Not general aviation but a real world example.
CX138 SYD-HKG, a B-777, diverted to Cairns a short time ago. They were squawking 7700 and added Mayday to their callsign when contacting approach.
They check in at 22:10 into this clip:
http://archive-server.liveatc.net/yb...2018-1530Z.mp3
They diverted for a medical emergency:
https://flightaware.com/live/flight/...212Z/YSSY/YBCS