Lattices relation

All three metals form a wide variety of binary chalcogenides which frequently differ both in stoichiometry and in structure from the oxides. Many have complex structures which are not easily described, and detailed discussion is therefore inappropriate. The various sulfide phases are listed in Table 22.4 phases approximating to the stoichiometry MS have the NiAs-type structure (p. 556) whereas MS2 have layer lattices related to M0S2 (p. 1018), Cdl2, or CdCl2 (p. 1212). Sometimes complex layer-sequences occur in which the 6-coordinate metal atom is alternatively octahedral and trigonal prismatic. Most of the phases exhibit... 

Using the self-consistently obtained solutions of Eq. 19, the calculated chemical shift (Jiso = (To + a(T) is calculated and compared to the experimental data in Fig. 4. Even though the experimentally observed transition is broader than the calculated one, the agreement between theory and experiment is good. As the discontinuity in the lattice-related mode is small at Tc, where Tc corresponds to a = 0, the chemical shift does not show a discontinuity at Tc within numerical accuracy. It is important to note here that the S-shape in the cf T) data is a direct consequence of using the renormalized frequencies as defined in Eq. 19. 

The corresponding relation between the host and guest crystals when evaluating the misfit ratio may be a one-to-one lattice relation in the same direction (a X b to a xb axes), or in different axial directions (aX b axes versus aX <110> axes), or on the basis of one unit cell versus a few unit cell sizes (see Fig. 7.13). Royer s misfit ratio is generally a two-dimensional correspondence, but Hartman [13] extended this relation to the misfit ratio in PBCs (see Section 4.2), which is a one-dimensional correspondence. Royer s epitaxial relations correspond to a relation between the F faces of the host and guest crystals containing more than two PBCs, and an epitaxial relation is not allowed between S faces or K faces. In Hartman s analysis, rela-... 

A detailed investigation of the nuclear spin-lattice relation time, T l. in liquid [Ni(CO)J and [Fe(CO)s] as a function of temperature and resonance frequency has been carried out 212). It was concluded that relaxation occurs only by two mechanisms, i.e., spin-rotation interaction and anisotropic chemical shift. It was possible to obtain the anisotropic chemical shift difference of 440 ppm for [Ni(CO)4] and 408 ppm for [Fe(CO)s] and the spin-rotation constants. Apparent activation energies for diffusion of 1.0 kcal/mole for [Ni(CO)4] and 2.9 kcal/mole for [Fe(CO)5] were derived. 

The transition from the atom to the cluster to the bulk metal can best be understood in the alkali metals. For example, the ionization potential (IP) (and also the electron affinity (EA)) of sodium clusters Na must approach the metallic sodium work function in the limit N - . We previously displayed this (1) by showing these values from the beautiful experiments by Schumacher et al. (36, 37) (also described in this volume 38)) plotted versus N". The electron affinity values also shown are from (39), (40) and (34) for N = 1,2 and 3, respectively. A better plot still is versus the radius R of the N-mer, equivalent to a plot versus as shown in Figure 1. The slopes of the lines labelled "metal sphere" are slightly uncertain those shown are 4/3 times the slope of Wood ( j ) and assume a simple cubic lattice relation of R and N. It is clear that reasonably accurate interpolation between the bulk work function and the IP and EA values for small clusters is now possible. There are, of course, important quantum and statistical effects for small N, e.g. the trimer has an anomalously low IP and high EA, which can be readily understood in terms of molecular orbital theory (, ). The positive trimer ions may in fact be "ionization sinks" in alkali vapor discharges a possible explanation for the "violet bands" seen in sodium vapor (20) is the radiative recombination of Na. Csj may be the hypothetical negative ion corresponding to EA == 1.2 eV... 

Table 3. Energetic parameters of oxide and halide lattices relating to upconversion involving the I9/2 state of Er +, compiled from various literature sources. A (cm 0 is the average Er + " 19/2 energy gap, (cm ) is the highest-energy lattice phonon energy,p is the reduced energy gap, /c p is the estimated multiphonon-relaxation rate constant, is the estimated range of radiative rate constants, and /Ctot = Kad + /c p. Adapted from [26]...

