A substrate is coated with a multi-layer coating, comprising in order: (i) a first functional layer comprising ta-C, (ii) a second functional layer comprising ta-C, (iii) (a) a third functional layer comprising ta-C and a first intermediate layer comprising a carbide of a first element, or (b) a first intermediate layer comprising a carbide of a first element, and a second intermediate layer comprising the first element, wherein the ta-C has a hydrogen content less than 10% and an sp2 content less than 30%; wherein (i) the Young's modulus or (ii) the hardness or (iii) both the Young's modulus and the hardness independently stay the same or increase from layer to layer in (iii) (a) from the first intermediate layer to the first functional layer, or in (iii) (b) from the second intermediate layer to the first functional layer.