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

Ferroelectric materials are used in a variety of applications, for example, medical ultrasound, sonar, capacitors, transducers, and actuators. In many uses, these materials are subjected to multi-modal loading (e.g., temperature, electric field, and mechanical stress).¹ The application of these loadings has been shown to induce a variety of response mechanisms: charge displacement (dielectric), lattice expansion (piezoelectric), dipole reorientation (ferroelectric/ferroelastic and extrinsic piezoelectric), and phase transitions. Understanding and quantifying the atomic evolution of ferroelectric materials is critical to optimize their performance.

In recent years, researchers have leveraged neutron and synchrotron X-ray facilities to probe how the underlying arrangement of atoms in ferroelectric materials evolves in response to an external electric field and mechanical loads.^2–14 These experiments were initially limited to static measurements, where diffraction data were measured at discrete applied fields and accumulated over the time necessary to reach sufficient statistical significance.^15,16 Advances in detector sensitivity and source power have enabled the investigation of dynamic material response, providing a wealth of information about field response (e.g., field induced polymorphic phase transitions, domain wall motion, and lattice strain).^11,17,18 Often these investigations are conducted at X-ray synchrotron facilities in a “single-shot” mode using hard X-rays (>80 keV) during application of a single period of the predefined measurement waveform. However, dynamic single shot experiments use two-dimensional medical detectors that are plagued by limited data readout rates (<10 Hz). Consequently, stroboscopic methods have been developed to achieve both a high time-resolution (<1 μs) and counting statistics that are needed to quantify subtle features in the measured data.^4,19–23 While stroboscopic experiments open a new avenue to study materials, they require precise timing hardware to synchronize data acquisition (DAQ) and sort data measured over many cycles of an applied stimulus into their predefined registers.^24–27 

The use of a defined set of registers for histogramed data is a limitation that can inhibit the success of an experiment, imposing a maximum Δtime = 1/(ωN), where N is the number of registers. While final data can be further binned to improve signal-to-noise by sacrificing time-resolution, histogramed data cannot be subdivided to improve time-resolution. This rigid binning scheme imposes constraints on the measurements because the necessary timing is dependent on the phenomena of interest. For example, investigating the dynamic response of a ferroelectric material to an oscillating electric field requires different timing than the kinetics of domain wall motion during application of static electric fields. These limitations can be mitigated if the binning of measured diffraction data were not governed by timing hardware. A new avenue for measuring time-resolved data appeared with the advent of “event-based” data acquisition systems.²⁸ Event-based data acquisition at the spallation neutron source (SNS) at Oak Ridge National Laboratory (ORNL) time-stamps each measured neutron event maintaining global timing information (so-called wall clock time²⁸), which would have been discarded using a histogram data acquisition approach (Ref. 28 provides a detailed comparison of event-based and histogram data acquisition). Correlating the diffraction event time-stamp with metadata about an external stimulus provides the tools needed to resample a single dataset using an arbitrarily defined scheme. While slower than X-ray stroboscopic methods, equivalent neutron tools are advantageous because neutron diffraction complements X-ray diffraction in several ways. Neutrons scatter as strongly from light atoms (e.g., hydrogen) as they do from heavy atoms, giving greater sensitivity to identify atomic positions and displacement parameters. This sensitivity makes neutron diffraction ideal for the investigation of molecular ferroelectric materials that are comprised entirely of light atoms. The intrinsic magnetic moment of neutrons makes neutron scattering invaluable for magnetic structure determination.²⁹ Unlike the ionizing nature of X-rays, the weak interaction of neutrons with matter makes neutron probes uniquely suited for the investigation of materials that are beam sensitive and would quickly degrade when exposed to an intense X-ray beam.

In this paper, we present a framework for correlating measured diffraction data with an external stimulus. The presented methods leverage data filtering algorithms in the Mantid framework.³⁰ While this work demonstrates the time-filtering approach by investigating the field-response mechanisms of BaTiO₃, the developed framework can be applied to any material system and external stimuli.

High purity (100) BaTiO₃ single crystals with dimensions of 5 × 5 × 0.5 mm³ were purchased from Surfacenet GmbH. The as-received sample was cut using a diamond dicing saw to achieve a final dimension of 2 × 2 × 0.5 mm³. Cut samples were cleaned first with acetone and then with ethanol to ensure that the surface was free of debris or contaminates. Electrodes were applied to parallel 2 × 2 mm² faces using silver paint and allowed to dry overnight at room temperature.

