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In this paper it is shown that the statistical theory of the distribution of extreme values is pertinent to the study of the way in which the breakdown strengths of paper capacitors depend on capacitor size. The theory presented in this paper permits a quantitative explanation of this phenomenon and results are given which should be useful to design engineers.

The dynamic Young's moduli of various types of paper were measured by the vibrating reed method. The Young's modulus of paper increases statistically at a rate approximately proportional to the square of its density. The modulus and density of paper increase with the degree of beating. The sulfite and sulfate fibers behave differently during beating. The angular dependence of Young's modulus, tensile strength, and elongation at break was analyzed mathematically; and the results were verified by experiments. According to this theory, the mean value of Young's modulus and tensile strength of machine‐made paper should be expressed by the geometrical mean of the values of the machine and cross directions, whereas the mean value of elongation can be given by the arithmetical mean. The removal of parenchyma cells is very effective in reducing the Young's modulus of dissolving pulp. The viscoelastic properties of paper were observed within the frequency range from 20 to 180 cps. The dynamic modulus and mechanical loss factor of the sheets employed were found to be smaller than one‐tenth of those of cellulose films. The interfiber deformation influences the dynamic properties of paper.

A stress‐strain analysis of single cubic crystals is developed which utilizes the strain data supplied by the x‐ray back‐reflection divergent beam method. The principal strains and their directions are determined and from the principal strains and the known elastic constants the complete stress‐strain configuration is obtained. Thus the maximum magnitude and the direction of the shearing strain on a given set of crystallographic planes are obtained and the set of planes on which the maximum value of the shearing maxima occurs is also determined. From a knowledge of the stress‐strain configuration, the stored elastic energy of the crystal is deduced; it can be partitioned into two components, that due to shearing strains and that due to a mixture of normal and shearing strains.The conditions under which the principal stress system coincides with the principal strain system are also investigated. Furthermore, a number is constructed that measures the distortion of the crystal in terms of the energy incremen...

An infinite sum transformation is defined and applied to a system of linear difference equations discussed by Faust and Beck in their paper on single tuned amplifiers. Some transforms of the more common functions are given and points of superiority of the transform method over the classical methods of solution of difference equations are emphasized.

This paper describes a pulse technique for measuring the properties and charge‐transfer characteristics of electrographic receptors. This method has the unique capability, as compared with electrometer methods or ac bridge methods, of separately measuring the charge deposited on the surface of the dielectric layer, the displacement charge, and the charge passing through the dielectric. The technique is used to obtain a detailed analysis of the electrographic properties of a dielectric coated paper, including the relaxation of the paper substrate, the capacitances of the virtual air gap and the dielectric layer, and the threshold voltage for charge transfer.

A computer program has been written to produce pole figures using the data from an x‐ray texture goniometer. The data are corrected for background and absorption. The pole figure is also stored on magnetic or paper tape in a form suitable for quantitative calculations. As an example, the Hall coefficient of a poly‐crystalline sample of a close‐packed hexagonal material is computed from the pole figure of the sample in terms of the single‐crystal components of the Hall tensor.

Two scanning techniques are now being used to determine the vibrational patterns and far‐field sound radiation of complex vibratory systems. One technique is a near‐field scanning apparatus which scans the vibrator and gives a three‐dimensional display on graph paper of the nodal patterns. The other scanning technique uses the principles of holography to locate far‐field sound sources on the vibrator. These two methods, coupled together, have demonstrated a unique capability to locate acoustic sources and hot spots on vibratory systems.

The detection statistics of a light beam with randomly fluctuating intensity are of considerable interest. This paper derives an explicit form for the photocount statistics of a laser beam in the presence of an interfering background radiation. The result can be readily utilized to obtain the over‐all photocount statistics by appropriate averaging over the random laser‐beam intensity. The technique is quite suited to experimentally determined probability density. The analysis developed in this paper is applied to the propagation of light through turbulent media. Numerical results are obtained for the over‐all photocount statistics for the two often considered probability distributions in this case: lognormal and Rice‐Nakagami. The photocount distribution for the lognormally fluctuating medium is then utilized to obtain the probability of error and information rate for a laser binary communication system.

