Defects elastic properties

Using solid-state physics and physical metallurgy concepts, advanced non-destructive electronic tools can be developed to rapidly characterize material properties. Non-destructive tools operate at the electronic level, therefore assessing the electronic structure of the material and any perturbations in the structure due to crystallinity, defects, microstructural phases and their features, manufacturing and processing, and service-induced strains.1 Electronic, magnetic, and elastic properties have all been correlated to fundamental properties of materials.2 5 An analysis of the relationship of physics to properties can be found in Olson et al.1... 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

H NMR may be sensitive to the presence of defects or heterogeneities at various spatial scales, which are often believed to play a major role in limiting or enhancing the elastic properties of the materials. 

The simplest defect in a semiconductor is a substitutional impurity, such as was discussed in Section 6-E. There are also structural defects even in pure materials, such as vacant lattice sites, interstitial atoms, stacking faults (which were introduced at the end of Section 3-A) and dislocations (see, for example, Kittel, 1971, p. 669). They are always in small concentration but can be important in modifying conduction properties (doping is an example of this) or elastic properties (dislocations arc an example of this). 

Radiation damage to metals has been studied principally by electrical conductivity and elastic properties. These bulk measurements do not do much to characterize the defects responsible, but yield estimates of... 

Thus, in this case, flexibility is not related to tacticity defects, as happens for polystyrene. The glass transition temperature is lower than — 100°C and the polymer in bulk is known to have good elastic properties. 

Farlow and Hayward described the development of an automated air-coupled Lamb wave scanner for rapid inspection and imaging of defects in carbon fiber composites [142]. It can detect disbonding of the fiber-matrix interface, broken or missing fibers, and changes in elastic properties of the adherend, which may indicate a change in thickness (i.e., a void) [14]. 

The anisotropy of cortical bone tissue has been described in two symmetry arrangements. Lang [1969], Katz and Ukraincik [1971], and Yoon and Katz [1976a,b] assumed bone to be transversely isotropic with the bone axis of symmetry (the 3 direction) as the unique axis of symmetry. Any small difference in elastic properties between the radial (1 direction) and transverse (2 direction) axes, due to the apparent gradient in porosity from the periosteal to the endosteal sides of bone, was deemed to be due essentially to the defect and did not alter the basic symmetry. For a transverse isotropic material, the stiffness matrix [Qj] is given by... 

The static continuum theory of elasticity for nematic liquid crystals has been developed by Oseen, Ericksen, Frank and others [4]. It was Oseen who introduced the concept of the vector field of the director into the physics of liquid crystals and found that a nematic is completely described by four moduli of elasticity Kn, K22, K33, and K24 [4,5] that will be discussed below. Ericksen was the first who understood the importance of asymmetry of the stress tensor for the hydrostatics of nematic liquid crystals [6] and developed the theoretical basis for the general continuum theory of liquid crystals based on conservation equations for mass, linear and angular momentum. Later the dynamic approach was further developed by Leslie (Chapter 9) and nowadays the continuum theory of liquid crystal is called Ericksen-Leslie theory. As to Frank, he presented a very clear description of the hydrostatic part of the problem and made a great contribution to the theory of defects. In this Chapter we shall discuss elastic properties of nematics based on the most popular version of Frank [7]. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

This paper focuses mainly on the mechanical properties of carbon nanotubes and di.scusses their elastic properties and strain-induced transformations. Only. single-walled nanotubes are di.scussed, since they can be grown with many fewer defects and are thus much stronger. It is shown that under suitable conditions some nanotubes can deform plasiically, while others must break in a brittle fashion. A map of brittle vs. ductile behavior of carbon nanotubes with indices up to (100,100) is presented. The electrical properties of nanotubes are also affected by strain. We will focus here on quantum (ballistic) conductance, which is very sensitive to the atomic and electronic structure. It turns out that some nanotubes can tolerate fairly large deformations without much change to their ballistic conductance, while others are quite sensitive. Both properties can be used in applications, provided that nanotubes of the appropriate symmetry can be reliably prepared or selected. 

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