Linking far-from-equilibrium defect structures in ceramics to electromagnetic driving forces

Locally intensified, low energy electromagnetic fields can directly affect atomic arrangements through defect-driven structural distortions.


Introduction
Electromagnetic (EM) elds have been shown to generate eldstabilized phases 1 and promote rapid low-temperature crystallization 2,3 in a wide range of ceramic oxide materials. 3,4 Electric eld exposure can also induce ionic movement, mediating phase transitions and controlling material properties. [5][6][7] However, the application of electric and EM elds in materials synthesis is limited by a lack of understanding regarding how applied elds inuence atomic structure and promote phase transitions. 8,9 Multiple mechanisms have been proposed to explain the phenomena observed during eld-assisted methods, including enhanced mass transport, 10 increased defect formation, 11 enhanced grain boundary heating, 12 and rapid heating rates due to eld absorption. 13 It is generally accepted that synthesis temperature and the corresponding reaction kinetics remain an important factor, but many questions remain regarding the interactions of applied elds with matter. Specically, detailed information characterizing how applied elds impact local atomic structure, how these changes affect phase stability, and what elds strengths are needed to induce structural changes remains unknown.
Early work in low-temperature microwave radiation (MWR)assisted synthesis, using low energy EM elds at 2.4-2.5 GHz, found that additional structural disorder remained in MWRgrown materials relative to conventional hydrothermal synthesis. 14 More recently, X-ray synchrotron studies have shown that the reaction kinetics of MWR-assisted Ag nanoparticle differs signicantly from the kinetics without MWR exposure, demonstrating the capability of EM elds to alter phase transitions. 15 Additionally, MWR exposure can inuence polar bonds and ionic species during oxide nanoparticle synthesis, indicating that eld-driven changes in structure may help promote the rapid, low-temperature phase formation observed. 16 In electric eld-assisted sintering (ash) experiments, in which a DC or AC electric eld is applied across a ceramic material, anisotropic lattice expansion of 3 mol% yttria-stabilized ZrO 2 and CeO 2 was found to be consistent with defect generation. 17,18 The application of electric elds also led to high oxygen atomic displacement parameters attributed to the presence of oxygen defects, 19 phase transitions to substoichiometric Magnéli phases in TiO 2 , 20 and improved plasticity in TiO 2 due to eld-induced stacking faults. 21 While these studies represent a growing body of literature reporting on the multiscale effects of EM elds on materials, they do not directly connect external eld parameters to changes in local atomic structure and phase stability.
Our work demonstrates that localizing EM eld absorption promotes an orders-of-magnitude increase in electric eld strength, which distorts atomic structure and impacts crystalline phase stability. EM eld interactions are localized to a conducting substrate, allowing us to locally probe eldassisted ceramic growth at a site of high eld-matter interaction. Distortions in local atomic structure are then quantied using synchrotron X-ray characterization techniques. Integration with rst-principles calculations indicates that these distortions are consistent with oxygen defect formation and can explain the crystalline phase stability observed at low temperatures. We further demonstrate the rst experimental measurements of local electric eld intensity using a cyclic voltammetry-based technique, revealing the existence of high local eld strengths at the growth interface. The magnitude of these high local electric elds is found to inuence local atomic structure, indicating that the extent of defect formation is dependent on local eld intensity. These results demonstrate that high local eld strengths serve as a driving force for changes in local atomic structure and suggest that EM eldinduced phase transitions are defect-mediated processes. Understanding this mechanism yields new insight into how synthesis and phase transitions progress under EM eld exposure and provides an attractive starting point for the use of EM elds as an additional input parameter in materials design.

