r → −r

LITA crystal is centrosymmetric if inversion through a point (r → −r) maps it onto itself. Of the 32 crystallographic point groups, 11 are centrosymmetric and 21 are not. Of the 21, 20 are piezoelectric (squeeze them and a voltage appears); cubic 432 is the exception. Quartz (point group 32) is the classic piezoelectric. The 230 space groups of batch 11 are built on these 32 classes.

COMPUTEDA 2D toy cell of charges: +q at the centre and −q/2 at two sites. Strain the cell and the dipole moment is computed exactly. With the two −q/2 placed symmetrically through the centre, the dipole stays zero; shift them off-centre and strain produces a net dipole (the piezo effect).

strain switch lattice

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