Phase-field crystal approach for modeling the role of microstructure in multiferroic composite materials
Bibliographic record
Abstract
This paper introduces a phase-field crystal (PFC) approach that couples the atomic-scale PFC density field to order parameters describing ferromagnetic and ferroelectric ordering, as well to a solute impurity field. This model extends the magnetic PFC model introduced by Faghihi et al. [N. Faghihi, Ph.D. Thesis, The University of Western Ontario, 2012; N. Faghihi, N. Provatas, K. R. Elder, M. Grant, and M. Karttunen, Phys. Rev. E 88, 032407 (2013)] to incorporate polarization and concentration fields, as well as anisotropic ordering of the magnetization and polarization fields as determined by the local crystalline orientation. Magnetoelectric coupling is incorporated through the elastic coupling. Analytic calculations for a body centered-cubic (BCC) system are presented to illustrate that the model reduces to the standard multiferroic phase-field models when only a single crystal is considered. Two special cases of the model are then studied, the first focusing on magnetocrystalline interactions in a system described by the two-point correlation function of the XPFC model developed by Greenwood et al. [M. Greenwood, N. Provatas, and J. Rottler, Phys. Rev. Lett. 105, 045702 (2010); M. Greenwood, J. Rottler, and N. Provatas, Phys. Rev. E 83, 031601 (2011)], and the second focusing on electrocrystalline interactions in a system described by the original PFC kernel developed by Elder et al. K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. 88, 245701 (2002); K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)]. We examine the small deformation properties of these two realizations of the model . Numerical simulations are performed to illustrate how magnetocrystalline coupling can be exploited to design a preferential grain texture and how defects and grain boundaries influence the ferroelectric coercivity.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".