Dielectrics cubic 43/»

Fig. tr.1-157 ZnS, cubic. Dielectric-function spectrum e E), measured by spectroscopic ellipsometry at 300 K after chemomechanical polishing of the sample (circles). The solid lines show values calculated from a model dielectric function for interband critical points. The dashed lines represent the best-fit standard critical-point lineshapes [1.132]... 

In isotropic and cubic dielectric materials, the electric displacement field D, the electric field E, and the polarization P are connected by the relation... 

Figure C2.17.13. A model calculation of the optical absorjDtion of gold nanocrystals. The fonnalism outlined in the text is used to calculate the absorjDtion cross section of bulk gold (solid curve) and of gold nanoparticles of 3 mn (long dashes), 2 mn (short dashes) and 1 mn (dots) radius. The bulk dielectric properties are obtained from a cubic spline fit to the data of [237]. The small blue shift and substantial broadening which result from the mean free path limitation are...

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

Material Cubic lattice constant, pm Band gap, eV Inttinsic carrier concentration, cm Relative dielectric constant, S Mobihty, Electrons cm"/(Vs) Holes... 

Table 3. Band Gaps and Dielectric Properties of Cubic Binary Compound Semiconductors at RT...

Gray cubic crystal density 5.316 g/cm melts at 1,227°C hardness 4.5 Mohs lattice constant 5.653A dielectric constant 11.1 resistivity (intrinsic) at 27°C, 3.7x10 ohm-cm. 

Pale orange to yellow transparent cubic crystals or long whiskers lattice constant 5.450A density 4.138 g/cm melts at 1,477°C dielectric constant 8.4 electroluminescent in visible light. 

Grayish-white cubic crystals lustrous and brittle density 5.323 g/cm hardness 6.0 Mohs melts at 938.2°C vaporizes at 2,833°C a poor conductor of electricity electrical resistivity 47 microhm-cm dielectric constant 15.7 specific magnetic susceptibility (at 20°C) 0.122x10 insoluble in water, dilute acids and dilute alkalies attacked by concentrated nitric and sulfuric acids, aqua regia and fused alkalies. 

Black cubic crystal zincblende structure density 5.775 g/cm melts at 525°C density of melt 6.48 g/mL dielectric constant 15.9 insoluble in water. 

Greenish blue to black crystalline solid hexagonal or cubic crystals dia-mond-like structure density 3.217g/cm3 exceedingly hard, Mohs hardness 9.5 sublimes at about 2,700°C dielectric constant 7.0 electron mobility >100 cm /volt-sec hole mobility >20cm2/volt-sec band gap energy 2.8 eV insoluble in water and acids solubilized by fusion with caustic potash. 

Up to this point we have restricted consideration to materials for which the dielectric function is a scalar. However, except for amorphous materials and crystals with cubic symmetry, the dielectric function is a tensor therefore, the constitutive relation connecting D and E is... 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

Figure 6.55 Distortion of TiOg octahedron in the tetragonal BaTiOs (top) and possible orientations of the polar axis when an electric field is applied along the pseudo-cubic (001) direction of BaTi03 (middle). Polar axes are shown by arrows inside each cube. Phase transitions in BaTiOj accompanied by changes in (a) dielectric constant (b) spontaneous polarization (c) heat capacity and (d) lattice dimensions (bottom).

Viscoelastic and Dielectric Functions of the linear and Cubic Oscillator... 

A summary of analytic expressions obtained in this manner for all the viscoelastic functions is presented in Table 4 and 5 for the linear and cubic arrays. The well-known phenomenological analogy (8) between dynamic compliance and dielectric permittivity allows the formal use of Eqs. (T 5), (T 6), and (T 11), (T 12) for the dielectric constant, e (co), and loss, e"(co), of the linear and cubic arrays, respectively (see Table 6). The derivations of these equations are elaborated in the next section and certain molecular weight trends are discussed. 

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