Volume 33, Issue 9, 01 September 1962
Index of content:
Solutions for the Infinite Layer and the Half‐Space for Quasi‐Static Consolidating Elastic and Viscoelastic Media33(1962); http://dx.doi.org/10.1063/1.1702529View Description Hide Description
Solutions are presented for an infinite viscoelastic consolidating layer and an elastic and viscoelastic consolidating half‐space considering the quasi‐static response. The analogous coupled thermoelastic problems and applications in the field of secondary consolidation are discussed.
33(1962); http://dx.doi.org/10.1063/1.1702530View Description Hide Description
Negative resistance and large current densities have been observed in the direct‐current—voltage characteristics of five metal‐oxide‐metal sandwiches prepared from evaporated metal films. The systems studied and their voltages for maximum current are: Al‐SiO‐Au, 3.1 V; Al‐Al2O3‐Au, 2.9 V; Ta‐Ta2O5‐Au, 2.2 V; Zr‐ZrO2‐Au, 2.1 V; and Ti‐TiO2‐Au, 1.7 V. For aluminum oxide, which has been most extensively studied, the voltage for maximum current is independent of film thickness for films between 150 and 1000 Å thick; the phenomenon is not field dependent. Peak‐to‐valley ratios of 30:1 and current densities of 10 A/cm2 are typical. Maximum current densities at peak voltage are 25 A/cm2; minimum current densities are 0.01 A/cm2. Switching time from peak current to valley current is <0.5 μsec but negative resistance is not found for 60‐cycle voltages. Establishment of the dc characteristics and dependence on temperature and atmosphere are described. Electron emission from aluminum oxide sandwiches can occur at 2.5 V. Space‐charge‐limited currents in the insulator provide a possible mechanism for the current‐voltage curves and large currents below the voltage for maximum current through the oxide films. The mechanism responsible for negative resistance is uncertain.
33(1962); http://dx.doi.org/10.1063/1.1702531View Description Hide Description
An experimental investigation of the interdiffusion behavior of gases in a low permeability graphite was performed by sweeping the opposite faces of a graphite septum with helium and argon at uniform pressure and measuring the diffusive flux of both gases. The objectives were to ascertain the diffusion mechanism, to verify the applicable equations and associated theories, and to determine the parameters required to use these equations. At all experimental pressures, contributions of both normal and Knudsen diffusion effects were detectable via the pressure dependence of the diffusion fluxes. It was found that a previously proposed dusty‐gas model formed an excellent basis for correlating the results. The dusty‐gas model yields flux equations which predict the diffusion behavior over a wide range of pressures for particular gas concentrations at the boundaries. Only two experimentally determined parameters (characteristic of the gases and graphite) are required. These are: an effective normal‐diffusion coefficient obtained through interdiffusion experiments and a Knudsen coefficient obtained through single‐gas (permeability) experiments. The procedures used to evaluate these parameters in terms of the experimental data are described in detail.
33(1962); http://dx.doi.org/10.1063/1.1702532View Description Hide Description
Thermal dilation measurements through the temperature of transformation of some zirconium—rareearth alloys were utilized to compare the effect of the elements Nd, Y, Dy, Ho, and Er on the hcp‐bcc transformation temperature of Zr. Binary alloys were vacuum arc melted and concentrations of the individual rare earths were varied up to slightly beyond their solubility limits. All the elements investigated raised the transformation temperature similarly per atomic percent. Electrical resistivitymeasurements at room temperature and below also showed the same trend of equal change in property, irregardless of the alloying element at least up to the solubility limit.
33(1962); http://dx.doi.org/10.1063/1.1702533View Description Hide Description
The friction and wear of spherical single crystals of sapphire (α‐Al2O3) sliding on a wet steel surface were observed. As a result of changing only the crystal orientation of the single‐crystal sphere, the rate of wear varied by more than three orders of magnitude, and the coefficient of friction varied by a factor of three. The rate of wear of the sapphire was greatest when the crystal structure offered least resistance to shear parallel to the sliding surface and in the direction of slide. It is concluded that wear of sapphire sliding on steel proceeds by shear through the sapphire, although interfaceadhesion may involve the formation of chemical bonds.
33(1962); http://dx.doi.org/10.1063/1.1702534View Description Hide Description
A relation between the surface coverage and the surface potential of an adsorbed film is developed from a thermodynamic argument. It is found that the proper variables to be used in the theory of films are the temperature of the surface and the saturation temperature corresponding to the pressure of the vapor in equilibrium with the surface. The analysis is applied to the experimental data of Taylor and Langmuir for cesium on tungsten with good results. In the Appendix an estimate of the range over which the surface forces extend is obtained by means of a simple microscopic model.
33(1962); http://dx.doi.org/10.1063/1.1702535View Description Hide Description
Strain‐hardening caused by ``debris'' produced by multiple cross‐glide is discussed. This form of strain‐hardening is often linearly proportional to strain, because the debris concentration increases in proportion to strain. The rate of debris production should be sensitive to the applied stress, crystal structure, and crystal orientation as is observed.
