Dopant Concentration Controls Quasi-Static Electrostrictive Strain Response of Ceria Ceramics

Electromechanically active ceramic materials, piezoelectrics and electrostrictors, provide the backbone of a variety of consumer technologies. Gd- and Sm-doped ceria are ion conducting ceramics, finding application in fuel cells, oxygen sensors, and, potentially, as memristor materials. While optimal design of ceria-based devices requires a thorough understanding of their mechanical and electromechanical properties, reports of systematic study of the effect of dopant concentration on the electromechanical behavior of ceria-based ceramics are lacking. Here we report the longitudinal electrostriction strain coefficient (M33) of dense RExCe1–xO2–x/2 (x ≤ 0.25) ceramic pellets, where RE = Gd or Sm, measured under ambient conditions as a function of dopant concentration within the frequency range f = 0.15–350 Hz and electric field amplitude E ≤ 0.5 MV/m. For >100 Hz, all ceramic pellets tested, independent of dopant concentration, exhibit longitudinal electrostriction strain coefficient with magnitude on the order of 10–18 m2/V2. The quasi-static (f < 1 Hz) electrostriction strain coefficient for undoped ceria is comparable in magnitude, while introducing 5 mol % Gd or 5 mol % Sm produces an increase in M33 by up to 2 orders of magnitude. For x ≤ 0.1 (Gd)–0.15 (Sm), the Debye-type relaxation time constant (τ) is in the range 60–300 ms. The inverse relationship between dopant concentration and quasi-static electrostrictive strain parallels the anelasticity and ionic conductivity of Gd- and Sm-doped ceria ceramics, indicating that electrostriction is partially governed by ordering of vacancies and changes in local symmetry.


INTRODUCTION
Gd-and Sm-doped ceria are among the most extensively studied examples of solid-state ionic conductors, 1 finding application in fuel cells, sensors, 2 and, potentially, as memristor materials. 3 Optimal engineering design of ceria-based devices requires understanding their mechanical and electromechanical properties, which have recently been shown to be unexpectedly complex. Gd-doped ceria (GdDC, a.k.a. cerium gadolinium oxide, CGO) ceramics and thin films, although equilibrium solids, exhibit time-dependent elastic moduli; that is, they are anelastic under anisotropic applied stress. 4−7 Gd-and Smdoped ceria (SmDC, a.k.a. cerium samarium oxide, CSO) ceramics and thin films exhibit room temperature, recoverable, mechanical creep under nanoindenter load hold. 8−10 The dependence of Poisson's ratio on strain magnitude, 11,12 spontaneous volume expansion over time, and hysteresis of the cubic lattice parameter during thermal cycling 5,13 have also been reported. These mechanical anomalies have tentatively been ascribed to symmetry-lowering lattice distortions, that is, elastic dipoles created in the vicinity of charge-compensating oxygen vacancies, which, depending on the dopant concentration, can occupy a few percent of the anion sublattice sites. 14−17 We have recently shown 9 that the dominant anelastic behavior of Sm-doped ceria ceramics decreases with dopant concentration (x = 0.05−0.25). From these data, we concluded that the transition at x ≈ 0.25−0.3 from the fluorite (Fm3m) phase to the double-fluorite (Ia3) phase, with attendant oxygen vacancy ordering, can restore predominantly elastic behavior.
Although mechanical properties of Sm-and Gd-doped ceria ceramics have been reported, how the electromechanical behavior, in particular, nonclassical electrostriction, observed to date in Gd-doped ceria, 14,18−21 (Y,Nb)-stabilized δ-Bi 2 O 3 , 22 and La 2 Mo 2 O 9 23 depends on dopant concentration has not been systematically studied. Previously published data 21,24,25 from 10 mol % Gd-doped ceria (10GdDC) ceramics exhibit strain saturation in strong electric fields and frequency relaxation with a characteristic relaxation time of a fraction of a second. A deeper understanding of the phenomenon of electrostriction in aliovalent doped ceria ceramics requires systematic investigation of the concentration dependence of the electrostriction properties in phases with randomly distributed oxygen vacancies as well as those where the onset of ordering can be detected. Here we report results of a systematic study of the longitudinal electrostriction strain coefficient where RE = Gd 3+ or Sm 3+ , as a function of dopant concentration within the frequency range 0.15−350 Hz and electric field amplitude 0−0.5 MV/m.

