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
APA StyleRerak, M., Makowska, J., Adamczyk-Habrajska, M., & Kozielski, L. (2022). Impedance Spectroscopy of Pr-Doped BaBi2Nb2O9 Aurivillius Ceramics. Materials, 15(18), 6308. https://doi.org/10.3390/ma15186308