solubility constants for oxygen and nitrogen obtained by the static sorption method with values obtained dynamically indicate that the glassy crystalline polymer is an isotropic diffusion medium. Sorption in the glassy amorphous and crystalline polymers generally takes place by two processes operating concurrently: ordinary dissolution plus ``hole‐filling.'' The ``hole‐filling'' process obeys a Langmuir expression and dissolution obeys Henry's law for sorption of carbon dioxide in the amorphous polymer at 25°C. Crystallinity reduces gas solubility in the gla...
TL;DR: The piezoresistive properties of n and p-type diffused layers formed by the diffusion of impurities into silicon have been investigated in this paper, and the results show a change in the symmetry and the temperature dependence of the large coefficients.
Abstract: The piezoresistive properties of n‐ and p‐type layers formed by the diffusion of impurities into silicon have been investigated. The values of the three piezoresistance coefficients and the temperature dependence of the large coefficients have been measured on layers having surface concentration values from 1018 to 1021 cm−3. The piezoresistance effect in p‐type diffused layers follows qualitatively the behavior expected in a degenerate semiconductor. n‐type layers having high surface concentration values show a change in the symmetry of the piezoresistance effect at room temperature and a decrease in the coefficient π11 at lower temperatures. A discussion of the piezoresistance effect in diffused layers and its relation to the piezoresistance effect in uniformly doped material is also given.
TL;DR: In this article, it was shown that the spatial variation in the field intensity of the various modes produces non-uniform distributions in the inverted population and one can show that there is little tendency for these distributions to smooth out due to spatial cross relaxation.
Abstract: Experiments show that conventional solid‐state lasers can go into oscillation simultaneously in many modes. This is somewhat surprising since it appears impossible to ``eat holes'' in temperature‐broadened lines and thus only one or, at most, a few modes should be able to oscillate. However, the spatial variation in the field intensity of the various modes produces nonuniform distributions in the inverted population and one can show that there is little tendency for these distributions to smooth out due to spatial cross relaxation. Such nonuniform distributions could lead to simultaneous oscillation in many modes. Formulas which relate the number of unstable modes to the pump power and various other maser parameters are obtained. The results show that it is exceedingly difficult to obtain single mode operation in conventional masers at high pumping levels. Ways to avoid a nonuniform distribution density and methods to achieve high‐power single‐mode operation in practice are discussed. It is also possible to show the effect of slow spatial cross relaxation on the spiking behavior.
TL;DR: In this article, the equations governing inversion and photon density in a laser were solved for giant pulse operation, and the simplifying assumptions which permit solution involve homogeneous excitation of the laser and the neglecting of changes produced by pumping and fluorescence during the formation of the giant pulse.
Abstract: The differential equations governing inversion and photon density in a laser are solved for giant pulse operation. The simplifying assumptions which permit solution involve homogeneous excitation of the laser and the neglecting of changes produced by pumping and fluorescence during the formation of the giant pulse. Energy, peak output power, pulse delay, and pulse width are calculated.
TL;DR: In this paper, an approximate expression for the power output of a gas maser oscillating simultaneously at many longitudinal cavity resonances, based on the assumption that the gain saturates independently at each frequency.
Abstract: The nonlinear gain characteristics of optical maser amplifiers at high beam intensities, and the optimum cavity coupling of maser oscillators for maximum output power, are computed for maser media with homogeneous and inhomogeneous line broadening. An approximate expression is derived for the power output of a gas maser oscillating simultaneously at many longitudinal cavity resonances, based on the assumption that the gain saturates independently at each frequency. In each case, the decrease of maser gain with radiation intensity involves an empiric constant, or saturation parameter, which is characteristic of the active medium.Power and gain measurements at 1.15 μ on three He–Ne maser tubes of different diameter, in a cavity 1.75 m long, are found to satisfy the derived multifrequency power expression, and permit evaluation of the gain—saturation parameter for this gas mixture. The power expression, derived for a single transverse mode, is unexpectedly found to hold for multimode oscillations as well, within the range of measurements. From the measured saturation parameter and the derived expressions, the performance of amplifiers and other oscillators with the same active medium can be predicted.
