Simultaneous resonant x-ray diffraction measurement of polarization inversion and lattice strain in polycrystalline ferroelectrics

Electric-field-induced non-ergodic relaxor to ferroelectric transition in BiFeO3-xSrTiO3 ceramics

While BiFeO₃-based solid solutions show great promise for applications in energy conversion and storage, realizing this promise necessitates understanding the structure-property relationship in particular pertaining to the relaxor-like characteristics often exhibited by solid solutions with polar-to-non-polar morphotropic phase boundaries. To this end, we investigated the role of the compositionally-driven relaxor state in (100 - x)BiFeO₃-xSrTiO₃ [BFO-xSTO], via in situ synchrotron X-ray diffraction under bipolar electric-field cycling. The electric-field induced changes to the crystal structure, phase fraction and domain textures were monitored via the {111}_pc, {200}_pc, and 1/2{311}_pc Bragg peaks. The dynamics of the intensities and positions of the (111) and (111̄) reflections reveal an initial non-ergodic regime followed by long-range ferroelectric ordering after extended poling cycles. The increased degree of random multi-site occupation in BFO-42STO compared to BFO-35STO is correlated with an increase of the critical electric field needed to induce the non-ergodic-to-ferroelectric transition, and a decrease in the degree of domain reorientation. Although both compositions show an irreversible transition to a long-range ferroelectric state, our results suggest that the weaker ferroelectric response in BFO-42STO is related to an increase in ergodicity. This, in turn, serves to guide the development of BFO-based systems into promising platform for further property engineering towards specific capacitor applications.

Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain

The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different photon energies near an absorption edge. Comparing the obtained reconstructions with a parametric model that includes calculating the scattering amplitude as a function of wavelength and the unit-cell configuration, the contributions of the lattice deformation and the structure factor are separated. Simulations of the ferroelectric material BaTiO₃ demonstrate the possibility of simultaneous probing of the strain and displacement of the Ti atoms. The proposed method opens up an opportunity to apply coherent X-ray diffraction for nanoscale-resolved 3D mapping of polarization domains in micro- and nanocrystals.

In situmonitoring of epitaxial ferroelectric thin-film growth

In ferroelectric thin films, the polarization state and the domain configuration define the macroscopic ferroelectric properties such as the switching dynamics. Engineering of the ferroelectric domain configuration during synthesis is in permanent evolution and can be achieved by a range of approaches, extending from epitaxial strain tuning over electrostatic environment control to the influence of interface atomic termination. Exotic polar states are now designed in the technologically relevant ultrathin regime. The promise of energy-efficient devices based on ultrathin ferroelectric films depends on the ability to create, probe, and manipulate polar states in ever more complex epitaxial architectures. Because most ferroelectric oxides exhibit ferroelectricity during the epitaxial deposition process, the direct access to the polarization emergence and its evolution during the growth process, beyond the realm of existing structuralin situdiagnostic tools, is becoming of paramount importance. We review the recent progress in the field of monitoring polar states with an emphasis on the non-invasive probes allowing investigations of polarization during the thin film growth of ferroelectric oxides. A particular importance is given to optical second harmonic generationin situ. The ability to determine the net polarization and domain configuration of ultrathin films and multilayers during the growth of multilayers brings new insights towards a better understanding of the physics of ultrathin ferroelectrics and further control of ferroelectric-based heterostructures for devices.

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

Laboratory X-ray diffractometers play a crucial role in X-ray crystallography and materials science. Such instruments still vastly outnumber synchrotron facilities and are responsible for most of the X-ray characterization of materials around the world. The efforts to enhance the design and performance of in-house X-ray diffraction instruments benefit a broad research community. Here, the realization of a custom-built multipurpose four-circle diffractometer in the laboratory for X-ray crystallography of functional materials at Tel Aviv University, Israel, is reported. The instrument is equipped with a microfocus Cu-based X-ray source, collimating X-ray optics, four-bounce monochromator, four-circle goniometer, large (PILATUS3 R 1M) pixel area detector, analyser crystal and scintillating counter. It is suitable for a broad range of tasks in X-ray crystallography/structure analysis and materials science. All the relevant X-ray beam parameters (total flux, flux density, beam divergence, monochromaticity) are reported and several applications such as determination of the crystal orientation matrix and high-resolution reciprocal-space mapping are demonstrated. The diffractometer is suitable for measuring X-ray diffraction in situ under an external electric field, as demonstrated by the measurement of electric-field-dependent rocking curves of a quartz single crystal. The diffractometer can be used as an independent research instrument, but also as a training platform and for preparation for synchrotron experiments.