A custom electric field loading apparatus was constructed by routing electrical lead wires through Kapton® tubes that were secured to the stainless steel pin attached to a magnetic base, as shown in Fig. 1 of the supplementary material. The stainless steel pin provides rigidity to the setup, while the magnetic base is used to securely mount the apparatus on the goniometer head. Kapton was used to electrically isolate both the samples and electrical leads (drive and return wires) from the magnetic base. Electrical leads (drive and return) were attached to the electrode from the samples and glued in place using silver paste. The drive and return wires were coated in an insulating varnish to electrically isolate the drive and return from the instrument. Figure 1 shows a picture of the mounted sample that has been loaded on the TOPAZ goniometer.

Diffraction data were measured using the TOPAZ diffractometer at the spallation neutron source (SNS) at Oak Ridge National Laboratory (ORNL). TOPAZ is a high-resolution Laue diffractometer with a wavelength bandwidth of 3.1 Å encompassing neutrons from 0.4 Å to 3.5 Å. A comprehensive detector coverage captures a wide scattering angle around the sample position collecting data from 20° to 160° 2θ and approximately +/−54° out of plane. TOPAZ measures wavelength-resolved data in the time-of-flight (TOF) mode, by following the time of each detected neutron from creation in the source (Time₍₀₎) to arrival at the detector. Each neutron has a kinetic energy related to its wavelength, which is directly related to the travel time (TOF) between the source and detector, where faster neutrons have shorter wavelengths than slower neutrons with longer wavelengths. The time stamp is created at Time₍₀₎ of each neutron pulse which starts with a proton pulse being shot into a mercury target, spalling off very high energy neutrons, which then traverse a moderator to slow down to a range of useful energies for neutron scattering experiments. This provides a wavelength band of neutrons that can be collected in real time readout detectors in sequence, providing a wavelength-resolved dataset and spanning a three-dimensional volume of collected reciprocal space. As the wavelength changes with the diffraction angle, according to Bragg’s Law, the sample does not move but sits in one orientation during one exposure. This is a unique advantage as full Bragg peaks are collected for integration and data analysis, while it is possible to reliably follow the sample response to individual or changing stimuli, without the possible introduction of instrument dependent errors.

During data collection, each neutron event captured is saved with the associated metadata of time of flight and order of detection. This allows re-sorting and re-binning of measured neutrons according to a metadata signifier of choice during the data processing step, a concept only recently being employed in neutron scattering. The detector coverage of TOPAZ, however, is not complete, and more than one orientation is generally necessary to cover the representative section (e.g., for full structure solution) of reciprocal space with respect to sample symmetry. The crystal orientation can be optimized with the local CrystalPlan software³¹ for highly efficient reciprocal space surveys. CrystalPlan calculates the full reciprocal space coverage and redundancy according to the applied symmetry of the sample. This provides a rapid overview of the desired data to be collected and the time necessary to cover a representative volume of reciprocal space in a certain symmetry.

Figure 1 shows a schematic representation of the experimental setup. The electric field is applied along the large parallel {001} faces. Diffraction data were measured continuously during the application of a ∼1.333 Hz waveform. A modified triangular waveform with a 2 times slower ramp from 0 to +/−E_max than from +/−E_max to 0 was used (as shown in Fig. 2). Such a ramp was specifically chosen to maximize the counting time during the initial ramp from 0 to +/−E_max because domain reorientation is dominantly induced during this electric field segment.

A bespoke analog-to-digital readout card (ADC-ROC) data acquisition (DAQ) board developed at the SNS to collect analog and digital signals (metadata) synchronously to the neutron source pulses was used.^32,33 Metadata are acquired in the same single event manner as the neutrons (TOF and Pixel ID recorded for each single event with 100 ns resolution), making integration of the ADC-ROC seamless to the existing SNS neutron DAQ system. The ADC-ROC has two AD7606 8-channel 16-bit analog-to-digital converters for acquiring analog signals and a Xilinx Spartan field programmable gate array XC3S1000 microchip for processing analog data, for acquiring digital signals, and to support standard communication to the rest of the DAQ system. Metadata information about the amplifier input (waveform generator), output (HV drive), and current flow through the system is recorded. Measured metadata are later used to merge diffraction data measured over many cycles into a single representative cycle.

