The stability of metallic phases and structures: phases with the AlB 2 and related structures

Abstract

Phases (MN 2 ) with the AIB 2 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 <202 ¯ 3> M–N distances which are equal to the c. n. 12 radii sums (R M + 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 (R M +R N ) and ( c ) the diameter of the N atoms (D Z ). 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 AIB 2 structure. The observations also allow it to be shown why phases of In and TI take the related Caln 2 or Ni 2 Instructures, rather than the AIB 2 structure and point to some reasons for the occurrence of the ω phase structure.