T. Vreeland

X‐ray rocking curve analysis of superlattices

We present detailed analyses of x-ray double-crystal rocking curve measurements of superlattices. The technique measures depth profiles of structure factor, and profiles of perpendicular and parallel strains relative to the underlying substrate. In addition to providing a detailed picture of the state of stress, the profiles are a direct measure of the composition modulation. The thickness of the period of modulation and the average strain are determined with a precision of ~1%. The detailed structure of the period is determined to ~5%. We obtain an expression relating the structure of the rocking curve to the structure of the period. This expression allows analytic determination of the structure without Fourier transformation or computer fitting. We show the influence of small random fluctuations in layer thicknesses and strains. The technique is applied to a 15-period GaAlAs/GaAs and a ten-period AlSb/GaSb superlattice grown on GaAs and GaSb substrates, respectively. In the former, the thickness of the period was 676 A and the perpendicular strain varied between zero for the GaAs layer and 0.249% for the layer with peak (93%) Al concentration. Transition regions, ~100 A thick, with continuously varying composition, were found between the GaAs and the Ga0.07 Al0.93As layers. Fluctuations in structural properties were less than 5% of the average. The AlSb/GaSb superlattice had a period of 610 A with sharp transition regions between the layers and negligible fluctuations from period to period. The perpendicular strains were −0.03% and 1.25%, respectively, for the GaSb and AlSb layers. A uniform parallel strain of 0.03% was found throughout the superlattice. Nonzero parallel strain indicates that a small fraction of the misfit between the superlattice and the substrate is plastically accommodated by net edge dislocations lying in a narrow region (a few hundred A thick) at the interface with the substrate. The net number of edge dislocations was calculated to be ~1×10^4/cm^2. The measured perpendicular strains were in excellent agreement with the values calculated from bulk lattice parameters, elastic properties, and the parallel strain. For both superlattices, the standard deviation of random atomic displacements away from perfect crystal sites was below 0.1 A, in agreement with reported ion channeling and electron diffraction measurements of superlattices. The rocking curve method is a major tool for quantitative analysis of superlattices.

Dynamical x‐ray diffraction from nonuniform crystalline films: Application to x‐ray rocking curve analysis

A dynamical model for the general case of Bragg x-ray diffraction from arbitrarily thick nonuniform crystalline films is presented. The model incorporates depth-dependent strain and a spherically symmetric Gaussian distribution of randomly displaced atoms and can be applied to the rocking curve analysis of ion-damaged single crystals and strained layer superlattices. The analysis of x-ray rocking curves using this model provides detailed strain and damage depth distributions for ion-implanted or MeV-ion-bombarded crystals and layer thickness, and lattice strain distributions for epitaxial layers and superlattices. The computation time using the dynamical model is comparable to that using a kinematical model. We also present detailed strain and damage depth distributions in MeV-ion-bombarded GaAs(100) crystals. The perpendicular strain at the sample surface, measured as a function of ion-beam dose (D), nuclear stopping power (Sn), and electronic stopping power (Se) is shown to vary according to (1–kSe)DSn and saturate at high doses.

A theory for the shock-wave consolidation of powders

A model for the shock consolidation of powders is developed which predicts, for a given powder density, the regimes of shock pressure P and shock duration t_d expected to yield fully densified compacts of near optimum strength. Most of the densification work is assumed deposited near particle boundaries, leading to partial melting. The model gives an upper bound to the amount of melt. The condition that the melt between particles must exceed a critical thickness and must solidify within the duration of the shocked state leads to necessary conditions for P and t_d.These requirements are presented in “maps of shock consolidation,” using normalized parameters. The model predicts that for a shock energy (normalized to that required to heat iron to the melting point) of 0.7, a minimum shock duration of 2μs is required to consolidate 60μm diameter iron-based powder.

An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K. Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress. The relation between dislocation velocity and resolved shear stress is: v = v_o(τ_r/τ_o)^n where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K. The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

Mobility of Dislocations in Aluminum

The velocities of individual dislocations of edge and mixed types in pure aluminum single crystals were determined as a function of applied‐resolved shear stress and temperature. The dislocation velocities were determined from measurements of the displacements of individual dislocations produced by stress pulses of known duration. The Berg‐Barrett x‐ray technique was employed to observe the dislocations, and stress pulses of 15 to 108 μsec duration were applied by propagating torsional waves along the axes of [111]‐oriented cylindrical crystals. Resolved shear stresses up to 16×10^6 dynes∕cm^2 were applied at temperatures ranging from −150° to +70°C, and dislocation velocities were found to vary from 10 to 2800 cm∕sec over these ranges of stress and temperature. The experimental conditions were such that the dislocation velocities were not significantly influenced by impurities, dislocation curvature, dislocation‐dislocation interactions, or long‐range internal stress fields in the crystals. The velocity of dislocations is found to be linearly proportional to the applied‐resolved shear stress, and to decrease with increasing temperature. Qualitative comparison of these results with existing theories leads to the conclusion that the mobility of individual dislocations in pure aluminum is governed by dislocation‐phonon interactions. The phonon‐viscosity theory of dislocation mobility can be brought into agreement with the experimental results by reasonable choices of the values of certain constants appearing in the theory.

