The work of many investigators has strongly indicated that sigma phase is characterized by a certain averaged electronic structure. The characteristic was first thought to be the ``electron vacancy'' concentration in thedband, but it is now appreciated that the density of electrons outside the argon shells may also be a valid criterion. The latter characteristic is used here with the application of H. Jones' theory. The result shows a definite correlation between the homogeneity ranges and the x‐ray diffraction patterns for sigma phase and several other complicated structures which occur in alloys of transition metals.