Impedance Spectroscopy of Pr-Doped BaBi2Nb2O9 Aurivillius Ceramics
Abstract
:1. Introduction
2. Materials and Methods
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Element | Parameter | T = 800 K | ||||
---|---|---|---|---|---|---|
x = 0.02 | x = 0.04 | x = 0.06 | x = 0.08 | x = 0.10 | ||
R1 | Value [Ω] | 13,613 | 20,446 | 26,273 | 314,920 | 36,673 |
Relative error [Ω] | 58.67 | 178 | 491 | 1693 | 419 | |
Absolute error [%] | 0.43 | 0.87 | 1.22 | 0.54 | 1.14 | |
CPE-T | Value [F] | 5.99 × 10−7 | 3.64 × 10−7 | 1.26 × 10−7 | 2.38 × 10−8 | 1.43 × 10−8 |
Relative error [F] | 2.31 × 10−8 | 1.02 × 10−8 | 7.81 × 10−13 | 9.11 × 10−10 | 5.36 × 10−10 | |
Absolute error [%] | 3.87 | 2.80 | 0.41 | 3.83 | 3.73 | |
CPE-P | Value [a.u.] | 0.38 | 0.39 | 0.38 | 0.38 | 0.5451 |
Relative error [a.u.] | 0.0032 | 0.0029 | 0.008 | 0.0031 | 0.0022 | |
Absolute error [%] | 0.84 | 0.74 | 6.2 | 0.83 | 0.41 | |
C | Value [F] | 2.88 × 10−10 | 3.27 × 10−10 | 1.25 × 10−10 | 9.06 × 10−11 | 9.921 × 10−11 |
Relative error [F] | 61.55 | 5.85 × 10−12 | 5.16 × 10−13 | 3.97 × 10−13 | 3.27 × 10−13 | |
Absolute error [%] | 0.70 | 1.79 | 0.41 | 0.44 | 0.33 | |
R2 | Value [Ω] | 13,989 | 18,166 | 23,729 | 79,871 | 22,069 |
Relative error [Ω] | 61.88 | 169 | 416 | 1850 | 452 | |
Absolute error [%] | 0.44 | 0.93 | 1.75 | 2.32 | 2.04 | |
CPE-T | Value [F] | 4.196 × 10−10 | 2.48 × 10−10 | 4.74 × 10−11 | 1.14 × 10−9 | 3.47 × 10−10 |
Relative error [F] | 4.75 × 10−12 | 2.08 × 10−12 | 1.44 × 10−11 | 2.51 × 10−11 | 6.37 × 10−12 | |
Absolute error [%] | 1.13 | 0.84 | 30 | 2.20 | 1.84 | |
CPE-P | Value [a.u.] | 0.96 | 0.99 | 0.97 | 0.98 | 0.97 |
Relative error [a.u.] | 0.0007 | 0.0006 | 0.04 | 0.002 | 0.004 | |
Absolute error [%] | 0.08 | 0.06 | 4.12 | 0.18 | 0.41 | |
χ2 | 5.5 × 10−6 | 1.71 × 10−5 | 9.7 × 10−5 | 1.6 × 10−5 | 2.45 × 10−5 | |
Element | Parameter | T = 600 K | ||||
x = 0.02 | x = 0.04 | x = 0.06 | x = 0.08 | x = 0.10 | ||
R1 | Value [Ω] | 5.13 × 106 | 5.33 × 106 | 6.7743 × 106 | 2.6679 × 107 | 2.0817 × 107 |
Relative error [Ω] | 494,494 | 95,650 | 91,936 | 1.24 × 105 | 1.26 × 105 | |
Absolute error [%] | 0.97 | 1.79 | 1.36 | 0.45 | 0.61 | |
CPE-T | Value [F] | 2.86 × 10−8 | 3.18 × 10−8 | 1.47 × 10−8 | 6.9 × 10−10 | 1.42 × 10−9 |
Relative error [F] | 6.44 × 10−10 | 9.21 × 10−10 | 4.24 × 10−10 | 1.62 × 10−11 | 3.16 × 10−11 | |
Absolute error [%] | 2.25 | 2.90 | 2.87 | 2.34 | 2.22 | |
CPE-P | Value [a.u.] | 0.41 | 0.46 | 0.52441 | 0.54 | 0.5874 |
Relative error [a.u.] | 0.003 | 0.0044 | 0.0041 | 0.004 | 0.0028 | |
Absolute error [%] | 0.73 | 0.97 | 0.79 | 0.66 | 0.47 | |
C | Value [F] | 3.48 × 10−10 | 4.80 × 10−10 | 3.89 × 10−10 | 1.05 × 10−10 | 1.372 × 10−10 |
Relative error [F] | 1.17 | 2.63 × 10−12 | 2.44 × 10−12 | 4.68 × 10−13 | 8.59 × 10−13 | |
Absolute error [%] | 0.34 | 0.55 | 0.63 | 0.44 | 0.62 | |
R2 | Value [Ω] | 1.6833 × 106 | 2.1603 × 106 | 2.4574 × 106 | 1.2728 × 106 | 1.5381 × 106 |
Relative error [Ω] | 7437 | 6414 | 9826 | 1.09 × 104 | 1.45 × 104 | |
Absolute error [%] | 0.44 | 0.30 | 0.4 | 0.86 | 0.92 | |
CPE-T | Value [F] | 5.60 × 10−10 | 3.14 × 10−10 | 3.74 × 10−10 | 2.84 × 10−8 | 5.636 × 10−8 |
Relative error [F] | 3.73 × 10−12 | 1.48 × 10−12 | 2.15 × 10−12 | 1.10 × 10−10 | 2.68 × 10−10 | |
Absolute error [%] | 0.67 | 0.47 | 0.58 | 0.38 | 0.48 | |
CPE-P | Value [a.u.] | 0.96 | 0.99 | 0.98015 | 0.89929 | 0.81243 |
Relative error [a.u.] | 0.0003 | 0.0003 | 0.0005 | 0.031 | 0.023 | |
Absolute error [%] | 0.036 | 0.031 | 0.049 | 3.41 | 2.77 | |
χ2 | 1.35 × 10−5 | 4.55 × 10−5 | 6.67 × 10−5 | 1.9 × 10−5 | 2.41 × 10−5 |
x (Pr) | EG [eV] | EGB [eV] |
---|---|---|
0.02 | 1.13 | 1.00 |
0.04 | 1.15 | 1.00 |
0.06 | 1.14 | 0.98 |
0.08 | 1.44 | 0.95 |
0.10 | 1.35 | 0.85 |
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Rerak, M.; Makowska, J.; Adamczyk-Habrajska, M.; Kozielski, L. Impedance Spectroscopy of Pr-Doped BaBi2Nb2O9 Aurivillius Ceramics. Materials 2022, 15, 6308. https://doi.org/10.3390/ma15186308
Rerak M, Makowska J, Adamczyk-Habrajska M, Kozielski L. Impedance Spectroscopy of Pr-Doped BaBi2Nb2O9 Aurivillius Ceramics. Materials. 2022; 15(18):6308. https://doi.org/10.3390/ma15186308
Chicago/Turabian StyleRerak, Michał, Jolanta Makowska, Małgorzata Adamczyk-Habrajska, and Lucjan Kozielski. 2022. "Impedance Spectroscopy of Pr-Doped BaBi2Nb2O9 Aurivillius Ceramics" Materials 15, no. 18: 6308. https://doi.org/10.3390/ma15186308