Garnets theory

Figure 19 Observed and predicted dependence of garnet-melt DVDxh on the radius of the X-site for 3 -h ions Solid curve was calculated from lattice strain theory and was obtained from Equation (60) ( VanWestrenen et al. (1999) Van Westrenen et al. (2000b) A La Tourrette et al. (1993) O McDade et al. (2003a) V Salters et al. (2002) Hauri et al. (1994) A Beattie (1993b) A Salters and Longhi (1999) T Landwehr et al. (2001) and Klemme et al. (2002)).

In addition to ligand field theory and group-theoretical engineering rationalizing the excited levels of chromium(ni) since about 1954, it is important to remember the extensive studies by Neuhaus of absorption spectra of minerals coloured by this 3d system, such as ruby, emerald, the cubic garnet-type uvarovite, the... 

Maxwell-Garnet relation A theory by which a refractive index of nano-composite is... 

Althoiigh, experimentally, SrTiOj is not ferroelectric even at low temperatures, it is very close to the ferroelectric threshold. The isotopic replacement of oxygen or partial cation substitution reduces quantum fluctuations and makes it ferroelectric. Hence, SrTiOs will serve as a model material to apply the Landau theory to a quantitative description of the displacive phase transition. Similar descriptions of structural phase transitions have been provided for many minerals, including feldspars (e.g.. Carpenter, 1988), garnets (Carpenter and Boffa Ballaran, 2001), quartz (Carpenter et al., 1998), or cristobaUte (Schmahl et al., 1992). 

Theory of ferromagnetic resonance in rare earth garnets II. (Lines with (with C. Kittel and A.M. Portis), Phvs. Rev.. 116. 323 0959). 

The Neel theory of antiferromagnetism (a molecular field treatment for three sublattices of the garnet structure), as applied to ferrimagnetism (Neel, 1948), shows that the fields acting at a-, d-, and c-sites, respectively, are... 

The magnetocrystalline anisotropy is a direct measure of the contributions from individual cations in the lattice. The success of the single ion model of the anisotropy theory (Yoshida and Tachiki, 1957 Wolf, 1957), as applied to the ferrites and garnets, makes the anisotropy constants very useful. 

The theory of the effect of crystal structure on k is still in a very rudimentary state. It is generally observed that the larger the number of optical branches in the phonon spectrum, the lower the thermal conductivity. In garnets, there are 80 atoms in the primitive unit cells, and there are 97 optical modes at the zone center (Hurrell et al., 1%8). The combination of infrared and Raman studies has... 

In the case of alumina scales formed on alumina-forming materials, the presence of the garnet phases is explained by the diffusion of RE from the underlying metal to the oxide surface via the oxide grain boundaries. This theory, called dynamic segregation , has been proposed by Pint and is based on ihe oxygen potential gradient across the oxide scale [128], The consequences of the diffusion of the RE towards the gas-oxide interface are, on the one hand, to suppress the diffusion of metal ions, and on the other hand, to form a mixed Al-RE oxide at the oxide surface. 

The refractive index of polymer films can be related to the polymer density by using effeaive medium theories such as Maxwell-Garnet or Bmggemann theory that in the limit of small polymer volume content give identical results. These theories can be applied for random mixtures of a polymer and a solvent where the size of grains (or pore size) is much smaller than the wavelength X. The polymer volume content in a swollen polymer (hydrogel) can be calculated from the optical properties of a film as... 

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