Volume 28, Issue 11, 01 November 1957

Dislocation Arrays in Germanium
View Description Hide DescriptionDislocation arrays have been observed in deformed germanium using a technique based on the selective etching of lithium precipitates which prefer to nucleate on or near dislocations. Evidence is presented which indicates that both internal Frank‐Read sources and surface dislocation sources are of importance in the deformation of germanium.

Theory of the Ferromagnetic Microwave Amplifier
View Description Hide DescriptionThe theory of ferromagneticmicrowave amplification is presented in detail. All three possible types of operation using, respectively, two electromagnetic cavity modes, two sample modes, and one sample and one cavity mode, are discussed. One especially simple case, that of a sphere in the first type of operation is treated separately. Thereafter all three cases are discussed in terms of scaler and vector potentials. An appendix deals with the gain‐band‐width problem and gives an expression for the equivalent ``negative Q'' of the sample.

Hillocks, Pits, and Etch Rate in Germanium Crystals
View Description Hide DescriptionSymmetric faceted etch hillocks have been observed on certain germanium surface orientations exposed to an H_{2}O_{2}–HF (Superoxol) etchant. Considerations of surface curvature and etch rate lead to the conclusion that the faces bounding the hillocks must be at saddle points on an etch rate vs orientation surface. A measurement of etch rate throughout the stereographic triangle has supported this conclusion. The formation of dislocation pits and hillocks is discussed in terms of the variation of surface etch rate with orientation.

Preparation of Large‐Area p‐n Junctions in Silicon by Surface Melting
View Description Hide DescriptionTwo methods have been developed for the preparation of large‐area p‐n junctions in monocrystalline silicon by surface melting and overdoping of the molten material. In one method, direct rf power coupling is used to form a cylindrical p‐n junction in a rod of silicon. Also, radiation heating has been used to melt the surface of thin disks of silicon. The junctions can sustain a peak inverse voltage (PIV) given approximately by PIV=40ρ_{ n } or PIV=10ρ_{ p } depending on the polarity of the base material, of resistivity ρ_{ n } or ρ_{ p }. Low‐resistivity n‐type base material overdoped with aluminium forms junctions exhibiting very sharp breakdown characteristics, and PIV=40ρ_{ n } holds for material at least up to 15 ohm cm. Some results obtained by using a gas doping technique are also given.

Focusing in Collision Problems in Solids
View Description Hide DescriptionIn treating problems of sputtering and radiation damage of solids, a billiard ball model is frequently assumed. An attempt is made to indicate to what extent such a model is justified. Using this model it is noted that the lattice structure of a crystal implies a correlation between successive collisions in a damage process which can lead to the propagation of an energy pulse, or a sequence of collisions, along a close‐packed line of atoms. The rate of attenuation of these pulses is estimated for a particular case and certain implications of the effect are discussed.

Electron Multiplication Processes in High‐Voltage Electrical Discharge in Vacuum
View Description Hide DescriptionThe efficiency of a class of electron‐multiplication processes previously considered to be possible initiators of high‐voltage vacuum arcs has been studied as a function of applied voltage in the voltage range below about one hundred fifty kilovolts. This efficiency is found to be typically less than one part in ten thousand, in contrast to the unity or greater required for arc initiation by such processes. The variation of the efficiency with field is noted. The conclusion is drawn that this class of processes apparently plays no significant role in arc initiation, and the remaining possibilities are briefly discussed.

Temperature‐Dependent Equations of State of Solids
View Description Hide DescriptionAn isothermal equation of state of a solid is considered, which contains as special cases the equations of Birch, Murnaghan, Bardeen, and others. The equation is generalized to arbitrary temperature by replacing two constants of the equation by temperature‐dependent parameters, whose functional form is determined by considerations of thermodynamic consistency. The thermal properties of the solid implied by this equation of state are examined. It is shown that the generalized equation is consistent with the Mie‐Grüneisen relation for the thermal pressure of the lattice, and that the corresponding Grüneisen parameter is only slightly dependent on temperature, in general. The form of the generalized equation of state at low temperature is exhibited as an explicit function of volume and temperature for a solid whose heat capacity obeys the Debye law. A comparison with pressure‐volume data of Swenson for potassium at low temperatures shows excellent agreement of the generalized equation of state with experiment.

Surface Studies on Single‐Crystal Germanium
View Description Hide DescriptionThe condition of the surface of germanium crystals has been studied by chemical, electron microscope,electron diffraction, and other techniques after several of the standard etching procedures. The surface is often partially covered by particles believed to be germanium monoxide. An etch has been devised which gives a controlled thickness of germanium monoxide on the crystal. Another etch minimizes the oxide formation. A simple light‐scattering method for checking the surface cleanliness is described. The results of surface recombination velocity and channel effect measurements on crystals treated by these methods are described as is a method for obtaining low surface recombination on n‐type crystals.

