January-March 1967

Symmetrical bending of thin circular elastic plates on equally spaced point supports, A. F. Kirstein and R. M. Woolley, J. Res. NBS, 71C1-438, pp. 1-10 (Jan.-Mar. 1967).

Key words: Circular plates; concentric loading; design; elasticity; experiment; maximum stresses; symmetrical bending; symmetrically distributed load; theory.

A special application of Bassali's solution for transverse flexure of thin elastic plates supported at several points is presented for the case of symmetrical bending. Equations for moments, shearing forces, and stresses are developed which may be useful for design purposes. The experimental results although limited in quantity are in good agreement with the theoretical predictions.

Ultrasonic measurement of cylinder expansion at pressures to 40 kilobars, P. L. M. Heydemann and J. C. Houck, J. Res. NBS, 71C1-439, pp. 11-17 (Jan.-Mar. 1967).

Key words: Compressibility; cylinder distortion; high pressure; nickel; tellurium; ultrasonics.

For the accurate determination of internal pressures in solidfilled piston and cylinder devices the effective area and its change with pressure are very significant factors. The computation of the change of area with pressure from elastic theory leads however to considerable uncertainties.

The present paper describes how ultrasonic measurements made in solid-filled piston and cylinder devices to 45 kilobars are combined with measurements of the lengths of the samples as function of pressure and with ultrasonic measurements under hydrostatic pressure to yield values for cylinder expansion. The results are compared with values obtained from modified elastic theory.

A comparison of absorbed dose determinations in graphite by cavity ionization measurements and by calorimetry, B. Petree and P. Lamperti, J. Res. NBS, 71C1-440, pp. 19-27 (Jan.-Mar. 1967).

Key words: Absorbed dose; calorimeter; cavity ionization chamber; cobalt-60 gamma rays; comparison; graphite; W.Sm.

The absorbed dose in graphite from a cobalt-60 gamma-ray source was measured with a spherical air-filled cavity ionization chamber and with two spherical calorimeters. The instruments were constructed from high-purity graphite. The current per unit mass of air and the absorbed power per unit mass of graphite were determined with uncertainties of 0.40 and 0.17 percent respectively. When the two results are combined the value of Wair 5m is found to be 33.72 electron volts in graphite per ion pair in air, with an uncertainty of ±0.14 electron volts.

Germanium resistance thermometry in the range 2.1 to 5.0 °K, M. H. Edlow and H. H. Plumb, J. Res. NBS, 71C1-441, pp. 29-41 (Jan.-Mar 1967).

Key words: Calibration of germanium resistors; germanium resistors; thermometry.

The resistances of three encapsulated, hermetically sealed, arsenic-doped germanium resistors from a commercial source have been measured at every 0.1 °K from 2.1 to 5.0 °K in highly stabilized liquid helium baths; values of temperature were derived from vapor pressure measurements associated with the liquid bath.

Ten similar germanium resistors of common origin have been calibrated from 2.1 to 5.0 °K in a calibration comparator apparatus that is similar to a calorimeter in design. Calibrations were performed against a resistor that had been previously referenced to temperature through a helium-4 vapor pressure calibration.

Next, three of the resistors that were calibrated in the comparator apparatus were recalibrated in a liquid helium bath (at 2.2, 3.0 and 4.2 °K) and results from the two methods agree within 1 milli-degree. The resistance-temperature data from both methods have been fitted to the polynomial equation

Least squares technique for the analysis of periodic temperatures of the earth's surface region, T. Kusuda, J. Res. NBS, 71C1442, pp. 43-50 (Jan.-Mar. 1967).

Key words: Earth temperature; least squares technique; thermal diffusivity of earth.

A least squares technique has been applied to periodic earth temperature data for the purpose of determining basic characteristics of earth temperature cycles, such as thermal diffusivity, average temperature, amplitude, and phase angle of the temperature cycle. A new procedure was developed for obtaining a single thermal diffusivity which represents an average over time and depth at a particular temperature site. This thermal diffusivity was obtained as a nonlinear part of least squares constants which yielded a best-fit harmonic curve to a given set of observed earth temperatures. The thermal diffusivity thus calculated and the calculation method developed are preferred to those obtained by current practice, which yields two thermal diffusivities, one based on amplitude decay and another on phase angle shift.