Stroboscopic measurements often use trigger information associated with the start of each stimulus to track the waveform timing. While our experiment does not receive these trigger data, the ADC metadata used in this experiment capture a continuous stream of data about the input waveform, HV output, and current draw. These pieces of data provide a far richer set of data that enables the identification of discrepancies between the input and HV drive directly which is evidence that the experimental conditions (e.g., electric discharge, sample breakdown, or exceeding the amplifier’s maximum power output) prevent the amplifier from applying the desired measurement waveform. Current flow through the sample provides critical information about the material response to the applied waveform and enables tracking of the fatigue behavior of the sample. An overview of the electrical design for the current probe is shown in Fig. 2 of the supplementary material.

The Mantid framework provides algorithms for filtering of measured diffraction data into their respective register by time and metadata log values. While Mantid can directly filter electric field metadata, these algorithms have been developed to filter metadata logs that gradually changed with time, e.g., temperature and applied stress, which are free of noise. These methods rely on the derivative of log values to filter data into their respective register, and the presence of noise could influence the results. Instead, the filter by time capability offers the needed flexibility to define specific time intervals that are associated with a respective register. The flexibility of defining specific time intervals enables the investigation of both kinetic (e.g., evolution with increasing time) and dynamic phenomena (e.g., evolution with a cyclic time). Time filtering of dynamic phenomena requires precise information about the cyclic behavior of the driving stimuli and their stability. In this work, recorded metadata about the applied electric field are used to determine the necessary timing information.

Time filtering stroboscopic event neutron data requires precise timing information about the measurement waveform [stimulus frequency (ω) and start time (t_o)]. These data are extracted from the electric field metadata by modeling the input waveform using a predefined function that represents the waveform used in the experiment (see Fig. 1). The model modified triangular waveform was constructed using the sawtooth function from the scipy.signal python package. The required timing information is determined by a least-squares refinement of the input parameters for the modeled waveform (frequency, amplitude, and start time) using the scipy.optimize package (version 0.12.1). Below is provided an overview of the workflow:

1. First, the maximum in the sample log is identified to estimate the start time for the first full cycle.

2. The maximum and minimum of the input log are determined to find initial estimates of an offset and the amplitude of the waveform in sample log space (Fig. 3).

3. Initial estimates of the frequency, start time, log amplitude, and log offset are first refined against a small subset of the metadata (first 20 000 data points) to coarse optimize the initial timing parameters (Fig. 4).

4. Coarse timing parameters are further refined against the entire input log to determine the timing for the start of the first cycle and waveform frequency (Fig. 5).

The above approach only requires the user to input a rough estimate of ω for the measurement waveform. A two-step parameter refinement (local and global) of the timing parameters serves two roles: (1) a coarse optimization of the initial guesses decreased computation time needed to reach a final solution (metadata logs often contain >1 × 10⁶ points) and (2) independently refining a subset and whole range provides a natural method to examine the data and ensure that the stimuli did not drift during a single run.

Figures 1–3 highlight the evolution of the refinement process and initial guesses (Fig. 3) that do not match the timing characteristic of the measurement to the final refinement of the entire dataset (Fig. 5). The difference plots confirm that the refined and measured waveforms from the local and global refinements do not differ substantially. This result demonstrates that the applied measurement waveform is well behaved, with the local and global regiments determining a measurement frequency that differed by 5 × 10⁻⁹ Hz. The root mean square analysis for local and global refinement is nearly identical, suggesting that the applied electric field is stable through the experiment.

The timing information (t_o and ω) extracted from the metadata is then used to define the time intervals (Δt = 1/ω/registers) that Mantid use to filter event data. These intervals are then stamped with their corresponding register; for example, register 1 corresponds to all time intervals (t_o + Δt + N*1/ω to t_o + 2Δt + N*1/ω), where N denotes the cycle number. Mantid filters neutron data measured from t_o until the end of the experiment into the individual registers based on the time when neutrons interact with the sample. An advantage of this method over traditional predefined register size methods is that the number of registers is not fixed and can be adjusted to suit the requirement of the respective experiment. In addition to filtering diffraction data, the time-filtering algorithm also filters all metadata log information into their respective register. An example python script is provided in the supplementary material.

