Corresponding Author

Qiu-an HUANG(qiuan_huang@shu.edu.cn);
Juan WANG(juanwang168@gmail.com);
Jiu-jun ZHANG(jiujun.zhang@i.shu.edu.cn)


Electrochemical impedance spectroscopy (EIS) is a powerful electrochemical characterization technology, which has been widely used in the field of electrochemical energy, such as lithium-ion batteries, supercapacitors, fuel cells, etc. Distribution of relaxation time (DRT) is an EIS deconvolution technique which does not depend on the prior knowledge of the targeted research object. Furthermore, DRT can serve to separate and analyze physical and chemical processes which are highly overlapped in their EIS data. In order to encourage the application and popularization of DRT deconvolution technology, several core questions are addressed in this paper: (1) DRT deconvolution principle, implementation steps and important extensions; (2) DRT deconvolution method for typical circuit elements; (3) DRT implementation software and typical electrochemical energy application examples; (4) achievements, challenges and development trends for DRT deconvolution technique.

Graphical Abstract


electrochemical impedance spectroscopy, distribution of relaxation time, distribution of differential capacity, distribution of diffusion time, characteristic time constant, lithium-ion battery, supercapacitor, fuel cell

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[1]Chu S, Majumdar A. Opportunities and challenges for a sustainable energy future[J]. Nature, 2012,488(7411):294-303.
doi: 10.1038/nature11475 URL pmid: 22895334

[2]Khan M A, Zhao H B, Zou W W, et al. Recent progresses in electrocatalysts for water electrolysis[J]. Electrochemical Energy Reviews, 2018,1(4):483-530.

[3]Lu J, Chen Z W, Pan F, et al. High-performance anode materials for rechargeable Li-thiumion batteries[J]. Electrochemical Energy Reviews, 2018,1(1):35-53.

[4]Tian N, Lu B A, Yang X D, et al. Rational design and synjournal of low-temperature fuel cell electrocatalysts[J]. Electrochemical Energy Reviews, 2018,1(1):54-83.

[5]Wang Y J, Fang B, Zhang D, et al. A review of carbon-composited materials as air-electrode bifunctional electrocatalysts for metal-air batteries[J]. Electrochemical Energy Reviews, 2018,1(1):1-34.

[6]Zhang H M, Lu W J, Li X F. Progress and perspectives of flow battery technologies[J]. Electrochemical Energy Reviews, 2019,2(1):1-15.

[7]Bouwmeester H, Gellings P J. The CRC handbook of solid state electrochemistry[M]. New York: CRC Press, 1997.

[8]Bard A J, Faulkner L R, Leddy J, et al. Electrochemical methods: fundamentals and applications[M]. New York: wiley, 1980.

[9]Huang J(黄俊). Electrochemical impedance spectroscopy for electrocatalytic interfaces and reactions: Classics never die[J]. Journal of Electrochemistry (电化学), 2020,26(1):3-18.

[10]Macdonald D D. Reflections on the history of electrochemical impedance spectroscopy[J]. Electrochimica Acta, 2006,51(8/9):1376-1388.

[11]Randviir E P, Banks C E. Electrochemical impedance spectroscopy: an overview of bioanalytical applications[J]. Analytical Methods, 2013,5(5):1098-1115.

[12]Rupp G M, Opitz A K, Nenning A, et al. Real-time impedance monitoring of oxygen reduction during surface modification of thin film cathodes[J]. Nature Materials, 2017,16(6):640-645.
doi: 10.1038/nmat4879 URL pmid: 28346431

[13]Barsoukov E, Macdonald J R. Impedance spectroscopy: theory, experiment, and applications[M]. Hoboken, NJ: Wiley, 2018.

[14]Zhuang Q C(庄全超), Xu S D(徐守冬), Qiu X Y(邱祥云), et al. Diagnosis of electrochemical impedance spectroscopy in lithium ion batteries[J]. Progress in Chemistry (化学进展), 2010,22(6):1044-1057.

[15]Lasia A. Electrochemical impedance spectroscopy and its applications[M] //Modern aspects of electrochemistry. Springer, Boston, MA, 2002: 143-248.