A new near-zone electric-field-strength meter, F. M. Greene, J. Res. NBS, 71C1-443, pp. 51-57 (Jan.-Mar. 1967).

Key words: Device, electroexplosive ordnance; field, nearzone electromagnetic; hazards, electromagnetic radiation; line, nonmetallic electrical transmission; line, semiconducting plastic transmission; meter, electric field-strength; telemetry, novel form of.

The National Bureau of Standards has recently completed the development of prototype instrumentation for measuring the electric-field components of complex, high-level, near-zone electromagnetic fields. The instrumentation is intended for use in evaluating hazards of high-level electromagnetic radiation to electroexplosive ordnance devices at military installations. The

measuring range is from 0.1 to 1000 V per meter, at frequencies from 150 kHz to 30 MHz, with a present uncertainty of less than +2 dB.

The design of the NBS meters is based on the use of a novel form of telemetry, which apparently has not been fully exploited heretofore. This involves the use of a completely nonmetallic electrical transmission line over which the field information is transmitted from the measuring antenna to a remote readout unit. The line is essentially "transparent" to the field being measured, and reduces the perturbation of the field two orders of magnitude below that normally experienced when using a metallic line. The high r-f line loss involved necessitates miniaturizing the r-f portions of the receiving and calibrating instrumentation and placing them and their associated battery supplies inside the measuring antenna. The design and performance of the meters are discussed in some detail.

Inductance and characteristic impedance of a strip-transmission line, R. L. Brooke, C. A. Hoer, and C. H. Love, J. Res. NBS, 71C1-444, pp. 59-67 (Jan.-Mar. 1967).

Key words: Characteristic impedance; inductance; and strip-transmission lines.

A general method is developed for determining the inductance and characteristic impedance of uniform transmission lines. A non-uniform current distribution is allowed in the transverse plane. The system is represented by a matrix equation which can be programmed for computer solution. The correct inductance and impedance are obtained as the result of a simple limiting process. The method is applied to one particular geometry, a four-tape stripline system. Results are given for the inductance, resistance, and current distribution as functions of frequency and resistivity for a particular geometry. A method for extending the results to strip lines with proportional dimensions is developed. An accuracy of one part in 105 was found to be feasible for the determination of the inductance per unit length.

Tensor permeability measurements at L-band frequencies using a degenerate mode cavity, L. B. Schmidt, R. D. Harrington, and W. E. Case, J. Res. NBS, 71C1-445, pp. 69-75 (Jan.-Mar. 1967).

Key words: Degenerate mode cavity; L-band cavity; polycrystalline garnets; tensor permeability.

The exact solution for the field equations of a cylindrical TM110 mode cavity has previously allowed accurate measurements of tensor permeability to be obtained at X-band frequencies. It is demonstrated that this method is also applicable at frequencies down to 1 GHz. A brief description of the cavity and measurement system for obtaining data at these lower frequencies is given. Both intrinsic and external permeability results on three commercially available polycrystalline garnets are shown. The larger size rods required for measurements at these frequencies result in some sample size effects in the data. In addition, a previously unreported absorption in the external tensor permeability of the materials was observed.

April-June 1967

An apparatus for measuring thermal expansion at elevated temperatures, B. D. Rothrock and R. K. Kirby, J. Res. NBS, 71C2-247, pp. 85-91 (Apr.-June 1967).

Key words: Controlled-gradient vacuum furnace; elevated temperatures; optical comparator; thermal expansion.

An apparatus has been developed for making precise measurements of the absolute thermal expansion of refractory materials at temperatures up to 1600 °C. This apparatus consists

of an optical comparator and a controlled gradient vacuum furnace. Special care was taken on the techniques of measuring length and temperature and on the calibration of the microscopes and thermometers. The expansion data obtained with this apparatus on specimens of platinum and sapphire have a standard deviation of less than 30 ppm and are estimated to be accurate to within 50 ppm.

