Temperature dependence of the capacitance of a ferroelectric material
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Bibliographic record
Abstract
We present an alternate version of the undergraduate laboratory experiment developed by Dixon [Am. J. Phys. 75, 1038–1045 (2007)] that is suitable for second-year students. We study the temperature variation of the capacitance of a ferroelectric ceramic derived from barium titanate, the Ba(Ti0.9Sn0.1)O3 solid solution. The ratio of tin to titanium is chosen to provide a convenient Curie temperature near 50°C. Using careful temperature control and real-time capacitance measurements, we track the time evolution of the capacitance in response to temperature changes at 5Hz for runs that last up to a day. At temperatures well above the Curie temperature, TC, the capacitance relaxation is well-described by a single exponential decay. Near TC, the relaxation is linear in the logarithm of time over more than three decades. For T>TC, the permittivity deviates from the Curie–Weiss law and follows another phenomenological form commonly used to describe relaxor perovskite-ceramic capacitors.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it