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A narrow two-phase region (of composition width about 1 at. %) separates alloys of types AuCu and AuCu3 in the neighbourhood of the composition Au36Cu64. A tetragonal deformation of the unit cell is observed as much in the ordered AuCu3 I structure as in the periodic antiphase structure, AuCu II, the deformation being due to preferential occupation of certain sites by gold atoms. Two one-dimensional periodic antiphase structures of the type AuCu3 II are observed, with one antiphase direction parallel to a, AuCu3 II'-a, the other parallel to c, AuCu3 II'-c. The symmetry of the elementary cell of AuCu3 II'-a would appear to be not tetragonal but orthorhombic.