Practical implementation of Particle-Induced X-ray Emission (PIXE) on a focused ion beam apparatus or on a dual-beam apparatus comprising both focused-ion beam and scanning microscopy capabilities is described. Accordingly, an analytical method comprises: directing and focusing a beam of ions comprising a mixture of protons and non-hydrogen ions onto a sample, wherein the kinetic energy of ions of the mixture is not greater than 50 kilo-electron-Volts (keV); and detecting and measuring X-rays that are emitted from the sample in response to the impingement of the protons and non-hydrogen ions onto the sample.