Thermoelectric measurements of energy deposition during shock-wave consolidation of metal powders of several sizes

The degree of shock energy localization within individual particles and between neighboring particles of different size was explored during shock-wave consolidation of spherical metal powders. The thermoelectric voltage generated by the passage of a shock wave through a copper powder-constantan powder interface was recorded. The sizes of the copper and constantan powders were varied between mean diameters of 40 and 98 µm. Shock-wave pressures of 5 GPa were applied by flyer plate impact, and the resulting voltage versus time signals were collected with a 10 ns time resolution. In order to analyze the signals, a simulation of the thermocouple system was developed to account for the effects of multiple particle interactions and a slightly nonplanar copper-constantan interface. The resulting simulated voltage versus time signals are a good match for the observed signals when the size ratio of the copper and constantan particles is less than a factor of 2, and reveal the preferential deposition of energy in smaller particles at the expense of larger particles within the size range examined. The amount of energy localized near particle surfaces was found to be a majority of all the energy, with a significant minority deposited throughout the particle bulk

Strain measurement in heteroepitaxial layers - Silicon on sapphire

An x-ray diffraction technique is presented for the determination of the strain tensor in an epitaxial layer grown on a crystallographically distinct substrate. The technique utilizes different diffracting planes in the layer and in a reference crystal fixed to the layer, and is illustrated by application to an ∼4000 Å (001) silicon layer grown on a (0112) sapphire wafer. The principal strains were measured, and the measured strain normal to the layer was found to agree with the normal strain calculated from the measured in-plane strains within the experimental uncertainty of strain measurement. The principal stresses in the plane of the silicon film, calculated from the measured strains were −0.92 ± 0.16 GPa in the [100] direction and −0.98 ± 0.17 GPa in the [010] direction

Correlation of shock initiated and thermally initiated chemical reactions in a 1:1 atomic ratio nickel-silicon mixture

Shock initiated chemical reaction experiments have been performed on a 1:1 atomic ratio mixture of 20- to 45-µm nickel and –325 mesh crystalline silicon powders. It has been observed that no detectable or only minor surface reactions occur between the constituents until a thermal energy threshold is reached, above which the reaction goes to completion. The experiments show the energy difference between virtually no and full reaction is on the order of 5 percent. Differential scanning calorimetery (DSC) of statically pressed powders shows an exothermic reaction beginning at a temperature which decreases with decreasing porosity. Powder, shock compressed to just below the threshold energy, starts to react in the DSC at 621 °C while powder statically pressed to 23% porosity starts to react at about 30 °C higher. Tap density powder starts to react at 891 °C. The DSC reaction initiation temperature of the shock compressed but unreacted powder corresponds to a thermal energy in the powder of 382 J/g which agrees well with the thermal energy produced by a shock wave with the threshold energy (between 384 and 396 J/g). (Thermal energies referenced to 20 °C.) A sharp energy threshold and a direct correlation with DSC results indicates that the mean thermal energy determines whether or not the reaction will propagate in the elemental Ni+Si powder mixture rather than local, particle level conditions. From this it may be concluded that the reaction occurs on a time scale greater than the time constant for thermal diffusion into the particle interiors

The Analysis of Stress and Deformation

This book was prepared for a course in the mechanics of deformable bodies at the authors' institution, and is at a level suitable for advanced undergraduate or first-year graduate students. It differs from the traditional treatment by going more deeply into the fundamentals and giving less emphasis to the design aspects of the subject. In the first two chapters the principles of stress and strain are presented and a sufficient introduction is given to the theory of elasticity so that the student can see how exact solutions of problems can be derived, and can appreciate the nature of the approximations embodied in some commonly used simplified solutions. The third chapter is devoted to the bending of beams, and the fourth chapter treats the instability of elastic systems. Applications to axially symmetric problems, curved beams, and stress concentrations are discussed in Chapter 5; applications to torsion problems are discussed in Chapter 6; applications to problems of plates and shells are discussed in Chapter 7. Applications to problems involving viscous and plastic behavior are treated in Chapter 8, and problems of wave propagation are treated in Chapter 9. An introduction to numerical methods of solving problems is given in Chapter 10. An introduction to tensor notation by means of the equations of elasticity is given in Appendix I. Experimental methods of determining stresses by means of strain gages, brittle coatings, and photoelasticity are described in Appendices II and III. A brief introduction to variational methods is presented in Appendix IV. The material in the book is laid out so that a short course can be based on Chapters 1, 2, 3, 4, and 8 and Appendices II and III. Some of the special aspects of the subject and some of the details of the derivations are left to the problems; the assignment of homework should be made with this in mind. To indicate to the student the nature of the more advanced parts of the subject, some topics are included that would not necessarily be covered in the formal course work. The book is aimed primarily at those students who will pursue graduate work, and it is intended to give a good preparation for advanced studies in the field. It should also give a good foundation to students primarily interested in design who would cover the more applied aspects of the subject in courses on design. The authors wish to express their appreciation to those members of the California lnstitute of Technology community whose suggestions and efforts have helped to bring our lecture notes into book form

