Volume 44, Issue 5, 01 May 1973

Radiation temperature and radiation power of thermal phonon radiators using diamond as transmission medium
View Description Hide DescriptionThermal phonon radiators allow short pulses of incoherent thermal phonon beams to generate in a simple manner and the center frequency of the broad frequency distribution of the emitted phonons to vary up to the acoustic cutoff frequencies. This paper reports experimental investigations of the connection between radiation temperature and radiation power using films of several metals (copper,nickel,gold, and lead) as phonon radiators on diamond. The measured dependencies of the radiation temperature on the radiation power show that the radiation process is by far better described by assuming acoustic mismatch between radiator and transmission medium than using the model of perfect match. Some metals on diamond give a phononradiation power of several kilowatts per square millimeter radiator area. With a diamond substrate held at liquid‐helium temperature, a radiation temperature of a few hundred degrees Kelvin was achieved. If the phonon radiator deposited on diamond is immersed in liquid helium, the transport of heat to the liquid helium becomes important at radiation temperature below 30 °K and is dominant below 20 °K. This effect can be explained by assuming a thin vapor layer between the hot radiator and the liquid helium, and a gas kinetic energy transfer.

Effect of concentration‐dependent diffusion coefficients in diffusion couples with fixed surface composition
View Description Hide DescriptionThe problem of diffusion coefficients with fixed surface composition and variable diffusion coefficients is considered in the present paper. The rate of solute uptake or loss is given using the same equations as for constant diffusion coefficients taking the diffusion coefficient equal to approximately the first moment of the diffusion coefficient about the surface composition. When a new phase forms on the surface of the diffusion couple and it has a small composition range the rate of movement of the phase boundary is given by the same equations as for constant diffusion coefficients, but using D̄, the weighted mean diffusion coefficient. As the composition range of the phase increases, the diffusion coefficient to be used deviates towards the value of the diffusion coefficient at the surface. The results are illustrated with calculated single‐and two‐phase composition profiles for carburization of a steel specimen.

X‐ray diffraction approach to grain boundary and volume diffusion
View Description Hide DescriptionA generalized two‐dimensional diffusionmodel has been developed which consists of an array of boundaries coupled to the free surface and to the substrate lattice. The model makes use of three nonlinear partial differential equations which describe lattice, grain boundary, and surfacediffusion. This two‐dimensional model has been programmed for the IBM 360 computer using a finite‐difference solution to give concentrations as a function of time. An x‐ray intensity simulation program is developed to give integrated diffracted intensity for a given concentration distribution. This simulated intensity is compared with experimental intensity. Data are presented from a sample containing 8 μ of Ni on a (111)‐oriented Cu crystal diffused for various times at 900°C and a similar sample with 6.5 μ of Ni diffused at 600°C. The simulations are in good agreement with experimental intensity bands. Activation energies and frequency factors are given for volume and grain boundarydiffusion which are in good agreement with those literature values that are available. After a diffusion treatment at 600°C, it was found that pipe diffusion makes an important contribution to the volume diffusion coefficient. At 900°C this does not appear to be true. The contribution from pipe diffusion correlates with rocking curve data except for compositions close to that of the free surface.

Experimental and computer‐simulated studies of changing surface morphology during free evaporation
View Description Hide DescriptionSurface morphology of the (0001) face of arsenic was characterized by the formation and growth of equilateral triangular and truncated triangular etch pits during free evaporation. The evaporation rate was correlated with observed changes in etch pit geometry and with the variation in intensity of a reflected gas‐laser beam. Experiments were supplemented by a computer simulation of free evaporation on the (0001) surface to provide a means for delineating the effect of the primary variables which control the morphology as well as the kinetic phenomena. The important controllable variables included the distribution between triangular and truncated forms, the growth rate, birth time, and the general geometric features of each pit. The birth time distribution strongly influenced the relationship between pit geometry and laser intensity. Other independent variables, such as the variation in the growth rate and degree of truncation, affected these quantities to a lesser extent.

A study on zone refining: solid‐phase impurity diffusion and the influence of separating the impure end
View Description Hide DescriptionCrystal quality during zone refining is usually poor. Owing to the great density of high‐diffusivity paths, solid‐statediffusion should not be neglected. Its influence on the concentration profile is described by experiment and theory. Since the concentration gradient and curvature become very large at the end of the bar (k<1), diffusion rates are especially high in this region. A successive separation of this enriched region may lead to a considerable improvement of zone refining. Theoretical and experimental results obtained with this method will be described.

