Bandwidth, tight-binding

The tight-binding bandwidth Wa = 2zrJ for the a electrons of a single-phase Mn03 array with z = 6 like nearest neighbors is, from eqs. (7) and (8),... 

The tight-binding bandwidth, W, or band dispersion, is given by ... 

In the absence of a localized spin on the M atoms, the tight-binding bandwidths are... 

This compares the width for a given value of V0 with the bandwidth for the crystalline state. The factor 1.75 comes, as in (40), from comparing N(E) in midband for a simple cubic, using the tight-binding approximation. 

Itinerant-electron magnetism is found in a narrow range of bandwidths AW near W C/eff-For broader bands, localized spins on the M atoms are suppressed, and the tight-binding band-... 

We then proceed with a semiempirical i.s,px,py,pz) tight-binding (ETB) approach, the parameters of which were fitted to a large LDA data base of carbon molecules and solid structures. Details of this Hamiltonian are published elsewhere [9]. For Ceo its predictions agree well with LDA results (e.g., the overall bandwidth, the density of states, and the symmetry of states near the gap). With this Hamiltonian we not only calculate band structures, but we also obtain the approximate deformation potentials for electronic states. The additional ingredient here... 

Figure 8.07 (top) One-electron tight-binding picture for Anderson transition, (a) Band width (left) and potential well structure in the absenee of disorder, (b) Variation of band disorder in site energies. The horizontal marks are the energies EjS (schematic). When the width W of the disorder exceeds the overlap bandwidth B, disorder-induced localization takes place, (bottom) Schematic density-of-states diagram for a crystalline and an amorphous semiconductor, in the vicinity of the highest occupied and lowest empty states. 

There are many theories on the mechanism of the segregation effect that suggest either a chemical or an electronic mechanism or both types of mechanisms. However, it seems that the most reliable mechanism is electronic as proposed by Mukheijee and Moran [35]. This electronic model calculates the chemical properties of the pure constituents from their physical parameters and then estimates those of the alloys. It employs the tight-binding electronic theory, the band filling of the density of states, and the bandwidth of the pure components for the calculations. However, it seems that the 2D Monte Carlo simulations produce better results by using the embedded atom and superposition methods. The latter allows for the calculation of the compositions from the relative atom positions, and the strain and the vibrational energies has been reviewed for 25 different metal combinations in [36]. It was also possible to predict composition oscillations as a consequence of the size mismatch. 

There are numerous approaches to describe the effect of disorder on the n-electron structure. In a general way, in a tight-binding approximation, disorder will reduce the transfer integral and the bandwidth, and increase the gap. Compared with the rod conformation, curvature fluctuations in flexible chains in solution... 

Pig. 5. Schematic illustration of the density of states per unit energy for a one-dimensional tight-binding band. p(ei)Js is the number of electrons of the same spin which can be accommodated in an energy range Je centered at et. The bandwidth, IV, is 4/. 

Equation (10.2a) expresses the interaction energy in terms of the tight-binding overlap energy 0 and the surface atom LDOS p ( p). This local electronic density of states is considered independent of the energy and is the inverse of the surface metal atom local electron density bandwidth of Eigure 10.1. The dispersion... 

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