al 2 o 3 layer is virtually free of cracks and halogen impurities furthermore the al 2 o 3 layer gives the cutting edge of the tool an extremely smooth surface finish application_number US 78222601 A description the u03b3 al 2 o 3 layers according to the invention further give the cutting edges of the tool an extremely smooth surface finish which compared to prior art u03b1 al 2 o 3 coated tools results in an improved surface finish also of the workpiece being machined the very smooth surface finish can be attributed to the very fine crystallinity of the coating the u201c u03b3 al 2 o 3 u201d layers may also partially contain other phases from the u201c u03b3 series u201d like u03b8 u03b4 and u03b7 identification of the u03b3 and or u03b8 phases in the al 2 o 3 layers according to the invention can preferably be made by x ray diffraction reflexes from the 400 and 440 planes of the u03b3 al 2 o 3 layers occurring at the 2 u03b8 angles 45 8 u00b0 and 66 8 u00b0 when using cu k u03b1 radiation unequivocally identifies the u03b3 phase fig3 weaker reflexes from the 222 200 and 311 planes of the u03b3 phase can occasionally be identified when the u03b8 phase is present in the al 2 o 3 layers according to the invention said phase.