Computation of coincident and near-coincident cells for any two lattices – related DSC-1 and DSC-2 lattices

A computation method is presented for determining: (i) pairs of non-primitive cells M1 and M2, constructed on three translation vectors of a lattice 1 and three vectors of a lattice 2 respectively, such that the sizes of M1 and M2 are (almost) identical; (ii) Σ₁ (Σ₂), defined by the number of primitive cells of lattice 1 (lattice 2) contained in M1 (M2); (iii) a characteristic relative orientation of the two lattices for which M1 and M2 coincide exactly or approximately, for which the transformation relating M1 to M2 (denoted A in general) is a pure deformation, whose principal strains are calculated; (iv) base vectors for the DSC-1 and DSC-2 lattices, so that the Burgers vectors of intrinsic phase (or grain) boundary dislocations are determined. The DSC-1 lattice is constructed by summing the vectors of lattice 1 and lattice 2', deduced from lattice 2 by A^-1. The DSC-2 lattice is derived from the DSC-1 lattice by A. Tables of results are presented for a lattice 1/lattice 2 of Zn/Zn, up to Σ₁ = Σ₂ = 25, and for Ni₃Al (cubic)/Ni₃Nb (orthorhombic), up to Σ₁ = 21 and Σ₂ = 10.