Local electrical and dielectric properties of nanocrystalline yttria-stabilized zirconia
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Grain core and grain boundary electrical and dielectric properties of nanocrystalline yttria-stabilized zirconia (YSZ) were analyzed using a novel nano-Grain Composite Model (n-GCM). Partially sintered pellets with average grain sizes ranging from 10 to 73 nm were analyzed over a range of temperatures using AC impedance spectroscopy (AC-IS). Local grain core and grain boundary conductivities, grain boundary dielectric constants, and effective grain boundary space charge widths were determined from the fitted circuit parameters. Required grain core dielectric constant data were provided by AC-IS measurements of single crystal YSZ over a range of temperatures. The local grain core conductivity of all the nanocrystalline samples was slightly decreased with respect to that of microcrystalline YSZ. Conversely, the local grain boundary conductivity was enhanced up to an order of magnitude compared to microcrystalline YSZ. At the nanoscale, there was a noticeable increase in local grain boundary dielectric constant versus single crystal values at the same temperature.
KeywordsDielectric Constant Oxygen Vacancy Boundary Conductivity Boundary Core Nanocrystalline Sample
Yttria-stabilized zirconia (YSZ) is the workhorse electrolyte in electrochemical devices, including solid oxide fuel cells (SOFCs), oxygen pumps, and oxygen sensors . Much recent research has focused on enhancing the transport properties of YSZ at low temperatures to improve the commercial viability of SOFCs [2, 3]. By operating at lower temperatures (<600 °C) problems associated with deleterious interfacial reactions, differential thermal expansion, and gas sealing can be ameliorated. Also, less expensive interconnect materials (e.g., stainless steel) can be employed. To improve the transport properties, researchers have investigated nano-scale YSZ electrolytes, where the grain size and/or film thickness is <100 nm.
There are conflicting reports concerning the grain size-dependence of transport properties in nano- versus micro-scale YSZ. In a recent review, Guo and Waser noted that, for several acceptor-doped zirconias, the specific grain boundary conductivity increases as the grain size decreases into the nanocrystalline regime, while the grain core conductivity decreases slightly . Mondal et al.  reported enhanced specific grain boundary conductivities in YSZ of grain size 25–50 nm, at doping levels of 1.7 and 2.9 mol% Y2O3. Mandani et al.  reported higher grain boundary conductivity than grain core conductivity in 4 mol% Y2O3-doped ZrO2, but not at the 9 mol% level. Verkerk et al.  found increasing specific grain boundary conductivity with decreasing grain size in microcrystalline 8 mol% Y2O3-doped ZrO2, but only at large grain sizes. The most dramatic result was that of Kosacki et al. , who showed a 1–2 order of magnitude increase in the total conductivity in spin-coated YSZ thin films with ∼20 nm grain size versus a polycrystalline bulk sample with large grains (2.4 μm). Karthikeyan et al.  reported an increase of conductivity up to one order of magnitude in e-beam deposited YSZ thin films as the film thickness was reduced to 17 nm. In contradistinction to these studies, Guo et al.  saw a slight decrease in the conductivity of 12 nm and 25 nm films compared to bulk polycrystalline values.
The aforementioned papers relied upon the brick-layer model (BLM) to extract grain boundary properties (e.g., the “specific grain boundary conductivity”) and grain core properties. We recently demonstrated that the BLM is no longer valid when the grain size is reduced into the nanocrystalline regime, i.e., at grain sizes <100 nm [10, 11]. The present work employs our recently developed “nano-Grain Composite Model” or n-GCM to extract local grain boundary and grain core properties for nano- versus micro-crystalline YSZ.
The nano-grain composite model (n-GCM)
Extracting local properties (grain core, grain boundary) from AC impedance spectroscopy (AC-IS) measurements requires a representative microstructural model and a corresponding equivalent circuit. The original equivalent circuit used to describe YSZ and microcrystalline electrolytes in general was developed by Bauerle , for ceramics with resistive grain boundaries and conductive grain cores. This simple boundary-layer model was further developed by Beekmans and Heyne  and was labeled as the “brick-layer model” or BLM by Burggraaf and co-workers [6, 14]. The equivalent circuit consists of two RC parallel elements in series, one representing the grain cores and the other representing the grain boundaries. In the well-known Boukamp notation , this circuit is represented as (RC)(RC). For microcrystalline electroceramics, with thin and less conductive grain boundaries (vis-à-vis grain core values), the BLM is quite appropriate [10, 11].
