This rosette, that goes behind a door knob, is probably cast bronze. It has an Eastlake pattern which dates this item from 1870 to 1890. During this period of hardware manufacturing, many of the casting houses favored bronze over brass.
The rosette measures 2 inches round. The inside dimension for the knob neck is a breath under 5/8 inch. The knob neck needs to be thin in order to fit this rosette.
This is a very fine old piece of hardware.