Evidence for anisotropic polar nanoregions in relaxor Pb(Mg<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math>Nb<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mrow><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math>)O<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>3</mml:mn></mml:msub></mml:math>: A neutron study of the elastic constants and anomalous TA phonon damping in PMN
Bibliographic record
Abstract
We use neutron inelastic scattering to characterize the acoustic phonons in the relaxor Pb(Mg${}_{1/3}$Nb${}_{2/3}$)O${}_{3}$ (PMN) and demonstrate the presence of a highly anisotropic damping mechanism that is directly related to short-range polar correlations. For a large range of temperatures above ${T}_{c}\ensuremath{\sim}210$ K, where dynamic, short-range polar correlations are present, acoustic phonons propagating along [1$\overline{1}$0] and polarized along [110] (TA${}_{2}$ phonons) are overdamped and softened across most of the Brillouin zone. By contrast, acoustic phonons propagating along [100] and polarized along [001] (TA${}_{1}$ phonons) are overdamped and softened for a more limited range of wave vectors $q$. The anisotropy and temperature dependence of the acoustic phonon energy linewidth $\ensuremath{\Gamma}$ are directly correlated with neutron diffuse scattering cross section, indicating that polar nanoregions are the cause of the anomalous behavior. The damping and softening vanish for $q\ensuremath{\rightarrow}0$, i.e., for long-wavelength acoustic phonons near the zone center, which supports the notion that the anomalous damping is a result of the coupling between the relaxational component of the diffuse scattering and the harmonic TA phonons. Therefore, these effects are not due to large changes in the elastic constants with temperature because the elastic constants correspond to the long-wavelength limit. We compare the elastic constants we measure to those from Brillouin scattering experiments and to values reported for pure PbTiO${}_{3}$. We show that while the values of C${}_{44}$ are quite similar, those for C${}_{11}$ and C${}_{12}$ are significantly less in PMN and result in a softening of (C${}_{11}\ensuremath{-}{C}_{12}$) over PbTiO${}_{3}$. The elastic constants also show an increased elastic anisotropy [2C${}_{44}$/(C${}_{11}\ensuremath{-}{C}_{12}$)] in PMN versus that in PbTiO${}_{3}$. These results are suggestive of an instability to TA${}_{2}$ acoustic fluctuations in PMN and other relaxor ferroelectrics. We discuss our results in the context of the current debate over the ``waterfall'' effect and show that they are inconsistent with acoustic-optic phonon coupling or other models that invoke the presence of a second, low-energy optic mode.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".