Time-of-flight neutron total scattering with applied electric fields: Ex situ and in situ studies of ferroelectric materials

In situ X-ray and neutron scattering experiments facilitate understanding of the structural responses of a material to external stimuli (e.g., pressure, temperature, atmosphere, electric field, or stress), as required for establishing structure-property relationships. Examples of material classes that benefit from such measurements are ferroelectrics and piezoelectrics,¹ which are used in numerous electromechanical applications due to their ability to interconvert electrical and mechanical energy (e.g., sonar, actuators, transducers, microelectromechanical devices, ferroelectric memories, and energy-harvesting).^2–5 

Recently, conventional Bragg X-ray diffraction under applied electric fields has been extended to the measurements of X-ray total scattering (Bragg peaks plus diffuse background), which can be used to derive (via the Fourier transform) directional atomic pair distribution functions (PDFs) that enable the observation of field-induced local-scale structural changes in real space.^6–9 While this method has proven to be informative, it is limited by the relative insensitivity of X-ray scattering to light elements in the presence of the heavy ones, which hinders measurements of metal-oxygen distances in typical ferroelectric oxides. Likewise, X-ray scattering cannot differentiate elements that have similar atomic numbers. On the instrument side, X-ray total scattering, which is typically measured using 2D detectors, must balance the need for an extended Q-range (>25 Å⁻¹) with the available reciprocal-space resolution, which is limited by the number of pixels on a 2D detector (e.g., 2048 × 2048).¹⁰ These limitations can be addressed by using in situ time-of-flight neutron total scattering to complement the X-ray data. In the present contribution, we report the development of this method for applying electric fields to samples while measuring neutron total scattering, which was performed using the instrument NOMAD at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL).^11,12 We present the data reduction and analysis approach, the high-voltage sample cells, the experimental setup, relevant details of the NOMAD diffractometer, and experimental difficulties and limitations. Results and discussion are presented for the ferroelectric ceramic sodium bismuth titanate, Na_1/2Bi_1/2TiO₃, which shows electric-field induced strain and changes in the metal-oxygen bond distances.

As-synthesized bulk polycrystalline (i.e., ceramic) ferroelectrics are effectively isotropic.¹³ Each grain is a single crystal that contains multiple ferroelectric domains with distinct orientations of the polarization vector; the macroscopic polarization is zero. For polycrystalline ferroelectrics to be useful for applications, a “poling” process must be performed in which a strong electric field is applied to the sample.¹³ This causes domain reorientation such that electric dipoles become preferentially aligned with the electric-field vector and the sample symmetry is reduced to cylindrical (∞m).¹⁴ Additionally, lattice strain typically accompanies domain reorientation and is positive parallel to the electric field and negative perpendicular to the electric field.¹⁵ Other possible electric-field-induced effects include interphase boundary motion and reorientation of local-scale polar displacements.^6,16

We used a ferroelectric perovskite-structured oxide, Na_1/2Bi_1/2TiO₃, in the development of the ex situ and in situ neutron total-scattering technique. This lead (Pb)-free relaxor ferroelectric Na_1/2Bi_1/2TiO₃ has a complex hierarchical room temperature structure^17,18 and exhibits large electric-field-induced local structural changes.⁶ The sample synthesis is described in Ref. 19 but was modified by increasing the calcining and sintering hold times to 4 h to accommodate larger powder volumes, and the pellets were pressed in a 25 mm square die without the use of a binder. Neutron and X-ray PDF studies of Na_1/2Bi_1/2TiO₃ have shown that Na⁺ and Bi³⁺ have distinct oxygen bonding environments.²⁰ For initial tests, the sample was measured ex situ in the isotropic unpoled state and the anisotropic poled state. Neutron PDF studies following the behavior of the local correlations in these and other oxides under applied electric fields have not previously been completed and will offer potential new insights into the structure-property mechanisms enabling the functionalities of these materials.

Time-of-flight (ToF) neutron scattering utilizes pulses of white-beam neutrons with a range of energies. Neutrons with different energies (and different wavelengths, according to the de Broglie relationship) travel at different speeds from a fixed source. Thus, a fixed-position detector can measure wide-angle diffraction or total scattering by sorting incident neutrons according to the time at which they arrive at the detector and calculating their wavelengths with the knowledge of the distances traveled from the source to the sample to the detector.²¹ The ToF instrument NOMAD at the SNS at ORNL is optimized for high intensity diffraction and total scattering measurements on amorphous, nanostructured, and disordered crystalline materials.¹¹ It features a large bandwidth of neutron energies, extensive detector coverage, and count rates exceeding comparable instruments by one to two orders of magnitude.¹¹ A schematic diagram of the instrument detector banks is shown in Fig. 1(a). As of 2018 50 ³He linear position sensitive detector 8-packs are installed of the originally designed 99. This corresponds to 51 000 pixels, grouped into six default banks. The normalized and background subtracted scattering intensities are shown separately for each of the six default banks in Fig. 1(b). In a typical total scattering experiment, the corrected intensity from each bank of detectors is merged to a single S(Q) pattern prior to its Fourier transformation into the real space PDF, G(r). Contributions to the pattern from each of the separate solid angle detector banks span different ranges in Q, with the lower angle (forward scattering banks) featuring lower Q and lower resolution and the higher angle (backscattering banks) featuring higher Q and higher resolution. In the case of an isotropic scatterer, the sample orientation relative to the incident neutron beam is not important and the signals from all the detectors are combined. In this work, however, we specifically want to investigate the orientation dependence induced by an electric field in ferroelectric ceramics.