Ionization in the Trail of High‐Velocity Pellets
View Description Hide DescriptionAluminum,magnesium, and lithium‐magnesium pellets were accelerated to velocities as high as 4.5 km/sec by means of an explosive. The ionization in the trails of these pellets was determined by measuring the reflection of a microwave signal from the trail. It was found that the ion density in the trail is an increasing function of the velocity and for the velocity range between 1 and 4.5 km/sec lies between 10^{10} and 10^{15} electrons per cm of path. It was observed that aluminum pellets do not produce ionization at velocities below approximately 2.9 km/sec, while magnesium leaves an ionized trail at velocities down to approximately 1.6 km/sec and lithium‐magnesium alloy down to approximately 1.3 km/sec.

Study of Phase Transitions in WO_{3} with a High‐Temperature X‐Ray Diffractometer
View Description Hide DescriptionWO_{3} undergoes a phase transformation from monoclinic to orthorhombic at approximately 320°C and from orthorhombic to tetragonal at 720°C. A detailed study of the variation of the unit cell dimensions over the range from room temperature to 1000°C has been carried out using high‐temperature x‐ray diffraction techniques. Some unique features of the apparatus are described in this paper.
Between the 320°C and 720°C transformations, the a and c axes increase uniformly in length while the b axis decreases. There is a marked increase in the volume of the unit cell below the orthorhombic to tetragonal transformation; the volume decreases sharply in the transformation and resumes its ``normal'' increase above 720°C.

Solution of the Bloch Equations for Determination of Relaxation Times in Liquids
View Description Hide DescriptionA solution of the Bloch differential equations is given in which both audio modulation and linear variation of the external magnetic field are explicitly included. For the case of T _{1} approximately equal to T _{2} and (γH _{1})^{2} T _{1} T _{2}»1, the solution assumes a simple form which agrees well with experiment. T _{1} can be determined by comparison of the predicted line shapes with those obtained experimentally.

Low‐Temperature Thermal Conductivity of Some Commercial Coppers
View Description Hide DescriptionValues are given for the thermal conductivity between 4°K and 273°K of six commercial coppers and copper alloys: coalesced, electrolytic tough‐pitch, free‐cutting (tellurium) and phosphorus deoxidized coppers, free‐cutting leaded brass, and silicon bronze A. The first three show the conductivity maximum typical of pure metals; the last three show the monotonic increase characteristic of alloys. The intrinsic thermal resistance in the three purer coppers varies appreciably with the concentration of chemical impurities but is much less affected by physical imperfections. In the heavily worked copper alloys the lattice contribution to the conductivity is minor and the total conductivity is essentially the electronic conductivity as limited by the imperfection scattering.

Viscosity of Suspensions of Uniform Spheres
View Description Hide DescriptionA mathematical development of the viscosity of suspensions is presented based on the steady‐state Stokes‐Navier equations of motion omitting inertia terms. The disturbance due to each sphere is assumed to be confined to a frictionless envelope surrounding it similar to the stream tube for flow inside ducts.
The relationship obtained between relative viscosity and solids concentration is in good agreement with existing data over a wide concentration range without the necessity of introducing empirical constants. It is thus thought that it may be a suitable model for further theoretical study as well as furnishing a basis for empirical correlation equations of rheological properties. In very dilute systems it does not agree with the well‐known Einstein formula, and possible reasons for this variation are advanced.

Dimensional Changes Resulting from Dezincification of Alpha Brass
View Description Hide DescriptionSmall sheet and wire samples of high purity 70–30 brass were dezincified in vacuo at various temperatures, and the dimensional changes were observed as a function of the amount of zinc removed. The fractional changes in the dimensions normal to the diffusion direction were comparable to the changes in the diffusion direction. The dimensional changes were directly proportional to the amount of zinc removed and were independent of the temperature. The observed dimensional changes are explained as a combination of a net loss of lattice sites from the sample and the substitution of vacancies for zinc atoms at some of the other lattice sites. From the observed dimensional changes can be calculated both the ratio of diffusivities of copper and zinc atoms in the lattice and the effective size of the vacancies introduced. The ratio D _{Cu}/D _{Zn} is found to be 0.0832, and the volume dilation (fractional expansion per lattice fraction vacancies introduced) is −0.120.

Reflection of Sound from a Surface of Saw‐Tooth Profile
View Description Hide DescriptionA variational method is used to calculate the energy diffracted into the various orders produced when a plane acoustic wave is incident on a periodic, pressure‐release surface of saw‐tooth shape. The results of companion experiments performed with a cork‐covered surface, using techniques of underwater sound are also presented. The relative energies reflected in various orders are plotted as a function of the ratio of acoustic wavelength to spatial period of the surface for a range of angles of incidence. Theory and experiment agree within 10% for all angles of incidence examined and for a large part of the frequency range covered.