[16]Song J, Bazant M Z. Electrochemical impedance imaging via the distribution of diffusion times[J]. Physical Review letters, 2018,120(11):116001.
URL pmid: 29601735

[17]Macdonald D D. Why electrochemical impedance spectroscopy is the ultimate tool in mechanistic analysis[M]. ECS Transactions, 2009,19(20):55-79.

[18]Huang Q A, Hui R, Wang B, et al. A review of AC impedance modeling and validation in SOFC diagnosis[J]. Electrochimica Acta, 2007,52(28):8144-8164.
doi: 10.1016/j.electacta.2007.05.071 URL

[19]Huang Q A(黄秋安), Li W H(李伟恒), Tang Z P(汤哲鹏), et al. Fundamentals of electrochemical impedance spectroscopy[J]. Chinese Journal of Nature (自然), 2020,42(1):1-15.

[20]Schichlein H, Müller A C, Voigts M, et al. Deconvolution of electrochemical impedance spectra for the identification of electrode reaction mechanisms in solid oxide fuel cells[J]. Journal of Applied Electrochemistry, 2002,32(8):875-882.
doi: 10.1023/A:1020599525160 URL

[21]Ciucci F. Modeling electrochemical impedance spectroscopy[J]. Current Opinion in Electrochemistry, 2019,13:132-139.
doi: 10.1016/j.coelec.2018.12.003 URL

[22]Huang J, Li Z, Liaw B Y, et al. Graphical analysis of electrochemical impedance spectroscopy data in Bode and Nyquist representations[J]. Journal of Power Sources, 2016,309:82-98.
doi: 10.1016/j.jpowsour.2016.01.073 URL

[23]Ivers-Tiffee E, Weber A. Evaluation of electrochemical impedance spectra by the distribution of relaxation times[J]. Journal of the Ceramic Society of Japan, 2017,125(4):193-201.
doi: 10.2109/jcersj2.16267 URL

[24]Kobayashi K, Suzuki T S. Distribution of relaxation time analysis for non-ideal immittance spectrum: discussion and progress[J]. Journal of the Physical Society of Japan, 2018,87(9):094002.
doi: 10.7566/JPSJ.87.094002 URL

[25]Shi W Y(施王影), Jia C(贾川), Zhang Y L(张永亮), et al. Differentiation and decomposition of solid oxide fuel cell electrochemical impedance spectra[J]. Acta Physico-Chimica Sinica (物理化学学报), 2019,35(5):509-516.

[26]Fuoss R M, Kirkwoo J G. Electrical properties of solids. VIII. Dipole moments in polyvinyl chloride-diphenyl systems[J]. The Journal of Chemical Physics, 1941,63(2):385-394.

[27]Colonomos P, Gordon R G. Bounded error analysis of experimental distributions of relaxation times[J]. The Journal of Chemical Physics, 1979,71(3):1159-1166.

[28]Misell D L, Sheppard R J. The application of deconvolution techniques to dielectric data[J]. Journal of Physics D (Applied Physics), 1973,6(4):379-389.

[29]Salefran J L, Dutuit Y. The use of a discriminative window in deconvolution method applied to dielectric data[J]. The Journal of Chemical Physics, 1981,74(5):3056-3063.

[30]Morgan F D, Lesmes D P. Inversion for dielectric relaxation spectra[J]. The Journal of Chemical Physics, 1994,100(1):671-681.

[31]Paulson K S, Jouravleva S, McLeod C N. Dielectric relaxation time spectroscopy[J]. IEEE Transactions on Bio-Me-dical Engineering, 2000,47(11):1510-1517.

[32] Schichlein H, Feuerstein M, Müller A, et al. System identification: a new modelling approach for SOFC single cells[C]//The electrochemical society. Solid Oxide Fuel Cells:(SOFC VI): Proceedings of the Sixth International Symposium. October 17-22, 1999, Honolulu, Hawaii, USA. Pennington, New Jersey: the electrochemical society Electrochem, 1999: 1069-1077.

[33]Danzer M A. Generalized distribution of relaxation times analysis for the characterization of impedance spectra[J]. Batteries, 2019,5(3):53.

[34]Boukamp B A. Fourier transform distribution function of relaxation times; application and limitations[J]. Electro-chimica Acta, 2015,154:35-46.

[35]Boukamp B A, Rolle A. Analysis and application of distribution of relaxation times in solid state ionics[J]. Solid State Ionics, 2017,302(SI):12-18.

