Hydrodynamic model of wave-ordered structures formed by ion bombardment ofsolids

The model of a wave-ordered structures (WOS) formed by ion-bombardment on a surfaces of amorphous materials is put forward. The model is based on the assumption that amorphous layer under ion-bombardment may be considered as Newtonian fluid on a hard substrate in the field of external force. Within this approach the mathematical model of an amorphous layer is formulated as a boundary value problem for Navier-Stokes and continuity equations for in compressible liquid. Analysis of the problem results in two quasi-stationar y spatial-periodic solutions governed by two control parameters: one of the m a(perpendicular to) is a capillary constant under a vertical ion beam inc idence, normalized to layer thickness, another is an angle of incidence The ta. In the general case a capillary constant a(perpendicular to)(L, Theta) is a convex function of both variables viz. normalized spatial-period L and an angle of incidence Theta. With energy E-0 = 9 keV this function exhibit s a local maximum at L = 1.77, Theta = 50.4 degrees which is already global a(perpendicular to c) = 0.375 when E-0 = 5 keV and (as judged by indirect measurements) becomes more convex with further energy reduction. Collation of a(perpendicular to)(L, Theta) with experimental data reveals that the ob served maximum value of capillary constant a(perpendicular to)(ob) = 0.367, which due to an inherent supercriticality is a little bit lower than a(per pendicular to c), falls at Theta = 55 degrees, i.e., with energy diminution angular range should contract to this point. This outcome is consistent wi th our experimental results on Ni-2(+)-Si system, manifesting that angular range reduces to a small vicinity of Theta(c)(in) = 55 degrees when ion ene rgy tends to minimum energy of WOS formation E-0 = 1.5 keV. (C) 1999 Elsevi er Science B.V. All rights reserved.