The usefulness of ion‐induced x‐ray yields to detect low‐Z impurity atoms at low concentration in medium‐Z targets and to locate their lattice sites in single crystals is established in this and the paper that follows. In paper I we describe the technique used with specific reference to phosphorus and sulfur implants in germanium crystals. Particular attention was given to the origin of the different components that constitute the backgrounds in the x‐ray energy spectrum. Peak‐to‐background ratios for these two impurity signals were then determined for H and He ions in the energy region from 0.5 to 2.0 MeV. Some results for N and Ar ions were also obtained. A beam of 0.5‐MeV H+ gave optimum conditions for foreign atom location studies.

In the preceding paper, Paper I, we described an analytical technique, based on ion‐induced x‐ray yields, for detecting low‐Z impurities in medium‐Z targets. In this paper, Paper II, we report the application of this method to the lattice location of impurity atoms. Two systems have been examined to test the method, viz., P and S implants in Ge single crystals. The channeling effect was applied to the phosphorus and sulfur K x‐ray yields excited by 0.5‐MeV protons. Some 93% of implanted 31P (0.7 × 1015 atoms cm−2, room‐temperature implant, 450°C anneal), were found to occupy substitutional sites; the fraction dropped to [inverted lazy s] 63% for an implant dose of 2.7 × 1015 atoms cm−2. Channeling effect results in 〈110〉, 〈111〉, and 〈100〉 directions for Ge(S), implanted at room temperature and annealed at 450°C, prescribe a preferred off‐lattice (> 0.3 A) site for the sulfur, necessarily different from the regular tetrahedral or hexagonal interstitial sites. For hot (220°C) implantation conditions, poorer...

Thin films of bismuth‐germanium have been fabricated in vacuum by the method of codeposit vapor quenching onto liquid nitrogen or water‐cooled substrates. In this paper, Paper II of a two‐paper series, the optical and photoelectrical characterization of these films are reported. Transmittance, reflectance, and absorptance data are reported in the spectral range 0.2–3.0 μ for BixGe1−x thin films in the composition range 0 ≤ x ≤ 0.25. Ultraviolet/visible near‐normal reflectance spectra for films in the amorphous phase (0 ≤ x ≤ 0.2) closely resemble the optical reflectance spectra of amorphous germanium. The reflectance spectra of the amorphous films were static and insensitive to an increase in bismuth concentration. Additionally the spectra were devoid of any optical remnants of the crystalline spectra of either germanium or bismuth. The reflectance spectra of a Bi0.25Ge0.75 film which was x‐ray polycrystalline revealed a broad local maximum near 2 eV, indicating crystalline bismuth transitions and the exi...

This paper supplements and assesses an optical measuring technique for the local determination of the cubic and uniaxial anisotropy fields K1/Ms and Ku/Ms in uniaxial magnetic films reported in a recent paper. Graphs for the quick evaluation of the Ku/Ms values are given. The accuracy of the method is assessed by comparison with FMR measurements. The origin of the nonuniformity in the domain pattern of a (111) LPE garnet film with the chemical composition Y2.5Gd0.5Fe4Ga1O12 grown on a GGG substrate is investigated by local optical measurements of the magnetic film parameters K1/Ms, Ku/Ms, compensation temperature, and magneto‐optic Faraday rotation. It is correlated with local structural parameters of the substrate as stress birefringence from ellipsometric measurements and inhomogeneity of the lattice constant measured by x‐ray topography.

This paper presents parametric studies of the performance of a 10‐liter atmospheric‐pressure CO2 laser system controlled by a 4‐μsec pulse of electrons from a cold‐cathode gun. The experimental results are compared to the predictions of a theoretical model described in this paper. For various laser gas mixtures and values of E/P the peak small‐signal‐gain coefficients range up to 4.7% cm−1. Measurements of gain uniformity across the laser medium and of the time dependence of the small‐signal gain are also presented. Operation of the device as an oscillator over a range of parameters has shown that the output pulse typically consists of a sharp gain‐switched spike followed by a longer tail with energies up to 30 J in the spike and 200 J in the entire pulse. The theoretical model generally predicts peak small‐signal gain well for gas mixtures containing nitrogen; the largest discrepancy is for pure CO2 gas. The model also predicts the shapes of oscillator pulses satisfactorily.

