The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Paul Wynblatt - One of the best experts on this subject based on the ideXlab platform.
-
Step Step Interactions and universal exponents studied via three dimensional equilibrium crystal shapes
New Journal of Physics, 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:Equilibrated three-dimensional Pb crystallites, supported on Ru(001) and of about 1 µm diameter, were imaged by scanning tunnelling microscopy at 298-393 K. The top section of the crystallites exhibited large (111) facets and, depending on temperature, smaller (112) facets. The vicinal shapes close to (111) were analysed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. Analyzing the complete shape in sections of 1° or 3° azimuthal increments and averaging over all sections of one crystallite, we found a shape exponent of 1.490. The exponent is very close to the theoretically predicted universal value of 3/2 and as such clear evidence for the 1/x2 Step Interaction potential. Several crystallites had dislocations threading the (111) facet. For those crystallites the Step Interaction energy was determined as 16 meV A-2 at about 350 K, equivalent to a dipole Interaction energy of 8.1 meV A-2 at 0 K. The Interaction constant for the dipole-dipole part of Step Interaction was found to be 115 meV A.
-
Universal exponents and Step-Step Interactions on vicinal Pb(111) surfaces
Europhysics Letters (EPL), 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:A 1 μm diameter Pb crystallite, supported on Ru(001), was equilibrated and imaged by scanning tunneling microscopy at 298 K. The vicinal shapes close to the (111) facet at the top of the crystal were analyzed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. An average shape exponent of 1.47 and a Step Interaction energy of ~ 32 meV/A2 were obtained. The exponent is very close to the theoretically predicted universal value of 3/2 and as such provides clear evidence for a dominant 1/x2 Step Interaction potential. The ratio of Step free energy to Step Interaction energy for Pb at 298 K is ~ 0.34.
-
Continuous and discontinuous transitions on 3D equilibrium crystal shapes : a new look at Pb and Au
Surface Science, 2001Co-Authors: A. Emundts, K. Thürmer, H.p. Bonzel, Paul Wynblatt, Janice Reutt-robey, Ellen D. WilliamsAbstract:Abstract Equilibrium crystal shapes exhibit flat facets and rough vicinal surfaces, with transitions between them being either continuous or discontinuous, the latter recognizable by a sharp edge. In general, mixed repulsive/attractive Step–Step Interactions may lead to continuous or discontinuous facet-to-vicinal transitions. In can be shown that the contact angle at the facet for a discontinuous transition is directly related to the ratio of the Step Interaction strengths. Alternatively, surface reconstruction of facets can also be responsible for sharp edges at the facet boundary. In this case the contact angle is related to the difference between surface free energies of the reconstructed and unreconstructed facet as well as the corresponding difference of Step Interaction energies. Fitting the experimental shapes by theoretical expressions can be used to extract the relevant surface and Step free energies and also Step Interaction energies. Experimental examples of Pb and Au equilibrium shapes are evaluated and discussed. Step free energies of vicinal Au(1 1 1) and Au(1 0 0) surfaces, evaluated by both models, are 30 and 10 meV/A 2 , respectively.
-
Step energetics of Pb(111) vicinal surfaces from facet shape
Surface Science, 1999Co-Authors: K. Arenhold, H.p. Bonzel, S. Surnev, Paul WynblattAbstract:Abstract The Step stiffness, Step Interaction and kink formation energies of Steps vicinal to (111) have been derived from the equilibrium shape of a (111) facet on a small three-dimensional Pb crystal imaged by scanning tunneling microscopy. In addition, the azimuthal dependence of the Step free energy for vicinal (111) surfaces has been obtained by an ‘inverse’ Wulff construction from the facet shape. Most of these energetic quantities can be quoted for both types of Step (A- and B-Steps). By also taking into account the curved portion of the vicinal surface, consisting primarily of B-Steps, the entropic and total Step Interaction energy of B-Steps can be separately obtained.
M. Nowicki - One of the best experts on this subject based on the ideXlab platform.
-
3d equilibrium crystal shapes of pb the significance of Step resolved images
Progress in Surface Science, 2003Co-Authors: M. Nowicki, A. Emundts, H.p. BonzelAbstract:Abstract Scanning tunnelling microscopy has proven to be an extremely useful technique for imaging small crystallites equilibrated at elevated temperature. As an example, we review recent work on three-dimensional Pb crystallites of 1–2 μm diameter, supported on Ru(0 0 1). Large (1 1 1) facets and, depending on temperature, small (1 1 2) facets were observed in the top section of the crystallites. The temperature dependent facet anisotropy was analyzed to yield the absolute Step free energies of Pb(1 1 1) vicinal Steps. The vicinal region close to the (1 1 1) facet was studied in detail to determine the shape exponent, the Step–Step Interaction energy and the constant of the dipole Interaction potential. Boundary conditions of the evaluated vicinal region have been specified for proving the universality of shapes, characterized by the exponent of 3/2, which is clear evidence for the 1/ x 2 Step Interaction potential. The role of the activation barrier for facet growth or shrinkage is discussed in the context of attaining 3D equilibrium of crystallites. A comparative study of crystallites with defect-free and dislocated facets shows significant differences, providing direct evidence of the activation barrier. Reliable Step–Step Interaction energies were obtained for dislocated crystallites. Extrapolating the temperature dependent total Step Interaction energy to 0 K yields for the first time values of the structure dependent dipole–dipole Step Interaction energies of A- and B-Steps.
