By Hans Radder
First-class anthology at the philosophy of test, with many well-known individuals of the sphere contributing. vital to philosophers and scientists alike.
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Extra resources for The Philosophy Of Scientific Experimentation
Example text
19), yields the value of f in terms of L and d, 1 E d . 22) k = c2 wd3 . 25) and which involve the parameter set { L, d, w, k, f }. The solution of these two equations gives the value of each parameter in terms of the others. 3, where each parameter is expressed in terms of the other two. 5, where each parameter is expressed in terms of the other three parameters. 5 The permutations for all the unique pairs belonging to the set { L, d, w, k, f }, where each parameter is expressed in terms of the others.
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. 2 shows the slope of the cantilever, θz ( x ), as a function of the distance x from its base for Fz = 10 (solid line), 20 (dashed line), and 30 nN (dotted line).
In the following sections we treat the bending and buckling of the cantilever due to the tip–sample forces Fy and Fz that act in the yˆ and zˆ directions, respectively. Unlike uniform cantilevers, here it is important to account for the position of the tip, δ, because the free end of the cantilever is a sharp point. The numerical results presented in this chapter will be associated with Fi = 10 (solid line), 20 (dashed line), and 30 nN (dotted line), for i = y and z. The resonance frequencies of the cantilever with their associated characteristic functions are presented for the case where the AFM operates in the noncontact mode.