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The triple-crystal synchrotron X-ray diffractometry data described by Nikulin, Stevenson, Hashizume, Wilkins, Cookson, Foran & Garrett [J. Appl. Cryst. (1995), 28, 57–60] has been analyzed to map out two-dimensional (two-dimensional) lattice distortions in silicon (111) crystals implanted with B+ ions of 100 keV energy through a periodic SiO2 strip pattern. The lateral periodic structure produced a series of satellite reflections associated with the 111 Bragg peak. The 2D reconstruction incorporates the use of the Petrashen–Chukhovskii method, which retrieves the phases of the Bragg waves for these satellite reflections, together with that for the fundamental. The finite Fourier series is then synthesized with the relative phases determined. Localized distortions perpendicular to the surface arising from deposited B+ ions in near-surface layers of the crystal are clearly displayed with spatial resolutions of 0.016 and 0.265 μm in the depth and lateral directions, respectively. For a sample with the oxide layer removed from the surface, two equally plausible strain maps have been obtained by assigning relative phases to 11 satellites using a sequential trial method and a minimum-energy method. Failed map reconstructions for the oxide-covered sample are discussed in terms of the non-unique solutions of the Petrashen–Chukhovskii phase-recovery algorithm and the ambiguous phases determined for the satellites.
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