Bilayers buckling

Figure 5.47 Electrostatic model for buckling of bilayer ribbon of length l and width w based on attraction between lines of charge on opposite edges.168 Left Side view. Right Top view of curvature of ribbon. Reprinted with permission from Ref. 139. Copyright 2001 by the American Chemical Society.

We have seen that a symmetric bilayer composed of chemically identical monolayers will spontaneously buckle so that the mid-surface of the bilayer wraps onto a minimal surface. Since the average Gaussian curvature, , of a minimal surface must be non-positive, eq. 4.9 implies the constraint on the... 

The bulk crystal form of the alkaline earth oxides is the NaCl structure. The bulk termination at the (100) surface consists of a stack of coplanar bilayers each containing one cation and an anion. CaO(lOO) has been the subject of a LEED study which found a contraction of top interlayer spacing by —1.2% (Prutton et al., 1979). Buckling of the top bilayer was not investigated. Buckling of the top bilayer was found in a recent LEED study of MgO(lOO) (Blanchard et al. 1990). In this case, the oxygen atom moves out of the surface by 0.05 0.025 A whilst the Mg atom sinks into the surface the same distance. The center-of-mass plane of the top MgO bilayer is unrelaxed. The (100) surface of transition metal oxide CoO, which also has... 

The (100) surface of the perovskite structure oxide SrTiC>3(100) has been studied by LEED (Bickel et al., 1989). Parallel to the (100) plane, SrTiO.i consists of alternate planes of O-Ti-O and Sr O. The O-Ti-O trilayer terminated surface has a buckled top trilayer in which the O atoms move out of the surface by 0.04 0.04 A whilst the Ti atoms sink into the surface by the same distance. The position of the reference plane of the originally coplanar top layer is unchanged. The behavior resembles that of MgO(lOO) described above. The Sr-0 terminated surface terminates in a buckled bilayer with the O atom moving out of the surface. The buckling amplitude is 0.16 0.08 A. The entire Sr-O bilayer relaxes towards the bulk by —6 2% of the bulk Sr-O/O-Ti-O interlayer spacing. 

S. J. Kwon and H. H. Lee, Theoretical analysis of two-dimensional buckling patterns of thin metal-polymer bilayer on the substrate. J. Appl. Phys. 98, 063526 (2005). 

Ga atoms are missing, and the remaining atoms are almost coplanar with the first As layer, within 0.20 A. Ga bonding is sp rehybridized, instead of the normal sp configuration. There are first bilayer lateral motions of -0.2 A, and some buckling in the third layer to maintain optimum bond lengths and angles. 

The small size and fact that they can operate in a liquid environment make CP microactuators interesting for applications in microfluidics and drug delivery. The CP-actuated valves can be designed using different mechanical principles such as bilayer hinges, buckling actuators, and bulk-swelling layers. 

Ru(0001)h-(V3xV3) R30°-2H20 1 H20athigh top site LEED no no 4.2 0.9 0 0.5 0.9 -2.8 0.9 0 0 0 0 0 0 2.23 0.02 0 94H1 intact molecular adsorption in two different top sites (bilayer) on unreconstmeted relaxed substrate significant buckling in top metal layer contraction of first two metal interlayer spacings... 

The next, less Si-rich phase on SiC(OOOl) is the (V3xV3)R30° reconstruction that can be prepared by anneahng the (3 x 3) phase. In this reconstraction, a Si adatom is positioned on top of the SiC surface in a (V3xV3)R30° periodicity. The adatom is positioned in the so-called T4-site, that is, in a hollow with coordination to three Si atoms of the topmost Si layer and to the carbon atom direcdy below in the carbon layer of the topmost bilayer (Figure 4.44c). In this carbon layer, additionally a moderate buckling is found [125], which compensates the bond misfit of the Si adatom on top of the SiC surface (Figure 4.44d). The structure model was confirmed by an XRD study [126], where also small lateral displacements of the three Si atoms... 

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