EXPERIMENTAL SECTION
2.1. Ceramic Preparation. Samples of SmDC, Sm x Ce 1−x O 2−x/2 (0.05 ≤ x ≤ 0.25), were synthesized via conventional solid-state reactions and procedures as previously described. 26,27 Briefly, Sm 2 O 3 and CeO 2 powders (both 99.99% purity, Alpha Aesar) were ballmilled, dried, and calcined at 1450°C for 10 h. Up to 2 wt % binder (PVA dissolved in deionized water) was added to the powders, and cylindrical pellets were formed in metal dies by uniaxial pressing. It is important to note that the presence of PVA does not modify mechanical properties, particularly since the green ceramics undergo sintering. 9 The pellets were then subjected to isostatic pressing at 250 MPa for 3 min. The pellets were sintered at 1600°C for 10 h (x ≤ 0.25) or 1690°C for 5 h (0.30 ≤ x ≤ 0.35). Gd x Ce 1−x O 2−x/2 (0 ≤ x ≤ 0.25) powders were synthesized by a coprecipitation method. 28 A 0.7 M aqueous solution of (NH 4 ) 2 CO 3 (99% extra pure, Arcos Organics) was added dropwise to an aqueous solution containing the amounts of Gd(NO 3 ) 3 ·6H 2 O and Ce(NO 3 ) 3 · 6H 2 O (0.3 M, total solute, purity 99.9%, Strem) required to provide the Gd concentrations desired. This mixture was kept at 80°C under continuous stirring for 1 h. The precipitates were then collected by centrifugation, washed three times with water and then with ethanol, and afterward allowed to dry at 120°C for 12 h. The resulting powders were ground, sifted through a 50 μm mesh, and calcined in air at 495°C for 2 h. Cylindrical pellets were then formed by cold isostatic pressing of the powders at 300 MPa, followed by rapid sintering, with optimal temperatures and times as reported in refs 21 and 28.
2.2. Ceramic Pellet Characterization. X-ray diffraction profiles have been reported previously 9,28 and demonstrate that all pellets are in the fluorite phase, with only a weak admixture of the double fluorite phase in the 27 mol % Gd-doped sample. 26 The number-average grain size of the SmDC pellets was determined by the lineal intercept method 29 on SEM images (Zeiss Sigma 500) to be ≥10 μm, 9 without obvious dependence on Sm concentration (Figure 1a−c).
The number-average grain size of the Gd-doped ceramic pellets was determined by SEM to be ∼0.5 μm for the doped samples and ∼1.5 μm for undoped CeO 2 (Figure 1b,c) and is weakly dependent on doping level. One 5 mol % Sm-doped ceria pellet was also prepared according to the coprecipitation protocol. The number-average grain size was ∼0.7 μm according to SEM. EDAX (Bruker XFlash/60) was used to estimate dopant concentration; the uncertainty in the reported concentration is ±1 mol %. The pellet density was measured by the conventional Archimedes method ( Figure 2). 28 At 25 mol % doping and below, the porosity (1 − density measured /density theoretical ) of both Sm-and Gd-doped pellets was <4%. Sample pellets were polished; top and bottom faces were made parallel with silicon carbide polishing papers (up to 1600 mesh) and then washed with 100% ethanol in an ultrasonic bath for 30 min to remove silicon carbide residue. All samples were reoxidized, prior to electromechanical measurements, at 500°C for 5 h in a pure oxygen atmosphere. Pellet dimensions were 6−8 mm in diameter and ∼1 mm thickness.
