A first stage turbine nozzle includes a first stage hub portion extending axially along a central axis, a first stage disk portion attached to the first stage hub portion and centered on the central axis, and a plurality of first stage vanes positioned radially around and attached to the first stage disk portion. Each vane extends a vane height H away from the first stage disk portion and each vane has a first end positioned at a diameter D away from the central axis. The first stage turbine nozzle also includes a plurality of first stage throats defined between radially adjacent first stage vanes. Each first stage throat has a throat width W between radially adjacent first stage vanes. The first stage turbine nozzle also includes a coating on a sidewall of each first stage vane.