### Abstract

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.

Original language | English |
---|---|

Article number | 104101 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 90 |

Issue number | 10 |

DOIs | |

Publication status | Published - Sep 2 2014 |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*90*(10), [104101]. https://doi.org/10.1103/PhysRevB.90.104101

**Advanced Ginzburg-Landau theory of freezing : A density-functional approach.** / Tóth, G.; Provatas, Nikolas.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 90, no. 10, 104101. https://doi.org/10.1103/PhysRevB.90.104101

}

TY - JOUR

T1 - Advanced Ginzburg-Landau theory of freezing

T2 - A density-functional approach

AU - Tóth, G.

AU - Provatas, Nikolas

PY - 2014/9/2

Y1 - 2014/9/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84908408425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908408425&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.90.104101

DO - 10.1103/PhysRevB.90.104101

M3 - Article

AN - SCOPUS:84908408425

VL - 90

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 10

M1 - 104101

ER -