Biomedical Engineering Reference
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gives,
10
3
N m
−1
, which is much less than the bulk
k
a
calculated. The implication is that the contact deformation must be
distributed transversely beyond the contact area, and in fact this is the
case: There is considerable deformation in material adjacent to the
contact outside the contact area, giving rise to an elements-in-parallel
stiffening.
The contact displacement is given by
k
a, Winkler
3
×
F
k
a
w
=
(2-12)
and taking a (small) nanoindentation load of
F
= 1 mN gives
w
= 50 nm.
In contrast the deformation of the indentation column under this load is
about 0.01 nm, negligible by comparison with the contact displacement.
3. Contact Behavior Sensed by an Atomic Force Microscope
Atomic force microscopy (AFM) typically operates at the other extreme
of partitioning the imposed displacement of the probe between the
contact and the spring. Similar to IIT, AFM enables the displacement of
a probe to be measured along with the load during loading onto a test
surface. However, in AFM the resistance of the tip to elastic and plastic
deformation is not always much greater than that of the surface (often the
tip and surface are the same material), and AFM, as the name implies, is
often used to measure adhesive force behavior. AFM displacements
< 100 nm, measured with < 0.1 nm resolution, are typical and thus the
technique is well suited to measure contact responses at ultra-small
length scales and contact areas and thus the “atomic” in AFM. If these
forces are used in a closed feedback loop as part of a lateral scanning
system, images of the surface may be generated and thus the
“microscope” part of AFM. (AFM is one of the many scanned-probe
microscopy, acronym SPM, techniques in which attention is focused on
the force interactions between the tip and the surface, as opposed to the
electrical or magnetic interactions that are also commonly used to image
surfaces.) Such imaging is not considered here, but instead the operation
of an AFM with open force feedback is considered; contact
measurements performed in this manner are known as force spectroscopy
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