Complete Mechanistic Elucidation of Current–Voltage Characteristics

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Complete Mechanistic Elucidation of Current−Voltage Characteristics of Grain Boundaries in a Proton-Conducting Solid Electrolyte Chih-Yuan S. Chang,† Igor Lubomirsky,*,‡ and Sangtae Kim*,† †

Department of Materials Science and Engineering, University of California, Davis 95616, United States Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel

‡

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S Supporting Information *

ABSTRACT: Ionic current in proton-conducting polycrystalline ceramics is often hampered a great deal by the grain boundaries, limiting their prospective applications as solid electrolytes for next-generation solid oxide fuel cells. To elucidate the conduction mechanism at the grain boundaries, we use a linear diffusion model and impedance spectroscopy to report complete current−voltage (I−V) characteristics of the grain boundaries in 0.5 mol % Sr-doped LaNbO4. We provide the first experimental evidence of complete annihilation of the space charge-induced proton depletion at the grain boundaries upon applying moderate bias voltages. We also show that it is possible to distinguish between the grain boundary resistance caused by the space charge and other sources by analyzing the I−V characteristics. The analysis is equally valid for other solid ionic conductors such that it can serve as an important tool to guide further optimization of the conductivity of polycrystalline solid electrolytes.

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present study employs a linear diffusion model15,18,19 we developed earlier to interpret current−voltage (I−V) characteristics of grain boundaries in 0.5 mol % Sr-doped LaNbO4 (LSN0.5), a proton-conducting solid electrolyte. This model allows one to estimate Ψgb more accurately. Acceptor-doped LaNbO4 features in high chemical stability in CO2/H2O atmospheres and good sintering capability as compared to more popular doped-BaCeO3 and BaZrO3 systems, respectively.20−22 Comparison of Ψgb from the I−V analysis with the value obtained from RR method reveals whether the high grain boundary resistivity has a single origin. This approach can be universally applicable to all solid ionic conductors to serve as a powerful tool for their performance optimization.

INTRODUCTION Solid-state proton conductors have attracted much attention because of their potential use as solid electrolytes in electrochemical devices such as solid oxide fuel cells,1−3 hydrogen separation membranes,4,5 hydrogen sensors,6 and also in ammonia synthesis.7,8 One of the major challenges for their commercial applications, however, lies with the fact that proton transport across the grain boundaries in such materials is obstructed substantially.9,10 As a result, the resistivity of the grain boundary is often higher than that of the grain interior by several orders of magnitude, greatly reducing the performance of the material. The prevailing view on the reason for such high grain boundary resistivity is trapping of positive charges at grain boundary cores, which causes subsequent depletion of protons nearby because of Columbic repulsion.9,11 The net result of this process is that the grain boundaries contain a fewnanometer thick space charge layers almost completely devoid of protons and therefore become poorly conductive. High grain boundary resistivity has also been ascribed to similar phenomena in other ionic conductors.12−14 The degree of proton depletion is characterized by the height of the potential barrier Ψgb formed at the grain boundary (Figure 1); accurate determination of its value is hence essential.15 The value of Ψgb has long been estimated from the ratio of grain boundary resistivity to bulk counterpart (hereafter RR method)16 which is based on the assumption that the space charge is the sole source of the grain boundary resistivity. Although this assumption may not be always valid, until recently there was no alternative to determine Ψgb with higher accuracy.17−19 The © XXXX American Chemical Society

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EXPERIMENTAL SECTION

Sr-doped LaNbO4 (0.5 mol %, LSN0.5) powder was synthesized through solid-state reactions. A bulk sample was prepared via cold isostatic pressing, followed by sintering and grain growth at 1550 °C. Relative sintered density was above 96%, and the sample had 150 μm in thickness after polishing. Phase purity was confirmed by an X-ray diffractometer (Malvern Panalytical, United Kingdom) with Cu Kα (λ ≈ 1.54 Å) as the radiation source, whereas average grain size (6.5 ± 0.2 μm) was estimated via a linear intercept method under a scanning electron microscope (Quattro SEM, Thermo Scientific, USA). Electrical properties of grain boundaries Received: January 18, 2019

