pith. sign in

arxiv: 1907.01906 · v1 · pith:GZQHPW5Rnew · submitted 2019-07-03 · ❄️ cond-mat.mtrl-sci · physics.chem-ph

Effect of Oxygen Defects Blocking Barriers on Gadolinium Doped Ceria (GDC) Electro-Chemo-Mechanical Properties

Ahsanul Kabir , Simone Santucci , Ngo Van Nong , Maxim Varenik , Igor Lubomirsky , Robin Nigon , Paul Muralt , Vincenzo Esposito This is my paper

Pith reviewed 2026-05-25 10:10 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.chem-ph
keywords gadolinium doped ceriaelectrostrictionoxygen vacanciesoxygen defect blocking barrierssintering methodselectro-chemo-mechanical propertiesceria
0
0 comments X

The pith

Oxygen vacancy distribution governs electrostriction in gadolinium-doped ceria beyond grain size or dopant concentration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how the configuration of oxygen defects influences electro-chemo-mechanical behavior in gadolinium-doped ceria with fixed vacancy concentration. Different sintering routes were applied to nanopowders to change the density of oxygen-defect blocking barriers while attempting to hold other variables steady. Correlations between the resulting properties indicate that vacancy distribution, set by the barriers, drives electrostrictive response more strongly than grain size or dopant levels. This points to defect arrangement as a tunable factor in materials whose electromechanical action does not rely on crystal symmetry.

Core claim

In Ce0.9Gd0.1O2-x (x=0.05), tuning the density of oxygen-defect blocking barriers via spark plasma sintering, fast firing, and conventional sintering shows that oxygen vacancy distribution controls electrostriction, outweighing contributions from grain size and dopant concentration.

What carries the argument

Oxygen-defect blocking barriers, whose density is adjusted by sintering conditions to alter oxygen vacancy distribution and thereby set electrostrictive response.

If this is right

  • Electrostriction in these ceria materials depends primarily on how oxygen vacancies are distributed by blocking barriers.
  • Sintering conditions can modify electro-chemo-mechanical properties through changes in barrier density.
  • Grain size and dopant concentration effects are secondary once vacancy distribution is accounted for.
  • Thermally driven solute drag during sintering influences dopant placement and resulting properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar barrier-density control might be applied to other oxygen-defective oxides such as bismuth oxides to tune their electromechanical response.
  • Grain-boundary engineering could become a primary design lever for optimizing electrostrictors in this class of materials.
  • The results suggest testing whether minimizing blocking barriers improves performance in devices that rely on oxygen-ion transport.

Load-bearing premise

Different sintering routes change mainly the density and distribution of oxygen-defect blocking barriers while leaving grain size, dopant diffusion, density, and composition sufficiently independent of that change.

What would settle it

Electrostrictive coefficients that correlate with grain size or dopant diffusion across the sintered samples rather than with measured blocking-barrier density would contradict the central claim.

Figures

Figures reproduced from arXiv: 1907.01906 by Ahsanul Kabir, Igor Lubomirsky, Maxim Varenik, Ngo Van Nong, Paul Muralt, Robin Nigon, Simone Santucci, Vincenzo Esposito.

Figure 3
Figure 3. Figure 3: c, 3.d [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Some oxygen defective metal oxides, such as cerium and bismuth oxides, have recently shown exceptional electrostrictive properties that are even superior to the best performing lead-based electrostrictors, e.g. lead-magnesium-niobates (PMN). Compared to piezoelectric ceramics, electromechanical mechanisms of such materials do not depend on crystalline symmetry, but on the concentration of oxygen vacancy in the lattice. In this work, we investigate for the first time the role of oxygen defect configuration on the electro-chemo-mechanical properties. This is achieved by tuning the oxygen defects blocking barrier density in polycrystalline gadolinium doped ceria with known oxygen vacancy concentration, Ce0.9Gd0.1O2-x,x= 0.05. Nanometric starting powders of ca. 12 nm are sintered in different conditions, including field assisted spark plasma sintering (SPS), fast firing and conventional method at high temperatures. These approaches allow controlling grain size and Gd-dopant diffusion, i.e. via thermally driven solute drag mechanism. By correlating the electro-chemo-mechanical properties, we show that oxygen vacancy distribution in the materials play a key role in ceria electrostriction, overcoming the expected contributions from grain size and dopant concentration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates the electro-chemo-mechanical properties of gadolinium-doped ceria (Ce0.9Gd0.1O2-x with x=0.05) by sintering nanometric powders via spark plasma sintering, fast firing, and conventional high-temperature routes. These routes are used to tune the density of oxygen-defect blocking barriers while attempting to control grain size and Gd diffusion via solute drag. The central claim is that oxygen vacancy distribution dominates the electrostrictive response, overcoming the expected contributions from grain size and dopant concentration.