To obtain anisotropic PDFs such that the scattering vectors are at a desired orientation to the electric-field vector, one approach could involve the utilization of scattering information from a single default bank. However, given the varying Q-ranges and Q-resolutions from each standard bank, it is not possible to calculate complete and comparable G(r) functions from the individual banks that are sufficient for studies of disordered crystalline materials. Rietveld²² refinement-based texture analysis has previously been performed on neutron diffraction patterns from NOMAD for Al alloys by dividing the detectors into 65 half-panels, but such analysis can be performed with limited Q-ranges (10 diffraction peaks are sufficient), unlike PDF studies.²³ (The available resolution and range of a single NOMAD bank could be amenable to orientation-dependent studies of glasses and amorphous materials,^24,25 where Q-resolution requirements are significantly diminished.) Instead, the pixels are grouped according to the angular relationship between the scattering vectors Q and the sample electric field vector E described in Sec. IV. For the ex situ measurements, data from different sample rotations are combined to access total scattering covering the range 1 < Q < 30 Å⁻¹.

The geometry involved in neutron total-scattering measurements is much more complex than that of a 2D detector used for in situ high energy X-ray scattering due to the multiple banks that measure scattering at various angles to the sample electric field. In the X-ray case, a PDF along a specific direction relative to the electric field is obtained simply by integrating the scattered intensity over a narrow azimuthal sector with the desired orientation (e.g., parallel or perpendicular to the field vector).²⁶ 

We developed a data reduction and processing routine utilizing the Mantid framework²⁷ which involves summing data from different sample rotations to mitigate the distinct Q-ranges and Q-resolutions of the standard detector banks. The detector pixels are divided into groupings based on their position relative to the electric field vector for three different orientations. In this case, we used 15° sectors, e.g., the red region in Fig. 2 represents pixels that are within 0°–15° of the desired scattering vector, which is parallel to the sample electric field vector and oriented at 45° to the incident neutron beam. In this figure, different angular ranges are color coded as following: orange—15°–30°; green—30°–45°; cyan—45°–60°; blue—60°–75°; and purple—75°–90°. By dividing the 51 000 available pixels into such orientation-based groupings, we are no longer locked into the Q-ranges and Q-resolutions provided by the individual default banks. However, it was found that at least two sample rotations are required to access sufficient detector space for a specific angular range (e.g., scattering within 15° of the electric field vector, shown in red in Fig. 2). The required sample rotations for scattering parallel and perpendicular to the field are shown in Figs. 3 and 4, respectively.

Here, we focus on the 0°–15° grouping, which captures scattering closely parallel to the electric field vector. This grouping routine was created for three different sample rotations defined by the electric field vector: (1) electric field vector, E, parallel to the incident neutron beam [Fig. 3(a)]; (2) E rotated in plane by 45° from the incident neutron beam [Fig. 3(b)]; and (3) E perpendicular to the incident neutron beam [Fig. 3(c)]. These different sample orientations provide unique regions of pixels that detect neutrons with scattering vectors Q at a given angle to E (i.e., in this case, closely parallel to the field). The total scattering patterns from these three detector regions are shown in Fig. 3(d); together, they provide sufficient Q-coverage. The three patterns can then be merged to create a single S(Q), as shown in Fig. 3(e). The resulting G(r) is shown in Fig. 3(f). We also created this grouping routine for scattering closely perpendicular to the electric field. In this case, only the sample rotations where the electric field is perpendicular and 45°, respectively, to the incident neutrons are needed, as shown in Figs. 4(a)–4(c). The backscattering [Fig. 4(a)] and forward scattering [Fig. 4(b)] neutrons for the sample electric field perpendicular to the incident neutrons are reduced separately due to the different resolutions of those detectors. The total scattering patterns for each pixel grouping are shown in Fig. 4(d), and the resulting merged S(Q) and G(r) are shown in Figs. 4(e) and 4(f), respectively.