Electrical Conductivity of Plexiglas
View Description Hide DescriptionThe electrical conductivity of Plexiglas in an electric field of 2.6 kv/cm in the temperature range from 21° to 90°C was found to be represented by the sum of two exponentials, which have activation energies of 1.45 and 2.7 ev. At the higher temperatures the curves of current as a function of electric field strength from 2.6 to 29 kv/cm were resolved into the sum of a linear and an exponential term. The results suggest that ionic conduction dominates at low fields.

Time Lag between High‐Speed Pellets and the Ionization in Their Trails
View Description Hide DescriptionAn investigation of the spatial relation between high‐speed projectiles fired at velocities of from 1 to 2.5 km per sec shows that the ionization and light in their trail does not occur at a point along the projectile path at the same instant the projectile passes. The time lag has been measured by letting the projectile and ionization in its trail obstruct the transmission of microwaves through a short length of wave guide. The time lag between the pellet and the ionization was observed for magnesium,aluminum, and titanium projectiles, but attempts to obtain the same data for copper, steel, and zinc were unsuccessful because these materials did not seem to produce ionization in their flight at the velocities being investigated. Time lags of up to 1000 μsec were measured at the lower velocities for aluminum projectiles. At velocities of 2.5 km per sec no time lag was observed. That is, the ionization occurred immediately as the pellet passed. Measurements of the luminosity associated with these pellets by means of photocells indicated that the ionization and the luminous region occurred simultaneously. The variations of this time lag as a function of velocity is explained by some thermodynamic properties of the metal in the pellet.

Semiconductor Properties of Recrystallized Silicon in Aluminum Alloy Junction Diodes
View Description Hide DescriptionThis is a study of the basic electrical properties of thin recrystallized regions formed in the fabrication of PN junctions by the alloying of pure aluminum on N‐type silicon single crystals. The average aluminum concentration is about 7×10^{18} cm^{−3}, and varies by a factor of 4 to 5; being largest in the region first recrystallized and decreasing in a linear manner to the surface immediately beneath the aluminum‐silicon eutectic. The average Hall‐hole mobility is about 55 cm^{2} volt^{−1} sec^{−1} and varies from 35 to 75 cm^{2} volt^{−1} sec^{−1} across a region formed by precipating from 977°C to the eutectic. Across the same region the conductivity varies from 72 to 35 mho cm^{−1}. The built‐in field which is both a function of depth and total width can vary from 10 to 200 v per cm in typical cases. The minority carrier (electron) diffusion length ranges from 4 to 12 μ. The temperature dependence of the distribution coefficient corresponds to an enthalpy change (differential heat of solution) of +0.43 ev necessary for the transfer of an atom of aluminum from the liquid to the solid.

Radiation Resulting from an Impulsive Current in a Vertical Antenna Placed on a Dielectric Ground
View Description Hide DescriptionWe consider the electromagnetic field generated by passing an impulsive current of the form of a delta function δ(t) through a vertical Dipole antenna placed on a dielectric ground. The problem is formulated in operational form, and the Hertzian potential Π is expressed as an integral over a Bessel function. This operational solution is then inverted, and the Hertzian potential Π(r,z,t) is expressed in terms of finite complex integrals over a fixed range. The integrals for Π were evaluated on the electronic computer of the Weizmann Institute, and the results for the case of a dielectric constant ε=9 are shown in Fig. 1. The field in the air starts with a finite value at the time of arrival of the wave front, and then increases in a monotone fashion towards the steady state value. In the ground, there is a cone of angle centered around the downward vertical, inside which the field starts again with a finite value and then decreases toward the steady state value. Outside this cone, the direct wave in the ground is preceded by a diffracted wave originating from secondary radiation emanating from the portion of the boundary where the air wave passed in advance of the ground wave. This diffracted wave starts with zero amplitude and increases thereafter, becoming logarithmically infinite at the time of arrival of the direct wave in the ground. After that the amplitude decreases continuously toward the steady‐state value.

Absorption of Rayleigh Waves in Low‐Loss Media
View Description Hide DescriptionMany materials are characterized by internal dissipation parameter 1/Q«1. An expression is derived for such media relating the Rayleigh wave absorption coefficient to compressional and shear wave absorption coefficients with the elastic velocities as parameters. Ultrasonic experiments are described in which the three absorption coefficients are measured in thin Plexiglas sheets. The theoretically derived expression satisfactorily relates the observed absorption coefficients.