INSTRUMENTATION AND EXPERIMENTATION - Nanoindentation with Biological Applications - page 56

of such a spring is independent of k magnitude, the OLS is a function of
cantilever reflectivity and system properties that may change over time.
Thus, it is advisable to measure k of even a repeatedly used cantilever in
this way, prior to each experiment. The load resolution of these
cantilevers is limited by the OLS and sensitive to thermal fluctuations
and acoustical noise; it can be measured directly via in-contact and out-
of-contact deflection oscillations of the cantilever, and is on the order of
pN for commercially available cantilevers.
Although AFM cantilevers are often depicted as translating normal to
the sample surface, for two reasons the cantilever is fact sharply inclined
toward the surface ( Fig. 3-2 ) . This angle θ varies among AFM designs

but is approximately = 10-15°. The first reason for this attack angle is

the optics by which cantilever deflection is reflected and detected at
sufficient distance to maximize accuracy. The second reason is that the
probe extending from the cantilever free-end is only μm-scale in height,
such that the cantilever of 100s μm length should be inclined to ensure
that the probe contacts the sample surface without the rest of the
cantilever contacting the surface and impeding deflection. As a result,
there are significant tangential forces generated upon contact of the probe
with the indented biomaterial, in addition to the intended normal forces
of indentation. It remains challenging to quantify the magnitude of these
competing shear forces and distinguish the onset of normal loading from
the “digging in” to a compliant sample or “sliding along” a stiff sample
under such conditions. At present, the most judicious option is to
minimize

θ

to the extent possible via cantilever mounting modifications,
and to consider in one's analysis the possible effects of shear forces at
early stages of contact loading.

θ

3.1.3. Piezoactuator as displacement transducer

The cantilever base is typically translated via a piezoelectric crystal that
can actuate by increasing or decreasing in overall length as a function of
applied voltage bias. The typical voltage and displacement range of
BaTiO 3 piezocrystals is 150 V over a 10 m excursion, such that ~65 nm

of displacement can be achieved per Volt. These devices remain useful
tools because of the rapidity of actuation (>

μ

μ m/s), but also confers