Surface morphology of liquid‐phase epitaxial layers
View Description Hide DescriptionThe surface morphology of GaPliquid‐phaseepitaxial layers has been studied for a wide range of growth conditions in order to determine the origin of the commonly observed corrugated or lamellar surface structure. A double slider apparatus was used for decanting the melts to preserve the high‐temperature morphologies and to permit controlled growth or meltback over selected areas of the substrate. The effect of melt supercooling was examined by varying the cooling rate and melt thickness. These results when combined with observations of the selected area meltback and regrowth experiments demonstrate that the lamellar morphology does not result from the action of capillarity forces on the last liquid to freeze or from interface instabilities associated with constitutional supercooling, as previously suggested. It is shown that the morphology is determined by the substrate orientation and is principally a manifestation of the microscopically layered nature of the liquid‐solid interface.

Work hardening in ordered and disordered alloys
View Description Hide DescriptionA work‐hardening model for ordered and disordered single‐crystalline alloys, where only one slip system is operative, is presented. The model is based on the experimental observation that most of the dislocations on parallel slip planes are locked as dipoles and this dipole formation is believed to be the principal source of work hardening. A detailed analysis of the behavior of passing dislocations is made as a function of frictional stress and vertical separation. Qualitative arguments for the observed strengthening in ordered and disordered alloys are presented based on the above analysis. The pronounced work hardening observed in ordered alloys is related to increased dipole strength as well as to reduced cross slip occasioned by atomic ordering.

Electromigration‐stimulated motion of a liquid alloy defect in aluminum thin films
View Description Hide DescriptionA large defect ([inverted lazy s]600 μ in diameter) was observed to move below the surface in aluminumthin film at a velocity in excess of 40 μ/h (1.11×10^{−8} m/sec). X‐ray stress topography was used to trace the migration, which was in the direction of electron flow, with dislocations in the silicon (under the aluminum) serving as location references for measuring the velocity. The migration direction and velocity of the subsurface defect were reproduced by forming an Al–Sn eutectic zone in the central part of an aluminum stripe. The movement of a liquid alloy inclusion in solidaluminumfilm under an electromigration driving force was proposed to explain the experimental observations.

Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness
View Description Hide DescriptionTheory of the propagation of a surface wave related both to Bleustein‐Gulyaev waves and Love waves is developed. The wave has unidirectional particle motion perpendicular to the direction of propagation and parallel to the surface of a piezoelectric material which is covered with a finite‐thickness layer of an isotropic conducting material. An equation relating phase velocity to material costants is solved in closed form for a piezoelectric material of class 6mm, and conditions for the existence of various modes are presented. Piezoelectricity allows a nonleaky but dispersive wave to exist under conditions is which no love wave is possible, namely, when the shear wave velocity in the layer is greater than that in the substrate. Numerical results are presented for aluminium,gold, and zinc layers on PZT 4 ceramic.

Low‐energy ion bombardment of silicon dioxide films on silicon
View Description Hide DescriptionExposure of SiO_{2} layers on silicon to a plasma environment during sputtering or backsputtering leads to degradation of the electrical properties of the interface. In this paper the effects of the ion bombardment occurring during such exposure are detailed. A low‐energy ion‐bombardment apparatus, capable of giving ion beams ranging from 100 nA at 10 eV to 5 μA at 3.0 keV of mass‐analyzed gas ions, constructed for this study, is described. Bombardment of SiO_{2} layers by Ar^{+}, N^{+}, or ions of any energy from 10 to 2800 eV leads to increase in interface state density and oxide interface charge. The oxide charge after bombardment is located both in the region of the Si/SiO_{2} interface and in the outside 50 Å of the SiO_{2}. Both induced oxide interface charge and interface state density increase linearly with dose to a saturation value, typically to 8×10^{12} charges/cm^{2} and 10^{13} interface states/cm^{2} eV at midgap after a dose of 8×10^{13} ions/cm^{2} at 600 eV, on 1000Å of SiO_{2}. At constant dose the induced charge and interface state density increase linearly with energy to approximately 500 eV, then are independent of energy to the maximum energy studied. After ion bombardment to a dose of ions of 5×10^{13}/cm^{2} or greater, SiO_{2}films exhibit a significant reduction in dielectric strength. This reduction is not completely recoverable by annealing to temperatures up to 600°C. Annealing to 600°C does, however, remove all interface charge, interface states, and room‐temperature trapping instabilities produced by the bombardment, as measured at room temperature after annealing. These experiments show that ion bombardment is capable of producing MOS degradation similar to some of the MOS degradation observed after sputter deposition of metals over oxide films. The increase in charge and interface states is a function of dose, so adjustment of plasma parameters during sputtering to give minimum ion bombardment should minimize this buildup of charge.