Determination and smoothing of Fourier coefficients representing piecewise continuous functions, B. A. Peavy, J. Res. NBS, 71C2-248, pp. 93-100 (Apr.-June 1967).

Key words: Continuous function; Fourier series; piecewise; smoothing.

This paper presents a method of solving for Fourier coefficients where the dependent variable can be expressed as a piecewise continuous function, when various conditions of continuity and smoothing are assumed. An example is included to show the effect of smoothing in the region of a discontinuity for a system composed of two materials that exhibit a discontinuity at their interface and surrounded by a third material which does not have a discontinuity. An advantage to be gained from smoothing is an increase in the convergence of a finite Fourier series representation of a piecewise continuous function in the region of the discontinuities.

A 2:1 ratio inductive voltage divider with less than 0.1 ppm error to 1 MHz, C. A. Hoer and W. L. Smith, J. Res. NBS, 71C2-249, pp. 101-109 (Apr.-June 1967).

Key words: Attenuator; bridge; high frequency; inductive voltage divider; ratio transformer.

A simple ratio transformer having a 2:1 ratio of input voltage to output voltage can be made with a ratio error less than 0.1 ppm from 1 kHz to above 1 MHz. Applications and sources of error are discussed. Experimental results leading to an optimum transformer design are given. A bridge to measure the ratio error to 0.025 ppm from 1 kHz to 1 MHz is also described.

A dual-load flow calorimeter for rf power measurement to 4 GHz, M. L. Crawford and P. A. Hudson, J. Res. NBS, 71C2-250, pp. 111-117 (Apr.-June 1967).

Key words: Coaxial; flow calorimeter; radio frequency power.

A new dual-load flow coaxial calorimeter power meter has been constructed at the National Bureau of Standards, Boulder Laboratories. Designed for use as a reference standard, the frequency range of the calorimeter extends up to 4 GHz and beyond. The power range extends from 2W to 100W with an error limit of 0.38 percent.

Design details, error analysis, and results of intercomparison with other standards are given.

Polymeric materials for dielectric reference specimens, A. H. Scott and J. R. Kinard, Jr., J. Res. NBS, 71C2-251, pp. 119125 (Apr.- June 1967).

Key words: Dielectric constant; dissipation factor; frequency; fluorinated ethylene-propylene; humidity; polycarbonate; polyethylene; poly(1,4-cyclohexylenedimethylene terephthalate); polystyrene; poly(tetrafluoroethylene); time; reference specimens.

The results from a study of the effects of aging and humidity change on certain polymer specimens indicate it is possible to establish stable dielectric reference specimens. Specimens of polyethylene, polystyrene, polycarbonate, poly(tetrafluoroethylene) (PTFE), fluorinated ethylene-propylene polymer (FEP), and poly(1,4-cyclohexylenedimethylene terephthalate) were used in the investigation. Slow changes in the dielectric proper

ties were observed on some specimens over a period as long as three years. Very long timed humidity runs indicate PTFE, and FEP to only a slightly less degree, are best suited for dielectric reference specimen preparation.

The sensitivity of the Dicke radiometer, D. F. Wait, J. Res. NBS, 71C2-252, pp. 127-152 (Apr.-June 1967).

Key words: Dicke; microwave; radiometer; sensitivity; switching.

The literature is reviewed concerning the sensitivity of the Dicke radiometer, excluding gain fluctuations. Discrepancies are pointed out and a new derivation of sensitivity using a Fourier transform method is used to resolve these discrepancies and to extend the results to radiometers with lossy switches.

Experimentally it is shown that radiometers using a half-wave square-law, linear-law, intermediate-law, or envelope detectors all have a sensitivity equal to the theoretical full-wave squarelaw detector (within the ±20 percent uncertainty of the experiment).

