I have measured total conductivity (electrical + ionic) of a ceria-based oxide by impedance analyzer in two ways:
1. By keeping the temperature constant at a time (like 400, 500, 600 700 °C etc.) and changed the frequency from 1 KHz to 10 MHz
2. By keeping the frequency constant at a time (like 1, 10, 100, 500, 1000 KHz etc.) and changed the temperature from 300 to1000 °C.
Is total conductivity measured by both methods would be similar for the data taken at the same frequency and temperature (for example at a frequency of 10 MHz and temperature of 1000 °C) or it would be different? Please explain.
Theoretically, as the temperature and the frequency are the same the electrical conductivity must be the same. However, practically some differences may be observed. A statistical analysis is required to make sure that this is a significant difference or not.
The rate of heating, the speed of frequency swapping, and the time duration before taking the read affect the results as they decide whether the sample is in its steady state, when the read is taken, or not.
Imad is right, however, we should think what could happen within the defined parameter field. Change of frequency will probably be harmless. Ceria is prone to reduction at high temperature due to thermodynamic boundary conditions. So if at high temperature some reduction takes place and the numer of oxygen vacancies are increased, this would affect subsequent measurements at lower temperature as under this conditions re-oxidation would be extremely slow. To be sure that the sample history does not interfere with the measurement better use a fresh sample for each measurement.
No, it must be same for different approaches. Depending on the method, there could be variations in the results which comes from the accuracy of the method, not technique-dependency of the thermal conductivity.
Dr. Kern is right. Process of oxygen exchance with media is relatively slow (especcialy at lower temperatures). Therefore, it is better to use fixed temperatures and run frequency measurements. And, an exposure at each temperature and few the trial measurements (in time) is needed to make sure that the sample has come to equilibrium...
Thank you all for sharing the knowledge
@ Vadim S. Gorshkov sir: CeO2 has the reduction property at higher temperature i.e. it reduced from Ce4+ to Ce3+. So, may be exposing it at higher temperature for longer time (measurement carried out when temperature is fixed) can lead to difference in conductivity than the second approach (where we are increasing the temperature linearly).
I'm not talking about a complete reducing, but about the equilibrium with the gas media. At relatively low temperatures (600-900 ° C) oxygen vacancies defects appear in CeO2 . See, for example:
- Defects and Defect Processes in Nonmetallic Solids By William Hayes, A. M. Stoneham. Courier Dover Publications, 2004;
- Bulfin, B .; Lowe, A. J .; Keogh, K.A .; Murphy, B.E .; Lübben, O .; Krasnikov, S.A .; Shvets, I. V. (2013). "Analytical Model of CeO2 Oxidation and Reduction". The Journal of Physical Chemistry C. 117 (46): 24129-24137.
And defectiveness in solids, as it is well known, greatly affects all properties, including conductivity. Of course, trivalent doping increases the defectiveness in oxygen sublattice of CeO2, this is also a well-known fact:
- Badwal, S.P.S .; Daniel Fini; Fabio Ciacchi; Christopher Munnings; Justin Kimpton; John Drennan (2013). "Structural and microstructural stability of ceria - gadolinia electrolyte exposed to reducing environments. J. Mater. Chem. A. 1 (36): 10768-10782. doi: 10.1039 / C3TA11752A
So, cerium oxide has its own defects in oxygen sublattice (and associated charge defects), its concentration depend on the temperature and concentration of oxygen in the media. And, by the way, the impurities present in any real reagent. Therefore defeсt-sensitive properties may vary in different samples. Own defectiveness is not achieved instantaneously, but requires exposure, especially at relatively low temperatures (about 500 C and little bit above). At much lower temperatures we are dealing with a "frozen" defects, which concentration depends on the prehistory of the sample. The chemistry of non-stoichiometric compounds can not be stated in this short text, but it is!
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