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DOI: 10.1021/acs.jpcc.9b00556 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Left: illustration of potential barrier and depleted protons due to net positive grain boundary cores in solid-state polycrystalline Sr-doped LaNbO4. Right: crystallographic X-ray diffraction patterns of synthesized LSN0.5 powder and a sintered bulk pellet in this study. All peaks match ICSD collection code 262599.

resistance remains constant, regardless of the applied bias. This implies that the concentration of protons in the bulk is little affected by the applied bias. On the basis of the brick layer model,27 Igb was estimated from Vdc/Rtotal, where Vdc denotes dc bias voltage and Rtotal is total resistance of the sample obtained from impedance spectra. Ugb was estimated from28

were studied through a two-probe impedance analyzer (Alpha A, Novocontrol Technologies, Germany) measured in wet N2 (PH2O ≈ 0.017 atm). For more details, please refer to the Supporting Information.

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RESULTS AND DISCUSSION The synthesized LSN0.5 powder and sintered bulk pellets are both pure phases as verified by X-ray diffraction (no unindexed peaks23−25 in Figure 1). To obtain current (Igb) and average voltage drop across a grain boundary (Ugb), impedance of bulk LSN0.5 was measured under multiple dc bias voltages at different temperatures. Figure 2 shows a set of impedance

Ugb =

Vdc jij R gb zyz j z Ngb jjk R total zz{

(1)

where Ngb is number of grain boundaries across the sample and Rgb is the total grain boundary resistance. As shown in Figure 3a, upon increasing the bias voltage, the experimental log(Igb)−log(Ugb) curves of grain boundaries show up to

Figure 2. Representative impedance spectra of LSN0.5 under different dc bias voltages at 275 °C in wet N2. The inset magnifies the spectra at higher frequency region.

spectra measured at 275 °C under 5 mV to 40 V bias voltage in wet N2 as an example. By fitting each spectrum with parallel RQ equivalent circuits connected in series (where R and Q denote a resistor and constant phase element, respectively), the resistance and capacitance of bulk (Cb ≈ 10−12 F) and grain boundaries (Cgb ≈ 10−9 F) were identified. It can be seen from Figure 2 that the total grain boundary resistance decreases when the bias voltage is larger than 2 V, which agrees with the presence of space charge as protons from the grain interiors are injected into the depletion regions.26 However, the impedance arc corresponding to the grain boundaries stops shrinking beyond 20 V dc, indicating that the grain boundary resistance becomes independent of the voltage applied again, that is, Ohmic behavior. On the other hand, the bulk (grain interior)

Figure 3. (a) Experimental grain boundary current−voltage curves of LSN0.5 at 200−275 °C. The inset magnifies the 250 °C curve for better clarity. (b) Illustration of changes in proton distribution profiles at a grain boundary in LSN0.5 under different extents of bias voltages. B

DOI: 10.1021/acs.jpcc.9b00556 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 4. (a) Verification of the applicability of I−V method. (b) Comparison of Ψgb estimated from I−V and RR methods at 200−275 °C. (c) Comparison of total grain boundary resistivity and contribution from space charge.

three linear regions (Ugb is expressed in unit of thermal voltage, Vth = kB·T/q, where kB is Boltzmann constant, T is absolute temperature, and q is elemental charge): the slope starts from unity (Ohmic, Igb ∝ Ugb) to a value larger than one (superOhmic, Igb ∝ (Ugb)n) and then ends up with unity again (Ohmic, Igb ∝ Ugb), consistent with our theoretical calculations previously reported.15,19 The changes in the depletion levels at a grain boundary under bias voltages are schematically illustrated in Figure 3b. The first Ohmic region results from lower applied bias which is not sufficient to inject protons in the amount comparable to trapped charges. As the bias voltage increases, injected protons into the space charge region decrease the degree of depletion, causing the grain boundary resistance to drop in a superOhmic way (Igb ∝ (Ugb)n).15,18,19 At even higher bias, the grain boundary becomes completely flooded by protons, resulting in constant resistance and thus shows Ohmic behavior again. It should be noted that although the linear diffusion model predicts the existence of the second Ohmic region,19 it has not been experimentally observed before this work because in most cases it requires too high voltages for the sample to sustain. In this view, the difference between the resistivity of the first Ohmic region and the second Ohmic region is the contribution of the space charge effects to the overall resistivity of the grain boundaries, which can be determined directly from the I−V curve.

