Crystal structure refinement using a number of orthonormal axial systems

A least-squares refinement procedure is developed in which different groups of parameters are defined with respect to different axial systems. The parameters are refined by describing the reciprocal-lattice vector for a given reflexion with respect to the relevant axial system for each refinable parameter. With this procedure features of the structure can be refined in the space most suitable for their description and correlations between parameters are either reduced or at least more readily understood. Constrained refinement is much simpler algebraically and can be made to be extremely flexible.