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In this work the spectroscopic performance of a pnCCD detector in the ultra-hard energy range between 40 and 140 keV is tested by means of an energy-dispersive Laue diffraction experiment on a GaAs crystal. About 100 Bragg peaks were collected in a single-shot exposure of the arbitrarily oriented sample to white synchrotron radiation provided by a wiggler at BESSY II and resolved in a large reciprocal-space volume. The positions and energies of individual Laue spots could be determined with a spatial accuracy of less than one pixel and a relative energy resolution better than 1%. In this way the unit-cell parameters of GaAs were extracted with an accuracy of 0.5%, allowing for a complete indexing of the recorded Laue pattern. Despite the low quantum efficiency of the pnCCD (below 7%), experimental structure factors could be obtained from the three-dimensional data sets, taking into account photoelectric absorption as well as Compton scattering processes inside the detector. The agreement between measured and theoretical kinematical structure factors calculated from the known crystal structure is of the order of 10%. The results of this experiment demonstrate the potential of pnCCD detectors for applications in X-ray structure analysis using the complete energy spectrum of synchrotron radiation.