Thermal expansion

Abstract: This chapter discusses some aspects of the mechanical and thermal properties of carbon nano-tubes. The tensile and bending stiffness constants of ideal multi-walled and single-walled carbon nano-tubes are derived in terms of the known elastic properties of graphite. Tensile strengths are estimated by scaling the 20 GPa tensile strength of Bacon's graphite whiskers. The natural resonance (fundamental vibrational frequency) of a cantilevered single-wall nanotube of length 1 micron is shown to be about 12 MHz. It is suggested that the thermal expansion of carbon nanotubes will be essentially isotropic, which can be contrasted with the strongly anisotropic expansion in “conventional” (large diameter) carbon fibers and in graphite. In contrast, the thermal conductivity may be highly anisotropic and (along the long axis) perhaps higher than any other material. A short discussion of topological constraints to surface chemistry in idealized multi-walled nanotubes is presented, and the importance of a strong interface between nano-tube and matrix for formation of high strength nanotube-reinforced composites is highlighted.

Abstract: Negative thermal expansion was found for ZrW 2 O 8 from 0.3 kelvin to its decomposition temperature of about 1050 kelvin. Both neutron and x-ray diffraction data were used to solve and refine the structure of this compound at various temperatures. Cubic symmetry persists for ZrW 2 O 8 over its entire stability range. Thus, the negative thermal expansion behavior is isotropic. Essentially the same behavior was found for isostructural HfW 2 O 8 . No other materials are known to exhibit such behavior over such a broad temperature range. These materials are finding applications as components in composites in order to reduce the composites9 overall thermal expansion to near zero.

Abstract: Introduction. Fundamentals of the Glassy State. Glass Formation Principles. Glass Microstructure: Phase Separation and Liquid Immiscibility. Glass Compositions and Structures. Composition-Structure-Property Relationship Principles. Density and Molar Volume. Elastic Properties and Microhardness of Glass. The Viscosity of Glass. Thermal Expansion of Glass. Heat Capacity of Glass. Thermal Conductivity and Heat Transfer in Glass. Glass Transition Range Behavior. Permeation, Diffusion and Ionic Conduction in Glass. Dielectric Properties. Electronic Conduction. Chemical Durability. Strength and Toughness. Optical Properties. Fundamentals of Inorganic Glassmaking. Appendix I: Elements of Linear Elasticity. Appendix II: Units and General Data Conversions. Subject Index.

Abstract: Preface. Chapter 1. Bonding characteristics. 2. Crystal defects. 3. Elasticity. Basic relations. 4. What values do the elastic constants take? 5. Sound waves. 6. The phonon spectrum. 7. Thermal properties of harmonic lattice vibrations. 8. Phonons in real crystals: anharmonic effects. 9. Atomic vibrations in defect lattices. 10. Thermodynamic properties of conduction electrons. 11. Thermal properties of few-level systems and spin waves. 12. Melting and liquids. 13. Equation of state and thermal expansion: macroscopic relations. 14. Thermal expansion: microscopic aspects. 15. Electrical conductivity of metals and alloys. 16. Thermal conductivity. 17. Transport, elastic and thermal expansion parameters of composite materials. 18. Anisotropic and polycrystalline materials. 19. Estimations and correlations. Appendices. Author index. Subject index. Materials index.

Abstract: Free volume vf is defined as that part of the thermal expansion, or excess volume Δv which can be redistributed without energy change. Assuming a Lennard‐Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv considerable energy is required to redistribute the excess volume; however, at Δv considerably greater than some value δvg (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass‐forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.