In the nanoscale regime, however, the BLM is no longer reliable, owing to the contribution of grain boundary conduction parallel to the direction of current flow. Näfe  developed a modified BLM by connecting the central grain core/grain boundary serial path in parallel with the side-wall grain boundary path. This series/parallel BLM, or SP-BLM, was applied to the analysis of AC-IS measurements on nanocrystalline CeO2 . We subsequently demonstrated, however, that the SP-BLM also fails in the nanocrystalline regime [10, 11].
To correct the deficiencies in the BLM and variants in the nanocrystalline regime, we recently developed a “nano-Grain Composite Model” or n-GCM [10, 11]. First, a 3D pixel-based computer representation was developed for the BLM, taking into account the true 3D current distribution in the brick-layer structure. This model, referred to in our prior work as the “nested cube model” or NCM, accurately models the electrical and dielectric properties of the 3D-BLM over the entire range of grain core volume fractions (ϕ) from microcrystalline (ϕ = 1) to nanocrystalline (ϕ = 0). Upon evaluating other microstructural and effective media models, it was demonstrated that only the NCM and the Maxwell-Wagner/Hashin-Shtrikman (MW-HS) effective medium model are capable of representing composite AC-IS behavior over all values of ϕ . Furthermore, the predictions of the NCM and the MW-HS model are in relatively close agreement over all ranges of ϕ and of local properties (σgb = grain boundary conductivity, εgb = grain boundary dielectric constant, σgc = grain core conductivity, and εgc = grain core dielectric constant). This agreement is fortuitous, since Bonanos and Lilley  were able to develop an (RC)(RC) equivalent circuit corresponding to the MW-HS model and a set of closed-form solutions allowing the four RC elements to be calculated from ϕ and the local properties (σgb, εgb, σgc, and εgc). For the n-GCM, a reverse set of equations was developed to go from the four AC-IS-derived (RC)(RC) values to the underlying (σgb, εgb, σgc, εgc, ϕ) values .
It should be noted that the extraction of the local properties, using the n-GCM, requires that one of the five unknown parameters (σgb, εgb, σgc, εgc, and ϕ) be known. It is reasonable to assume that the grain core dielectric constant will be the same as the single crystal dielectric constant at the corresponding temperature. In the present work, the dielectric constant of single crystal YSZ of comparable composition was measured versus temperature to provide the necessary data.
It should also be stressed that the n-GCM takes into account actual grain shape, i.e., that grains in polycrystalline ceramics are not cubic bricks. We were able to demonstrate that the electrical behaviors of icosahedral or dodecahedral grains fall intermediate to the nested cube and MW-HS models, and are most likely closer to the MW-HS situation . Furthermore, it is likely that grain core shape is nearly spherical as ϕ goes to zero (the nanocrystalline regime), such that the n-GCM becomes indistinguishable from the MW-HS model in this limit. In this case the n-GCM, which employs a methodology based upon the MW-HS equivalent circuit, is the most accurate representation of the electrical/dielectric structure-property relations of nanocrystalline ceramics.
Nanocrystalline YSZ (8 mol% Y2O3) with an average particle size of 5–10 nm was obtained from Fuel Cell Materials (Lewis Center, OH, USA). Quoted impurity concentrations were Si, Ca, Al, Mg, and Cr <100 ppm, with Ca sometimes slightly higher, and Fe, Zn, Cu at <10 ppm. The powder was ground and uniaxially pressed at 125 MPa to a green density of 40%, then isostatically pressed at 270 MPa to 50% green density, into ∼2 mm thick pellets with an average diameter of 10 mm. The pellets were partially sintered for 1 h in air on a YSZ powder bed of identical composition to avoid contamination, with gradual heating and cooling (at 5 °C/min) to minimize thermal shock and cracking. Each pellet was sintered at a different temperature between 800 and 1,050 °C, to achieve a range of grain sizes. Average grain size was determined by X-ray diffraction (XRD) peak broadening, using a Williamson-Hall plot with Jade software  to separate contributions to peak broadening from grain size, strain, and instrumental effects. XRD scans were carried out from 20 to 80° 2θ on a Geigerflex diffractometer (Rigaku, Japan). Grain sizes were verified with field emission SEM (Hitachi S4800) images of fracture surfaces. All pellets were polished with diamond paste to 1 μm roughness prior to electroding. Sample densities were calculated from the measured masses and dimensions (final thickness ∼1.7 mm).
