Dimensional analysis of phases having the ThMn12, CaCu5 and MgZn2 structures: study of the influence of Kagomé nets of atoms

Abstract

Abstract The cell dimensions of phases having the ThMn12, CaCu5 and MgZn2, MNx 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 ThMn12 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 MMn12 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 CaCu5 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 MgZn2 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 MMn12 phases and the a dimension of MCo5, MNi5 and MCu5 phases. Lines of trigonal bipyramids of N atoms along [001] control the c dimension of all phases with the CaCu5 structure.