TL;DR: In this paper, a modified cleavage technique was applied to the glassy polymers poly(methyl methacrylate) and polystyrene for which comparative data are available from both tensile and cleavage experiments.
Abstract: The fracture surface energy of a material can be obtained by the cleavage technique, in which a crack is propagated along the median plane of a strip sample by forces applied at the free ends. Unfortunately, the stress distribution in a conventional sample is such that the crack tends to deviate from its original direction, so that, for isotropic materials, external constraints must be imposed to overcome this tendency. To interpret the data, relations have been derived, based on the assumption that simple beam theory can be applied to the system; this assumption is not strictly valid. The use of the constraints can be avoided by machining fine slots along the opposing faces of the sample, and the system can then be analyzed by a direct and unambiguous method. The modified technique has been applied to the glassy polymers poly(methyl methacrylate) and polystyrene for which comparative data are available from both tensile and cleavage experiments.
TL;DR: The absolute Seebeck coefficient, electrical resistivity, and thermal resistivity were simultaneously measured on pure bismuth single crystals of various orientations between approximately 80° and 300°K.
Abstract: The absolute Seebeck coefficient, electrical resistivity, and thermal resistivity were simultaneously measured on pure bismuth single crystals of various orientations between approximately 80° and 300°K. Using an overlapping two‐band many‐valley model, numerical values for the temperature dependence and anisotropy (where appropriate) of the following parameters have been calculated: (1) the overlap energy and the Fermi energy of the electrons and of the holes, (2) the density of states effective mass of the electrons and of the holes, (3) the separate electronic and lattice thermal conductivities, (4) the actual index of thermo‐electric efficiency, and (5) the hypothetical ``optimum'' index of thermoelectric efficiency. The calculated electronic thermal conductivity includes a new term due to bipolar diffusion.
TL;DR: In this paper, the Bridgman method of combined temperature and pressure was applied to polycrystalline black phosphorus and found to be p type with room-temperature resistivity around one Ω•cm.
Abstract: Polycrystalline black phosphorus has been produced by the Bridgman method of combined temperature and pressure and found to be p type with room‐temperature resistivity around one Ω‐cm, in agreement with the observations of previous workers. From 300° to 700°K, the resistivity can be fitted by an expression ρav=4.6×10−3 exp(0.35/2kT) Ω‐cm, and the Hall data by (ReT32)−1 = constant exp(−0.34/2kT). The product Rσ can be represented in this temperature range by (Rσ)av = 9×105T−1.4 cm2/V‐sec. The deviation from this law toward lower mobility observed by Keyes from 250° to 350°K does not occur in these samples. The resistivity continues to rise even near liquid‐helium temperature, and maxima in the Hall coefficient occur between 24° and 30°K. The low‐temperature Rσ products also exhibit maxima, and the magnitude of this product is small near liquid‐helium temperature. Although these characteristics are consistent with two‐band conduction, the relative appearance of the two sets of maxima is not consistent with ...
TL;DR: The crystallographic polarity of the noncentrosymmetric material zincite (ZnO) has been determined by a rapid x-ray absorption edge method as discussed by the authors.
Abstract: The crystallographic polarity of the noncentrosymmetric material zincite (ZnO) has been determined by a rapid x‐ray absorption edge method. The polarity results have been correlated to marked differences in etching behavior and crystal morphology in opposite polar directions of ZnO crystals. These differences are shown to be consistent with the proposed surface bonding model for AII‐BVI compounds. Crystal morphology is shown to be a useful criterion to indicate crystallographic polarity in well‐formed wurtzite‐type crystals.
TL;DR: In this paper, it was shown that for any value of f, σ/σ0 for a medium containing a square array of nonconducting cylinders is the reciprocal of σ for the same array of perfectly conducting circular cylinders.
