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[20]
contribution in the poled condition is responsible for the high piezoelectricity of poled crystals . One
could also expect such low-temperature behavior in glassy tweed meso-states due to a coupling between
[11]
non-local elasticity and compositional inhomogeneity .

The strength of the adaptive phase theory is in its simple elegance in making invariant the lattice parameter
changes with temperature and field based on a crystallographic/geometric theory. The strength of the
approach by Li et al. is in its ability to bring together numerous gradient contributions and elastic boundary
conditions into a phase field theory that could be used for piezoelectricity by computational design [18-20] . The
overall weakness has been that the majority of research efforts have been devoted to investigations within
the framework of a homogenous single-phase monoclinic structure. To date, monoclinic phases in these
complex Pb-based perovskites have only been reported in polydomain materials - there has yet to be the
finding of a single-domain single-crystal monoclinic phase.

DECLARATIONS
Acknowledgments
Much thanks to prior authors of referenced papers in the figures, and to the American Institute of Physics
and to the Nature Publishing Group for figure reproduction.

Authors’ contributions
The author contributed solely to the article.

Availability of data and materials
Not applicable.

Financial support and sponsorship
None.

Conflicts of interest
The author declared that there are no conflicts of interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.

Copyright
© The Author(s) 2023.

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