Ordered Structures on the BCC Lattice with First, Second, Third and Fifth Neighbour Interactions

Using a method of linear inequalities similar to that introduced previously by Kanamori and others, we determine the ground state of the Ising model on the BCC lattice in the presence of first, second, thirdand fifth neighbour interactions. Thirteen new structures are found ; the C 11 b (MoSi 2 )and B 11 (γ - TiCu) in particular are found to be stabilized by third and /for fifth neighbour interactions. Some regions of the phase diagram however are still not completely known.