  Since AlN has emerged as an important piezoelectric material for a wide
variety of applications, efforts have been made to increase its piezoelectric
response via alloying with transition metals that can substitute for Al in the
wurtzite lattice. Herein, we report density functional theory calculations of
structure and properties of the Cr-AlN system for Cr concentrations ranging
past the wurtzite-rocksalt transition point. By studying the different
contributions to the longitudinal piezoelectric coefficient, we propose that
the physical origin of the enhanced piezoelectricity in Cr$_x$Al$_{1-x}$N
alloys is the increase of the internal parameter $u$ of the wurtzite structure
upon substitution of Al with the larger Cr ions. Among a set of
wurtzite-structured materials, we have found that Cr-AlN has the most sensitive
piezoelectric coefficient with respect to alloying concentration. Based on
these results, we propose that Cr-AlN is a viable piezoelectric material whose
properties can be tuned via Cr composition; we support this proposal by
combinatorial synthesis experiments, which show that Cr can be incorporated in
the AlN lattice up to 30\% before a detectable transition to rocksalt occurs.
At this Cr content, the piezoelectric modulus $d_{33}$ is approximately four
times larger than that of pure AlN. This finding, combined with the relative
ease of synthesis, may propel Cr-AlN as the prime piezoelectric material for
applications such as resonators and acoustic wave generators.
