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The cell dimensions of phases having the ThMn 12 , CaCu 5  and MgZn 2 , MN x  structures are analysed as a function of the CN-12 diameters of the component atoms M and N, which avoids the usual problems of effective coordination numbers and appropriate atomic sizes, since the equations obtained are independent there of, except for a constant term. In the ThMn 12  structure the intersecting Kagomé nets of N atoms about (100) and (010) planes, control the cell dimensions and lead to the constant axial ratio, except for MMn 12  phases where M is a rare-earth atom, or Th. The Kagomé net of N atoms in the (0001) plane controls the a dimension of phases with the CaCu 5  structure except for phases of Co, Ni, Cu (and Fe) with the rare earths, but it does not control the  a  dimension of phases with the MgZn 2  structure. Contacts between rare-earth metals and transition metals of the first long period, can not be compressed greatly, so arrays of atoms involving M–N contacts control the  a  and  c  dimensions of MMn 12  phases and the  a  dimension of MCo 5 , MNi 5  and MCu 5  phases. Lines of trigonal bipyramids of N atoms along [001] control the c dimension of all phases with the CaCu 5  structure.

Dimensional analysis of phases having the ThMn 12 , CaCu 5 and MgZn 2 structures: study of the influence of Kagomé nets of atoms