The quantification of grain boundary segregation levels, as measured with X-ray energy dispersive spectroscopy (XEDS) in a scanning transmission electron microscope (STEM), is dependent on the size and shape of the interaction volume. The segregation level T (in atoms/nm2) is related to the intensities of the characteristic peaks in the X-ray spectrum, Is and Im, by
where ρ is the density of the matrix in atoms/nm3, Am and As are the atomic masses of the matrix and segregant respectively and ksm is the usual k-factor. The geometric factor, V/A, is the ratio of the volume of interaction to the area of the grain boundary inside in the interaction volume. Different models have been used to describe the interaction volume and these are illustrated in Fig. 1 and the appropriate expression for V/A is given in each case. In the simplest case, beam broadening is neglected and the interaction volume can be described as a cylinder with diameter equal to the probe size, d.