By Dror Sarid

ISBN-10: 3527406174

ISBN-13: 9783527406173

This new and fully up-to-date variation beneficial properties not just an accompanying CD-ROM, but additionally a brand new purposes part, reflecting the numerous breakthroughs within the box during the last few years. It presents an entire set of computational types that describe the actual phenomena linked to scanning tunneling microscopy, atomic strength microscopy, and similar technologies.The result's either an exceptional specialist reference and an advanced-level textual content, starting with the fundamentals and relocating directly to the most recent recommendations, experiments, and concept. within the part dedicated to atomic strength microscopy, the writer describes the mechanical houses of cantilevers, atomic strength microscope tip-sample interactions, and cantilever vibration features. this is often through an in-depth therapy of theoretical and sensible elements of tunneling phenomena, together with metal-insulator-metal tunneling and Fowler-Nordheim box emission. the ultimate part positive aspects functions, facing, between others, Kelvin and Raman probe microscopy.

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**Example text**

3) f = 2π ρ L2 49 50 3 Cantilever Conversion Tables Next, define two material-related constants, c1 and c2 , by c1 = 1 2π 3E ρ c2 = 3π E. 5) Selecting a given cantilever material dictates the values of c1 and c2 . 9) and respectively, by the two equations and which involve the parameter set { L, r, k, f }. The solution of these two equations gives the value of each parameter in terms of two others. 1, where each parameter is expressed in terms of two other parameters. 2 for a cantilever made of PtIr.

23), δx ( x ) = 6 x2 ht Fx . 5 Linear Spring Constant The cantilever linear spring constant, k x , is defined as the ratio of the force acting on its tip to the resultant displacement at x = L, kx = Fx . 28) Inserting Eq. 27) into Eq. 28) yields kx = 1 Ewd3 . 29) Note the strong dependence of k x on the thickness and length of the cantilever. The ratio of the angular and linear spring constants, given by the function ξ x ( x ), is kθ (x) ξ x (x) = x . 30) kx Inserting Eq. 26) and Eq. 29) into Eq.

It is therefore of interest to examine the ratio of the angular and linear spring constants, given by the function ξ z ( x ), ξ z (x) = k θz ( x ) . 17) Inserting Eq. 11) and Eq. 16) into Eq. 17) gives ξ z (x) = 3(2L − x ) x . 2 Bending Due to Fz The function ξ z ( x ) is used by the software of the AFM to calibrate the tip– sample force using the specifications of the particular cantilever in use. 6 Numerical Example: Si We can now present numerical examples for the response of the Si cantilever to a force acting in the zˆ direction.

### Exploring Scanning Probe Microscopy with MATHEMATICA by Dror Sarid

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