[36]Hörlin T. Deconvolution and maximum entropy in imped-ance spectroscopy of noninductive systems[J]. Solid State Ionics, 1998,107(3/4):241-253.

[37]Tuncer E, Gubanski S M. On dielectric data analysis. Using the Monte Carlo method to obtain relaxation time distribution and comparing non-linear spectral function fits[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2001,8(3):310-320.

[38]Tesler A B, Lewin D R, Baltianski S, et al. Analyzing results of impedance spectroscopy using novel evolutionary programming techniques[J]. Journal of Electroceramics, 2010,24(4):245-260.

[39]Hershkovitz S, Baltianski S, Tsur Y. Harnessing evolutionary programming for impedance spectroscopy analysis: A case study of mixed ionic-electronic conductors[J]. Solid State Ionics, 2011,188(1):104-109.

[40]Hershkovitz S, Tomer S, Baltianski S, et al. ISGP: Imped-ance spectroscopy analysis using evolutionary programming procedure[M]. ECS Transactions, 2011,33(40):67-73.

[41]Hershkovitz S, Baltianski S, Tsur Y. Electrochemical im-pedance analysis of SOFC cathode reaction using evolutionary programming[J]. Fuel Cells, 2012,12(1):77-85.

[42]Žic M, Pereverzyev S, Subotic V, et al. Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times[J]. GEM-International Journal on Geomathematics, 2020,11(1):2.
doi: 10.1007/s13137-019-0138-2 URL pmid: 31839841

[43]Saccoccio M, Wan T H, Chen C, et al. Optimal regularization in distribution of relaxation times applied to electrochemical impedance spectroscopy: Ridge and lasso regression methods - a theoretical and experimental study[J]. Electrochimica Acta, 2014,147:470-482.

[44]Wan T H, Saccoccio M, Chen C, et al. Influence of the discretization methods on the distribution of relaxation times deconvolution: implementing radial basis functions with DRT tools[J]. Electrochimica Acta, 2015,184:483-499.

[45]Zhang Y X, Chen Y, Yan M F, et al. Reconstruction of relaxation time distribution from linear electrochemical impedance spectroscopy[J]. Journal of Power Sources, 2015,283:464-477.

[46]Zhang Y X, Chen Y, Li M, et al. A high-precision approach to reconstruct distribution of relaxation times from electrochemical impedance spectroscopy[J]. Journal of Power Sources, 2016,308:1-6.

[47]Li X, Ahmadi M, Collins L, et al. Deconvolving distribution of relaxation times, resistances and inductance from electrochemical impedance spectroscopy via statistical model selection: Exploiting structural-sparsity regularization and data-driven parameter tuning[J]. Electrochimica Acta, 2019,313:570-583.

[48]Hahn M, Schindler S, Triebs L C, et al. Optimized process parameters for a reproducible distribution of relaxation times analysis of electrochemical systems[J]. Batteries, 2019,5(2):43.
doi: 10.3390/batteries5020043 URL

[49]Garda B, Galias Z. Tikhonov regularization and constrained quadratic programming for magnetic coil design problems[J]. International Journal of Applied Mathematics and Computer Science, 2014,24(2):249-257.
doi: 10.2478/amcs-2014-0018 URL

[50]Tikhonov A N, Goncharsky A V, Stepanov V V, et al. Numerical methods for the solution of ill-posed problems[M]. Dordrecht: Springer, 2013.

[51]Hansen P C, O’Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM Journal on Scientific Computing, 1993,14(6):1487-1503.
doi: 10.1137/0914086 URL

[52]Golub G H, Hansen P C, O'Leary D P. Tikhonov regularization and total least squares[J]. SIAM Journal on Matrix Analysis and Applications, 1999,21(1):185-194.
doi: 10.1137/S0895479897326432 URL

[53]Smirnova A L, Ellwood K R, Crosbie G M. Application of fourier-based transforms to impedance spectra of small-diameter tubular solid oxide fuel cells[J]. Journal of The Electrochemical Society, 2001,148(6):A610-A615.

