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84926798894
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Figure 6 illustrates that the diffracted intensity from the Al(332) surface is made up of a superposition of diffracted intensities from three different facets. The reciprocal-lattice rods are seen to cross one another at the 3D reciprocal-lattice points. In fact, at these conditions all possible facets of the surface diffract into the same directions. For example, at an incident wave vector of ki= 6.67 ~ A ang-1 (23.25 meV) the first-order diffraction from (111) facets and the zeroth-order diffraction from (221) facets coincide and these two peaks are indistinguishable at the three-dimensional (3D) Bragg condition. Note that this discussion only considers the intensities but not the phases of the individual scattered beams. The same 3D Bragg condition is also satisfied by considering the constructive (in-phase) scattering from any rough surface. In that case a sharp diffraction peak at the 3D Bragg points comes from the coherent addition of scattering amplitudes from many randomly distributed terraces.
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For illustration, see Fig. 4 of Conrad et al., J. Chem. Phys. 84, 1015 (1986).
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0023310510
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An Experimental Study of the Roughening Transition on a Stepped Surface: Cu(115)
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To estimate the relative energies for roughening and facetting, we thus note that roughening requires the overcoming of the kink-creation energy Wkink and the step-step repulsion energy Wstep. In the case of the Cu(113) and Cu(115) faces, Fabre et al. [, ] found for (113), values of Wkink= 69 meV and Wstep= 48 meV, and, for (115), Wkink= 60 meV and Wstep= 12 meV, respectively. We next estimate the facetting energy as follows. A possible driving force for facetting is the lowering of the surface tension. The difference in surface tension is assumed equal to the facetting energy. McLean [, M. McLean, Acta Metall., 19, 387, ] reported for the Cu(100) surface a surface tension of approximately γ = 1.67 ~ J / m2, and observed an anisotropy of about 15% in gamma between the (100) and (110) poles of the sterographic projection. As a rough estimate, we assume a similar change in going from the (111) to the (115) surface. For one surface unit cell this corresponds to a [Truncated]
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(1971)
Europhysics Letters (EPL)
, vol.3
, pp. 737
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Fabre, F.1
Gorse, D.2
Lapujoulade, J.3
Salanon, B.4
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