Electrical Resistivity of BoronE. S. Greiner and J. A. Gutowski Citation: Journal of Applied Physics 28, 1364 (1957); doi: 10.1063/1.1722660 View online: http://dx.doi.org/10.1063/1.1722660 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/28/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Electrical transport of tetragonal boron nanobelts J. Vac. Sci. Technol. B 23, 2510 (2005); 10.1116/1.2131870 Electrical transport in boron nanowires Appl. Phys. Lett. 83, 5280 (2003); 10.1063/1.1630380 Anisotropy of the electrical conductivity of boron carbide AIP Conf. Proc. 140, 234 (1986); 10.1063/1.35599 Boron deactivation and the contact resistance problem J. Appl. Phys. 59, 2072 (1986); 10.1063/1.336393 Electrical Resistivity of BoronPhosphorus Alloys J. Appl. Phys. 30, 1842 (1959); 10.1063/1.1735069

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1364 LETTERS TO THE EDITOR

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FIG. 2. Typical attenuation characteristics.

arrangement using 0.030-in. diameter Kanthal wire did not exhibit the effect. The change in attenuation with magnetic flux density is thought to be due to a variation of the coupling wavelength which, in turn, is due to a variation of the magnetic permeability of the Kanthal wire with applied magnetic field. Since the effect was not observed with larger diameter wires, it is believed to be associated with the crystalline directional properties of the fine wire resulting, possibly, from a drawing process during its manufacture.

It was also observed that a change in temperature yielded the same type of variation of attenuation. This characteristic was noted in the course of passing current through the coupling helix to provide a self-biasing magnetic field and a semiqualitative verification was made using the interior of a large electromagnet (having a large thermal time constant) as an oven.

Using a coupling helix which had been adjusted to deliver maximum attenuation in the center of the pass band, it was possible to shift the attenuation vs frequency characteristic with the magnetic field.

A novel application of this effect is its use as a stabilizing element in a traveling-wave tube to optimize operation at low- and high-power levels, respectively, by compensating for the five or six db gain difference between these two levels of operation. Other possible uses are as an electronically controllable attenuator and a low-frequency modulator.

Electrical Resistivity of Boron E. S. GREINER AND J. A. GUTOWSKI

Bell Telephone Laboratories, Inc., Murray Hill, New Jersey (Received July 29, 1957)

E LECTRICAL resistivity of polycrystalline boron has been measured at temperatures between -160 and 700°C on

three specimens prepared by the reduction of boron trichloride

TEMPERATURE IN DEGREES C 700 300 100 0 -50 -100 -150 -170

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FIG. 1. Resistivity of three specimens of boron as a function of the reciprocal of the absolute temperature.

with hydrogen on heated tungsten or tantalum filaments. Speci­mens A and B were deposited at 13800 e and specimen C was deposited at 1530°C.

The specimens for electrical tests, separated from the tungsten or tantalum core, were about 0.3 cm long and 0.03 cm2 in cross­sectional area. Platinum wires were fused to the ends of the specimens for electrical contacts. Resistivities at low tempera­tures were measured with a high impedance meter!; at high temperatures, the microammeter-potentiometer method was used. The thermocouples were calibrated to a precision of ±l°e. Resistances were measured to an accuracy of one percent, but owing to irregularities of the electrical contacts, the resistivities are accurate to five percent.

The values of electrical resistivity, Fig. 1, are in close agreement over the range measured. The differences in resistivity at low temperatures reflect variations in impurity content. Spectro­chemical qualitative analysis revealed that specimens A and B contained not more than ,...,().1% silicon and only slight traces or less «0.005%) of a few other elements. Specimen C, the most

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LETTERS TO THE EDITOR 1365

impure, contained "-'2% silicon and traces «0.03%) of a few other elements.

The resistivity of the boron prepared in this investigation is about 106 ohm-em at room temperature. Essentially the same value has been reported from early studies on polycrystalline boron2,3 and from recent studies on microscopic single crystals.' The intrinsic conduction range begins at about 200°C. Extra­polation of the linear portion of the curves in Fig. 1, for intrinsic conductivity, shows that ideally pure boron would have a resis­tivity of about 2X107 ohm-em at room temperature.

