Two-dimensional equilibrium island shape and step free energies of Cu(001)

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Abstract

We have derived expressions for the free energies of the densely packed [110] and 100% kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., F[010]/F[110]). Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at T=0 K is not a perfect square.
Original languageUndefined
Pages (from-to)193407-1-193407-4
Number of pages4
JournalPhysical Review B (Condensed Matter and Materials Physics)
Volume67
Issue number19
DOIs
Publication statusPublished - 2003

Keywords

  • METIS-214138
  • IR-40720

Cite this

@article{1a8a509164b04da1894c8e8c76c1cb14,
title = "Two-dimensional equilibrium island shape and step free energies of Cu(001)",
abstract = "We have derived expressions for the free energies of the densely packed [110] and 100{\%} kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., F[010]/F[110]). Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at T=0 K is not a perfect square.",
keywords = "METIS-214138, IR-40720",
author = "{van Moere}, R. and Zandvliet, {Henricus J.W.} and Bene Poelsema",
year = "2003",
doi = "10.1103/PhysRevB.67.193407",
language = "Undefined",
volume = "67",
pages = "193407--1--193407--4",
journal = "Physical review B: Covering condensed matter and materials physics",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "19",

}

Two-dimensional equilibrium island shape and step free energies of Cu(001). / van Moere, R.; Zandvliet, Henricus J.W.; Poelsema, Bene.

In: Physical Review B (Condensed Matter and Materials Physics), Vol. 67, No. 19, 2003, p. 193407-1-193407-4.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Two-dimensional equilibrium island shape and step free energies of Cu(001)

AU - van Moere, R.

AU - Zandvliet, Henricus J.W.

AU - Poelsema, Bene

PY - 2003

Y1 - 2003

N2 - We have derived expressions for the free energies of the densely packed [110] and 100% kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., F[010]/F[110]). Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at T=0 K is not a perfect square.

AB - We have derived expressions for the free energies of the densely packed [110] and 100% kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., F[010]/F[110]). Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at T=0 K is not a perfect square.

KW - METIS-214138

KW - IR-40720

U2 - 10.1103/PhysRevB.67.193407

DO - 10.1103/PhysRevB.67.193407

M3 - Article

VL - 67

SP - 193407-1-193407-4

JO - Physical review B: Covering condensed matter and materials physics

JF - Physical review B: Covering condensed matter and materials physics

SN - 2469-9950

IS - 19

ER -