[54]Oz A, Hershkovitz S, Belman N, et al. Analysis of imped-ance spectroscopy of aqueous supercapacitors by evolutionary programming: Finding DFRT from complex capacitance[J]. Solid State Ionics, 2016,288(SI):311-314.
doi: 10.1016/j.ssi.2015.11.008 URL

[55]Schönleber M, Ivers-Tiffée E. The distribution function of differential capacity as a new tool for analyzing the capacitive properties of lithium-ion batteries[J]. Electrochemistry Communications, 2015,61:45-48.
doi: 10.1016/j.elecom.2015.09.024 URL

[56]Guo D X, Yang G, Zhao G J, et al. Determination of the differential capacity of lithium-ion batteries by the deconvolution of electrochemical impedance spectra[J]. Energies, 2020,13(4):915.
doi: 10.3390/en13040915 URL

[57]Oz A, Gelman D, Goren E, et al. A novel approach for supercapacitors degradation characterization[J]. Journal of Power Sources, 2017,355:74-82.
doi: 10.1016/j.jpowsour.2017.04.048 URL

[58]Quattrocchi E, Wan T H, Curcio A, et al. A general model for the impedance of batteries and supercapacitors: The non-linear distribution of diffusion times[J]. Electro-chimica Acta, 2019, 324: UNSP 134853.

[59]Pereverzev S V, Solodky S G, Vasylyk V B, et al. Regularized collocation in distribution of diffusion times applied to electrochemical impedance spectroscopy[J]. Com-putational Methods in Applied Mathematics, 2020,20(3):517-530.

[60]Schönleber M, Ivers-Tiffée E. Approximability of imped-ance spectra by RC elements and implications for impedance analysis[J]. Electrochemistry Communications, 2015,58:15-19.
doi: 10.1016/j.elecom.2015.05.018 URL

[61]Žic M, Pereverzyev S, Subotic V, et al. Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times[J]. GEM-International Journal on Geomathematics, 2020,11(1):2.
doi: 10.1007/s13137-019-0138-2 URL pmid: 31839841

[62]Dion F, Lasia A. The use of regularization methods in the deconvolution of underlying distributions in electrochemical processes[J]. Journal of Electroanalytical Chemistry, 1999,475(1):28-37.
doi: 10.1016/S0022-0728(99)00334-4 URL

[63]Gavrilyuk A L, Osinkin D A, Bronin D I. The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy[J]. Russian Journal of Electrochemistry, 2017,53(6):575-588.
doi: 10.1134/S1023193517060040 URL

[64]Leonide A, Apel Y, Ivers-Tiffee E. SOFC modeling and parameter identification by means of impedance spectroscopy[M]. ECS Transactions, 2009,19(20):81-109.

[65]Huang Q A, Shen Y, Huang Y, et al. Impedance characteristics and diagnoses of automotive lithium-ion batteries at 7.5% to 93.0% state of charge[J]. Electrochimica Acta, 2016,219:751-765.

[66]Huang Q A, Li Y, Tsay K C, et al. Multi-scale impedance model for supercapacitor porous electrodes: Theoretical prediction and experimental validation[J]. Journal of Power Sources, 2018,400:69-86.

[67]Boukamp B A. Derivation of a distribution function of relaxation times for the (fractal) finite length warburg[J]. Electrochimica Acta, 2017,252:154-163.

[68]Boukamp B A, Rolle A. Use of a distribution function of relaxation times (DFRT) in impedance analysis of SOFC electrodes[J]. Solid State Ionics, 2018,314:103-111.

[69]Malkow K T. A theory of distribution functions of relaxation times for the deconvolution of immittance data[J]. Journal of Electroanalytical Chemistry, 2019,838:221-231.

[70]Liu J, Ciucci F. The Gaussian process distribution of relaxation times: A machine learning tool for the analysis and prediction of electrochemical impedance spectroscopy data[J]. Electrochimica Acta, 2020,331:135316.

[71]Schmidt J P, Chrobak T, Ender M, et al. Studies on LiFePO4 as cathode material using impedance spectroscopy[J]. Journal of Power Sources, 2011,196(12):5342-5348.

[72]Illig J, Ender M, Chrobak T, et al. Separation of charge transfer and contact resistance in LiFePO4-cathodes by impedance modeling[J]. Journal of The Electrochemical Society, 2012,159(7):A952-A960.

[73]Illig J, Schmidt J P, Weiss M, et al. Understanding the impedance spectrum of 18650 LiFePO4-cells[J]. Journal of Power Sources, 2013,239:670-679.