-
Step Step Interactions and universal exponents studied via three dimensional equilibrium crystal shapes
New Journal of Physics, 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:Equilibrated three-dimensional Pb crystallites, supported on Ru(001) and of about 1 µm diameter, were imaged by scanning tunnelling microscopy at 298-393 K. The top section of the crystallites exhibited large (111) facets and, depending on temperature, smaller (112) facets. The vicinal shapes close to (111) were analysed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. Analyzing the complete shape in sections of 1° or 3° azimuthal increments and averaging over all sections of one crystallite, we found a shape exponent of 1.490. The exponent is very close to the theoretically predicted universal value of 3/2 and as such clear evidence for the 1/x2 Step Interaction potential. Several crystallites had dislocations threading the (111) facet. For those crystallites the Step Interaction energy was determined as 16 meV A-2 at about 350 K, equivalent to a dipole Interaction energy of 8.1 meV A-2 at 0 K. The Interaction constant for the dipole-dipole part of Step Interaction was found to be 115 meV A.
-
Universal exponents and Step-Step Interactions on vicinal Pb(111) surfaces
Europhysics Letters (EPL), 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:A 1 μm diameter Pb crystallite, supported on Ru(001), was equilibrated and imaged by scanning tunneling microscopy at 298 K. The vicinal shapes close to the (111) facet at the top of the crystal were analyzed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. An average shape exponent of 1.47 and a Step Interaction energy of ~ 32 meV/A2 were obtained. The exponent is very close to the theoretically predicted universal value of 3/2 and as such provides clear evidence for a dominant 1/x2 Step Interaction potential. The ratio of Step free energy to Step Interaction energy for Pb at 298 K is ~ 0.34.
H.p. Bonzel - One of the best experts on this subject based on the ideXlab platform.
-
3d equilibrium crystal shapes of pb the significance of Step resolved images
Progress in Surface Science, 2003Co-Authors: M. Nowicki, A. Emundts, H.p. BonzelAbstract:Abstract Scanning tunnelling microscopy has proven to be an extremely useful technique for imaging small crystallites equilibrated at elevated temperature. As an example, we review recent work on three-dimensional Pb crystallites of 1–2 μm diameter, supported on Ru(0 0 1). Large (1 1 1) facets and, depending on temperature, small (1 1 2) facets were observed in the top section of the crystallites. The temperature dependent facet anisotropy was analyzed to yield the absolute Step free energies of Pb(1 1 1) vicinal Steps. The vicinal region close to the (1 1 1) facet was studied in detail to determine the shape exponent, the Step–Step Interaction energy and the constant of the dipole Interaction potential. Boundary conditions of the evaluated vicinal region have been specified for proving the universality of shapes, characterized by the exponent of 3/2, which is clear evidence for the 1/ x 2 Step Interaction potential. The role of the activation barrier for facet growth or shrinkage is discussed in the context of attaining 3D equilibrium of crystallites. A comparative study of crystallites with defect-free and dislocated facets shows significant differences, providing direct evidence of the activation barrier. Reliable Step–Step Interaction energies were obtained for dislocated crystallites. Extrapolating the temperature dependent total Step Interaction energy to 0 K yields for the first time values of the structure dependent dipole–dipole Step Interaction energies of A- and B-Steps.
-
Step Step Interactions and universal exponents studied via three dimensional equilibrium crystal shapes
New Journal of Physics, 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:Equilibrated three-dimensional Pb crystallites, supported on Ru(001) and of about 1 µm diameter, were imaged by scanning tunnelling microscopy at 298-393 K. The top section of the crystallites exhibited large (111) facets and, depending on temperature, smaller (112) facets. The vicinal shapes close to (111) were analysed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. Analyzing the complete shape in sections of 1° or 3° azimuthal increments and averaging over all sections of one crystallite, we found a shape exponent of 1.490. The exponent is very close to the theoretically predicted universal value of 3/2 and as such clear evidence for the 1/x2 Step Interaction potential. Several crystallites had dislocations threading the (111) facet. For those crystallites the Step Interaction energy was determined as 16 meV A-2 at about 350 K, equivalent to a dipole Interaction energy of 8.1 meV A-2 at 0 K. The Interaction constant for the dipole-dipole part of Step Interaction was found to be 115 meV A.