Thin films of bismuth‐germanium have been fabricated by the method of codeposit vapor quenching onto liquid nitrogen or water‐cooled substrates. Structural, electrical, optical, and photoelectrical characterizations of these films have been accomplished. In this paper, Paper I of a two‐paper series, the structural and electrical characterization results are reported. X‐ray diffraction measurements indicate that a stable amorphous phase exists for the BixGe1−x thin‐film system for 0 ≤ x ≤ 0.12. Low‐field dc resistivity as a function of temperature from room temperature to liquid‐nitrogen temperature and relative thermopower measurements show that in the amorphous range the BixGe1−x thin films are n‐type semiconductors with a continuously decreasing thermal activation energy as x increases. The resistivity of amorphous bismuth‐germanium films decreases with an increase in bismuth concentration. Current‐voltage data taken on several films at 300 and 162°K indicate Ohmic behavior with no evidence of Poole‐Fre...

The polymer crystal lamellar growth rate G is an often‐measured property of semicrystalline polymers. In this paper, we investigate the dependence of G upon the length of the substrate, L, the surface nucleation rate of new growth layers per unit length per unit time, i, the velocity with which the growth layer covers the substrate, g, and the thickness of the growth layer, b. For the purposes of this paper, L is the average length where the polymer segments in the substrate are in crystallographic register. We show that G = biL/n, where n is the average number of nuclei that contribute to each growth layer. We show that n depends only on the dimensionless parameter z = iL2/4g. We have not obtained n explicitly, but we can place upper and lower limits on n that closely define G in regime I, where G ≃ biL and into a transition region between regime I and regime II where G ∞ b(ig)1/2. The experimental results for several polymers are analyzed and some are found to be in or near regime I, and others in ...

This paper extends the theory of magnetic domains with emphasis on recent developments in ``hard bubbles''. A spin configuration of a planar Bloch wall containing periodic Bloch lines is presented which minimizes the magnetostatic energy to first order in the parameter 2πMs2/Ku for arbitrary period. The form of this solution is found to suggest the form of the dynamic breakdown of this spin configuration. The remainder of the paper consists of applications of the gyrocoupling force and vector, fg = g × v and g = − (Ms/|γ|)sinθ(▿θ) × (▿φ), respectively, and the dissipation force and dyadic, fa = d · v and d = − α(Ms/|γ|)[(▿θ)(▿θ) + sin2θ(▿φ)(▿φ)]. The use of fg and fa produces results with fewer assumptions and with less calculation than with previous methods. The magnitude of g is found to be an invariant local measure of the ``hardness'' of the domains. Integrating fg and fα produces a general planar wall response function from which the hard bubble dynamic equation is obtained. It is found that the difference between the hard bubble and normal bubble damping parameters can be accounted for by examination of the hard bubble spin‐wave spectrum. An estimate of the velocity required for the production of horizontal Bloch lines is made using fg. This velocity is a substantial fraction of the Walker velocity. The vector g is used as an aid in the visualization of the mechanism by which ion implantation suppresses hard bubbles. From the point of view of both mobility and hard bubble suppression, materials having a large in‐plane anisotropy are found to be desirable.

In a previous paper, the simple Maxwell‐Garnett theory of aggregated metal systems was analyzed in the free‐electron regime for low damping (ωpτ>1). Expressions were derived for the magnitude and resonance frequencies of plasma and conduction resonances as functions of particle constants and the aggregation parameter. In this paper the effect of moderate and high damping (ωpτ≲1) and the effect of a dielectric interparticle matrix with n > 1 is examined, and the results are compared with experiment.