[74] Schmidt J P, Berg P, Schönleber M, et al. The distribution of relaxation times as basis for generalized time-domain models for Li-ion batteries[J]. Journal of Power Sources, 2013,221:70-77.

[75] Gantenbein S, Weiss M, Ivers-Tiffée E. Impedance based time-domain modeling of lithium-ion batteries: Part I[J]. Journal of Power Sources, 2018,379:317-327.

[76] Schönleber M, Uhlmann C, Braun P, et al. A consistent derivation of the impedance of a lithium-ion battery electrode and its dependency on the state-of-charge[J]. Electrochimica Acta, 2017,243:250-259.

[77] Schmidt J P, Ivers-Tiffée E. Pulse-fitting - A novel method for the evaluation of pulse measurements, demonstrated for the low frequency behavior of lithium-ion cells[J]. Journal of Power Sources, 2016,315:316-323.

[78] Zhou X, Huang J, Pan Z Q, et al. Impedance characterization of lithium-ion batteries aging under high-temperature cycling: Importance of electrolyte-phase diffusion[J]. Journal of Power Sources, 2019,426:216-222.

[79] Wang G P, Zhang L, Zhang J J. A review of electrode materials for electrochemical supercapacitors[J]. Chemical Society Reviews, 2012,41(2):797-828.
doi: 10.1039/c1cs15060j URL pmid: 21779609

[80] Fletcher S, Kirkpatrick I, Dring R, et al. The modelling of carbon-based supercapacitors: distributions of time constants and pascal equivalent circuits[J]. Journal of Power Sources, 2017,345:247-253.

[81] Helseth L E. Modelling supercapacitors using a dynamic equivalent circuit with a distribution of relaxation times[J]. Journal of Energy Storage, 2019, 25: UNSP 10912.

[82] Zhang J. PEM fuel cell electrocatalysts and catalyst layers: fundamentals and applications[M]. London: Springer, 2008.

[83] Mertens A, Granwehr J. Two-dimensional impedance data analysis by the distribution of relaxation times[J]. Journal of Energy Storage, 2017,13:401-408.

[84] Schindler S, Weiss A, Galbiati S, et al. Identification of polarization losses in high-temperature PEM fuel cells by distribution of relaxation times analysis[M]. ECS Transactions, 2016,75(14):45-53.

[85] Weiss A, Schindler S, Galbiati S, et al. Distribution of relaxation times analysis of high-temperature PEM fuel cell impedance spectra[J]. Electrochimica Acta, 2017,230:391-398.

[86] Bevilacqua N, Gokhale R R, Serov A, et al. Comparing novel PGM-Free, Platinum, and alloyed platinum catalysts for HT-PEMFCs[M]. ECS Transactions, 2018,86(13):221-229.

[87] Heinzmann M, Weber A, Ivers-Tiffée E. Advanced im-pedance study of polymer electrolyte membrane single cells by means of distribution of relaxation times[J]. Journal of Power Sources, 2018,402:24-33.

[88] Simon Araya S, Zhou F, Lennart Sahlin S, et al. Fault characterization of a proton exchange membrane fuel cell stack[J]. Energies, 2019,12(1):152.

[89] Guo J W(郭建伟), Wang J L(王建龙). The pilot application of electrochemical impedance spectroscopy on dynamic proton exchange membrane fuel cell[J]. Journal of Electrochemistry (电化学), 2018,24(6):668-696.

[90] Yuan X Z, Wang H J, Sun J C, et al. AC impedance technique in PEM fuel cell diagnosis — A review[J]. International Journal of Hydrogen Energy, 2007,32(17):4365-4380.

[91] Yuan X-Z R, Song C, Wang H, et al. Electrochemical impedance spectroscopy in PEM fuel cells: fundamentals and applications[M]. London: Springer Verlag-London, 2010.

[92] Yezerska K, Liu F, Dushina A, et al. Analysis of the regeneration behavior of high temperature polymer electrolyte membrane fuel cells after hydrogen starvation[J]. Journal of Power Sources, 2020,449:227562.

[93] Yao Y F(姚颖方), Liu J G(刘建国) L, Zou Z G(邹志刚). Degradation mechanism and anti-aging strategies of membrane electrode assembly of fuel cells[J]. Journal of Electrochemistry (电化学), 2018,24(6):664-676.

