Doublets cubic

FIGURE 5.13 Effective -values for integer spin systems in axial symmetry. The scheme gives the g-values for all transitions within the non-Kramer s doublets of S = n systems assuming greal = 2.00 and 5 5 5 B cubic zero-field terms are ignored. 

For higher integer spins the number of allowed zero-field interaction terms further increases, and so does the convolution of comparable effects, except once more for a unique term that directly splits the highest non-Kramer s doublet. For S > 3 we have the addition, valid in cubic (and, therefore, in tetragonal, rhombic, and triclinic) symmetry ... 

As an illustration consider then a zero-field Hamiltonian for S = 4 in which we have retained only the familiar axial D- and rhombic E-term plus the cubic terms that split the non-Kramer s doublets in first order ... 

At 5 K, the spectrum is dominated (area fraction of 80%) by a singlet, typical for one of the rare cases of cubic local symmetry for low-spin Fe(II). In addition, two distinct high-spin Fe(II) doublets are observed, contributing 16 and 4%, respectively. The presence of two high-spin Fe(II) doublets together with the fact that the Mossbauer resonance lines arising from the... 

The Mossbauer spectrum of paramagnetic magnetite consists of one broad line which can be resolved into a component for the cubic A sites and a quadrupole split doublet for the B sites. Between the Gurie and Verwey temperatures (see Ghap. 6), magnetite is ferrimagnetic and the Mossbauer spectrum can be fitted with two sextets (Fig. 7.7),... 

As expected for a material with cubic sites, the RT spectrum of stoichiometric wiis-tite consists of a single line. The spectrum of the non-stoichiometric material shows an asymmetrically broadened doublet with contributions from Fe " resonance and from two quadrupole split Fe" doublets. The component peaks which contribute to this spectrum have not been fully resolved owing to the range of Fe" environments in the structure (i. e. the variation in Fe content and vacancy level). At 77 K the Mossbauer spectrum consists of a broad doublet with contributions from Fe" and Fe ". Fe(OH)2 shows a sextet corresponding to a Bhf of 16.6 T at 20 K (Miyamoto, 1976 Genin et al. 1986) and to -20 Tat 4K (Refait et al. 1999). The Tn is at 34 K (Miyamoto et al., 1967). The spectrum of high pressure FeOOH at room temperature consists of a sextet (Peret et al. 1973). 

Fig. 11 Diffraction profile from Sc-II at 23 GPa obtained on beamline 9.5 at the SRS synchrotron using an exposure time of 25 min. The tick marks show the calculated peak positions for the bestfitting body-centred cubic cell [242]. The inset shows an enlarged view of the low-angle part of the profile, highlighting the doublet peak at 20 11.1° which is not accounted for by the cubic unit cell...

Most of the stereochemical arrangements found in these complexes are based oil the octahedron or on the tetrahedron, and may be derived from these configurations by a suitable distortion. Both basic systems have cubic symmetry and d-orbital energies are split into a triplet and a doublet. The group-theoretical notation will be used for their description. ... 

An example of the complexity of the frequency variations in the cubic cell is given in the extreme by the splitting of a peak into a doublet for ions excited to very large orbits. A similar phenomenon was noted by Marshall (47). In the example reported here, the ions were excited by a 0.385 volt peak-to-base RF burst in a 0.0254 m cubic cell with a 1 volt trap and a magnetic field of 1.2 T. Two maxima are discernible for ion-cyclotron-orbit sizes larger than the noptimaln orbit size at about 760 psec excitation time. Local centroids are measurable one increases by ca. 50 Hz and the other... 

According to Kramers theorem, half-integer spin states like 85/2 will always be doubly degenerate as long as no strong external magnetic fields are applied. The 85/2 state splits into three Kramers doublets if the crystal field exhibits a symmetry lower than cubic. 

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