Significance. If the experimental design successfully isolates oxygen-vacancy distribution as the dominant variable, the result would clarify the mechanism of electrostriction in defective fluorites and offer a processing route to enhance electromechanical performance independent of crystallographic symmetry. The work is experimental and directly correlates processing conditions with measured properties, which is a strength when controls are demonstrated.

major comments (2)
  1. [Abstract] Abstract: the statement that the three sintering routes 'allow controlling grain size and Gd-dopant diffusion' is not accompanied by any reported grain-size distributions, mean grain sizes, or local Gd concentration maps; without these quantitative controls the attribution of property changes solely to blocking-barrier density cannot be verified and remains load-bearing for the central claim.
  2. [Abstract] Abstract: the oxygen non-stoichiometry is described as 'known' (x=0.05), yet no data or discussion addresses whether SPS or fast-firing alter the actual oxygen content relative to conventional sintering; any shift in x would confound the isolation of vacancy-distribution effects from changes in total vacancy concentration.
minor comments (1)
  1. [Abstract] The notation 'Ce0.9Gd0.1O2-x,x= 0.05' contains a typographical spacing issue after the comma.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable feedback on our manuscript. We address each major comment below and have made revisions to improve the clarity and support for our claims where possible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the three sintering routes 'allow controlling grain size and Gd-dopant diffusion' is not accompanied by any reported grain-size distributions, mean grain sizes, or local Gd concentration maps; without these quantitative controls the attribution of property changes solely to blocking-barrier density cannot be verified and remains load-bearing for the central claim.

    Authors: The referee is correct that the abstract statement is not supported by quantitative data in the manuscript. The different sintering routes are intended to control these parameters via the mechanisms described, but we did not include the full distributions or maps. In the revised manuscript, we have modified the abstract to state that the routes are used to tune the density of oxygen-defect blocking barriers, and we have added a paragraph in the discussion acknowledging that grain size and dopant diffusion were not quantitatively mapped but that the property trends support the dominance of vacancy distribution. We believe this maintains the central claim while being transparent about the controls. revision: partial

  2. Referee: [Abstract] Abstract: the oxygen non-stoichiometry is described as 'known' (x=0.05), yet no data or discussion addresses whether SPS or fast-firing alter the actual oxygen content relative to conventional sintering; any shift in x would confound the isolation of vacancy-distribution effects from changes in total vacancy concentration.

    Authors: The oxygen non-stoichiometry is taken as known from the nominal composition, and all samples were processed in air. We agree that direct measurement would be ideal to rule out changes in total vacancy concentration. In the revision, we have added a sentence in the methods and a short discussion explaining that the fast firing and SPS are short duration processes in oxidizing atmosphere, making significant deviation from x=0.05 unlikely. However, we do not have additional experimental data on oxygen content for the different routes. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental correlation study with no derivations or self-referential reductions

full rationale

The paper is an experimental materials science study that varies sintering routes (SPS, fast firing, conventional) on Ce0.9Gd0.1O2-x powders, measures electro-chemo-mechanical properties, and correlates differences to oxygen vacancy distribution via blocking barriers. No equations, derivations, fitted parameters presented as predictions, or load-bearing self-citations appear in the provided text. The central claim rests on observed property changes under controlled processing, not on any reduction of results to inputs by construction. This is the expected non-finding for a purely empirical correlation paper.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that sintering-induced changes act selectively on blocking-barrier density; no free parameters, new entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • domain assumption Oxygen vacancy concentration remains fixed at x=0.05 across all processed samples regardless of sintering route
    Stated directly in the abstract as the target composition Ce0.9Gd0.1O2-x, x=0.05
  • domain assumption Thermally driven solute drag and grain-boundary formation are the dominant mechanisms by which sintering controls oxygen-defect blocking barriers
    Invoked when the abstract links sintering conditions to 'Gd-dopant diffusion, i.e. via thermally driven solute drag mechanism'

pith-pipeline@v0.9.0 · 5786 in / 1446 out tokens · 43318 ms · 2026-05-25T10:10:25.051195+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    brick model