[94] Sonn V, Leonide A, Ivers-Tiffée E. Combined deconvolution and CNLS fitting approach applied on the imped-ance response of technical Ni/8YSZ cermet electrodes[J]. Journal of The Electrochemical Society, 2008,155(7):B675-B679.

[95] Leonide A, Weber A, Ivers-Tiffée E. Electrochemical analysis of biogas fueled anode supported SOFC[M]. ECS Transactions, 2011,35(1):2961-2968.

[96] Leonide A, Sonn V, Weber A, et al. Evaluation and modeling of the cell resistance in anode-supported solid oxide fuel cells[J]. Journal of The Electrochemical Society, 2007,155(1):B36-B41.

[97] Kornely M, Neumann A, Menzler N H, et al. Degradation of anode supported cell (ASC) performance by Cr-poisoning[J]. Journal of Power Sources, 2011,196(17):7203-7208.

[98] Endler C, Leonide A, Weber A, et al. Time-dependent electrode performance changes in intermediate temperature solid oxide fuel cells[J]. Journal of The Electrochemical Society, 2009,157(2):B292-B298.

[99] Ma Q L, Tietz F, Leonide A, et al. Impedance studies on solid oxide fuel cells with yttrium-substituted SrTiO3 ceramic anodes[M]. ECS Transactions, 2011,35(1):1421-1433.

[100] Weber A, Dierickx S, Kromp A, et al. Sulfur poisoning of anode-supported SOFCs under reformate operation[J]. Fuel Cells, 2013,13(4):487-493.

[101] Sumi H, Yamaguchi T, Hamamoto K, et al. Electrochemical analysis for anode-supported microtubular solid oxide fuel cells in partial reducing and oxidizing conditions[J]. Solid State Ionics, 2014,262(SI):407-410.

[102] Kornely M, Menzler N H, Weber A, et al. Degradation of a high performance SOFC cathode by Cr-poisoning at OCV-conditions[J]. Fuel Cells, 2013,13(4):506-510.

[103] Nechache A, Mansuy A, Petitjean M, et al. Diagnosis of a cathode-supported solid oxide electrolysis cell by electrochemical impedance spectroscopy[J]. Electrochimica Acta, 2016,210:596-605.

[104] Oz A, Gelman D, Tsur Y, et al. Evolutionary programming based approach for SOFC cathode characterization: A case study on Co-free mixed conducting perovskites[M]. ECS Transactions, 2017,78(1):2099-2108.

[105] Li W, Huang Q A, Yang C, et al. A fast measurement of Warburg-like impedance spectra with Morlet wavelet transform for electrochemical energy devices[J]. Electro-chimica Acta, 2019,322:134760.

[106] Subotic V, Schluckner C, Strasser J, et al. In-situ electrochemical characterization methods for industrial-sized planar solid oxide fuel cells Part I: Methodology, qualification and detection of carbon deposition[J]. Electrochimica Acta, 2016,207:224-236.

[107] Graves C, Ebbesen S D, Mogensen M. Co-electrolysis of CO2 and H2O in solid oxide cells: Performance and durability[J]. Solid State Ionics, 2011,192(1):398-403.

[108] Wuillemin Z, Antonetti Y, Beetschen C, et al. Local activation and degradation of electrochemical processes in a SOFC[M]. ECS Transactions, 2013,57(1):561-570.

[109] Fang Q, Blum L, Menzler N H. Performance and degradation of solid oxide electrolysis cells in stack[J]. Journal of The Electrochemical Society, 2015,162(8):F907-F912.

[110] Paul T, Yavo N, Lubomirsky I, et al. Determination of grain boundary conductivity using distribution function of relaxation times (DFRT) analysis at room temperature in 10mol% Gd doped ceria: A non-classical electrostrictor[J]. Solid State Ionics, 2019,331:18-21.

[111] Baral A K, Tsur Y. Sintering aid (ZnO) effect on proton transport in BaCe0.35ZR0.5Y0.15O3-δ and electrode phenomena studied by distribution function of relaxation times[J]. Journal of the American Ceramic Society, 2019,102(1):239-250.

[112] Baral A K, Tsur Y. Impedance spectroscopy of Gd-doped ceria analyzed by genetic programming (ISGP) method[J]. Solid State Ionics, 2017,304:145-149.



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