Electrical properties macroscopic parameters

The lanthanide higher oxides have not only peculiar thermodynamic properties, but also unique physical and chemical properties. The physical and chemical properties are presented as a macroscopic parameter, such as the electrical conductivity, the coefficient of expansion, and the conversion rate of a catalysis process. Due to the lack of knowledge of the wide range of non-stoichiometry of the oxygen-deficient fluorite-related homologous series of the lanthanide higher oxides, the macroscopically measured data of the physical and chemical properties are scattered, and therefore, based on the structural principle of the module ideas a deep understanding the relationship between the properties and structures is needed. 

The purpose of this chapter is to characterize the electrical conductivity. This task is not easy, because g is generally a macroscopic parameter (an effective conductivity ) that represents the electrical properties of the tissue averaged over many cells. The effective conductivity can vary with direction, can be complex (contain real and imaginary parts), and can depend on the temporal and spatial frequencies. 

All the macroscopic properties of the rocks depend on the microstructure and thus of porosity. It is clear that microscopic information is only partially accessible and fiom thoe comes the importance given to certain macroscopic parameters, which are mrasurable like porosity, specific surface, ftie curves of imbibition and drainage, the formation fictor (electric conductivity) and the permeability. We will ap xtadh here only the concepts essential fi>r comprehension of calculations. 

The observations on which thermodynamics is based refer to macroscopic properties only, and only those features of a system that appear to be temporally independent are therefore recorded. This limitation restricts a thermodynamic analysis to the static states of macrosystems. To facilitate the construction of a theoretical framework for thermodynamics [113] it is sufficient to consider only systems that are macroscopically homogeneous, isotropic, uncharged, and large enough so that surface effects can be neglected, and that are not acted on by electric, magnetic or gravitational fields. The only mechanical parameter to be retained is the volume V. For a mixed system the chemical composition is specified in terms of the mole numbers Ni, or the mole fractions [Ak — 1,2,..., r] of the chemically pure components of the system. The quantity V/(Y j=iNj) is called the molar... 

This idea is elegant for its simplicity and also for its usefulness. While often in phenomenological theories of materials, control of parameters with molecular structure would provide useful properties, but the parameters are not related in any obvious way to controllable molecular structural features. Meyer s idea, however, is just the opposite. Chemists have the ability to control enantiomeric purity and thus can easily create an LC phase lacking reflection symmetry. In the case of the SmC, the macroscopic polar symmetry of this fluid phase can lead to a macroscopic electric dipole, and such a dipole was indeed detected by Meyer and his collaborators in a SmC material, as reported in 1975.2... 

The main goal in material science is to provide behaviour laws, i.e. to be able to predict the material properties under given conditions (mechanical, electrical, environmental conditions, temperature, etc.). This requires relating microscopic parameters and local mechanisms to macroscopic behaviours, as there is no other way to express such behaviour laws based on chemical-physical parameters. In other words, the study of materials requires a large part of microstructural observation and analysis. 

Therefore, now we have one tensorial material parameter Xe, composed of the primary optical properties that are driven by the macroscopic electric field E(r,t). A simple form of the constitutive equation is now available for the frequency-domain relating P(r,t) to E(k,(o). 

It is known that the crystal symmetry defines point symmetry group of any macroscopic physical property, and this symmetry cannot be lower than corresponding point symmetry of a whole crystal. The simplest example is the spontaneous electric polarization that cannot exist in centrosymmetric lattice as the symmetry elements of polarization vector have no operation of inversion. We remind that inversion operation means that a system remains intact when coordinates x, y, z are substituted by —x, —y, —z. If the inversion center is lost under the phase transition in a ferroic at T < 7), Tc is the temperature of ferroelectric phase transition or, equivalently, the Curie temperature), the appearance of spontaneous electrical polarization is allowed. Spontaneous polarization P named order parameter appears smoothly... 

The interest in the surface structures with their special properties has increased considerably due to extensive applications in micro- and optoelectronics. It is known that the properties of films of submicron size can be different from those of structures having macroscopic dimensions. The parameters that change the properties of films, are the thickness, number of layers, uniformity of the films, the size of clusters and nanocrystals. The presence of small particles and nano-sized elements leads to changes in material properties such as electrical conductivity, refractive index, band gap, magnetic properties, strength, and others (Suzdalev, 2006 Kobayashi, 2005). 

As noted earlier, Qa/9 may be equally well-defined in terms of other macroscopic properties such as the refractive index or dielectric tensor. However, the simple relation [Eq. (3.6)] cannot be expected to hold for the dielectric anisotropy Ae and electric polarizability aij. This is due to complicated depolarization effects caused by the relatively large near-neighbor electrostatic interaction. The internal field corrections [3.3] are necessary in the electric case. It has been shown that Qa can be used to describe orientational order both in uniaxial and biaxial phases. Furthermore, measurement of Qa/3 is particularly useful when description of flexible molecules using microscopic order parameters becomes problematic. Experimentally, both magnetic resonance and Raman scattering techniques [3.3] may be employed to monitor the orientational order of individual molecules and to determine microscopic order parameters. 

All these methods lead to a set of parameters (membrane thickness, pore volmne, hydraulic radius) which are related to the working (macroscopic) permselective membrane properties. In the case of liquid permeation in a porous membrane, macro- and mesoporous structures are more concerned with viscous flow described by the Hagen-Poiseuille and Carman-Kozeny equations whereas the extended Nernst-Plank equation must be considered for microporous membranes in which diffusion and electrical charge phenomena can occur (Mulder, 1991). For gas and vapor transport, different permeation mechanisms have been described depending on pore sizes ranging from viscous flow for macropores to different diffusion regimes as the pore size is decreased to micro and ultra-micropores (Burggraaf, 1996). 

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