Solid material anisotropic

The shock-compression pulse carries a solid into a state of homogeneous, isotropic compression whose properties can be described in terms of perfect-crystal lattices in thermodynamic equilibrium. Influences of anisotropic stress on solid materials behaviors can be treated as a perturbation to the isotropic equilibrium state. ... 

The measurement of the work needed to increase the surface area of a solid material (e.g., an electrode metal) is more difficult. The work required to form unit area of new surface by stretching under equilibrium conditions is the surface stress (g1 ) which is a tensor because it is generally anisotropic. For an isotropic solid the work, the generalized surface parameter , or specific surface energy (ys) is the sum of two contributions ... 

This synthetic strategy for nanowires makes use of anisotropic growth dictated by the crystallographic structure of a solid material or confined and directed by templates or kinetically controlled by supersaturation or by the use of appropriate capping agents. 

The thermal expansion of solids depends on their structure symmetry, and may be either isotropic or anisotropic. For example, graphite has a layered structure, and its expansion in the direction perpendicular to the layers is quite different from that in the layers. For isotropic materials, ay w 3 a . However, in anisotropic solid materials the total volume expansion is distributed unequally among the three crystallographic axes and, as a rule, cannot be correctly measured by most dilatometric techniques. The true thermal expansion in such case should be studied using in situ X-ray diffraction (XRD) to determine any temperature dependence of the lattice parameters. 

Liquid-crystalline materials of types A-I and A-II exhibit homogeneous (non-phase separated) mesophases by the association of identical or different molecules. A new class of mesomorphic H-bonded materials, anisotropic liquid-crystalline gels (Fig. 2, Type B), has recently been prepared by the selfaggregation of H-bonded molecules in non-hydrogen-bonded normal liquid crystals [29, 30]. These materials are macroscopically soft solids and form heterogeneous (phase-separated) structures consisting of liquid crystals and fibrous solids. 

The previous sections reviewed recent advancements in sequential electrostatic assembly to form NP-shelled structures. An alternate route to NP assembly arises from interfacial activity and stabilization of NPs. Colloidal particles with partial hydrophilic and hydrophobic character are known to behave like surface-active molecules (surfactants), particularly when adsorbed to a fluid-fluid interface. The assembly of small particles at interfaces is of relevance to advance fields that traditionally feature emulsions, foams, and flotation systems. It is also of pertinence to the development of new fields such as the synthesis of novel materials that include Janus particles, colloidosomes, porous solids, and anisotropic particles, all recently prepared by particle assembly at interfaces [36,38]. 

Paramagnetic species trapped in solid materials usually possess anisotropic g- and hyperfine couplings. Zero-field splittings occur when 5 > V2. The spin Hamiltonian formalism described in Appendix A3.1 is a convenient means to summarise the different interactions. The following spin-Hamiltonian is adequate to illustrate most aspects of the analysis. 

On the contrary, a solid material with more than one principal refractive index is called anisotropic. Anisotropic materials are divided into two subgroups ... 

Theory and Physics of Piezoelectricity. The discussion that follows constitutes a very brief introduction to the theoretical formulation of the physical properties of crystals. If a solid is piezoelectric (and therefore also anisotropic), acoustic displacement and strain will result in electrical polarization of the solid material along certain of its dimensions. The nature and extent of the changes are related to the relationships between the electric field (E) and electric polarization (P). which are treated as vectors, and such elastic factors as stress Tand strain (S), which are treated as tensors. In piezoelectric crystals an applied stress produces an electric polarization. Assuming Ihe dependence is linear, the direct piezoelectric effect can be described by the equation ... 

After the way in which the materials particles are distributed inside the phase, we distinguish (after Tamman) isotropic phases (gaseous, liquid and amorphous solids) and anisotropic phases (crystalline solids). 

Based on methods which rely on the manipulation of the anisotropic terms of the nuclear spin interactions and on the combination of different basic NMR techniques, such as MAS and decoupling, an enormous number of solid-state NMR pulse sequences were proposed in the last 20 years. SoUd-state NMR provides powerful techniques for elucidating details of segmental dynamics and local conformation in solid materials. NMR methods allow the study of dynamics occurring in a wide frequency range (fi om the order of 1 Hz to... 

Most crystalline solids are anisotropic. Since our main conc is polymeric liquids and rubbery solids, we generally do not need to worry about anisotropy. The general roach to constitutive equations for anisotnqnc materials is to use a different elastic constant for each direction. In general, to relate stress to deformation requires a fourth rank tensor with 3 components... 

A distinct advantage of solid-state NMR over solution NMR is the fact that solid material is more or less anisotropic in nature and hence changes in structure and molecular motion are directly visualized as changes in the spectral pattern. On the other hand, in solution NMR such an anisotropy is averaged out in the spectrum, and it can only be deduced through an exhaustive analysis of NMR relaxation mechanisms. In that sense it can be said that solid-state NMR is, in principle, more informative than solution NMR. Yet a combination of both, of course, leads to a much better understanding of the structure and dynamics of biological substances because the majority of these naturally occur in solution or in solution-like states. 

The situation is more complex for rigid media (solids and glasses) and more complex fluids that is, for most materials. These materials have finite yield strengths, support shears and may be anisotropic. As samples, they usually do not relax to hydrostatic equilibrium during an experiment, even when surrounded by a hydrostatic pressure medium. For these materials, P should be replaced by a stress tensor, <3-j, and the appropriate thermodynamic equations are more complex. 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Equations (2.9) and (2.10) are representative of all isotropic, homogeneous solids, regardless of the stress-strain relations of a solid. What is strongly materials specific and uncertain is the appropriate value for shear stress, particularly if materials are in an inelastic condition or anisotropic, inhomogeneous properties are involved. The limiting shear stress controlled by strength is termed r. ... 

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