Corrections conduction electrons

The interaction between two ions in a metal is screened by the gas of conduction electrons. Although corrections for exchange and correlation are required, the features of the screened interaction are what one would expect from the preceding calculation of the... 

In the case of PuP, Psat is unkown, but from neutron diffraction the easy axis is (100) thus Psat = 1.27 Ppowder 0-6 Pb and not 0.42 pg. This correction is important because the difference between Poid = 0.77 ps obtained by neutron diffraction and Ppowder = 0.42 Pb has been attributed to a huge conduction electron polarization of - 0.35 Pb Although important, this term should in reality reach only half this value (- 0.17 pb). 

The most recent calculations, however, of the photoemission final state multiplet intensity for the 5 f initial state show also an intensity distribution different from the measured one. This may be partially corrected by accounting for the spectrometer transmission and the varying energy resolution of 0.12, 0.17, 0.17 and 1,3 eV for 21.2, 40.8, 48.4, and 1253.6 eV excitation. However, the UPS spectra are additionally distorted by a much stronger contribution of secondary electrons and the 5 f emission is superimposed upon the (6d7s) conduction electron density of states, background intensity of which was not considered in the calculated spectrum In the calculations, furthermore, in order to account for the excitation of electron-hole pairs, and in order to simulate instrumental resolution, the multiplet lines were broadened by a convolution with Doniach-Sunjic line shapes (for the first effect) and Gaussian profiles (for the second effect). The same parameters as in the case of the calculations for lanthanide metals were used for the asymmetry and the halfwidths ... 

It was noted earlier that the charge density of a narrow resonance band lies within the atoms rather than in the interstitial regions of the crystal in contrast to the main conduction electron density. In this sense it is sometimes said to be localized. However, the charge density from each state in the band is divided among many atoms and it is only when all states up to the Fermi level have contributed that the correct average number of electrons per atom is produced. In a rare earth such as terbium the 8 4f electrons are essentially in atomic 4f states and the number of 4f electrons per atom is fixed without reference to the Fermi level. In this case the f-states are also said to be locaUzed but in a very different sense. Unfortunately the two senses are often confused in literature on the actinides and, in order not to do so here, we shall refer to resonant states and Mott-localized states specifically. 

While the effective g value is expressed in terms of three principal values directed along three axes or directions in a single crystal, only the principal values of g can be extracted from the powder spectrum rather than the principal directions of the tensor with respect to the molecular axes. (Therefore it is more correct to label the observed g values as gi, g2, g3 rather than g gyy, in a powder sample.) In the simplest case, an isotropic g tensor can be observed, such that all three principal axes of the paramagnetic center are identical (x = y = z and therefore gi= gi = g-i). In this case, only a single EPR line would be observed (in the absence of any hyperfine interaction). With the exception of certain point defects in oxides and the presence of signals from conduction electrons, such high symmetry cases are rarely encountered in studies of oxides and surfaces. 

The absence of localized states is clearly supported by the small, Pauli-type paramagnetism of Lal2, 0 db 5 and (30 dz 10) X 10 e.m.u. mole at 299° and 78°K., respectively. Values of this magnitude are characteristic of metals where they are (ideally) associated with the Pauli spin paramagnetism of the conduction electrons. In the present case the results of correction for the diamagnetic contribution of the iodide ions in LaL [ (104 dz 5) and (134 dz 10) X 10 , respectively] are again remarkably (and probably fortuitously) close to those for the metal (113 and 139 X 10" ) (22). 

This use of bulk dielectric constants for nanoparticle calculations is appropriate for particles that are large enough (larger than the conduction electron mean free path), such as particles having radii > 20 nm considered in Fig. 4.2. For smaller particles, one needs to correct the dielectric constant for the effect of scattering of the conduction electrons from the particle surfaces. Procedures for doing this have been studied in several places, as recently reviewed by Coronado and Schatz [37]. 

Fig. 4.6a considers a spherical core-shell particle in which the core is taken to be vacuum and the shell is silver. The particle radius is 50 nm, so when the shell thickness is 50 nm we recover the solid particle result. As the shell becomes thinner, the plasmon resonance red-shifts considerably, very much like we see for highly oblate spheroids. Fig. 4.6a assumes that the dielectric constant of silver is independent of shell thickness, so the resonance width does not change much when the shell becomes thin. However, the correct dielectric response needs to include for finite size effects (as noted above) when the shell thickness is smaller than the conduction electron mean free path. Fig. 4.6b shows what happens to the spectrum in Fig. 4.6a when the finite size effect is incorporated, and we see that it has a significant effect for shells below 10 nm thickness, leading to much broader plasmon lineshapes. 

Figure 9.16a shows the temperature dependence of the energy gap, A(T) (solid curve), as obtained from a measurement of the magnetic susceptibility of the conduction electrons (see Sect 9.6.4 and [24]). With this information, the experimental temperature dependence a(1) was fitted to Eq. (9.14) (Fig. 9.17). The fit shows that the essential characteristics of a (7) from room temperature down to about 50 K, with a variation of more than eight orders of magnitude, are correctly described by this equation. It is thus justified to use Eq. (9.14) alone for the determination of the energy gap A(7) and the constant C. Figure 9.16a shows the energy gap A(T) (dashed curve), as determined directly from the conductivity a(T) (Fig. 1.13) using Eq. (9.14). From this fit, the constant C is also obtained (Table 9.3).

The temperature dependence of the reduced magnetization m T,0), as calculated by Lindg d and Danielsen (1975) is compared in fig. 6.3 with the available experimental results. The conduction electron polarization has been subtracted from the measured magnetization using eq. 6.20 but the effect of ignoring this correction is very small. To a good approximation the data may be characterized by the analytic expression of Mackintosh (1963) after the suggestion of Niira (1960)... 

Fig. 3.2. Electronic, paramagnetic volume susceptibility of liquid cesium (derived from data of Preyland, 1979) as a function of reduced density p/p. Total susceptibility data are corrected for ionic diamagnetism and, for the liquid state, are corrected for conduction electron diamagnetism using theories of I nazawa and Matsudawa (1960) solid line) and Vignale et al. (1988) dot-dash line). Dashed line represents Curie law susceptibility along liquid-vapor coexistence curve, calculated for monovalent, atomic cesium. Note the deviation from Curie law behavior of the vapor for p/p. 2.

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