Multiplet structures cluster models

Fig 1. The cluster model adopted for the first-principles calculation of the multiplet structure of ruby. The small black sphere at the center of the cluster represents the impurity chromium ion. Small gray spheres and lEtrge gray spheres represent aluminum ions emd oxygen ions, respectively. 

The multiplet structures of ruV calculated by the DV-LFT method using the point charge model and the cluster model are shown in Fig. 3. For comparison, the peak positions of the experimental absorption spectra of ruby obtained by Fairbank et al. (13) are shown together. Here each state is labeled according to the notation in the octahedral symmetry for simplicity. 

As we know, a few first-principles calculations for multiplet structure have been tried by several researchers. Ohnishi and Sugano calculated the energy positions of the (R line) and Ti (U band) states in ruby, under one-electron approximation (12). Xia et al. carried out similar calculations using more realistic model cluster (13). They could, however, only consider the energies of lower-lying two states in multiplet structure. Watanabe and Kamimura combined one-electron calculations with ligand field theory, and carried out first-principles calculation for the "full" multiplet structure of several transition metal impurities... 

For the calculation of the multiplet structure of emerald, we used three types of model clusters, shown in Fig. 1 (1) [Cr06] in hypothetical Oh symmetry, (2) [Cr06] in D3 symmetry, and (3) [CrBe,t Al3Si6042] 2" including cations making up of the host lattice. The model (1) is a model where the trigonal distortion is removed to have a cubic symmetry for a comparison with the model... 

Fig. 3. Calculated multiplet structures for model cluster (1), (2), and (3). The experimental absorption spectrum is drawn in the right column for comparison. The levels are classified into quartet and doublet state, respectively right and left columns in each datum.

Fig 1. Model clusters used for the calculation of the multiplet structures of ruby and emerald ... 

X-ray diffraction work (11,15) shows that there is an ionomer peak at 4°C which is absent in the acid precursor. This low, broad peak is not affected by annealing or ion type and persists up to 300°C. Since the 4°C peak corresponds to a spacing of about 2.5 nm, it is reasonable to propose a structural feature of this dimension in the ionomer. The concept of ionic clusters was initially suggested to explain the large effects on properties of relatively sparse ionic species (1). The exact size of the clusters has been the subject of much debate and has been discussed in a substantial body of literature (3,4,18—20). A theoretical treatment has shown that various models can give rise to supramolecular structures containing ionic multiplets which are about 10 nm in diameter (19). 

A new model for the clustering of charges in dry ionomers is presented. The basic idea is that, under the influence of electrostatic interactions, the multiplets of charges coalesce in clusters that have an internal structure compatible with the steric hindrances due to the polymeric material. The size of the cluster is shown to be independent of the concentration of charges. The tension of the chains within the matrix is discussed, and it is suggested that the clusters are arranged in small hypercrystallites with a local order of the diamond type. 

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