Sensitivity of a correlation radiometer, J. J. Faris, J. Res. NBS, 71C2-253, pp. 153-170 (Apr.-June 1967).

Key words: Correlation radiometer; differential time delay; gain fluctuations; imperfect multiplier; noise comparison; nonidentical amplifiers; sine-wave comparison signal.

The correlation radiometer is analyzed to determine the sensitivity that can be obtained under various operating conditions.

The radiometer using a sine wave comparison signal is analyzed and compared with the usual radiometer that employs a random noise for the comparison signal. It is found that the radiometer employing the sine wave comparison signal is the more sensitive of the two circuits, particularly in the case that the effective temperature of the input noise signal is greater than the effective input temperature of the amplifiers.

It is shown that if nonidentical amplifiers are used in the correlation circuit, the properties of the radiometer are determined by the portion of the amplifier response functions in the frequency interval that the two response functions overlap. The effect of amplifier gain fluctuations are considered, and although the correlation scheme reduces the effect of gain fluctuations, it is shown that they still do contribute to the output fluctuations of the radiometer.

Calculations are included showing that the effect of a differential phase shift between the two channels is a reduction in radiometer sensitivity. The same conclusion is reached concerning the effect of a differential time delay.

Finally, it is shown that if the comparison signal and the input signal have the same statistical properties, the requirements on the multiplier are less stringent than if the two signals have different statistical properties.

July-September 1967

Procedure for high precision density determinations by hydrostatic weighing, H. A. Bowman and R. M. Schoonover with Appendix by M. W. Jones. J. Res. NBS 71C3-254, pp. 179198 (July-Aug. 1967).

Key words: Air density; balance: balance calibration; balance equilibrium; balance sensitivity; density; double substitution weighing; hydrostatic balance; hydrostatic weighing; silicon density: substitution balance; volumetric measurement; water density; water weighing.

There are several simplifications which can be made in the performance of the hydrostatic experiment which lead to more

reproducible results. The operation of single-pan two-knife balances is discussed, and simple modifications suggested to adapt it to hydrostatic work. A data philosophy is presented which will be particularly applicable to a generation of nowdeveloping force measuring instruments when used in hydrostatic work. A simplified formula for air density is presented and a formula for estimating day-to-day variability in the density of water. A simple balance calibration procedure is presented in an appendix, and simplified methods of fabricating suspension wires and degassing sample surfaces are described. The use of these techniques is illustrated by measurements on silicon crystals which indicate process reproducibility of a standard deviation to about one part per million.

Study of the storage stability of the barium fluoride film electric hygrometer element, F. E. Jones, J. Res. NBS 71C3-255, pp. 199-207 (July-Sept. 1967).

Key words:

Adsorption; barium fluoride; electric hygrometer; humidity; thin films; vacuum.

A study of the aging properties of the barium fluoride film electric hygrometer element and of possible causes of the drift of calibration with time in storage has been made. It was found that exposure of aged elements to glow discharge bombardment resulted in near recovery of the prestorage calibration. indicating that the calibration drift was not irreversible and providing insight into the mechanism of aging. Based on the likelihood that aging was due, at least in part, to contamination of the barium fluoride film. production procedures were formulated which resulted in elements with significantly reduced drift. If an adjustment is made similar to the "lock-in" procedure in the operational use of radiosonde humidity elements, then the poststorage resistance values can be adjusted to correspond closely to the prestorage calibration curves. Experimental evidence supports the hypothesis that contamination of the elements by diffusion pumping fluid in the production process was a source of the calibration drift. Applications of the element as a research tool in cloud physics, atmospheric turbulence and radio refractive index structure studies. evaporation and evaporation reduction studies, water vapor flux determinations. and tropospheric humidity distribution studies are mentioned. Torsion creep of circular and noncircular tubes, L. Mordfin, J. Res. NBS 71C3-256, pp. 209-225 (July-Sept. 1967).

Key words: Creep; primary creep; shear; shell; stress analysis; thin wall; torsion; tube.

