I don't think those cryocoolers use a mix of exotic refrigerants, they use medium-pressure helium (~300 psi) always in the gas phase. This is rapidly compressed and relaxed (60 hz) with about a %25 pressure swing. Some designs use a moving part in the cold head, but some don't (pulse tubes). Even the ones with moving parts are generally wear free, for some reason the displacer centers itself in its bore and although the tolerances are fairly tight, deos not contact the tube wall during operation. The cold head is designed with metal screens and free volume spaces arranged in such a way that at the operating frequency, a phase "mismatch" is introduced which I think is between pressure and flow, or perhaps pressure and volume. Although the device is strictly linear(classicly: new designs use U tubes and/or have ports at the top end that feed back to the bottom), somehow the gas is tricked into expanding in the far (cold) end and compressing/dumping heat into the near (hot) end almost continuosly. I don't think I've ever fully understood them, or if I did I've forgotten the physics. This technology is virtualy identical to that use in cryopumps for high vacuum. Anyone interested in experimenting with this technology should be able to purchase a used cryopump on e-bay for ~$250. However, whereas the Qdrive system seem to use voice coils and other "acoustic" engines mated directly to the pulse tubes, cryopumps use an external compressor. The compressor supplies helium, but this helium is not circulated through the cold head. Instead it is used to drive a "scotch yolk" mechanism attached to the cold head, which provides the mechanical "accoustic" energy. Nevertheless high purity helium is required: else water and ice may form in the scotch yolk. I've heard that traditional refrigerator compressors are used, the important thing being to follow the compressor with a large activated carbon filter bed to trap compressor oil. The traps must be periodically replaced (dunno how often) and they're quite a bit pricier than they should be.
-Jeff