A procedure for the refinement of the crystal unit cell from a powder diffraction scan is presented. In this procedure knowledge of the crystal structure is not required, and at the end of the refinement a list of indexed intensities is produced. This list may well be usable as the starting point for the application of direct methods. The problems of least‐squares ill‐conditioning due to overlapping reflections are overcome by constraints. An example, using decafluorocyclohexene, C6F10, shows the quality of fit obtained in a case which may even be a false minimum. The method should become more relevant as powder scans of improved resolution become available, through the use of pulsed neutron sources.

This paper describes a computational method for the determination of all possible phonon modes in framework crystal structures that leave the fundamental structural units (tetrahedra and octahedra) undistorted. Such rigid-unit modes (RUMs) are prime candidates as soft modes for displacive phase transitions, such as in the perovskite structure, and this computational method can be used to rationalize the phase transitions in any framework structure. The method has been programmed for general use. The RUM approach is illustrated by consideration of the perovskite, quartz and cristobalite structures.

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The application of the method of Hopfield and Tank to the Travelling Salesman Problem (1985) has been re-examined in an effort to find a procedure for scaling to system sizes of real interest. As this failed, methods were tried to improve the algorithm, recognizing the importance of a "silicon implementation". No satisfactory refinement was found, and the reasons for algorithm failure have been identified.

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A powder profile refinement program written specifically for the easy application of structural constraints is made generally available. It is based on ORFLS and written in Fortran IV. Details of the philosophy of the program are outlined, with emphasis on the areas where more research is necessary. Examples of usage in the literature are cited.