Fourier transforms of EELFS spectra from various microareas on the surface of worn craters of cutting tools with the TiAlCrSiYN monolayer coating (a, b) and TiAlCrSiYN/TiAlCrN multilayer coating (c, d). The nearest atomic surrounding has characteristics of sapphire (a) and mullite (b) structure; the standard interatomic bonds lengths in sapphire and mullite are presented at the top and the bottom, respectively. (Reproduced with permission from [17, 24], Elsevier, AIP.)