The time-resolved hard X-ray diffraction endstation KMC-3 XPP at BESSY II

The time-resolved hard X-ray diffraction endstation KMC-3 XPP for optical pump/X-ray probe experiments at the electron storage ring BESSY II is dedicated to investigating the structural response of thin film samples and heterostructures after their excitation with ultrashort laser pulses and/or electric field pulses. It enables experiments with access to symmetric and asymmetric Bragg reflections via a four-circle diffractometer and it is possible to keep the sample in high vacuum and vary the sample temperature between ∼15 K and 350 K. The femtosecond laser system permanently installed at the beamline allows for optical excitation of the sample at 1028 nm. A non-linear optical setup enables the sample excitation also at 514 nm and 343 nm. A time-resolution of 17 ps is achieved with the `low-α' operation mode of the storage ring and an electronic variation of the delay between optical pump and hard X-ray probe pulse conveniently accesses picosecond to microsecond timescales. Direct time-resolved detection of the diffracted hard X-ray synchrotron pulses use a gated area pixel detector or a fast point detector in single photon counting mode. The range of experiments that are reliably conducted at the endstation and that detect structural dynamics of samples excited by laser pulses or electric fields are presented.

In Situ Imaging of Ferroelastic Domain Dynamics in CsPbBr3 Perovskite Nanowires by Nanofocused Scanning X-ray Diffraction

The interest in metal halide perovskites has grown as impressive results have been shown in solar cells, light emitting devices, and scintillators, but this class of materials have a complex crystal structure that is only partially understood. In particular, the dynamics of the nanoscale ferroelastic domains in metal halide perovskites remains difficult to study. An ideal in situ imaging method for ferroelastic domains requires a challenging combination of high spatial resolution and long penetration depth. Here, we demonstrate in situ temperature-dependent imaging of ferroelastic domains in a single nanowire of metal halide perovskite, CsPbBr3. Scanning X-ray diffraction with a 60 nm beam was used to retrieve local structural properties for temperatures up to 140 °C. We observed a single Bragg peak at room temperature, but at 80 °C, four new Bragg peaks appeared, originating in different real-space domains. The domains were arranged in periodic stripes in the center and with a hatched pattern close to the edges. Reciprocal space mapping at 80 °C was used to quantify the local strain and lattice tilts, revealing the ferroelastic nature of the domains. The domains display a partial stability to further temperature changes. Our results show the dynamics of nanoscale ferroelastic domain formation within a single-crystal perovskite nanostructure, which is important both for the fundamental understanding of these materials and for the development of perovskite-based devices.

Local Strain and Polarization Mapping in Ferrielectric Materials

CuInP₂S₆ (CIPS) is a van der Waals material that has attracted attention because of its unusual properties. Recently, a combination of density functional theory (DFT) calculations and piezoresponse force microscopy (PFM) showed that CIPS is a uniaxial quadruple-well ferrielectric featuring two polar phases and a total of four polarization states that can be controlled by external strain. Here, we combine DFT and PFM to investigate the stress-dependent piezoelectric properties of CIPS, which have so far remained unexplored. The two different polarization phases are predicted to differ in their mechanical properties and the stress sensitivity of their piezoelectric constants. This knowledge is applied to the interpretation of ferroelectric domain images, which enables investigation of local strain and stress distributions. The interplay of theory and experiment produces polarization maps and layer spacings which we compare to macroscopic X-ray measurements. We found that the sample contains only the low-polarization phase and that domains of one polarization orientation are strained, whereas domains of the opposite polarization direction are fully relaxed. The described nanoscale imaging methodology is applicable to any material for which the relationship between electromechanical and mechanical characteristics is known, providing insight on structural, mechanical, and electromechanical properties down to ∼10 nm length scales.

