I'm baffled about what you are trying to do but it sounds like your goal is at least worthy. Sounds like an underwater Sterling Engine prototype designed to harness black smoker vents in the sea floor to me

Here's the help I can give you:

You need to worry about the compressive strength rather than the tensile strength. These are generally very different quantities for non-metals.

Secondly, I'm not sure I agree with Geoff that it is doomed to fail with multiple cavities but I'd have to say that it is likely to be a lot easier to do with one big cavity. He has more experience than I do. He's definitely right that any sharp transitions inside will provide stress concentration points which could cause the crystals to shatter.

I expect you could make a very thick sapphire bubble in two halves with a flange in the middle to preload whatever type of gasket you would use for that kind of high pressure application.

I would suggest that you look at an engineering handbook for the equations for collapse of an externally pressurized sphere. It will probably be somewhere near wherever the index says you will find hoop stress.

Good luck.

--Cameron