Free-electron bands simple cubic

In particular, let us consider the band structure along where kr = (0,0,0) and kx = (2n/a)(l, 0,0) with a the edge length of the face-central cubic unit celL (Note that the X point for fee is In/a not nfa like for simple cubic.) In this direction the two lowest free-electron bands correspond to Ek = (H2/2m)k2 and k+I = (H2/2m)(k + g)2 respectively. The term g is the reciprocal lattice vector (2n/a)(2,0,0) that folds-back5 the free-electron states into the Brillouin zone along so that Ek and k+l... 

Figure 17.3. Energy bands for the simple cubic Bravais lattice in the free-electron approximation at A on rx. The symmetry of the eigenfunctions at T and at X given in the diagram satisfy compatibility requirements (Koster et al. (1963)). Degeneracies are not marked, but may be easily calculated from the dimensions of the representations.

We saw how formulae for the matrix elements can be obtained by equating band energies from LCAO theory and from free-electron theory in Fig. 2-2. Froyen and Harrison (1979) made the corresponding treatment of the tetrahedral solids, again including only matrix elements between nearest-neighbor atoms. The form of their results is just as found for the simple cubic case... 

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