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Synchrotron radiation Laue diffraction is applied to an investigation of the modulated phases of nearly perfect single crystals of tetramethylammonium tetrachlorozincate. Well resolved satellite reflections, consistent with the superspace group Pcmn (1s1), are observed in cooling from the paraelectric room temperature phase I to the incommensurate pseudoquintupled phase II. The transformation to the tripled phase IV is accompanied by the generation of much lattice disorder. The high lattice perfection of the samples is illustrated by the observation of anomalous-dispersion contrast in X-ray topographs.