A torsion creep theory for noncircular tubes was developed by applying a multiaxial creep theory to a derived generalization of Bredt's equations.

A review of the literature revealed no torsion creep data on noncircular tubes. Hence, to evaluate the theory, a test program was carried out on twelve specimens of aluminum alloy structural tubing, of four configurations, at 400 °F.

Observed discrepancies between the torsion creep theory and experiment are smaller than variations in the measured creep properties of the specimen material from one tube configuration to another and are not appreciably greater than discrepancies between elastic torsion theory and experiment. Most of the observed discrepancies are consistent with measured anisotropy in the tubes. while other discrepancies are ascribed to nonhomogeneity in creep properties and a hydrostatic stress effect in multiaxial creep.

For the calculation of torsion stresses in circular tubes the thin-wall approximation is adequate for thickness-to-radius ratios up to one-tenth. For straight-sided tubes equivalent accuracy is obtained for effective ratios up to only one-twentieth. These criteria apply to creep conditions as well as to elastic conditions.

Digitized low-frequency phasemeter assembled from logic modules, J. E. McKinney, J. Res. NBS 71C3-257, pp. 227-238 (July-Sept. 1967).

Key words: Digital; phasemeter; logic circuit; low frequency; measurements; phase.

A digital phasemeter is described which is capable of operating from arbitrarily low frequencies to 10 kHz, for which the lower limit depends essentially upon the time available to the operator to make the measurement. The phasemeter involves a logic circuit which can be assembled easily from commercially available logic modules without the necessity of a proficiency in electronics. The output of the logic circuit is read into a conventional digital preset frequency-ratio meter. determination is absolute and utilizes a time base. Accordingly. no calibration against a phase standard is necessary. agreement between this phase meter and a quality phase shifter was found to be within ±0.01° at 400 Hz, which is the accuracy specified by the manufacturer of the phase shifter. Considerable ability to ignore signal imperfections is inherent in this device.

October-December 1967

The

The

Measurements of the thermal conductivity and electrical resistivity of platinum from 100 to 900 °C, D. R. Flynn and M. E. O'Hagan. J. Res. NBS 71C4-258, pp. 255-284 (Oct.-Dec. 1967).

Key words: Conductivity; electrical conductivity; electrical resistivity: heat conductivity; Lorenz function; platinum; reference material; resistivity: standard: thermal conductivity.

Measurements have been made of the thermal conductivity and the electrical resistivity of commercial grade platinum (99.98% pure) in the temperature range 100 to 900 °C. The measurements have been made with a view to providing accurate data on the thermal conductivity of platinum to serve as a basis for establishing platinum as a thermal conductivity standard reference material. Two methods of measuring the thermal conductivity have been employed, one an electrical method and the other a nonelectrical method. In the electrical method, a direct current passed through a necked-down portion of the specimen and the thermal conductivity was determined in terms of the temperature and electrical potential distributions in the necked-down region. The second method was of the absolute guarded longitudinal heat flow type. The experiment was designed to permit measurements by both methods in the same apparatus and on the same specimen thereby providing as direct a comparison as possible between the methods. The data given by the two methods agree within experimental error and show the thermal conductivity of platinum to be a smoothly increasing function of temperature in the measured range. Additional measurements on samples of differing purities are necessary before platinum could be adopted as a thermal conductivity reference material.

Thermal conductivity and electrical resistivity of Armco iron, T. W. Watson, D. R. Flynn, and H. E. Robinson, J. Res. NBS 71C4-259. pp. 285-291 (Oct.-Dec. 1967).

Key words: Armco iron; conductivity: electrical conductivity; electrical resistivity: heat conductivity; heat transfer: iron: Lorenz function: resistivity: thermal conductivity.

New data are presented for the thermal conductivity and electrical resistivity of two samples of Armco iron. On a sample of material used in a round robin comparison between several laboratories, thermal conductivity was measured from - 160 to +640 °C and electrical resistivity was measured from 195 to

+1380 °C. On a sample of cold-worked Armco iron from a different lot, data are reported from 150 to + 200 °C.