The criterion of the applicability of the linear diffusion model for determination of Ψgb is the relation (np − f KL)·T ≈ constant, where f KL = 0.41 is a constant (Kim−Lubomirsky factor) derived from numerical simulations.18 Figure 4a shows that this criterion is fulfilled for LSN0.5; therefore, Ψgb can be determined from the power exponents (np) at super-Ohmic region of Igb−Ugb curves through the following relation15 Ψgb/Vth = n p/fKL

(2)

The resulting values of Ψgb/Vth are 3.7−4.3 (Ψgb ≈ 0.18 V), which is also within the applicability range of the I−V model.18 Ψgb estimated from I−V and RR methods are summarized in Figure 4b, where the RR method determines Ψgb from rgb, the ratio of grain boundary resistivity (ρgb) to bulk resistivity (ρbulk), through the following equation16,19 rgb =

ρgb ρbulk

=

exp(z Ψgb/Vth) 2z Ψgb/Vth

(3)

Equation 3 can be approximated to19 Ψgb = Vth(1.176 × ln (rgb) + 1.835)

(4)

for charge number z = 1 and Ψgb larger than a few Vth. As can be seen from Figure 4b, Ψgb estimated from the RR method shows an increasing trend with T, which is in contradiction with the fact that rgb is smaller at higher T,9,10 whereas the I−V 19

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DOI: 10.1021/acs.jpcc.9b00556 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C method gives rather consistent values within the temperature range of interest. One has to emphasize that the RR method attributes ρgb solely to space charge, whereas the linear diffusion method yields the effective Ψgb. The difference between the experimentally measured ρgb and that determined based on Ψgb thus represents the part of ρgb which is not related to the space charge. In fact, one can see from Figure 4c that for LSN0.5, the space charge-related contribution to ρgb is relatively minor, which probably originates from the fact that the effective mobility of protons at the grain boundaries is lower than that in the bulk, as structural disorders would increase the distance between the adjacent oxygen ions, obstructing proton hopping.3 The speculation is also supported by the fact that the proton transfer has large anisotropy29 and by transmission electron microscopy/energydispersive system results showing that LSN0.5 has rather clean grain boundaries except at some triple junctions.9 As a result, the source of constant resistance when space charge vanishes can be attributed to local crystal structure misalignments at grain boundary cores that hinders proton transport.

ACKNOWLEDGMENTS

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REFERENCES

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CONCLUSIONS In summary, we demonstrate the first experimental evidence of complete annihilation of the space charge-induced proton depletion at grain boundaries upon applying moderate bias voltages. LSN0.5 is so far the first case where all three regions of the grain boundary I−V curve can be observed. Such observation was predicted by the linear diffusion model we had previously developed and provides another strong argument to the validity of the model. Our report also shows that the I−V analysis, based on the diffusion model, can effectively distinguish between the grain boundary resistance induced by the space charge and by other sources. Because this analysis is universal, it can serve as a viable tool to guide further optimization of ionic conductivity of polycrystalline ceramics. Specifically for LSN0.5, the experimental evidence indicates that the space charge-induced proton depletion is not the major cause of the grain boundary resistivity. This implies that further research on LSN is to be directed toward understanding the proton transport mechanisms at grain boundaries at an atomic level. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b00556.

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The authors would like to thank the U.S.Israel Binational Science Foundation (2016006) for funding this research. The research is also made possible in part by the generosity of the Harold Perlman Family.

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Article

More detailed experimental procedures, an SEM image, impedance spectra, capacitance, and variation of resistivity ratios with temperature (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (I.L.). *E-mail: [email protected] (S.K.). ORCID

Chih-Yuan S. Chang: 0000-0001-9325-6408 Igor Lubomirsky: 0000-0002-2359-2059 Sangtae Kim: 0000-0001-6259-5132 Notes

The authors declare no competing financial interest. D

DOI: 10.1021/acs.jpcc.9b00556 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.9b00556 J. Phys. Chem. C XXXX, XXX, XXX−XXX