-
Universal exponents and Step-Step Interactions on vicinal Pb(111) surfaces
Europhysics Letters (EPL), 2002Co-Authors: M. Nowicki, C. Bombis, A. Emundts, H.p. Bonzel, Paul WynblattAbstract:A 1 μm diameter Pb crystallite, supported on Ru(001), was equilibrated and imaged by scanning tunneling microscopy at 298 K. The vicinal shapes close to the (111) facet at the top of the crystal were analyzed in detail to determine the critical shape exponent and the Step-Step Interaction energy as well as the Interaction constant of the potential. An average shape exponent of 1.47 and a Step Interaction energy of ~ 32 meV/A2 were obtained. The exponent is very close to the theoretically predicted universal value of 3/2 and as such provides clear evidence for a dominant 1/x2 Step Interaction potential. The ratio of Step free energy to Step Interaction energy for Pb at 298 K is ~ 0.34.
-
Continuous and discontinuous transitions on 3D equilibrium crystal shapes : a new look at Pb and Au
Surface Science, 2001Co-Authors: A. Emundts, K. Thürmer, H.p. Bonzel, Paul Wynblatt, Janice Reutt-robey, Ellen D. WilliamsAbstract:Abstract Equilibrium crystal shapes exhibit flat facets and rough vicinal surfaces, with transitions between them being either continuous or discontinuous, the latter recognizable by a sharp edge. In general, mixed repulsive/attractive Step–Step Interactions may lead to continuous or discontinuous facet-to-vicinal transitions. In can be shown that the contact angle at the facet for a discontinuous transition is directly related to the ratio of the Step Interaction strengths. Alternatively, surface reconstruction of facets can also be responsible for sharp edges at the facet boundary. In this case the contact angle is related to the difference between surface free energies of the reconstructed and unreconstructed facet as well as the corresponding difference of Step Interaction energies. Fitting the experimental shapes by theoretical expressions can be used to extract the relevant surface and Step free energies and also Step Interaction energies. Experimental examples of Pb and Au equilibrium shapes are evaluated and discussed. Step free energies of vicinal Au(1 1 1) and Au(1 0 0) surfaces, evaluated by both models, are 30 and 10 meV/A 2 , respectively.
-
Continuous and discontinuous transitions on 3D equilibrium crystal shapes: a new look at Pb and Au
Surface Science, 2001Co-Authors: A. Emundts, K. Thürmer, H.p. Bonzel, Janice Reutt-robey, P. Wynblatt, E.d. WilliamsAbstract:Equilibrium crystal shapes exhibit flat facets and rough vicinal surfaces. with transitions between them being either continuous or discontinuous, the latter recognizable by a sharp edge. In general, mixed repulsive/attractive Step-Step Interactions may lead to continuous or discontinuous facet-to-vicinal transitions. In can be shown that the contact angle at the facet for a discontinuous transition is directly related to the ratio of the Step Interaction strengths. Alternatively, surface reconstruction of facets can also be responsible for sharp edges at the facet boundary. In this case the contact angle is related to the difference between surface free energies of the reconstructed and unreconstructed facet as well as the corresponding difference of Step Interaction energies. Fitting the experimental shapes by theoretical expressions can be used to extract the relevant surface and Step free energies and also Step Interaction energies. Experimental examples of Pb and Au equilibrium shapes are evaluated and discussed. Step free energies of vicinal Au(1 1 1) and Au(1 0 0) surfaces, evaluated by both models, are 30 and 10 meV/A(2), respectively. (C) 2001 Elsevier Science B.V. All rights reserved
Adalberto Balzarotti - One of the best experts on this subject based on the ideXlab platform.
-
Step-Step Interaction on vicinal Si(001) surfaces studied by scanning tunneling microscopy
Physical Review B, 2009Co-Authors: Luca Persichetti, Anna Sgarlata, Massimo Fanfoni, Marco Bernardi, Adalberto BalzarottiAbstract:We report on measurements of Step-Step Interaction on a flat Si(111)−(7×7) surface and on vicinal Si(001) surfaces with miscut angles ranging between 0.2° and 8°. Starting from scanning tunneling microscopy images of these surfaces and describing Steps profile and Interactions by the continuum Step model, we measured the self-correlation function of single Steps and the distribution of terrace widths. Empirical parameters, such as Step stiffness and Step-Step Interaction strength, were evaluated from the images. The present experiment allows to assess the dependence of the Step-Step repulsion on miscut angle, showing how parameters drawn from tunneling images can be used to interpolate between continuum mesoscopic models and atomistic calculations of vicinal surfaces.