Temperature dependence of the single‐crystal elastic constants of Co‐rich Co–Fe alloys
View Description Hide DescriptionThe single‐crystal elastic moduli,C _{11}, C _{12}, and C _{44} of three fcc cobalt‐iron alloys (Co–6 at.% Fe, Co–8 at.% Fe, Co–10 at.% Fe) were measured in the range 0–315°C. In addition C _{11} for the Co–6 at.% Fe alloy, and C′=(1/2)(C _{11}+C _{12}+2C _{44}) for the three alloys are measured over the temperature range 0–1250°C. Plots of the elastic moduli vs temperature exhibit a change in slope and deviation from linearity in the neighborhood of the Curie temperature. The temperature variation of the shear anisotropy in the fcc phase A _{fcc} (≡2C _{44}/C _{11}−C _{12}) differs among the three alloys. A _{fcc} exhibits a highly positive temperature dependence in the Co–10 at.% Fe alloy and a slight negative dependence in the Co–6 at.% Fe and Co–8 at.% Fe alloys. Previous statements in the literature that the hcp⇄fcc transformation in cobalt is preceded by a highly negative temperature dependence of the shear anisotropy ratio A (≡C _{44}/C _{66}) in the hcp phase between 523°K and the transition at about 743°K is not borne out by the present results. Rather it appears that the hcp⇄fcc transformation involves a change from A>1 in the hcp phase to A<1 in the fcc phase.

Acoustic surface‐wave scattering on a homogeneous three‐quarter space
View Description Hide DescriptionThe full‐wave solution to the problem of acoustic surface‐wave scattering on a homogeneous isotropic three‐quarter space of Poisson's ratio σ=0.245 has been obtained by a finite‐difference iterative method. The amplitude coefficients for Rayleigh wave transmission and reflection at the 270° corner were found to be 0.28±0.02 and 0.09±0.01, respectively, while the corresponding phase shifts were 140±10° and −125±10°. All of these results, which are independent of wavelength, agree well with previously published experimental and theoretical work. About 90% of the incident energy is lost to body waves and the scattered energy‐density pattern indicates that over half of this energy sweeps past the corner and propagates into the body of the medium in the form of bulk modes. Some of the incident energy tends to follow the free surface by swinging around the corner while the reflected wave appears to be launched mainly by the action of a virtual source located at the corner which is excited by the incoming wave and radiates into the three‐quarter space. The accuracy of the finite‐difference technique has also been verified by comparing the iterated results for Rayleigh wave propagation on a homogeneous isotropic semi‐infinite half‐space with the analytically exact results. This basic method may be extended to solve problems involving layered geometries.

Statistical calculation of dislocation movements in thin films
View Description Hide DescriptionA statistical method for calculating the effects of dislocation movements is described; the method is based on a realistic model although the effects of cross slip are not included. The long‐range interactions between dislocations are considered to be limited by large intrinsic stresses and image stresses. The numerical results indicate that with sufficient time, about half of the dislocations are annihilated while the other half are bound in dipoles. The maximum strain is found to be almost independent of either the initial dislocation density or the initial dipole density. The calculated maximum strains are in fair agreement with the experimental data published by other investigators.

Diffusion‐limited Si precipitation in evaporated Al/Si films
View Description Hide DescriptionThe precipitation behavior of evaporated Al/Si films with up to 1.8% Si is studied by microscopy as well as by resistance measurements after isochronal and isothermal aging. After deposition of the film most of the Si is precipitated. Temperature treatments above 300°C cause the solution of Si into Al. Aging of a supersaturated solution results in precipitation on grain boundaries at a rate that is much greater than in bulk Al/Si. The precipitation is described as a two‐dimensional diffusion‐limited process. A theoretical expression for the rate constant permits the determination of the diffusion coefficient of Si in Al. This is much greater than in bulk Al/Si and has an activation energy of about 0.85 eV. In view of the small vacancy concentration in the film, these results are explained by diffusion along dislocations, in agreement with electron micrographs revealing a dislocation density of about 10^{10} cm^{−2}.

Lattice theory of fracture and crack creep
View Description Hide DescriptionA quasianalytic solution for the atomic displacements of a discrete two‐dimensional lattice containing a crack is obtained. We assume that the force laws are linear up to a critical displacement when the bond snaps, which is the basic assumption of the lattice static approximation. When compared to the classic Griffith continuum description, new results are: (i) a predicted and observable lattice trapping of the crack, (ii) difficulties with the interpretations of the crystal surface energy in a cleavage experiment, and (iii) a predicted characteristic crackcreep phenomenon under external constant stress. The present theory shows how two separate ``surface energies'' are inferred from the stress to open and to close a crack, and on our model these energies differ from one another by a large factor of 5.7. The thermodynamic ``surface energy'' is not related to either of these quantities. Experimental verification of the lattice trapping of cracks is thought to be most readily and directly obtained by observations of the creep of a crack under high vacuum conditions.

