Ifound a diaphragm system should avoid seals problems specially with metallics diaph.thinking in a high pressure pump..So i found CR4 still i've not an answer may be the same for you.i just made this picture.
I don't think edignan was off topic as yesyen asked about an engine. He did not specify it to be internal combustion.
What sort of material could be used as a diaphragm at IC temperatures? I would suppose that stainless steel would work for a short while but I cannot imagine it would have a very long service life.
Off topic but related would be the screw compressors. It always seemed to me that they should be configurable to become an IC motor, using one unit to compress the air and a second as a rotary combustion chamber.
Chas.
__________________
En la casa del herrero, cuchillos de palo!
Even IC engine is relevant for this matter. In IC engines, aluminum pistons are standing to prevailing temperature conditions, why not SS?
Well for flexing diaphragm at this temperature can be subjective. As you have rightly indicated, "would work for a short while", can be good for racecar engines to enable high efficiency.
"Using one unit to compress the air and a second as a rotary combustion chamber", is a very good indication, even for new thread (Capblanc, would you start a new thread on your pointing?). Other than 'turbo engines' were there attempts made with this combination, compressor (other than centrifugal but like rotary and reciprocating) to combustion chamber then to expander (other than centrifugal but like rotary and reciprocating expander)?
__________________
A picture worth thousand words: needless to say if it is animated.