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Bibliographic record
Abstract
The dielectric permittivity \ensuremath{\varepsilon} at frequencies from ${(10}^{\ensuremath{-}1}--{10}^{\ensuremath{-}5})\mathrm{Hz}$ to ${10}^{5}\mathrm{Hz}$ is studied in perovskite $(1\ensuremath{-}x)\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\ensuremath{-}x{\mathrm{PbTiO}}_{3}$ relaxor ferroelectric ceramics of different compositions $x=0.35,$ 0.25, and 0, which exhibit, below the temperature of the diffuse $\ensuremath{\varepsilon}(T)$ maximum ${T}_{m},$ a tetragonal ferroelectric, a rhombohedral ferroelectric, and a nonergodic relaxor phase, respectively. The universal relaxor dispersion previously observed at temperatures near and above ${T}_{m}$ in the ceramics of $x=0.25$ is also found to exist in other compositions. This dispersion is described by the fractional power dependence of the real and imaginary parts of susceptibility on frequency, ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}(f)\ensuremath{\propto}{\ensuremath{\chi}}_{U}^{\ensuremath{''}}(f)\ensuremath{\propto}{f}^{n\ensuremath{-}1}.$ The real part of the universal relaxor susceptibility ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}$ is only a comparatively small fraction of the total permittivity ${\ensuremath{\varepsilon}}^{\ensuremath{'}},$ but ${\ensuremath{\chi}}_{U}^{\ensuremath{''}}$ is the dominant contribution to the losses in a wide frequency-temperature range above ${T}_{m}.$ In the high-temperature phase a divergent temperature behavior is observed, ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}(T)\ensuremath{\propto}(T\ensuremath{-}{T}_{0}{)}^{\ensuremath{-}\ensuremath{\gamma}}$ and ${\ensuremath{\chi}}_{U}^{\ensuremath{''}}(T)\ensuremath{\propto}(T\ensuremath{-}{T}_{0}{)}^{\ensuremath{-}\ensuremath{\gamma}},$ with ${T}_{0}<{T}_{m}$ and $\ensuremath{\gamma}\ensuremath{\cong}2,$ for all the three compositions studied. The universal relaxor susceptibility is attributed to the polarization of polar nanoregions, which are inherent in the relaxor ferroelectrics. A microscopic model of this polarization is proposed, according to which the dipole moments of some ``free'' unit cells inside the polar nanoregion can freely choose several different directions, while the direction of the total moment of the nanoregion remains the same. The ensemble of interacting polar nanoregions is described in terms of a standard spherical model, which predicts the quadratic divergence of susceptibility above the critical temperature, in agreement with the experimental results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.423 | 0.218 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".