Results of a precise determination of the ir absorption strength of H and D in rutile are presented, which permit determination of H or D concentration to an accuracy of 3%. The integrated absorption per ion was (2.51±0.09)×10−17 and (1.33±0.05)×10−17 cm for H and D, respectively. The procedure for calculating the H or D concentration in a particular sample from the ir absorption peaks is illustrated. Used in conjunction with the results of the theoretical analysis of the preceding paper, this technique makes possible the accurate determination of the energy and density of all electron trapping levels in TiO2 crystals. We also describe results showing that heat treatment in a dry H2 atmosphere at ∼800 °C results in the introduction of Ti intersititials but negligible H in the crystal, as predicted by the preceding paper. A technique for measuring diffusion parameters of H and D under conditions of strict chemical equilibrium, thus avoiding the large departures from Fick's law which usually plague such measurements in materials such as TiO2, is also described.

In the present paper we investigate theoretically the generation of thickness‐twist modes in a plate of piezoceramic material. The poling axis is chosen parallel to the plane boundaries of the plate. On one of the faces of the plate a finite number of cylindrical strip electrodes of vanishing thickness is present. If an electric generator is connected to the electrodes, piezoelectric thickness‐twist modes are generated. Our problem is to calculate the amplitudes of the different modes and the input impedance of the transducer. To this aim we employ our integral equation formulation of piezoelectric diffraction problems that has been presented in an earlier paper. Once the resulting system of integral equations has been solved, the field distribution on the electrodes is obtained. Then the input impedance of the transducer can be calculated, and with the aid of appropriate integral representations the amplitudes of the different modes are obtained.

The theory of prediction described in this paper is essentially an extension of Wiener's theory. It differs from the latter in the following respects.1. The signal (message) component of the given time series is assumed to consist of two parts, (a) a non‐random function of time which is representable as a polynomial of degree not greater than a specified number n and about which no information other than n is available; and (b) a stationary random function of time which is described statistically by a given correlation function. (In Wiener's theory, the signal may not contain a non‐random part except when such a part is a known function of time.)2. The impulsive response of the predictor or, in other words, the weighting function used in the process of prediction is required to vanish outside of a specified time interval 0≤t≤T. (In Wiener's theory T is assumed to be infinite.)The theory developed in this paper is applicable to a broader and more practical class of problems than that covered in Wiener's theory. As in Wiener's theory, the determination of the optimum predictor reduces to the solution of an integral equation which, however, is a modified form of the Wiener‐Hopf equation. A simple method of solution of the equation is developed. This method can also be applied with advantage to the solution of the particular case considered by Wiener. The use of the theory is illustrated by several examples of practical interest.

With certain systems the cross section for desorption of surface atoms by low‐energy electrons is negligibly small. Desorption will not take place unless the electrons have sufficient energy to impart the required momentum by direct exchange. The present paper is relevant to such systems. Given a high‐energy electron traversing a solid and emerging from the surface, there exists a finite probability that the electron will suffer a deflection in the Coulomb field of the nucleus of a surface atom and thereby impart sufficient momentum to the atom to result in its desorption. Assuming that a value for the binding energy is given, the paper sets forth the several considerations which must have a part in the computation of the desorption cross section as a function of electron energy. Calculated values are presented for the case of adsorbed thorium over a wide range of assumed binding energies and for electron energies up to 2 MeV. Results of the mechanical integrations are plotted in such a form that cross sections for other atomic species can be obtained by simple calculation.

The dielectric constant and permeability of a metallic‐obstacle medium are obtained in this paper by various static methods. The equivalent shunt capacitive susceptance and series inductive reactance of the individual obstacles are also determined. In the first part of the paper, a correspondence is established between an infinitely thin conducting obstacle and an aperture in an infinitely thin conducting wall. With the aid of this correspondence, delay medium formulas are given for several obstacle shapes. Formulas are then derived for the effect on the magnetic field of moderate obstacle thickness. Finally, it is shown how the electric and magnetic constants may be evaluated by electrolytic tank measurements in the case of obstacles having completely arbitrary shape and thickness. This has been done for a typical delay medium, and the effect of obstacle thickness on the index of refraction is shown.