Abstract We derive a mean field equation for a [001] twist grain boundary. For the description of the one-site probability function we use the coincident-site lattice symmetry and the displacement shift complete lattice with two order parameters: one corresponding to the direction of the coincident-site lattice supercell lattice vector and one to the [001] direction (normal to the boundary). We then present a new method to obtain an analytical solution to the linearized mean-field equation for the disordered state (T > T c) using a general arbitrary-range pair potential decaying exponentially with distance. The solution describes the segregation profile (decay lengths and amplitudes) around a grain boundary or free surface. The method reveals several more length scales (compared with an analysis based on a simple nearest-neighbour or next-nearest-neighbour interaction). Their relative amplitudes vary differently with temperature, giving a richer description of the shape of the segregation profile dependin...