Piezoelectric Properties of Pb1-xLax(Zr0.52Ti0.48)1-x/4O3 Thin Films Studied by In Situ X-ray Diffraction

The piezoelectric properties of lanthanum-modified lead zirconate titanate Pb_1-xLa_x(Zr_0.52Ti_0.48)_1-x/4O₃ thin films, with x = 0, 3 and 12 mol% La, were studied by in situ synchrotron X-ray diffraction under direct (DC) and alternating (AC) electric fields, with AC frequencies covering more than four orders of magnitude. The Bragg reflections for thin films with low lanthanum concentration exhibit a double-peak structure, indicating two contributions, whereas thin films with 12% La possess a well-defined Bragg peak with a single component. In addition, built-in electric fields are revealed for low La concentrations, while they are absent for thin films with 12% of La. For static and low frequency AC electric fields, all lanthanum-modified lead zirconate titanate thin films exhibit butterfly loops, whereas linear piezoelectric behavior is found for AC frequencies larger than 1 Hz.

New method to measure domain-wall motion contribution to piezoelectricity: the case of PbZr0.65Ti0.35O3 ferroelectric

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.

Intrinsic Ferroelectricity in Charge-Ordered Magnetite

Single crystalline magnetite Fe 3 O 4 was investigated at low temperatures in the charge ordered state by electric measurements and time-resolved diffraction with voltage applied in-situ. Dielectric spectroscopy indicates relaxor ferroelectric characteristics, with polarization switching observably only at sufficiently low temperatures and in a suitably chosen time-window. PUND measurements with a ms time scale indicate a switchable polarization of about 0 . 6 μ C / cm 2 . Significant switching occurs only above a threshold field of about 3 kV / mm , and it occurs with a time delay of about 20 μ s . The time-resolved diffraction experiment yields, for sufficiently high voltage pulses, a systematic variation by about 0 . 1 % of the intensity of the ( 2 , 2 ¯ , 10 ¯ ) Bragg reflection, which is attributed to structural switching of domains of the non-centrosymmetric C c structure to its inversion twins, providing proof of intrinsic ferroelectricity in charge ordered magnetite.

Time filtering of event based neutron scattering data: A pathway to study the dynamic structural responses of materials

Time-resolved diffraction has become a vital tool for probing dynamic responses to an applied stimulus. Such experiments traditionally use hardware solutions to histogram measured data into their respective bin. We will show that a major advantage of event-based data acquisition, which time-stamps measured diffraction data with 100 ns accuracy, is much preferred over hardware histogramming of the data by enabling postprocessing for advanced custom binning using a software solution. This approach is made even more powerful by coupling measured diffraction data with metadata about the applied stimuli and material response. In this work, we present a time-filter approach that leverages the power of event-based diffraction collection to reduce stroboscopic data measured over many hours into equally weighted segments that represent subsets of the response to a single cycle of the applied stimulus. We demonstrate this approach by observing ferroelectric/ferroelastic domain wall motion during electric field cycling of BaTiO₃. The developed approach can readily be expanded to investigate other dynamic phenomena using complex sample environments.

Monoclinic distortion, polarization rotation and piezoelectricity in the ferroelectric Na0.5Bi0.5TiO3

The relationship between crystal structure and physical properties in the ferroelectric Na0.5Bi0.5TiO3 (NBT) has been of interest for the last two decades. Originally, the average structure was held to be of rhombohedral (R3c) symmetry with a fixed polarization direction. This has undergone a series of revisions, however, based on high-resolution X-ray diffraction, total neutron scattering, and optical and electron microscopy. The recent experimental findings suggest that the true average symmetry is monoclinic (space group Cc), which allows for a rotatable spontaneous polarization. Neither polarization rotation nor its potentially important real role in enhanced piezoelectricity is well understood. The present work describes an in situ investigation of the average monoclinic distortion in NBT by time-resolved single-crystal X-ray diffraction under external electric fields. The study presents a high-resolution inspection of the characteristic diffraction features of the monoclinic distortion - splitting of specific Bragg reflections - and their changes under a cyclic electric field. The results favour a model in which there is direct coupling between the shear monoclinic strain and the polarization rotation. This suggests that the angle of polarization rotation under a sub-coercive electric field could be 30° or more.