The theory of superlattice critical scattering

The behaviour of the neutron or X-ray scattering cross section near a continuous Ising-like phase transition is studied. It is established that the resolution-induced crossover from the pure (T c -T) 2 beta power-law behaviour, characteristic of the regime below T c where the superlattice scattering is dominant, to the (T-T c ) - gamma behaviour of the fluctuation-scattering sufficiently far above T c , is described by a scaling function with universal features. The crossover behaviour is studied numerically with the aid of a renormalisation-group representation of the response function. The results are used to assess the reliability with which scattering experiments can be used to determine the critical exponents beta and gamma .