a non-centrosymmetric crystal

A non-centrosymmetric crystal is one that lacks a centre of inversion, there is no interior point through which every atom has an identical opposite partner. Its structure looks genuinely different from its point-inverted twin. Where a centrosymmetric crystal is perfectly balanced through its middle, a non-centrosymmetric one has a built-in lopsidedness that physics can exploit.

Exactly 21 of the 32 crystal classes are non-centrosymmetric (all except the 11 centrosymmetric ones). Of those 21, 20 are piezoelectric, squeeze them and they develop a voltage, apply a voltage and they change shape. The lone exception is class 432, whose high rotational symmetry cancels the piezoelectric effect even though it has no inversion centre. A further subset, the 10 polar classes, are pyroelectric and can be ferroelectric.

Non-centrosymmetry is the gateway property for a huge range of technology: quartz oscillators in watches, ultrasound transducers, sonar, medical imaging, the piezo actuators that focus camera lenses, and the crystals (like lithium niobate and KDP) that double laser frequencies. Whenever a device turns mechanical push into electrical signal or vice versa, or doubles a light frequency, a non-centrosymmetric crystal is usually at its heart.