Fig. 6: Understanding the origin of piezoelectric and ferroelectric effects in the NbOX2 family.
From: Data-driven discovery of high performance layered van der Waals piezoelectric NbOI2
a Dynamical charges for Nb and O, \({{{{{{\boldsymbol{Z}}}}}}}_{{Nbx},x}^{{{{{{\boldsymbol{* }}}}}}}\) and \({{{{{{\boldsymbol{Z}}}}}}}_{{Ox},x}^{{{{{{\boldsymbol{* }}}}}}}\). as a function of δx, the difference between the longer and shorter Nb-O bonds. The inset shows the integral of \({{{{{{\boldsymbol{Z}}}}}}}_{{Nbx},x}^{{{{{{\boldsymbol{* }}}}}}}\) with respect to the x-displacement away from the high-symmetry site. In both the main figure and the inset, dashed lines indicate the values in the equilibrium structures. b\(\left|\frac{\partial {{{{{{\boldsymbol{u}}}}}}}_{{{{{{{\boldsymbol{m}}}}}}}^{{{{{{\boldsymbol{x}}}}}}}}}{\partial {{{{{{\boldsymbol{\eta }}}}}}}_{1}}\right|\) in the equilibrium structures of NbOX2, indicating the rate of change of x-displacement of each atom (Nb, O, or X) with strain in the x-direction. NbOI2 has the largest lattice response to strain, due to the smaller stiffness tensor elements and weaker Nb-O bonds. c Schematic illustrating the origins of the trends in ferroelectricity and piezoelectricity in NbOX2.
