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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 ...

The capability of a He-scattering experiment to detect the migration of adsorbed molecules on monocrystal surfaces is demonstrated for the first time. CO migration and island formation can be investigated at very low coverages because of the very large cross section for He scattering of CO adsorbed on Pt(lll). The activation energy for CO migration on Pt(lll) is found to be 7 kcal/mole. No island formation at low CO coverages on a defect-free Pt(lll) surface was detected in the temperature range 120-400 K.

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Absolute values for step energies can be determined from the temperature dependence of island equilibrium shapes and the size dependence of island shape fluctuations. Experimental data on island fluctuations are evaluated and the resulting step energies are compared to those obtained earlier from the temperature dependence of the equilibrium shape. For islands on Cu͑100͒, Cu͑111͒, and Ag͑111͒, the step energies obtained by the two entirely different and independent methods agree within the experimental error. The advantages and disadvantages of the two methods are discussed.