Methods and apparatus are provided for performing back-reflection energy-dispersive X-ray diffraction (XRD). This exhibits extremely low sensitivity to the morphology of the sample under investigation. As a consequence of this insensitivity, unprepared samples can be analyzed using this method. For example, in a geological context, whole rock samples become amenable to analysis. A composite diffraction spectrum can be produced using information from different recorded spectra in different energy sub-ranges. The composite spectrum excludes fluorescence signals that would otherwise obscure the diffraction signals.