What does one learn from equilibrium shapes of two-dimensional islands on surfaces?

Giesen, Margret; Steimer, C.; Ibach, H.

doi:10.1016/s0039-6028(00)00888-8

Cited by 111 publications

(103 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is implicit experimental information for ⑀ 2 : from island shapes 18 and fluctuations 21 ␤͑0͒ = 220± 11 meV. Since related measurements showed 1 2 ⑀ 1 = −128 meV, we deduce ⑀ 2 = −92 meV if ⑀ RT is insignificant.…”

Section: Discussionmentioning

confidence: 63%

See 1 more Smart Citation

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

et al. 2004

View full text Add to dashboard Cite

Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest-and next-nearest-neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, nonpairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two highsymmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).

show abstract

Section: Discussionmentioning

confidence: 63%

“…3,18,19 By considering just the lowest and second lowest energy configurations, 9,10 Zandvliet et al obtained the result 10 (expressed with our sign convention for ⑀ 2 ) for the maximally misoriented case m =1,…”

Section: ͑16͒mentioning

confidence: 99%

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

et al. 2004

View full text Add to dashboard Cite

show abstract

“…where , sometimes 10 called the "Ising parameter," is the bonding energy associated with the "severed half" of the NN lattice-gas bond. Since the NN lattice-gas energy ⑀ 1 is attractive ͑negative͒, and half of it is attributed to the atom on each end, it "costs" a positive energy =− 1 2 ⑀ 1 for each step-edge atom.…”

Section: A Recap Of Results For Square Latticementioning

confidence: 99%

“…From the equilibrium shape of islands over a broad temperature range, Giesen et al 10 deduced that the free energy per lattice spacing in the maximally kinked directions is 0.27± 0.03 eV on Cu͕111͖ and slightly smaller, 0.25± 0.03 eV, on Ag͕111͖. Combining these results with Eq.…”

Section: ͑10͒mentioning

confidence: 89%

Low-temperature orientation dependence of step stiffness on {111} surfaces

et al. 2005

View full text Add to dashboard Cite

For hexagonal nets, descriptive of ͕111͖ fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction, based on the Ising model with nearest-neighbor ͑NN͒ interactions. Our formula agrees well with experimental data for both Ag and Cu͕111͖ surfaces, indicating that NN interactions alone can account for the data in these cases ͑in contrast to results for Cu͕001͖͒. Experimentally significant corollaries of the low-temperature derivation show that the step line tension cannot be extracted from the stiffness and that with plausible assumptions the low-temperature stiffness should have six-fold symmetry, in contrast to the three fold symmetry of the crystal shape. We examine Zia's exact implicit solution in detail, using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high-symmetry directions. From these exact results we rederive our simple result and explore subtle behavior near close-packed directions. To account for the three-fold symmetry in a lattice gas model, we invoke an orientation-dependent trio interaction and examine its consequences.

show abstract

“…The formation of facets below the roughening temperature, and the Pakrovsky-Talapov predictions [26] for the edge shape (z(x)) of crystals have been demonstrated in a number of clean systems [27][28][29][30][31][32][33][34]. In addition to studies on 3D crystals, there has been substantial work on the 2D ECS of islands [15,[35][36][37][38][39]] to obtain the edge free energy, equilibrium edge fluctuations and decay kinetics.…”

Section: Introductionmentioning

confidence: 99%

Nano-scale equilibrium crystal shapes

Degawa¹,

Szalma²,

Williams³

2005

Surface Science

View full text Add to dashboard Cite

The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a shape parameter c. The total crystallite free energy, including interface energy, is minimized for c=0, yielding in all cases the traditional PT shape (z~x 3/2 ). Solutions of the crystal shape for c≠0 are presented and discussed in the context of meta-stable states due to the energy barrier for nucleation. Explicit scaled relationships for the ECS and meta-stable states in terms of the measurable step parameters and the interfacial energy are presented.

show abstract

What does one learn from equilibrium shapes of two-dimensional islands on surfaces?

Cited by 111 publications

References 55 publications

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

Low-temperature orientation dependence of step stiffness on {111} surfaces

Nano-scale equilibrium crystal shapes

Contact Info

Product

Resources

About