Garnet cation substitutions

Similarly to spinel ferrites, garnet ferrites present a wide variety of cation substitutions, which leads to a large range of magnetic properties. 

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). 

In order better to understand the apparent dependence of r on cation charge and to elucidate the dependence of on charge of the substituent, we have performed computer modeling studies of trace substitution into clinopyroxene, wollasto-nite, and garnet. We summarize the results for garnet in order to illustrate the kinds of information which can be obtained. 

Simulated structures for pyrope, ahnandine, spessartme, and grossular were used as the basis for calculations of the energies required to introduce various trace-element defects. In every computational run, one or more defects are introduced into the crystaL e.g., for homo-valent (same-charge) substitution, one divalent cation at the X-site of a perfect garnet lattice is replaced by one trace-element divalent cation. Initial, unrelaxed defect energies were... 

In the olivine example above, two different cations exchange on one equivalent site. With garnet we had three different sites (X, Y, and Si) each of which could exchange different ions here, could substitute on either the octahedral Y sites or the tetrahedral Si sites. To round out the possibilities, we should discuss how to handle such situations, where one species (ion, molecule, or whatever) substitutes on two or more different sites in a crystal—something which is very common in minerals. 

Rare-earth cations usually enter the large dodecahedral sites due simply to their cation radius. The lattice constants of rare-earth garnets are presented in Table 2.5. In addition to the rare earths listed in Table 2.5, Nd3+ Pr3+ cg3+ gj3+ ca2+ La3+, Mn, Na+, Sr +, Pb + and Fe enter c sites, at least as a partial substitution. 

Roschmann, P. Hansen, P. (1981). Molecular field coefficients and cation distribution of substituted yttrium iron garnets. Journal of Applied Physics,... 

Spinels have anion lattices with tetrahedral and octahedral sites for transition metal dopants. Garnets have three types of cation lattice sites. Some cation sites are coordinated by eight oxide ions on the corners of a distorted cube around the cation, four-coordinated (tetrahedral), and six-coordinated (octahedral) lattice sites. By substituting the right transition metal or lanthanide ions in these sites the color and optical activity of garnet pigments can be controlled. 

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