Bravais crystal approximation

Note that in a particular case of the disordered alloy with a Bravais crystal lattice, when Pj = c = N y N)fox any 7=l,2,...,v (c is the concentration of the A-type atoms, A/ is the total number of these atoms in the considered system), the obtained expression (16) for the free energy correspond to those for the grand thermodynamic potential derived within the ring approximation in Ref. 4. We shall also call the approximation obtained... 

We start this section with the conventional lattice dynamics in the harmonic approximation. Using (3.27,29), the eigenvalue equation for a harmonic Bravais crystal has the form... 

The A V(r) value is substantial in the interatomic area where eigenfunction is small and on the contrary potential correction vanishes in the lattice site. is quite a good approximation to a stationary state of the crystal for all R in the Bravais lattice. So will also be for tpn r — R), where R is the lattice translation vector, n is the energetic band level and collectively represents a full set of atomic quantum numbers. 

This completes our detailed description of the four most important A-type lattices and their unit cells. An analysis of Table 7.2 shows that more than 80% of the elements crystallize in one of these four lattices. In addition, a number of molecular substances in which the individual molecules closely approximate spheres (for example, CH4, HCl, and H2) assume these structures. There are actually 14 possible A-type lattices. First formulated by M. A. Bravais in 1850, these are still... 

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