    Introduction Cerium oxide (CeO2) has been comprehensively investigated in last few decades due to its multifold applications , more specifically in electro -ceramics and catalysts [1]–[4]. It has a centrosymmetric fluorite structure with a pronounced oxygen defectivity, i.e. oxygen vacancies (VO ∙∙). This feature makes ceria an excellent ionic conductor, ...

    work page

  2. [2]

    (Cole-Cole plots), and as ρ

    Experimental Procedure 2.1 Powder Synthesis Nano size gadolinium doped ceria GDC10 powders were prepared by co-precipitation method using diamine in aqueous solution [3]. Cerium nitrate hexahydrate (Sigma-Aldrich, USA) and gadolinium nitrate hexahydrate (Sigma-Aldrich, USA) salts were mixed together in stoichiometric proportions to prepare 0.1 M solution ...

    work page

  3. [3]

    ) and (b) imaginary ρ

    Results and Discussion Use of nano-powder in ceramic processing allows a fine control of the microstructural features in final bulk materials. The morphology and structure of the starting nano-powder used in this work is shown in Fig. 1. TEM analysis revealed that particles have spherical shape and are loosely agglomerated. The nano-powders have a narrow ...

    work page

  4. [4]

    Conclusion In this work, highly dense GDC ceramic pellets were fabricated by both non-conventional and conventional sintering methods. Non-conventional sintering was performed by SPS and fast firing to achieve similar nanometric microstructures with tuned oxygen vacancy configurations, with the same nominal oxygen vacancy concentration. The resulting poly...

    work page

  5. [5]

    The authors would like to thank Massimo Rosa for assistance in TEM

    Acknowledgements This research was supported by DFF-Research Project Grants from the Danish Council for Independent Research, Technology and Production Sciences, June 2016 and European H2020-FETOPEN-2016-2017 project BioWings (Partially), grant number 801267. The authors would like to thank Massimo Rosa for assistance in TEM

    work page 2016

  6. [6]

    Doped Ceria as a Solid Oxide Electrolyte,

    H. L. Tuller, “Doped Ceria as a Solid Oxide Electrolyte,” J. Electrochem. Soc., vol. 122, no. 2, p. 255, 1975

    work page 1975

  7. [7]

    Ceria-based solid electrolytes,

    H. Inaba, “Ceria-based solid electrolytes,” Solid State Ionics, vol. 83, no. 1–2, pp. 1–16, 1996

    work page 1996

  8. [8]

    Design of electroceramics for solid oxides fuel cell applications: Playing with ceria,

    V. Esposito and E. Traversa, “Design of electroceramics for solid oxides fuel cell applications: Playing with ceria,” J. Am. Ceram. Soc., vol. 91, no. 4, pp. 1037–1051, 2008

    work page 2008

  9. [9]

    Physical, chemical and electrochemical properties of pure and doped ceria,

    M. Mogensen, N. M. Sammes, and G. A. Tompsett, “Physical, chemical and electrochemical properties of pure and doped ceria,” Solid State Ionics, vol. 129, no. 1, pp. 63–94, 2000

    work page 2000

  10. [10]

    Electrical conductivity and defect equilibria of Pr0.1Ce0.9O2−δ,

    S. R. Bishop, T. S. Stefanik, and H. L. Tuller, “Electrical conductivity and defect equilibria of Pr0.1Ce0.9O2−δ,” Phys. Chem. Chem. Phys., vol. 13, no. 21, p. 10165, 2011

    work page 2011

  11. [11]

    Grain boundary conductivity of Ce0.8Ln0.2O2-δ ceramics (Ln = Y, La, Gd, Sm) with and without Co-doping,

    D. Pérez-Coll, D. Marrero-López, P. Núñez, S. Piñol, and J. R. Frade, “Grain boundary conductivity of Ce0.8Ln0.2O2-δ ceramics (Ln = Y, La, Gd, Sm) with and without Co-doping,” Electrochim. Acta, vol. 51, no. 28, pp. 6463–6469, 2006

    work page 2006

  12. [12]

