Abstract: Below its critical temperature (668 K), crystals of the binary alloy Cu$-3$/Au consist of antiphase domains with a length scale determined by growth conditions and annealing history. Superstructure Bragg reflections indicate the extent of long-range ordering of the domains. The use of a coherent beam causes these superstructure peaks to have the appearance of speckles, which have a size determined by the size of the beam. The speckles result from a scattering process with no ensemble averaging and thus describe the specific microscopic arrangement of the domains within the illuminated volume of the sample. However, in real experiments only the diffracted beam intensity can be measured while all phase information is lost. This problem is overcome in conventional holography by the construction of a reference wave; however, the special requirements of x- ray optical design have precluded the direct applications of this approach, and so the use of numerical analysis is required. Iterative methods, including the Gerchberg-Saxton algorithm and the hybrid input-output algorithm, have been successfully demonstrated for computer simulations of Cu$- 3$/Au and show early promise for reconstruction of domain structure from real measurements. Data obtained at the Advanced Photon Source beamline 33-ID-D at 8.5 keV are presented, and the requirements for successful reconstruction of images from such data are discussed.!20
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