“…All crystallite sizes were calculated from full width of half maximum (FWHM) of the XRD peaks by using the Debye-Scherrer equation ( τ = Kλ / βcosθ ) 61,62 ( τ is the size of the crystallite, K is Scherrer constant 0.94, λ is the X-ray wavelength which in this case is 1.54Å produced by a copper pole, β is Δ(2 θ ) (FWHM) of the XRD peaks, and θ represents the angles where the peaks are positioned 63 ). The crystallite sizes of the crystal structures formed in the bottom layer were calculated to be 30 nm for c-TiN and 30 nm for c-TiCrN, in TiAlN layer; 12 nm for c-TiN, 6.5 nm for h-TiAlN, and 22 nm for c-AlN, in the third layer, TiAlSiN; 9.8 nm for c-TiN, 11.1 nm for h-TiAlN, and 22.73 nm for h-Si 3 N 4 , and in the fourth layer (TiAlSiCN) crystallite sizes where 6.47 nm for c-TiN, 6.14 nm for c-TiCN, and 16.7 nm for c-AlN.…”