Rigorously, the anisotropic S(Q) must be converted to G(r) using a spherical harmonics expansion instead of the sine Fourier transform that is applicable for isotropic samples.^24,25 However, prior work with X-ray PDFs on the same composition showed that the results from the spherical harmonics method and the Fourier transform yield nearly identical PDFs.⁶ It was therefore decided to employ preexisting routines with the standard Fourier transform for this proof-of-concept.

In order to test our methodology on a standard sample, we first performed the data reduction and pixel groupings on a powder diamond sample in a standard vanadium can, which is used for instrument calibration on NOMAD. Electric fields were not applied to the diamond sample; this measurement was done to verify the data reduction routine with an isotropic powder. A small-box fit using PDFgui²⁸ to the diamond G(r) from the standard 6-bank data reduction method resulted in a lattice parameter of 3.5662(14) Å and an R_w of 17.1%. The weighted residual, R_w, quantifies the goodness-of-fit between the experimentally measured and calculated PDFs and is calculated as shown in Ref. 29. For the pixel groupings with scattering closely parallel to the sample electric field (Fig. 3), an R_w of 17.1% was also achieved, and the obtained lattice parameter was the same, 3.5662(14) Å. For the pixel groupings with scattering closely perpendicular to the sample electric field (Fig. 4), a similar R_w was obtained (17.2%) and the lattice parameter was within error of the others, 3.5656(15) Å. Figure 5 shows the fit to the G(r) from scattering closely parallel to the sample electric field vector; the other fits are visually similar. Ideally, R_w’s as low as 10% can be achieved for data from materials with uncomplicated structures, but in this case, the most important observation is that nearly identical R_w’s were achieved for both the standard 6-bank reduction strategy and the pixel groupings for scattering parallel and perpendicular to the field. The similarities of the fits give confidence in the novel pixel grouping strategy.

Unpoled and poled samples of Na_1/2Bi_1/2TiO₃ were mounted on the NOMAD sample changer. The poled samples were measured at three different orientations, defined by the electric field vector E: parallel, perpendicular, and at 45° to the incident neutron beam. The unpoled sample was measured only in the parallel orientation because it is assumed to be isotropic, as discussed in Sec. II.

The total scattering function S(Q) for unpoled and poled Na_1/2Bi_1/2TiO₃ and the difference curve are shown in Fig. 6(a) for scattering parallel to the electric field and in Fig. 6(b) for scattering perpendicular to the electric field. Parallel to the electric field, the peaks generally shift to lower Q, indicating a shift to higher d-spacing, consistent with expansion along the electric-field direction. The converse occurs for scattering closely perpendicular to the electric field. The strain behavior is consistent with prior X-ray total scattering-based reports.⁶ However, the previously observed sharpening of X-ray diffraction peaks with increasing electric field amplitude is not observed here.^6,30,31

The PDFs of unpoled and poled Na_1/2Bi_1/2TiO₃ are shown in Figs. 7(a) and 7(b) for scattering closely parallel and perpendicular to the field, respectively, highlighting changes observed in the low- and high-r regions. At low r, there are small changes to the shape of the peaks for both geometries. For scattering parallel to the electric field, the peak at 2.8 Å, which is mainly composed of O–O distances and Bi–O distances,³² slightly narrows for the poled sample, as shown in Fig. 7(a). Additionally, the shoulder at ∼3.25 Å, attributed to the Bi-Ti nearest neighbor peak [negative in the neutron G(r)], appears to shift to lower r for the poled sample parallel to the electric field, as was also found using X-rays.⁶ More detailed analysis of field-dependent and orientation-dependent metal-oxygen distances is possible but outside the scope of this contribution.

Parallel to the field, at high r, the peaks shift to higher r, indicating positive lattice strain parallel to the electric field vector. Perpendicular to the field, the peaks slightly shift to lower r, indicating lattice compression. This is consistent with the inferences from the Q-space data and with the previous X-ray work.⁶ One notable difference between the neutron and X-ray results is that for the X-rays, the PDF peaks narrowed in width and increased in height with increasing electric field, suggesting increasing structural order due to the applied field. This is not observed here and can be attributed to the fact that while the X-ray PDF emphasizes interatomic distances involving the Bi³⁺ cations, the neutron PDF contains significant contributions from the distances involving all the atomic species, including the O²⁻ anions.

The in situ sample cells, one of which is shown in Fig. 8, were custom built at ORNL and can accommodate solid samples of ∼3 × 3 × 20 mm. In order to apply a voltage across the width of the sample, silver electrodes were painted on two opposing ∼3 × 20 mm sides, to which lead wires were attached using silver paint and epoxy. A stiff Kapton tube surrounds the sample and the lead wires, which were fed into the body of the sample cell. The wires inside the sample cell were separated from each other by insulating ceramic rings and connected to the external high voltage (HV) and ground connections. The body of the cell and the stiff Kapton tube were filled with Fluorinert (FC-770) insulating liquid to prevent electrical breakdown around the sample. The cell is attached to the insertion rod and placed at the correct depth within the NOMAD well for the neutron beam to interact with the sample.

