Polyduranium was a very rare material.
In 2153, polyduranium was encountered by Enterprise in the doors of the Delphic Expanse sphere and the Osaarian merchant ship's hull. (ENT: "Anomaly")
Polyduranium was used in a bulkhead on the bridge of the USS Defiant. In 2371, Ornithar expressed an interest in it but he believed it had no real value. (DS9: "The Search, Part I")