MWR-assisted synthesis
MWR-assisted synthesis was performed in an Anton Paar Monowave 300 reaction system, at a frequency of 2.45 GHz. ZrO 2 thin lms were synthesized by submerging an indium tin oxide (ITO)-coated glass substrate in a sol-gel precursor and introducing MWR. The conducting ITO layer promotes localized EM eld absorption, leading to thin lm nucleation and growth (Fig. 1). The conducting ITO layer is chosen due to its ideal MWR absorption at 2.45 GHz, 22 and was purchased from Nanocs. The sol-gel precursor solution is based on ethanol, acetic acid, acetylacetone, DI water, and zirconium(IV) tert-butoxide. Chemicals were procured from either Sigma Aldrich or Alfa Aesar and used without further purication. 3 ml of the sol-gel was mixed with 12 ml tetraethylene glycol and sealed inside a 30 ml glass reaction vial. Details regarding sol-gel preparation and thin lm growth using this experimental setup have been reported previously. 22,23 MWRassisted reactions were performed at a solution temperature of 225 C and MWR input powers of 40, 80, and 120 W. All reactions were held at the prescribed temperature for 60 minutes.
For furnace-grown samples without EM eld exposure, the precursor solution was spin-coated onto an ITO-coated slide, placed in the furnace at 225 C, and held for 1 hour. Samples synthesized without EM eld exposure use the spin-coating method to ensure lm growth on the substrate, as no lm forms on the ITO slide if it is simply held in the solution in a fashion similar to the MWR-assisted synthesis experiments. 22 2.2 PDF data collection and analysis PDF data were collected at the X-ray Powder Diffraction (XPD) beamline, 28-ID-2, at the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory. Data was collected using a 2D PerkinElmer amorphous silicon detector and the rapid acquisition PDF method (RAPDF) was used. 24 The sample to detector distance was 204.2 mm, and the wavelength of the monochromatic radiation was 0.1848Å. Calibration for the measurements was done using Ni (Table S1 †), and datasets were collected at room temperature.
2D diffraction data were integrated using Fit2D to obtain the 1D diffraction intensities. 25 Further processing was carried out using the xPDFsuite soware 26 to generate the PDFs, G(r), given by, where F(Q) is the background subtracted, corrected, and normalized reduced total scattering structure function, Q is the scattering momentum transfer, and r is the interatomic distance away from an arbitrary reference atom. The PDF data was transformed using the limits Q min ¼ 0.7Å À1 and Q max ¼ 16.0Å À1 . The process for generating G(r) is shown in Fig. S1. † Subtraction of a bare ITO-coated glass background sample from a ZrO 2 thin lm synthesized on an identical substrate results in a PDF signal from only the ZrO 2 lm. The resultant PDF data is a real-space function, meaning that peaks in G(r) correspond directly to interatomic distances within the material. PDF analysis incorporates both Bragg and diffuse scattering, so G(r) contains information regarding both crystalline phases and amorphous or short-range-ordered regions. PDFgui was used for structural renements and modeling. 27 The models were t against experimental PDFs by rening the following parameters: global and phase specic scaling factors, lattice parameters, isotropic thermal displacement parameters (U iso ), a low-r peak sharpening coefficient for correlated motion of nearby atoms (d 1 ), 28 and a PDF peak envelope function, which dampens the signal as a function of r to account for nite structural coherence or crystallite size (D c ) in separate phases. 29 Details on D c and PDF signal dampening from nite structural coherence and instrumental broadening is given in ESI Section S1.1 and Fig Structure les for the defect-free ZrO 2 phases used in renements were obtained from the materials project, numbers 2858 (monoclinic), 2574 (tetragonal), and 1565 (cubic). Structures used in PDF renements were identical to those used as inputs for the defect-free DFT calculations. The goodness-of-t, R w , was dened as where G obs is the experimental PDF, G calc is the calculated PDF, and P is the set of renable parameters used in the structure model. Lower values of R w correspond to a higher quality t, or a better match between the experimental PDF data and the calculated PDF from the rened structure.