    Effect of Sm and Gd dopants on structural characteristics and ionic conductivity of ceria,

    A. Arabaci, “Effect of Sm and Gd dopants on structural characteristics and ionic conductivity of ceria,” Ceram. Int., vol. 41, no. 4, pp. 5836–5842, 2015

    work page 2015

  13. [13]

    Small polaron electron transport in reduced CeO2 single crystals,

    H. L. Tuller and A. S. Nowick, “Small polaron electron transport in reduced CeO2 single crystals,” J. Phys. Chem. Solids, 1977

    work page 1977

  14. [14]

    Nonstoichiometry and defect chemistry in praseodymium-cerium oxide,

    T. S. Stefanik and H. L. Tuller, “Nonstoichiometry and defect chemistry in praseodymium-cerium oxide,” in Journal of Electroceramics, 2004

    work page 2004

  15. [15]

    Giant electrostriction in Gd-doped ceria,

    R. Korobko et al., “Giant electrostriction in Gd-doped ceria,” Adv. Mater., vol. 24, no. 43, pp. 5857–5861, 2012

    work page 2012

  16. [16]

    Key-features in processing and microstructure for achieving giant electrostriction in gadolinium doped ceria thin films,

    M. Hadad, H. Ashraf, G. Mohanty, C. Sandu, and P. Muralt, “Key-features in processing and microstructure for achieving giant electrostriction in gadolinium doped ceria thin films,” Acta Mater., 2016

    work page 2016

  17. [17]

    Relaxation and saturation of electrostriction in 10 mol% Gd-doped ceria ceramics,

    N. Yavo, O. Yeheskel, E. Wachtel, D. Ehre, A. I. Frenkel, and I. Lubomirsky, “Relaxation and saturation of electrostriction in 10 mol% Gd-doped ceria ceramics,” Acta Mater., vol. 144, pp. 411–418, 2018

    work page 2018

  18. [18]

    Low temperature dielectric properties 17 of Ce0.8Gd0.2O1.9 films,

    V. Shelukhin, I. Zon, E. Wachtel, Y. Feldman, and I. Lubomirsky, “Low temperature dielectric properties 17 of Ce0.8Gd0.2O1.9 films,” Solid State Ionics, 2012

    work page 2012

  19. [19]

    Electrostriction: Nonlinear Electromechanical Coupling in Solid Dielectrics,

    R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: Nonlinear Electromechanical Coupling in Solid Dielectrics,” J. Phys. Chem. B, vol. 101, no. 48, pp. 10141–10150, 1997

    work page 1997

  20. [20]

    Large Nonclassical Electrostriction in (Y, Nb)-Stabilized δ-Bi2O3,

    N. Yavo et al., “Large Nonclassical Electrostriction in (Y, Nb)-Stabilized δ-Bi2O3,” Adv. Funct. Mater., vol. 26, no. 7, pp. 1138–1142, 2016

    work page 2016

  21. [21]

    Geometry of electromechanically active structures in Gadolinium - Doped Cerium oxides,

    Y. Li et al., “Geometry of electromechanically active structures in Gadolinium - Doped Cerium oxides,” AIP Adv., vol. 6, no. 5, 2016

    work page 2016

  22. [22]

    Anelastic Relaxation in Crystalline Solids,

    A. S. Nowick, B. S. Berry, and J. L. Katz, “Anelastic Relaxation in Crystalline Solids,” J. Appl. Mech., vol. 42, no. 3, p. 750, 1975

    work page 1975

  23. [23]

    How to interpret current-voltage relationships of blocking grain boundaries in oxygen ionic conductors,

    S. K. Kim, S. Khodorov, C. T. Chen, S. Kim, and I. Lubomirsky, “How to interpret current-voltage relationships of blocking grain boundaries in oxygen ionic conductors,” Phys. Chem. Chem. Phys., 2013

    work page 2013

  24. [24]

    On determining the height of the potential barrier at grain boundaries in ion-conducting oxides,

    S. Kim, S. K. Kim, S. Khodorov, J. Maier, and I. Lubomirsky, “On determining the height of the potential barrier at grain boundaries in ion-conducting oxides,” Phys. Chem. Chem. Phys., 2016

    work page 2016

  25. [25]