In the range of intrinsic conductivity, p=A expE./2kT where p is the resistivity, A is a constant, E. is the energy gap at OOK, k is the Boltzmann constant, and T is the absolute temperature. 6

From this relation and the linear portion of the plot of logp vs l/T, E. is calculated to be 1.39±0.05 electron volts. Both smaller and larger values of E. have been reported by various investigators; these results have been summarized in reference 4 (1957).

The authors are pleased to acknowledge the encouragement and constructive suggestions by W. C. Ellis. The work described here benefited from helpful discussions with H. C. Theuerer, F. J. Morin, and J. N. Hobstetter. The spectrochemical qualitative analyses were done by W. Hartmann.

I Clark. Watson, and Mergner, Trans. Am. Inst. Elec. Engrs. 72, Pt. I, 551 (1953).

2 E. Weintraub, J. Ind. Eng. Chern. 5, 106 (1913). IA. H. Warth, Maryland Acad. Sci. Bull. 3, 8 (1923). 'Shaw, Hudson, and Danielson, Phys. Rev. 89, 900 (1953); 107, 419

(1957). • G. L. Pearson and J. Bardeen, Phys. Rev. 75, 865 (1949).

Dislocation Mobility and Release of Cold Work in Cadmium

R. KAMEL AND E. A. ATTIA Physics Department, Faculty of Science, University of Cairo, Giza, EycPl

(Received May 27, 1957)

I NTERNAL friction and elastic modulus changes were used to study the dislocation mobility in cold-worked cadmium

of high purity, subjected to various heat treatments. The internal friction was measured by the resonance curve method, using clamped/free wire samples vibrating transversely in vacuo at frequencies of about 70 cps. The maximum strain amplitude was of the order 10-7. A description of the apparatus used for the detection and measurement of vibration has been given by one of the authorsl elsewhere.

The polycrystalline cadmium used in the measurement was first given a long anneal at 280°C before it was heavily cold­worked by swaging to provide rectangular strip samples having an

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FIG. 2. Annealing time "s reciprocal temperature for the rate process assumed to describe diffusion of dislocations in cadmium. Average acti­vation energy 17.5 kcal/mole.

initial standard history. Various amounts of heat treatment were given to the cold-worked sample. The corresponding isothermal internal friction (at 25°C) and the elastic modulus changes were measured as a function of the annealing time, with the annealing temperature as a parameter. The internal friction curve showed a sharp decrease, from an initial value of 0.056, in the starting interval of heat treatment, followed by a marked peak after which the internal friction settles down to a steady value. The position of the peak was found to depend on the annealing tem­perature. A shift towards higher annealing times occurred as the annealing temperature was decreased (Fig. 1). Modulus changes were found to be a mirror image of internal friction changes.

The observed initial decrease in the internal friction is thought to be due to some sort of recovery.2 The subsequent rise may be attributed, according to Mott,3 to the creation of vacancies as the dislocations climb out of their slip planes giving rise to polygoni­zation. As annealing proceeds, the increase in grain size decreases the internal friction. The steady value finally attained corre­sponds to the equilibrium grain size.

Considering polygonization to obey a rate process,3 the as­sociated heat of activation as deduced from Fig. 2, was found to be 17.5 kcal/mole, which is approximately equal to that pre­viously reported4 on self-diffusion of cadmium. The conclusion that polygonization and self-diffusion are activated by nearly the same energy is supported by the work of Gilmann5 on zinc.

1 R. Kamel, J. Appl. Phys. 24, 1308 (1953). • H. U. Astriim, Arkiv Fysik 10, paper 18. 197 (1956)., • N. F. Mott, Phil. Mag. 44, 742 (1953). 'Wajda, Shirn, and Huntington, Acta Met. 3, 39 (1955). • J. J. Gilmann, Acta Met. 3, 287 (1955).

Possible Explanation of "Mter-Jet" by the Detonation of Shaped Charges

SAMPOORAN SINGH Defence Science Laboratory, Ministry of Defence, New Delhi, India

(Received May 17, 1957)

RECENTLY Pugh et aU explained the formation of the entire jet produced by shaped charges by a simple extension of the

steady-state hydrodynamic theory.' The authors consider the "after-jet" 2 (the issuing of the jet from the slug long after the collapse process has been completed) an illusion, which is created by the fact that the last formed jet and slug elements travel at the same speed and by the fact that the velocity gradients stretch out all of the jet elements to great lengths. This letter presents some evidence that the after-jet is due to the relatively long time taken for the later stages of collapse and the ductile drawing between the last formed jet and slug elements.

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