EXAFS data collection and analysis
Zirconium K-edge spectra were collected at the Advanced Photon Source, Argonne National Laboratory, at the MR-CAT 10-ID-B beamline. 30 EXAFS yields local structural information centered around a specic absorber (e.g., Zr) spanning a few coordination shells (Fig. S4 †). Data was collected in uorescence mode. Five separate spectra were collected for each sample and averaged to achieve desirable signal-to-noise ratio, and the beamline energy was calibrated using a Zr foil. A Si (111) monochromator was used to select an energy range of 17 848 to 18 850 eV. Data were processed using the Athena soware and EXAFS modeling was performed in the Artemis soware package. 31 The amplitude reduction factor, S 0 2 , was determined to be 0.82 AE 0.04 from tting to a Zr foil standard. During tting, the coordination number N was then set to this value, allowing S 0 2 to be multiplied by the expected coordination number and rened as a constraint. Thus, S 0 2 (or N) is expected to be near a value of 1 in our renements, with values varying from 1 indicating that the starting model may not accurately represent the coordination observed experimentally. Other constraints included the energy shi E 0 , change in path length DR, and atomic displacement parameters, s 2 . E 0 and DR were set to be equivalent for every path in all ts. s 2 values were rened independently for each path in the defect-free tetragonal, cubic, and monoclinic phases. However, for the defective ZrO 1.936 structure, the number of relevant Zr-O paths was too large to independently constrain each s 2 . In this case, three s 2 values were used and paths were grouped based on path length, with similar paths together. The t range was set from 4-14Å À1 in kspace and 1.2-3.0Å in real-space to encompass Zr-O interatomic distances. The quality of EXAFS ts was determined by calculating an R-factor, dened as where data i is the experimental EXAFS data, t i is the t to the model structure, and N is the total number of data points.

X-ray diffraction
Laboratory X-ray diffraction (XRD) was carried out using a Panalytical X'Pert Pro MPD Diffractometer with Cu Ka radiation of wavelength 1.54Å. A scan range of 20-85 was used, with a step size of 0.01 .

In situ microwave cyclic voltammetry
Cyclic voltammetry (CV) measurements were conducted using a Biologic SP-150 (Bio-Logic Science Instruments) at a constant scan rate of 10 mV s À1 in the voltage range of À0.5 to 0.5 V. The in situ microwave CV (MW-CV) experiments were carried out in a custom-designed microwave waveguide (Fig. S5 †). Two ITO electrodes are partially submerged in a ZrO 2 precursor solution, and a voltage is applied across the two electrodes as in a typical CV experiment. The corresponding change both with and without MWR is then measured ( Fig. 2A and B). The underlying mechanism of the observed peaks in MW-CV and their connection to atomic structure is explored further in the Results and discussion. The ITO-coated slides and precursor solution were held inside the waveguide while the electrode connections from the potentiostat were held outside to avoid interaction with the EM eld. MWR at a frequency of 2.45 GHz was switched on/off at various voltage points and the resultant current was monitored during the scan. The solution temperature was maintained between 45-55 C during the experiment, as determined from a ber optic temperature sensor (Neoptix T1) inserted into the precursor solution.
The capacitance, C, of the setup was calculated from the following relationship: where I is the measured current and dU/dt is the scan rate held at 10 mV s À1 . The increase in surface charge induced by MWR exposure, DQ, was found by integration under the CV curve with and without MWR exposure (Fig. 2C). The voltage generated by this charge is then found by: where DU is the change in potential caused by the increase in surface charge. The corresponding electric eld intensity can then be calculated by: where E is the electric eld intensity and d is the double layer thickness. d is approximated by the Debye length, found by: where 3 is the permittivity of the solution, k is the Boltzmann constant, T is the solution temperature, e is the charge of electron, c is the concentration of Zr ions, and z is the charge of Zr. The concentration of Zr in the sol-gel precursor is 0.004 M. The permittivity of the solution is assumed to be equal to that of TEG at 50 C, as TEG makes up the majority of the precursor solution. 32 This leads to a d value of 0.6 nm. Due to the uncertainty in actual solution permittivity value, we have assumed a conservative estimate of 1 nm for double layer thickness in all calculations to ensure that the electric eld intensity is not overestimated. 33

Density function theory calculations
The Density Functional Theory (DFT) calculations presented used the generalized-gradient approximation and projector-augmented wave functions as implemented in VASP. 34 A 566 eV planewave cutoff was used for the basis set. Ion positions and supercell lattice constants were relaxed until residual forces were less than 2 meVÅ À1 . A Monkhorst-Pack special k-point grid of 6 Â 6 Â 4 was used for the Zr 2 O 4 primitive cell; equivalent meshes were used for the larger cells. All defect calculations were performed in charged supercells containing a single defect. We did not consider clustering of oxygen vacancies or interstitials. 35 We used +2 charge states for oxygen vacancies and À2 charge states for oxygen interstitials. 36,37 The excess charge was balanced via the jellium model, in which the charge compensating for the vacancies is distributed evenly across the entire simulation cell.

