%0 Book Section %1 statphys23_0835 %A Cuerno, R. %A noz garc\'ıa, J. Mu\ %A Castro, M. %A Gago, R. %A Vázquez, L. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K coarsening formation hydrodynamic ion-beam kinetic models nanopattern pattern roughening sputtering statphys23 topic-4 %T Coupled model for nanopattern formation and dynamics on ion-sputtered surfaces %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=835 %X Recently, a ``hydrodynamic model’’ has been proposed to describe nanopattern formation and dynamics on amorphous surfaces eroded by ion-beam sputtering 1. In the spirit of Ref.\ 2, this model is related to previous models of pattern formation in aeolian sand dunes 3. In contrast to previous theoretical continuum models that describe the morphology of sputtered-surfaces, in which the only field considered is the height, $h$, of the bombarded surface 4, in this new model an additional field, $R$, is coupled with the former, and represents the thickness of material that diffuses onto the surface. In this work, we describe a multi-scale analysis of the model, in which we consider normal ion incidence and oblique incidence, for both fixed and rotating targets. The diffusive field $R$ turns out to be adiabatically eliminated in the dynamics, and a closed equation for the surface height evolution can be obtained in the vicinity of the instability threshold. The interface equations thus obtained are generalizations of the anisotropic Kuramoto-Sivashinshy equation that contain additional conserved Kardar-Parisi-Zhang type nonlinearities. For each incidence condition, the corresponding equation reflects the symmetries of the experimental setup. We present results of numerical integration of these effective interface equations. In general a pattern formation process occurs leading to e.g.\ dot or ripple formation, that later evolve exhibiting complex nonlinear dynamics. Thus, we observe interrupted coarsening behavior 5 in such a way that for the stationary state morphology and in appropriate parameter regions, domains of hexagonally ordered structures appear, that compare favourably with those obtained in experiments of nanodot formation by IBS 6. This lateral order and coarsening could not be described by one-field approaches 4. Meanwhile, in other parameter regions, this short-range ordered pattern coexists with long range disorder and kinetic roughening. In the case of oblique incidence, a ripple pattern is generically obtained 4. In our model, these ripples also show interrupted coarsening and feature additional nonlinear features, such as non-uniform transverse motion, that again compare with experimental observations on nanoripples 7 better than previous one-field models. 1) M.\ Castro, R.\ Cuerno, L.\ Vázquez, R.\ Gago, Phys. Rev. Lett. 94, 016102 (2005); J.\ Muñoz-Garc\'ıa, M.\ Castro, R.\ Cuerno, ibid. 96, 086101 (2006).\\ 2) T.\ Aste, U.\ Valbusa, Physica A 332, 548 (2004).\\ 3) See Z.\ Csahók, C.\ Misbah, F.\ Rioual, A.\ Valance, Eur. Phys. J. E 3, 71 (2000) and refs.\ therein.\\ 4) See e.g.\ M.\ Makeev, R.\ Cuerno, A.-L.\ Barabási, Nucl. Instrum. Methods 5) Phys. Res. B 197, 185 (2002) and refs.\ therein.\\ 6) P.\ Politi, C.\ Misbah, Phys.\ Rev.\ Lett.\ 92, 090601 (2004).\\ 7) R.\ Gago, L.\ Vázquez, O.\ Plantevin, T.\ H.\ Metzger, J.\ Muñoz-Garc\'ıa, R.\ Cuerno, M.\ Castro, Appl.\ Phys.\ Lett.\ 89 233101 (2006).

@incollection{statphys23_0835, abstract = {Recently, a ``hydrodynamic model’’ has been proposed to describe nanopattern formation and dynamics on amorphous surfaces eroded by ion-beam sputtering [1]. In the spirit of Ref.\ [2], this model is related to previous models of pattern formation in aeolian sand dunes [3]. In contrast to previous theoretical continuum models that describe the morphology of sputtered-surfaces, in which the only field considered is the height, $h$, of the bombarded surface [4], in this new model an additional field, $R$, is coupled with the former, and represents the thickness of material that diffuses onto the surface. In this work, we describe a multi-scale analysis of the model, in which we consider normal ion incidence and oblique incidence, for both fixed and rotating targets. The diffusive field $R$ turns out to be adiabatically eliminated in the dynamics, and a closed equation for the surface height evolution can be obtained in the vicinity of the instability threshold. The interface equations thus obtained are generalizations of the anisotropic Kuramoto-Sivashinshy equation that contain additional conserved Kardar-Parisi-Zhang type nonlinearities. For each incidence condition, the corresponding equation reflects the symmetries of the experimental setup. We present results of numerical integration of these effective interface equations. In general a pattern formation process occurs leading to e.g.\ dot or ripple formation, that later evolve exhibiting complex nonlinear dynamics. Thus, we observe interrupted coarsening behavior [5] in such a way that for the stationary state morphology and in appropriate parameter regions, domains of hexagonally ordered structures appear, that compare favourably with those obtained in experiments of nanodot formation by IBS [6]. This lateral order and coarsening could not be described by one-field approaches [4]. Meanwhile, in other parameter regions, this short-range ordered pattern coexists with long range disorder and kinetic roughening. In the case of oblique incidence, a ripple pattern is generically obtained [4]. In our model, these ripples also show interrupted coarsening and feature additional nonlinear features, such as non-uniform transverse motion, that again compare with experimental observations on nanoripples [7] better than previous one-field models. 1) M.\ Castro, R.\ Cuerno, L.\ V\'azquez, R.\ Gago, Phys. Rev. Lett. 94, 016102 (2005); J.\ Mu\~noz-Garc\'{\i}a, M.\ Castro, R.\ Cuerno, {\em ibid.} 96, 086101 (2006).\\ 2) T.\ Aste, U.\ Valbusa, Physica A 332, 548 (2004).\\ 3) See Z.\ Csah\'ok, C.\ Misbah, F.\ Rioual, A.\ Valance, Eur. Phys. J. E 3, 71 (2000) and refs.\ therein.\\ 4) See e.g.\ M.\ Makeev, R.\ Cuerno, A.-L.\ Barab\'asi, Nucl. Instrum. Methods 5) Phys. Res. B 197, 185 (2002) and refs.\ therein.\\ 6) P.\ Politi, C.\ Misbah, Phys.\ Rev.\ Lett.\ 92, 090601 (2004).\\ 7) R.\ Gago, L.\ V\'azquez, O.\ Plantevin, T.\ H.\ Metzger, J.\ Mu\~noz-Garc\'{\i}a, R.\ Cuerno, M.\ Castro, Appl.\ Phys.\ Lett.\ 89 233101 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Cuerno, R. and noz \uppercase{g}arc\'{\i}a, J. Mu\ and Castro, M. and Gago, R. and V\'azquez, L.}, biburl = {https://www.bibsonomy.org/bibtex/2ec0b9d0d96619842d7054dff3c5da2ea/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {5779c320f833138b98efeb23a29ece6e}, intrahash = {ec0b9d0d96619842d7054dff3c5da2ea}, keywords = {coarsening formation hydrodynamic ion-beam kinetic models nanopattern pattern roughening sputtering statphys23 topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:30.000+0200}, title = {Coupled model for nanopattern formation and dynamics on ion-sputtered surfaces}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=835}, year = 2007 }