Equilibrium fluctuations and decay of step bumps on vicinal Cu (111) surfaces

Giesen, Margret; Icking-Konert, G. Schulze

doi:10.1016/s0039-6028(98)00499-3

Cited by 62 publications

(57 citation statements)

References 31 publications

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“…Other studies of molecular layers, step atoms, and substituted surface atoms have shown that fractions of molecules can be observed if the molecules diffuse faster than the imaging rate. [26,[38][39][40][41] These "partial molecule" features are dynamic and change from image to image, unlike the present data in which fractional molecules in the H 2 ensembles on Ni/Au(111) appear to be static. This can be explained by the spatial distribution of a quantized collective state available for tunneling, and not by the physical arrangement of molecules or time-averaged imaging of a dynamic system.…”

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confidence: 96%

Collective effects in physisorbed molecular hydrogen onNi/Au(111)

et al. 2015

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contrasting

confidence: 96%

Collective effects in physisorbed molecular hydrogen onNi/Au(111)

et al. 2015

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“…As an upper bound for this contribution we can use the literature value for the step entropy of close-packed steps on Cu(111) at temperatures between 1100 and 1300 K of 1.2 3 10 24 eV͞a K [6,19], yielding an entropic contribution to the step free energy at 330 K of 20.04 eV͞a. A more realistic estimate can be obtained on the basis of the configurational step entropy 2k exp 3 ͑2e͞kT ͒ [20] with a kink creation energy e 0.13 eV [21] resulting in an entropic contribution of less than 210 23 eV͞a. Hence, one can conclude that the entropic contribution to the step free energy at the temperatures used here is most likely to be smaller than the error bar of the measurement.…”

Section: (Received 25 September 1998)mentioning

confidence: 99%

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

et al. 1999

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The absolute measurement of free energies associated with crystal steps on a metal surface has been a long-standing problem. We report a reliable estimate of the step free energy on a Cu(111) crystal surface, based on an analysis of island shape fluctuations directly imaged by scanning tunneling microscopy. The result of 0.22 eV per atomic distance for steps running into close-packed directions is in good agreement with theoretical predictions. [S0031-9007(99)09095-X] PACS numbers: 68.35. Md, 61.16.Ch, 68.35.Ja The step free energy is one of the fundamental quantities used to describe real crystal surfaces. It is defined as the free energy required to create a crystal step and it can be regarded as the low-dimensional analog of the surface free energy. Just as the angular variation of the surface free energy determines the equilibrium shape of threedimensional crystals via the famous Wulff construction [1], the variation of the step free energy with angle determines the equilibrium shape of monolayer islands on a crystal surface. Moreover, as stated by the well-known GibbsThomson relation [1], this quantity is proportional to the chemical potential of monolayer islands and curved steps, and hence its magnitude is directly linked to mass transport rates close to equilibrium.Given the fundamental importance of this material parameter, it is amazing how little experimental information is available on this quantity, at least for metal surfaces. While several estimates based on various computational schemes exist, experiments have mostly been limited to the determination of the relative magnitude of the free energies of differently oriented steps from equilibrium island shapes. A prominent example of studies of this type is the work of Michely et al. who determined a ratio of 0.87 6 0.02 for the step energies of so-called type B and type A steps on Pt(111), i.e., the (111)-and (100)-microfaceted close-packed steps [2]. This experimental result has been a challenge for advanced ab initio energy calculations [3], and could be reproduced only recently by calculations of Boisvert et al. [4]. Experiments suited to reliably determine the absolute value of the step free energy on metal surfaces, however, are hardly available [5]. Bonzel has estimated absolute step energies on metals by extrapolating old results on surface free energies at temperatures close to the melting point to low temperatures using the terrace-ledge-kink model and available estimates of step entropies [6]. For the Ag(111) surface, Morgenstern et al. have estimated the step free energy at about room temperature to 0.22 eV per atomic distance a by studying the decay of Ag adatom islands and fitting the shape of island decay curves with a theoretical model based on the Gibbs-Thomson equation [7]. This result is not unreasonable but still significantly larger than the corresponding theory result for the step formation energy of 0.156 eV͞a at 0 K as calculated by Stoltze using effective medium theory (EMT) [8]. The same experimental procedure applied to ...

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“…Also, similar phenomena have been observed for metal͑111͒ homoepitaxial systems, where equilibrium island shapes are near-hexagonal rather than near-square. For both Ag/Ag͑111͒ 10 and Cu/Cu͑111͒, 11 it is believed that again PD dominates. For the sintering of advacancy island pairs in the Ag/Ag͑111͒ system at 300 K, deviations from the predictions of continuum theory for PD have been suggested ͑al-though again uncertainty in experimental data precludes a definitive analysis͒.…”

Section: Introductionmentioning

confidence: 99%

Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory

Liu

Evans

2002

Phys. Rev. B

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We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the (100) surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion (PD) of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness (reflecting the energetics and adsorption site lattice structure in the atomistic model), and can also account for anisotropy in the step edge mobility (reflecting details of the kinetics). In such continuum treatments, the characteristic time τeqfor relaxation of clusters with linear size of order L satisfies τeq∼L4. Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters (formed by corner-to-corner coalescence of square clusters), atomistic simulations for PD with no kink rounding barrier (δ=0) reveal that τeq∼L4 always applies. In contrast, atomistic simulations with a large kink rounding barrier (δ>0) reveal distinct scaling with τeq∼L3, for low T or small L, thus providing an effective way to test for δ>0. For the relaxation of faceted rectangular clusters (formed by side-toside coalescence of square clusters), atomistic simulations for PD with δ=0 reveal that τeq∼L2, for low T or small L. This is consistent with a recent proposal by Combe and Larralde. For large δ>0, τeq has an even weaker dependence on L. We elucidate scaling behavior and the effective activation barrier for relaxation in terms of the individual atomistic PD processes and their barriers. We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the ͑100͒ surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion ͑PD͒ of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness ͑reflecting the energetics and adsorption site lattice structure in the atomistic model͒, and can also account for anisotropy in the step edge mobility ͑reflecting details of the kinetics͒. In such continuum treatments, the characteristic time eq for relaxation of clusters with linear size of order L satisfies eq ϳL 4 . Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters ͑formed by corner-to-corner coalescence of square clusters͒, atomistic simulations for PD with no kink rounding barrier ͑␦ϭ0͒ reveal that eq ϳL 4 always applies. In contrast, atomistic simulations with a large kink rounding barrier ͑␦Ͼ0͒ reveal distinct scaling with eq ϳL 3 , for low T or small L, thus providing an effective way to test for ␦Ͼ0. For the relaxation of faceted rectangular clusters ͑formed by side-to-side coalescence of square clusters͒, a...

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Equilibrium fluctuations and decay of step bumps on vicinal Cu (111) surfaces

Cited by 62 publications

References 31 publications

Collective effects in physisorbed molecular hydrogen onNi/Au(111)

Collective effects in physisorbed molecular hydrogen onNi/Au(111)

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory

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