Transmission electron microscopy
TEM samples were prepared via manual grinding, polishing, dimpling, and a nal polishing step in an ion milling system (PIPS II, Gatan). Microstructure was characterized using a FEI Talos T200X transmission electron microscope operated at 200 kV.

Results and discussion
To characterize the role of the applied eld on MWR-grown ZrO 2 atomic structure, we utilize synchrotron X-ray PDF analysis. 38 Peaks in the PDF directly relate to interatomic distances in the atomic structure ( Fig. 3A and B), allowing for quantitative characterization of short-range (SRO), medium-range (MRO), and long-range (LRO) atomic order. 39 LRO and MRO correspond to higher-r regions of the PDF data and represent the crystalline atomic structure, while the SRO component represents the local atomic order. The PDF technique compliments conventional XRD. However, XRD characterizes only LRO and thus is illequipped to study nanoscale or locally disordered materials. The ability to characterize both local and long-range atomic structure makes PDF analysis an ideal method to investigate the inuence of EM elds on structural distortions and phase stability. PDF renements on a ZrO 2 lm synthesized at 225 C and 40 W MWR power reveal tetragonal ZrO 2 MRO and LRO, indicating crystalline phase formation ( Fig. 3C and D). Renements were compared with other common ZrO 2 polymorphs, namely the monoclinic and cubic phases (Fig. S6 †). The tetragonal phase best represents the crystalline structure observed, indicated by the lower goodness-of-t, R w . Despite the LRO, the SRO is not well described by the crystalline tetragonal phase, particularly with regards to nearest neighbor distances (Fig. 3B). This suggests a local Zr-O coordination environment which differs from the tetragonal phase, potentially due to symmetry lowering relaxations. Computational models have postulated that oxygen point defects can induce structural changes that impact Zr-O nearest neighbor distances and the resultant phase stability, 40,41 providing one potential source of such relaxations. To investigate how defect-based local distortions impact phase stability and compare to MWR-grown ZrO 2 , rst-principles Density Functional Theory (DFT) calculations were performed spanning a range of oxygen defect concentrations.
In defect-free ZrO 2 , we nd that the relative energies are ordered E monoclinic < E tetragonal < E cubic , as expected. 42 This phase stability changes as a function of oxygen defect concentration, with a defective tetragonal phase becoming energetically favorable at a vacancy concentration of 3.2% (Fig. 4A). All ZrO 2 phases explored are indicated in Fig. S7 and Table S2. † The defect concentrations studied were limited by the system size of DFT calculations, yielding uncertainty regarding the exact vacancy concentration at which the defective tetragonal phase becomes favorable. However, the defective tetragonal structure shown here (ZrO 1.936 ) contains local atomic relaxations around vacancy sites which break the local symmetry ( Fig. S8 and S9 †) and provides a suitable representation of oxygen vacancy-based structural distortions. This allows us to utilize the ZrO 1.936 structure as a model system to explore the possibility of defect formation in MWR-grown ZrO 2 .
The reduced local symmetry caused by oxygen vacancies accurately represents the local atomic structure observed  The DFT-predicted defective tetragonal structure. (C and D) PDF refinements of the monoclinic phase and DFT-predicted defect model (red) to MWR-grown ZrO 2 (blue). Refinements to the SRO (C) indicate that the defective phase better represents the local atomic environment than monoclinic. Comparison with the defect-free tetragonal phase in Fig. 3B indicates that the SRO is better described by oxygen-vacancy-induced structural distortions. Refinements to the MRO confirm that the local structural distortions present from defects do not break the tetragonal structure (D). experimentally, as the defective model greatly improves the t to the nearest neighbor Zr-O peak in the PDF. The lower symmetry monoclinic phase also improves the t to nearest neighbor distances but does not describe the local order as well as the DFT-predicted defective phase (Fig. S10 †). Extended X-ray absorption ne structure (EXAFS) at the Zr k-edge (1s) conrms that the defect model effectively represents the oxygen coordination environment, shown by rened values for coordination number closer to unity and a reduction in atomic displacement parameters relative to the monoclinic phase ( Fig. S11 and Table  S4 †). PDF tting of the defective phase to the SRO of MWRgrown ZrO 2 results in a lower R w value than the defect-free tetragonal or monoclinic phase, indicating that the local atomic order is better described by vacancy-induced relaxations (Fig. 4C). Overall, the defective phase improves the t to the SRO while remaining consistent with the MRO and LRO observed experimentally but does not improve upon the MRO and LRO from the defect-free phase. The monoclinic phase is a poor descriptor of the observed structure beyond the nearest neighbor peaks, and conventional XRD conrms that only tetragonal LRO is present ( Fig. 4D and S12 †). This structural information suggests that the topology of MWR-grown ZrO 2 remains tetragonal, with EM eld-assisted phase stability mediated by oxygen vacancy-induced local structural distortions. The potential presence of other oxygen point defects, namely oxygen interstitials, was also investigated via PDF analysis. The DFT calculations suggest that if interstitial oxygen defects were indeed present, the monoclinic phase is expected to be stable. Due to the presence of the LRO tetragonal phase, PDF renements to interstitial models were performed for both the monoclinic and tetragonal phases. In both cases the interstitial models resulted in poorer ts and higher R w values than either the vacancy defect model or the defect-free phases, indicating that the addition of oxygen atoms to the lattice does not suitably describe the experimentally observed structure (Fig. S13 and S14 †).