In situ neutron total scattering was measured for 2 h while high voltage (10 kV) was applied to the Na_1/2Bi_1/2TiO₃ sample, resulting in an electric field across the sample of >3 kV/mm. The sample cell was oriented such that the sample electric field vector was 45° to the incident neutron beam; this orientation is shown schematically in Fig. 4(b). The resultant G(r) before field application and during high voltage is shown in Fig. 9. There are additional peaks present (marked with a * in Fig. 9) due to the sample cell and/or the electrically insulating liquid Fluorinert. Obtaining an effective background subtraction is challenging; the sample cell without a sample contains a greater volume of Fluorinert than when the sample is also present. However, the results are similar to those from the ex situ experiment shown in Fig. 8(a). The PDF peaks at high r shift to higher r, indicating lattice expansion along the field direction. A PDF from scattering closely perpendicular to the electric field was not possible with the set of in situ measurements completed. A sample rotation to the −45° position was attempted, which would allow scattering closely perpendicular to the electric field direction to be measured with the same pixel grouping, but the sample position moved during rotation, yielding unreliable data.

In order to analyze the lattice expansion observed for both the ex situ and in situ measurements, we performed an analysis that quantifies r-dependent shifts, described in Ref. 8. The relative shift of the G(r) from the poled sample relative to the G(r) of the unpoled sample, Δr, is calculated using a sliding boxcar approach with a box size of 5 Å and a step size of 0.5 Å. For the ex situ measurement, the lattice strain is positive in the electric field direction and negative perpendicular to the field shown in Fig. 10, as expected for a piezoelectric ceramic. For scattering closely parallel to the electric field direction, Δr is nearly the same for both the in situ and ex situ measurements. The fact that the strain remains after the field is removed indicates that the electric-field-induced changes to the local structure of Na_1/2Bi_1/2TiO₃ are irreversible (i.e., remain after the field is removed). Previously, it had been shown that the long-range structure of Na_1/2Bi_1/2TiO₃ is irreversibly changed by a strong electric field.³⁰ This result confirms that the structure is changed irreversibly at the local scale (i.e., a few nm).

Electric field-dependent and directional PDFs from in situ neutron total scattering were obtained for the first time and are validated by their similarity to the ex situ measurements, despite challenges involving sample positioning and background subtraction. The sample environment and data reduction routines developed here enable future studies where the local structure can be probed as the electric field is ramped or cycled.

Neutron total scattering experiments were undertaken on the instrument NOMAD at the SNS with both in situ and ex situ electric fields applied to ferroelectric ceramics. The sample cells for these experiments were built in-house. In order to obtain scattering data with sufficient coverage and resolution in Q-space, different groupings of pixels were combined from different physical rotations of the samples relative to the incident neutron beam. This new data reduction and processing routine was developed to probe neutron total scattering at selected angles to a given sample electric field and was validated using a standard diamond powder sample. Scattering parallel and perpendicular to the sample electric field vector was analyzed here, but the developed routine allows for a range of intermediate angles to be investigated. Reproducibility of the sample position for sample rotations is exceptionally important for these types of experiments, and higher precision sample stage hardware is being integrated with the NOMAD beamline. The capability to measure angle-dependent PDFs will be improved with the installation of the full planned detector coverage in NOMAD, which will nearly double the number of detector pixels.

The development of a high voltage sample cell and associated data reduction routines will enable novel future experiments. For example, the magnetic response of multiferroic or magnetoelectric materials could be probed with neutron total scattering while electric fields are applied. The capability to probe the local structure of materials as a function of in situ electric field can clarify whether electric-field-induced phase transitions are due to polarization rotation or adaptive phases.^9,30,33 Additionally, due to the nature of the time-of-flight source at the SNS and neutron event-based data collection,³⁴ it will be possible with future development to explore these structural responses stroboscopically with very fine time resolution. The time resolved responses of the local structure of materials with interesting frequency-dependent long-range structures or properties could be investigated.^16,35 Further details on the implementation of time-resolved neutron time-of-flight data collection and analysis can be found in the work of Fancher et al.³⁶ 

T.-M.U. and J.L.J. acknowledge support from the U.S. Department of Commerce under Award No. 70NANB13H197. Time spent by T.-M.U. and K.P. was partially supported through the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Early Career Research Program Award No. KC040602. The authors thank Dr. Matthew Tucker (ORNL) for his valuable advice and Dr. Andrei T. Savici (ORNL) for his help with grouping of detectors and data reduction. The authors also thank Dr. Thanakorn Iamsasri and Frank Luciano for their help with experiments and preliminary data reduction. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.