2.3. Electrostrictive Strain Measurements. Longitudinal (i.e., parallel to the applied electric field) electrostrictive strain, u 33 , was measured with instrumentation described previously. 21,22 Briefly, the ceramic pellet was inserted between two electrodes, the top electrode being spring-loaded ( Figure 3).
A pushrod was used to transfer displacement from the electrodes to a proximity sensor (Capacitance, CPL190 Lion); the signal from the proximity sensor was read with a lock-in amplifier (DSP 7265).  Longitudinal electrostrictive strain is calculated as the ratio between the displacement and the original thickness of the ceramic pellets as measured with a micrometer screw gauge (Mitutoyo 193-111, ±2 μm). Measurements were performed under ambient conditions (24 ± 2°C, relative humidity 20%−55%). Commercial samples of PMN-PT with silver metal contacts (TRS Technologies; our measurement M 33 = (3.5 ± 0.5) × 10 −16 m 2 /V 2 ) and a piezoelectric 100-cut quartz single crystal without additional sputtered metal contacts (our measurement, longitudinal piezoelectric coefficient d 33 = 2.3 ± 0.2 pm/V) were used to calibrate the proximity sensor/lockin-in amplifier pair. For these samples, no dependence on frequency (150 mHz− 1000 Hz) could be detected. Mirror-polished aluminum plates were used as the electrodes for these measurements. Metallic contacts that block ion transport (e.g., Ni, Cr, Ag, and Au) have been shown to suppress electrostriction in ceria-based thin films due to the formation of blocking layers, 18,19,30,31 which presumably develop as a result of ion migration and spacecharge formation. When metals support oxygen ion exchange with aliovalent cation-doped ceria thin films, then the electro-chemomechanical effect (material expansion due to electric-field-induced oxygen diffusion) becomes dominant at low frequencies. 30 Therefore, in earlier work, 21 aluminum electrodes were generally used. In the present report, we have also tested the effects of the addition of sputtered TiN films, as conductive but nonmetallic contacts, as well as sputtered Ta 2 O 5 (20 nm)/Ta films. Although TiN and Ta 2 O 5 (20 nm)/Ta are apparently superior to metallic contacts, they are nevertheless inferior to bare Al electrodes ( Figure S1) at frequencies below 10 Hz, where the influence of contact chemistry is strong.

RESULTS AND DISCUSSION
3.1. Longitudinal Electrostrictive Strain. Unlike piezoelectric materials, all dielectric solids, irrespective of symmetry, can display electrostrictive behavior in an externally applied electric field. In the case of electrostrictors, the induced longitudinal strain (u 33 ) is linearly proportional to the square of the amplitude of the applied field (E 2 ) and is detected at the second harmonic of the field frequency: Because of the work of Newnham et al., 32,33 we also know that the magnitude of the electrostrictive response of materials as diverse as inorganic oxides and relaxor ferroelectrics generally scales with the ratio of the elastic compliance (inverse Young's modulus) to the dielectric constant. As such, doped ceria ceramics with elastic moduli in the GPa range would not appear to be promising candidates for displaying large electrostrictive strain. However, quadratic electromechanical coupling is also commonly attributed to the anharmonic form of interatomic potentials, for which strong evidence has been found for ceria solid solutions. 16 Figure S1).   electric field excludes the possibility that the observed effect is related to thermal expansion or to expansion derived from chemical reduction. 35 Other materials with M 33 < 0 include fluorides that crystallize in the same space group as ceria (Fm3m), such as CaF 2 ; 32 however, most electrostrictive oxides expand in an electric field 32 (see sections 2 and 3 in the Supporting Information). For undoped ceria and for RE x Ce 1−x O 2−x/2 (x ≤ 0.25) samples with x > 0.15 (RE = Sm 3+ ) or x > 0.1 (RE = Gd 3+ ), the longitudinal strain |u 33 | is linearly related to the square of the electric field (Figures 4b  and 5b) over the complete range tested (E ≤ 0.5 MV/m; f = 0.15−350 Hz). This, in addition to the second harmonic response, clearly identifies the dimensional change as being due to electrostriction. However, for more lightly doped samples with x ≤ 0.15 (Sm) or x ≤ 0.1 (Gd), the observable electrostrictive strain deviates from linear behavior in strong, quasi-static (f < 2 Hz) electric fields (Figures 4a and 5a) where the onset of nonlinearity was determined to be 0.1−0.2 MV/m. Because nonlinearity is observed only at low frequencies and high field, we suggest that under these conditions elastic dipoles begin to fully align with the electric field. At full alignment, no additional strain can be produced. This behavior is similar to that observed by 21 in which the onset of nonlinearity for 10 mol % GdDC ceramic pellets was found to be approximately at field strength 0.17 MV/m. The electrostriction strain coefficients derived for quasi-static measurements on lightly doped samples are calculated by linear fitting (eq 1) below 0.2 MV/m.