The BaTiO₃ single crystal used in this study was initially polydomained, containing multiple twins associated with the related domain variants. Application of electric fields along a polar direction biases a domain configuration with a larger volume fraction of domains oriented in the field direction rather than perpendicular. The measured three-dimensional reciprocal space volumes were reduced into one-dimensional intensity vs d (line profiles) by binning each detector in TOF, and then each dataset is converted from TOF into d. This procedure achieves 25 independent datasets with an average d step size of 0.007 Å. Figure 6 compares the line profiles of the {113} reflections measured at zero field and during the application of a static electric field. The observation of diffraction intensity from two {113} reflections is evidence of the presence of a polydomain state, with the weak peak near 1.275 Å corresponding to the twin 311 reflections. The intensity of the twin reflection decreases during the application of a 250 V/mm static electric field.

The diffraction data in Fig. 6 represent the average response during the 30 min that the data were measured. Additional information can be extracted from these data by leveraging the event data and filtering capabilities of Mantid to investigate the time evolution through a single experiment. To accomplish this, the measurement data are split into sub-segments or 3-min segments. Peak intensity information can be used to quantify the volume fraction of domains aligned in the field direction.³⁴ These data were analyzed via single peak fitting using the LIPRAS program to extract additional information about the peak position and intensity.³⁵ Data were modeled with a linear background and asymmetric Pearson VII and Gaussian peak shape functions for the 113 and 311 reflections, respectively. See Fig. 5 of the supplementary material for a representative fit of the data. An asymmetric function was needed to account for the long TOF tail that contributes significantly to the 113 intensity.

Figure 7 compares the ratio of the intensity of the 113/311 reflections during the static electric field. The low ratio of the intensity of the twin related 113/311 suggests that the domain configuration is dominated by dipoles oriented in the field direction. The observation of an exponential type reduction in the intensity of the 311 reflection hints at the fact that the population of domain walls has differing energy barriers and that the energy barriers might evolve with the domain configuration (e.g., interactions between domain walls), agreeing with both theory and experimental studies.^36,37 These data suggest that additional insight into the response of a given material can be extracted by analyzing sub-time slices of larger datasets.

Due to flux limitations, a neutron diffraction data collection is inherently slower than what can be achieved using advanced X-ray sources. Therefore, time-resolved studies are conducted using a stroboscopic measurement method that bins diffraction data measured over many cycles of applied stimuli. Studying the dynamic structural evolution of ferroelectric materials in relation to an external electric field is not different. As discussed in Sec. II C, metadata about the electrical input, drive, and current flow through the system are continuously recorded to facilitate time-filtering of the measured diffraction data using an arbitrary, or experiment dependent, timing width. Representative outputs of these metadata streams are shown in Fig. 3 of the supplementary material. The measured current flow can be used to approximate a polarization loop; a representative loop is shown in Fig. 4 of the supplementary material. It is important to note that the electric field frequency must be asynchronous from the neutron pulse frequency of 60 Hz to achieve a full spectrum of neutrons of all wavelengths in each register. If the two frequencies are synchronized (stimulus frequency is an integer multiple of 60 Hz), each time register would correspond to a specific range of neutron wavelengths. For example, a 60 Hz measurement frequency imposes that all 0.5 Å neutrons probe zero electric field, all 1.2 Å neutrons at maximum field, and so on. Such a situation would result in a gradient in the number of peaks in each register. Therefore, the electric frequency must have an asynchronous beat to sample all areas of the neutron pulse frequency. Only a subtle deviation (60.01 Hz) is needed to achieve an asynchronous beat.

Diffraction data for time-filtering were measured for 2.75 h. These data were processed into 30 registers using the procedures presented in Sec. II D. Subdivided data were reduced into line profiles for further analysis. The electric field dependent diffraction data for the 220 reflections are shown in Fig. 8. The intensity of the 022 exhibits an oscillatory increase and decrease corresponding to the magnitude of the electric field that evidences reversible domain wall motion (DWM). Maxima in the measured intensity peak profiles are observed at +/−E_max. The observation of intensity interchange demonstrates that the developed approach properly resamples the diffraction data measured over many hours into their respective time segment.