Strain in epitaxial CoSi2 films on Si (111) and inference for pseudomorphic growth

The perpendicular x-ray strain of epitaxial CoSi2 films grown on Si(111) substrates at ~600 °C was measured at temperatures from 24 up to 650 °C. At 600 °C, the perpendicular x-ray strain is –0.86%, which is about the x-ray strain that a stress-free CoSi2 film on Si(111) would have at that temperature. This result shows that the stress in the epitaxial CoSi2 film is fully relaxed at the growth temperature. Strains in the film below the growth temperature are induced by the difference in the thermal expansion coefficient of CoSi2 and Si, alphaf–alphas=0.65×10^–5/°C. Within experimental error margins, the strain increases linearly with decreasing temperature at a rate of (1.3±0.1)×10^–5/C. The slope of the strain-temperature dependence, obtained by assuming that the density of misfit dislocations formed at the growth temperature remains unchanged, agrees with the measured slope if the unknown Poisson ratio of CoSi2 is assumed to be nuf=1/3. These observations support three rules postulated for epitaxial growth

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

A Hugoniot theory for solid and powder mixtures

A model is presented from which one can calculate the Hugoniot of solid and porous two‐component mixtures up to moderate pressures using only static thermodynamic properties of the components. The model does not presuppose either the relative magnitude of the thermal and elastic energies or temperature equilibrium between the two components. It is shown that for a mixture, the conservation equations define a Hugoniot surface and that the ratio of the thermal energy of the components determines where the shocked state of the mixture lies on this surface. This ratio, which may strongly affect shock‐initiated chemical reactions and the properties of consolidated powder mixtures, is found to have only a minor effect on the Hugoniot of a mixture. It is also found that the Hugoniot of solids and solid mixtures is sensitive to the pressure derivative of the isentropic bulk modulus at constant entropy

A study of dislocation mobility and density in metallic crystals

This report summarizes the research accomplishments under the Atomic Energy Commission contracts, CALT-473 and CALT-767-P3b for the ten-year period, November 1, 1963 to October 31, 1973. The research was stimulated by technological advances which required improvements in our ability to predict the deformation behavior of materials. In the mid 1930's, theoreticians first recognized that crystal defects could play a central role in plastic deformation, and since that time a number of experiments have conclusively demonstrated the one-to-one correspondence between the motion of line defects (dislocations) and plastic deformation. Before the existence and significance of dislocations was recognized, theoreticians faced a puzzling problem: the predicted strength of crystals was several orders of magnitude larger than the strength actually observed. With the realization that crystal deformation is caused by the motion of dislocations, the theoretical problem reversed. The new problem became one of understanding the origin of the resistance to dislocation motion in order to explain the observed strength of crystals. The Atomic Energy Commission Sponsored Research on dislocation mobility and density in metallic crystals at the California Institute of Technology has focused on an understanding of the dynamics of dislocations. Important interactions between a moving dislocation and lattice phonons, conduction electrons, other dislocations, and point defects such as those introduced by neutron irradiation have been studied. The experimental phase of this research involved the introduction of isolated dislocations into a crystal, the observation of these dislocations by chemical or electrolytic etching, X-ray topography, and transmission electron microscopy (TEM); the application of appropriate stresses of controlled amplitude and duration, and finally determination of the stress-induced motion of the dislocations by observation of their new locations. The nature of the resistance to dislocation motion is deduced from these experiments

Misoriented Epitaxial Growth of (111)CoSi_2 on Offset (111)Si Substrates

Single crystal epitaxial films of CoSi_2 were grown by MBE on various (111)Si single crystal substrates, whose surfaces were purposely tilted towards the _g, direction by small angles ϕ_g,†, 0°, ≤ ϕ_g, ≤, 4° measured between the surface normal and the _g, direction of Si. The actual offset angle, ϕ_g was determined by back Laue reflection method. The average perpendicular strain of the CoSi_2 epilayer, ε┵, and the _f orientation of the epitaxial CoSi_2 film were determined by double crystal diffractometry. We find that the misorientation angle, a, measured between the Si _g, and CoSi_2 _f directions, increases linearly with the offset angle, ϕ_g, up to ϕ_g = 4°. A simple geometrical model is developed which predicts that α = ε┵ × tan ϕ_g. The model agrees quantitatively with the experimental data. The equivalent strain energy associated with the misorientation is approximated by that of a low angle tilt boundary. The misorientation angle α of the equilibrium state, determined by minimizing the total strain energy of the epitaxial film, is nonzero in general