Heat flow in a right circular cylinder with internal heat generation: Applications to the determination of thermal conductivity, D. R. Flynn. J. Res. NBS 71C4-260, pp. 293-298 (Oct.-Dec. 1967). Key words: Heat conduction: heat generation; heat transfer: neutron absorption; radioactive decay: thermal conductivity.

Expressions are developed which permit calculation of the temperature-dependent thermal conductivity of a cylindrical specimen in which heat is generated internally. e.g.. by radioactive decay. The information needed consists of the experimentally determined temperature distributions on the surfaces of the cylinder, the heat flow through a central circular area at one end of the cylinder, and the rate of internal heat generation (which in general may be position-dependent). Numerical coefficients are tabulated for the case of uniform internal heat generation. The application of this calculation procedure to published methods of thermal conductivity determination is shown and an example is given.

Radiation-induced acoustic cavitation: Apparatus and some results, M. Greenspan and C. E. Tschiegg. J. Res. NBS 71C4261, pp. 299-312 (Oct.-Dec. 1967).

Key words: Acoustic cavitation; alpha-particle-induced cavitation; cavitation; cavitation nucleus; cavitation threshold: fission-induced cavitation: neutron-induced cavitation; radiation-induced cavitation: threshold. Equipment and techniques for acoustic cavitation work are described. The test liquid and its container form part of a selfsustaining programmable oscillator. Emphasis is laid on the treatment of the liquid necessary to yield reproducible results after artificial nucleation, especially by neutrons. a-recoils, and fission. With neutrons, for instance, the cavitation rate rises rapidly with acoustic (negative) pressure, and at fixed pressure is proportional to neutron flux. The cavitation events are random. and no appreciable induction or decay times are observed. Each cavitation arises from the action of a single neutron (or a-recoil. or fission). The cavitation "threshold" (roughly negative pressure below which cavitation is rare) is highly variable from liquid to liquid. Thresholds at about room temperature for liquids irradiated with 10 MeV neutrons ranged from 1 to 2 bars for n-pentane, ether, and freon 113 to over 50 bars for water. Design of a new Kossel pattern generator, D. L. Vieth and H. Yakowitz, J. Res. NBS 71C4-262. pp. 313-318 (Oct.-Dec. 1967).

Key words: Divergent x-ray beam: instrument design:
Kossel camera: Kossel method: x-ray instrumentation.

A Kossel pattern generator. designed and built at the National Bureau of Standards, is described in detail. The unit is modular and consists of an electron beam column, vacuum system, light microscope, film cassette, and Kossel camera. The camera component includes microgoniometric capabilities. The Kossel x-ray technique enables the investigator to obtain lattice spacing data precise to two or three parts per million, and orientation of crystals to 0.1° of arc. The Kossel pattern generator described permits data for such determinations to be obtained quickly and precisely.

The near-zone magnetic field of a small circular-loop antenna, F. M. Greene. J. Res. NBS 71C4-263, pp. 319-326 (Oct.-Dec. 1967).

Key words: Loop-antenna field strength; magnetic fieldstrength standard; mutual inductance of coaxial circular filaments: near-zone magnetic field; transmitting loop

antenna.

An improved formula is derived for accurately computing the near-zone magnetic field of a small circular transmitting loop antenna. Such a field can serve as a reference standard for calibrating field-strength meters employing small receiving loop antennas in the frequency range 30 Hz to 30 MHz.

This formula includes correction terms for frequency (due to the finite time of propagation), as well as corrections for the finite radii of both the transmitting and receiving loops. Other formulas appearing in the literature often fail to include such

corrections which can result in errors of up to 20 percent and more in computing standard-field values.

The NBS formula is derived by expanding the integrand of the retarded vector potential into an infinite series of spherical Hankel functions of increasing order. The resulting series expression is in error by less than 0.2 percent, is rapidly converging and simple to use without recourse to a table of functions or a computer.