The intensity variation during field cycling is highlighted, Fig. 9, through a comparison of the intensity vs d-spacing line scans for +/−E_max and 0 field (dashed lines in Fig. 8). While Figs. 8 and 9 demonstrate that the application of a 250 V/mm field does induce ferroelectric/ferroelastic domain reorientation, it should be mentioned that the fraction of domains aligned in the field direction is lower than what was induced during electric poling. The reduction in 90° domain alignment is evidenced by an increase in the intensity of the twin related reflection, suggesting that the prolonged field cycling reduces the alignment of the domains in the field direction. Tutuncu et al. observed a similar reduction during weak field cycling of poled 0.36BiScO₃-0.64PbTiO₃.³⁸ The authors attributed the reduction in the volume fraction of aligned domains to an irreversible de-aging effect that randomizes 90° domains. The observation of minimal 90° is not entirely unexpected, as domain inversion (180° switching) has been suggested to be the dominant polarization mechanism in BaTiO₃.³⁹ The effect of prolonged cycling on 180° alignment cannot be readily assessed from neutron diffraction data because BaTiO₃ does not give rise to anomalous scattering; thus, the measured diffraction intensity is not sensitive to the inversion of spontaneous dipoles. However, a comparison of the current response measured at the beginning and at the end of the data collection suggests that the sample is minimally affected by the prolonged cycling (>9000 cycles), Fig. 6 of the supplementary material.

Time filtering of event based single crystal neutron diffraction data, coupled with the wavelength-resolved Laue technique, has opened a new avenue to probe structure responses related to periodical, changing, external stimuli, circumventing the flux limitations by allowing cyclic repetition instead of a single shot experiment. This is possible through the development of flexible processing tools for re-sorting and re-binning of measured neutron events and associated metadata into representative registers. This may become relevant for parametric studies where stroboscopic or cycling experiments provide insight that mimics the pump-probe protocols used in X-ray studies but also extends the measured parameter space to 4+ dimensions (neutron event data in 3D Qx, Qy, Qz and one or more external stimuli at time stamp t). The resultant data can be used to determine the time-dependent structures of various phenomena:

1. Dynamic field response information is crucial to develop structure-property relationships in potential technical applications, where the current trend moves toward low-impact, low-waste, organic components. Here the hydrogen position and movement are of major interest and a unique strength of neutron diffraction. The sensitivity of neutrons to hydrogen atom positions, occupancies, and atomic displacement parameters is critical to understanding the mechanisms of structural changes that involve hydrogen bonds. Furthermore, multimodal loads (field and temperature) can be applied and studied simultaneously, enabling the identification of pathways for symmetry breaking that facilitate, for example, electric field induced paraelectric to ferroelectric and ferroelectric-ferroelectric polymorphic phase transitions.⁴⁰ 

2. Non-equilibrium: Potential applications in dynamic single-crystal diffraction study of structurally photoresponsive metal–organic frameworks,⁴¹ for example, to improve our understanding of chemistry and its connection to physical properties that may have significant impact on optoelectronics and energy technologies.

3. 3D diffuse scattering structures (non-isomorphic shape and directionality of diffuse scattering) provide key insight into local displacements and distortions, often the key for functionality in a technically exploitable material. For example, recent work has shown that the shape of features in the diffuse scattering signal of relaxor ferroelectrics evolves with an applied electric field, which evidences the field dependent response of polar nano-regions.^42,43 Previous studies have been limited to static electric field measurement. The results presented in Secs. III A and III B demonstrate that these approaches do not necessarily capture the true dynamics of the systems, leaving room for exciting further development and expansion to other TOF diffractometers, i.e., CORELLI, which is specifically optimized for single crystal diffuse scattering measurements.

4. Pair distribution functions (PDF) is a local structure technique that enables the determination of nearest neighbor correlations and bonding. Similar to diffuse scattering, PDF analysis of the local structure evolution of ferroelectric materials with an electric field stimulus has been relegated to discreet constant electric fields, specifically using X-ray tools.⁴⁴ Usher et al. has expanded these methods to enable neutron PDF analysis using the NOMAD instrument at the SNS, which provides sensitivity to oxygen that is complementary to X-ray sensitivity to heavy metals.⁴⁵ The time-filtering methods presented in this paper provide the missing framework to augment the work of Usher et al. to enable time-resolved neutron PDF analysis.

However, it needs to be noted that this is valid for highly repeatable cycles that accumulate sufficient statistics for time filtering within the available experiment time. Systems that are easily fatigued, instable, or breakdown do not lend themselves to the discussed cycling or stroboscopic experiments.

See supplementary material for a picture of the sample in the electric field cell, supporting electrical design, raw and processed electrical metadata, and an example python script used to reduce neutron event data against measured metadata.

The authors thank Matt Rucker for his invaluable help with the development of the electric loading cell. This research used resources at the High Flux Isotope Reactor and Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.

This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).