Frequency
Relaxation. The electrostrictive strain coefficient |M 33 | for samples with dopant concentration ≤15 mol % Sm or ≤10 mol % Gd exhibits marked Debye-type relaxation with increasing E-field frequency f (Figure 6a,c). The Debye relaxation of the electrostrictive strain coefficient as a function of frequency is described by the equation where M 33 ∞ and M 33 0 are the electrostriction coefficients at f → ∞ and f → 0, respectively and τ is a characteristic relaxation time ( Table 1).
3.3. Role of Aliovalent Dopant Concentration in Ceria Electrostriction; Comparisons with Anelasticity and Ionic Conductivity. Two concentration-dependent phenomena are observed for the longitudinal electrostriction strain coefficients: (1) frequency relaxation at concentrations <15 mol % dopant and (2) a 100-fold difference in strain magnitude between low-and high-concentration samples. To summarize these data and to remove the possible influence of preparation protocols, we calculated the ratio between the lowand high-frequency electrostriction coefficients as a function of dopant concentration. These values are presented in Figure 7. The nonmonotonic concentration dependence is similar to what was observed during recent anelasticity studies in ceria ceramics 8,9,36 (time-dependent rearrangement of intrinsic strain fields under applied anisotropic stress 37 ). Both anelasticity and the unusually large electrostriction strain coefficients have been ascribed to local symmetry breaking in the vicinity of oxygen vacancies. 9,21,34 Such local symmetry breaking in the fluorite unit cell has recently been explored with reverse Monte Carlo (RMC) simulations of Fourier transformed EXAFS spectra of doped ceria thin films. 34 The initial introduction of randomly distributed lattice defectsaliovalent dopants and chargecompensating oxygen vacanciescauses the Ce−O and Sm− O bond length distributions (mol % Sm ∼ 5) to become bimodal; that is, the length distributions display two distinct maxima. An elastic dipole produced in this way can react either to applied mechanical stress, resulting in anelastic behavior, or to an applied electric field, resulting in larger than expected electrostriction (Figures 6 and 7). Because the elastic dipole is relatively massive (comprised of a few atoms), the response is largest at low electric field frequencies. Increased doping, but still within the fluorite phase, extends the bimodality to the Ce−Sm distance distribution. In the current report, we tentatively identify this additional symmetry breaking as the Figure 6. Log−log graphs of the longitudinal electrostriction strain coefficients, |M 33 |, as a function of frequency (f) for the two series: SmDC (a, b) and GdDC (c, d) with various dopant concentrations ≤25 mol %. The weak field value of |M 33 | is used (eq 1). (a, c) |M 33 | frequency dependence can be described by a Debye-type relaxation curve (solid lines) only for sample pellets containing ≤15 mol % Sm or ≤10 mol % Gd (Table 1). Error bars include both statistical uncertainty and instrumental accuracy; to increase clarity, only the upper error bar is drawn. Comparison of |M 33 | for small and large grain 5 mol % Sm-doped ceria ceramics as a function of frequency shows similar behavior as is shown in Figure S3.

