Application Crystal-Field Potentials

The action of the crystal field potential should be considered in relationship to other perturbations such as the interelectron repulsion F 6 and eventually the spin-orbit coupling operator IT0. According to these relationships, several types of crystal field are distinguished (Table 8.8). The principal difference between them is which basis set is generated prior to the application of the actual perturbation operator. 

For the simplest case of a one-electron configuration dl the term functions are identical with the d-orbitals, and thus the formulae for the pertinent matrix elements listed in Table 8.10 are directly applicable. Then the 5 x 5 secular determinant is solved. For the case of an octahedral complex the matrix elements of the crystal field potential in the basis set of spherical harmonic functions Yi m form the matrix... 

Judd considered the odd part of the crystal-field potential as the perturbation for mixing states of different parity into the f configuration. He cast his intensity formula in a form which allows an easy parametrization and he gave expressions for the intensity of rare-earth ions in solution. Therefore, all practical applications of the Judd-Ofelt theory to rare-earth ions in solutions and glasses are based on Judd s paper, although Judd and Ofelt are mostly cited simultaneously. It is interesting to note that Judd considered solution spectra, rather than single-crystal spectra, because of the lack of intensity data of rare-earth ions in crystalline matrices at that time. 

Crystal Field Theory (CFT) has also been used considerably to rationalize visible absorption spectra, hydration energies, stabilities of complexes, rates and mechanism of reaction, and redox potentials of transition element ions. These applications of CFT are summarized in a book by Basolo and Pearson 1B6). 

Perhaps a more fundamental application of crystal field spectral measurements, and the one that heralded the re-discovery of crystal field theory by Orgel in 1952, is the evaluation of thermodynamic data for transition metal ions in minerals. Energy separations between the 3d orbital energy levels may be deduced from the positions of crystal field bands in an optical spectrum, malting it potentially possible to estimate relative crystal field stabilization energies (CFSE s) of the cations in each coordination site of a mineral structure. These data, once obtained, form the basis for discussions of thermodynamic properties of minerals and interpretations of transition metal geochemistry described in later chapters. 

Fig. 14 Passive film growth on Cr following application of a potential step from (a) 0.0 to 0.4 V and (b) 0.4 to 0.8 V. Full line is film thickness calculated from QCM frequency response (with widely spaced dots indicating uncertainty, 2or). The predictions of the interface and high-field models (explained in main text) are also indicated by the line-styles marked IFM and HFM, respectively. Electrodes Crfilm on Au supported on 10-MHz AT quartz crystal. Solution ...

The quest for new materials, whether driven by their potential for applications or simply by natural scientific curiosity about structure/property relations (i.e., as part of fundamental research programs) has always been and is today a vital part of the liquid crystal scenario. Indeed, it is often the case that the free-thinking fundamental research on new materials opens the door to new applications or improvements in existing device performance. The fascination of the liquid crystal field in fact derives from this continuing materials-knowledge-applica-tions knock-on effect. Importantly, it can occur in both directions. 

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