Geoffroy Prévot - One of the best experts on this subject based on the ideXlab platform.
-
Elastic relaxations and Interactions on metallic vicinal surfaces: Testing the dipole model
Physical Review B, 2006Co-Authors: Geoffroy Prévot, Bernard CrosetAbstract:We have studied, by quenched molecular dynamics using a second-moment approximation (SMA) potential, the atomic relaxations and Step Interaction energies on Ni, Cu, Pt, and Au vicinal surfaces for which Steps run along the $[1\overline{1}0]$ direction. The results have been compared to anisotropic linear elasticity calculations (ALE). We show that Steps are well described with a model of lines of force dipoles buried under the surface. The elastic Interaction energies between Steps obtained by SMA and ALE are in good agreement. This demonstrates that the elastic Step Interaction energy can be determined from the measurement of the atomic relaxations.
-
Elastic relaxations and Interactions on metallic vicinal surfaces: testing the dipole model
Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2006Co-Authors: Geoffroy Prévot, Bernard CrosetAbstract:We have studied, by quenched molecular dynamics (QMD) using a second-moment approximation (SMA) potential, the atomic relaxations and Step Interaction energies on Ni, Cu, Pt and Au vicinal surfaces for which Steps run along the [1-10] direction. The results have been compared to anisotropic linear elasticity calculations (ALE). We show that Steps are well described with a model of lines of force dipoles buried under the surface. The elastic Interaction energies between Steps obtained by SMA and ALE are in good agreement. This demonstrates that the elastic Step Interaction energy can be determined from the measurement of the atomic relaxations.
-
GIXD measurement of the relaxations and elastic Step Interactions on Cu(211) and Cu(322)
Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2004Co-Authors: Geoffroy Prévot, A. Coati, Y. GarreauAbstract:We have studied by grazing incidence x-ray diffraction the atomic positions near the surface of Cu(211) and Cu(322). For Cu(211), the relaxations are confined to the first atoms, and show a contraction of the Step edge. For Cu(322), they extend deeper in the bulk. In that case, by comparing the experimental results with molecular dynamics simulation of the relaxations, we are able to extract precisely the value of the elastic dipoles equivalent to the Steps that cause the long range atomic relaxations. The elastic dipole has a stretch component of 2.8×10–10 N/at and a torque component of 3.6×10–10 N/at. It is related to the surface stress of the (111) terraces, that is deduced to be of the order of 2 Nm–1. Using the elasticity theory and by comparison with theoretical results, we are able to derive the elastic Interaction between Steps. It is found one order of magnitude higher than the value of the Step Interaction that has been in the past extracted from terrace width distributions.
-
Grazing-incidence x-ray diffraction measurement of the relaxations and elastic Step Interactions on Cu(211) and Cu(322)
Physical Review B, 2004Co-Authors: Geoffroy Prévot, A. Coati, Y. GarreauAbstract:We have studied by grazing incidence x-ray diffraction the atomic positions near the surface of Cu(211) and Cu(322). For Cu(211), the relaxations are confined to the first atoms, and show a contraction of the Step edge. For Cu(322), they extend deeper in the bulk. In that case, by comparing the experimental results with molecular dynamics simulation of the relaxations, we are able to extract precisely the value of the elastic dipoles equivalent to the Steps that cause the long range atomic relaxations. The elastic dipole has a stretch component of $2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}\mathrm{N}∕\mathrm{at}$ and a torque component of $3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}\mathrm{N}∕\mathrm{at}$. It is related to the surface stress of the (111) terraces, that is deduced to be of the order of $2\phantom{\rule{0.3em}{0ex}}{\mathrm{Nm}}^{\ensuremath{-}1}$. Using the elasticity theory and by comparison with theoretical results, we are able to derive the elastic Interaction between Steps. It is found one order of magnitude higher than the value of the Step Interaction that has been in the past extracted from terrace width distributions.
-
Determination of the elastic dipole at the atomic Steps of Pt(977) from surface x-ray diffraction
Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2003Co-Authors: Geoffroy Prévot, P. Steadman, S. FerrerAbstract:Molecular dynamics calculations have been performed to reanalyze the previously published x-ray diffraction data from Pt(977) [Steadman et al., Phys. Rev. B 64, 125418 (2001)] which exhibited intense oscillations of the diffracted intensities at widely spaced intervals of the perpendicular momentum transfer. The largely improved fit to the data allows one to precisely determine the strain field at the surface region and the magnitude of the elastic dipole density associated with a Step, p = 1.10–9 N, which is at the origin of the strong repulsive Step–Step Interaction.