Abstract: The effective electrical conductivity σ is computed for a composite medium consisting of a dense cubic array of identical, perfectly conducting spheres imbedded in a medium of conductivity σ0. When f, the fractional volume occupied by the spheres, is near its maximum value π/6, the result is σ/σ0=−(π/2)log [(π/6)−f]+…,(π/6)−f≪1. This result exhibits the singularity of σ at f=π/6, when the spheres touch each other. The previous results of Maxwell, of Rayleigh and of Meredith and Tobias are not valid near the singularity and they fail to reveal it. For f=0.5161 our result yields σ/σ0=7.65, while the measurement of Meredith and Tobias yielded σ/σ0=7.6.For a medium containing a square array of perfectly conducting circular cylinders we obtain σ/σ0=π32/2[(π/4−f)]12+…,(π/4)−f≪1. This result agrees well with the numerical results of H. B. Keller and D. Sachs. We also prove that for any value of f, σ/σ0 for a medium containing a square array of nonconducting cylinders is the reciprocal of σ/σ0 for the same array ...
TL;DR: In this paper, a model for diffusion in glassy amorphous and crystalline polymers is proposed, assuming that the driving force for diffusion is the concentration gradient of dissolved molecules which are assumed to be in local equilibrium with molecules in the ''holes'' The model predicts that actual diffusion constants and activation energies are larger than those experimentally measured.
Abstract: Diffusion of helium, oxygen, nitrogen, argon, carbon dioxide, and methane in glassy and rubbery polythylene terephthalate has been studied in the range 25° to 130°C Despite the abnormal solution behavior of these gases in the glassypolymer, the diffusion process is evidently normal and Fickian: Correlation of solubility constants for oxygen and nitrogen, obtained by the time‐lag method, with data obtained by a static sorption method, indicates that glassy crystalline polyethylene terephthalate may be considered an isotropic diffusion medium Diffusion is impeded purely geometrically by the presence of the crystallites, and the impedance factor is equal to the reciprocal of the amorphous volume fraction In the rubbery crystalline state of the polymer,diffusion is Fickian and apparent activation energies for diffusion are larger than those in the glassy crystalline polymer A model for diffusion in the glassy amorphous and crystalline polymers is proposed, assuming that the driving force for diffusion is the concentration gradient of dissolved molecules which are assumed to be in local equilibrium with molecules in the ``holes'' The model predicts that actual diffusion constants and activation energies are larger than those experimentally measured Thus, part of the observed difference between values of EDa in the glassy and rubbery states may be reconciled Correlations of D and EDa with the square of gas molecular diameters are obtained in both the glassy and rubbery states In the latter plots, the helium data fall above the correlations, showing evidence of partially non‐activated diffusion in both states of the polymer
TL;DR: In this paper, the Poiseuille flow of a rarefied gas between two parallel plates is analyzed numerically for an inverse Knudsen number ranging from 0 to 10.5.
Abstract: The Poiseuille flow of a rarefied gas between two parallel plates is analyzed numerically for an inverse Knudsen number ranging from 0 to 10.5. The Bhatnagar, Gross, and Krook model is used and the transport integrodifferential equation is reduced to a purely integral one, which is solved numerically by the discrete ordinate method.The plot of the volume flow rate vs pressure is shown to have the expected minimum; besides, it fits well with experimental results and previous approximate calculations.In particular, the results given by Takao, properly corrected, are in good agreement with ours.
TL;DR: In this paper, the Neel temperatures of 304 stainless steel and γ-Fe precipitates stabilized in the copper lattice have been determined by making use of the Mossbauer effect.
Abstract: The Neel temperatures of 304 stainless steel and γ‐Fe precipitates stabilized in the copper lattice have been determined by making use of the Mossbauer effect. The Neel temperature for the stainless steel is 38°±2°K and for two different sizes of γ‐Fe precipitates, the Neel temperatures are 55°±3°K and 67°±2°K. The measured Neel temperatures are compared with previous determinations by other methods and the variation of the Neel temperature of precipitates in the Cu—Fe system is discussed. Estimates are made of the magnetic field at the iron nucleus for each case.