The presence of distorted local structure as a stabilizing presence in MWR-grown ZrO 2 invites investigation into the mechanisms of defect formation during MWR-assisted synthesis. Experiments utilizing an identical experimental setup and heating conditions found that no phase formation occurs without MWR exposure, indicating that the chemical environment is not responsible for the observed effects. 43 Synthesis using an MWR absorbing SiC vial (in place of the standard borosilicate glass) shields the growth solution from EM eld exposure while maintaining similar heating rates, 44 and also results in no thin lm growth. 22 Additionally, thin lms synthesized at identical temperatures in a conventional furnace were found to have a completely disordered atomic structure (Fig. S15 †). This aligns with prior work demonstrating that the ITO layer preferentially absorbs EM radiation and impacts the synthesis process. 22 It is suspected that electric elds on the . MWR is absorbed by the conducting layer, creating an electric field at the surface. This draws additional ions or molecules to the surface, leading to a spike in current to balance the additional surface charge and a large local electric field due to the formation of an electric double layer (E). When MWR is turned off, the ions drawn to the surface release back to a random orientation, leading to a sharp negative flow in current (F). order of 10 6 V m À1 , such as those present in an electric double layer, are high enough to drive ionic motion. 5,6 This suggests that a potential driving force for oxygen vacancy formation is the presence of anomalously high eld intensities at the substrate-solution interface. However, this local eld strength has not previously been experimentally measured, making it difficult to link local electric elds with the resultant atomic structure.
To measure local electric eld intensity, we developed a microwave cyclic voltammetry (MW-CV) technique capable of quantifying the change in electric eld at the ITO layer due to MWR exposure. MW-CV represents the rst experimental technique capable of monitoring local electric eld intensities for EM eld-assisted synthesis. When MWR is applied to the system, a positive spike in the current is observed. Conversely, when MWR is removed, a negative spike in the current occurs (Fig. 5A). This change in current is related to a buildup of surface charge, from which the electric eld intensity can be calculated. More details on the MW-CV measurements and resultant electric eld intensity calculations can be found in Materials and methods Section 2.5. At 40 W of applied power, the increase in measured current due to MWR corresponds to an electric eld on the order of 10 6 V m À1 , orders of magnitude higher than prior predictions in EM eld-assisted processes. 45 The dependence of eld intensity on interactions between MWR and the substrate material is demonstrated by an order of magnitude increase in local electric eld intensity, up to 10 7 V m À1 , when replacing one ITO layer with a higher electrical conductivity Ti layer ( Fig. 5B and S16 †). Additionally, varying the H + concentration in the solution to alter the interaction between MWR and the solution led to an increase in the peak intensity and faster ionic motion to the ITO surface, but no signicant change in the electric eld intensity (Fig. 5C, S17 and S18 †). These results indicate that MWR absorption by the conducting layer is essential to the high electric eld intensities observed. Prior work related to EM eld absorption in materials has demonstrated that MWR absorption results in an electric eld strength distribution at the material surface. [46][47][48] This electric eld buildup at the ITO layer draws ions to the surface, resulting in the formation of an electric double layer and a positive spike in the measured current to balance the additional surface charge. The high electric eld present in the electric double layer is what is measured experimentally during MW-CV measurements, as opposed to the smaller electric eld formed from MWR absorption by the ITO which promotes double layer formation. When MWR is removed from the system, the ions drawn to the surface release back to a random orientation, resulting in the negative spike in current observed. This process is shown schematically in Fig. 5D-F.
The magnitude of the electric eld intensity is found to increase with increasing MWR power levels, with higher power levels leading to higher electric eld intensities (Fig. 6A). Despite the increase in eld intensity, the LRO of all lms remains consistent with the tetragonal phase (Fig. 6B). The SRO, however, experiences changes based on applied power. Higher electric eld intensities promote more local atomic Fig. 6 Effects of MWR power on local electric field intensity and atomic structure. (A) Higher applied power leads to higher local electric fields at the ito layer. (B) Higher power levels do not eliminate the LRO tetragonal phase, as shown by tetragonal refinements (red) to MWR-grown ZrO 2 synthesized at 225 C and 40, 80, and 120 W. (C) The SRO is impacted by the power level, as shown by refinements to the defective model (red). (D) EXAFS spectra indicating additional local atomic disorder with increasing MWR power, as seen by the broadening and decrease in intensity of Zr-O peaks at higher power levels. This suggests that larger local electric fields can promote higher defect concentrations and can increase local atomic disorder without sacrificing the overall tetragonal topology. distortions, suggesting that higher power levels can induce more defects on the oxygen sub-lattice. This effect can be deduced from a noticeable change in the nearest neighbor peaks in the PDF data, leading to a decreasing quality of t to the defective model structure (Fig. 6C). EXAFS spectra conrm this trend, with broader and less intense Zr-O peaks indicative of more structural disorder present at higher electric eld intensities (Fig. 6D). This increased structural disorder is not correlated to the grain size, as the average size found from PDF modeling remains similar regardless of the MWR power level (Table S3 †). This observation suggests that higher local electric eld magnitudes can impact defect concentrations and local structural changes without breaking the crystalline LRO of a material.
While no prior studies have experimentally linked local electric eld strengths with local atomic structure, evidence exists to support the claim that applied elds can inuence defect formation. In electric eld-assisted sintering of yttriastabilized zirconia, it has been suggested that the injection of additional carriers can lower defect formation energy. 49 Additionally, polarization effects have been found to lower oxygen vacancy formation energy in oxide materials. 50 Previous work has also found that suspected high electric elds at interfaces can drive ionic motion, inuencing defect concentrations and phase transitions. 5,6 This evidence, coupled with the local electrical and structural characterization presented here, suggests that high local electric eld strengths can serve as a driving force for defect-based structural changes during ceramic synthesis.

