4-Regular Vertex-Transitive Tilings of E^3 by Friedrichs O.D., Huson D.H.

By Friedrichs O.D., Huson D.H.

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The Hamaker constant is in the order of 10 J - 19 J for most of the solids. To call into mind the relation between the potential force and the force gradient (both measurable with AFM) one can compare potential force and force gradient for the two different geometries of a spring and a sphere-plane contact (see Tab. 3). [111] These relationships illustrate what happens between an AFM tip and a surface. In Tab. 4 one can see the different possibilities for forces between tip and sample. [111] So basicly one can draw the potential between tip and sample as Lenard-JonesPotential (Fig.

1: Comparison of important dates of the used substrates and MgB2. 1 one can see that all chosen substrates fit well to the MgB2 dates. In case of sapphire during annealing at high temperatures above 850 °C, there could take place some reactions and therefore in this temperature regime, there is a good probability for the formation of MgO in the interface region at the substrate surface. For LiNbO3 which also fits pretty well from the crystal structure there could be some problems with stress at temperature changes because of the almost factor 2 difference in the thermal expansion coefficient.

113-115] In the imaging process the AFM uses a pyramidal tip, ideally refined to the size of a few atoms, which is installed under a miniaturized leaf spring for scanning the sample surface line by line in the mechanical contact with the sample. During scan the cantilever is moved by topography and friction. The result of the tip-sample interaction is monitored by a laser beam. The laser beam which is reflected from the metal coated backside of the leaf spring impinges on a segmented photodiode.

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