INSTRUMENTATION AND EXPERIMENTATION - Nanoindentation with Biological Applications - page 57

disadvantages related to inherent piezoelectric material limitations. First,
there is limited extent of actuation in such crystals (piezostacks moving
in staggered x , y , and z steps typically exhibit maximum displacement
of 10 m, and material cost rises prohibitively with physical size

and displacement range). Second, as the piezoelectric effect proceeds
via motion of atoms to produce a net increase or decrease of the crystal
unit cell dimensions, there is a natural inertial effect and apparent
nonlinearity in displacement as a function of voltage. For example,
piezoactuators continue to displace in the direction of driving force even
after the voltage bias has been removed, eventually reestablishing
equilibrium. For these reasons, feedback control of actuation and also
calculations of indentation depth, the difference between cantilever
base displacement and cantilever free-end deflection ( h = D -

μ

) can be
inaccurate. This can be addressed in several ways. For example, one
commercial instrument actuates via the piezocrystal but conducts
feedback and depth calculations based on a tandem, linearized voltage-
displacement transducer.

δ

3.1.4. Limitations of linearized signal acquisition

Position sensitive detectors (PSD) such as quadrant photodiodes also
have a limited and defined linear range of operation. In such PSDs, this
range is defined by the position of the reflected laser spot with respect to
the photodiode center. If the cantilever bends beyond this linear range,
the linearized OLS used to calculate deflection and then force will be in
error, creating nonlinear errors in load-displacement ( P-h ) responses. If
one is constrained to work within the linear regime of the PSD, the
maximum force achievable with a cantilever of a particular stiffness will
not be realized.
This limitation can be overcome by a straightforward procedure to
linearize this nonlinear signal over the full operating (deflecting) range of
the cantilever of interest. This approach is detailed, 9 with results
summarized in Fig. 3-3 . Application of this approach reduces the
maximum systematic error on calculated quantities, including d P /d h
from which E may be inferred, from 50% to 5%, and at least doubles the
range of calibrated force one can apply to the biomaterial surface. 8