The debris mechanism is the only one that explains the self‐hardening of isolated half‐loops. It also explains the negative temperature dependence of strain‐hardening at low temperatures, unlike other theories.
The cross‐gliding that leads to debris production is influenced by free surfaces which exert a cross‐glide force on obliquely incident dislocations, and which cause extended dislocations to become contracted so they can more easily cross‐glide.
33(1962); http://dx.doi.org/10.1063/1.1702536View Description Hide Description
When a series of uniform acoustic pulses is transmitted through a medium whose refractive index varies in a random manner, the received pulses vary randomly about an average amplitude. A theory developed by Mintzer [J. Acoust. Soc. Am. 25, 922 (1953)] predicts that the coefficient of variation V, defined as the fractional standard deviation of a series of pulses, is directly proportional to k (2π/acoustic wavelength), provided that the range from the source to receiver is greater than ka 2, where a is the correlation distance of the refractive index variations. In a scaled modelexperiment the refractive index variations are caused by heating the medium (water) from below, thus causing turbulent convection. Observations show the linear dependence of V upon frequency for r>ka 2 as predicted by the theory. At the higher frequencies, observations indicate possible oscillations in V as it tends toward a frequency independent value.
33(1962); http://dx.doi.org/10.1063/1.1702537View Description Hide Description
33(1962); http://dx.doi.org/10.1063/1.1702538View Description Hide Description
Stress‐strain curves and transient creep curves for single crystals are obtained from calculations based on the observed behavior of dislocations in LiF, and the strain rate equation, ε̇=bnv. The pronounced yield drops and apparent ``delay times'' predicted by the calculations are observed experimentally. This agreement between calculation and experiment implies that further consideration of the calculations may give some insight into the yield point and transient creep behavior of single crystals. Several parameters are varied in the calculation in order to determine the effect of such things as testing machine speed, machine hardness, rate of dislocation multiplication, work‐hardening rate, number of mobile dislocations initially present, and the dependence of dislocation velocity on stress. The parameter that most strongly influences the yield points and transient creep behavior of a given material is n 0, the number of mobile dislocations initially present. The wide range of observed yield point and transient creep behavior of various materials can be rationalized in terms of how dislocation velocity varies with stress; the less sensitive is the velocity to the applied stress, the more pronounced will be the yield drop or delay time. The calculation is applicable only when n 0≠0; and the yield points and yield drops develop continuously and relatively gradually as dislocation motion and multiplication begin before the upper yield point is reached. The upper yield stress is not closely related to the stress required to unpin dislocations. It is necessary to distinguish between this type of yield point, which is commonly observed, and the Cottrell type of yield point in which dislocation motion begins at the upper yield stress, and in which the upper yield stress is related to the unpinning stress.
33(1962); http://dx.doi.org/10.1063/1.1702539View Description Hide Description
Ignition of a thermionic cathode discharge in mercury vapor at the low applied potential of 2.4 V is shown to be the result of a potential minimum in space 0.8 V below the cathode, and of a favorable contact potential difference. Good emitters require more voltage to fire than high work functioncathodes. Using an argon buffer gas at about 3.5 mm Hgpressure, ignition is easiest with an added Hgvapor pressure of 1.85 mm. Adequate pressure is required because of the two‐stage ionization which produces ignition. This process applies also to the noble gases, and requires that ignition cannot occur with electron energy less than half the ionization potential.
33(1962); http://dx.doi.org/10.1063/1.1702540View Description Hide Description
The average velocities of dislocations have been measured in four semiconductor crystals‐silicon, germanium,gallium antimonide, and indium antimonide. The range of measuredvelocities was between 10−6 and 2×10−1 cm/sec. The dislocationvelocities in these crystals are relatively insensitive to stress when compared to LiF or Si‐Fe. The effect of temperature, in the range 0.5 to 0.8TM , on the velocities at various constant stresses was measured and the activation energies for the dislocationvelocities were obtained in each of the crystals. No marked dependence of activation energy as a function of the applied stress was obtained.
The effect of strain on the dislocation densities was measured as a function of orientation, temperature, and strain rate. It was found that even in initially dislocation‐free crystals, dislocations were generated at quite low stresses. From direct measurements of etch pits and dislocationvelocities it was possible to estimate the fraction of mobile dislocations. Under certain conditions the percentage of mobile dislocations was as low as 3 to 8%.
33(1962); http://dx.doi.org/10.1063/1.1702541View Description Hide Description
Based on the theory of anisotropicelasticity, the stress field of a single dislocation, the force between two parallel dislocations, and the stress field of various types of infinite dislocation walls and arrays are fully analyzed for a hexagonal crystal.
The attraction sector of an edge dislocation with respect to another edge dislocation of the same sign is no longer the half‐quadrant as in the isotropic case. For graphite crystals the attraction sector is about 70° instead of 45°.
The force between two parallel screw dislocations is not central. A tangential component exists, being zero along x and y axes. The tangential force will retard the formation of screw dislocation arrays along any plane except those parallel or normal to the basal plane. Cross slip may be aided or opposed by this force, depending on the direction of applied stress.
