Measurement of step and kink energies and of the step-edge stiffness from island studies on Pt(111)

Abstract

By using temperature-variable scanning tunneling microscopy, we studied two-dimensional vacancy islands on Pt͑111͒ between 593 and 713 K. Due to the difference in the step free energies of A and B steps, the equilibrium shape of the vacancy islands has a threefold symmetry. From the analysis of the equilibrium shape of the vacancy islands, we calculate the angular dependence of the step free energy on Pt͑111͒. The absolute values for the step free energies per atom of A and B steps are determined from the equilibrium shape fluctuations to be ␤ A = 348± 16 meV/atom and ␤ B = 300± 14 meV/atom, respectively. Furthermore, we derive the temperature dependence of the step-edge stiffness ␤ with ␤ A between 510 and 453 meV/atom and ␤ B between 1974 and 1104 meV/atom in the temperature range considered. From the stiffness, we obtain the kink formation energies for A and B steps, A = 143± 9 meV and B = 206± 9 meV, respectively.

Hillock formation of Pt thin films on single-crystal yttria-stabilized zirconia

“…However, although the absolute values for ǫ A,B found in this work are slightly larger than in reference 45 , the ratios of the kink energies are with δ ǫ = ǫA ǫB ≈ 0.5 in good accordance. The numerical values of ǫ A,B can now be used to determine the step depended bond energy J A,B = 2ǫ A,B which serves as a key parameter in solid-on-solid KMC models 7 simulating thin film instabilities.…”

“…The experimental step line stiffness of A and B steps obtained at T = 923 K shows a significant anisotropy and is in the magnitude of stiffnesses obtained from vacancy island formed on Pt(111) single crystals at T = 713 K 45 . Therebyβ A is slightly smaller compared to the equivalent step line stiffness measured by Ikonomov et al 45 andβ B slightly larger. This difference obviously refers to the enhanced anisotropy of the A and B step length in this work and to the different annealing temperature.…”

“…The anisotropic kink energy ǫ is a physical key property that impacts the physics and decay kinetics of two-dimensional Ostwald ripening 29 , island growth 37,39 , vacancy island formation 45 , fingering instabilities 7 , thin film agglomeration 6 and hillock formation. Due to the anisotropy of the found equilibrium hillock shapes, ǫ andβ depend on the step orientation A, B.…”

Step interactions on Pt(111) vicinal surfaces determined by grazing incidence X-ray diffraction: Influence of the step orientation

“…We have used the recent STM measurements [10] of the step stiffness on Pt(111) to reanalyze the results of Hahn et al [8]. Since it is not the aim of this paper to discuss how step interactions energies can be derived from TWDs, we shall only mention the procedure used in our present analysis.…”

“…The TWDs were analyzed in the capillary wave approximation [37,38]. In this model, the kink formation energy along a step k E and the step interaction energy A are analytically related to the step stiffness β and to the variance and β =1.16 eV/at measured respectively at 900 K [8] and at 653 K [10], one gets k E =0.223 eV/at for the kink energy and = A 2.60 eV.Å for the step interaction energy, in agreement with ref. [23].…”