A functional micromechanical timepiece assembly including at least a first component, including a first layer defining a first contact surface configured to come into friction contact with a second contact surface defined by a second layer, the second layer belonging, either to the first component, or to at least a second micromechanical component forming the assembly with the first component. The first and second layers each include carbon with at least 50% carbon atoms and, on the first and second contact surfaces, the layers have different surface crystalline plane orientations from each other.