    Electromechanical properties of electrostrictive CeO2:Gd membranes: Effects of frequency and temperature,

    A. D. Ushakov et al., “Electromechanical properties of electrostrictive CeO2:Gd membranes: Effects of frequency and temperature,” Appl. Phys. Lett., 2017

    work page 2017

  26. [26]

    Grain growth in CeO2: Dopant effects, defect mechanism, and solute drag,

    P. L. Chen and I. W. Chen, “Grain growth in CeO2: Dopant effects, defect mechanism, and solute drag,” J. Am. Ceram. Soc., vol. 79, no. 7, pp. 1793–1800, 1996

    work page 1996

  27. [27]

    Role of Defect Interaction in Boundary Mobility and Cation Diffusivity of CeO2,

    P. ­L Chen and I. ­W Chen, “Role of Defect Interaction in Boundary Mobility and Cation Diffusivity of CeO2,” J. Am. Ceram. Soc., vol. 77, no. 9, pp. 2289–2297, 1994

    work page 1994

  28. [28]

    Enhanced mass diffusion phenomena in highly defective doped ceria,

    V. Esposito et al., “Enhanced mass diffusion phenomena in highly defective doped ceria,” Acta Mater., vol. 61, no. 16, pp. 6290–6300, 2013

    work page 2013

  29. [29]

    Effect of chemical redox on Gd-doped ceria mass diffusion,

    D. W. Ni, D. Z. de Florio, D. Marani, A. Kaiser, V. B. Tinti, and V. Esposito, “Effect of chemical redox on Gd-doped ceria mass diffusion,” J. Mater. Chem. A, vol. 3, no. 37, pp. 18835–18838, 2015

    work page 2015

  30. [30]

    Fast mass interdiffusion in ceria/alumina composite,

    F. Teocoli, D. W. Ni, S. Sanna, K. Thydén, F. C. Fonseca, and V. Esposito, “Fast mass interdiffusion in ceria/alumina composite,” J. Mater. Chem. A, 2015

    work page 2015

  31. [31]

    Densification of Highly Defective Ceria by High Temperature Controlled Re-Oxidation,

    D. W. Ni et al., “Densification of Highly Defective Ceria by High Temperature Controlled Re-Oxidation,” J. Electrochem. Soc., 2014

    work page 2014

  32. [32]

    Direct Observation of Oxygen Vacancy Distribution across Yttria-Stabilized Zirconia Grain Boundaries,

    B. Feng, N. R. Lugg, A. Kumamoto, Y. Ikuhara, and N. Shibata, “Direct Observation of Oxygen Vacancy Distribution across Yttria-Stabilized Zirconia Grain Boundaries,” ACS Nano, 2017

    work page 2017

  33. [33]

    Grain Size Effect in the Electrical Properties of Nanostructured Functional Oxides through Pressure Modification of the Spark Plasma Sintering Method,

    D. V. Quach, S. Kim, R. A. De Souza, M. Martin, and Z. A. Munir, “Grain Size Effect in the Electrical Properties of Nanostructured Functional Oxides through Pressure Modification of the Spark Plasma Sintering Method,” Key Eng. Mater., 2011

    work page 2011

  34. [34]

    Electrical properties of the grain boundaries of oxygen ion conductors: Acceptor- doped zirconia and ceria,

    X. Guo and R. Waser, “Electrical properties of the grain boundaries of oxygen ion conductors: Acceptor- doped zirconia and ceria,” Prog. Mater. Sci., 2006

    work page 2006

  35. [35]

    Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis,

    X. Guo and J. Maier, “Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis,” J. Electrochem. Soc., vol. 148, no. 3, p. E121, 2001

    work page 2001

  36. [36]

    Space charge conduction: Simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria,

    S. Kim, J. Fleig, and J. Maier, “Space charge conduction: Simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria,” in Physical Chemistry Chemical Physics, 2003

    work page 2003

  37. [37]

    Ionic conduction in space charge regions,

    J. Maier, “Ionic conduction in space charge regions,” Progress in Solid State Chemistry, vol. 23, no. 3. pp. 171–263, 1995

    work page 1995

  38. [38]

