Table 3 Λ tensors for the symmetry-inequivalent atoms of the ferroelectric phase of HfO2 (in eV Å−1).

From: Piezoelectricity in hafnia

Hf

\(\left[\begin{array}{llllll}-4.02&0.00&-2.29&8.39&0.83&0.79\\ -1.04&11.52&-1.40&4.50&3.58&5.87\\ -1.87&1.45&{{{{{{{\bf{-4.07}}}}}}}}&-2.83&-2.61&3.42\end{array}\right]\)

OI

\(\left[\begin{array}{llllll}2.06&-0.63&1.09&-5.87&-3.29&0.91\\ -1.97&-1.75&-1.43&-2.77&-4.60&-2.34\\ -1.61&0.42&{{{{{{{\bf{3.22}}}}}}}}&1.36&0.29&-4.53\end{array}\right]\)

OII

\(\left[\begin{array}{llllll}-5.87&1.10&-1.07&4.67&2.46&0.06\\ 0.79&7.87&0.54&-1.71&4.10&0.52\\ 3.46&1.86&{{{{{{{\bf{0.85}}}}}}}}&1.27&-1.36&5.44\end{array}\right]\)

  1. The 3 rows correspond, respectively, to the 3 spatial directions; the 6 columns correspond, respectively, to the 6 strain indices in Voigt notation. Marked in bold are the entries controlling the longitudinal piezoresponse, as discussed in the text.
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