ABSTRACT
In the book published by Mott and Jones in 1936, they discussed how to approach the Hume-Rothery electron concentration rule by referring to the gamma-brass phase, which occurs at the ratio of 21 valence electrons to 13 atoms: the value of e/a is obviously equal to 21/13 for both Cu5Zn8 and Cu9Al4 gamma-brasses [1]. ἀ ey assumed that the free energy against solute concentration would suddenly increase, as the concentration passes across the boundary of the phase and that it would be most likely caused by an increase in the electronic energy at absolute zero. ἀ ough they admitted that no precise calculation had yet been carried out, they proposed its critical concentration to be estimated from the FsBz interaction for a given phase. ἀ ey tried to explain its mechanism by using a schematic DOS curve, as reproduced from [1] in Figure 3.1. A round maximum “A” with a subsequent rapid declining slope in the DOS was attributed to the FsBz interaction. When the Fermi surface approaches and touches the Brillouin zone planes, they could naturally assume a grad E in the energy dispersion to become very small and, hence, the DOS to be sharply enhanced. ἀ ey considered the electronic energy of a system to rise rapidly, once electrons fill up the band to just beyond the point A, as shown by the shaded area.
