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Download fileAdvanced Ginzburg–Landau theory of freezing: a density-functional approach
This paper revisits the weakly fourth-order anisotropic Ginzburg-Landau (GL) theory of freezing (also known
as the Landau-Brazowskii model or theory of weak crystallization) by comparing it to a recent density functional
approach, the phase-field crystal (PFC) model. First we study the critical behavior of a generalized PFC model
and show that (i) the so-called one-mode approximation is exact in the leading order, and (ii) the direct correlation
function has no contribution to the phase diagram near the critical point. Next, we calculate the anisotropy of
the crystal-liquid interfacial free energy in the phase-field crystal (PFC) model analytically. For comparison,
we also determine the anisotropy numerically and show that no range of parameters can be found for which
the phase-field crystal equation can quantitatively model anisotropy for metallic materials. Finally, we derive
the leading order PFC amplitude model and show that it coincides with the weakly fourth-order anisotropic GL
theory, as a consequence of the assumptions of the GL theory being inherent in the PFC model. We also propose
a way to calibrate the anisotropy in the Ginzburg-Landau theory via a generalized gradient operator emerging
from the direct correlation function appearing in the generating PFC free energy functional.
Funding
This work has been supported by the Postdoctoral Programme of The Hungarian Academy of Sciences and the Natural Sciences and Engineering Research Council of Canada.
History
School
- Science
Department
- Mathematical Sciences
Published in
Physical Review BVolume
90Issue
10Citation
TOTH, G. and PROVATAS, N., 2014. Advanced Ginzburg–Landau theory of freezing: a density-functional approach. Physical Review. B, Condensed matter and materials physics, 90 (10), DOI: 10.1103/PhysRevB.90.104101.Publisher
© American Physical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2014ISSN
1098-0121eISSN
1550-235XPublisher version
Language
- en