The stress field of an infinite dislocation wall or array, either parallel or normal to the basal plane, has similar characteristics to those from isotropic treatment, although their magnitudes and geometries may differ considerably.
Numerical data of six important material constants are tabulated for many common hexagonal crystals.
33(1962); http://dx.doi.org/10.1063/1.1702542View Description Hide Description
The temperature variation of the saturationmagnetization of a γ‐ferric oxide sample has been interpreted by use of Néel's molecular‐field model, with neglect of A‐A and B‐B interactions. The parameters assumed are: j of the Brillouin function= ; a net moment of 1.25 Bohr magnetons per iron atom; ratio of the number of atoms on A sites to the number on B sites, 8/(40/3)=3/5. From these parameters the function M/M ∞=G(T/θ) was calculated numerically; M=magnetization at temperature T, M ∞=magnetization at T=0, θ=Curie temperature. The data fit the theoretical curve very well if θ is assigned the value 1020°K.
33(1962); http://dx.doi.org/10.1063/1.1702543View Description Hide Description
The Schiff small‐angle approximation for plane‐wave scattering by a dielectric is integrated over an appropriate angular distribution of incident plane waves in order to represent finite‐beam scattering. The intensity distribution near the forward direction where incident and scattered waves interfere can now be expressed in a meaningful way. If the radius of the incident beam is not large relative to the dimensions of the scattering system, the scattered wave is seriously modified. A simple definition of cross section is chosen, and an extended optical theorem for total cross sections is derived.
33(1962); http://dx.doi.org/10.1063/1.1702544View Description Hide Description
An experimental technique for the direct observation of imperfections in single crystals is described. It is based on the anomalous transmission effect of x rays observed in crystals of high perfection. The parallel beam method previously used only for the mapping of dislocations has been improved so that large area x‐ray topographs are recorded. It can now be applied to the detection of impurities, segregation, and precipitation effects in semiconductor materials. Microsegregation of oxygen in silicon,precipitation of copper in silicon, and arsenic segregation in germanium were used to study the influence of segregation and precipitation on the anomalous transmission. Working conditions of x‐ray diffraction microscopy are discussed, and it is shown that segregation phenomena produce typical impurity contrast which is reflection‐dependent if the impurities are in solid solution. For precipitated impurities, this relation does not exist.
33(1962); http://dx.doi.org/10.1063/1.1702545View Description Hide Description
The internal friction peak for nitrogen in dilute solutions in very pure chromium occurs at 160°C for ∼1 cps but is unstable due to partial precipitation of nitrogen. Interpretation of internal friction data at low frequencies and elastic aftereffect measurements in terms of the theory of Snoek gives the lattice diffusion rate of nitrogen in chromium as D=3×10−4 exp (−24 300/RT).
33(1962); http://dx.doi.org/10.1063/1.1702546View Description Hide Description
Seven compositions were prepared in the system As2Te3‐Tl2Te‐As2Se3. Some of the samples were amorphous while others were diphasal including both amorphous and crystalline phases. The electrical and thermal properties of the samples were structure dependent. At room temperature the resistivity values ranged from 4.7×10−3 to 1.8×105 Ω‐cm, Seebeck coefficient values were 40 to 1210 μV/°K and thermal conductivity values were 18.1 to 2.2 mW/cm‐deg.
33(1962); http://dx.doi.org/10.1063/1.1702547View Description Hide Description
When total internal reflection of light occurs, radiation penetrates beyond the reflecting surface into the rarer medium where the intensity decreases with distance from the interface in an exponential manner. Since the degree of coupling to this radiation can be controlled by adjusting the proximity of another object to this interface, it is possible to utilize this phenomenon in the measurement of film thickness and to obtain high contrast images of surface reliefs.
33(1962); http://dx.doi.org/10.1063/1.1702548View Description Hide Description
The quenched‐in resistivity in gold was measured for cooling rates from 104 to 105 °C/sec. The quenched‐in resistivity increases considerably with increasing cooling rate and depends strongly on the quenching temperature over much of the range investigated; for example, for a cooling rate of 20 000°C/sec about 12% of the residual resistivity recovers during the quenching process for a quench from 700°C and about 20% recovers for a quench from 800°C. For the lower quenching temperatures the quenched‐in resistivity appears to approach saturation at the fastest quenching rates obtained. A linear relation between the logarithm of quenched‐in resistivity and the reciprocal of quenching rate was observed. This allowed linear extrapolation to infinite quenching rate. The quenched‐in resistivity ρ∞ obtained by extrapolating to infinite rate, is expressed by ρ∞=ρ0 exp(−Hf/kT), where ρ0=5.0×10−4 Ω‐cm and the formation enthalpy,Hf =0.97 eV. Assuming ρ∞ corresponds to single vacancies rather than clusters, measurements of the length change of the quenched specimens and using Tewordt's result that a vacancy has 0.47 atomic volume, the following constants were obtained: The resistivity of 1 at. % of vacancies, 1.7×10−6 Ω‐cm; the entropy of formation of a vacancy, 0.95×10−4 eV/°K; and the fractional concentration at the melting point, 6.4×10−4.