  The origin of the anomalous, 400% increase of the piezoelectric coefficient
in Sc$_x$Al$_{1-x}$N alloys is revealed. Quantum mechanical calculations show
that the effect is intrinsic. It comes from a strong change in the response of
the internal atomic coordinates to strain and pronounced softening of C$_{33}$
elastic constant. The underlying mechanism is the flattening of the energy
landscape due to a competition between the parent wurtzite and the so far
experimentally unknown hexagonal phases of the alloy. Our observation provides
a route for the design of materials with high piezoelectric response.
