Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Strain localization in ductile crystals deforming by single slip was analyzed. The plastic flow is modeled as rate-in-sensitive; and localization, viewed as a bifurcation from a homogeneous deformation mode to one which is concentrated in a narrow ''shear band'', is found to be possible only when the plastic hardening modulus for the slip system has fallen to a certain critical value, h/sub cr/, where h/sub cr/ is sensitive to the precise form of the constitutive law governing incremental shear. The general form of this constitutive law is developed. Incorporated within it is the possibility of deviations from the Schmid rule of a critical resolved shear stress. It is shown that h/sub cr/ may in fact be positive when there are deviations from the Schmid rule. It is suggested that micromechanical processes such as ''cross-slip'' in crystals provide specific cases for which stresses other than the Schmid stress may influence plastic response and, further, there is an experimental association of localization with the onset of large amounts of cross-slip. The specific form of h/sub cr/ is given for a constitutive model that corresponds to the non-Schmid effects in cross-slip, and a dislocation model of the process is developed from which anmore » estimate of the magnitude of the parameters involved is made. The work supports the notion that localization can occur with positive strainhardening, h/sub cr/ greater than 0, and the often-invoked notions of the attainment of an ideally plastic or strain softening state for localization may be unnecessary. 6 figures.« less

http://esag.harvard.edu/rice/066_AsaroRice_SingleCryst_JMPS77.pdf

Strain localization in ductile single crystals

Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

Ultrasonic Guided Waves in Solid Media

A phenomenological description of crystallographic slip and pencil glide in single crystals is outlined, with emphasis on the behavior under prescribed strains Theoretical relations are established between these single-crystal properties and the behavior of quasi-homogeneous, quasi-isotropic polycrystals deforming uniformly on a macroscopic scale, at subdiffusive temperatures Experimental comparisons between single crystals and polycrystals are reviewed, considering flow stress, work hardening, temperature and strain rate effects, and various effects of grain size

The relation between polycrystal deformation and single-crystal deformation

The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.

Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review

Ultrasonic Methods in Solid State Physics

The experimental evidence and the associated theory are presented for the dislocation contribution to the generation of the second harmonic of an ultrasonic wave in solids. The contribution is measured through the changes, as a function of static bias stress, in the amplitude of the second harmonic of a fundamental wave (10 Mc/sec compressional wave) propagating in the specimen.In aluminum single crystals the amplitude of the second harmonic, for a given amplitude of the fundamental, changes markedly with static bias stresses ranging from 0 to 106 dyn/cm2. In alloys, there are essentially no changes of the amplitude of the second harmonic even for bias stresses up to 107 dyn/cm2. These observations are consistent with the predicted dependence of the amplitude on dislocation loop length and on the static stress. The effects of small amounts of plastic deformation were consistent with the proposed model.

Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves

Effect of dislocations on finite amplitude ultrasonic waves in aluminum

The generation, due to glide motion of dislocations, of the second harmonic of an ultrasonic stress or strain wave propagating in a crystal is studied by using the string model of dislocations in the presence of a static bias stress. The calculated results agree semiquantitatively with the experiment by Hikata, Chick, and Elbaum. The dependence of the amplitude of the second harmonic on bias stress, when this stress is sufficient to cause dislocation unpinning, can be accounted for by the dislocation damping effect that is associated with the anomalous velocity change due to unpinning.

Anharmonicity Due to Glide Motion of Dislocations

Extraordinary anisotropy (${10}^{8}$) and unusual temperature dependence of the electrical conductivity have been observed in plastically deformed CdS. These features are attributed to metallic-type conductivity along a pseudo-one-dimensional system consisting of arrays of dislocations. The observed temperature dependence of the conductivity is consistent with a Peierls-type metal-semiconductor transition at 125 K.

Charles Elbaum

Papers

Ultrasonic Methods in Solid State Physics

Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves

Effect of dislocations on finite amplitude ultrasonic waves in aluminum

Anharmonicity Due to Glide Motion of Dislocations

Pseudo-One-Dimensional Conductor-Plastically Deformed CdS