The stability of metallic phases and structures: phases with the AlB2 and related structures

Phases (MN2) with the AIB2 structure form two groups each having a distinctly different variation of axial ratio as a function of the radius ratio of the component atoms. The two groups are seen to result from: (i) the M–N distances which are equal to the c. n. 12 radii sums (RM + R N) and are the invariant feature of the structure and (ii) the N–N distances in the (001) graphite-like nets which depend on (a) the Group of the Periodic Table from which the N atom comes, (b) the radius ratio (RM+RN) and (c) the diameter of the N atoms (DZ). The axial ratio of the unit cell (c/a)is the free parameter that couples these two constraints. These observations can be expressed by an equation the only parameters of which are the sizes of the M and N atoms and the Group of the Periodic Table of the N atom, and which allows calculation of the N–N distances to an average accuracy of |0.022| ņ and the axial ratio of the hexagonal unit cells to an average accuracy of |0.028‌| for 46 phases with the AIB2structure. The observations also allow it to be shown why phases of In and TI take the related Caln2 or Ni2 Instructures, rather than the AIB2 structure and point to some reasons for the occurrence of the ω phase structure.