Elastic Physical Properties

The second- and higher-order elastic constant studies in single crystals with large Hugoniot limits have provided an examination of elastic behavior 

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

The most distinctive aspect of the shock work is the determination of higher-order piezoelectric constants. The values determined for the constants are, by far, the most accurate available for quartz and lithium niobate, again due to the direct nature of the measurements. Unfortunately it has not been possible to determine the full set of constants. Given the expense and destructive nature of the shock experiment, it is unlikely that a full set of higher-order piezoelectric constants can be determined. A less expensive investigation of higher-order constants could be conducted with the ramp wave or acceleration wave loading experiment described in the chapter. 

The piezoelectric response investigation also provides direct evidence that significant inelastic deformation and defect generation can occur well within the elastic range as determined by the Hugoniot elastic limit. In quartz, the Hugoniot elastic limit is 6 GPa, but there is clear evidence for strong nonideal mechanical and electrical effects between 2.5 and 6 GPa. The unusual dielectric breakdown phenomenon that occurs at 800 MPa under certain 

96 Chapter 4. Physical Properties Under Elastic Shock Compression 

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In this chapter nonlinear piezoelectric and dielectric behavior shock-induced electrical conductance semiconductors elastic physical properties. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

To develop a terse, broad description of mechanical, physical, and chemical processes in solids, this book is divided into five parts. Part I contains one chapter with introductory material. Part II summarizes aspects of mechanical responses of shock-compressed solids and contains one chapter on materials descriptions and one on experimental procedures. Part III describes certain physical properties of shock-compressed solids with one chapter on such effects under elastic compression and one chapter on effects under elastic-plastic conditions. Part IV describes work on chemical processes in shock-compressed solids and contains three chapters. Finally, Part V summarizes and brings together a description of shock-compressed solids. The information contained in Part II is available in much better detail in other reliable sources. The information in Parts III and IV is perhaps presented best in this book. 

In this chapter physical properties of solids at finite strain within their purely elastic ranges will be investigated. Although the strain levels of a few percent are small relative to the total compressions of typical shock-compression studies, they are large compared to those typically encountered in higher-order elastic property investigations. 

Chapter 4. Physical Properties Under Elastic Shock Compression Table 4.5. Shear deformation potentials. (See Davison and Graham [79D01].)... 

Physical Properties Under Elastic-Plastic Compression... 

In this chapter piezoelectric crystals and polymers ferroelectric and ferromagnetic solids resistance of metals shock-induced electrical polarization electrochemistry elastic-plastic physical properties. 

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