Sputtered silver electrodes (∼100 nm thick) were employed rather than silver paint electrodes, to avoid the wicking of paint into the porous surfaces. Additionally, sputtered electrodes above a certain thickness on polished specimens have been shown to reduce spreading resistance/gap capacitance problems associated with thin electrodes on rough surfaces . Silver was chosen over gold as it reportedly exhibits better chemisorption of oxygen, and the electrode polarization arc in Nyquist plots is less significant . AC-IS measurements were made over the frequency range of 13 MHz to 10 Hz, with a voltage amplitude of 1 V using an Agilent Technolgies 4192A impedance analyzer (Santa Clara, CA). The sample was held in a tube furnace, and measurements were taken over the temperature range, 250–600 °C, low enough to avoid the onset of grain growth (see below). Temperature was monitored with an S-type thermocouple.
After correcting for geometry, the impedance data, consisting of two slightly depressed Nyquist arcs, were fitted to an (RQ)(RQ) Boukamp circuit using the “Equivalent Circuit” program , where Q stands for a constant phase element. These values were subsequently corrected for varying degrees of porosity (see below). The following procedure was implemented to extract the local properties from the raw impedance data.
As mentioned previously, one parameter must be known to solve for the other four parameters. For the present work, it was assumed that the grain core dielectric constant (εgc) should be the same as the single crystal dielectric constant at the corresponding temperature. Unfortunately, literature data covering our experimental temperature range appear to be unavailable. Single crystals of YSZ (7 mol% Y2O3) with dimensions 10 mm by 10 mm by 1 mm were obtained from MTI Corp. (Richmond, CA, USA). The large faces were electroded with thin, porous layers of silver paste. AC-IS measurements were made in the  direction from 13 MHz to 10 Hz over the temperature range of 20–500 °C with the Agilent Technologies 4192A impedance analyzer.
Note that the BLM assumes identical values for grain boundary and grain core dielectric constant (εgb = εgc).
Results and discussion
Space charge widths (one-half the apparent grain boundary width) for samples with different average grain sizes
Average grain size (nm)
Half of apparent GB width (nm)
Figure 7b compares the conductivities of microcrystalline and nanocrystalline samples for all the grain sizes studied. The grain core conductivities lie in a narrow band slightly below that of a representative microcrystalline specimen (16 μm grain size, Guo et al. —the upper dashed line). These results suggest that nanocrystalline specimens exhibit a slightly lower grain core conductivity vis-à-vis the microcrystalline specimens. There are several possible explanations for such an effect, including grain size-dependent impurity segregation and possible de-doping of the major acceptor impurity (yttrium) in grain cores as the grain size decreases .
The grain boundary conductivities of the nanocrystalline specimens fall in a narrow band lying significantly above the data for the representative microcrystalline specimen (Guo et al. —dashed line). For the microcrystalline data, the specific grain boundary conductivity is plotted, which was obtained from the BLM (Eq. 11), assuming εgb = εgc. For the nanocrystalline specimens, the local grain boundary conductivities are plotted, as obtained by n-GCM analysis. (This comparison of local and specific conductivities uses the assumption of nearly isotropic grain boundary transport, i.e., that conductivity is not substantially different perpendicular versus parallel to the grain boundary. This limitation is discussed further later in the article.) In this case, the enhancement of grain boundary conductivity is significant, in agreement with prior reports in the literature [1, 4].
As can be seen from Fig. 8, the calculated grain boundary potential decreases monotonically with decreasing average grain size. This result would suggest that nanocrystalline samples have higher concentrations of oxygen vacancies in the grain boundaries than their microcrystalline counterparts, even though oxygen vacancies are still depleted within the grain boundaries relative to the grain interiors. This increase in carrier concentration could explain the improvement in the grain boundary conductivity. However, it should be pointed out that this explanation is usually reserved for high purity specimens .
An alternate explanation involves grain size-modified segregation, with dilution of the impurities that segregate to grain boundaries in nanocrystalline specimens. This effect is due to the dramatic increase in grain boundary area (in nanograined samples) over which to distribute such segregating impurities. In other words, the grain boundaries are actually cleaner in nanocrystalline versus microcrystalline specimens.
