Lattice broad band

As a relevant example, Figure 6.4 shows the room temperature absorption spectrum of Eu + in sodium chloride (NaCl). In this crystal, europium is incorporated in the divalent state, replacing Na+ lattice ions. The spectrum of Eu + ion in NaCl consists of two broad bands, centered at about 240 nm and 340 nm, which correspond to transitions from the ground state ( 87/2) of the 4f electronic configuration to states of the 4f 5d excited electronic configuration. In fact, the energy separation between... 

The second difficulty is not encountered in proton spectroscopy, where proportionality between peak area and concentration of the respective sequence is virtually guaranteed, but is present in caibon spectroscopy where one works under heteronuclear broad-band decoupling conditions. Under such conditions, both the nuclear Oveihauser effect (NOE) and the differences in spin-lattice relaxation time T, can alter the intensity. In this connection, however, Schaefer showed that for the different C nuclei inside the polymer chain, because of the restricted molecular movement, there are no large differences in NOE (121). 

Usually, however, the Bi3+ emission spectrum does not show vibrational structure at all, not even at 4.2 K. An outstanding example is B GejOi 2 [15]. It shows a broad-band emission with an enormous Stokes shift ( 2 eV). It is interesting to note that the Stokes shift of the Bi3+ emission varies from less than 1000 cm"1 (Cs2NaYCl6 Bi3+) to 20000 cm"1 (Bi2Ge309). This is illustrated in Table 2 [2], A large Stokes shift implies a high value of the electron-lattice... 

Cr can be doped into the cubic elpasolite lattices Cs2NaInCl and Cs2NaYClg. The Cr + site symmetry is exactly octahedral, which makes these elpasolite systems particularly attractive. With Cr + doping levels of approximately 2% broad-band luminescence corresponding to the 2g— 22 transition is observed. Figure 6 shows the 6K emission spectra. They exhibit a great deal of fine structure, much more than in any spin-allowed d-d band ever measured in absorption. We also notice some differences in the intensity distribution between the two lattices. They result from a difference of approximately 0.1 8 in the M + - Cl distance in the host lattices. 

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

Figure 6. Sketches of the relationship between the energy E and wave vector k, when electron scattering with the periodic lattice is taken into account, (a) Nearly free electrons the scattering is relatively weak, the free electron model is approximately valid for k < n/d. (b) Strong interaction the free electron model is not valid. Tiny bands are separated by broad band gaps.

Fig. 2 shows the changes in the emission spectra of the CdS-DMF solution by excess addition of Cd + at 400 nm excitation. The spectra consist of two broad bands at X=650 and 480 nm, attributed to radiative recombination at deep trap sites originating from lattice imjjerfection at the surface, i.e., the surface states, and the direct recombination of electron and hole pairs at the band gap, respectively. The emission intensity at X=650 nm increased as excess Cd + increased up to 0.2 equivalent, and then decreased until 1.0 equivalent. 

In Table 5 the features that have been found in the luminescence spectra of the (UOs Vp) centre have been assigned. The vibronic features assigned to vibronic transitions involving the vs and V4 vibrational modes have a broad band character. This is probably due to anharmonic interaction of these modes with lattice phonons occuring in the same frequency region... 

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