New method to measure domain-wall motion contribution to piezoelectricity: the case of PbZr_0.65Ti_0.35O₃ ferroelectric

Abstract

A new data analysis routine is introduced to reconstruct the change in lattice parameters in individual ferroelastic domains and the role of domain-wall motion in the piezoelectric effect. Using special electronics for the synchronization of a PILATUS X-ray area detector with a voltage signal generator, the X-ray diffraction intensity distribution was measured around seven split Bragg peaks as a function of external electric field. The new data analysis algorithm allows the calculation of `extrinsic' (related to domain-wall motion) and `intrinsic' (related to the change in lattice parameters) contributions to the electric-field-induced deformation. Compared with previously existing approaches, the new method benefits from the availability of a three-dimensional diffraction intensity distribution, which enables the separation of Bragg peaks diffracted from differently oriented domain sets. The new technique is applied to calculate the extrinsic and intrinsic contributions to the piezoelectricity in a single crystal of the ferroelectric PbZr1−x Ti x O3 (x = 0.35). The root-mean-square value of the piezoelectric coefficient was obtained as 112 pC N−1. The contribution of the domain-wall motion is estimated as 99 pC N−1. The contribution of electric-field-induced changes to the lattice parameters averaged over all the domains is 71 pC N−1. The equivalent value corresponding to the change in lattice parameters in individual domains may reach up to 189 pC N−1.

Multipurpose diffractometer for in situ X-ray crystallography of functional materials

“…The instrument is equipped with commercial and custom-built electric signal function generators and high-voltage amplifiers. Synchronization between the detector and the function generators may be realized using a point detector (Schmidt et al, 2009;Gorfman et al, 2013Gorfman et al, , 2015Gorfman et al, , 2016Gorfman, 2014;Khanbabaee et al, 2016;Iamsasri et al, 2017;Choe et al, 2018) or the PILATUS3 R 1M (Choe et al, 2017;Zhang et al, 2018;Gorfman et al, 2020 Example of the results of high-resolution reciprocal-space mapping of X-ray diffraction intensity distribution around the {200} family of reflections from a BaTiO 3 crystal. Two-and one-dimensional plots are obtained by the integration of the three-dimensional intensity distribution along the 'missing' direction, e.g.…”

“…One particular application is the measurement of reflection splitting in ferroelectric/ ferroelastic materials, arising from the presence of ferroelastic domains. Such splitting has been used to derive the symmetry of a single domain of ferroelectric material (Gorfman & Thomas, 2010;Datta et al, 2009;Gorfman et al, 2011Gorfman et al, , 2020Choe et al, 2018;Zhang et al, 2018). A high degree of beam monochromaticity and low angular divergence is mandatory to observe and measure this splitting.…”

“…Three-dimensional diffraction intensity was reconstructed as a function of scattering vector H ¼ ðs þ dÞ= (here s and d are the unitary vectors pointing from the crystal to the source and detector pixels, respectively). This intensity distribution is displayed as two-dimensional and one-dimensional projections in the reciprocal space, described by the Cartesian coordinates H x , H y , H z [H x is the component of the scattering vector parallel to the reciprocal-lattice vector of the reflection as previously used by Zhang et al (2018) and Gorfman et al (2020)]. The tetragonal symmetry of ferroelastic domains (with c > a) results in the clear separation of the peaks along the x axis.…”

“…Such separation of peaks can be used to reconstruct domain structure/domain walls as well as for the investigation of the response of individual domains to external perturbation (see e.g. Harrison et al, 2004;Zhang et al, 2018;Gorfman et al, 2020).…”

Recognition of domain patterns using high-resolution single-crystal X-ray diffraction

“…The experimental part of the work is done at the single crystal four-circle X-ray diffractometer in Tel Aviv University (Tel Aviv, Israel) and Swiss-Norwegian Beamlines at the European Synchrotron (Grenoble, France). We used the methodology outlined in [4] to accumulate three-dimension X-ray diffraction intensity distribution in the reciprocal space around split Bragg reflection diffracted from the domains in BaTiO3 (BT) and Na0.5Bi0.5TiO3 (NBT). The positions of individual sub-peaks in the reciprocal space can be marked and geometrical parameters of the peak groups (e.g.…”