A careful investigation of the spin-lattice relation rate of the protons ofV,AT-bis(salicylidene)-/>phcnylcncdiaminc (189) and of/V,/V -di(2-hydroxy-l-naphthy-lidene)-p-phenylenediamine (193) crystals provided detailed information on the... 

Interesting results have been obtained by a combination of NMR and quasi-elastic incoherent neutron scattering. The presence of one single line in an NMR spectrum, for all the water concentrations, can be interpreted in two ways either we have only one kind of water molecule with a very well defined environment or we have different kinds subject to a fast chemical exchange (t < 10 3 sec.). Two regimes of absorption have been demonstrated and two different motions have been characterized both by NMR spin lattice relation time measurements and quasi-elastic incoherent neutron scattering. From these results and from results obtained on the Nafion salts W a structural model will be proposed (9). 

Blue powder. Constitution double-layer lattice, related to C 6 type. 

The concentration of Nd can also affect the lineshape and width of the absorption and emission lines in a selective manner, through the crystal field effect related to the ensembles of the Nd " ions. For instance, the linewidth of the " 19/2 " F3/2 absorption of Nd YAG ceramics can be increased by up to 10 %, in the CNd range of 1-9 at.%. This increase in linewidth inevitably leads to reduction in the peak cross sections. In addition, the asymmetric perturbation effects and the variation in the crystal lattice, related to the variation in CNd. also slightly shift the position of... 

To complete the section on lattice-related properties we report on measurements of the thermal conductivity of SmS by Benbachir et al. (1985) between 1.5 and 300 K where it is shown that above 150 K, for pure SmS as well as for SmSi j Sci alloys, the thermal conductivity obeys a law, typical for phonon point defect scattering. 

The situation becomes even more obvious by a recent paper by Tsiok et al. (1991) who measured on SmSe and SmTe very precisely (with strain gauges) the volume change and, via conductivity, the energy gap under pressure. It became evident, as shown in fig. 46, that the energy gap was driven to zero before a softening of the lattice occurred. This clearly shows again that it is the concentration of carriers which triggers the lattice-related properties and not vice versa. 

Lattice-related properties. The phonon dispersion of Y-substituted Smo.75Yo.25S and high-pressure IV SmS has been measured with inelastic neutron scattering by Mook et al. (1978, 1982) and Mook and Holtzberg (1981) it is shown in fig. 54 for the three principal directions. The Sm used was isotopically pure Sm. Figure 54 should be compared with fig. 38 where the phonon dispersion of semiconducting SmS is shown and also with fig. 23 which is the phonon dispersion of IV SmBe. 

It is quite remarkable that the moment quenching observed in the metallic intermediate-valent compounds is not present in the semiconducting intermediate-valent compositions where the observed effective magnetic moments can be obtained by using the standard L, S and J values. Nevertheless, the latter compounds show dramatic effects and softenings in all lattice-related properties, where however, the phonon energies remain practically unrenormalized. Here we conclude the section on TniSei- tTe which certainly has been one of the richest fields in intennediate valence. 

The pH dependence of the rate constants proves that chemical bonds of Fe atoms with solution species contribute to a determining extent to the generation of active sites of dissolution, even in atomistic models where surfece lattice features (kinks, steps, terraces, etc.) are generally put forward. Large similarities of glassy metals (amorphous) with crystalline ones [83,61] must also be regarded as arguing in fevor of chemical bonds as predominant entities with respect to lattice related sites. 

Spin 1/2. As in Section III.B.2 for ADMR, we can calculate the PL-ODMR figure of merit, 8I/I, on the basis of )Lt-wave saturation conditions and spin-lattice relation time much longer than the photoexcitation lifetime. Following the same arguments as those leading to Eq. (17) for ADMR, we can readily calculate 81 = Ion - /off, where Ion and loft are the respective PL intensities for a fx wave turned on and off. Denoting 7 p and / X as the radiative rates for pairs with parallel and antiparallel spin configurations, respectively (obviously Rp < R ap), we get... 

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