Pyroelectricity in polyvinylidene fluoride
View Description Hide DescriptionThe pyroelectric behavior of as‐received 2‐mil polyvinylidene fluoride films was studied as a function of the poling treatment. It is shown that poling induces a thermally reversible electric polarization in addition to an electric polarization which vanishes upon the first heating of the sample. Experimental evidence is given that the reversible polarization involves charge injection from the electrodes in addition to a field‐induced structural change (probably the formation of oriented crystalline form I). For short poling times ([inverted lazy s] seconds) the mechanism of charge injection appears to be dominant. Initial results of the temperature and voltage dependence of the dc conductivity and of the temperature dependence of the dielectric loss at 50 and 100 Hz for unpoled and poled 2‐mil polyvinylidene fluoride (PVF_{2}) films are presented.

Two‐oscillator description of optical properties of oxygen‐octahedra ferroelectrics
View Description Hide DescriptionRefractive index,birefringence, and linear electro‐optic (EO) effect of BO_{6}‐type oxides have been analyzed using a two‐term Sellmeier dispersion relation. Two oscillators correspond to two main transitions; the transition to dε conduction band with a transition energy of 4–6 eV and that to the dγ band with an energy of 9–11 eV. It is found that the contribution of the latter dγ transition to the refractive index in the visible to the infrared region is larger than that of the former, and that the dispersion energy for the dγ transition is approximately equal to that for the average single oscillator. The birefringence and the linear EO effect are explainable by the polarization‐induced changes in the position and the strength of the dε transition. In the ferroelectric phase, the change in the oscillator position is found to be proportional to the square of the spontaneous polarization. On the other hand, the change in the oscillator strength consists of the terms proportional to and . The second term leads directly to two observed features: the quadratic EO coefficient depends on P_{s} ; and a slight difference exists between the coefficients derived from the spontaneous birefringence and the linear EO effect.

Perturbation theory for the electric potential in a thin‐film overlay acoustic surface‐wave transducer
View Description Hide DescriptionA perturbation theory for the electric potential associated with a Rayleigh wave propagating on a layered surface is presented. The case analyzed is that of a thin piezoelectric film on a nonpiezoelectric substrate. The film is regarded as perturbing the Rayleigh wave of the substrate. The velocity, stress, and electric potential within the film are approximated by power series, and the coefficients of the series are found from Poisson's equation and the mechanical equations of motion in terms of the particle displacements of the unperturbed Rayleigh wave of the substrate. The results obtained using unperturbed Rayleigh wave displacements are shown to be in good agreement with exact calculations in the thin‐film limit (kh≤0.2), while the use of exact particle displacements and phase velocity are shown to yield excellent agreement out to kh≤0.9. Generalities regarding the properties of the two media that control the coupling of thin‐film overlay acoustic surface‐wave transducers are obtained.

Effect of hydrostatic pressure on torsional stress‐strain curves of single‐crystal copper
View Description Hide DescriptionThe torsional stress‐strain curves for single‐crystal copper samples were determined at hydrostatic pressures from 1 bar to 15 kbar. The pressure derivative of the yield stress was found to be 3.8×10^{−3}. At strains of about six, the pressure derivative of the flow stress increased to 1.78×10^{−2}. Stress‐strain curves for the various pressures are provided. A simple model of dislocation cell structure is presented in an attempt to explain the experimental results.

Controlled thermonuclear reactor first wall sputtering and wall life estimates
View Description Hide DescriptionEquations and graphs are developed for rapid estimation of sputtering rates at the first wall of controlled thermonuclear reactors (CTR). High‐energy particle sputtering yield data and potential particle fluxes are presently not readily available for most materials and many reactor designs, thus the equations were set up to provide rapid estimation of sputtering effects when data become available. Limiting wall sputtering‐yield‐particle‐flux products were determined according to the equation ΣS _{μ}φ_{μ} < Kd(t′)/t′, where S _{μ} and φ_{μ} are the sputtering yield (atoms/particle) and flux (particles/cm^{2} sec) of bombarding species μ, d(t′) is the allowable wall thickness removal (in cm) in t′ years, and K is a material constant. K varied little (from 1.36×10^{15} to 3.28×10^{15}) for the wall materials considered (V, Mo,Nb,Ta, Zr, stainless steel, and Al_{2}O_{3}), so that a conservative estimate for the limiting sputtering‐yield‐particle‐flux product is 10^{15} times the allowable sputtering rate in cm/yr. The sputtering yield in molecules per particle given for compounds such as Al_{2}O_{3} must be multiplied by the number of atoms in the molecule to satisfy this relationship. Use of the equations to estimate wall sputtering of pulsed (high‐β) and steady‐state (low‐β) reactors indicated that sputtering rates will be sufficiently high that they cannot be ignored. Factors reducing sputteringerosion rates, such as surface roughness, impurity effects, and sputtered material redeposition, are discussed.