Conclusion
We use a unique blend of materials chemistry, electromagnetics, and engineering methods to demonstrate that high local electric elds can serve as a driving force for local structural changes which impact phase stability during EM eld-assisted ceramic growth. High electric elds are present even while a ceramic oxide layer is present on the substrate (Fig. S19 †) and prior experiments have demonstrated the success of MWRassisted synthesis on particles that are not electrically conducting. 43 This indicates that local EM eld absorption, regardless of the electrical properties of the absorber, can promote material growth. With this evidence, we have obtained new insight into how synthesis and phase transitions progress under EM excitation, demonstrating that local electric eld strengths are dependent on the applied power and can impact local atomic order without signicantly altering the crystalline atomic structure. With these new insights, complementary directions open up for further exploring the role of EM eld effects during ceramic synthesis. For example, high resolution scanning transmission electron microscopy (STEM) can potentially image local defect structure near the ITO-thin lm interface. Finally, the characterization approaches such as the MW-CV technique introduced here provides a template for future studies to investigate the interplay between EM elds, local structure, and phase stability in a variety of material systems. Our work thus lays the practical and theoretical foundations for deploying EM elds as a synthesis tool to access new materials with minimal thermal input, enabling exploration of regions of phase space, microstructures, and properties not accessible via conventional chemical synthesis routes. Understanding such eld-driven structural transitions also has important implications in engineering low temperature techniques to integrate ceramics with temperature-sensitive polymer materials for exible electronics and in tailoring ceramic properties for energy generation and storage applications.

Conflicts of interest
There are no conicts of interest to declare.