It is worthwhile to note some of the limitations of the n-GCM approach. In theory, the n-GCM should be applicable at all grain sizes (grain core volume fractions). For example, in our prior work [10, 11], the n-GCM approach was shown to be in good agreement with the 3D BLM simulation (which included the true current distribution) across the entire range of volume fractions. In reality, the approach will most likely become intractable at grain core volume fractions of 0.9 or larger, owing to experimental uncertainties associated with establishment of reliable grain core fractions (as per the n-GCM procedure demonstrated in Fig. 5a and b). If we arbitrarily assume a space charge width of 2 nm, a grain core volume fraction of 0.9 would be reached at a grain size of ∼100 nm. Therefore, we would anticipate a working grain size range for the n-GCM of 10–100 nm.
In reality, the situation can be even further constrained. We have established that the n-GCM requires equiaxed nanostructures with a narrow distribution of grain sizes. In the present study, the AC-IS data for the 73 nm grain size specimen could not be successfully analyzed by n-GCM; it was not possible to match the measured single crystal dielectric constant in the n-GCM-derived εgc versus ϕ plot (e.g., see Fig. 5a). We attribute this limitation to a broad distribution of grain sizes leading to significant arc-depression in AC-IS plots. Of course, better processing resulting in nanostructures with the requisite equiaxed/monosized grains should extend the applicability of the n-GCM to the 10–100 nm range of grain size, as described above.
Another limitation of the n-GCM is that it assumes a two-phase microstructure, where grain boundaries and grain cores are considered isotropic and homogeneous. (The n-GCM approach does not explicitly incorporate the gradually changing defect populations or conductivities expected at the grain core—grain boundary interface of real electroceramics. Such behavior has been modeled in preliminary simulations, by nesting multiple grain boundary layers in the 3D-BLM structure .) The n-GCM also assumes that conductivity along the grain boundary (σgb||) is equal to conductivity across the grain boundary (σgb⊥). Nonetheless, the n-GCM can be used to analyze samples with anisotropic grain boundaries if the impedance spectra exhibit dual arc behavior, which is the case as long as σgb⊥ < σgb|| ≪ σgc. Equations for the case when σgb|| is only slightly smaller than σgc have been provided by Kidner .
Finally, the n-GCM requires high quality impedance data with minimal contributions from stray inductive effects or parallel capacitances . Extreme care should be taken to avoid such parasitic contributions by minimizing cable/lead lengths and by employing separate shielded/grounded leads in AC-IS measurements. More information about the n-GCM analysis and its limitations can be found in our recent review .
This paper has demonstrated the applicability of the n-GCM to the determination of local properties (conductivities and dielectric constants) of nanocrystalline YSZ. This model replaces the traditionally used BLM at the smallest grain sizes, and in this case characterized samples with average grain sizes between 10 and 73 nm. In order to apply the model, AC-IS was carried out on nanocrystalline and microcrystalline samples over a range of temperatures. The dielectric constant of a single crystal of a similar dopant concentration was also determined over the same temperature range for use in the analysis as the grain core dielectric constant. The sharp increase in single crystal dielectric constant with temperature was attributed to the onset of dipolar relaxation. The grain boundary dielectric constants were consistently higher than the single crystal (grain core) dielectric constant, likely due to an enhanced dipolar response in the disordered grain boundaries, consistent with the enhancement of certain defect populations and/or mobilities in the grain boundaries. The grain core conductivities were slightly lower in nanocrystalline samples relative to microcrystalline values, but local grain boundary conductivities were significantly enhanced in the nanocrystalline samples, albeit still at levels less than that of the grain cores (i.e., they remain barriers to transport). The enhancement in the local grain boundary conductivity in the nanocrystalline samples is consistent with the observed decrease in grain boundary space charge potential with decreasing grain size, but may be also be attributable to the dilution of impurities at grain boundaries, i.e., grain-size mediated impurity segregation. In spite of the local grain boundary conductivity increase at the nanoscale, the total conductivity decreased with decreasing grain size, owing to the increase in the number of blocking grain boundaries in the nanocrystalline specimens.
The authors acknowledge support from the U.S. Department of Energy under contract no. DE-FG02-05ER-46255 (NHP, TOM) and a National Science Foundation Graduate Research Fellowship (NHP).
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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