Deriving surface-energy anisotropy for phenomenological phase-field models of solidification

Sami Majaniemi, Nikolas Provatas

Research output: Contribution to journalArticleScientificpeer-review

33 Citations (Scopus)

Abstract

The free energy of classical density functional theory of an inhomogeneous fluid at coexistence with its solid is used to describe solidification in two-dimensional hexagonal crystals. A coarse-graining formalism from the microscopic density functional level to the macroscopic single order parameter level is provided. An analytic expression for the surface energy and the angular dependence of its anisotropy is derived and its coefficients related to the two-point direct correlation function of the liquid phase at coexistence.
Original languageEnglish
Article number011607
Number of pages12
JournalPhysical review E
Volume79
Issue number1
DOIs
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed

Fingerprint

Phase Field Model
Surface Energy
Solidification
Density Functional
Coexistence
solidification
surface energy
Anisotropy
anisotropy
Coarse-graining
Hexagon
Order Parameter
Correlation Function
Free Energy
liquid phases
Crystal
free energy
Liquid
density functional theory
formalism

Keywords

  • density functional theory
  • free energy
  • liquid theory
  • solidification
  • surface energy

Cite this

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title = "Deriving surface-energy anisotropy for phenomenological phase-field models of solidification",
abstract = "The free energy of classical density functional theory of an inhomogeneous fluid at coexistence with its solid is used to describe solidification in two-dimensional hexagonal crystals. A coarse-graining formalism from the microscopic density functional level to the macroscopic single order parameter level is provided. An analytic expression for the surface energy and the angular dependence of its anisotropy is derived and its coefficients related to the two-point direct correlation function of the liquid phase at coexistence.",
keywords = "density functional theory, free energy, liquid theory, solidification, surface energy",
author = "Sami Majaniemi and Nikolas Provatas",
note = "Project code: 24173",
year = "2009",
doi = "10.1103/PhysRevE.79.011607",
language = "English",
volume = "79",
journal = "Physical review E",
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Deriving surface-energy anisotropy for phenomenological phase-field models of solidification. / Majaniemi, Sami; Provatas, Nikolas.

In: Physical review E, Vol. 79, No. 1, 011607, 2009.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Deriving surface-energy anisotropy for phenomenological phase-field models of solidification

AU - Majaniemi, Sami

AU - Provatas, Nikolas

N1 - Project code: 24173

PY - 2009

Y1 - 2009

N2 - The free energy of classical density functional theory of an inhomogeneous fluid at coexistence with its solid is used to describe solidification in two-dimensional hexagonal crystals. A coarse-graining formalism from the microscopic density functional level to the macroscopic single order parameter level is provided. An analytic expression for the surface energy and the angular dependence of its anisotropy is derived and its coefficients related to the two-point direct correlation function of the liquid phase at coexistence.

AB - The free energy of classical density functional theory of an inhomogeneous fluid at coexistence with its solid is used to describe solidification in two-dimensional hexagonal crystals. A coarse-graining formalism from the microscopic density functional level to the macroscopic single order parameter level is provided. An analytic expression for the surface energy and the angular dependence of its anisotropy is derived and its coefficients related to the two-point direct correlation function of the liquid phase at coexistence.

KW - density functional theory

KW - free energy

KW - liquid theory

KW - solidification

KW - surface energy

UR - http://www.physics.mcgill.ca/~provatas/papers/Anisotropy_derivation.pdf

U2 - 10.1103/PhysRevE.79.011607

DO - 10.1103/PhysRevE.79.011607

M3 - Article

VL - 79

JO - Physical review E

JF - Physical review E

SN - 2470-0045

IS - 1

M1 - 011607

ER -