    Role of space charge in the grain boundary blocking effect in doped zirconia,

    X. Guo, W. Sigle, J. U. Fleig, and J. Maier, “Role of space charge in the grain boundary blocking effect in doped zirconia,” Solid State Ionics, 2002

    work page 2002

  39. [39]

    Space charge conduction: Simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria,

    S. Kim, J. Fleig, and J. Maier, “Space charge conduction: Simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria,” Phys. Chem. Chem. Phys., vol. 5, no. 11, pp. 2268– 2273, 2003

    work page 2003

  40. [40]

    The grain boundary impedance of random microstructures: Numerical simulations and implications for the analysis of experimental data,

    J. Fleig, “The grain boundary impedance of random microstructures: Numerical simulations and implications for the analysis of experimental data,” in Solid State Ionics, 2002

    work page 2002

  41. [41]

    Nanoscale effects on the ionic conductivity of highly doped bulk nanometric 18 cerium oxide,

    U. Anselmi-Tamburini et al., “Nanoscale effects on the ionic conductivity of highly doped bulk nanometric 18 cerium oxide,” Adv. Funct. Mater., vol. 16, no. 18, pp. 2363–2368, 2006

    work page 2006

  42. [42]

    Spark plasma sintering studies of nanosize lanthanidedoped ceria obtained by sol-gel method,

    C. Plapcianu, C. Valsangiacom, J. E. Schaffer, A. Wieg, J. Garay, and L. Stanciu, “Spark plasma sintering studies of nanosize lanthanidedoped ceria obtained by sol-gel method,” J. Optoelectron. Adv. Mater., vol. 13, no. 9, pp. 1101–1108, 2011

    work page 2011

  43. [43]

    Field-assisted sintering technology/spark plasma sintering: Mechanisms, materials, and technology developments,

    O. Guillon et al., “Field-assisted sintering technology/spark plasma sintering: Mechanisms, materials, and technology developments,” Advanced Engineering Materials, vol. 16, no. 7. pp. 830–849, 2014

    work page 2014

  44. [44]

    The effect of forming stresses on the sintering of ultra-fine Ce0.9Gd0.1O2-δ powders,

    J. A. Glasscock et al., “The effect of forming stresses on the sintering of ultra-fine Ce0.9Gd0.1O2-δ powders,” J. Eur. Ceram. Soc., 2013

    work page 2013

  45. [45]

    Average Grain Size in Polycrystalline Ceramics,

    M. I. MENDELSON, “Average Grain Size in Polycrystalline Ceramics,” J. Am. Ceram. Soc., 1969

    work page 1969

  46. [46]

    The scherrer formula for X-ray particle size determination,

    A. L. Patterson, “The scherrer formula for X-ray particle size determination,” Phys. Rev., 1939

    work page 1939

  47. [47]

    Nonlinear Electrical Properties of Grain Boundaries in Oxygen Ion Conductors: Acceptor-Doped Ceria,

    X. Guo, S. Mi, and R. Waser, “Nonlinear Electrical Properties of Grain Boundaries in Oxygen Ion Conductors: Acceptor-Doped Ceria,” Electrochem. Solid-State Lett., 2005

    work page 2005

  48. [48]

    Preparation and Electrochemical Characterization of Perovskite/YSZ Ceramic Films,

    D. Z. de Florio, R. Muccillo, V. Esposito, E. Di Bartolomeo, and E. Traversa, “Preparation and Electrochemical Characterization of Perovskite/YSZ Ceramic Films,” J. Electrochem. Soc., 2005

    work page 2005

  49. [49]

    Grain size dependence of electrical properties of Gd-doped ceria,

    A. HARA, Y. HIRATA, S. SAMESHIMA, N. MATSUNAGA, and T. HORITA, “Grain size dependence of electrical properties of Gd-doped ceria,” J. Ceram. Soc. Japan, 2008

    work page 2008

  50. [50]

    Ionic and Electronic Conductivity of Nanostructured, Samaria-Doped Ceria,

    E. C. C. Souza, W. C. Chueh, W. Jung, E. N. S. Muccillo, and S. M. Haile, “Ionic and Electronic Conductivity of Nanostructured, Samaria-Doped Ceria,” J. Electrochem. Soc., vol. 159, no. 5, p. K127, 2012

    work page 2012