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Research Article structural feature, that limits the amplitude of the electrostrictive strain at higher doping concentrations (Figure 7). We note in addition ( Figure S3) that for 5 mol % SmDC ceramics a 35-fold reduction in grain size results in at most ∼30% increase in |M 33 |. Clearly, the dependence of ceria electrostriction strain coefficients on dopant concentration at room temperature ( Figure 7) bears a strong resemblance to that of ceria ionic conductivity at moderately elevated temperatures (300−500°C ). The ionic conductivity increases sharply upon introduction of ∼5 mol % Gd or Sm and gradually decreases at higher doping levels due to a phenomenon often ascribed to the blocking/trapping of oxygen ion diffusion and/or stiffening of the lattice in the vicinity of defect associates. 38 Such a resemblance certainly does not suggest that the origin of giant electrostriction is ionic conductivity; rather, it points to the understanding that both ionic conductivity and electrostriction in ceria originate from lattice defects induced by doping; therefore, both might be expected to display a similarly limited range in which they show an optimum. This correlation, as well as measurement of the dopant concentration dependence of anelastic creep, 9 suggests that there may be an optimal concentration and size of aliovalent dopant that would present an industrially useful combination of ionic conductivity, electrostrictive dimensional change, and minimal frequency relaxation. For example, the largest room temperature electrostriction strain coefficients of ceria have been observed with the dopants (Gd and Sm) and dopant concentrations which, at moderately elevated temperature, also exhibit the highest ionic conductivity. This combination may not be industrially useful because it can lead to chemical degradation of the electrode material. According to the findings presented in this paper, introducing a higher dopant concentration to reduce ionic conductivity, in combination with a tolerable loss of electromechanical response, may prove to be a possible engineering strategy. We furthermore note that for dense ceria ceramics atomic level organization, that is, intrinsic strain due to lattice defects, appears to be the primary determinant of both the frequency and dopant concentration dependence displayed by the electrostrictive strain, while differences in sample morphology and/or in standard preparation protocols introduce secondary perturbations to the electromechanical behavior.

CONCLUSIONS
Optimal engineering design of ceria-based devices requires thorough understanding of their mechanical and electromechanical properties. Here, we have demonstrated that dense ceramic pellets of the well-known ionic conductors RE x Ce 1−x O 2−x/2 (x ≤ 0.25, with RE = Gd 3+ or Sm 3+ ) exhibit electrostrictive strain which exceeds that predicted on the basis of Newnham's classical scaling law by up to 3 orders of magnitude. At frequencies in the range f = 1−350 Hz, all samples exhibit longitudinal electrostriction strain coefficients |M 33 | on the order of ≥10 −18 m 2 /V 2 . The quasi-static (<1 Hz) longitudinal electrostriction strain coefficients of undoped ceria, as well as doped ceramics with x > 0.15 (Sm) or 0.10 (Gd), are comparable. Upon replacing 5 mol % Ce 4+ with Sm 3+ or Gd 3+ , the quasi-static (f < 1 Hz) electrostriction coefficient increases by an additional 1−2 orders of magnitude. For SmDC with x = 0.05−0.15 and GdDC with x = 0.05−0.1, the quasi-static, longitudinal electrostriction coefficient |M 33 0 | reaches 10 −17 −10 −16 m 2 /V 2 , but it exhibits Debye relaxation with a characteristic time τ in the range 60−300 ms. The known anelastic properties of ceria solid solutions have been implicated as the source of this relaxation. On the basis of the similarity of electromechanical behavior of ceria solid solutions as thin films and small or large grain ceramics, we conclude that atomic level organization, that is, intrinsic strain due to lattice defects, is the primary determinant of time and dopantconcentration dependence, while differences in sample morphology and/or standard preparation protocols introduce secondary perturbations to the electrostrictive behavior.
Choice of electrode materials ( Figure S1); derivation of electrostriction strain coefficients; anisotropy of the elastic compliance of fluorite single crystals ( Figure S2); comparison of electrostrictive coupling of small and large grain Sm-doped ceria ceramics ( Figure S3) (PDF)