The effect of stress and temperature on the velocity of dislocations in pure iron monocrystals

The velocity of edge oriented dislocations in pure iron single crystals was determined as a function of stress and temperature. The velocities were determined from measurements of the growth of slip bands which had been subjected to constant amplitude stress pulses of known duration. Slip bands were observed using the Berg-Barrett X-ray technique. Measurements were made for temperatures of 77, 198, 295 and 373°K. Resolved shear stresses covered a range of 10–500 Mdyn/cm^2. Measured velocities ranged from 10^(−2) to 1 cm/sec. A strong temperature dependence of the dislocation velocity was observed. The results can only be correlated with theories of a single thermally activated mechanism if a substantial entropy of activation exists. Alternative explanations of the experimental results in terms of multiple processes and differences in slip band structure are proposed.

Dislocation Mobility in Copper

The velocity of dislocations of mixed edge-screw type in copper crystals of 99.999% purity has been measured as a function of stress at room temperature. Dislocation displacements produced by torsion stress pulses of microsecond duration were detected by etch pitting {100} surfaces. A nearly linear relationship between dislocation velocity and resolved shear stress was found. Stresses from 2.8×10^6 to 23.1×10^6 dyn/cm^2 produced velocities from 160 to 710 cm/sec. These data give a value of the damping constant for high-velocity dislocations of 7×10^(-4) dyn·sec/cm^2, in good agreement with the values deduced from internalfriction measurements. The results also agree, within experimental and theoretical uncertainties, with the phonon viscosity model for the mobility of dislocations.

Enhanced adhesion from high energy ion irradiation

We have found that irradiation of a variety of thin film-substrate combinations by heavy ion beams at energies of mega-electronvolts per atomic mass unit will produce a remarkable enhancement in the adherence of the film. For example, gold films can be firmly attached to soft materials such as Teflon using a 1 MeV beam of protons (10^(14) cm^(−2)) or helium ions (10^(13) cm^(−2)) and to harder materials such as silicon (10^(15) cm^(−2)), quartz (2 × 10^(15) cm^(−2)) and tungsten (2 × 10^(14) cm^(−2)) with 0.5 MeV a.m.u.^(−1) beams of fluorine or chlorine ions. In the case of metal films on semiconductors a low resistance contact results. The mixed layer at the interface is observed to be quite thin (approximately 50 A or less); for silver on silicon electron diffraction and imaging studies of the interface region reveal the presence of crystalline silver compounds.

Damage and strain in epitaxial GexSi1–x films irradiated with Si

The damage and strain induced by irradiation of both relaxed and pseudomorphic GexSi1–x films on Si(100) with 100 keV 28Si ions at room temperature have been studied by MeV 4He channeling spectrometry and x-ray double-crystal diffractometry. The ion energy was chosen to confine the major damage to the films. The results are compared with experiments for room temprature Si irradiation of Si(100) and Ge(100). The maximum relative damage created in low-Ge content films studied here (x=10%, 13%, 15%, 20%, and 22%) is considerably higher than the values obtained by interpolating between the results for relative damage in Si-irradiated single crystal Si and Ge. This, together with other facts, indicates that a relatively small fraction of Ge in Si has a significant stabilizing effect on the retained damage generated by room-temperature irradiation with Si ions. The damage induced by irradiation produces positive perpendicular strain in GexSi1–x, which superimposes on the intrinsic positive perpendicular strain of the pseudomorphic or partially relaxed films. In all of the cases studied here, the induced maximum perpendicular strain and the maximum relative damage initially increase slowly with the dose, but start to rise at an accelerated rate above a threshold value of ~0.15% and 15%, respectively, until the samples are amorphized. The pre-existing pseudomorphic strain in the GexSi1–x film does not significantly influence the maximum relative damage created by Si ion irradiation for all doses and x values. The relationship between the induced maximum perpendicular strain and the maximum relative damage differs from that found in bulk Si(100) and Ge(100).

Mobility of Edge Dislocations in the Basal‐Slip System of Zinc

This paper presents the results of measurements of the velocities of 〈1210〉 (0001) edge dislocations in zinc as a function of applied shear stress. All tests were conducted at room temperature on 99.999% pure zinc monocrystals. Dislocations were revealed by means of the Berg‐Barrett x‐ray technique. Stress pulses of microsecond duration were applied to the test specimens by means of a torsion testing machine. Applied resolved shear stresses ranged from 0 to 17.2×10^6 dyn∕cm^2 and measured dislocation velocities ranged from 40–700 cm∕sec. The results of this study indicate that the velocity of edge dislocations in the basal slip system of zinc is linearly proportional to the applied resolved shear stress. These results are analyzed in terms of the phonon drag theory. Agreement between this theory and the results reported here is quite good.