The idea for this stirling is called, crystal metal heat expansion. It was given a name so this article can be separated from the other stirling engine articles.
This engine is simple and easy, I will explain it as quickly as possible. You have your basic stirling engine, except in one of the heat exchanging chambers, there are two pieces of crystal with a piece of metal wedged between them.
As the hot air fills the heat exchange, the metal gets warmer and expands. This causes the metal to press against the crystals creating an electric current out of them.
Now the heat exchange is trading the gas inside and the gas is cooled off. This causes the metal plate to cool off retracting the crystals. This produces an electric current going into the crystals.
That heat and cool process continues, it is a stirling engine. A stirling engine that produces electricity using a set of crystals and metal plates.
It can use a set of metal plates that are wedged on one end, with one end being a heat exchange. This would use the metal plates side without crystals to be used as a heat sink, expanding and retracting the metal to put pressure, and retract pressure on crystals.
I lack the engineering skills to produce a prototype. Maybe someone will see my self published article and know what to do with the idea, if the idea is valid in anyway.