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Application of mechanical stress to a piezo crystal generates a charge.

Quoting from wikipedia, a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500 V.

What happens when the crystal is exposed to a vacuum? Is the converse true? If the structural deformation occurs as a result of exposure to vacuum, is a voltage still generated?

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Any mechanical strain creates electricity.

You can use a piezo sensor as a pressure gauge, it's common for very high/fast pressure changes because the crystal can survive a very high pressures and it's small so responds quickly.

edit: to make a pressure sensor you need one side of the crystal exposed to vacuum and the other to a fixed pressure - so that the crystal bends when the pressure changes.

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