Fermi vector

The strength of the lattice instability near the Fermi vector depends on the magnitude of the electron-phonon coupling and on the phase space available for electron-hole pair excitation around 2kf. Thus, a reconstructive surface phase transition has to fulfill the following requirements in order to be ascribed to an electronically driven lattice instability ... 

The most famous example of the crystal structure correlating with the average number of valence electrons per atom or band filling, N, is the Hume-Rothery alloy system of noble metals with sp-valent elements, such as Zn, Al, Si, Ge, and Sn. Assuming that Cu and Ag have a valence of 1, then the fee -phase is found to extend to a value of N around 1.38, the bcc / -phase to be stabilized around 1.48, the -phase around 1.62, and the hep e-phase around 1.75, as illustrated for the specific case of Cu-Zn alloys in Fig. 6.15. In 1936 Mott and Jones pointed out that the fee and bcc electron per atom ratios correlate with the number of electrons required for a free-electron Fermi sphere first to make contact with the fee and bcc Brillouin zone faces. The corresponding values of the Fermi vector, fcF, are given by... 

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

The boundary surfaces dividing the region of the occupied and unoccupied wave vectors are known as Fermi surfaces. Thus a Fermi surface occurs as a surface in a 3D band description, a line in a 2D band description, and a pair of points in a ID band description. The wave vectors lying on the Fermi surface are called the Fermi vectors, which... 

AEband can also be calculated from perturbation theory via the pseudo-potential matrix elements " ). The pseudo-potential approach, however, is only justified if the parent metals have the same valency and the same Fermi vector, and if furthermore no charge transfer takes place and the AB compounds have the same atomic volumes as A and B ). 

Berlinsky, on the other hand, has since shown that a rigorously one-dimensional (SN)x band structure will always produce Fermi vectors... 

If one chooses the formula for the Fermi vector that is appropriate for the uniform electron gas (Equation 1.113), one recovers the TF + W (A, = 1) functional. Although... 

The conventional WDA for the kinetic energy results when the effective Fermi vector is determined by substituting the asymmetric one-matrix (Equation 1.110) into the diagonal idempotency condition (Equation 1.115). This functional is also exact for the uniform electron gas, but the kinetic energies of atoms and molecules are still predicted to be far too high. Indeed, this functional is only slightly more accurate than the Thomas-Fermi functional. This is surprising, since the WDA and the TF functional were derived from the same formula for the one-matrix, but the WDA adds an additional exact constraint. 

F/ Fermi vector along the three principal Mb Bohr magneton... 

X, y and z component of wave vector of a magnetic structure the Fermi vector anisotropy constant transition heat thermal expansion electron rest mass effective electron mass magnetization saturation magnetization... 

In an isotropic RKKY model with a spherical Fermi surface, the Fermi vector is strongly dependent on the da ratio and on the number of free electrons Z per magnetic ion ... 

Fig. 26, A plot of the F(k) function against the wave vector Ic for different values of 2k, (Fermi vector) in TbRujSi (Slasiti et al. 1984).

With a given number of electrons per unit cell in the solid the levels, doubly occupied, will be filled from the lowest energy level to a certain energy ep, called the Fermi level. Here, we assume that each level is doubly filled. The Fermi level corresponds to a specific value of k, called the Fermi vector, kp. The total one electron energy per unit cell, /N, is then obtained by integrating equation 13.13... 

---