Fe-Ni meteorites have cooled at rates ∼1-10°C/106 years giving rise to a characteristic microstructure of Widmanstatten bcc α plates that have nucleated and grown from the parent fcc γ phase. This transformation results in rejection of Ni into the remaining γ, which also exhibits a variety of internal precipitation reactions. The Ni concentration at the α/γ interface should be close to the equilibrium value between the two phases and this has been determined in several meteorites, using a Philips EM300 TEM/STEM equipped with X-ray microanalytical facilities. The sharp α/γ interface also permits a practical determination to be made of the spatial resolution of the technique. This has been performed and the result compared with the predictions of two theoretical models describing the spatial resolution in terms of the spreading of the electron beam within specimens of finite thickness.Specimens of the meteorites were sectioned such that the α/γ interface was normal to the surface, then 3mm discs were spark machined, ground to ∼100 μm thick, then ion beam thinned to electron transparency